Advances in Electronics and Electron Physics, Volume 56

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 56 CONTRIBUTORS TO THISVOLUME D. BERENYI EMILE-JACQUES BLUM RIC...

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 56

CONTRIBUTORS TO THISVOLUME

D. BERENYI EMILE-JACQUES BLUM RICHARDH. BUBE R. J . CELOTTA ALANL. FAHRENBRUCH MICHAEL J . HIGATSBERGER ALLENG. LINDGREN D. T. PIERCE PAULA. RATTEY V. N. SMILEY

Advances in

Electronics and Electron Physics EDITEDBY CLAIRE MARTON Smithsonian Institution Washington, D . C.

VOLUME 56

1981

ACADEMIC PRESS A Subsidiary of Harcourt Brace Jovanovich, Publishers

New York London Toronto Sydney San Francisco

COPYRIGHT @ 1981, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. N O PART O F THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.

ACADEMIC PRESS,INC.

111 Fifth Avenue, New York, New York 10003

Uiiited Kiiigdorn Edition published by ACADEMlC PRESS, INC. ( L O N D O N ) LTD. 24/28 Oval Road, London N W I 7DX

LIBRARY OF CONGRESS CATALOG CARDNUMBER:49-7504 ISBN 0-12-014656-8 PRINTED IN THE UNITED STATES O F AMERICA 81 82 83 84

9 8 7 6 5 4 3 2 1

CONTENTS CONTRIBUTORS TO VOLUME 56 . . . . . . . . . . . . . . . . . . . . . FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix xi

Recent Advances in High-Power Tunable Lasers (W. Visible. and Near IR) V . N . SMILEY I . Introduction . . . . . . . . . . . . . . . . . I1. Dye Laser Developments . . . . . . . . . . . . I11. Picosecond and SubpicosecondTunable Sources . IV . Color Center Lasers . . . . . . . . . . . . . . V . Nonlinear Coherent Sources . . . . . . . . . VI . Other High-Power Tunable Lasers . . . . . . . References . . . . . . . . . . . . . . . . . .

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54

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98 99

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107 114

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124

2 3 38

60 79 89

Radioastronomy on Millimeter Wavelengths EMiLE-JACQUES BLUM I . Introduction . . . . . . . . . . . . . . . . . . . . I1. The Development of Millimeter Radioastronomy . . . I11. Astrophysical Achievements and Prospects of Millimeter-Wave Astronomy . . . . . . . . . . . . IV. Observing Conditions and Sites . . . . . . . . . . . V . Radiotelescope Fundamentals and the Millimeter Range VI . Antennas . . . . . . . . . . . . . . . . . . . . . VII . Receivers . . . . . . . . . . . . . . . . . . . . . VIII . Evolution and Projects . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . .

. . . . .

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

133 142 152 159

Photovoltaic Effect RICHARD H . BUBEAND ALANL. FAHRENBRUCH I . Introduction . . . . . . . . . . . . . . . . I1. An Overview of Photovoltaic Effects . . . . . 111. Current Generation . . . . . . . . . . . . . IV . Junction Currents . . . . . . . . . . . . . . V . Examples of Photovoltaic Materials Systems . References . . . . . . . . . . . . . . . . . V

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163 166 189 193 200 211

vi

CONTENTS

Spin Polarization in Electron Scattering from Surfaces D . T . PIERCEAND R . J . CELOTTA

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Spin-Dependent Parameters and Interactions . . . . . . . . . . . . 111. Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . IV . Spin-Dependent Scattering Due to the Spin-Orbit Interaction . . . . . V . Spin-Dependent Scattering from Ferromagnetic Materials . . . . . . V1 . Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

219 225 234 240 261 281 284

Solid Surfaces Analysis MICHAEL J . HIGATSBERGER I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . I1 . Surface Analytical Techniques and Methods . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . .

291 294 356

The Inverse Discrete Radon Transform with Applications to Tomographic Imaging Using Projection Data ALLENG . LINDGREN AND PAUL A . RATTEY

I . Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 111. The Continuous Radon Transform Pair . . . . . . . . . . . . . IV . Applications of the Radon Transform in Imaging . . . . . . . . . V . Historical Background and Review of Reconstruction Algorithms . . VI . Properties of the Radon Transform . . . . . . . . . . . . . . . VII . Sampling the Radon Transform with Parallel-Beam Projections . . . VIII . Sampling the Radon Transform with Fan-Beam Projections . . . . . IX . The Inverse Discrete Radon Transform . . . . . . . . . . . . . X . Effects of Nonideal Sampling . . . . . . . . . . . . . . . . . . XI . Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . XI1. Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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.

360 360 362 368 312 316 380 388 394 401 406 401 408

Spectroscopy of Electrons from High-Energy Ion-Atom Collisions D . BERENYI 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . I1 . A Brief Survey of Instrumentation and Basic Concepts of Collision Mechanism . . . . . . . . . . . . . . . . . . . . . 111. Projectiles of Intermediate Energy . . . . . . . . . . . . . . . . .

411

414 417

CONTENTS

vii

IV . High-Energy Projectiles . . . . . . . . . . . . . . . . . . . . . V . Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

432 437 438

AUTHORINDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . .

443 461

SUBJECT INDEX .

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CONTRIBUTORS TO VOLUME 56 Numbers in parentheses indicate the pages on which the authors’ contributions begin.

D. BERENYI, Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), Debrecen, Pf. 51 ., H-4001 Hungary (411) EMILE-JACQUES BLUM,Institut de Radio Astronomie Millimetrique, B.P. 391, 38017 Grenoble Cedex, France (97) RICHARD H. BUBE. Department of Materials Science and Engineering, Stanford University, Stanford, California 94305 (163) R. J. CELOTTA,National Bureau of Standards, Washington, D. C. 20234 (219) ALANL. FAHRENBRUCH, Department of Materials Science and Engineering, Stanford University, Stanford, California 94305 (163) MICHAEL J. HIGATSBERGER, Institute of Experimental Physics, University of Vienna, Vienna, Austria (291) ALLENG. LINDGREN, Department of Electrical Engineering, University of Rhode Island, Kingston, Rhode Island 0288 1 (359) D. T. PIERCE, National Bureau of Standards, Washington, D. C. 20234 (219)

PAULA. RATTEY,Department of Electrical Engineering, University of Rhode Island, Kingston, Rhode Island 02881 (359) V. N. SMILEY, EG & G, Inc., Las Vegas, Nevada 89101 (1)

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FOREWORD This volume again covers a full range of subjects on electron physics. Three chapters interface with condensed matter studies. One chapter deals with high-powered tunable lasers which in themselves are tools to study a whole range of phenomena. Another chapter summarizes an aspect of radio astronomy. The last chapter approaches more classical physics in analyzing high-energy ion-atom collisions. The authors, all well known in their respective fields, have produced a volume that should be of extraordinary value due to the high caliber of each presentation. Once again, we include here 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 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 xi

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 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

xii

FOREWORD

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 Pridciples, Interfaces and Microcomputers in Intelligent Instruments Fine-Line Pattern Definition and Etching for VLSI Recent Trends in Photomultipliers for Nuclear Physics 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 Supplementary Volumes: Microwave Field-Effect Transistors Volume 57: Elementary Attachment and Detachmint Processes. I1 Fiber Optics in Local Area Network Applications Surface Analysis Using Charged Particle Beams

Microwave Landing System-The International Standard Microprocessor Systems Volume 58: Modeling of Irradiation-Induced Changes in the Electrical Properties of MOS Structures

Point Defects in Gap, GaAs, and InP The Collisional Detachment of Negative Ions Ion Implantation for Very Large-Scale Integration Stimulated Cerenkov Radiation Materials Considerations for Advances in Submicron Very Large-Scale Integration

E. Sivowitch P. Vogl G . DeMey 0. Dragoun

J . F. Gibbons H. F. Glavish K. H. Purser W. G . Wolber Roy A. Coiclaser J. P. Bontet, J. Nussli, and D. Vallat F. E. Gardiol K. J. Hanssen R. N. Lee and C . Anderson Robert D. Hayes Henry Krakaner R. F. Stebbings Robert T. Longo

J. Frey

R. S. Berry and S. Leach D. C. Hanson P. Braun, F. Rudenauer, and F. P. Viehbock H. W. Redlien and R. J. Kelly D. J. David

J. N. Churchill, P. E. Holmstrom, and T. W. Colt ins J . Schneider and V. Kaufmann R. L. Champion Heiner Ryssel J. W. Walsh

D. K. Ferry

My sincere thanks to all of the authors for such splendid and valuable reviews. C. MARTON

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 56

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOLUME 56

Recent Advances in High-Power Tunable Lasers (UV, Visible, and Near IR)

V. N. SMILEY* EG&G, Inc. Las Vegas, Nevada

I. Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Dye Laser Developments.. . . . A. Introduction . . . . . . . . . . . B. Principles and Limitations. . . . . . . . . . . . . C. Flashlamp-Pumped Dye Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Laser-Pumped Pulsed Dye E. cw Dye Lasers.. . . . . . . . . F. Injection-Locked Dye Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Vapor Phase Dye Lasers ...................... .................... 111. Picosecond and Subpicosecond .... A. Introduction B. Flashlamp-Pumped Dye Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Pulsed Laser-Pumped Dye Lasers D. cw Dye Lasers.. ...................................................... E. Color Center Lasers . . . . . . ............. ............... F. Excimer Lasers . . . . . . . . . . ............. ............... H. Future Prospects IV. Color Center Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Introduction . . B. cw Color Center Lasers in Alkali Halides.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Nonlinear Coherent Sources ............. .......... B. Harmonic Generation in Pulsed Dye Lasers. .............................. C. Intracavity Frequency-Double D. Optical Parametric Oscillators E. Sum-Frequency Mixing (SFG) F. Raman Generation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Other High-Power Tunable Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Blue-Green Lasers .................................................... B. Lyman-ol Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Metal-Doped Solid State Lasers. . . . ......... ..... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

7

35 36

42

45

54 55

60

74 79 79 83 85 89

* Formerly with the Desert Research Institute, University of Nevada System, Reno, Nevada 89506. 1 Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-0146564

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V. N . SMILEY

I.

INTRODUCTION

The first laser, a flashlamp-pumped ruby device, was operated two decades ago by Maiman (1 960). Available laser materials, operating wavelengths, power and energy, pulse rates, degree of spectral narrowing, tunability, and number of applications have been increasing ever since. Multibeam lasers intended for fusion are presently capable of more than 10 kJ pulse energy and tens of terawatts peak power. Plans call for hundreds of kJ in the next few years. Laser weapons also require extremely high power. The subject of this review article, however, concerns recent advances in more easily obtainable lasers which have the combined properties of high power and tunability. In general, these lasers have much lower output energies and powers than lasers used for fusion. In part, the lower output characteristics are a result of the fact that available performance is sufficient to accomplish desired tasks. For example, a 100-5 pulsed dye laser is not required to conduct laboratory spectroscopy measurements. Often a few mJ or even pJ will suffice. Some lasers are so inefficient at present that it is not practical to scale them to extremely large output power or energy. Other factors limiting development include material damage and cost. It is apparent then that the terms high power or high energy applied to lasers are somewhat arbitrary and depend greatly on the application. Tunable lasers became important as soon as the first tunable dye laser was discovered accidentally in 1966. Within two years dye lasers had been operated over the entire visible spectrum, the near UV, and the near IR. As a result of these successes many investigators became involved in finding new tunable laser sources, expanding tuning ranges, and increasing output powers. In 1976, a conference on tunable lasers and their applications was held in Norway (Mooradian et al., 1976). Most of the papers were very current regarding kinds of sources, tuning ranges, and powers. However, significant advances in all three categories have been made since then, and expectations are that this will be a continually dynamic field for many years to come. High-power tunable lasers is a subject that covers a large number of sources. Included in the discussion are dye lasers, color center lasers, excimer lasers, mercuric halide lasers, stimulated Raman scattering sources, second and higher order harmonic frequency multiplication of tunable sources, parametric oscillators, sum and difference frequency mixing sources, and metal-doped crystal lasers. The aim of this article is to provide a descriptive review of recent advances (up to about mid-1980) in development of high-power tunable laser devices, to consider their future potential, and to discuss possible new developments. Necessarily such broad coverage in an article of this length does not permit

HIGH-POWER TUNABLE LASERS

3

detailed treatments of the fundamental properties of the various lasers and techniques mentioned. References to thorough fundamental discussions will be given. Except for a few examples where an overlap exists, intermediate and far IR sources will not be presented in this article, in deference to the fact that another review in this series is to cover that topic. 11. DYELASERDEVELOPMENTS

A . Introduction Dye lasers have become extremely popular since the fortuitous discovery at IBM of laser action at 755.5 nm in chloroaluminum phthalocyanine by Sorokin and Lankard ( 1966) while they were looking for resonance Raman scattering in that substance when excited by a ruby laser. Similarly, there was a report in the same year of laser action in 3,3’-diethyltricarbocyanine which was obtained in the near IR by Volze in Schafer’s laboratory (Schafer et al., 1966) at the University of Marburg while he was studying saturated fluorescence of cyanine dyes pumped with a Q-switched ruby laser. Soon thereafter other investigators obtained tunable laser action in a large number of dyes in the UV, visible, and near IR using laser pumping and later flashlamp excitation. A large number of applications for tunable dye lasers has appeared in the last few years. These include use as a spectroscopic tool, production of photochemical reactions, photobiological investigations such a selective breaking of specific bonds in DNA, isotope separation, and pollution monitoring. Most of these applications require high average or peak power levels. For that reason it is important to continue attempts to increase the efficiency and power output of liquid dye lasers and to pursue the direct electrical excitation of vapor phase dyes. The popularity of dye lasers is a result of several beneficial features including broad tunability, operation from broadband to extremely narrow spectral widths, high energy and power, operation in cw and pulsed modes with available pulse lengths as short as the subpicosecond range, laser or flashlamp pumping, inexpensive laser materials, and ease of switching to a different wavelength range. This section deals with recent advances in dye laser technology in five categories: flashlamp-pumped, laser-pumped (pulsed and cw), vapor phase, and injection-locked dye lasers. The discussion of the relevant basic physics and chemistry is extremely brief in this article. Extensive treatments of these topics are to be found in some very thorough reviews of dye lasers by Schafer

4

V. N. SMILEY

(1977), Snavely (1969), and Peterson (1979). Other tunable sources have been derived from dye lasers using nonlinear effects in various materials. These are described in Section V. A brief representative list of dye laser energies, average powers, and tuning ranges for the five categories to be discussed is given in Table I. The entries there show that pulsed energies up to many joules and cw powers up to tens of watts are obtainable, and that spectral widths from broadband (tens of nm) down to 1 MHz have been achieved.

-=

TABLE I REPRESENTATIVE LISTOF DYELASERPROPERTIES Pumping method

Tuning range (nm)

Linear flashlamp

340-950

Coaxial flashlamp

340-950

Ruby laser (fundamental)

720-1090

> 347

Ruby laser (2nd harm.) Nitrogen laser

360-930

Nd:YAG

220-3000

output energy (power)

Comments

Up to 100 W 1 kW average power predicted (Schafer, (avg.) power, 1978a,b), typical energy 0.1-1 J, pulse widths 0.7 to several psec, pulse rates up to 10 J per UP to -200 HZ pulse Typical pulse energy 0.5-1 J in 1 to a Up to 400 J in 10-psec pulse few psec, not a good configuration for high average power. Typical pulse (Baltakov e t a / . , rate for maximum energy <1 Hz or 1974) -25 Hz at reduced energy First successful dye laser (Sorokin and > 1 GW (peak) Lankard, 1966). In one example Bierry ef a/. (1977) obtained 0.4-1.0 GW peak powers in 2.5-nsec pulses from several IR dyes with linewidth of 0.02 cm-' when pumped with 2-GW pulses from ruby oscillator-amplifier system. Also see Loth el a/. (1976) and Browell era/. (1979) Useful for pumping shorter wavelength dyes > 100 kW (peak) Less expensive than most laser pumped systems. Linewidths down to 50 MHz. Pulse width durations from 0.2-10 nsec > 200 mJ Pulsed (3- I5 nsec or greater) Various schemes t o obtain different > 0.2 W (avg.) spectral ranges (see Fig. 21) including direct pumping with fundamental, 2nd and 3rd harmonic of 1.06 Nd:YAG output; mixing fundamental or 2nd harmonic dye output with 1.06-pm radiation; and Raman shifting (continued)

5

HIGH-POWER TUNABLE LASERS TABLE I (continued) Pumping method

Tuning range (nm)

output energy (power)

400-1000

Up to 34 W cw

Optical, electrical discharge, or e-beam with vapor phase dyes Copper vapor

550-800

50 kW (peak)

GaAlAs Alexandrite laser

930-990 700

> I W (peak)

Ion laser (Kr and Ar)

Comments

-

Typical maximum cw power 1 W. Mode-locked, cavity dumped operation produces psec-pulses > 1 kW peak power at very high repetition rates Optical pumping has worked on several dyes at low efficiency; electrical discharge not successful yet, but gain achieved with e-beam pumping; see review by Marowsky (1980) Repetition rate, 6 kHz, pulse width, 20 nsec Useful for IR dyes Potentially useful for IR dyes

The cost and complexity of various dye laser instruments vary over a wide range from the very simple and inexpensive untuned flashlamp-pumped system to complicated and expensive ion-laser-pumped cw ring dye lasers capable of producing spectrally narrow, stable radiation at power levels up to several watts.

B. Priiiciples ciiid Limitutiotis The properties of dye lasers can be better understood after considering the energy states of organic dye molecules. The electronic energy level structure of a typical organic dye is shown in Fig. 1. The levels shown consist of ground state (So), first excited singlet state (S,), second excited singlet state (S2),and two triplet states (TI)and (T2L Important radiative and nonradiative transitions for laser action are indicated in Fig. 1 and their associated lifetimes in the text. Fluorescence and laser transitions occur between the lowest S, state and various S o states. The excitation takes place from the lowest ground state to upper S, states which rapidly decay to the lowest S, state by nonradiative transitions shown with wavy lines. The singlet fluorescence radiative lifetime is of the order of a few nsec, whereas all the nonradiative transitions have extremely short lifetimes of the order of psec. An important spin-forbidden singlettriplet transition (S, +T1)is shown in Fig. 1 which has a lifetime of tens of nsec or longer. This transition coupled with the relaxation transition from

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V. N. SMILEY

s2

s1

5-9

I

-f

-

LUORESCE

8-5

-

LBSORPTIOL

T-S

PHOSPHORESCENCE (Slow)

I

FIG.I . Energy level diagram for an organic dye (Weber and Bass, 1969).

the lowest triplet state to the singlet ground level (lifetime of the order of 100 nsec for Rh6G) forms a competing path for excitation decay of the upper laser level. Self-absorption can take place in the singlet states from higher, thermally populated S1 levels to Sz levels. The upper singlet state decays very rapidly back to S1 by nonradiative transitions, and therefore laser threshold is not increased, but the optimum operational wavelength of the laser is shifted. Also in the triplet states, self-absorption occurs from T, to T, levels which results in a direct energy loss of the stimulated emission photons. These triplet-triplet absorptions do not present a severe problem for short-pulse dye lasers since the lowest triplet state population (n,)does not have time to build up significantly. However, n, will reach an equilibrium value for long

HIGH-POWER TUNABLE LASERS

7

pulse ( > l o 0 nsec) or cw operation, and therefore the efficiency of lasers operating in those modes is reduced.

C . Flashlamp-Puniped Dye Lasers Flashlamps with pulse lengths of -0.5 msec used for excitation of ruby rods, Nd :YAG, or other solid state laser materials are not suitable for pumping dyes since laser threshold cannot be reached with them. More intense short-pulse flashlamps had to be developed with pulse durations ranging from several psec down to about 200 nsec. Even with the shortest flashlamp pulses, operation of the laser can be considered to be nearly steady state, since the excitation time is longer than the lifetime associated with the lowest triplet state. The energy storage time of the excited singlet dye molecules is only 1-5 nsec. Therefore the molecules are excited again and again during each excitation pulse. The pumping power in the dye absorption band required to maintain a laser dye at stimulated emission threshold is given by

p =

[hv(l?,)th/Ts]

v

(1)

where hv is the pumping photon energy, (n,),h is the threshold value for excited singlet state density, t, is the lifetime of the lowest excited singlet state, and V is the volume of excited dye. Peterson (1979) has shown that this power is about 85 kW/cm2 of dye cell cross section for Rh6G when cavity losses are 10%. This is a stringent requirement. The efficiency of a flashlamp-pumped dye laser is very low for another reason, which can be easily understood from the spectrum shown in Fig. 2. This figure contains the spectral intensity as a function of wavelength emitted from a typical flashlamp designed for dye laser use. Only a small fraction of the lamp radiation is effective in pumping a given dye. About 2%of the pump radiation falls in the useful absorption band of Rh6G, which is mainly in a 10-nm wide region centered at about 530 nm. At present, efficiencies referred to the electrical input are not much better than 0.5%. Several configurations have been used for flashlamp excitation, including linear cells with helical Aashlamps, linear cells and single or multiple linear flashlamps in elliptic cross section cylindrical cavities, linear flashlamps with planar dye cells, and coaxial flashlamp cell designs. Some important kinds of flashlamp-pumped systems are discussed briefly in the following subsections with emphasis on recent achievements. 1. Linear Cell with Linear Flashlamps Linear flashlamps are usually xenon filled and excited at high voltage from storage capacitors with low inductance circuits in order to obtain

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V. N. SMILEY

+I-

n+

1 1000

in

1

1

I

I

I

2000

3000

4000

6000

6000

WAVELENQTH

(A)

FIG.2. Absolute ( + ) and relative ( 0 )spectral brightness (B,) of a coaxial flashlamp with 50-J discharge energy compared with the spectral brightness of a 21,000-K blackbody (shown by solid line) (Furumoto and Ceccon, 1969).

short excitation pulses in the vicinity of 1 psec. The lamps may be fired by applying the, high voltage with triggered spark gaps or thyratrons or by applying a high-voltage trigger pulse to a wire wrapped around the flash tube. If high pulse rates are used, it is better to have some current flowing through the lamp continuously to keep the gas ionized. This technique is described later. For high average power applications the low thermal conductivity of the quartz walls of the flashlamp is a limitation, and water cooling must be used. Special flashlamps have been found to be useful for high-power applications. Ablating flashlamps (see Ferrar, 1969; and Goldstein and Mastrup, 1967) can produce very high brightness but at the expense of short lamp lifetimes. This kind of lamp is simply a quartz tube connected to hollow metal

HIGH-POWER TUNABLE LASERS

9

SIMMER POWER SUPPLY

FIG.3. A flashlamp circuit with enhanced simmer capability (Yee er al., 1979).

electrodes. It usually uses air and is connected to a gas supply line and vacuum pump. An intense discharge vaporizes some of the quartz which forms the high-temperature plasma. The quartz tube must be replaced periodically. Another lamp referred to as a vortex-stabilized lamp is capable of high peak brightness as well as high average power applications. These lamps have been described by Mack (1971, 1974) and Morey and Glen (1976a,b). This device utilizes a continuous argon gas flow at such a high velocity that a vortex is produced at the center of the lamp. The vortex reduces the pressure, which increases the effectiveness of the electric field by increasing the E/p ratio. This lamp can produce more excitation than can be presently utilized by dye cells because of thermally induced optical inhomogeneities. A recent significant advance in dye laser excitation by flashlamps has been developed by Yee et al. (1979) in which they used an enhanced simmer technique for improving laser efficiency. The circuit is shown in Fig. 3. A steady current of 30 mA flows through two series-connected linear flashlamps with a 50-pHchoke used to block the high-voltage discharge pulse. About 150 msec before the thyratron triggers the main discharge, the simmer current is enhanced to 3 A, which causes the entire bore of each discharge

10

V. N. SMILEY

lamp to be filled with the discharge, and lamp inductance is reduced to a minimum. This technique produces a fast rise time and a high peak intensity. The performance with Rh6G pumped at 10 and 20 J is shown in Fig. 4. An increase in output energy up to seven times that of the same laser without simmer enhancement was obtained. This technique is more effective than earlier prepulsing techniques by Ornstein and Derr (1974) and Marotta and Arguello (1976), but unfortunately it works best at low pump levels. It would be worthwhile investigating its performance with larger pump powers. A typical linear cell with linear flashlamp arrangement is shown in Fig. 5 . The flashlamp and dye cell are at foci of a reflective cylindrical cavity with elliptical cross section. In this example the dye flows through the cell longitudinally. This is adequate for low average power systems, but high average power systems require transverse flow through the cell. The flow should be turbulent so as to minimize optical distortion from thermal effects.

FIG.4. Dye laser pulses with and without simmer enhancement. The horizontal scale is 1 pseclcm, and the vertical scale is arbitrary but identical in each oscillogram. The smaller pulses are without and the larger pulses with simmer enhancement. Pump energies are 10 and 20 J, respectively, for (a) and (b) (Yee er al., 1979).

11

HIGH-POWER TUNABLE LASERS CYLINDER WlTH ElLlPTlCAL CROSS SECTION

r - - - - - I

FLASHLAW

I

I MNDOW

I I

- - - - _ _ _

TO CIRCULATING PUhR AND RESERVOIR

FIG.5. Typical linear dye cell with linear flashlamp.

Transverse flow systems unfortunately shadow cylindrical cells from the pump radiation and result in asymmetrical pumping. This effect was partially overcome by Pratesi’s group in Florence, Italy. Pucci et ul. (1977) compensated for this by using a slab cell with slightly curved inner surfaces. The curved optical guide provided a focusing action that confined the laser radiation and also reduced the inhomogeneous pump light distribution across the cell. A cross section of the cell is shown in Fig. 6 (also see Burlamacchi et ul., 1974, 1975, 1976). Systems like this could possibly be scaled up to obtain high average power. Free jets of dye have been examined by Foley et ul. (1975) for flashlamppumped systems. The air-liquid interface does not collect decomposition products and is an important feature for continuous operation at high average powers. Schafer ( 1976) has described a multiple-lamp arrangement using longitudinal flow as shown in Fig. 7. Pump radiation uniformity was obtained with the aid of lenses and mirrors as shown. The four commercial xenon lamps are capable of handling 27 kW average power. Copper sulfate solution was used to cool the lamps and also to absorb UV radiation which shortens the life of the dye. Average powers of > 100 W have been obtained by Schafer (1978a,b) with a similar device. He expects that average powers of at least 1 kW can be reached.

12

V. N. SMILEY

FIG.6. Schematic diagram of a curved planar dye cell (Pucci er al., 1977).

Generally high power dye lasers requiring narrow spectral bandwidths and small divergence angles have smaller average powers. One example of such a dye laser used for remote sensing in the atmosphere has been described by Allain (1979). Results were obtained with bielliptical, quadrelliptical, and hexelliptical heads containing two, four, and six flashlamps, respec-

HIGH-POWER TUNABLE LASERS

13

\ \

\ \

\ \

/

I

FLASHLAMPI I

I I I I

I I I I

I I I

id W

Fm.7. A multiple flashlamp head. Each flashlamp has a back reflector,aplanatic lens, and mirror-lens system which concentrates the pump radiation into 85" cones (Schafer, 1976).

tively, as shown in Fig. 8. Flashlamps up to 50.5 cm long and with diameters up to 6 mm were used, each lamp was connected to a 2.5-pF capacitor through a common air spark gap. The hexelliptical configuration with total electrical input energy of 750 J, produced the highest efficiency: 0.8% for Rh6G M in methanol), 0.53% for Rh640 (1.2 x M in methanol), (8 x 0.5% for coumarin C14 (2 x M in ethanol), and 0.26% for Rh6G ( I .2 x M in water). Single pulse broadband output energies obtained were 5 , 3, 6, and 0.8 J, respectively. Average power up to 1 W was obtained with the four-lamp head.

14

V. N. SMILEY

Dye Cell

+ -SO-

ELLRTICAL REFLECTOR

-

OUADRELLlPTlC REFLECTOR

HEXELLIPTIC REFLECTOR

FIG. 8. Multiple-flashlamp heads: bielliptical configuration normal and parallel to the axis, respectively; quadrellipticalreflector; and hexelliptical head (Allain, 1979).

Another design using multiple linear flashlamps was developed recently by Candela Corporation (H. W. Furumoto, private communication) and delivered to Sandia for their Combustion Research Facility. This laser uses four heads in tandem in an oscillator-amplifier configuration and has produced up to 10 W average power with 1 J per pulse at 10 Hz. 2. Coaxial Flashlamp Dye Lasers

An important development was carried out by Furumoto and Ceccon (1969, 1970) and Bunkenberg (1972) in which the dye cell and flashlamp were incorporated into a single coaxial configuration. The discharge occurred in a thin annulus around the dye cell. Careful attention to design parameters produced an impedance matched to the driving source and permitted near critically damped operation resulting in a low inductance load. These systems use a coaxial energy storage capacitor with the flashlamp-

HIGH-POWER TUNABLE LASERS

15

Fic. 9. State-of-the-art coaxial dye laser with quadraxial configuration to reduce thermal coupling between the discharge section and dye cell and a diffuser to reduce pressure Ructuations. (Courtesy of Candela Corporation.)

dye cell close-mounted as shown in the photograph in Fig. 9. The coaxial design results in an efficient system and allows operation at pulse lengths as short as 190 nsec. Large peak energies are attainable from these lamps, but difficulty with cooling prevents operation at high average power, even though the dye solution is circulated. This problem has been partially alleviated by a triaxial design in which another coaxial element, through which circulates a coolant-UV filter liquid, has been added between the discharge region and the dye cell. A further improvement has been made recently (Lucatorto et al., 1980); an evacuated region has been added to form a quadraxial configuration for better thermal isolation (see Fig. 10). Although the plasma temperature in these lamps may be as high as 25,000 K so that most of the spectral output is in the blue and UV, it is still more efficient for single-pulse operation than lower temperature discharges in linear lamps because of the increased brightness. Operation over the spectral range 340-950 nm has been achieved

16

V. N. SMILEY

DYE

FIG. 10. Section of latest modification of coaxial flashlamp dye cell showing end cap of quadraxial arrangement (Lucatorto et al., 1980).

with coaxial flashlamp-pumped dye lasers. Figure 1 1 is a plot of relative pulse energy obtainable from a coaxial laser as a function of wavelength for several dyes. A Soviet design (Baltakov et al., 1974), operated with Rh6G in alcohol, has produced a single pulse output of 400 J in a 10-pec pulse when a 50-kJ FLASHLAMP PUMPED DYES (Candola) RHODAYINE

450

500

650

600

850

700

WAVELENQTH (nm)

FIG. 1 1 . Relative pulse energy output vs. wavelength for coaxial flashlamp-pumped dyes. (Courtesy of Candela Corporation.)

17

HIGH-POWER TUNABLE LASERS

Q

. .D .

.F )a.l .a. ;. i. DOUBLER

AMPLIFIER

ALIGNMENT LASER

. '

/ ..........0.......... 0..

..4.4..

....+.0/

FOLDING

FOLDING MIRRORS

4''RR0Rs

I.. . .$.

OSCILLATOR

\Q.

'\

.Q

,

.. . .$. i . 0 . .. . . 4 . \

REFLECTOR

GRATING

FIG. 12. Schematic diagram of a triaxial flashlamp-pumped dye laser incorporating an oscillator and amplifier (Schotland, 19801.

electrical pulse was applied to the discharge. The output beam quality of this laser deteriorated during the pulse as a result of shock waves produced by the discharge. This problem would be difficult to solve for coaxial systems, whereas the problem can be alleviated in linear systems through separation of lamp and dye cell by a few centimeters. In addition this laser would not be very useful for narrowband operation or for frequency multiplication, since both require good beam quality. A high-power oscillator-amplifier system (see Fig. 12) with more general usefulness has been described by Schotland (1980).This laser has a triaxial configuration and is a modification of a commercial oscillator-amplifier. Cooling water was circulated through an inner jacket between the discharge region and dye cell. The temperature difference between the coolant and the flowing dye was maintained at <0.05"C in order to maintain good beam quality. The flashlamps were rated at 500 J and dye cell measurements were 1.6-cm diameter and a length of 30 cm. The oscillator cavity consisted of a 40% reflecting plane output mirror and a grating separated by 125 cm. The amplifier was identical to the oscillator but without optical elements. A single pass produced a gain of -4. A dye mixture of Rh6G and Kiton Red 5 dissolved in methanol was used. The maximum output energy at 610 nm was 1.4 J and the spectral width was 0.02 nm. The pulses were used to produce 305-nm radiation by frequency doubling in an ADA crystal as described in Section V. A useful coaxial dye laser of moderate energy ( 1 J), repetition rate of I Hz, and good beam quality ( 1 mrad divergence) was developed by Bigio (1978) using an unstable resonator. 3. Infrcirecl Flushlamp-Pumped Dye Lusers There are several dyes capable of producing laser action in the near infrared out to about 1 pm ; however, high-power flashlamp-pumped dye

18

V. N. SMILEY

lasers for this spectral region present a special problem. The problem becomes clear when one looks at the flashlamp spectral emission data presented in Fig. 2. The absorption spectra for IR dyes are at even longer wavelengths than for visible laser dyes (see Fig. 13 for the absorption spectrum for IR-140).The pumping source emission is obviously not ideally matched to the dye absorption spectrum. In spite of this drawback, some IR lasers have been developed that achieve moderately high powers. Early work on flashlamp-pumped IR lasers was carried out by Carboni and Dibene (19711, Maeda and Miyazoe (19721, and Hirth er al. (1973)using fast (about 100-nsecrise time) coaxial flashlamps with di- and tricarbocyanine dyes dissolved in dimethylsulfoxide (DMSO). More recently Webb et al. (1975), using an air-filled linear flashlamp with a rise time of -700 nsec, attained laser action in 16 dyes over the spectral range of 810-972 nm with pulse energies of tens of mJ and peak powers of tens of kW. The output energies obtained in some of these experiments

x106

WAVELENGTH nm FIG. 13. Absorption coefficient 1975).

(6)

as a function of wavelength for IR-140 (Webb et al.,

HIGH-POWER TUNABLE LASERS

19

were not very large compared to results with Rh6G, and lower values are produced when some of these dyes are pumped in coaxial flashlamps. One reason for mediocre performance, in addition to poor spectral matching of the pump and dye absorption spectra, is loss arising from triplet-triplet absorption as described earlier. Loth and Gacoin (1975) looked at the use of additives to quench the triplet states and found a large improvement with the additive, N-aminohomopiperidine (AHP) in the dyes 3,3’-dimethyl-2,2’-oxatricarbocyanine iodide (DOTC), 3,3’-dimethyl-2,2‘-thiatricarbocyanineiodide (DTTC), and 1.3,3,1’,3’,3‘-hexamethyl-2,2’-indotricarbocyanine iodide (HITC) dissolved in DMSO. A twofold action was found to take place. The AHP removed dissolved oxygen in the DMSO by chemical reaction and also acted as a triplet state quencher. The experiments were carried out in a 3-mm-i.d., 80-mm-long quartz dye cell pumped by a 4-mm-i.d., 80-mm-long linear flashlamp both of which were mounted in an elliptical cavity. The flashlamp produced a 4.8-psec pulse with a 1.4-psec rise time. The cell was placed in a 34-cm-long cavity having flat mirrors with 99% reflectance at one end and a 55% reflecting output mirror. A large improvement was found with the three dyes in an air-equilibrated solution with AHP added. Deoxygenation of the solution helped to further lower the laser threshold energy and increase laser output energy. The largest improvement was found with DOTC, in which a 14-mJ pulse energy was attained in a deoxygenated solution to which AHP had been added. Loth and Flamant (1977) later developed a flashlamp-pumped laser source at 8 10 nm using an oscillator-amplifier configuration which produced lOO-mJ, 1-psec pulses from DOTC in DMSO. Triaxial or quadraxial dye cells may be useful for more efficient pumping of IR dyes by utilizing an energy conversion scheme in which an intermediate dye is used between the discharge region and the IR dye to produce fluorescent radiation in the long-wavelength absorption bands for the IR dye. This technique has an advantage over simply mixing the two dyes, since direct chemical and physical interaction is avoided and decomposition products from one dye will not affect the operation of the other dye (Whitcomb and Smiley, 1981). For example, the absorption spectrum of IR-140 dye shown in Fig. 13 could be pumped efficiently by DOTC, cryptocyanine, HITC, or DTTC which absorb in the 650-780 nm spectral region and have maximum fluorescence at wavelengths near 725, 733, 785, and 815 nm, respectively, when dissolved in DMSO (Matsutani, 1975). Energy transfer schemes using multiple dyes in the visible have been considered by Burlamacchi and Cotter (1977). Laser pumping of IR dyes is more efficient (optically) than flashlamp pumping and is discussed in the following section.

20

V. N. SMILEY

D . Laser- Pumped Pulsed Dye Lasers 1. Introduction

The efficiency (optical) and output energy of many dye lasers can be increased and laser threshold decreased over flashlamp pumping by using the appropriate lasers as pumps. This is particularly true for longer-wavelength visible and near IR dye lasers and is partly a result of the shape of the spectral output of flashlamps which peak at shorter wavelengths. In addition several pulsed lasers have rise times of a few nsec or less, which is smaller than the triplet lifetime; therefore, triplet-triplet absorption does not produce much loss as is the case with flashlamp-pumped or cw dye lasers. Laser-pumped dyes cover the range from 336 nm, reported by Abakumov et al. (1969a,b) in nitrogen laser-pumped P-terphenyl in cyclohexane or ethanol, to 1176 nm obtained by Varga et al. (1969) in a polymethine dye pumped by a Nd: glass laser. Lasers that have been useful for pumping highpower dye lasers include ruby; nitrogen; frequency-doubled, -tripled, or -quadrupled Nd :YAG ;excimer ;and laser- or flashlamp-pumped dye lasers operating at shorter wavelengths. Some of the more common sources are discussed in this section. Generally, three kinds of pumping geometries have been used for laser pumping of dye lasers : longitudinal, axial, and off-axis arrangement. The three basic schemes are illustrated in Fig. 14. The nitrogen laser already has a rectangular-shaped output beam which is ideally suitable for longitudinal pumping but can be further optimized with a cylindrical lens. Most lasers have a circular beam cross section which can be spread out in one dimension with cylindrical lenses for optimum transverse pumping. A better adaptation of this method is one in which the cell is a small-diameter capillary tube, since the pump radiation is absorbed in a very short distance. This causes the population inversion to be nonuniform along the pumping beam in a larger cell and results in large diffraction loss. Axial or longitudinal pumping requires that the laser pumping beam pass through the dye laser mirrors and cell (see Fig. 14b). The dye laser mirrors must be highly reflecting at the dye laser wavelength and highly transmitting at the pump wavelength. This is not too difficult with multilayer dielectric film techniques ; however, some reflection loss is experienced for the pump radiation. In Fig. 14c the pumping beam is at an angle with respect to the dye laser axis so that it misses the cavity and traverses the cell, which usually has AR-coated windows or Brewster-angled windows. This is also a more convenient arrangement, since the pump and dye laser beams are then spatially separated. Further details of specific pumping arrangements are discussed in the next subsection.

21

HIGH-POWER TUNABLE LASERS

puMp LASER

-

P U W RADIATION

D Y E LASER REFLECTORS

DYE LASER RADIATION

DYE LASER RADlATlON

DYE LASER /REFLECTORS\ LASER

PUW RADIATION

-

1

I

&

-

7

-

DYE 'CELL

(b)

-

.

I

__DYE LASER -RADIATION

'

DYE CELL (C 1

FIG. 14. Simplified schematic diagram of three schemes for laser-pumped dye lasers: (a) transverse, (b)axial (longitudinal),and (c) off-axis excitation.

2 . Ruby Laser-Pumped Dye Lasers

The first ruby laser pumping experiments (also the first successful dye laser) with dye lasers were carried out by Sorokin and Lankard (1966) in which they found laser action in chloroaluminum phthalocyanine at 755.5 nm. Soon thereafter many successful ruby-pumped dye laser experiments

t -- 11

-

PF

An CnJ

m 11 I/ A

n

w

a

I MI

FIG. 15. Ruby laser-pumped dye oscillator-amplifier. D, Oscillator dye cell; a, 0.8-mm diaphragm; PF, Fabry-Perot etalons; M1, mirror with maximum reflection coefficient; M2, output mirror; E2, El, beam expanders; A1 to A4, amplifier stages; L2 to L8, beam splitters or mirrors; L1, cylindrical lens (Loth et al., 1976).

23

HIGH-POWER TUNABLE LASERS

were reported in cyanine dyes by Schlfer et al. (1966), Spaeth and Bortfield (1966), and Stepanov et af. (1967a,b). Following this, several xanthine dyes emitting at shorter wavelengths were made to lase by using shorter wavelength excitation obtained from frequency-doubled ruby lasers at 347 nm. Ruby laser emission occurs at 694 nm and therefore is useful only for pumping lasers for the near IR. Several experimenters have wanted to use high power tunable lasers in this wavelength region for remote sensing in the troposphere or at higher altitudes. The use of flashlamp-pumped systems for this application was discussed in the previous section. Loth et a[. (1976) developed a powerful laser source at 769.9 nm for a lidar system capable of measuring atomic potassium at an altitude of 90 km by resonance fluorescence on the D, line. The dye used was DOTC in DMSO. Laser output specifications were spectral width (FWHM), 0.0065 nm; pulse width (FWHM), 15 nsec; pulse energy, 1 J ; and repetition rate, 0.1 Hz. The laser system was designed as an oscillator-amplifier configuration with four stages of amplification in which optical taps with mirrors and beam splitters were used to obtain simultaneous pumping energy from the same ruby laser. The laser system is shown in Fig. 15. The pump energy was 2.8 J in a 12-nm diameter beam. The cells were Duralumin with an amplification length of 1.2 cm. Dye concentrations in the oscillator and amplifiers were M and 5 x 10-4 M , respectively, and a flow rate of 8 cm3/sec was used. These concentrations were chosen so that the oscillator, without wavelength narrowing, would oscillate with broadband emission centered at 770 nm, and the amplifier concentration was picked for maximum power. Wavelength narrowing and tuning were accomplished by using three temperaturestabilized Fabry-Perot (FP) etalons of different spacings in tandem. Table 11 contains the performance characteristics for the oscillator and each sucTABLE I1

EXCITATION AND OUTPUT ENERGIES OF THE DIFFERENT

AMPLIFYING STAGES AT 769.896 nm WITH AA = 0.0065 nm'

OsciIlator Amplifier I Amplifier I1 Amplifier I11 Amplifier IV

0.35 0.35 0.4 0.63 1.12

0.005 0.022 0.195 0.470 I .oo

0.3 1.46 13 31.3 66

1.4 4.9 43 44 47

W,, excitation energy for the stage; Wnv,:output energy; P, output peak power; q, energy conversion efficiency for the stage, 4 = (W,,, - wn)/Wp (Loth et d.,1976).

24

V. N. SMILEY

cessive amplifier stage. The output beam spread was 0.7 mrad and no drift in wavelength was observed during 8 hr of continuous operation. Bierry et al. (1977) developed a powerful near IR ruby laser-pumped dye laser, which was capable of producing peak powers up to 1 GW in 2.5-nsec pulses, as a primary laser for a tunable IR device out to 7.7 pm using the dye laser as a driving source for stimulated Raman scattering. These authors used an oscillator that produced a narrow, tunable spectral bandwidth down to 0.02 cm-' with low beam divergence. Spectral narrowing and tuning was accomplished with an echelle grating and Fabry-Perot etalon. This high-quality beam was then amplified by three successive amplifier stages to produce tunable radiation over the range 0.72- 1.09 pm. Nine dyes supplied by a Japanese firm (Nippon Kankoh-Shikiso Kenkyusho Co., Ltd.) were required to cover the range. Output power tuning curves are presented for these dyes in Fig. 16. The chemical names for the nine dyes are given in Table 111.

-7

.a

.o

1.O

hfum)

FIG. 16. Dye output power obtained with nine different dyes pumped by 2-GW, 2.5-nsec pulses from a ruby laser; p is the quantum efficiency of the last two amplifiers (Bierry er al., 1977).

HIGH-POWER TUNABLE LASERS

25

TABLE 111 CHEMICAL NAMES OF I R Dyts NK NK NK NK NK NK

NK NK NK

IN

FIG. 16“

136: 3,3’-diethyL2,2’-thiadicarbocyanineiodide (DTDC) 3,3’-diethyl-2,2’-oxatricarbocyanine iodide 125: 1,3,3,1’,3’,3-hexamethyl-2,2’-indotricarbocyanine iodide (HITC) 126: 3,3’-diethyL2,2‘-thiatricarbocyanineiodide (DITC) thiatricarbocyanine iodide (DDTTC) 427: 3,3-diethyl-2,2’-(4,5,4’,5‘-dibenzo) 123: l,l’-diethyl-2,2’-quinotricarbocyanine iodide 1748: 1,2’acetoxy-3,3’-diethyl-2,2’-thiatetracarbocyanine perchlorate 124: 1,1 ’-diethyl-4,4-quinotricarbocyanine iodide 1948: 1,1 ’-diethyl-6,6’-dimetoxy-4,4‘-quinotricarbocyanine iodide 1511:

” Bierry et al. (1977).

As previously mentioned, remote sensing of gases in the atmosphere by backscatter methods requires high-power tunable laser systems. One such method is differential absorption lidar (DIAL) which utilizes a two-wavelength laser transmitter and a receiver that measures the radiation backscattered by atmospheric particulates and molecules at both wavelengths. One wavelength is tuned to coincide with an absorption line of the gas considered, and the other to an atmospheric window. Comparison of the two signals allows the determination of spatially resolved gas concentrations. Browell et al. (1979) constructed a DIAL system based on a ruby laserpumped dye to measure water vapor concentrations remotely. The dye used was ethyl-2-[5-(3-ethyl-2-benzothialzolinylidene~1,3-pentadienyl]benzothiazolium iodide dissolved in DMSO with a concentration of 1.2 x M. The dye laser is tunable over the range 715-740 nm. The scheme utilized, shown in Fig. 17, consists of an oscillator-amplifier with horizontal polarization and Brewster angle dye cells with an etalon and grating tuning elements. With I .5 J of total ruby laser energy at a repetition rate of 1 Hz, the dye output is about 165 mJ with a spectral width of 0.01 nm. Two water lines at 724.348 and 724.372 nm have been used, while a portion of the ruby output itself at 694.3 nm is used for the window wavelength. With a suitable receiver, water vapor measurements, with 100-m spatial resolution and averaging over 100 shots, could be made to altitudes of 1.8 km in daytime and 4.6 km at night. The same group later constructed a system for airborne use with Nd-YAG, (second harmonic) laser-pumped dye cells (Browell et al., 1979). 3. Nitrogen Laser-Pumped Dye Lasers The pulsed nitrogen laser, operating at a wavelength of 337.1 nm with a pulse duration of a few nsec and a rectangular-shaped output beam, is ideal for transverse pumping of dye cells. Early cavities used grating-mirror com-

26

V. N. SMILEY

LASER OUTPUT RUBY OUTPUT

TO ABSORPTION CELL (74 PASS 300m)

FIG. 17. Ruby laser-pumped dye laser with output beams at two wavelengths for use as a transmitter for an H,O DIAL instrument (Browell er al., 1979).

binations, and later a tuning arrangement developed by Hansch (1972) for dye lasers was incorporated in nitrogen-pumped systems. The Hansch cell concept uses tuning elements consisting of a grating with an etalon and an intracavity beam expander, resulting in a high-quality tunable optical beam. A nitrogen laser-pumped oscillator-amplifier utilizing a Hansch cell oscillator configuration is shown in Fig. 18. This system is produced commercially by Molectron Corporation and is capable of producing up to 1 mJ per pulse at 460 nm, 0.0 1-nm linewidth, 0.5-mrad beam divergence (diffractionlimited), and pulse width of -6 nsec with dye 7D4MC. In another version a linewidth of 0.001 nm is achieved with 0.7 mJ output pulse. The use of another amplification stage was required in the Wallenstein and Hansch (1975) modification, which included a confocal Fabry-Perot interferometer after the oscillator to narrow the linewidth to 50 MHz. This system also required isolation because of feedback from the interferometer. These authors used the system to produce UV radiation by frequency doubling the laser output. The relative output characteristics of a commercially available nitrogen laser-pumped dye laser are given in Fig. 19 for several dyes covering the spectral range 360-930 nm. A nitrogen laser with a shorter pulse has recently become available from Photochemical Research Associates, Inc. The output pulse width is variable from 100 to 350 psec and is useful for obtaining psec pulses from dye lasers without mode locking. The properties are discussed further in Section 111.

HIGH-POWER TUNABLE LASERS

II I

27

--

I I

FIG.18. Nitrogen laser-pumped dye oscillator-amplifier configurationused in a commercial laser. (Courtesy of Molectron Corporation.)

4. Nd: YAG-Pumped Dye L a w s

The wavelength of the Nd: YAG laser is 1.06 pm, so it is generally only useful for pumping dyes when the output is frequency-doubled to 532 nm, tripled to 355 nm, or quadrupled to 266 nm. The properties of Nd:YAG lasers that make them ideal for pumping high-power dye lasers include : 1. Moderately large pulse energy in a small package 2. High repetition rate 3. Easily Q-switched for operation in the nsec range 4. High-optical-quality laser medium which provides an output with narrow wavelength and small beam spread for working with nonlinear materials 5. Moderately efficient operation.

Recent advances in resonator design during the past few years have made N D :YAG lasers more efficient for producing high-power harmonic outputs for pumping dye lasers. Unstable resonators, first used with high-gain gas lasers such as CO, , were not thought to be very suitable for solid or liquid lasers because of thermal distortions present in such lasers. Nd :YAG, however, is a high-quality medium in which such distortions are small compared to ruby, for example. The unstable resonator has been described in

28

V. N. SMILEY

800600-

RHB*CVP

RHB*NM?

400-

RHHOXIP 200100-

620

Y

650

e'40

a'50

OXALlllE

sb0

650

BbO

do0

h0

1'10

h0

750

7140

hi0

1.

0

I

in- 144

a

WAVELENGTH (nm)

FIG. 19. Relative output energy tuning curves for several dyes pumped by a nitrogen laser. (Courtesy of Molectron Corporation.)

29

HIGH-POWER TUNABLE LASERS

several articles by Siegman (1965, 1974, 1976) and as applied to Nd:YAG lasers by Herbst et al. (1977). One commercial oscillator-amplifier Q-switched Nd :YAG laser using an unstable resonator in the oscillator stage produces 700 mJ per pulse, 8-9 nsec pulse width at 10 Hz, and second, third, and fourth harmonic output energies of 225, 125, and 60 mJ, respectively (Quanta-Ray). Other cavity designs have also been developed for obtaining high power frequencymultiplied Nd:YAG laser outputs suitable for pumping dye lasers. For example, a unique method that uses a double-passed oscillator in which the polarization of the second beam has been rotated 90" has produced even higher pulse energies in a commercial laser (Quantel). According to one manufacturer, if more energy is needed from a Nd: YAG laser, another amplifier stage is required. However, this leads to problems with amplified spontaneous emission in both of the previously discussed designs, and isolators would be required. A new design using two amplifier stages developed by Quantel produces 1500,650,220, and 110 mJ in the fundamental, second, third and fourth harmonic frequencies, respectively, in 15-nsec pulses. Optical pumping efficiencies are fairly high for Nd: YAG pumped dye lasers, approaching 45% in some situations. A representative output efficiency curve for laser dyes pumped at 532 nm in a configuration using an oscillator and either one or two amplifiers is shown in Fig. 20. Spectral

*

h

40

Y

> 0 z W 3 iYi W

I-

3

n I-

s pc W

10

v)

5

W

> 0

0

540

560

580

800

820

840

860

880

700

720

WAVELENGTH (nm)

FIG.20. Typical tuning efficiencies for eight dyes pumped by a Nd:YAG laser (second harmonic).Pump wavelength is 532 nm. Dyes used: 1, exciton R590; 2, exciton R610; 3, exciton kiton red; 4, exciton R640;5, exciton sulforhodamine640; 6, exciton DCM;7, exciton oxazine 720; 8, exciton carbazine. Curve 6 taken using oscillator, preamplifier, and end-pumped amplifier. All other curves were taken using oscillator and end-pumped amplifier only. Dyes are all dissolved in methanol. (Courtesy of Quanta-Ray.)

740

30

V. N. SMILEY

FIG.21. Tuning curves for a commercial Nd:YAG laser-pumped dye laser including outputs derived from direct pumping by second and third harmonics of 1.064-pm beam, frequencydoubled dye laser output, mixing of frequency-doubled dye output with I .064-pm radiation. and Raman-shifted dye laser output. Block diagram on left shows configuration required to

bandwidths can be relatively narrow with fairly simple optics. For example, an oscillator stage with a near grazing incidence grating can produce a spectral width of ~ 0 . 0 1nm. Further spectral narrowing can be obtained, as discussed before, by the addition of an etalon; however, some energy loss will result. Representative output pulse energies as a function of wavelength for a commercially available tunable dye laser are shown in Fig. 21 with pumping at 532 and 355 nm. This dye laser (Quantel TDL-111) consists of a dye oscillator followed by three successive dye laser amplifiers of progressively larger diameters. This figure also contains outputs from the dye laser generated by Raman shifting, frequency doubling, and frequency mixing of frequency-doubled

HIGH-POWER TUNABLE LASERS

31

achieve energy shown. Heavy bars indicate highest energy configuration. Stippled bars indicate possible but not preferred configuration. EnerBes shown are for a standard Quantel YG 481A laser pump operating at 10 pulseslsec. Higher energies are attainable (by about a factor of 2) with a Quantel YG 482 laser pump. (Courtesy of Quantel International.)

dye laser output with primary Nd:YAG laser output. These other techniques will be discussed in later sections. Laser operation of Nd:YAG-pumped dyes in the near IR beyond the fundamental 1.06-ktmwavelength has been attained by Kato (1978).This technique had been used earlier with a Nd :glass laser pump (see, for example, Derkacheva et al., 1968, 1969; Varga et al., 1968, 1969; and Dyadyusha et al., 1976). The advantage of Nd:YAG over Nd:glass is that higher average power can be achieved. Two dyes investigated by Kato were 3,3’-diethyl-9,11,15,17-dineopentylene-thiapentacarbocyanine perchlorate (DNTPC-perchlorate) and 3,3’diethyl-9,11,15,17-dineopentylene-(6,7,6’7’-dibenzo~thiapentacarbocyan~ne

32

V. N. SMILEY

perchlorate (DNDTPC-perchlorate) dissolved in DMSO. The former was tunable over the range 1.102-1.148 pm and the latter over the range 1.1511.216pm. Peak powers up to 4 MW and average powers up to 390 mW were achieved. E. cw Dye Lasers Peterson et rrl. (1970) were the first to produce cw laser action in a dye solution flowing between two mirrors. They used an Ar laser pump source with the pump radiation focused to a small spot in the dye. The 488-nm and 514.5-nm Ar lines effectively pump Rh6G and a large number of other dyes. Krypton ion lasers also have several Lines suitable for pumping dye lasers, including lines at 647 and 676 nm which are useful for pumping red and near IR dyes. Even though a few watts are obtainable from cw ion lasers, the pump radiation must be focused to a small spot, since the excitation required for organic dyes is of the order of 1 MW/cm2 (Peterson, 1979). Pumping beam cross sections then must be about 20-50 pm in diameter for 1 W of pump power focused in a TEM,, intensity profile. One advantage of a small active volume is that dye flows through this small region so fast, even for moderate flow rates, that thermal distortion problems are minimized. The first cw dye lasers experienced problems with decomposition products that accumulated on the cell walls and from heat buildup. Both problems were eliminated by the use of small jets (Johnston and Runge, 1972). This technique is now commonly employed in commercial cw dye lasers as well as in many experimenter-constructed dye lasers. Extended cavities had to be developed to permit incorporation of tuning elements, frequency doublers, etc. and still maintain the required small excitation volume. One example of a three-mirror folded cavity for dye jet lasers is shown in Fig. 22. The triplet-triplet absorption problem was overcome by sheer brute force. Pump photons arrive at a large enough rate to overcome the upper singlet state depletion by singlet-triplet interactions and subsequent loss by absorption as discussed earlier. Recently cw power of 34 W with 100 W of pumping power from an Ar laser was reported (Shafer, 1978b). Many improvements in cw tunable dye lasers have been made in recent years. Good references which discuss these developments and fundamentals of cw systems have been prepared by Peterson (1979) and Snavely (1977). A recently developed single frequency high-power cw tunable dye laser is the so-called ring laser. Early work was done on this device by Frolich

33

HIGH-POWER TUNABLE LASERS

BREWSTER'S COLLMATMG M#,ROR

OUTPUT MVlR-OR

- .IC NO

(adjustable

DYE LASER BEAM

an&)

FIG.22. Three-mirror (excluding the input mirror) folded cavity used in a commercial cw jet dye laser. (Courtesy of Spectra-Physics.)

et a/. (1976) and Schroder et a/. (1977). A ring dye laser is capable of producing watts of extremely narrowband tunable radiation. The reason for using a ring configuration as opposed to a conventional type of cavity is that standing waves occur in a conventional cavity, whereas traveling waves occur in a ring cavity. In a standing wave an upper limit to single mode output power occurs, since saturation of the dye by the input power takes place at the nodes of the standing wave. Further increase in input power results in a new mode reaching threshold with frequency such that its nodes occur at the antinodes of the first mode because the gain is higher there. Therefore multimode behavior develops as pump power is increased. Marowsky and Kaufmann (1976) have also shown that under single mode operation in a standing wave cavity the output still increases with increasing pump power as a result of the saturated regions increasing in size, but the dependence is not linear. As a result a traveling wave ring dye laser can produce a much higher single-mode output than a standing-wave configuration with the same dye volume and pump power. According to Johnston and Proffitt (1980) a ring dye laser can typically be pumped four times harder than a standing-wave laser and can produce 10 times the single-frequency output power.

34

V. N. SMILEY

Recent improvements in ring dye lasers have been made by Frolich (19771, Jarrett and Young (19791, Wagstaff and Dunn (1979A and Johnston and Proffitt (1980) in which the concept of an “optical diode” was used. A true traveling wave laser must have a nonreciprocal element such that waves moving in one direction only will propagate, while the countermoving wave must be rejected. All such devices developed to date have used the Faraday effect, in which a magnetic field is applied to an optical medium having a high Verdet constant. A linearly polarized wave will have its polarization rotated in a direction dependent only on the field direction, and therefore the effect is nonreciprocal. An efficient traveling wave ring dye design was developed recently by Johnston and Proffitt (1980). A key element in their work was modification of previous one-way systems to include an optical diode by inserting a Faraday rotator made of SF-2 glass and an optically active rotator made of quartz at the Brewster angle to lessen loss and eliminate the need for intracavity antireflection coatings on surfaces. Figure 23 illustrates the operation of an optical diode. In this system the forward wave has no net polarization INTRACAVlTY

STER

OPTICALLY ACTIVE ELEMEN AGNETIC FIELD

BEAM FOLDINQ OPTICS

T

8

P

POLARIZATION DIRECTION

FIG. 23. Operation of an “optical diode.” Polarization rotations produced by the active element and Faraday rotator are subtractive for (a) the forward wave, but additive for (b) the backward wave (Johnston and Proffitt, 1980).

35

HIGH-POWER TUNABLE LASERS

FIG.24. Tuning curves for several dyes in a commercial stabilized ring dye laser (current as of April 1981). Pumping was by argon or krypton laser lines with pump powers ranging from 24 W (blue green) for R6G to 3 W (W)for S1. S refers to stilbene, C to coumarin, R to rhodamine, DCM to dicyanomethylene, and LD to a laser dye manufactured by Exciton Chemical Company. Various solvents were usad, including ethylene glycol, methanol, ammonyx-LO, cyclo-octatetraene, benzyl alcohol, and DMSO. (Courtesy of Coherent, Inc.)

rotation after the combined effect of the active element and the Faraday rotator; hence this wave passes through the Brewster angle-surfaced elements with no loss. However, the backward wave suffers a net polarization rotation, since the active element and Faraday rotator now are additive. The backward wave undergoes reflection losses at the surfaces and is effectively lost. A single-frequency output power of 3.5 W was obtained with only 2-MHz frequency jitter with 24 W of pump power from an Ar ion laser. Stable operation has been obtained over the spectral range 425-810 nm. Commercially available ring dye lasers typically have output power approaching 1 W, short-term drift of 1 MHz, and long-term drift of 100 MHz. Typical output tuning curves for several dyes obtained in 1981 from a commercial ring dye laser are given in Fig. 24.

-

-

F. Injection-Locked Dye Lasers Several methods of obtaining narrowband tunable radiation from dye lasers have been discussed in this section. Another successful method is

36

V.

N. SMILEY

frequency locking by injecting a small amount of power from another lowpower narrowband laser into a high-power dye laser. The injected signal may be from a fixed-frequency laser whose output wavelength falls within the tuning range of the dye being used or from a tunable cw dye laser. Of course, the laser is tunable only in the latter case. This technique was first demonstrated by Erickson and Szabo (1971) who injection-locked a nitrogen laser pumped dye laser with an Ar laser. Later work on injection-locking of flashlamp-pumped dye lasers was carried out by Blit et al. (1977a), who achieved 50-mJ pulses at a bandwidth of 30 MHz, and by Gibson and Thomas (1978). Carney et al. (1980) injectionlocked a ring dye laser pumped by a pulsed Xe ion laser, with a cw He-Ne laser at 632.8 nm. The same dye laser was also injection-locked with a cw dye laser and was tunable over the range 586-600 nm. In the latter investigation injection of several mW of narrowband radiation resulted in several hundred W of narrowband radiation from the injection-locked laser. A 23-5 flashlamp-pumped dye laser was injection-locked in two stages by Okada et al. (1979). They injected narrowband cw radiation into a low-power flashlamp-pumped dye laser whose output was in turn injected into the cavity of the final oscillator. With an initial cw injected power of 15 mW, 70% of the final output energy was narrowed into the 0.7-GHz bandwidth of the original cw laser. This technique is a useful method for obtaining high-power narrowband radiation because of its simplicity. In addition, less intracavity loss is sustained compared to other methods that require one or more dispersive elements to accomplish the task. This advantage is especially important for high-power flashlamp-pumped dye lasers, since large beam divergences are normally incurred in the cavity which result in spectral broadening with etalons or gratings in noninjected lasers. G . Vapor Phase Dye Lasers

Organic dye vapor laser materials would offer certain advantages over liquid dyes, since the optical quality of a gas is higher than that of a liquid and therefore thermal distortions and mechanical problems should be much less. Several optically pumped dye vapors have produced laser action (Steyer and Schafer, 1975; Smith et al., 1975; and Borisevich, 1975); however, efficiencieshave not exceeded 1%. The dye most studied is the scintillator dye, p-phenylene-bis(5-phenyl-2-oxazole) (POPOPh Marowsky (1980) has shown that POPOP pumped by a nitrogen laser at 337.1 nm has optical gain approaching that of the same dye in liquid solution. Electrical excitation of

HIGH-POWER TUNABLE LASERS

37

POPOP or other dyes in the vapor state could possibly provide a more efficient laser scalable to high powers. So far, experiments with direct electron beam pumping by Marowsky el NI. (1976, 1977, 1978) have produced fluorescence and superradiant emission. Smith et a/. ( 1976) have attempted direct electrical discharge excitation, but laser threshold was not achieved. Excitation of POPOP with 10-nsec pulses of relativistic electrons at a voltage of 1 MeV and current of 20 kA over 10 cm2 has been carried out by Marowsky (1980) and co-workers in a cell heated to 300°C. The incident electrons from the accelerator were much more energetic than the 25-30 eV

ARGON BUFFER GAS PRESSURE, atm FIG.25. Net gain of POPOP vapor-Ar mixture as a function of Ar buffer gas pressure with POPOP vapor pressure constant at 1 Torr (Marowsky, 1980).

38

V. N. SMILEY

required to excite the dyes, so methods had to be found to convert the energy from these electrons to low-energy excitation. Marowsky et al. (1976, 1977, 1978) showed that Ar used as a buffer gas in the pressure range 2-6 atm could bring about the desired results. Various atomic and molecular metastables in the buffer gas are formed from interaction with the high-energy electrons. These metastables transfer their energy to higher excited singlet dye states which quickly relax into the first excited singlet state. Probe gain measurements were made by the above workers for different pressures of buffer gas. Results (see Fig. 25) show that net gain occurs at an Ar pressure of 3 atm and reaches a maximum of about 0.17 cm- near 5 atm. This result and other calculations showing that the conversion efficiency from highenergy electrons to stimulated dye emission was 5”/, have led Marowsky (1980) to conclude that an efficient tunable electron beam pumped dye vapor laser is feasible.

111. PICOSECOND AND SUBPICOSECOND TUNABLE SOURCES

A . Introduction Since the pioneering work of DeMaria et al. (19661, in which pulses shorter than 10 psec were produced in a passively mode-locked Nd:glass laser, rapid development of techniques for producing shorter pulses and extension of the spectral range and schemes for measuring extremely short pulses ensued. New research applications appeared including the study of ultrafast chemical, physical, and biological processes. For example, Ippen and Shank (1978) have shown that times of about 1 psec are important in the dynamics of light absorption by bacteriorhodopsin; Smith et al. (1977) have shown that in photolysis experiments with tetramethyldioxetane, singlet excited acetone, one of the products, had a fluorescent rise time less than 10 psec; and pulse dispersion measurements in optical fibers have been made by Bloom et al. (1979) (also see Chan, 1978). Available pulse widths have decreased steadily, and the subpsec regime has been reached by several investigators. As of late 1979, the record seems to be 0.13 psec (Diels and Sallaba, 1980). Several review articles and books have been prepared in the last few years covering this topic. See, for example, Shapiro (1977), Shank et al. (1979), Ippen and Shank (1978, 1979a,b), and Ryan (1979). The concept of a narrow-bandwidth high-power tunable pulsed source has to be modified somewhat as pulse durations grow shorter. In accordance with the uncertainty principle, Av At = 0.4 (for a Gaussian-shaped pulse) which leads to the constraint that a 1-psec pulse in the visible at 550 nm

HIGH-POWER TUNABLE LASERS

39

cannot have a spectral spread less than about 0.4 nm or 4 nm for a 0. I-psec pulse. Narrow spectral widths are, therefore, impossible in the subpsec region, and tunability has little meaning at all in the femtosecond (lo-’’ sec) time scale. Very recently a “white light” subpsec source has been developed by a French laboratory which produces 0.5-psec pulses over the spectral range 300-900 nm in a continuum (Spectra-Physics, 1980). The broad spectrum in this instance was not transform-limited, but produced through nonlinear interaction of powerful 0.5-psec pulses from a dye laser (oscillator plus three amplifiers) when focused into a water or CCI, cell. Tunable psec and subpsec pulses have been generated in mode-locked sources including flashlamp-pumpeddye lasers, cw dye lasers, excimer lasers, color center lasers, and nonlinear frequency-conversiondevices with excitation from tunable psec sources. Table IV gives some recent representative psec generators along with their tuning ranges, pulse energies and powers, pulse repetition rates, and average powers. Pulses of psec duration are usually formed by mode-locking, which means that the laser is operating multimode such that all modes are oscillating with pulse repetition rate equal to the reciprocal of the roundtrip transit time, c/2L, where L is the cavity length, and pulse width is inversely proportional to the oscillator spectral range or number of modes oscillating (see, for example, Yariv, 1973a). It therefore follows that dye lasers can potentially produce very short pulses as a result of their large gain-bandwidth. The highpower capability of dye lasers has already been discussed in Section 11. Mode-locking behavior can occur automatically (referred to as selfmode locking); however, for most practical purposes it is induced actively or passively. Passive mode-locking is obtained with the use of an intracavity saturable absorber which favors the buildup of intense short pulses. This technique, first carried out with flashlamp-pumped dye lasers by Schmidt and Schafer (1968), has produced the shortest pulses in cw dye lasers (see, for example, Ippen and Shank, 1975; Ruddock and Bradley, 1976; and Ruddock, 1979). However, absorbers, such as the polymethine cyanine dye DODCI, inhibit continuous tuning in cw dye lasers, but have not restricted the tuning range of flashlamp-pumped dye lasers where the intracavity intensities are much larger. Active mode-locking requires external modulation of an intracavity element. A technique currently in favor is synchronous pumping in which a broadband laser is pumped with a mode-locked source, such as a frequencydoubled Nd:YAG laser whose pulse repetition rate is precisely timed to coincide with the roundtrip time for the broadband laser cavity. This technique has been applied to pulsed dye lasers (Glenn rt al., 1968) and also cw dye lasers (see, for example, Ippen et ai., 1972; Ippen and Shank, 1975; and Ruddock, 1979). More intense pulses are obtained from synchronously

40

V. N. SMILEY TABLE IV REPRESENTATIVE PICOSECOND TUNABLE SOURCES AND PERTINENT SPECIFICATIONS

Laser or method Flashlamppumped dye

Pulsed, laserpumped dye

cw Dye, laser

Pulse width (psec) 2- > 100

0.5-500

0.13-100

Spectral range (nm)

Output power/ energy

470-490, 580-800

1 pJ-7 mJ

340- 650

10 pJ-4 ml

530-900

100W-7kW peak power, -0.5 W avg. power

Remarks Passive mode-locking usually used with saturable absorber. mJ energy range using flashlamp-pumped amplifier. Injection locking also useful for achieving high energy [see, for example, Negran and Glass (1978), Mialocq and Goujon (1978), and Adrain et a/. (19741 Pumping sources include mode-locked lasers such as Nd:YAG or Nd:glass (2nd or 3rd harmonics) and nonmode-locked short cavity N2 laser [see, for example, Shank et al. (1979) and Huppert and Rentzepis (197811 Pumped with ion laser. Shortest pulses achieved with passive mode-locking of dye laser. Wider tuning range achieved with synchronous pumping with mode-locked ion laser. Higher peak power achieved if dye laser cavitydumped [see, for example, Diels et al. (1978), Diels (1979), Diels and Sallaba (1980), Matveets and Semchishem (1979), Jain and Ausschnitt (1978). Heritage and Jain (1978), Chan and Sari (1974), Harris et al. (1979, Mahr and Hirsch (1975), Mahr (1976), Frigo et al. (1977), and Kuhl et al. (197711 (continued)

41

HIGH-POWER TUNABLE LASERS

TABLE IV (continued) Laser or method

Pulse width (psec)

Spectral range (nm)

Color center laser

3-75

Excimer laser (XeCI)

3-4

Near 308

Sum mixing

38

2 18-3 16

Four-wave mixing

-5

Near I70

“White light” source

0.5

300-900

1240-1450,

around 2700

Output power/ energy

Remarks

Achieved in F l centers in KF synchronously pumped with cw mode-locked Nd:YAG laser and F: center in LiF synchronously pumped with a Kr ion laser. Also achieved in FA(]]) centers [see, for example, Mollenauer and Bloom (1979) and Isganitis er al. (1980)l 15 mJ, 710 MW Operated as an amplifier of peak power psec dye laser pulses. Potential for 8 GW/cm2 out in multipass amplifier (Maeda et al., 1980) 0.1-3 ml Sum mixing of primary or 2nd harmonic radiation from a mode-locked Na:YAG laser with Stokes components from SRS generated in benzene, acetic acid, or carbon tetrachloride from 532-nm psec pulses (Angelov el a!., 1979) lo-’ peak Resonant four-wave mixing in power lo-’” Sr vapor with two dye lasers, one fixed, the other W avg. power tunable (Economou et al., 1980) Obtained from nonlinear effects of intense psec dye pulse focused into a water or CCI, cell (SpectraPhysics, 1980)

> I W avg. power

pumped cw dye lasers if in addition, the dye laser has a cavity dumper. Another scheme, consisting of injection of a mode-locked train of pulses from a cw dye laser into a flashlamp-pumped dye laser has produced 20-pJ, 20-psec pulses (Moses et al., 1976). Once produced, psec pulses from dye lasers can be amplified by dye laser amplifiers to much higher powers. Ippen

42

V. N. SMILEY

and Shank (1979a) have produced subpsec pulses this way and have achieved pulse energies up to 500 pJ. Another mode-locking scheme consists of bleaching the saturable absorber in one dye laser cavity with a train of pulses from another passively mode-locked dye laser. This technique has produced pulses 2-6 psec in duration (Lill et al., 1977a,b). In addition to the laser sources discussed in this section, pulsed, modelocked parametric oscillators pumped by mode-locked lasers have also produced psec pulses. Reference to this work is contained in Laubereau et al. (1974), Seilmeir et al. (1978), and Weisman and Rice (1976). B. Flashlamp-Pumped Dye Lasers

The technique of passively mode-locking flashlamp-pumped dye lasers with a saturable dye has been explored extensively in the first half of the 1970s by several experimenters [see review papers mentioned previously as well as Bradley (1974) and New (1974)l. Sources tunable over the spectral range 580-700 nm with pulse durations of 1.5-6 psec were obtained by Arthurs et af. (1971, 1972),and Adrain et al. (1974) produced 7 - d , 2-psec pulses by using a flashlamp-pumped dye laser amplifier. Other combinations include a laser-pumped dye laser amplifier with a flashlamp-pumped dye laser oscillator (Schmidt (1974), and synchronous mode-locking of one highpowered flashlamp dye laser oscillator with another low-powered oscillator (Moses et al., 1976). Negran and Glass (1978) have recently extended the tuning range to 580-800 nm with pulse energies up to 20 pJ, pulse durations as short as 7 psec, and pulse repetition rates greater than 10 Hz. Rh6G together with DODCI as a saturable absorber were used in a modified commercial dye laser to cover the spectral range 580-620 nm. When Rh640 mode-locked by DTDCI was used, 100-psec pulses were obtained over the range 630660 nm. The range beyond 680 nm was covered by using a second dye laser cavity containing near IR emitting dyes such as oxazine 170 perchlorate (680-720 nm), DTDCI (730-760 nm), and DOTCI (760-800 nm) pumped, respectively, by the first laser containing Rh6G, Rh640, and Rh640. A Pockels cell was used to select individual pump pulses from the Rh6G laser or four optimum pulses from the Rh640 laser. The near IR pulses had energies of 1 pJ per pulse. The wavelength range was extended to the blue range by Mialocq and Goujon (1978). They obtained 10-psec pulses in the spectral range 475490 nm. The technique employed was passive mode-locking of coumarin in conjunction with DOC1 as a saturable absorber.

-

HIGH-POWER TUNABLE LASERS

43

Another scheme using flashlamp-pumped dye lasers employs injection mode-locking. This method was developed by Belanger and Boivin (1 974) and further exploited by a few later workers [see, for example, Moses et ai. (1976)l. The technique consists of injecting a low-power pulse train from a master oscillator into a high-power slave oscillator, causing the latter to become mode-locked. The injected signal is low powered, but intense enough to dominate and control the buildup of energy in the slave oscillator cavity which would normally occur randomly by regenerative growth of spontaneous radiation. The lengths of the cavities for the master and slave oscillators must be critically adjusted to achieve proper time synchronization of the two pulse trains. Morrison et al. (1976) have used pulses from a lowenergy source injected into a coaxial flashlamp-pumped dye laser which had an unstable resonator. Injection mode-locking has not been employed very much, especially with tunable dye lasers, but it will probably be used to a greater extent in the future. The technique has been employed to a greater degree with fixed frequency lasers such as CO, and Nd :YAG and may well become a significant factor in the design of fusion lasers (Corkum, 1979). The pulse energy of psec pulses can be amplified by successive stages of flashlamp-pumped dye amplifiers ; however, this method of achieving extremely high- energy pulses is probably limited. Although several mJ per pulse have been attained for psec pulses using this method, the process is not very efficient because the energy storage time is short (a few nsec) in dyes compared to the flashlamp duration time which is several hundred nsec. A pulse traveling through a single amplifier cell in less than 1 nsec can capture only a small fraction of the available pumping energy. In this regard dye pulse amplifiers pumped with Q-switched lasers appear to have the edge.

C . Pulsed Laser-Pumped Djie Lasers The use of pulsed lasers to synchronously pump mode-locked dye laser oscillators and oscillator-amplifiers to produce psec pulses has been reported by several investigators (see, for example, Soffer and Linn, 1968; Lin et al., 1973; Ippen and Shank, 1979a; Goldberg and Moore, 1975; Coxet d., 1977; and Huppert and Rentzepis, 1978). Ippen and Shank (1979a) used a three-stage dye laser amplifier pumped by a Q-switched, frequency-doubled Nd :YAG laser. The input pulse train was obtained from a cw mode-locked dye laser, and the Nd:YAG laser, producing 10-nsec pulses at 10 Hz,was fired in synchronism with the input pulses. This system produced 0.5-mJ pulses with a pulse duration of 0.5 psec near 615 nm.

44

V. N. SMILEY

Larger pulse energies and tunability over a wide spectral range (340650 nm) were achieved by Huppert and Rentzepis (1978). Pulse energies up to 4 ml per pulse and pulse durations of 7 psec were obtained. The pulses were generated by the system shown in Fig. 26. A five-element dye cell oscillator-amplifier element was used (Fig. 26b) which contained a mirror (a) at one end (Fig. 26b,c). Section b was the oscillator, sections d and f served as a two-stage amplifier, and sections c and e contained simply transparent solvents. Mode-locked pulses were generated in section b by a mode-locked Nd: glass laser whose output was frequency-doubled by a KDP crystal (I in Fig. 26a). The two amplifier sections were pumped with a second frequency-doubled Q-switched Nd :glass oscillator-amplifier (I1 in Fig. 26a) which produced 50-nsec pulses. Proper synchronization between the amplifier pumping pulses and the mode-locked pulses was achieved

SINGLE PULSE DYE LASER DYE LASER OUTP

HIGH REFLECTIVE MIRROR

(C)

FIG. 26. Schematic diagram of psec dye laser oscillator-amplifier system. (a) I, modelocked Nd: glass laser (frequency-doubled) pumps the oscillator section, b ; 11, Q-switched frequency-doubled Nd: glass laser with relatively long pulse (50 nsec) pumps the two amplifier cells (dandy). (b) Five-element dye cell consists of five I-cm optically polished cells contacted to each other with index matching fluid. (c) Dye cell configuration; the mirror is in optical contact with the rear window, and the front window is angled to prevent multiple reflections (Huppert and Rentzepis, 1978).

HIGH-POWER TUNABLE LASERS

45

with the aid of a Pockels cell (3 in Fig. 26a) which was controlled electrically with a detector onto which a small amount of the mode-locked Nd :glass laser energy was sent. In order to cover a wide spectral range many dyes were used. Where appropriate, pumping was carried out by frequency-doubled, -tripled, or -quadrupled 1.064-pm radiation to correspond to optimum absorption bands for the particular dye used. Results obtained by Huppert and Rentzepis (1978) in this system are described in Table V. The blue region of the spectrum has been covered also by Cox et al. (1977) who pumped a short cavity dye laser with a frequency-tripled, passively mode-locked Nd: glass laser at 355 nm. Pulse energies up to 40 pJ and pulse lengths of about 11 psec were obtained with coumarin 1 in a 1 10-pm long cavity. The spectral range covered was 425-465 nm using coumarin 1, coumarin 120, and Bis-MSB. This technique did not work as well as the same method applied to longer-wavelength dyes (Fan and Gustafson, 1976), and the reason is not understood. Cox et al. (1977) expect that output energies in the blue can be increased by reducing the cell length to about 10 pm and using radiation from the pump source to pump an amplifier stage. Nearly all psec lasers are mode-locked devices. One exception to this is a recent commercial nitrogen laser-pumped dye laser made by Photochemical Research Associates, Inc. (PRA). They have developed a nitrogen laser which they claim has a shorter pulse than other similar commercial devices (100-350 psec compared to several nsec). The short pulse is a result of a short cavity and the higher gas pressure, 1-4 atm, at which the PRA laser operates. The pulse width is varied by changing the pressure. Some specifications of a dye laser pumped by this nitrogen laser are pulse energy, 1OpJ maximum; efficiency (optical), about 20% maximum (broadband) and 15% (with grating); pulse width, 50% of pump pulse width; beam divergence, 2 mrad; operational bandwidth, 360-720 nm.

D. cw D-ve Lasers The passively mode-locked cw dye laser was developed several years ago and now has become an important source for psec and subpsec pulses (see, for example, Shank and Ippen, 1974). This method has produced the shortest pulses. Diels et al. (1978) produced subpsec pulses as short as 0.2 psec in a cw Rh6G dye laser mode-locked by DODCI as a saturable absorber and pumped with an Ar ion laser, and recently pulse lengths of 0.16 and 0.13 psec have been achieved by the same group Diels (1979) and Diels and Sallaba (1980). Passive mode-locking has not been very useful in general for the purposes of this chapter since, as pointed out by Bradley and Ryan (1978), the tuning

TABLE V CHARACTERISTICS OF PICOSECOND DYELASERS"

Dye name

Pumping wavelength (nm)

Absorption 1(max) (nm)

1(lasing) (nm)

Pulse spectral width (nm)

Conversion efficiency

Pulse energy

(%)

015)

10 10

5 1

75 10

20

10 10

20

10

30 30 20

10 10

5 10 15 10 12 5

100 200 300 400 500 200

Tuning range (nm)

Amplified pulse energy (mJ)

~~

P-Terphenyl PPD (2,5-Diphenyl1,2,4-oxadiazole) DPS (4,4'-DiphenylstiIbene) Coumarin 120 Coumarin 102 Rhodamine 6G Rhodamine B Cresyl violet perchlorate a

Huppert and Rentzepis (1978).

265 265

275 280

340 350

355 355 355 530 530 530

345 340 380 520 540 600

405 430 470 560 600

640

10

4 4 2

HIGH-POWER TUNABLE LASERS

47

range of passively mode-locked cw dye lasers is restricted to a range < 2 nm because of the characteristics of the saturable absorber dyes. However, an exception to this finding is the result obtained recently by Matveets and Semchishen (1979) who reported 0.4-psec pulses at a peak power of several kW tunable over the range 590-610 nm. They used a passively mode-locked jet of Rh6G with a DODCI saturable absorber (in ethylene glycol) pumped by an Ar ion laser. The output of this laser was amplified further by a factor of 100 by a dye amplifier cell pumped by a pulsed nitrogen laser resulting in several kw peak power. Young (1979) developed an interesting modification to the folded off-axis mirror cavity configuration for mode-locked cw dye lasers. He replaced all the mirrors with planoconvex lenses of the same focal length to form an unfolded cavity. Young claims that this arrangement is simpler, more convenient to align, and possibly less detrimental optically than the folded cavity employing off-axis mirrors. A great deal of attention recently has been paid to synchronous pumping of cw cavity-dumped dye lasers pumped by mode-locked ion lasers to achieve wider tuning ranges and higher pulse energies. Early work using this technique was reported in several papers (see, for example, Chan and Sari, 1974; Harris et al., 1975; Mahr and Hirsch, 1975; Mahr, 1976; Frigo et al., 1977). Several workers reported pulse widths in the range of 3 to tens of psec and wide tuning ranges between 530 and 670 nm. Kuhl et a/. (1977) extended the tuning range into the near IR (685 to greater than 900 nm) using the dyes, oxazine-1-perchlorate, DOTC, and HITC dissolved in mixtures of DMSO and ethylene glycol in a jet stream dye laser using a three-mirror folded cavity. Pumping was provided by an acousto-optic cavity-dumped krypton laser which provided a mode-locked 200-psec pulse train with average power of 1.4 W. Pulse durations were 25 psec with conversion efficiencies as high as 30%, and average output powers greater than 400 mW were obtained. Jain and Heritage (1978) generated -5-psec pulse trains at two wavelengths both simultaneously in one Rh6G dye and in two independent Rh6G lasers by synchronous pumping with a mode-locked argon ion laser. Twowavelength operation of a single laser was accomplished by using intracavity prism dispersion with two output mirrors, whereas the other scheme simply involved two separate dye lasers synchronously pumped by the same laser. Peak powers of 100 W were obtained with conversion efficiencies of 16-20';/, (also see Yasa et al., 1977; and Bourkoff et al., 1979). A significant improvement was made by Jain and Ausschnitt (1978) (also see Heritage and Jain, 1978) who achieved subpsec pulses 0.6-1 psec in duration and peak power of 1 kW, tunable over the range 562.5-604.5 nm in Rh6G pumped by an Ar ion laser. The pump pulses were 100-psec long and were obtained by using an acousto-optic mode-locker driven by an ultra-

48

V. N. SMILEY

TUNABLE ETALON 70% R PUMP = 440mW

i

-

-1.5psec

-20 -10 0 10 20 RELATIVE PULSE DELAY, psec

WAVELENGTH, 8,

FIG. 27. (a) Autocorrelation trace of mode-locked pulse train from wedge etalon-tuned Rh6G laser. (b) Spectrum of the dye laser output with center wavelength -567.3 nm (Jain and Ausschnitt, 1978).

stable rf oscillator. The key factors that permitted the attainment of shorter pulses than previously obtained in synchronous pumping were the incorporation of a tuning element with wider bandwidth (a single-plate birefringent filter or a low-finesse etalon); the use of a very stable rf driver for the modelocker; and a slight detuning of the cavity length from the maximum output point by 5-10 pm. The cavity length in synchronously pumped lasers is a critical factor. The above-mentioned workers found noticeable changes in pulse duration or shape for changes in length of 2 pm. Nearly transformlimited pulses were obtained as indicated by the pulse duration and spectral bandwidth shown in Fig. 27. The trace shown at the top is an autocorrelation trace formed by measuring the dependence of the average intensity of second harmonic generation (SHG) on the delay time between two portions of the output beam, one of which has a variable delay. (A review of this technique is given by Ippen and Shank, 1978). The 1.5-psec autocorrelation trace width corresponds to a dye laser pulse duration of 0.75 psec. Ferguson et al. (1978) also obtained similar results. Figure 28 depicts a three-mirror folded cavity design similar to that used by the above-mentioned workers. Very recently a considerable improvement in conversion efficiency and peak power has been achieved by Blit and Tang (1980). They synchronously

-

49

HIGH-POWER TUNABLE LASERS

MODE-LOCKEDARGON ION U S E R

MODE-LOCKER

a~

~~

R=85cm T=20%

TUNING WEDGE

-'

c

b

R=%m

R = 5cm

A=%m

FIG.28. Synchronouslypumped subpsec dye laser. The Ar ion laser cavity length is 182 cm, and the dye laser cavity length is 91 cm (Ferguson er a]., 1978).

pumped a cavity-dumped, mode-locked cw dye laser using a ring cavity. With less than 1 W of average pumping power from an argon laser, synchronously pumping a jet of Rh6G, they achieved peak powers of 7 kW and pulse durations of 4 psec at pulse repetition rates from 940 kHz to 4.7 MHz with a 30% falloff in peak power at the higher repetition rate. The experimental configuration is shown in Fig. 29. M3

FIG. 29. Schematic of a mode-locked ring cavity dye laser. J, Dye jet; C, cavity dumper; B, birefringent tuning element; F, Faraday rotator; PI and P2, quartz plate polarization rotators; M2 to M5,highly reflecting curved mirrors; M I , M6, and M7, flat mirrors (M1 is dichroic); M6, output coupler. The dotted line indicates cavity-dumped output beam (not in plane of paper) (Blit and Tang, 1980).

50

V. N. SMILEY

In contrast to findings of experimenters using linear cavities, Blit and Tang (1980) found that they could use a high-Q cavity which is a necessity in order to store energy for efficient cavity dumping operation. They believe the reason linear cavities do not work as well and require low-Q, highoutput coupling mirrors is the necessity for eliminating one set of two oppositely traveling pulses in the cavity. Small differences in gain for the two pulses arising from nonlinear saturation effects result in favoring one over the other, and this asymmetry increases for larger output coupling. However, in a ring cavity, unidirectional travel (see Section 11) can be achieved by using a Faraday rotator in the cavity (see Fig. 23). As a result higher-Q cavities can then be employed. This technique has not been optimized. For example, the cavity dumper efficiency used by Blit and Tang (1980) was only about 20%. Higher pump powers could also be used and amplifiers could be employed to increase output power levels.

FIG.30. Commercial psec dye laser with folded optical delay line. (Courtesy of Coherent.)

51

HIGH-POWER TUNABLE LASERS

_ _ - _ _ _ _ - _ _ _ _ _ _ _ _ _ _ I FUSED QUARTZ

1

+-+ BIREFRINQENT FILTER

I I

)HuI

-,

- -

-

-

OU!PUT COUPLER (Trannlatabb)

-

I I

REFLECTOR

- - -

I I I I 1

- -

- INVAR-OPXALAAR-

-

1

FIG.31. Schematic diagram of commercial psec dye laser. (Courtesy of Coherent.)

A significant advance in commercial psec sources has been made recently in the form of a delay line dye laser. Synchronous pumping of a dye laser requires that the cavity length of the dye laser be closely matched to the cavity length of the pumping laser. This normally requires a long cavity extension of the dye laser with requirements for mechanical isolation. Coherent has overcome this problem by developing a folded path optical delay line cavity mounted in a fused quartz tube compensated for thermal expansion with an invar bar. A photograph of the delay line dye laser is shown in Fig. 30, and a schematic diagram in Fig. 3 1. E. Color Center Lasers

Color center lasers (see Section IV) are dyelike in nature, and it is therefore not surprising that techniques applied to achieving psec pulses in dye lasers would be applied to them also. Mollenauer and Bloom ( 1979)achieved more than 1 W average power in 3- to 5-psec pulses over the spectral range 1.24-1.45 pm in F: centers in KF by synchronous pumping with 1.064-pm radiation from a mode-locked cw Nd : YAG laser. The experimental configuration used is shown in Fig. 32. The same authors also reported, in the same reference, 4-psec wide pulses from LiF:F: synchronously pumped with a mode-locked Kr ion laser. Using a similar technique, Isganitis et al. (1980) achieved short pulses (75 psec) in a synchronously pumped, mode-locked F,(II) color center laser around 2.7 pm. These results are preliminary, and it is expected that shorter pulses at reasonable power levels will be achieved. One complication is that

52

V. N. SMILEY

IONIZING BEAM

I FILTER GLASS WINDOW

-

MODE LOCK ADJUST

INFRASlL WINDOW

FIG.32. Schematic diagram of mode-lockedcofor center laser, F: centers in KF. The crystal is mounted on a 77-K cold finger and oriented at the Brewster angle. Lens focal lengths: L, , - 50 mm; L, + 150 mm; L,, about + 33 mm (Mollenauer and Bloom, 1979).

.

this wavelength range coincides with the very strong 2.7-pm water absorption band, thereby necessitating an evacuated or purged cavity for the color center laser. The KF :F; laser operates in the spectral region near 1.3 pm where many low-loss fibers have zero dispersion. Experiments, already performed by Bloom et al. (1979) with this laser, demonstrate nearly distortionless pulse propagation over kilometer lengths of fibers.

F. Excimer Lasers Since some excimer lasers have fairly wide-gain-bandwidths, it might be expected that psec pulses could be obtained from them. Excimer lasers, in particular XeF, have been mode-locked by Christensen et al. (1976), but the smallest pulse widths achieved were about 2 nsec. This resulted because only three or four cavity round trips occur in the high-gain medium. However, the gain-bandwidth is large enough that excimer lasers can be used as amplifiers of psec pulses. This fact was demonstrated for a nontunable situation experimentally by Tomov et al. (1977a,b) who amplified 200-psec wide pulses from the third harmonic output at 355 nm from a mode-locked Nd :glass laser to achieve an output power of 8 MW/cmZper pulse (1.6 mJ/cm2) from a XeF amplifier. This technique was extended to XeCl to produce a potentially tunable source by Maeda et al. (1980). They used a XeCl excimer laser to amplify pulses of 3-4 psec duration derived from a mode-locked Rh6G dye laser at a wavelength near 308 nm. The experimental configuration is shown in Fig. 33. The dye laser source was flashlamp-pumped and passively

HIGH-POWER TUNABLE LASERS

cw /

M

E

Rh6G

BP

’

-’

-

ltn/ ’- / n unAnP w G--

SA+MRI

53

k XeCl LASER AMP.

~

FIG.33. Schematic diagram of mode-locked psec dye laser oscillator followed by one stage of dye amplification, a frequency doubler, and a XeCl amplifier stage. M, Flat mirror; E, Fabry-Perot etalon; BP, Brewster angle polarizer; SA, saturable absorber; C, collimating lens; and PFL. pulse forming network (Maeda i’t al.. 1980).

mode-locked (with DODCI as a saturable absorber) and was followed by one stage of flashlamp-pumped dye laser amplification containing a mixture of Rh6G and RhB. The pulse train from the dye laser was then frequencydoubled by an angle-matched ADP crystal to produce pulses at 308 nm with energies of 2-4 mJ. The XeCl amplifier was UV-preionized and discharge-pumped. The UV pulses from the excimer amplifier had energies of about 15 mJ and peak power of 710 MW corresponding to an amplifier gain of 151. The output energy could easily be increased by multipass amplification, since the active gain cross section of the amplifier was considerably larger than the beam diameter and saturation was not reached. The authors estimate that 8 GW/cm2 could be obtained for 3.5-psec pulses in a three-pass amplifier. However, problems from amplification of spontaneous emission must be overcome in order to achieve that goal. G . Vacuum UV Sources

Tunable vacuum UV psec pulses can also be obtained by nonlinear techniques. For example, Angelov et al. (1979) have used sum-mixing in a KDP crystal of the primary radiation or second harmonic radiation from a mode-locked Nd: YAG laser together with the Stokes components from stimulated Raman spectroscopy (SRS) in benzene, acetic acid, or carbon tetrachloride, produced by the 532-nm psec pulses, to produce UV pulses. Results were pulses of about 38-psec duration, energies from 0.1 to 3 mJ, and tuning range of 218-316 nm. The entire tuning range was covered by changing the Raman-shifting fluid and also by choosing either 532- or 1064-nm radiation. The range 269-316 nm was obtained by mixing 532-nm

54

V. N. SMILEY

radiation with SRS radiation from the three liquids, and the range 218-244 nm by mixing 1064-nmradiation with the resultant UV beam. This technique could be applied to produce shorter wavelengths, but the lower limit was set by the phase matching conditions in KDP. Other nonlinear materials or cooled KDP would probably extend the shortwave limit. Economou et uf. (1980) have generated psec pulses tunable near 170 nm using two-photon resonantly enhanced four-wave mixing in Sr vapor of outputs from two synchronously mode-locked cw dye lasers. One dye laser was tuned to 520.2 nm (corresponding to a two-photon resonance in Sr), and the other laser was tuned around 500 nm. Each dye laser had an average power of 5 mW. The UV pulse train had an average power of lo-'' W and peak power of lo-' W/pulse. H . Future Prospects

It is apparent that spectral tuning ranges, peak powers, and average powers can be increased considerably over the results just described. Excimer lasers, in particular, may be scaled to extremely large pulse energies, since recent evidence in target interaction studies indicates that target absorption is higher in the UV and that the hot electrons produced, which are deleterious to the implosion process, are lower in temperature. However, the pulse lengths of discharge- or electron-beam-pumped excimer lasers are too long to be effective for fusion. Pulse compression techniques using backwardwave Raman pulse compression (see for example, Krupke, 1979) can in principle provide a compression of KrF pulses to 1000 psec. However, the Raman compression technique is limited to narrow bandwidths, and, therefore, the tunable feature is lost.

IV. COLOR CENTER LASERS A . introduction

Color center lasers are versatile in that they are broadly tunable, operate in pulsed or cw modes, can produce psec pulses, have low thresholds for optical pumping, and cover a wide spectral range of about 0.8-3.3 pm (using a few different kinds ofcenters). These properties are similar to those of dye lasers and conveniently extend the range into the IR from the region where dyes stop being good laser materials. Color center lasers have been operated at cw powers of a few watts. Possible applications include pollution monitoring, high-resolution molecular spectroscopy, and measurement of fiber optic properties. The reader interested in the basic physics of color centers

HIGH-POWER TUNABLE LASERS

55

in alkali halides should see a book by Fowler (1968), and for an extensive review of color center lasers an article by Mollenauer (1979). In the last few years several significant advances have been made by groups at Bell Laboratories, the Institute for Applied Physics at the University of Hannover, the Institute for Thermophysics in Novosibirsk, the Naval Research Laboratory (NRL), the University of Rochester, and Burleigh Instruments. The latter produces a commercial color center laser instrument. Two problems which have arisen in using color center lasers are requirements for low-temperature storage and operation and bleaching of the centers by pump radiation. Recently Mollenauer (1980) announced a near IR laser based on an Fl-like color center in NaF which can be stored for months at room temperature and in which bleaching effects are greatly reduced. In other color center lasers the bleaching problem is overcome by continuous optical pumping at another wavelength in addition to the regular pump wavelength. Color center lasers have reached 70% slope efficiency, are capable of producing watts of cw power, and have also been mode-locked to produce 4- to 5-psec pulses (see Section 111). Their potential for future improvement is high, and they complement dye lasers by extending the continuously tunable high-power sources into the near and intermediate IR. Details of some of the latest developments are described in the following section.

B. cw Color Center Lareus iii Alkali Hcilides 1.

Fl

Ceriters

Continuous laser action in F: centers in NaF, continuously tunable over the range 0.89-1.0 pm and also in KCl near 1.69 pm, was attained by Mollenauer (1977) who later reported laser emission over the range 0.821.07 pm in LiF: F: and 1.26-1.48 pm in K F : F l (Mollenauer et al., 1978). Optical pumps for NaF :F: , KCl :F: , and K F : FZ were provided by a cw Kr ion laser operating at 0.7525 pm, a Nd : YAG laser operating at 1.34 pm, and a Nd :YAG laser operating at 1.064 pm, respectively. A slope efficiency of 30% and output power of 40 mW were achieved by the KF:F: laser. Output power greater than 1 W was obtained from the LiF:F: laser at a slope efficiency of 60%. The F: center in alkali halides consists of one electron shared by two adjacent halide ion (anion) vacancies along a [ 1 101 axis. A very good model consisting of a Hl molecular ion in a dielectric medium was suggested by Aegerter and Liity (1971) to describe the energy level structure of F l centers. The energy level diagram for this is given in Fig. 34. There are two strong transitions, one in the visible (lSa,+ 2P7c,) and one in the IR (lSa,+ 2Pa,).

56

V. N. SMILEY

BOUND STATES

RADIATIVE 2Pau

E x n 1sag

E p q ,

_--_ _ - -

FIG.34. Energy level diagram of the Ff center (Mollenauer, 1977).

However, the visible transition appears to be a poor candidate for efficient laser action owing in part to quenching by nonradiative transitions (except at very low temperatures) from the upper state for visible emission to the upper state for IR emission. Experimental considerations for F: center lasers vary somewhat with the particular host. Details for K F : F i lasers (Mollenauer et al., 1978) are given here. The F l centers were formed in KF crystals (1.8 x 10 x 10 mm) by bombardment with 1-MeV electrons with a current density of 1.6 pA/cmZ for 15 min for each 10 x 10 mm side at a temperature of 170-200 K. This process produces empty vacancies and F centers (electrons trapped at F vacancies). As described by Nahum (1968), F i centers can be formed by warming the crystal to room temperature, at which point the vacancies become mobile and attach themselves to the F centers thus forming F i centers. However, this did not work with KF because of the presence of F’ centers (anion vacancies containing two electrons) which released electrons and deionized the F: centers. Mollenauer et al. (1978) overcame this difficulty by irradiating the samples at 77 K with an additional source of radiation from a frequency-doubled, Raman-shifted Nd :YAG laser at 630 nm or a red Kr ion laser line which corresponds to a fundamental absorption of the F, band. This ionizes the F, centers selectivelyand does not ionize the F centers. In addition an absorption band of uncertain origin occurred in the center of the F l emission band, but it was eliminated by combined irradiation with fundamental and frequency-doubled radiation from a Nd: YAG laser. The experimental configuration for F; laser operation used by the above-mentioned authors is shown in Fig. 35.

HIGH-POWER TUNABLE LASERS

HIGH REFLECTOR r = 50mm

57

PUMP BEAM IN

UTPUT MIRROR FIG.35. Schematic diagram of an F,C color center laser with in siru processing of crystal (Mollenauer er al., 1978).

Theoretical considerations show that slope efficiencies of nearly 80% should be possible in F: color center lasers; so there is considerable room for improvement over the work just described. Optimization of the output coupling and improved surface treatment of the KF crystals should increase the efficiency. In addition, Mollenauer et cil. (1978) found that doping the crystals with a divalent metal ion such as Pd2+ produced electron traps, which eliminated the undesired absorption band and are expected to improve laser performance further. Considerable increase in output power (greater than 1 W) and slope efficiency (60%)were obtained by the same workers later in LiF: F l . In work reported the following year Mollenauer and Bloom (1979) produced 2.3-W cw output power at band center in a laser using F: color centers in Pd2+-dopedK F with 5 W of pump power from a Nd: YAG laser operating at 1.064 pm to achieve a slope efficiency of 55%. The same laser was operated in pulsed mode and was described further in Section III,E. 2.

( F l )A Centers

The first demonstration of cw laser action in (F: )A centers in Na-doped KCl crystals was reported by Schneider and Marrone (1979). The laser was pumped by a Nd :YAG laser at 1.32 and 1.34pm using a configuration similar to that shown in Fig. 35 and was continuously tunable from 1.62 to 1.91 pm. Storage at room temperature for at least a month did not cause deterioration of the laser output. A slope efficiency of 18% was obtained, which probably can be improved considerably, according to the authors, by using thicker

58

V. N. SMILEY

samples or more heavily doped crystals to absorb more pump radiation and a different host to achieve a better match between pump wavelength and absorption band. An (FiIA center in a Na-doped KCI crystal consists of one electron shared by two C1- vacancies and one Na' ion. These centers were formed by first forming F centers in KCl crystals containing between 0.75 and 1S O mol NaCl by heat treatment at 6 0 5 T and then rapid quenching to room temperature. The F centers were irradiated with 365-nm radiation, which produced (F21Aand F, centers as well as FA and F, centers. This was followed by reduction of the temperature to 77 K and continued radiation at 365 nm which converted F, centers to (FZ)A centers, thus enhancing the concentration of the latter. At the same time, the 365-nm radiation caused ( F i Acenters to form in which electrons from centers were trapped by FA and F, centers, forming FA and FL centers. But the same radiation also bleaches FA and F¢ers, thus creating a dynamic equilibrium of (Fl)A and (F2)Acenters. The FI, and F¢ers do not absorb the pump radiation. One potential problem occurred as the pump radiation bleached (F: IAcenters, but fortunately the 365-nm radiation restored the ( F i )A centers. 3. F2+-like Centers A key piece of work by Mollenauer (1980), with a color center whose origin is as yet undefined, has resulted in producing 400 mW of cw output power tunable over the range 0.99- 1.22 pm from NaF at 77 K when pumped with 1 W of pump power at 870 nm obtained from a LiF: F: laser, which was in turn pumped with a Kr ion laser at 648 nm. Slope efficiency was 47%. Unlike F2+ lasers, this material has a shelf life of several months at room temperature. This color center that has been termed (F: )* is unknown as to origin but has been seen previously by Chandra and Holcomb (1969) and is not thought

FIG.36. Absorption and luminescence bands of the fundamental transition in (Fi)*centers in NaF. The optical density scale refers to a crystal thickness of 1.7 mm (Mollenauer, 1980).

HIGH-POWER TUNABLE LASERS

59

-

FIG.37. Power output of the (F:)* laser vs. wavelength for I-W pump power at 870 nm. Output mirror transmission was 3% (Mollenauer, 1980).

to be the F, center described by Gusev et a / . (1979). This center is thought by Mollenauer (1980)to be an F i center modified by some impurity or defect. The absorption and luminescence bands for the center are shown in Fig. 36, and power output as a function of wavelength is given in Fig. 37. An important property of the NaF (F; )* laser, in addition to its room temperature stability, is that its pump band is well matched to the emission of GaAs laser emission. A GaAs-pumped NaF (F:)* color center laser would make a very efficient, inexpensive high-power tunable laser. Also in contrast to ordinary FZ color center lasers, data obtained by Mollenauer (1980) suggest that pump powers of several watts could be applied to this laser before bleaching effects would cause a problem. 4.

FA(II)-FB(lI) Color Centers

FA(I1) centers are found in Li+-doped crystals and consist of F centers next to Li+ impurities. F,(II) centers are F centers next to two Na' impurities. Laser action in FA(I1) centers in KCI:Li and RbC1:Li have demonstrated laser action (Mollenauer and Olson, 1975) over the spectral range 2.5-3.1 pm. Lasers based on F,(II) centers in KCI :Na and RbCl :Na were demonstrated by Litfin et al. (1977) and were tunable over the range 2.252.9 pm. Recently Koch et al. (1979) have extended the tuning range to 2.27-3.33 pm in only two samples by simultaneously creating both FA(I1) and F,(II) centers in the same host crystal. Host crystals were L i + : N a + doped KCI and RbC1. Output powers of several tens of mW were obtained from the lasers when pumped with Kr ion lasers (RbCl :Li :Na) and Ar ion lasers (KCl: Li: Na). Jackson et al. (1979) have operated FA(I1) color center lasers in a pulsed mode using a nitrogen laser pump. The lasing medium was KCI :Li. A peak power of 100 W, 2% energy conversion efficiency, and 0.03 cm- bandwidth were obtained.

60

V. N. SMILEY

V. NONLINEAR COHERENT SOURCES A . Introduction

Advances in the field of nonlinear optical sources have been rapid since Franken er al. (1961) first demonstrated second harmonic conversion 694.3 347.2 nm in a nonlinear crystal with a ruby laser beam. Second harmonic generation (SHG) has been used extensively with various singlefrequency lasers and nonlinear materials to produce UV outputs. High efficiency is obtained with pulse laser excitation, and considerably lower efficiency with cw lasers. Second harmonic generation has also been used to extend the tuning range of high-power dye lasers into the UV. Efficient parametric tunable sources in the IR, first demonstrated by Giordmaine and Miller (1965) in a LiNbO, crystal, have achieved optical conversion efficiencies of about 40%. Other materials such as potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP), LiIO, , HIO, , proustite, and CdSe have been used effectively as parametric converters, and a sophisticated device tunable over the range 0.7-2.6 pm is available commercially (Chromatix). Another very important discovery which has made possible high-power tunable sources in previously unattainable spectral regions is stimulated Raman generation (SRG). Several workers have achieved tunable operation from the vacuum UV to the far IR. Within the last year a commercial source (Quanta-Ray Model RS-1) has become available with the capability of producing a tunable output from Stokes and anti-Stokes radiation generated in a high-pressure H2 cell over the range 190 nm-3.0 pm. In addition resonant four-wave nonlinear interactions in atomic gases (Sorokin er al., 1973) and molecular gases (Frey et al., 1976)were shown to produce tunable IR radiation. A recent review of nonlinear optical devices, including theories of operation, has been prepared by Zernike (1979). --+

B. Harmonic Generation in Pulsed Dye Lasers Fixed frequency lasers were frequency-doubled fairly soon after the first laser was operated, as pointed out previously. The technique of placing a nonlinear crystal in the output beam was used. Pulsed dye lasers have sufficient peak power that the crystal can be placed outside the laser cavity, although the same condition does not apply for cw dye lasers, as discussed in Section V,C. Additional requirements for efficient doubling are that the laser beam should be of high quality, preferably operating in the fundamental transverse mode TEM,, , in order to reduce beam spread and therefore preserve phase matching of fundamental and harmonic radiation in the

HIGH-POWER TUNABLE LASERS

61

crystal (see Kuhl and Spitschan, 1972). The nonlinear crystal is rotated (or temperature tuned) as the dye laser is tuned to preserve phase matching conditions over the entire tuning range. Output beams from both laser-pumped and flashlamp-pumped dye lasers have been frequency-doubled to produce tunable UV sources. In early work megawatt peak powers were achieved at pulse energies of 20 mJ by Bradley et af.(1971) with a Nd:glass (second harmonic)-pumped Rh6G laser and ADP doubler over the range 280-290 nm, with a spectral width of 0.2 nm. Several other laser-pumped dye lasers were built by various investigators, including ruby laser (second harmonic)-pumped Rh6G doubled by LiIO, to produce about 20-mJ pulses in the range 280-290 nm with spectral width of 0.005 nm (Hamadani and Magyar, 1971); nitrogen laser-pumped, frequency-doubled dye doubled by ADP (60", Z-cut) tunable over 250325 nm; or lithium formate monohydride tunable over 230-300 nm (Dunning et al., 1972) with peak powers up to 6 kW (60-kW fundamental peak power). Several other investigators were active in producing tunable UV pulses from frequency-doubled (or tripled) laser-pumped dye lasers. See Schafer (1977) for a list of references through 1977. In two laser fusion laboratories 80% efficiency has been achieved in third harmonic generation of Nd:glass radiation in two KDP crystals. At the University of Rochester 8 J of output were obtained (Laser Focus, 1980b). The first KDP crystal doubled the frequency of the 1.064-pm radiation with an efficiency of 67%. The doubled output was then mixed with the fundamental in the second crystal to form the third harmonic by sum frequency mixing. Commercial laser-pumped, frequency-doubled dye lasers are available which produce up to about 45 mJ per pulse at 10 Hz. An often-used pump laser for commercial or laboratory-made systems is frequencydoubled or -tripled Nd:YAG or Nd:glass at 532 or 355 nm. The third harmonic can be used to pump blue dyes to achieve shorter wavelengths. Figure 21 shows the pulse energies and spectral ranges available from a commercial source which uses the technique just described to produce highpower tunable radiation over the range 275-375 nm with several different dyes pumped at 532 nm and outputs frequency-doubled with a nonlinear crystal (Quantel). A less expensive method of achieving UV radiation from harmonic generation from dye lasers is to use a flashlamp-pumped dye laser together with an extracavity frequency doubler. This technique was used by several workers in the early 1970s, with tunable operation in the region 250-310 nm (see, for example, Jennings and Varga, 1971; Kuhl and Spitschan, 1972; and references listed in Schafer, 1977). Conversion efficiencies were > 10%. Remote sensing is one application that has inspired a few investigators to develop high power tunable sources in the UV in order to take advantage

62

V. N. SMILEY CYLINDRICAL LENS

3 ISMS

CRYSTAL

R = 0.4

LASER HEAD CAVITY LENGTH 2 3 m

R MAX

FIG.38. SHG from an Rh6G dye laser (Allain, 1979).

of resonance fluorescence from various atmospheric constituents having emission lines in the near UV such as ozone (see, for example, Megie et af., 1977). In Section I1 a high-power flashlamp-pumped dye laser, developed by Allain (1979) for remote sensing, was described which was capable of producing several joules per pulse with Rh6G. In the same paper the author described the results of frequency-doubling the output by focusing the dye radiation in a 4-cm-long ADP crystal with a cylindrical lens as shown in Fig. 38 (also see Hirth et al., 1977). The author achieved a maximum UV pulse energy of 100 mJ and 85 mJ at 302 nm with a conversion efficiency of 9.7% and total efficiency of 0.012%. Schotland (1980) has also developed a flashlamp-pumped SHG device, with possible remote sensing applications in mind, employing a triaxial flashlamp-pumped oscillator-amplifier and a KDP frequency doubler. The

'-3 .20

3

1

.10

4

i

!??!?.

I

'

7

v

1''-

INPUT ENERGY AT 610 nm (JOULES)

FIG. 39. Frequency-doubled output at 305 nm for a nonlinear crystal as a function of fundamental input energy from a flashlamp-pumped dye laser (Schotland, 1980).

HIGH-POWER TUNABLE LASERS

63

Rh6G laser, which has already been described in Section 11, had a maximum output pulse energy of 1.4 J at 610 nm. The KDP doubler crystal was 3 cm long and 1.5 x 1.5 cm in cross section. In the final format a cylindrical lens was used to focus the dye radiation into the crystal. The way in which the frequency-doubled output energy at 305 nm varied with the fundamental is depicted in Fig. 39. The dependence is quadratic up to an output energy of 93 d,where it becomes nearly linear. Crystal damage was observed at an input energy of 1.6 J. Maximum pulse energy obtained was 140 mJ at a conversion efficiency of lo%, and maximum conversion efficiency achieved was 12%with an output energy of 93 mJ. The efficiency of the system could probably be improved somewhat, since the author states that at higher energies the divergence of the dye laser increased causing the change of slope observed in Fig. 39. However, material damage would impose an upper limit on the improvement.

C . Intracavity Frequency-Doubled cw Dye Lasers The wavelength range of cw tunable dye lasers can be extended easily into the UV by frequency doubling with intracavity nonlinear crystals. Several materials have proven successful and have been summarized by Singh (1971). They include KDP and its deuterated form (KD*P), lithium niobate (LiNi,03), ADP, and ammonium dihydrogen arsenate (ADA). The theory of nonlinear optical mixing has been reviewed by Bloembergen (1963, Terhune and Maker (1968), and Yariv (1973b). Flashlamp or pulsed laser-pumped dye lasers can be frequency-doubled efficiently by simply placing the nonlinear crystal in the external beam as described in Section V,B. This technique works well as long as the input power level is in the range of kW to MW. However, the efficiency is much lower with cw dye lasers because the cw extracavity power levels are only a few watts. The conversion efficiency at low-power levels is proportional to the input intensity because the second harmonic intensity varies as the square of the input beam intensity up to some level, after which the conversion efficiency levels off. In order to achieve maximum conversion efficiency in a cw dye laser the nonlinear crystal must be placed inside the laser cavity where the intensity is much higher. In addition, to increase the intensity still further, the input beam must be focused in the crystal (see, for example, Kuhl and Spitschan, 1972). It is not possible to generate UV wavelengths by harmonic generation much below 230 nm owing to a combination of material absorption and problems with achieving 90" phase matching.

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Intracavity frequency doubling applied to solid state lasers has been studied extensively by Polloni and Svelto (1968), Smith (1970L Dimitriev et af.(1975,1976), and Volosov et al. (1973, and some early work by Frolich et al. (1976) and Ferguson et al. (1976) was done on intracavity frequency doubling of cw dye lasers. The specialized problems associated with the production of high-power tunable UV radiation around 300 nm from an intracavity doubler have been treated recently by a group at St. Andrews University in Scotland. They obtained tunable radiation in the range 285-315 nm from a frequency-doubled Rh6G dye laser and an intracavity ADP crystal pumped with an Ar ion laser (Ferguson et af.,1976). The following year the same group reported higher power levels, 30 mW cw, tunable over nearly the same range, 292-302 nm, using ADA as the frequency doubler when the Rh6G laser was pumped with 4.5 W from an Ar ion laser (Ferguson and Dunn, 1977a). The discussion that follows is based primarily on the work of this group. Introduction of a nonlinear crystal into a laser cavity increases resonator losses resulting in smaller internal fields and reduced doubled output. Antireflection coatings can be applied to crystal faces, but then optical damage sometimes occurs. It is better to cut the crystal so it can be placed in the cavity with its entrance and exit surfaces at the Brewster angle. In this manner radiation polarized parallel to the plane of incidence passes through the surfaces with almost no loss. Hanna (1969) pointed out that a Brewster-angled element produces optical distortions in the forms of astigmatism and coma which degrade the performance. Kogelnik et al. (1972) showed how astigmatism can be corrected by using an off-axis resonator, and the detrimental effects of coma were later studied by Dunn and Ferguson (1977) using geometrical optics. Coma degrades the focus in the crystal and increases linear cavity losses. The effects of coma increase with length of the doubling crystal and with angle between the mirror axis and the beam. Three cavity designs were investigated : a three-mirror cavity with off-axis focusing, a four-mirror cavity with symmetrical focusing, and a four-mirror cavity with asymmetrical focusing. It was shown that two of the configurations could not be compensated for both astigmatism and coma at the focus and overall. The fourmirror cavity with symmetrical focusing could be properly compensated but only for a unique angle of incidence on the mirrors based on the index of refraction n of the nonlinear material given by tan 8 = n3/2(nz + 1)

(2)

and when the crystal is oriented such that the angle between the optical axis of the crystal and its surface and the angle 0 are of the same sign.

HIGH-POWER TUNABLE LASERS

65

In addition, designs for intracavity frequency doublers through 1976were based on a simple theory which did not take into account crystal absorption. Absorption within a resonant cavity not only increases linear loss, but also produces thermally induced phase mismatching between input and frequency-doubled beams. The phase mismatch occurs because the index of refraction, which is temperature dependent, becomes nonuniform across the beam as a result of a nonuniform temperature distribution. In addition, thermal self-focusing or defocusing is produced, although this effect can be minimized with a suitable choice of cavity parameters. Excited state absorption of pump radiation by the dye is another effect that was taken into account by Ferguson and Dunn (1977b), but was shown by them to be less important than thermal effects in the nonlinear crystal. For a given pump power, an optimum length of crystal exists for which the frequency-doubled power is maximum. The effects of crystal absorption, linear loss, and thermal effects were found to be quite serious. The variation of optimum crystal length Lo,, and second harmonic efficiency at L = Lo,, with pump power are shown in Fig. 40. In Fig. 40b the linear loss is held fixed at 5%. Crystal absorption coefficients for nonlinear materials are typically in the range 10-3-10-2 cm-'. Clearly, low-loss cavities and materials are needed for efficient high-power frequency doubling. Output power of 30 mW in one direction has been reached by Ferguson and Dunn (1977a) tunable over the range 292-302 nm in an astigmatic and coma compensated cavity containing a Rh6G dye cell and an ADA nonlinear crystal. The dye was pumped with a maximum of 6 W of 514.5-nm radiation in a single transverse mode from an Ar ion laser. The cavity design employed is shown in Fig. 41. A 15-mm-long ADA crystal (45", Z-cut) was used with surfaces at the Brewster angle. The dye laser radiation was focused in the material with an off-axis mirror R, with radius of 10 cm, and the fundamental beam along with the second harmonic radiation was collimated with an identical mirror R,. The UV output mirror R, had a UV transmittance of SO%, while R, and R, had UV reflectances of about 80%. All mirrors had high reflectance in the visible (less than 0.5% transmitting). Tuning was accomplished with a three-element birefringent filter which narrowed the primary beam and resulted in a second harmonic spectral linewidth of 0.02 nm. The four mirrors (R,-R,) form the optical compensation for astigmatism and coma in the nonlinear crystal and also the dye jet. Phase matching in the ADA crystal was accomplished by controlling temperature. Phase matching over the range 292-302 nm corresponds to a crystal temperature range of 15-80°C. A Gaussian beam was obtained over the entire spectral range. The second harmonic efficiency, defined as the second harmonic output power divided by the pump power, of intracavity

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frequency doubling in cw dye lasers has been improved but is still rather small, being of the order of 0.5% for the results just described. As discussed earlier, increasing pump power for given crystal absorption does not increase efficiency beyond an optimum value. Improvements in reducing cavity losses and absorption in nonlinear materials will be required to improve doubling efficiencies. Some applications in atomic and molecular spectroscopy, laser-induced chemistry, etc. require UV radiation with much narrower linewidths than obtained in the previous discussion. Wagstaff and Dunn (1979) have utilized a unidirectional Rh6G ring dye laser, pumped with an argon ion laser and incorporating an ADA frequency-doubling crystal, to obtain 3 mW of

(a)

FIG. 40. (a) Variation of optimum length Lo,, with pump power. Curve a, model includes thermal effects but neglects excited state absorption. Curve d, both thermal effects and excited state absorption are neglected. Curve c, excited state absorption included but thermal effects neglected. Curve b, both thermal effects and excited state absorption included. Curve e, simple model based on neglect of both thermal effects and excited state absorption, and in addition the laser is operated well above threshold. (b) Variation of second harmonic efficiency Eop,with crystal length with linear loss constant at 5% and absorption coefficient = 0.005 cm-'. A pump power of 10 W from an Ar ion laser operating at 514.5 nm is assumed. Curve a, based on excited cm2. Curve b, uaP= 0. Curve c and d, same assumption state cross section, oaP= 1.75 x as for a and b except that thermal effects neglected. Curves e and f,same assumption as for a and b but fixed harmonic output coupling is assumed (Ferguson and Dunn, 3977b).

HIGH-POWER TUNABLE LASERS

67

E (%)

*Or

FIG.40b

TUNING ELEMENT"

*

PUMP

FIG.41. Laser cavity for intracavity frequency doubling. Mirrors R, and R, focus into the nonlinear crystal, and mirror R, is the U V output coupler. This arrangement compensates for astigmatism and coma introduced by the nonlinear crystal (Ferguson and Dunn, 1977a).

radiation tunable over the range 292-302 nm with single-mode operation. The experimental arrangement is shown in Fig. 42. According to Dunn (M. H. Dunn, private communication) the frequency stability has very recently been improved to f 10 MHz, and the continuous tuning range is now 30 GHz anywhere in the previously mentioned range. Dunn also reported UV generation in a similar cavity containing coumarin dye over the range 240-250 nm using a lithium formate frequency doubler. Output power is presently about 50 pW.

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UNIDIRECTIONAL

Il

,

MIRROR

THREE-PLATE BIREFRINGENT FILTER

FIG.42. Schematic of ring laser cavity used for intracavity frequency doubling with cornpensation for astigmatism and coma. Mirror radii are R 2 = R3 = R, = 10 cm, R, = 5 cm, R , = Rs = co.and focusing mirror radius = 10 cm. Cavity distances are R, via R, and R, to R4 is I17 cm, and from R2 to R, is 45 cm. Angles are a = 6", j = 4", y = 30". 6 = 3", and 11 = 12" (Wagstaff and Dunn, 1979).

At present, available output powers of intracavity frequency-doubled dye lasers are limited by materials. Crystals of ADP can withstand intracavity powers of 50 W without suffering thermal damage; however, thermal lensing generally occurs in the same material at about 20 W (Ferguson and Dunn, 1977a,b). D. Optical Parametric Oscillators and Amplifers

1. Optical Parametric Oscillator (OPO) A parametric oscillator is a device in which a nonlinear crystal converts energy from a pumping source to two other waves satisfying the relation

u,+ wi

(3) where cop, a,,and wiare pump, signal, and idler frequencies, respectively. In the special case where o,= withe process is called "degenerate parametric generation." The phase matching condition 0,=

k,

=

k,

+ ki

(4)

must also be met, where the k's are the wave vectors for the three waves. The nonlinear crystal is placed in a resonator so that at some threshold value the signal or idler or both waves oscillate. The reader wishing more details on OPOs is referred to several review articles and references contained in them prepared by Harris (1969), Smith (1972), Byer (1975), and Zernike (1979). Much of the development of this device has been carried out by investigators at Stanford University. Early versions of the OPO had relatively low average and peak power; however, the situation has improved in the last few years owing to improvements in laser pump energy and beam quality and in the nonlinear materials themselves. One highly developed pump for the OPO is a pulsed Nd: YAG laser

69

HIGH-POWER TUNABLE LASERS

operating at energies of a few hundred mJ with an oscillator stage only or nearly 1 J with an oscillator-amplifier combination. Beam quality of the laser pump is very important in achieving high efficiency. The use of an unstable resonator in the Nd :YAG oscillator provided a better geometric filling factor than the more usual Gaussian beam profile resulting in increasing output energy (Byer, 1976). In a recent article Byer and Herbst (1978) described an unstable resonator incorporating a concave back mirror and small convex output mirror for Nd:YAG lasers. Figure 43 is a schematic diagram of an unstable resonator developed by those authors for a system which was pumped with 55 J per pulse at 10 Hz. The pumping power is important because the laser crystal acts like a thermal lens whose focal length f is dependent on the flashlamp average power. This effect is taken into account by increasing the radius of the back mirror. This cavity design, with a length of 59 cm and convenient mirror radii, results in Q-switched pulse lengths of about 10 nsec. Byer and Herbst found the unstable resonator laser to be five times more efficient than a laser with an ordinary resonator. The near-field wave front of an unstable resonator laser has a hole in the center produced by the output mirror, but the hole is absent in the far-field pat tern.

KDIP Q-SWITCH

OUTPUT MIRROR

I D=Brnm

ND:YAG

-

Roo

t

R2= 300cm

1 F

-

I

R2

I R;

FIG.43. (a) Schematic of an unstable-resonator cavity for an Nd:YAG laser pumped with an average power of 550 W. (b) Thermal focusing in laser rod is compensated by correction to the back mirror radius of curvature as shown (Byer and Herbst. 1978).

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Conversion efficiency up to 40% was achieved in an angle-tuned LiNbO, system operating over the range 1.4-4.0 pm with a spectral width of 1 cm-' (grating plus etalon) when pumped with a Nd :YAG oscillator-amplifier system (Byer, 1976; also see Herbst et af., 1977). Improvement based on earlier work by Bjorkholm et af. (1970) has been made by Byer (1976), by incorporating a double-pass OPO which increases the efficiency and output energy as well as eliminating undesired 1.064-pm radiation from the output. This modification requires the addition of a Faraday rotator isolator as shown in Fig. 44. The OPO has been developed into a sophisticated spectroscopic tool with minicomputer-controlled tuning and operating. A commercial OPO (Chromatix) is tunable over the range 0.72-2.6 pm with 0.9 mJ per pulse and pulse rate of 15 Hz at 0.8 pm.

114"YAO

UNSTABLE RESONATOR

318 It

YAQ AMP 1

1.Owm

POL

I A n , HR

TELESC,.

-

HR OPO

I

U

1.4-4.0pm TUNABLE 0uTPuT

*

FIG.44. Schematic diagram of a double-passed OPO. The output mirror has high reflectance (HR)at 1.06pm and reflects pump radiation back through the OPO, increasing efficiency and eliminating 1.06-pm radiation from the output (Byer, 19761.

HIGH-POWER TUNABLE LASERS

71

2. Optical Parametric Amplifier ( O P A ) Most parametric devices studied and developed have been oscillators or generators of tunable radiation; the fact that they can be used as practical amplifiers has been largely ignored. Recently Baumgartner and Byer (1978a, 1979) have investigated the optical parametric amplifier (OPA). Parametric amplification is the basic mechanism for the OPO, so the same matching conditions for pump, signal, and idler frequencies must be met. The parametric gain (Baumgartner and Byer, 1978a) is given by

G = r21,(sinh2 gr)/(g02

(5)

where g2 = [r2- (Ak/2),] is the net gain coefficient, r2= 20,wild12 Zp/nsnpni~0c3 is the parametric gain coefficient, and Ak = k, - k, - ki is the wave vector mismatch. In the above, I is the crystal length, d is the nonlinear coefficient, the n’s and k’s are the indices of refraction and wave vectors for the three frequencies, Zp is the pump intensity, co is the free space permittivity, and c the speed of light in vacuum. The above-mentioned authors studied an OPA by pumping a 6-cm-long angle-tuned LiNB03 crystal with a 1.06-pm Nd: YAG laser producing 10-nsecpulses. An input signal at 1.9 pm was provided by stimulated Raman scattering in H, at 1.06 pm. With 10-mJ input for both signal and idler wavelengths and 350-mJ pump energy, the OPA produced 70 mJ of energy resulting in a gain of 7 at 20% conversion efficiency. Another experiment by the same authors with KD*P, pumped at the third harmonic of 1.06 pm, resulted in an OPA tunable over the signal range of 0.46-1.5 pm and 0.7101.5 pm for the idler wave. A parametric amplifier-oscillator configuration was developed by Baumgartner and Byer (1978b) for the transmitter of a pollution detection lidar (see Fig. 45). This device used two LiNbO, crystals pumped by the same Nd : YAG oscillator-amplifier producing 125-mJ, 8-nsec pulses for the OPO and 325-mJ pulses for the OPA at a pulse rate of 10 Hz. The output energies, tuning ranges, and spectral linewidths corresponding, respectively, for atmospheric absorption, differential absorption lidar (DIAL) CH, measurements, and DIAL SO, measurements were 4 mJ, 1.65--2.53 pm, -0.001 pm; 15 mJ, 1.67-1.66 pm, -0.001 pm; and 0.63 mJ, 4.0-3.98 pm, 0.006 pm. In another recent development. Kabelka et ul. (1979) reported the achievement of psec pulse operation with energy conversion greater than 50% in an OPO-OPA combination using two KDP crystals (4 and 6 cm long) pumped with a psec Nd:YAG laser (also see Akhmanov et ul., 1977;

-

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V. N. SMILEY

BEAM SPLllTER /

/

UNSTABLE RESONATOR YAG LASER

ISOPTOR I I

I

38 YAG

I

AMPLIFIER

I I TELESCOPE

2TO 1 BEAM EXPANSION TELESCOPE

AMPLIFIER PUMP BEAM DELAY

COMBINING

!

I 1.06 urn

f

f,rMENUATOR

~

LB_E_A_M_D_u_M_? ----A

2.25 urn LONG PASS

FILTER

SPLllTER

b

BEAM STEERING MIRRORS

FIG.45. Schematic diagram of an OPOjOPA combination used as a tunable transmitting source for a lidar (Baumgartner and Byer, 1978b).

Kryukov et al., 1978; and Spanner et al., 1976). Pump powers up to 30 GW/cm2 were used. Pulse duration was 30 psec with a spectral width of 0.8 cm- near 900 nm. The authors experienced problems in achieving high conversion efficiency and broad tuning characteristics. Based on the results obtained so far by the group at Stanford University, it seems likely that OPO-OPA combinations could become useful for highpower spectroscopic applications over the spectral range 0.46-4 pm. E. Sum-Frequency Mixing (SFG)

An efficient method of generating coherent tunable W radiation is available in the form of sum-frequency mixing, which is simply a threewave, phase-matched parametric interaction between a tunable signal wave, a fixed wavelength source, and the generated output signal wave. The same method can produce different frequencies. This process has been described by Midwinter and Warner (1967). The output power is given by P, = (

~ 3 / ~ 2 ) sin2(///,) P 2

(6)

where P , is the tunable source power; w, and o2are the output and tunable source frequencies, respectively; lo = [(471d/c)(ozo,/n2n,)'iZE,1-;El is the

HIGH-POWER TUNABLE LASERS

73

electric field amplitude of the pump source. The conversion efficiency, P 3 / P , , is independent of the power of the tunable source to be converted. This method of producing tunable UV has been used by several investigators (see, for example, Moore and Goldberg, 1976; Abakumov et al., 1975; Blit et af., 1977b; Stickel et al., 1978; Stickel and Dunning, 1978; and Dudina et al., 1979). Tunable dye laser radiation in the spectral range 545-680 nm has been converted to tunable UV radiation in the range 360-415 nm with a high conversion efficiency of 60-70% by Dudina et al. (1979). They used a frequency-doubled Nd:YAG laser to pump the dye laser with 25- to 30-nsec pulses at 50 Hz, and the fundamental output at 1.064 pm from the same laser to mix with the dye laser beam in the mixing crystal. The mixing medium was a 20 x 20 x 40 mm KDP crystal, phase-matched at an angle which was varied between 58 and 56" to cover the tuning range. The power density of 1.064-pm radiation was 300 MW/cm2 in the KDP. The output linewidth was 0.05 nm. Shorter wavelengths have been reached covering the total

FIG.46. Sum frequency upconversion of second harmonic radiation from a commercial dye laser (pumped by a second harmonic Nd: YAG laser) mixed with the Nd: YAG fundamental output at 1064 nm. The nonlinear mixing crystal was KD*P. (Courtesy of Quanta-Ray.)

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N. SMILEY

spectral range 211-320 nm (see Stickel et al., 1978; Stickel and Dunning, 1978; and Blit et al., 1977a,b). Tunable UV radiation by sum mixing is available in commercial instruments; up to 60 mJ of pulsed energy tunable over the 362-373 nm region, and 10-mJ pulses in the 220-240 nm region can be obtained. In these schemes the dye laser output is frequency-doubled to extend the tuning range further into the UV. Figure 46 shows the pulse energy vs. wavelength for one instrument operating over the 220-240 nm range (also see Fig. 21). This same technique has been used by Jantz and Koidl(1977) to convert IR radiation at 10.6 pm into the visible spectral region by sum-frequency mixing with a dye laser. Quantum conversion efficiencies greater than 40% were achieved using a AgGaSz crystal as the mixing medium (also see Warner, 1975, and references therein). The interest in this work was to convert the IR radiation into a spectral region suitable for better detection with photomultiplier tubes. A similar technique, first carried out by Dewey and Hocker (1971), can be used to produce tunable difference frequency generation (DFG) whereby a tunable source is converted to a tunable longer-wavelength output. Wide tuning ranges in the IR are possible (Seymour and Zernike, 1976), and operation with cw sources has been achieved by Pine (1974).

F. Raman Generation

Probably the most important development for extending the tuning range of existing tunable high-power sources is stimulated Raman scattering (SRS). This effect was discovered by Woodbury and Ng (1962), and several new discrete wavelengths soon became available. Tunable SRS sources became possible in 1966 when the first dye laser was operated. Amplification of SRS was observed by Bass and Deutsch (1967) in dyes; however, it was not until 1972 that Schmidt and Appt produced a successful tunable SRS source. Since then tunable ranges and output powers have increased. This effect has been demonstrated in solids, liquids, atomic gases, and molecular gases. A recent review of high-power tunable Raman lasers operating in the near and middle IR including the basic physics, pumping schemes, nonlinear media and powers, tuning ranges, and spectral widths achieved, along with other details has been prepared by Grasiuk and Zubarev (1978). The basic scheme consists of generating stimulated Stokes or anti-Stokes Raman radiation in a suitable medium with an intense tunable beam. The Raman-shifted beam has a frequency given by 0 s = o,,- O R

(7)

HIGH-POWER TUNABLE LASERS

FIG.47. Schematic of (a) Stokes and (b) anti-Stokes Raman shifted radiation for a two-level , us,and oAsare system with Ievels E, and E , . The dashed lines are virtual levels. w e %wR, excitation, Raman, Stokes, and anti-Stokes frequencies, respectively.

for Stokes shifts or @AS = @ex

+ @R

(8 )

for anti-Stokes shifts, where we, is the frequency of the tunable source, and oRis the Raman shift corresponding to the difference between two energy levels in the particular atom or molecule chosen, as shown in Fig. 47. High-pressure H2 in gas cells has become an efficient, useful medium for producing tunable SRS. The reasons include the large Raman shift of 4155 cm-' for the Q1component of the fundamental vibration transition, freedom from absorption for visible and near IR excitation wavelengths, a high Raman gain, good optical quality (compared to liquids and solids), and relatively low cost. A high-pressure H2 cell was used by Wilke and Schmidt (1978) to obtain UV radiation at wavelengths as short as 175 nm by SRS with a frequencydoubled Rh6G dye laser. They obtained outputs from the fourth anti-Stokes to the fifth Stokes line, and using the undoubled dye laser obtained the eighth anti-Stokes to the third Stokes line. The experimental setup used by the above authors is shown in Fig. 48. They concluded that a tunable source over the range 189-2064 nm could be obtained. Indeed this technique has quickly surpassed expectations. A dye laser -SRS source developed at

76

V. N. SMILEY

M

BS

F43 D

FIG.48. Experimental apparatus for generating tunable UV radiation using SRS in H,. PL, Frequency-doubled Nd :YAG oscillator-amplifier system; BS, beam splitter; ODC, oscillator dye cell; M, totally reflecting mirror; BE, prism beam expander; G , grating; ADC, amplifier dye cell; ADP, angle-tuned frequency-doublingcrystal; MD, monitor diode; LI and L2, fused silica lenses with 160- or 140-mm focal lengths; C, H, Raman cell; P, fused silica prism; F, filters; and D, fast photodiode (Wilke and Schmidt, 1978).

Lawrence Livermore Laboratory exceeded the above-mentioned tuning range. Quanta-Ray Inc. has based a commercial instrument on the Livermore design and has recently announced a source capable of tuning over the range 195-3000 nm without gaps (see Fig. 49). Output energies vary from 0.003 mJ at 195 nm to a maximum of 17 mJ at 730 nm when excitation is 85 mJ at 560 nm from a dye laser pumped by a frequency-doubledNd :YAG laser. An improvement in the efficiency of energy conversion in SRS in H, has been made recently by Komine and Stappaerts (1979) for discrete multiple Stokes outputs using a frequency-tripledNd :YAG laser. Although a tunable laser was not used, the same method could be applied to tunable SRS sources. Poor conversion efficiency is obtained on higher Stokes orders, especially, because they are emitted in cones as described by the theory for four-wave mixing processes (Minck et al., 1963). Therefore beams of poor spatial quality are produced and the conversion efficiency is lowered. The above authors minimized the effects of four-wave processes by using a Raman oscillator-amplifier configuration with both components pumped by the third harmonic of a Nd :YAG laser. The multi-Stokes oscillator output was injected into the 2-m-long amplifier with low angles of dispersion to prevent angular phase matching. This precaution together with the lower intensities in the amplifier compared to those in the oscillator resulted in a reduction of energy loss arising from four-wave mixing processes. The authors achieved photon-conversion efficiencies of 49 and 5 lo/,, respectively, for first and second Stokes orders along with nearly complete pump depletion. This technique potentially could be used to improve conversion efficiencies especially at higher Stokes orders in other tunable SRS sources. Some excimer lasers are tunable, and therefore it is possible to convert high-power tunable outputs in the UV to the visible range. The 35 1-nm

HIGH-POWER TUNABLE LASERS

77

PUMP WAVELENQTH (nm) FIG.49. Family of curves representing wavelengths obtainable from a commercial H2 Raman shifter pumped by an Nd: YAG laser-pumped dye laser. (Courtesy Quanta-Ray and G . Bjorklund.)

78

V. N. SMILEY

output of a XeF laser has been shifted by resonant SRS in Ba vapor to 585 nm by Djeu and Burnham (1977). Loree et al. (1977) have used KrF and ArF lasers to generate SRS at several wavelengths in gaseous H2, D, ,CH, , and liquid N, . Djeu (1978) has shifted the output of a KrF laser at 248-285 nm and Burnham and Djeu (1978) have converted the XeCl output at 308 nm to several visible wavelengths using resonant SRS in metal vapors of Ba, T1, Pb, and Bi with conversion efficiencies up to 40%. None of these experiments involved tuning; however, the use of Ar,, XeF (C-A transition), or Xe,C1 lasers could provide tunable sources. The use of resonance enhances the Raman gain, and facilitates high conversion efficiency; however, the tuning range would be small compared to that attainable with nonresonant Raman scattering. The broad gain-bandwidth of fused silica has been used to advantage to obtain pulsed tunable SRS sources in the visible and near IR by Lin and French (1979) in a single-mode, low-loss (2 dB/km), Ge0,-doped, SiO, core fiber with a SiO, cladding. This is an extension of previous work by Jain et al. (19771, Hill et al. (1976), and Johnson et al. (1977). The tuning range 1.07-2.32 pm involving four orders of Stokes radiation in an 800-m-long single-mode fiber Raman oscillator synchronously pumped with 5 W of average power from a mode-locked Nd: YAG laser. Four separate resonator mirrors were employed, one for each Stokes order. The configuration is shown in Fig. 50. The longer-wavelength pulses undergo less time delay, so the cavity lengths have to be staggered for the different Stokes orders in order to achieve proper time synchronization in the Raman oscillator. A cw tunable near IR SRS fiber source covering the spectral ranges 1.085-1.13pm(S1)and 1.15-1.175pm(S2) was reported by Linetal. (1977) (also see Stolen et al., l977,1978).The 650-m-long, low-loss fiber was pumped

LENS

6

SPECTROMETER A N D IR PHOSPHOR MULTIPLE-STOKES MIRRORS ON RAILS

FIG.50. Experimental optical fiber Raman oscillator using synchronous pumping from a cw mode-locked Nd:YAG laser and multiple resonator (Lin and French, 19791.

HIGH-POWER TUNABLE LASERS

79

by a 5-W cw Nd :YAG laser operating at 1.064 pm. It is possible that the tuning range can be increased and threshold power decreased by using birefringent fibers, which preserve polarization and thus increase Raman gain, and by using lower-loss fibers. This source is important for the determination of fiber losses, pulse spreading, and other characteristics at the important spectral region near 1.3 pm where optical propagation in most low-loss fibers is optimum.

VI. OTHERHIGH-POWER TUNABLE LASERS A . Blue-Green Lasers

The U.S. Navy has had a long-standing interest in high-power optical sources which can be used underwater for communications and imaging. The optimum wavelength region for transmission through seawater is in the blue-green at 490 f 30 nm. The Navy is sponsoring a satellite-to-submarine laser communication project (Laser Focus, 1980a). Two schemes are under consideration. One would use a ground-based laser and a geosynchronous satellite having larger mirrors which would reflect the energy to desired areas where submarines are located. The other scheme would have a satellite-borne laser which would be aimed at submerged submarines and would receive communications from the ground by microwaves. The first method would require a laser with a few MW average power, and the second would need about 1 kW. Several laser development programs are underway to develop the required laser transmitter. While fixed-frequency lasers in the blue-green such as frequency-doubled Nd: YAG are under consideration, much of the development is aimed at tunable systems. This section describes recent advances in a few tunable blue-green laser sources. 1. X e F and Xe,Cl Excimer Lasers Two excimer lasers, XeF and Xe,Cl, have recently become candidates for high-power tunable blue-green lasers. The C - t A transition in XeF has a broad spectral width of about 70 nm peaked at about 470 nm. The level structure of XeF was not clearly understood prior to 1979. Some experimental investigations by Kligler et al. (1978) and Brashears and Setser (1978) showed that the C(3/2) state, contrary to previous notions (see, for example, Dunning and Hay, 1978),is the lowest ionic excited state and should be a good upper laser level at high buffer gas pressures as a result of collisional quenching of the B state to the C state. Hill et al. (1979) experimentally determined, with an ion laser probe, that gain of about 8% could be obtained on this

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transition at 488.0 and 475.9 nm in mixtures containing 16 atm of Ar, 2-3 Torr of Xe, and 10 Torr of NF,. A few months later Bischel et al. (1979) reported laser action on this transition using photodissociation of XeF, with electron-beam pumped Xe, radiation at 172 nm. This produced a population inversion on the C(3/2) state of XeF and resultant laser action at 483 nm over a bandwidth of 12 nm with a pulse energy of about 0.5 mJ. The laser cell contained a mixture of XeF, (1-4 Torr), Ar (3 atm), and SF6 (0-20 Torr). Laser action was also observed on this transition by Burnham (1979) and Fisher et al. (1979a) using UV-preionized discharge excitation in He-Xe-NF, mixtures, and by Ernst and Tittel (1979) using short-pulse electron beam excitation. The output energy was limited in the latter work by low-gain values and insufficient time for stimulated emission to build up in the discharge. Later in the same year Fisher et af. (1979b) achieved a large improvement by two orders of magnitude in pulse energy from a UV-preionized discharge in a mixture of 3-atm He, 3-Torr Xe, and 2-Torr NF,. The improvement was the result of injecting dye laser radiation tuned to the C ---t A transition into the XeF laser. The injected dye laser pulse was typically 0.5-1 mJ which provided a signal much larger than the C +A spontaneous emission and thus shortened the time required to build the stimulated emission up to threshold. The experimental apparatus is shown in Fig. 5 1. The dye laser pulse was derived from a dye cell containing 7-diethylamino-4-trifluoro-

i ,

.

.Ad-

,*

350 nm XeF LASER PUMP

&

GAIN MEDIUM

I -

\

ENERGY METER

TUNABLE DYE LASER FILTER PHOTODIODE

FIG.51. Schematic diagram of multipass XeF laser cell with dye laser injection operating in the blue-green spectral region (Fisher et al., 1979b).

HIGH-POWER TUNABLE LASERS

81

methylcoumarin (2.5 x 10- Mdissolved inp-dioxane) or 7-diethylamino-4methylcoumarin (2.5 x Min ethanol) pumped by a XeF laser operating on the UV 350-nm (B+X) transition. The dye laser pulse was injected off-axis and made many passes through the 20-cm final XeF cell. These investigators achieved pulse energies greater than 4 mJ, tunable over the range 460-515 nm. Tuning was accomplished merely by tuning the wavelength of the injected dye laser signal. It is probable that a wideband tunable source based on the C +A transition in XeF can be scaled to considerably higher pulse energy (Bischel, 1980). Triatomic rare-gas halides have also been investigated recently as highpower tunable sources. Single-pass gain of about 6% was measured in electron-beam-excited Xe,Cl at the Ar ion laser probe wavelength of 514.5 nm by Tang et al. (1980). Tittel et al. (1980) observed laser action from Xe,Cl in electron-beam-pumped mixtures of Ar (4-9 atm), Xe (200 Torr), and CC14 (1 Torr). This laser had a peak power of about 2 kW near 5 18 nm and a spectral bandwidth of 30 nm. A potential energy diagram for Xe,Cl is shown in Fig. 52, and the laser transition is indicated. Certain problems presently stand in the way of developing the Xe2Cl blue-green laser into a high-power tunable source. They include the short buildup time available for stimulated emission (same problem as for XeF),

1

Xe

xe,+ + CI' Xe

t

t

8W

\

z W

R1-

FIG.52. Simplified potential energy diagram for the triatomic excimer Xe,CI (Tittel er al., 1980).

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visible absorption effects, presence of XeCl emissions, and lack of a suitable low-loss dispersion element for tuning the laser. After solutions to these problems are found, Xe,C1 could become a high-power source tunable across a 100-nm-wide spectral range from 450 to 550 nm.

2. Raman Shifting of UV Sources The subject of Raman conversion of UV sources has already been discussed in Section V. Komine and Stappaerts (1979) showed that energy conversion efficiencies greater than 30% can be achieved by second Stokes radiation at 503 nm generated by stimulated Raman scattering in a highpressure H2 cell when excited by third harmonic laser radiation at 355 nm from a Nd:YAG laser. This source is, of course, not tunable; however, the same technique could be employed by using UV excitation from an excimer laser such as XeF emitting at 351 nm and using H, or D2 as a Raman shifter. The blue-green spectral region can be reached with the proper choice of laser and Raman shifter, but a wideband tunable laser in the blue-green will not result in this situation, since XeF (B-+A) is tunable only over 2 nm. A wider tunable range would be obtained using UV dye (such as P-terphenyl) laser excitation, but the resultant average power would be less than that obtainable from a blue-green dye directly.

-

3 . Mercuric Halides ( H g X )

Mercury halide radicals form a class of visible line tunable lasers. Of these, HgBr exhibits laser action in the blue-green spectral region and has received intensive study recently. Laser emission was first attained on the B+ X band of HgBr over the spectral range 502-504.6 nm by Schimitschek et al. (1977) by photodissociation of HgBr, using UV photons from an ArF excimer laser. An output pulse energy of 0.25 mJ was obtained for a pump energy of 7 mJ. An energy level diagram is shown in Fig. 53. The same group, Schimitschek and Celto (1978a,b), also produced laser action from HgBr in a transverse electric discharge containing 800-Torr He and a few Torr HgBr,. Laser action was also achieved with HgCl and HgI. Other investigators have studied this system to try to understand the kinetic processes involved (see, for example, Eden and Waynant, 1979; Chang and Burnham, 1980; and Nighan, 1980). Using buffer gases of Ne and N 2 , Schimitschek and Celto (1980) obtained 90 mJ of energy output. At somewhat lower output energies the efficiency (laser energy out divided by electrical energy stored in capacitors) approached 1%. In the same paper the amplifier properties were measured

HIGH-POWER TUNABLE LASERS

83

FIG.53. Energy level diagram for HgBr, and HgBr showing the photodissociationofHgBr,; a, b, c, and d are continuous absorption bands. Absorption into b only leads predominatiy to band emission B2Z+--c X f Z + (Schimitschek er a/., 1977).

and the following values obtained : single-pass gain, 6.6% per cm; absorption coefficient, 0.35% per cm; and saturation flux, 200 kW/cm2. Recently Schimitschek (E. J. Schimitschek, private communication) has obtained average power of 3 W (30 mJ/pulse at 100 Hz). Thus far the tuning is only line tunable over 6 lines (about 2 nm); however, Schimitschek believes that the tuning range can be extended and output power increased by using injection locking with a dye laser.

B. Lyman-a Sources Tunable vacuum-UV sources in general have been mentioned elsewhere in this article. As was the situation for blue-green laser source development, a recent specific requirement developed for high-power tunable sources at the Lyman-a wavelength of 121.567 nm. This source is needed to monitor and study neutral hydrogen atoms produced in fusion plasmas by resonance fluorescence at the hydrogen Lyman-cr line (see, for example, Koopman et al., 1978). The Lyman-cr lines for deuterum (121.534 nm) and tritium (121.523 nm) are also of interest. Such a source would also be invaluable for general vacuum-UV spectroscopic work.

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Cotter (1979) developed a narrow bandwidth (4 x nm) tunable source for the range 120.3-123.6 nm with peak power of 5 W (10'' photons/ pulse) and a repetition rate of 20-50 Hz. The scheme as depicted in Fig. 54 utilizes transverse pumping of a 2-(4'+butylphenyl)-5-(4"-biphenyl)-1,3,4oxadiazole(buty1-PBD) dye laser oscillator-amplifier with UV pulses at 337.1 nm from a nitrogen laser or 248.5-nm pulses from a KrF laser. Up to 1 MW peak power (with the KrF laser pump) was obtained out of the dye laser assembly, which was tuned around the 364.7 nm region. The dye laser emission was then focused to a confocal spot diameter of less than 1 mm in a cell containing high-pressure Kr (4-5 atm). Krypton has a small negative value for the phase mismatch, Ak = 6 ~ ( n 3- nl)/Al, where A1 is the dye laser wavelength, 364.7 nm, and n3 and n, are the indices of refraction at the frequency-tripled and fundamental wavelengths, respectively. This quantity must be negative in order that efficient third harmonic generation can occur (Ward and New, 1969; and Bjorklund, 1975). The energy conversion effiwhich was not very large, but sufficient photons were ciency was 5 x produced and the beam quality (about two times the diffraction limit) and spectral purity were good enough to carry out the desired experiments. This scheme has the advantageous characteristics of simplicity and reliability. McKee et al. (1978) had reported earlier a tunable source between 121.0 and 129.0 nm obtained by four-wave sum mixing in Mg vapor using two KrF-pumped dye lasers, one operating at 380.3 nm and the other at 340.0 nm. The sum frequency coincides with the first odd-parity autoionizing state in Mg. Conversion efficiency was about the same as for the scheme described by Cotter, but two dye lasers were required. It has been known for some time that the Ar, excimer laser has a moderately broad fluorescence of about 10 nm (Bradley et al., 1978) which overlaps

-

UKrF EXCIMER LASER OR Ng LASER

SOLAR.BLIND PMT

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-u

I

u

I

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I

VACUUM MONOCHROMATOR

U

NARROW BAND DYE LASER 10 rnA (0.1 cm-1)

TRlPLiNG CELL

1MW,7ns (KrF PUMP) 100 kW,35ns (Np PUMP)

FIG.54. Schematicdiagram of apparatusfor obtaining tunable radiation near the Lyman-a wavelength using third harmonic generation of -365-nm radiation in Kr gas (Cotter, 1979).

HIGH-POWER TUNABLE LASERS

85

the Lyman-a region. The Ar, laser was only recently tuned with a diffraction grating by Wrobel et al. (1980a,b) over the range 123.2-127.4 nm in an electron-beam-pumped gas cell containing Ar at high density (25-65 bars). The output power (untuned) was 1 kW when 50 J of electrical energy was deposited in 20 nsec in 5 cm3 of Ar.Output power and tuning range were limited by grating damage. It is expected by the authors that highest powers will be obtained and that the tuning range will reach the Lyman-a wavelength. The Lyman-fl transition in H could be used for the same purpose as the Lyman-a transition. Recently Reintzes (1980) has obtained tunable radiation near that transition at 102.57nm by third harmonic conversion of the output of a XeCl laser. C . Metal-Doped Solid State Lasers

Three important developments have taken place in high-power tunable metal-doped crystal lasers within the last two years. They include transition metal ions such as Ni2+,MnZ+,Co2+,and V2+ in hosts of MgF, and MgO, tunable in the 1-2 pm wavelength range; the rare-earth-doped laser Ce3+: YLF tunable near 325 nm; and an alexandrite (Cr3+:BeA1,OJ laser broadly tunable over a range greater than the 700-800 nm region. All three of these tunable lasers are potentially scalable to significant pulse energies as well as peak and average power levels. Therefore each is discussed in some detail in the following subsections.

1. Alexandrite Laser Very impressive results have been reported recently with a solid state laser based on alexandrite. Laser action had been reported on this material as early as 1974 by Morris and Cline at room temperature and by Bukin et al. (1978) at 77 K (on the R-line). Tunable operation was achieved in 1978 by a group at Allied Chemical Corp. (Walling et al., 1978). Further work resulted in tunable flashlamp-pumped operation over the range 701-794 nm Walling et al. (1979), and cw operation over the spectral range 744-788 nm with a maximum power of 6.5 W was reported by Walling et al. (1980b). Q-switched operation at 0.6 J/pulse operating on the R , , narrowband transition at 680.4 nm was described by Walling and Peterson (1980). The same group, Walling et al. (1980a), later reported efficient xenon flashlamppumped operation of alexandrite continuously tunable over the range 701-818 nm. Contrary to what is found with most doped crystal lasers, this laser not only works well at room temperature but its performance actually improves with increasing temperature. The stimulated emission cross section increased from 7 x lo-,' cm2 at 300 K to 2 x lo-,' cm2 at 475 K. Output

86

V. N. SMILEY

energies of 5 J per pulse and 35 W average power were obtained for long-pulse operation limited only by the available power supply, and 0.5 J in Q-switched operation with pulse lengths between 33 and 200 nsec. The energy level scheme in alexandrite is similar to that in ruby with sharp 'A+ 'E R lines and broad 'T and 4T absorption bands as shown in Fig. 55a. As in ruby the narrowband R, line at 680.4 nm demonstrates high optical

4T, (Vibrational Band)

'Ti

4T2

(Vibrational Band)

ZT>

I-

(LASING TRANSITION)

GROUND LEVEL (4A 2

MULTIPLET)

(b) FIG.55. (a) Energy level scheme for alexandrite. (b) Energy levels showing vibrationally excited ground levels, upper laser levels ('T,), and lasing transition (Walling el a/., 1980a).

HIGH-POWER TUNABLE LASERS

87

gain, and three-level laser action occurs. Unlike the situation with ruby, however, laser action can also take place on the broad emission involving the vibronic 4T2level, as broad upper level, and a lower vibrationally excited ground level as shown in Fig. 55b. This results in a four-level, broadly tunable laser having a low threshold. The low threshold is a result of the vibronic bands combined with efficient pump bands centered at 420 and 590 nm. The spectroscopic aspects of this laser material are discussed in great detail in a paper by Walling ef al. (1980a). The alexandrite laser is unique in several respects and offers a very useful tool to spectroscopy, remote sensing, and other applications in the 700-800 nm spectral region as well as a high-power fixed-frequency source in the visible red. The fact that it operates efficiently at room temperature in cw or pulsed modes greatly increases its practicality. The potential exists for increased pulse energy and average power. 2. Transition-Metal-Doped Lasers This class of lasers incorporating divalent transition metal ions in MgF, and MgO was discovered many years ago by Johnson et al. (1963, 1964, 1966). Development was not pursued because of the requirement for lowtemperature operation. Recent studies indicate that these metal ions may have energy storage density of 20-30 J/cm3, which is greater than in CO, lasers (Laser Focus, 1979), and therefore may be good candidates for scaling to fusion energies. Moulton et al. (1978) at Lincoln Laboratory produced cw operation in a fixed cavity Ni2+: MgF, laser by pumping the crystal with 1.32-pm radiation from a Nd:YAG laser. This laser was temperature tunable near 1.7 pm with somewhat limited tuning range. The same group, Moulton and Mooradian (1979a), later used an external cavity and attained cw and Q-switched operation on Ni2+:MgF, over the range 1.61-1.74 pm and cw operation of Co2+: MgF, , over the range 1.63-2.08 pm. A Brewster-angle crystal 1.2-cm long was mounted in a Dewar and cooled to 80 K. External tuning was used. The experimental arrangement is shown in Fig. 56. Average power output was 100 mW (untuned) and was free of spiking. The power reduced to 20 mW for frequency-narrowed operation. In @switched mode, the laser produced a peak power of 140 W at 100 Hz with pulses 490-nsec long. Those results are preliminary. Calculations by Moulton and Mooradian (1979b) show that the laser can be scaled to produce 100 W average power and overall efficiency of 10%. Also Q-switched pulses of 100 kW to 1 MW should be attainable (Moulton and Mooradian, 1979a). Further results were discussed at IQEC-1980 by Moulton and Mooradian.

88

V. N. SMILEY

\

I-.

I

\ ' \

I

DEWAR

L n

50 crn

8

QUARTZ BIREFRINGENT TUNINGELEMENT

2

MIRROR OUTPUT

FIG.56. Schematic of experimental arrangement for Ni2+:MgF, and CoZf :MgF, lasers. A three-mirror cavity is used (Moulton and Mooradian, 1979a).

The N i 2 + : M g 0 laser system has been analyzed recently by Iverson et al. (1980) from the standpoint of its potential for efficient room temperature operation as suggested by Moulton and Mooradian (1979b). The measurements of Iverson et al. (1980) showed that the lifetime of the 3T2g-+3Azg laser transition is not highly temperature dependent until the temperature goes above room temperature. The same work also suggested that Co2+: MgO should also be a good room temperature laser and that its large spinorbit split ground state should result in a broader tuning range. 3. Rare-Earth-Doped Lasers Another recent development at Lincoln Laboratory is the rare-earthdoped solid state laser, Ce3+:YLF operating in the UV near 325 nm (Ehrlich et al., 1979). The laser emission occurs on the 5d-t4f transition in Ce3+. This is the first reported laser emission on a 4f"-' 5d-t4f" transition in a trivalent rare earth. Previous rare-earth lasers have utilized transitions between 4f" levels which produce narrowband fluorescence and have long lifetimes. The 4f"-' 5d-+4f" transitions have broad fluorescence and short lifetimes. Figure 57 shows the laser levels involved and the absorption and fluorescence spectra. The energy level structure is not very complicated, since Ce3+ has only one 4f electron. This material is a particularly good candidate for a tunable laser, since the 5d excited state wave function has a large spatial extent and therefore interacts with the host crystal field so as to produce splitting into four levels and broadening as shown in Fig. 57. The and 'F,/, by spin-orbit coupling. The 4f state is split into two states 2F5/2 four peaks in the UV absorption correspond to the four 5d levels (tentative assignment), and the double-peaked fluorescence arises from emission to the split ground level out of the lowest-lying 5d state.

89

HIGH-POWER TUNABLE LASERS

25

f

3 t

200 f

3

FLUORESCENCE

W W

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m

Q

m

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I I

n

t

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I

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I

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FIG.57. Absorption and fluorescence (dashed curve) for Ce: YLF. Absorption measurement was for unpolarized light propagating parallel to the c axis of a 275-pm-thick crystal plate with 1% doping. No correction was added for surface reflections. Fluorescence is not corrected for self-absorption near 300 nm; therefore actual emission may be larger near there than indicated. Energy level diagram is shown in inset (Ehrlich et at., 1979).

Gain > 2 at 325 nm was observed when the crystal was pumped with a KrF laser and optically probed with a HeCd laser beam. The gain saturated at a fluence value of about 1 J/cmZ.Laser output of 1 pJ was also observed at 325.5 nm for a pump input energy of 300 pJ. Results with this laser are only preliminary at this stage. Problems that are being investigated include the possible generation of transient color centers, thermal effects in the crystal, possible low quantum efficiency of fluorescence, and excited state absorption. The authors estimate that the tunable range could cover 305-335 nm and that high power is potentially obtainable by using a high-energy KrF pump laser with large (perhaps up to 10-cm diameter) YLF crystals. In addition, flashlamp excitation appears feasible using lamps designed for dye laser pumping. Further improvements in attempts to reach high power with this laser were discussed by Ehrlich et al. (1980) at the IQEC-80. REFERENCES Abakumov, G. A., Simonov, A. P.,Fadeev, V. V., Kharitonov, L. A., and Khokhlov, R. V. (1969a). J E W Lett. 9,9. Abakumov, G. A., Simonov, A. P., Fadeev, V. V., Kharitonov, L. A., and Khokhlov, R. V. (1969b). Opto-Electronics 1,205. Abakumov, G . A., Buzgenda, Kh., Dorsenvil', R., Medvedeva, A. M., Sebekina, N. N., Simonov, A. P., and Fadeev, V. V. (1975). Sou. J . Quantum Electron 4, 1404. Adrain, R. S., Arthurs, E. G., Bradley, D. J., Roddie, A. G., and Taylor, J. R. (1974). Opt. Commun. 12, 140. Aegerter, M. A., and Liity, F. (1971). Phys. Status Solidi43,244.

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Akhmanov, S. A., Zhdanov, B. V., Kovrigin, A. I., Kuznetsov, V. I., Pershin, S. M., and Kholodnykh, A. I., (1977). Sov. J. Quantum Electron. 7 , 1271. Allain, J. Y. (1979). Appl. Opt. 18,287. Angelov, D. A., Gurzadyan, G. G., and Nikogosyan, D. N. (1979). Sou. J. Quantum Electron. 9, 1334. Arthurs, E. G., Bradley, D. J., and Roddie, A. G. (1971). AppI. Phys. Lett. 19,480. Arthurs, E. G., Bradley, D. J., and Roddie, A. G. (1972). Appl. Phys. Lett. 20, 125. Anonymous (1979). Laser Focus 15,24. Anonymous (1980a). Laser Focus 16, 14. Anonymous (1980b). Laser Focus 16,24. Anonymous (1980~).Laser Focus 16,32. Baltakov, F. N., Barikhin, B. A., and Sukhanov, L. V. (1974). JETP Lett. 19, 174. Bass, M., and Deutsch, T. F. (1967). Appl. Phys. Lett. 11,89. Baumgartner, R. A., and Byer, R. L. (1978a). Int. Quantum Electron. Conf, loth Digest, p. 688. Baumgartner, R. A., and Byer, R. L. (1978b). Appl. Opt. 17,3555. Baumgartner, R. H., and Byer, R. L. (1979). IEEE J. Quantum Electron. QJi-15, 432. Belanger, P. A., and Boivin, J. (1974). Phys. Can. 30,47. Bierry, M., Frey, R., and Pradtre, F. (1977). Rev. Sci. Instrum. 48, 733. Bigio, I. J. (1978). “High Power Lasers and Applications” (K. L. Kompa and H. Walther, eds.). Springer-Verlag, Berlin and New York. Bischel, W. K. (1980). Laser Focus 15, 16. Bischel, W. K., Nakano, H. H., Eckstrom, D. J., Hill, R. M., Huestis, D. L., and Lorents, D. C. (1979). Appl. Phys. Lett. 34,565. Bjorkholm, J. E., Ashkin, A., and Smith, R. G. (1970). IEEE J. Quantum Electron. QE-6,797. Bjorklund, G. C. (1975). IEEE J. Quantum Electron. QE-11, 287. Blit, S., and Tang, C. L. (1980). Appl. Phys. Lett. 36, 16. Blit, S.,Ganiel, U.,and Treves, D. (1977a). Appl. Phys. 12, 69. Blit, S.,Weaver, E. G., Dunning, F. B., and Tittel, F. K. (1977b). Opt. Lett. 1,58. Bloembergen, N. (1965). “Nonlinear Optics.” Wiley, New York. Bloom, D. M., Mollenauer, L. F., Lin, C. L., Taylor, D. W., and DelGaudio, A. M. (1979). Opt. Lett. 4, 297. Borisevich, N. A. (1975). Spectrosc. Lett. 8,607. Bourkoff, E., Dienes, A., and Whinnery, J. R. (1979). Appl. Phys. Lett. 34,455. Bradley, D. J. (1974). Opto-Electronics 6, 25. Bradley, D. J., and Ryan, J. P. (1978). Digest of Technical Papers, Int. Quantum Electron. Conf., 10th Digest, p. 664. Bradley. D. J., Hutchinson, M. H. R., and Ling, C. C. (1978). Int. Quantum Electron. Cons., 10th Digest, p. 702. Bradley, D. J., Nicholas, J. V., and Shaw, J. R. D. (1971). Appl. Phys. Lett. 19, 172. Brashears, H. C., and Setser, D. W. (1978). Appl. Phys. Lett. 33,821. Browell, E. V., Wilkerson, T. D., and McIlrath, T. J. (1979). Appl. Opt. 18,3474. Bukin, G. V., Volkov, S. Yu., Matrosov, V. N., Sevast’yanov, B. K., and Timoshechkin, M. I. (1978). Sou. J. Quantum Electron. 8, 671. Bunkenburg, J. (1972). Rev. Sci. Instrum. 43, 1611. Burlamacchi, P., and Cotter, D. (1977). Opt. Commun. 22,283. Burlamacchi, P.,Pratesi, R., and Salimbeni, R. (1974). Opt. Commun. 11, 109. Burlamacchi, P., Pratesi, R., and Ronchi, L. (1975). Appl. Opt. 14,79. Burlamacchi, P., Pratesi, R., and Vanni, U. (1976). Appl. Opt. 15,2684. Burnham, R. (1979). Appl. Phys. Lett. 35,48. Burnham, R., and Djeu, N. (1978). Opt. Lett. 3,215.

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Byer, R. L. (1975). In “Quantum Electronics: A Treatise” (H. Rabin and C. L. Tang, eds.), Vol. 1, Pt. B, p. 587. Academic Press, New York. Byer, R. L. (1976). In “Tunable Lasers and Applications” (A. Mooradian, T. Jaeger, and P. Stokseth, eds.), p. 71. Springer-Verlag. Berlin and New York. Byer, R. L., and Herbst, R. L. (1978). Laser Focus 14,48. Carboni, G., and Dibene, A. (1971). k t i . Nuouo Cimento 1,979. Carney, E. R., Fahey, D. W., and Schearer, L. D. (1980). IEEE J. Quantum Electron. QE16,9. Chan, C. K. (1978). Spectra-Phys. Laser Tech. Bull., No. 8. Chan, C. K., and Sari, S. 0. (1974). Appl. Phys. Lett. 25,403. Chandra, A., and Holcomb, D. F. (1969). J. Chem. Phys. 51, 1509. Chang, R. S. F., and Burnham, R.(1980). Appl. Phys. Lett. 36,397. Christensen, C. P., Braveman, L. W., Steier, W. H., and Wittig, C. (1976). Appl. Phys. Lett. 29,424. Corkum, P. B. (1979). Laser Focus 15,80. Cotter, D. (1979). Opt. Commun. 31, 397. Cox, A. J., Scott, G. W., and Talley, L. D. (1977). Appl. Phys. Lett. 31,389. DeMaria, A. J., Stetser, D. A,, and Heynau, H. (1966). Appl. Phys. Lett. 8,22. Derkacheva, L. D., Krymova, A. I., Malyshev, V. I., and Markin, A. S . (1968). JETP Lett. 7 , 362. Derkacheva, L. D., Krymova, A. I., Malyshev, V. I., and Markin, A. S. (1969). Opt. Spectrosc. 26,572. Dewey, C. F., Jr., and Hocker, L. 0. (1971). Appl. Phys. Lett. 18,58. Diels, J.-C. (1979). h e r Focus 15, 9. Diels, J.-C., and Sallaba, H. (1980). I R ~ Quantum. . Electron. ConJ, 11th Digest, p. 629. Diels, J.-C., Van Stryland, E., and Benedict, G. (1978). Int. Quantum Electron. ConJ, 10th Digest, p. 666. Dimitriev, V. G., and Itskhoki, I. Ya. (1975). Sou. 1. Quantum Electron. 5, 735. Dimitriev, V. G., Kornienko, N. E., Ryzhkov, A. I., Shizheviskii, V. L., and Shalaev, E. A. (1976). Sou. J. Quantum Electron. 6,209. Djeu, N. (1978). In “High Power Lasers and Applications” (K. L. Kompa and H. Walther, eds.). Springer-Verlag. Berlin and New York. Djeu, N., and Burnham, R. (1977). Appl. Phys. Lett. 30,473. Dudina, N. S., Kopylov, S. M., Mikhailov, L. K., and Cherednichenko, 0. B. (1979). Sou. J. Quantum Electron. 9, 1468. Dunn, M. H., and Ferguson, A. I. (1977). Opt. Commun. 20,214. Dunning, F. B., Stokes, E. D., and Stebbings, R. F. (1972). Opt. Commun. 6, 63. Dunning, T. H., Jr., and Hay, P. J. (1978). J . Chem. Phys. 69, 134. Dyadyusha, G. G., Il’chishin, Slominskii, Yu. L., Tikhonov, E. A., Tdomachev, A. I., and Shpak, M. T. (1976). Sou. J. Quantum Electron. 6, 349. Economou, N. P., Freeman, R. R., Heritage, J. P., and Liao, P. F. (1980). Appl. Phys. Lett. 36,21. Eden, J. G., and Waynant, R. W. (1979). Appl. Phys. Lett. 34,324. Ehrlich, D. J., Moulton, P. F., and Osgood, P. M., Jr. (1979). Opt. Lett. 4, 184. Ehrlich, D. J., Moulton, P. F., and Osgood, R. M., Jr. (1980). Digest of Technical Papers, Int. Quantum Electron. ConJ 11th Digest, p. 635. Erickson, L. E., and Szabo, A. (1971). Appl. Phys. Lett. IS, 433. Emst, W. E., and Tittel, F. K. (1979). Appl. Phys. Lett. 35, 36. Fan, B., and Gustafson, T. K. (1976). Appl. Phys. Lett. 28,202. Ferguson, A. I., and Dunn, M. H. (1977a). Opt. Commun. 23, 177. Ferguson, A. I., and Dunn, M. H. (1977b). IEEE J. Quantum Electron. QE13,751.

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ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS. VOLUME 56

Radioastronomy at Millimeter Wavelengths EMILE-JACQUES BLUM I Insritut de Radio Astronomie Millimetrique ( I R A M ) Grenoble, France

I. 11. The Development of A. The Early Period

111.

A. Interstellar Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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VI. A. B. C. D.

. . . . . . . . . . . . 124 ............................ 130 ............................ 133 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometry and Optics of Parabolic Dishes . . . . . Design and Construction of Dishes. . . . . . . . . . . . . . . . . . Adjustment of the Dish Surface .................................... 138 Overall Error Budget. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mount and Pointing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

E. F. G. Weather Protection . . . . . . . . . . . . . . . . . . . . . . . . .................................................... H. Summary ........... VII. Receivers ............................ A. Introduction ...................... B. Bolometer ................................................. C. Mixer.. ............................. D. Local Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Receiver Back Ends for Spectroscopy ........................ VIII. Evolution and Projects . . . . . . . . . . . . . . . A. Introduction ..................................... B. Receivers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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C. Improvement or Extension of Existing Radiotelescopes . . . . . . . . . . . . . . . . . . . D. Construction of New Millimeter Single Dish Radiotelescopes . . . . . . . . . . . . . . E. Construction of New Millimeter Interferometers . . . . . . . . . . . . . . . . . . . . . . . . . F. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I54 154 158 158 159

I. INTRODUCTION Remote sensing of the universe by light waves has been the fundamental method of astronomy until very recent times. More generally the electromagnetic spectrum is the privileged channel through which information comes from the sky. The existence of electromagnetic waves besides those in the optical spectrum was recognized more than a century ago, but it was only in 1931 that the first successful observation was reported in radioastronomy. A similar time lag occurred between the first experiments and the astronomical observations in other domains of the electromagnetic spectrum (the infrared, X rays, and y rays). The phenomenon is particularly clear for astronomy at millimeter wavelengths. We will see that the rate of technical progress is the main factor for this delay. Scientific knowledge, on the contrary, was suggesting since long ago that astronomical observations in several new ranges of wavelengths would afford new insight on the physical processes at the origin of several radiations. For instance, the thermal origin of the 2.7 K cosmic background was only assumed until its peak of brightness at the edge of the submillimeter waves was measured. Recognition of a flat spectrum linearly polarized is an indication of the synchrotron process. Some celestial objects have strange spectral behavior. For example pulsars radiate mostly at meter wavelengths; they are generally not detectable in the microwave range, and are weak but sometimes present in the optical and X-ray domains. Some celestial objects emit most of their energy in X rays and 1' rays. In general, maps of the sky at different wavelengths are surprisingly different. These differences are enhanced by the presence of line emission or absorption at specific wavelengths. Modern astronomy requires observations of a given object or region in the widest possible spectrum, because this affords clues to fundamental physics. The present observed spectrum extends from hectometer radio waves to y rays; the ratio between these extreme wavelengths is about lo2'. Millimeter waves cover 5% of this range; and one could imagine a proportional value of importance for millimeter radioastronomy. This naive argument is incorrect for several reasons. First, many simple molecules abundant in the universe have rotation lines radiating at millimeter wavelengths. Second, in

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99

the millimeter range, the transparency of the interstellar medium is good, the galactic background radiation is low, and the receiving bandwidths can be wide. It follows that sensitivity to low-temperature objects can in principle be made high in this range. Aside from these facts, millimeter radioastronomy is favored for practical reasons : Observations are generally possible from the ground, and high resolving power may be obtained with instruments having relatively small physical dimensions. Overall, astronomy on millimeter wavelengths has been in the last 10 years one of the most active and productive fields in astronomy, and its results have generated much interest among physicists and chemists. We can expect this situation to continue: Larger observing instruments will be in operation in a few years, and receivers with even greater sensitivity will be available soon. Penzias and Burrus (1973) have given a review of the techniques of astronomy on millimeter wavelengths. Some duplication with the present review is inevitable, but we have tried to put special emphasis on the difference between millimeter radioastronomy and radioastronomy at longer wavelengths, and we have included the recent progress and projects. With regard to radioastronomy in general, we have omitted many developments. The reader is referred to several books such as “Radiotelescopes” (Christiansen and Hogbom, 1969) on the theory of instrument and observation, and Vol. 12, Parts B and C, of “Methods of Experimental Physics” (Meeks, 1976) for a detailed discussion of radiotelescopes, observing methods, atmospheric effects, and computer use. Millimeter radioastronomy is a radio technique that uses coherent detectors, as does conventional radioastronomy. The literature on astronomy at submillimeter and shorter wavelengths where incoherent detection techniques are mostly used is then somewhat less relevant. However, millimeter radioastronomy has some aspects related to astronomy at shorter wavelengths, like the increasing influence of the atmosphere, or the use of quasioptical techniques in the receiver front ends. Millimeter radioastronomy is on the borderline of technical fields. 11. THEDEVELOPMENT OF MILLIMETER RADIOASTRONOMY

A . The Earljv Period

The first reported astronomical observation in the millimeter range was made in 1947 (Hagen, 1951).The solar emission was detected at a wavelength of 8.5 mm with a radiotelescope on the roof of the Naval Research Laboratory at Washington, D.C. This program was followed by measurements of

100

EMILE-JACQUES BLUM

the Sun during eclipses (Coates et al., 1958) and by measurements of the Moon (Gibson, 1961). The wavelength of 4.3 mm was used in 1956 in the same laboratory for solar and atmospheric observations, and later (Grant et al., 1963) to measure the temperature of Venus. The antenna was a parabolic dish, 3 m in diameter, with a surface accuracy of about 0.1 mm. Several larger millimeter waves dishes were completed around 1960. The biggest with a 22-m diameter was erected in the USSR, near Moscow; an improved version, usable down to 4-mm wavelength was built in Crimea. Two smaller dishes were good enough to reach shorter wavelengths. At the Aerospace Corporation a 4.6-m dish was completed in 1963, and used at I = 3 mm. The most advanced dish of the early 1960s was built at the University of Texas, Austin, and completed in 1963. The present observing site, at the MacDonald Observatory is at an altitude of 2000 m. The design incorporated the alloy invar, because of its low thermal expansion coefficient. The dish is protected by an astrodome (see Section V1,G). It still has a reasonable efficiency at a wavelength of 2 mm and is used down to 1.2 mm. The remarkable characteristics of this dish were attained at a time when the millimeter receiver were still in its infancy. Furthermore, during this period all observations were made in the continuum, and no search for line emission was attempted. Until 1970 the astrophysical results obtained from these few millimeter radiotelescopes were limited mostly to solar and planetary brightness. A review of the radiotelescopes of this early period is given by Cogdell et al. (1970). The review includes the 1 1-m dish built by the National Radioastronomy Observatory and erected at the Kitt Peak Observatory in Arizona (Plate l), under an astrodome. The discovery of the CO and CN molecules at 115 and 113.5 GHz with this dish and an improved receiver (Wilson et al., 1970; Jefferts et af., 1970) is the landmark of the beginning of millimeter radioastronomy as an important branch of astronomy. A review of the discovery of molecular lines at that time has been published (Rank et al., 1971). It is now clear that in the early 1960s several radiotelescopes were capable of discovering the lines of some molecules at millimeter wavelengths. The existence of such lines in the universe was suspected by physicists even earlier (see for instance Townes, 1957), and some lines were discovered at lower frequency in 1968-1969, in particular NH, and H,O lines, around 23.7 and 22.235 GHz. It is probably the development of improved receivers that triggered and eased the astronomical search for millimeter lines. A new generation of mixers, which used gallium arsenide Schottky barrier diodes, appeared (Young and Irvin, 1965; Lee and Burrus, 1968). This technique, like other improvements (McColl et al., 1967), allowed a considerable increase in reliability. Compared to previous receivers the actual sensitivity was better by almost one order of magnitude. The system noise around

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

101

PLATE1. The 11-rn ( 3 6 ) radiotelescope of the National Radio Astronomy Observatory at Kitt Peak, Arizona.

102

EMILE-JACQUES BLUM

I

= 3 mm used to be in the range 10,000-20,000 K. It decreased to about 2000 K in the early 1970s.

B. The1970s Some dishes of the previous period, equipped with new receivers, were used heavily during the 1970s, in particular the 4.8-m dish in Texas and the NRAO 1l-m dish, which has been responsible for the discovery of most new lines, up to about 200 GHz. The observation of many isotopic lines, like l 2 C 0 and ' T O , has given an additional impulse to the astrophysical interest: The ratio of intensity of isotopic lines from an object gives unique information on its physical and chemical evolution. About 50 molecules are now known by their lines in the millimeter range, and many more lines are observed because the same molecule can radiate by several transitions. Lovas el al. (1979) have listed all these lines. Very remote objects such as external galaxies have been observed through their CO lines. Several new instruments were completed from 1970 to 1979. An industrial design from ESSCO takes advantage of a closed radome to use a light dish structure. This design has been reproduced in Brazil (Universitad Mackenzie), Finland (Helsinski University), the United States (University of Massachusetts), and Spain (Madrid Observatory). The diameter of the dish is 13.7 m. A similar but larger model is now in operation in Sweden (Onsala, Chalmers University). Its diameter is 20 m with an rms surface accuracy of 0.2 mm (Menzel, 1976). A number of smaller dishes have been erected, for example, a 4-m in Australia and a 4.6-m in Canada. Two instruments have been designed with another geometry. At the Bell Laboratories an offset focus (Chu et al., 1978)solves the problem of blocking in front of the main reflector, which is 7 m in diameter (Plate 2). This results in low-level side lobes and gives room for a large receiver cabin. The dish surface accuracy is 0.1 mm rms. An original design, based on a ring of orientable panels is not yet fully completed in the USSR. The instrument, called RATAN is a ring, 600 m in diameter, made of panels, 7 m high. These panels are set to focus the radiation coming from some angle to a horn at ground level. The surface of the RATAN is comparable to that of a 35-m conventional dish. However, the resolving power defined by the diameter of the ring is very high. Several modes of operation are planned, and the minimum expected wavelength is 4 mm (Pulkovo Izvestia, 1972). The standard method to reach high resolving power in radioastronomy has also been introduced in the millimeter range. Two radio interferometers with relatively small dishes are operated at a wavelength of 8 mm. At the Bordeaux Observatory (France), two 2.5-m dishes are located 65 m apart. Their apparent distance varies when they track an object in the sky. This

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

103

PLATE2. The 7-m offset parabolic radiotelescope of the Bell Laboratory at Holmdel (Crawford Hill), New Jersey.

TABLE I

SINGLEDISHFS National Radio Astronomy Observatory

University of Texas

Organization

INPE/Univ. Mackenzie, Brazil

Chalmers University, Sweden

Bell Telephone Laboratories

Five College Radio AstronoObserv.”

California Institute of Technology

1972 13.7 Radome

1977 7 None 0.1

1979 13.7 Radome 0.2

1979 10.4 None 0.05

First operation Diameter (m)* Weather protection Surface accuracy (mm ms) Pointing accuracyd (arc sec) Focal arrangement F/D (prime focus) Aperture e5ciency’

1963 4.87 Astrodome 0.1

1967 11.0 Astrodome 0.14

-

1976 20 Radome 0.2

3

2

3-5

3-5

3

6

6

P.F. 0.5 29 at 345 GHz

Cass. and P.F. 0.8 39 at 100 GHz

Cass. 0.37 40 at 22 GHz

CaSS.

Cass. and N 0.4 60 at 99 GHz

Cass. 0.3 31 at 110 GHz

Usual operating range (GHz) Usual receiver type

70-345

30-230

22-43

0.45 38 at 87 GHz 20- 120

30-230

20- 150

Cass. and N 0.4 50 at 230 GHZ 70-300

Mixer

C. mixer

Mixer, maser

C. mixer,

C. mixer

C. mixer

Mixer, InSb

Corresponding systern temp. (K)

4OOO at 230 GHz

300at 100 GHZ

I50 at 22 GHz

Type of back end

Filter

Filter

Filter

Name of Site

McDonald Observatory

Kitt Peak Natl. Observatory,

Altitude (m) Latitude References

2000 31"N Cogdell er al. (1970)

1900 32"N Cogdell er al. (1970)

maser 350 at 80 GHz

310 at 81 GHz

450at 115 GHz

Filter and S.E. Crawford Hill, NJ

Filter and Corr.

Itapetinga

Filter and Corr. Onsala

800 23"s Kaufmann et al. (1978)

S.L. 57"N Menzel (1976)

S.L. 40"N Chu er al. (1978)

300 42"N Arny and Valeriani (1977)

New Salem, MA

Az

-

8

mixer 1500at 115 GHz 200 at 230 GHz AOS and Corr. Owens Valley, CA 1300 37"N Wannier et af. (1979)

Two radiotelescopes similar to the 13.7-m Five College Observatory are in operation. One is in Spain (Yebes), the other in Finland (Helsinki). All single-dish radiotelescopes listed are classical parabolic, with the exception of the Bell Laboratory dish, which is an offset parabolic. The distribution of the errors on the surface of the dish is not Gaussian. An rms accuracy has no meaning. The figures given for pointing accuracy should be taken with caution. They are based on nonhomogeneous criterion. Aperture efficiency includes the loss due to the radome when applicable. Abbreviations used: P.F., prime focus; Cass., Cassegrain focus; N, Nasmyth focus; C. mixer, cooled mixer; Corr., correlator spectrograph; S.E., spectral expander; AOS, acoustico-optical spectrograph; S.L., sea level. a

106

EMILE-JACQUES BLUM

gives some information on the brightness distribution of the object, but does not allow a full synthesis (Delannoy et al., 1973). The Jet Propulsion Laboratory operates an interferometer with three dishes at Table Mountain, California (Janssen et al., 1979).The Bordeaux and Table Mountain instruments are used mostly for solar and planetary observations. The interferometer at Hat Creek (University of California, Berkeley) has two 6-m dishes, which can be moved on a number of stations along a T-shaped baseline, 300 m EW x 200 m NS long. This allows observations by aperture synthesis. The interferometer is equipped with a spectroscopic back end. It was first used around 22 GHz, in particular for water line observations (Welch et al., 1977). The frequency is now shifted up to 90 GHz. Much effort has been made to improve the sensitivity of the receivers. The sensitivity of the mixers has again been increased by a large factor. This increase has been obtained by better control of diode construction, improved theoretical understanding of mixer models, and refrigeration down to 2: 15 K of the receiver front end. At a wavelength of 3 mm, the system temperature has decreased during the 1970s from ~ 2 0 0 0to ~ 4 0 K 0 single side band (SSB). Finally, the need for wide-band spectrographs for line observation of distant or large objects has resulted in the development of specialized back ends. Some of them use conventional circuitry-filters and digital correlators-specially designed for wide band. Other devices, such as the acoustico-optical spectrographs and the spectrum expander, have been recently introduced. This active period has also been rich in new projects, stimulated by the number and value of the astrophysical results. Some of these projects have been approved and are described later. They are expected to be in operation in the mid-1980s. They include dish diameters up to 45 m, surface accuracies allowing operation u p to the submillimeter range, observing sites at high altitude to take full advantage of the receivers’ sensitivity, and longer baselines for interferometry. These are expensive projects comparable in cost to large optical telescopes, and are planned to answer the needs of the astronomical community at large. C . Present Facilities of Millimeter Radioastronomy

The following sections discuss in some detail the principle, guidelines, and the various elements of the observing systems of millimeter radioastronomy. The present section summarizes in Tables I and I1 the characteristics of the most representative instruments in operation today. Singledish radiotelescopes with diameter under 4.5 m are omitted, as are inter-

107

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

TABLE I1 INTERFEROMETERS

Organization First operation

0bservatoire de Bordeaux, Jet Propulsion France Laboratory

1973

1976

Antenna diameter (m) 2.5 + 2.5 Frequency used (GHz) 35 Baseline 64 m EW

5.5 + 3. 35 60 m EW

Position of antennas

Fixed

Fixed

Back end Name of site

Continuum Obs. Bordeaux S.L. 44"N Delannoy et al. (1973)

Continuum Table Mountain, CA 2300 34"N Janssen et al. (1979)

Altitude (m) Lati tude References

University of California, Berkeley

1979 (1975at 22 GHz) 6+6 22 and 88 T-shaped 300 m EW 200 m NS Movable on 30 stations Filter Hat Creek, CA I300 41"N Welch et a/. (1977)

California Institute of Technology"

1980 10.4 + 10.4 1 IS 50 m EW Movable Owens Valley, CA 1300 37"N -

The California Institute of Technology instrument is under test (August, 1980). One of its dishes is used as a single dish (see Table I). The baseline will be. extended (see Section VIII).

ferometers with very small antennas. We also have omitted some of the instruments mentioned in the preceding pages, because no recent information on their operation in millimeter astronomy is available. 111. ASTROPHYSICAL ACHIEVEMENTS AND PROSPECTS OF

MILLIMETER-WAVE ASTRONOMY~ Although a considerable amount of information has been gathered by millimeter-wave astronomers on many cosmic objects, from planets and comets to quasars and the cosmological 2.7 K background, by far the most significant achievement of millimeter-wave astronomy has been the discovery and study of molecular clouds. The implications have been important in the fields of molecular physics, interstellar cloud structure, galactic structure, theories of star formation, and galactic evolution; and new fields such as interstellar chemistry have emerged from nothingness. Section 111 has been prepared by Robert Lucas, Groupe d'Astrophysique, Universite de Grenoble 1, France.

108

EMILE-JACQUES BLUM

A . interstellar Molecules

Since the first millimeter-wave discoveries of interstellar molecules, by the Bell Labs group in 1969, the number of molecules known to be present in interstellar clouds has increased to 52 (Table 111); see Mann and Williams (1980) for a recent compilation. A few interstellar molecules were found by optical (CH, CH', CN) or ultraviolet (H,, HD, C,) observations. Most of them are observed through pure rotational transitions which lie in the millimeter range. This list is not a comprehensive list of all the species present in the interstellar medium. Several symmetrical molecules such as N, , C,H,, or CzH2are not observable; they have no permanent dipole moment and thus no permitted rotation spectrum. The spectra of the observed molecules may be very simple or extremely complex, in relation with the structure of the molecule. In Fig. 1 we have plotted the energy level schemes of two common interstellar molecules, CO (carbon monoxide) and H,CO (formaldehyde). The observed transitions are shown. Carbon monoxide is a linear molecule and has a relatively simple spectrum; formaldehyde is a nearly symmetric top. Its energy levels are much more numerous. This is true for all complex molecules. Some transitions, such as the 18-cm OH lines, and the 6-cm l l 0 + i l l transition of H,CO, fall in the decimetric or the centimetric range; but these are exceptions. Most of the observed transitions are in the 2-4-mm band; these are mainly the J = 1 + 0 transitions of molecules with two heavy atoms, such as CO, HCN, HCO', HNC, C,H, N,H+, etc. A typical molecular line, the J = 1 + 0 transition of HCN, is shown in Fig. 2. The excess intensity is plotted as a function of frequency. The line is TABLE I11

INTERSTELLAR MOLECULES H,' CH CH CN

co cs

OH

HZO HZS HCN HCO HCO' C2H NzHC

so

ocs

SiO SiS NS C2' NO

HNC

NH3 HZCO HzCS HNCO C3N HNCS

HCOOH HCSN CHzNH CH4 C4Ha H&O NHZCN

SO2

HNO

Not observed at radio wavelengths.

CHSOH CH3CN CHONHz CH,SH

CH3CZH CH3CH0 HC,N CH3NHz CH,CHCN

HCOOCH, CH,OCH, CH,CH,OH CH,CH,CN HC,N HC9N

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS K,=O

K-l

(para)

tJ=5

401,

109

=I

(ortho)

-

31 2 9 GHz h ji3

J.4

14.5 GHz 150 GHz 4.t3 GHz

Jn3

345.0 GHz J=2

(a)

(b)

FIG. 1. Energy levels of (a) CO (carbon monoxide) and (bl H2C0 (formaldehyde) (the scales are different).

split into three hyperfine components, because of the nonzero magnetic quadrupole moment of the nucleus of 14N. Each component is broadened by Doppler effectsowing to internal motions in the emitting cloud (the Orion molecular cloud). Most molecules are observed through several transitions. These transitions have been studied in the laboratory, and their frequencies are accurately known. The observed lines of these molecules are then identified with

1 20.00

-

1

Y

15.00

HCN J = I - O

z 10.00

!I

8

z

-2g

5.00

0.00 -30 -20 -10

0

10

20

LSA Velocity (km/sl

-

30

40

FIG.2. Spectrum of the J = 1 +O rotational transitions toward Orion. Three hyperfine components are present. The rest frequency is 86.63185 GHz for the strongest component (F = 2 + 1). Frequency resolution is 100 kHz. [From Clark (1979.1 Note: Correspondence between velocity spread V and frequency broadening E is given by V (kmlsec) = 1 (mm) x B (MHz), where 1is the wavelength of observation.

110

EMILE-JACQUES BLUM

absolute certainty. However, a number of observed lines remain unidentified. In these cases no known laboratory-measured (or calculated) molecular frequency corresponds to the observed frequency. The most famous case was the strong line (X-ogen) found at 89.189 GHz by Buhl and Snyder (1970). This line is present in a large number of sources. The J = 1 0 transition of HCO+ was suggested as a candidate by Klemperer (1970). However this molecule is not easily made in the laboratory, and the measurement of the rotation frequency required new techniques. The laboratory frequency was measured by Woods et al. (1975) and was found to coincide with the astronomical frequency. In the mean time, the frequency of Hi3CO+ could be computed, assuming HCO' was responsible for the X-ogen line. The observation of H' 3CO+ in the interstellar medium firmly established (Snyder et al., 1976) that X-ogen was HCO'. This difficult identification procedure has now been repeated several times. For C,H, C3N, and C4H a close collaboration between radio astronomers and molecular physicists was necessary. As receivers become more and more sensitive, more unidentified lines are found. Eventually a confusion limit will be reached, at least in the galactic center source Sgr B2. At this limit at least one molecular line is present at each distinguishable frequency. The lines are blended and the identification process becomes difficult, and no improvement can be obtained from a better sensitivity. +

B. The Physics of Molecular Clouds Molecules have been observed mostly in two kinds of objects: 1. Dark clouds which have been known for long by optical astronomers to be regions of the sky where less stars are visible, since their light has been absorbed by dust. These have been systematically studied by mapping the CO and 13C0 lines. The density in these regions is of the order of lo3 to lo4 hydrogen molecules per cubic centimeter; these clouds are very cold (around 10 K). 2. Giant molecular clouds generally found close to HI1 regions (i.e., regions of the sky where newly born hot stars ionize the surrounding medium, enabling it to radiate at optical wavelengths). These contain higher density regions (105-107 molecules/cm3) and are hotter (30-70 K). It is in these regions that the most complex molecules are found. There are, of course, intermediate-type clouds : medium temperature clouds where no HI1 region is visible. The characteristic size of all these clouds is of order 1-10 pc [l parsec (pc) = 3.09 x lo'* cm].

How do we learn about the physics of molecular clouds from the observation of lines? We may obtain information either on local conditions

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

111

through the study of line excitation or globally through the study of largescale structure and dynamics. Usually the energy levels of a given molecule are not populated according to the laws of thermodynamic equilibrium. This is due to the low densities (with respect to laboratory standards) of interstellar clouds. One then defines the excitation temperature T,, of a given transition in the following way: The ratio of the upper level population to the lower level population of this transition is the same as if the molecular levels were populated according to thermal equilibrium, at temperature T,, . In fact, the populations are determined by a statistical equilibrium condition under the effects of upward and downward transitions due to emission and absorption of radiation and collision with other molecules, atoms, or ions. Should the density be extremely low, radiative transitions would dominate, and excitation temperatures for all transitions would all be equal to the radiation temperature, i.e., the cosmic background blackbody temperature of 2.7 K. At the limit where the density is extremely high, as it is in laboratory conditions, the excitation temperature would all be equal to the gas kinetic temperature, defined by the Maxwellian velocity distribution of molecules. The intermediate case is the most frequent one; its solution is complex and depends on the energy level scheme and the collisional cross sections. The latter are generally not well known; they are extremely difficult to measure experimentally and, in some cases, can be calculated from first principles, at the expense of considerable amounts of computer time. Extreme cases of nonequilibrium molecular level populations are the interstellar masers. The upper level of the transition is so overpopulated that stimulated emission of radiation overcomes absorption. The radiation field is thus amplified like a classical laboratory laser. Hydroxyl and H,O masers were already known in the centimeter range. The SiO molecule has been found to be masing in several millimeter-wave transitions. To obtain information on the large-scale structure and dynamics of molecular clouds one usually maps the cloud in a transition of a common molecule such as CO or the isotopically substituted species 13C0 or C ' ' 0 . Additional information is obtained from the Doppler frequency shift of the line, thus giving for each point the radial velocity of the cloud. One generally finds that the linewidths are rather large, corresponding to velocity spreads of about 1-3 km/sec for dark clouds, and larger for giant molecular clouds. This is much larger than the Doppler width due to pure thermal motions. This has been interpreted either as large-scale motions within the clouds or as random motions due to turbulence. Thus the clouds may either be undergoing a gravitational contraction or be sustained by turbulent pressure. All intermediate cases may also exist, and no definite general conclusion can be made.

112

EMILE-JACQUES BLUM

The interpretation of millimeter-wavelength molecular lines is further complicated by the saturation of the most intense transitions. This means that the density of emitting molecules is such that most of the line radiation is reabsorbed on its way out of the cloud. This has the effect of introducing a coupling of the molecular excitation problem with the cloud spatial and velocity structure. This is why the weaker 13C160line is generally observed in addition to l2Cl60 line in order to obtain valuable information on by a factor of 89 in the molecular clouds ("C is more abundant that solar system). C . Interstellar Chemistry

Interstellar chemistry is a rapidly developing field. Its results are still incomplete and its conclusions uncertain. If there is a kind of general agreement between authors on the formation mechanisms of the simplest molecules, the formation mechanisms of the large ones (more than two heavy atoms) have not yet been thoroughly investigated. A good review is given by Watson (1974). The time scales for photodissociation of interstellar molecules under the effect of the mean ultraviolet radiation from stars is rather short (- 100 yr). In dense clouds, absorption by dust will partly reduce the ultraviolet radiation field, and the molecular lifetimes will be larger. However, there is no doubt that a continuous formation mechanism is necessary to replenish the clouds in molecules in order to explain the observed abundances. Two sites of molecule formation may be considered, either in the gas phase or on the surface of dust grains. Atoms that hit dust grains will very efficiently stick to their surface and will rapidly form molecules. However, in general, the processes for ejecting the molecules back into the gas phase are inefficient, except for molecular hydrogen. Gas phase reactions in order to be considered must be efficient in the low temperature environment of molecular clouds. They should thus be exoenergetic, and with no activation potential. Then no minimum kinetic energy from the reactants is required for the reaction to process. Herbst and Klemperer (1973) have shown that reactions of positive ions with atoms or molecules generally fulfill these conditions and are likely to play a key role in the gas phase chemistry. The initial ionization is provided by energetic cosmic-ray protons which are able to penetrate the clouds. The main successes of this ion-molecule reaction scheme are (a) the prediction of high which are obabundances of molecular ions such as HCO' and N2H+, served; and (b) the prediction of high fractional abundance of deuterated molecules such as DCN, DCO', DNC, and HDCO. For instance, the observed DCN to HCN abundance ratio is much higher than the

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

113

D to H cosmic ratio (lo-’) (Wilson et al., 1973). This results from a binding energy difference of a few hundredths of electron volts between the H and D compounds, this difference being of the order of magnitude of the thermal kinetic energy of the molecules. D . Star Formation

Perhaps one of the most interesting developments of millimeter-wave astrophysics in the near future will be the study of the early stages of star formation. Stars form from molecular clouds ; and although very significant theoretical progress has been made recently, the details of the processes involved are still rather unclear. Protostars radiate mainly in the infrared and submillimeter wavelength range; but it is probable that high frequency resolution spectroscopic studies will be made intensively in the millimeterwave transitions of molecules, because observations are likely to be easier in this range. For these studies a very good angular resolution is needed, which will be obtained in the near future with synthesis interferometers operating at millimeter wavelengths.

E. Galactic Structure and Evolution Some molecular lines-mainly both 12C and 13C isotopic variations of the J = 1 --t 0 transition of carbon monoxide-are strong enough to be used as tracers of galactic structure, just as the 21-cm transition of neutral hydrogen has been used in the early days of radioastronomy as a tracer of the spiral arms of our galaxy (see Burton, 1976, for a review). From these observations the radial distribution of molecular gas can be deduced and compared to the distribution of atomic gas, derived from the 21-cm surveys. The bulk of the gas appears to be in molecular form in the inner parts of the disk (galactocentric distance 5 kpc, Fig. 3). Detecting molecules in other galaxies is a difficult task. The lines are very weak, of the order of tenths of a kelvin, and very broad. A few galaxies, such as M83 and NGC253, show strong CO emission from their nucleus. Emission from the galactic spiral arms is more common but is much weaker. This field will certainly develop rapidly with the next generation of large telescopes and sensitive receivers. By observation of isotopically substituted molecules, such as ”CO, H13CN,and HC”N, in different parts of the galaxy, one could in principle get information on the past history of nucleosynthesis- the way heavy elements are built out of hydrogen in stars by nuclear reactions (Audouze et al., 1975; Guelin and Lequeux, 1980). Since different isotopes are made by different reactions and in different environments, the isotopic ratios should

-

114

,

4.51 4.0

3.5 3.0 2.5 2.0 -

1.5

-

1.0

-

,

1

1

I

I

I

i:

-. :I,

Ia

,,

i

j

'1 ..

; ;; j I

E 0

1

I

-

km3)

2

4

4

6

I . ,

i

I

t3 10 12 14 16 It3 R (kpcl

FIG.3. Radial distribution of volume densities of atomic and molecular hydrogen in the plane of the galaxy. [From Gordon and Burton (1976).]

be different in the central parts of the galaxy, where star formation has proceeded at a higher rate. However, several problems in the interpretation of the observations make the derivation of isotopic ratios very uncertain : The line from the more abundant isotopic species is generally saturated; the excitation of both isotopic transitions may be different; the true isotopic ratio (e.g., 12C/'3C) may be different from the molecular isotopic ratio (e.g., ''CO/' 'CO) due to chemical fractionation effects. IV. OBSERVING CONDITIONS AND SITES A . Observing Conditions 1.

Man-Made Signals

Radioastronomy requires a low level of man-made interference to obtain good observations, and this condition is not easy to satisfy because of the heavy use for communication of the corresponding part of the spectrum. The situation is quite different for millimeter radioastronomy. At present, this part of the spectrum has a limited use in radio communication, and most transmitters have a relatively low power. Furthermore the transmitting antennas have a narrow beam: The chance of having a radiotelescope inside their main beam is small.

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

115

Aside from these reasons, the frequency bands officially allocated to remote sensing, including astronomical observations, are wider and more numerous than at longer wavelengths. Table IV summarizes the situation after the World Administrative Radio Conference, held in 1979 at Geneva. On the whole man-made interference has been until now a minor problem for millimeter radioastronomy. TABLE IV BANDSALLOCATED TO PASSIVE SERVICES BETWEEN 15 AND 275 GHZ ON AN EXCLUSIVE OR PRIMARY BASE"

FREQUENCY

General Use 15.35- 15.40 22.21-22.50 23.6-24.0 31.3-31.8 42.5-43.5 51.4-54.25 58.2-59 64-65

86-92 105-1 16 164-168 182-185 217-23 I 250-251 261-265 (in some countries) 265-275

Narrow Band for Observation of Peculiar Lines 48.94-49.04 97.88-98.08 140.60- 140.98

144.68-144.98 145.45- 145.75 146.82- 147.12

Frequencies are in GHz.

2. Sky Background The brightness of the sky background is an astronomical phenomenon, and is observed as such. Its level varies with wavelength, and in the meter wavelength range, the brightness is high owing to the galactic general emission. On shorter wavelength, and in particular in the millimeter range, the brightness of the background comes from the cosmological blackbody radiation at 2.7 K (Penzias and Wilson, 1963, which has its maximum around the wavelength of 1 mm. The brightness is isotropic with a high approximation. The measured K. anisotropy between northern and southern sky is of the order of 3 x (Smoot and Lubin, 1979). The blackbody radiation is a fundamental limit for the sensitivity of any observation in the millimeter range, as it is at centimeter and decimeter wavelengths. But natural and technical conditions allow wider bandwidth for the millimeter range. These conditions make the relative bandwidth approximately constant, and the absolute bandwidth increases then proportionally to frequency. This has an important con-

116

EMILE-JACQUES BLUM

sequence: As the sensitivity increases with the square root of the bandwidth, the millimeter range is potentially the domain enabling the highest sensitivity (see for instance Kardashev, 1979).

3. Atmospheric Effects, General The atmosphere affects the propagation of electromagnetic waves by its absorption, its radiation which adds noise to the propagating wave, and its refractive index which increases the electrical path length. Clouds and a fortiori rain are harmful to millimiter radioastronomy, but the effects are somewhat different than in optics. Clouds made of ice introduce little absorption; stratocumuli and small cumuli in good weather give an absorption in the range of 0.5-1 dB. The absorption given by thicker clouds (cumulonimbus, nimbostratus, etc.) is in the range 2-8 dB (around 100 GHz) which practically prohibits millimeter observations (Lo et al., 1975). Some information on these effects can be found in the CCIR publications, in particular, Reports 564 and 721 (CCIR, Geneva). There are many publications on the effects of rain, but they are aimed at the statistical evaluation of the communication between two earth stations, or between satellites and earth. The data of interest for observation in millimeter radioastronomy is often a by-product of these communication studies. In general, rain causes attenuation which makes millimeter radioastronomy observation practically impossible. When the sky is clear, there is still the effect of the gaseous atmosphere on propagation. The influence of two components is easily distinguished : dry air and water vapor.

4. Dry Air Dry air has approximately an exponential distribution with height which is rather stable. The scale height, i.e., the difference in height for which the pressure decreases by l/e, is about 8 km. Oxygen in dry air produces a band of spin rotation spectral lines near 60 GHz and a single line at 118 GHz. The corresponding attenuation curve is given in Fig. 4,curve C. Other minor components of dry air produce lines in the millimeter range; they are practically negligible, even for ozone which gives lines with a brightness temperature of 20 K, but on a limited band (50 MHz). This is discussed in detail by Waters (1976). We see from curve C in Fig. 4 that at sea level the oxygen lines around 60 GHz give an attenuation at the zenith which is over the level of 1 dB on a bandwidth of about 20 GHz. The attenuation at the zenith around 118 GHz is over 1 dB on about 7 GHz. The attenuation decreases with altitude, but the change is not really significant for ground based observations. The atmospheric temperature that

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117

FIG.4. Absorption curves at the zenith from sea level. Curve A, 15 mm integrated precipitable water vapor; curve B, I mm integrated precipitabie water vapor; curve C, dry air. R is an interval ofvariation due to several lines. Curve B is interpolated.[From CCIR (1978) Report 719; see also Waters (1976).]

corresponds to the radiation temperature of the above attenuation is in the range of 250-290 K. 5 . Water Vapor

The microwave spectrum of water vapor has been studied by several authors since Van Vleck (1947). There is still some difference between the calculated spectrum and the measured values. A semiempirical curve of the absorption coefficient is given in Fig. 5. The absorption coefficient steadily increases in the millimeter range, with lines superimposed at 22.2 and 183.3 GHz. There is also some uncertainty about the effect of dimers (complex water molecules). The main difficulty in getting a good estimate of the water vapor effects is evaluating the water vapor content of the atmosphere, not on the average, but locally.

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FIG.5. Absorption coefficient of oxygen and water vapor. Pressure 1013.6 mbar, temperature 20°C, water vapor concentration 7.5 gm/m3. [From CCIR (1978) Report 719; see also Waters (1976).]

First of all vertical distribution of water vapor can be considered exponential only in a rough approximation. Furthermore its scale height varies with latitude, season, etc., in the range of 1.5-2.5 km. Altogether the integrated quantity of water vapor in the line of sight, which is the most significant quantity for astronomical observations, can vary by a large factor. This integrated quantity, often denoted IPWV (integrated precipitable water vapor) is generally reduced at the zenith and given in millimeters of the equivalent column of liquid water.j At moderate latitude and at sea level, the IPWV is in the range of 10 mm in winter, 20 mm and more in summer. The winter values can be lower in cold weather. Other units are (a) the water vapor concentration e, in p / m 3 at some altitude (its product by the scale height gives the IPWV over this altitude); (6)the water vapor partial pressurep, in mbar is equal to 217e/T, where Tis the atmospheric temperature (K).

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Because of the small scale height of water vapor, the IPWV rapidly decreases with altitude. On mountain observatories IPWV values as low as 0.5 mm are sometimes reported, and 2-5 mm are representative of average conditions (moderate latitude, altitude of the order of 2 km). Large-scale atlases of the IPWV, based on measurements made from balloon-borne humidity sensors (radiosonde), are available (Gringorten et al., 1966; Bannon and Steele, 1960). They give the IPWV or its equivalent for standard altitudes, averaged by season on a number of years. Local IPWV estimates can be made from the measurement of humidity at ground level, extrapolated to the whole atmosphere by an assumed exponential distribution. The method is not always reliable because of the uncertainty on the distribution and also because of possible short-range local effects (see e.g., Hansen and Caimanque, 1975). More elaborate methods are based on local radio soundings or on measurement of the actual absorption through the atmosphere. The measurements are made in the infrared, optic, or radio wavelengths. They use an extinction method (see Section V,C,8) or a differential method. In the latter case the signal of an external source-generally the Sun-or the atmospheric radiation itself is observed in and outside a water vapor absorption line (see e.g., Westwater, 1978; Hogg, 1980). The average results generally fit with the atlases, but local effects are sometimes present, especially in mountain areas (Roosen and Angione, 1977). Altogether one can say that the average IPWV as a function of season is reasonably well known, but that the present knowledge of its short-term variations and eventual local anomalies is insufficient. 6 . The Complete Absorption Spectrum

The complete absorption spectrum of the atmosphere is given in Fig. 4,4 curve A, for an IPWV of 15 mm (water vapor concentration 7.5 gm/m3),and curve B for IPWV = 1 mm. These values are, respectively, typical of average sea level conditions and very good mountain conditions. Let us examine the influence of this absorption on the sensitivity of a radiotelescope. The which sensitivity is inversely proportional to the system temperature includes the receiver temperature T, and the fraction T, of the ground temperature present at the feed horn. To take into account the atmospheric attenuation, it is convenient to define the usable system temperature Tiy which corresponds to that of an equivalent system receiving the considered

zy,

Correspondence between absorption coefficients (as in Fig. 5) and integrated absorption is not linear, because the absorption coefficient curves have a shape varying with altitude, etc.

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signal outside the atmosphere. qyis the temperature that determines the minimum detectable signal, in Eq. (5), Section V. is readily obtained from the radiative transfer equation, and is given by :

ry

lysy = qyexp T

+ T,,,(exp

7:

- 1)

(1)

where T is the optical depth, or opacity of the atmosphere in the line of sight. If T~ is the optical depth at zenith, T =

ro sec z

(2)

where z is the zenithal angle of the line of sight. Sec z is often referred to as the number of air masses. Equation (2) assumes an atmosphere made of parallel-plane layers. Equation (I) is an approximation, because it assumes Tat,,, to be constant. We have noted that Tat,,, varies in a limited range with altitude, season, etc. However, Eq. (1) is quite sufficient to evaluate the atmospheric effects. The values of t oare given by Fig. 4.The scale in decibels multiplied by the number of air masses and converted in ratio corresponds to exp t.Table V gives some typical values of the influence of the atmosphere on system sensitivity. We take three values for system temperature (including ground contribution). Two correspond to present values : 400 K is conservative, 200 K is close to the best. The value 50 K is an extrapolation of current research, around 100 GHz. We assume that observation is made at z = 45" and c,, = 270 K. For each typical figure of atmospheric absorption, we give the resulting usable system temperature T)sy and the fractional sensitivity ZJqy,which compares the sensitivity with and without atmospheric absorption. At sea level, under average conditions, curve A of Fig. 4 applies; and in the atmospheric window centered at 90 GHz, absorption is of the order of 0.8 dB. The usable sensitivity of present systems is about 70% of its value without atmosphere; for future systems, the percentage is 35%. TABLE V INFLUENCE OF

ATMOSPHERIC ATTENUATION ON USABLE SYSTEM TEMPERATURE Atmospheric attenuation at zenith

T,;(K) T Y / G

~

400 200 50

T.; (K) T,/T,; ~~

422 215 60

0.95 0.93 0.82

1 dB

0.5 dB

0.1 dB

System temPeratwe(K)

2 dB

Ty(K) TY/G TY(K) Ty/ry

~~~

516

0.77

280

0.71

106

0.47

650 380 170

0.6

1000

0.5 0.3

620 340

0.4 0.32 0.15

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121

When curve B of Fig. 4 applies, i.e., attenuation in the range of 0.10.5 dB as in high mountains or cold weather, the system sensitivity, and especially the future one, is more efficiently used. However, it should be noted that in the vicinity of the oxygen lines, where water vapor is proportionally less harmful, better receivers will not, in any case, improve sensitivity in proportion to their noise temperature.

7 . Refraction Eflects The path length is a function of the index of refraction in the atmosphere, which has been thoroughly studied for its purely refractive effects (ray bending) and for range measurements. Refraction which is not dispersive has no particular influence on millimeter radioastronomy; it is the same as at other wavelengths. The index of refraction n of the air is n = 1 + lo6 N , where N is the coindex. It is given with a good approximation by:

N = 77.6(P/T,,,) + 3.73 x 105p/T&

(3)

where P is the atmospheric pressure in mbar, p the partial pressure of water vapor in mbar, and Tat,, the atmospheric temperature in K. There is no dispersive effect: N is not sensitive to frequency. Studies of path length at lower frequencies can be safely extrapolated to millimeter waves.

8. Atmospheric Inhomogeneity and Turbulence The atmosphere is a turbulent medium of masses of different size, density, and temperature, moving horizontally with the wind or vertically by convection. This results in time variations of atmospheric absorption. When the weather is stable, the variations are slow; and calibration at intervals of a few minutes is adequate. In general, cancellation of the effects of these fluctuations is possible (Sections V,C,5-7). The path length along a given line of sight is also affected by the variations of the index of refraction along this line. From Eq. (3) and for small variations of P, p , and T,,,, around their sea-level average value Po = 1015 mbar, p o = 10 mbar, To = 290 K, we can write: dN

=

--

0.27 dP - 0.95 dT,,, dry air

-

0.3 dT,,,

+ 5 dp

water vapor

For dry air the temperature variation is the main factor of change in N. For water vapor the partial pressure is the main parameter; since the variability of water vapor pressure is high, the fluctuations of the index of refraction of air occur mainly at sea level or low altitude, from water vapor.

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There is much uncertainty about the situation at altitudes over 2 km. First, there are several turbulent layers in the atmosphere. The conditions above or below a given layer are different. Furthermore, there is a layer often stationary around 2 km altitude in flat regions. To what extent is this true in mountain areas? Another cause of uncertainty is the relative effects of dry and wet air on path length fluctuations. Airborne measurements indicate small temperature fluctuations ; hence dry air would cause little fluctuations in path length. If this is true, a high-altitude observing site would allow not only a better sensitivity but also a higher resolving power, because proper operation of an interferometer requires a small variation of the difference in the path lengths for the rays reaching two different antennas. In fact, our general knowledge of the index of refraction of air is not yet sufficient to give figures for the fluctuations of differential path length at various altitudes, and for various distances between antennas. The best estimates come mostly from direct measurements at longer wavelengths (Section V,D,2). Extrapolation to millimeter waves is safe, but only at a given site. B. Conditions Required for Observing Sites Millimeter radioastronomy lies on a border line: Observations are possible for ground-based sites, but their efficiency increases with altitude, especially at the lower end of the millimeter range. Observations at submillimiter waves and in the far infrared are hardly possible from extreme terrestrial altitudes and often require airborne instruments along with the related practical problems. The choice of an observing site for millimeter astronomy must take into account a number of requirements, some of which are somewhat contradictory. Two requirements concern atmospheric effects : a large proportion of clear sky conditions and stable weather, and a low water vapor content of the atmosphere. One requirement is astronomical in nature : Low latitudes favor the observation of the galactic center and more generally allow observation of a larger part of the sky. The final requirement for an observing site is logistic: Staffing and operation are eased by proximity to a developed area. Until now, the majority of observing sites have been selected mostly for logistic reasons ;recent examples are the millimeter radiotelescope at Bell Laboratories, close to New York; the Swedish radiotelescope near Goteborg; the Five College radiotelescope not far from Amherst, Massachusetts. The existence of well-developed optical observatories has facilitated the installation of some millimeter radiotelescopes on sites where all requirements are reasonably fulfilled. This is the case for the 1 1-m radiotelescope of NRAO, at the Kitt Peak Observatory (altitude 1900 m, latitude 32"N) not

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far from Tucson, Arizona. The radiotelescope of the University of Texas is in a developed observatory (MacDonald Observatory) but far from any large town. We have noted, in Section IV,A,6, the increasing influence of the atmosphere when the receiver noise decreases. This is particularly important for observations made at the high-frequency end of the millimeter band because of the increase of atmospheric absorption with frequency. Improvement in receiver performance and more frequent use of the shortest wavelengths are both allowing more importance to be placed on the atmospheric qualities of sites. Estimates of these qualities for a number of places have been performed in recent years from existing data, in particular by Kuiper (1970), and for a final evaluation, from new measurements on the spot. For obvious reasons accessible locations have been mostly considered. Mauna Kea in Hawaii is one of the most interesting sites because of its altitude (4200 m), latitude (19"N), proportion of clear sky, and low water vapor content (IPWV 1-2 mm). Facilities for optical and infrared astronomy have been developed. However, the nearest large city is Honolulu on another island, and the average wind velocity is high (as in all high mountain sites). The highest usable mountain in the Canary Islands has an altitude of 2400m. There is development in progress for optical astronomy. The water vapor content is rather low (IPWV -2.5 mm), latitude is 28"N, the proportion of clear sky is high, but not as much as at Mauna Kea. Western Europe is within 5 hours by plane; the main towns of the Islands do not have much technical resources. Other sites, presumably excellent, but quite remote, certainly exist in the Andes, and perhaps in Central Asia. If a little more weight is given to logistic requirements, an intermediate class of sites appears with some loss on natural characteristics. The Sierra Nevada Range in Southern Spain, which culminates at 3400 m, is an example; the water vapor content is low (-2 mm IPWV, except during summer), and the town of Granada is nearby. However, the latitude (37"N), the moderate proportion of clear sky, and the severe winter weather condiditions balance the advantage of easy access, which in principle means easier staffing. We will see in Section VIII that no large project is being planned on a low altitude site. However, intermediate sites have been chosen for several projects. This is particularly true for interferometer projects which need some kind of horizontal baseline, a further requirement. At present no clear-cut argument allows us to decide if logistics should be outweighed by the other requirements. However, improved and more reliable instruments will probably appear in the coming years; the balance will then favor the sites that are the best from the point of view of natural requirements.

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V. RADIOTELESCOPE FUNDAMENTALS AND THE MILLIMETER RANGE A . Introduction

When the naked eye was the only detector in astronomy, the word telescope was quite naturally applied to the optical instrument itself. This leads to some ambiguity in radioastronomy where an observing instrument comprises a receiving system and one or several antennas. These antennas are commonly, and somewhat improperly, called radiotelescopes. In fact a radio interferometer is a radiotelescope with two or more antennas. Radiotelescopes are divided in two broad classes: the single dish instruments, sometimes called filled aperture radiotelescopes, and the interferometers, which have two distinct antennas, or more (arrays). The technique of aperture synthesis is a particular type of operation of the interferometers. A detailed discussion on the two classes of radiotelescopes is given, for instance, by Christiansen and Hogbom (1969). They also discuss the various types of sensitivity. The sensitivity for flux observations is given by

AS = M(kT,,/(B8)”2Ail)

(4)

and the sensitivity for brightness temperature observation, when the observed area is equal or wider than the antenna beam :

A T = M(T,,/(BO)’’2) where As (W/m2 Hz) and A T (K) are the limit in measurable flux or temJ/K), the system perature, k is the Boltzman constant (1.38 x temperature, B the bandwidth (Hz), 8 the observing time (sec), A the area of the antenna (m2), and q the aperture efficiency of the antenna. M is a figure that includes in particular a factor ensuring safe detection; it depends on the type of radiotelescope, and is in the range 5 to 10.

xy

B. Single Dish Radiotelescopes 1. Sensitivity

The sensitivity of the radiotelescope varies with the surface of the antenna and with the system temperature. These two quantities are less favorable by one order of magnitude each between centimeter/decimeter and millimeter wavelengths. Millimeter dishes now in operation have diameters up to 20 m;

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

125

diameters of 30 and 45 m will be reached in a few years, whereas diameters from 100 to 300 m have already been built for centimeter and decimeter radioastronomy. The present millimeter receivers have a noise temperature of about 300 K, giving a system temperature of 400 K or more. System temperatures of 40-50 K are not uncommon in radioastronomy on centimeter or decimeter wavelengths. The effect of these two considerable differences on relative sensitivity, may still be enhanced by the atmospheric absorption (see Section IV,A,6). Only one factor favors millimeter radioastronomy: it can use wider bandwidths. The flux of continuum radio sources is generally weaker in millimeter radioastronomy than in radioastronomy at longer wavelengths. Altogether, millimeter radioastronomy is severely limited by sensitivity; but in contrast to some other branches of astronomy, the sensitivity in millimeter radioastronomy is still far from its theoretical or practical limits. For example, the receiver noise temperature will certainly decrease by a significant factor in the coming years. Any major radiotelescope must accommodate several observing programs. The observing time in each program is then limited, as is the corresponding sensitivity; sensitivity increases as the square root of observing time. An alternative rarely used in radioastronomy is to use simultaneously several receivers at the same or at different frequencies,connected to different feeds. Such multibeam or multifrequency arrangements are particularly attractive in the millimeter range. Many interesting regions of the sky are much wider than a beam, which has a very narrow width of the order of 1’ or less. Mapping can then be speeded up by multibeam or multifrequency arrangements, with further advantages discussed in Section V,C,6. The only but also serious difficulty is the need for several receivers : The problems of cost and reliability need to be solved. These problems will probably be resolved in the coming years for the largest projects. 2. Lower Limit of Wavelength

The aperture efficiencyof an antenna varies exponentially with its surface accuracy; if E is the rms deviation’ from a perfect shape-in general the best fit paraboloid--and ti the aperture efficiency: 11 = qo exp - ( ~ ~ T E / A ) ~

(6)

We give here crude indications on the antennas tolerance theory. For more details see Ruze (1966,1978). For the astronomerthe aperture efficiency is the important parameter, which can be directly measured on a reference radio source. Its practical definition is easier than that for L . However, we prefer t in the following, because its physical meaning is tangible.

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EMILE-JACQUES BLUM

q decreases by a factor of 2 for I = I , = 1%. Assuming I , to be the minimum wavelength for efficient use of the antenna, we see that c should be 0.2 mm for I , = 3 mm, E = 70 pm for I , = 1 mm. Such accuracies require a quality factor of antenna of diameter D defined as t/D, of a few parts in loT6.This is considerably smaller than it is in centimeter radioastronomy where t/D is in the range 10-4-10-5. The designer of millimeter antennas faces the limits of structural engineering, and the final adjustment and control of the antennas is a difficult challenge. The situation for optical telescopes is somewhat different. The 10- for present instrumentsspecificationsare indeed still higher-c/D but the size allows a quite different approach for the design and the control.

-

'

3. Pointing Accuracy

This characteristic is directly connected to the quality factor t/D. The pointing accuracy should be a fraction of the beamwidth in order to enable efficient use of the antenna, allowing precise measurement of source position and flux. This fraction is not strictly defined: 2-5% of the beamwidth is considered quite satisfactory; l0-20% is barely adequate. The minimum beamwidth of a dish is close to 1.222,jD = 1.22 x 15clD. The pointing accuracy should be at least 1.22 x 15c/5D, and preferably 1.22 x 156/20D. With the value of t/D quoted above for large millimeter dishes, i.e., a few parts of we see that pointing accuracy should be of the order of one second of arc. This is extremely difficult to achieve, and most present dishes have an rms pointing accuracy of a few seconds of arc. 4. Cancellation of Atmospheric Fluctuations, General

The atmosphere in front of an antenna is equivalent to a lossy transmission line. Its losses occur at a temperature corresponding to an average of the atmospheric temperature in the column defined by the antenna beam. The fundamental effect of these losses and this temperature is to increase the overall temperature of the system. This is discussed in Section IV,A,6. In addition, the atmospheric loss and temperature slowly fluctuate, on a time scale of the order of seconds (Section IV,A,8). Without some type of cancellation, these atmospheric fluctuations dominate at the output of a radiotelescope; its sensitivity is not set anymore by the normal fluctuations of the temperature of the system. Continuum measurements are fully affected by this phenomenon. The shape of the observed spectrum is less affected in the case of line measurements, because the slow atmospheric fluctuations are not very frequency dependent.

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

127

5 . Beam Switching The cancellation of atmospheric fluctuations can be achieved by the method of beam switching, which takes advantage of the relatively large scale of atmospheric fluctuations. When an antenna observes a radio source through a given column of atmosphere, there are other columns with about the same characteristics within a few beamwidths of the observed direction (Emerson et al., 1979). These columns have a large volume in common,6 and the remaining volumes show no significant differences. The antenna beam is switched between the direction of the radio source and an empty region of the sky a few beamwidths distant. The difference between the outputs of the receiver for these two directions gives the signal from the source with the normal noise fluctuations. A further step is to calibrate the atmospheric attenuation in order to reach the true level of the source signal; this will be discussed later. Several switching techniques are available: ( a ) a waveguide switch which alternately connects the receiver to two different feeds. This technique is convenient in the centimeter range where adequate switches (ferrite switches) exist. This is not true in the millimeter range. (6) Switches using quasi-optical techniques. For instance, rotating mirrors are well suited to millimeter antennas. (4 Nutation of the secondary mirror of a Cassegrain dish. This method is used in the infrared. With the secondary mirror size of millimeter dishes (diameter of the order of 1 m), it is not easy for nutation to occur at a rate fast enough to cancel the atmospheric fluctuations, i.e., 1 Hz or more. For line measurements, switching can be made at a slower rate, one minute or so at a good observing site. This is conveniently accomplished by pointing the whole dish on and off the observed source at this rate, and is generally sufficient to get satisfactory cancellation of the atmospheric fluctuations.

6 . Beam Switching on Extended Sources Until recently the use of beam switching on sources with a size comparable to or larger than the beam separation was not considered. It was shown by Emerson et al. (1979) that mapping of such extended sources is quite feasible. The zone of the source is scanned by a number of beam switched observations. The results are reassembled to produce a map through A dish with a diameter of 10 m has a lobe of 1’ at 1 = 3 mm. The main absorbing region in the atmosphere, corresponding to the water vapor scale height, is up to about 2 km over the radiotelescope. At this height, the axis of two columns of atmosphereof one beamwidthdistance are only 1 m apart.

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convolution, with a sampling function removing the effects of overlap due to the dual beams. Within some limitations this method has proved its value in obtaining maps of angular sizes corresponding to at least three times the beam separation, with good cancellation of atmospheric effects. Wider fields can be measured if the beam switching can be made among three different beams. The convolution method was only recently introduced. Its use for millimeter observations has not yet been reported, but will probably soon be used, because the method appears quite valuable for such observations in the continuum.

7 . Frequency Switching This procedure has been widely used because of the importance of line observation in millimeter astronomy. Frequency switching cancels atmospheric and receiver instabilities, and is relatively simple to implement. The receiver frequency is switched (through the local oscillator frequency) between the frequency at which the radio source radiates and another frequency, at which no significant emission of the source occurs. The difference between these frequencies varies with the type of observation but is typically of the order of 1-20 MHz, which is a small percentage of the average frequency. One is limited to such values in order that no severe problems of band shape are introduced in the rf part of the radiotelescope. The propagation of millimeter waves in the atmosphere is practically identical for close frequencies, and the cancellation of atmospheric fluctuations is obtained. 8 . Calibration Conventional calibration is an easier problem to deal with in millimeter radioastronomy than at longer wavelengths. Hot and cold loads are small and can easily be placed in front of the generally small focal feeds. The calibration of the atmospheric attenuation is, on the contrary, a specific and difficult problem. A detailed discussion has been given by Ulich and Haas (1976) for the important case of line work. The basic procedure uses radiative transfer in the atmosphere. The radiation temperature of the atmosphere T R A is approximately given by : where Ztmis the true temperature of the atmosphere, and t its optical depth. Provided Tat,,, is close to the ambient temperature K m b , the difference between TRA and K m b measures the atmosphere transmission (1 - exp( - 7)) in a first approximation. The “chopper wheel” method automatically com-

129

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

pensates for the effect of this transmission (Penzias and Burrus, 1973; Davis and van den Bout, 1973). The astronomical signal measured by its temperature T, is attenuated to T, exp( -t) by its propagation through the atmosphere. The receiver input is alternately connected to a load at ambient temperature and to the antenna aimed at the sky through the atmosphere. The measured difference is

It is a direct measure of exp( - z), and gives a proper scaleby which to measure the true signal temperature on a spectrum, by comparing exp( -7) to T, exp( -z). An improved version of the chopper wheel method is currently in use, with the chopper load cooled to approximately the atmospheric temperature. Another solution used two comparison loads at different temperatures. An independent check of the value of exp( - 7 ) is currently made by the atmospheric extinction method. The variation of the atmospheric radiation TRA with elevation is measured. Since TRA = Ztm( 1 - exp( - z)) and t = to sec z (Section IV,A,6), t and zo are readily obtained by plotting exp( - z) against the number of air masses. Another and less common check is to track a given source for several hours. The signal received from the source is attenuated by the atmosphere, again following a sec z law. The attenuation by air mass is obtained as above (see for instance Davis and Van den Bout, 1973). Calibration by the extinction method is also valid for continuum observations, but it is a slow procedure. An absolute calibration scale based on accurate measurement of planetary brightness has been recently established (Ulich et al., 1980).

zmb

9. Baseline Ripple An antenna is never perfectly achromatic; its gain changes slightly with frequency. This is a negligible effect, but an imperfect match to the receiver input is more harmful. One significant spurious phenomenon is the rapid variation with frequency of the reflection coefficient of the antenna for the receiver noise radiated by the focal feed. The reflected noise combines with the original noise to give a ripple in the baseline of a spectrum at the output of the receiver. The fundamental period of this ripple corresponds to a wavelength equal to the distance of the feed to the secondary mirror, if it exists, and to the dish apex. But the ripple contains other periodicities, some of which are variable with elevation (ground effects), and thus difficult to take into account. Baseline ripple is minimized by prime focus operation of the antenna. It increases with magnification when secondary focus operation is used. Morris (1978) has studied the phenomenon and has given guidelines

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EMILE-JACQUES BLUM

on how to reduce it. Modulation of the path length between the antenna and the feed efficiently reduces the baseline ripple. Goldsmith and Scoville (1980) have proposed a practical method of modulation. Overall these chromatic effects may decrease sensitivity on spectral line observations compared to its normal limit set by noise fluctuations. Offset feed antennas are less sensitive to the phenomenon. C. Interferometer Radiorelescopes 1. General

An interferometer is made of several antennas and their receivers. Many considerations presented in the previous sections still hold, with one fundamental difference: The signals coming from two independent antennas have a part in common, the rest is uncorrelated. The detection procedure measures this common part. It involves a correlator which makes the product of the two signals. Any independent component in one of the signals gives no output other than noise. In particular, the atmospheric fluctuations in front of each antenna, like the noise of the independent receivers, are not correlated. Therefore, interferometers do not face the problem of cancellation of the fluctuation of atmospheric radiation and absorption, or most of the difficulties with baseline ripple. But to reach full sensitivity, the interferometer correlator must make the complex product of the incoming signals. Uncorrelated fluctuations of path length in the propagation and transmission of the common signals decrease the correlator output and are harmful for an interferometer. These phase fluctuations can come from the atmosphere and from the interferometer hardware. They constitute the most critical problem of millimeter interferometry. At longer wavelengths the technique of very long baseline interferometry meets with rather similar problems (see, e.g., Readhead and Wilkinson, 1978). 2 . The Atmosphere

The effects of the atmosphere on interferometer performance were analyzed for longer wavelength by Hargrave and Shaw (1978) and Hinder and Ryle (1971). Experiencewith the 5-km interferometer (Ryle and Elsmore, 1973) and extrapolation to millimeter waves show that at sea level and moderate latitude, differential fluctuation of path length allows reasonable observing conditions at a wavelength of 3 mm with antennas separated by 500 m for 25% of the time. Experience from other interferometers, as the WSRT (Hammaker, 1978) give other valuable data. Local conditions certainly play a role in atmospheric turbulence, and we do not know ifexperience

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

131

on one site can be safely extended to another one. We also do not know the exact decrease of path length fluctuation with altitude. It is certain, however, that water vapor is an essential factor in the refractive index of air. As water vapor content of the air decreases with altitude, one can expect to have reduced path length fluctuation ; this assumes that the relative turbulence is roughly constant with altitude-and there is some indication of that being true. 3. Phase Stability of the Radiotelescope- Transmission of Local Oscillalor Reference Signal Besides the obvious requirement of mechanical stability, the main problem in millimeter interferometers is getting a proper local oscillator signal at each antenna. The scheme generally employed in conventional interferometers can be used but is critical. A reference local oscillator (LO) signal is sent at a frequency of a few hundred MHz through coaxial cables. The length of the cable is monitored. An harmonic of the reference signal locks an oscillator at the required high frequency. This implies a high multiplication factor, for instance, from 300 MHz to 100 GHz; and frequency multipliers are phase sensitive to temperature. To reduce the multiplication factor, one should use a higher frequency reference signal. This has been done through oversized waveguides (Delannoy et al., 1973). The technique is satisfactory but because of the waveguides, it is expensive and not convenient for transportable antennas used in most interferometers. Transmission of a signal modulated at a high reference frequency through fiber optics is an interesting possibility, which has not yet been tested. 4. Reduction of Interferometer Data in the Presence of Phase Fluctuation

Considerable research has been carried out to make the best use of interferometer observations spoiled by phase fluctuations (see Schooneveld, 1979, part 11). Data reduction can take advantage of a priori known properties of the observed region, for example, the brightness distribution on the sky being real and positive. When an interferometer with at least three antennas is available, the phase closure relation (Jennisson, 1958 ; Rogers et al., 1974; Readhead et al., 1980a) may ease the reduction procedure. The phase closure relation states that the sum of the measured phase of the fringes between the antennas is equal to the sum of the true phase of the fringes for a perfect interferometer, without any atmospheric effects. However, the phase closure method can be of practical use only when the signalto-noise ratio is sufficient. The amplitude closure method has also been proposed recently (Readhead et al., 1980b).

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5 . Scaling Down Radioastronomy Interferometers The major interferometers now existing in centimeter or decimeter radioastronomy have dishes with diameters in the range 15-25 m and maximum baselines of 3 km and above. They are mainly used between 1.4 and 15 GHz. Scaling down the “average” of these instruments to I = 3 mm gives baselines of a few hundred meters and a dish diameter of the order of 1 m. Such baselines fit with the atmospheric constraints for phase stable observations (at sea level). But the dish diameters are too small for a reasonable sensitivity. Larger diameters are required (6 m or more); but then the beamwidth becomes very small. When an interferometer is used for position measurements of a source, a small beamwidth is acceptable. For mapping through some form of aperture synthesis, a small beamwidth is a severe restriction: The field of view-or the map size-is defined by the beamwidth. Celestial objects are of a size that is in general much larger than the few minutes of arc beamwidth of a dish with adequate sensitivity. Full mapping of a region would require a very long time, unless the interferometer is used with several simultaneous beams and the corresponding numbers of receiver systems. If partial mapping is acceptable, as it has been found in a number of astronomical programs, the problem becomes less severe. One can also envisage another approach: increasing the number of dishes and making their size smaller. For sensitivity the only important factor is the observing time and the total area of the antennas. If we fix observing time, total antenna area, and resolving power (maximum baseline), then the size of the maps obtained by synthesis increases (in surface) as the number of antennas does. In addition, many other parameters should be taken into account : variation of antenna cost with diameter, complexity and reliability of the radiotelescope, minimum time to map a region, and so on. What is quite clear is the difference of the effect of the compromise number/diameter of the dishes for interferometers in centimeter-decimeter and in millimeter radioastronomy : In the latter the field covered by the individual antennas is a major question. Multibeam arrangements in a few large antennas may be the best answer to this question if the reliability of receivers is sufficient. The interferometers for centimeter and decimeter radioastronomy are not facing the same difficulty with field, and the sensitivity is less critical. Increasing the number of their antennas is a logical trend. 6 . Calibration

The calibration problem specific to the interferometer is the definition of the geometry of the instrument (Ryle and Elsmore, 1973). Geodetic

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surveys give a first approximation; they have an accuracy limited by the surveying instruments and by the need for absolute references. Furthermore the interferometer itself is never perfectly stable, internally or against a terrestrial reference system. Calibration against a celestial reference system is required. The highest accuracies reported by centimeter wave interferometers reach 0.0 1” and even better for relative positions. One can expect comparable figures when large millimeter interferometer projects (Section VIII) are completed. We have been dealing until now with accurate position measurements, required in particular for astrometry and source identification. Mapping, measurement of the diameter of a source, etc. require less extreme accuracy. Calibration of the interferometer is still necessary to check the phase stability of the instrument, eventual large-scale atmospheric phenomena, etc. This is currently made by observing a narrow source with known position close to the field of interest. The periodicity of the calibration depends on the particular instrument and local conditions; it is of the order of 10 min to 1 hr at short wavelengths. When an antenna of an interferometer is moved, the easiest way to determine its new location and the corresponding baseline parameters with the other antennas is again a calibration on radio sources with known positions after a rough geodetic evaluation within one wavelength to avoid lobe ambiguities. Even if most radio sources are weaker on millimeter waves than at longer wavelengths, dish diameters of about 10 m and present receivers allow the observation of about 100 continuum calibration point sources in the entire sky, with adequate sensitivity. Nevertheless, the calibration of interferometers is a specialized and difficult problem.

VI. ANTENNAS A . Introduction

Most millimeter radiotelescopes in operation use the conventional parabolic dish as their antenna. The two exceptions are the offset parabolic at the Bell Laboratories and the Ratan in the USSR. Among projects or proposals only one design described by Fourikis (1978) is special; it uses a ring of small dishes combined to give the equivalent of a larger dish, having several beams. It can be compared to an array of dishes. We are then not losing much generality concentrating on conventional or offset parabolic dishes in this section. The conception and construction of parabolic dishes for millimeter waves is more critical than at longer wavelength in several respects. The

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required accuracy implies a good control of gravitational and thermal deformations and requires accurate methods to measure the dish surface. The location of some millimeter radiotelescopes on high-altitude sites requires adequate protection against adverse climatic conditions. At the same time, the cost per square meter of effective aperture is high; optimization of the receiving properties of millimeter dishes is important. We should then begin with a brief review of these aspects. B. Geometry and Optics of Parabolic Dishes

Several books or papers have appeared recently that discuss this problem (Von Hoerner, 1977; Love, 1978; Wood, 1980). For millimeter waves the scale is such that the geometrical approximation used in optics is a good first approach. 1. Basic Geometry

The modern millimeter receivers for radioastronomy are cryogenically cooled. This means relatively large and heavy receiver boxes, which are inconvenient to install at the primary focus of a dish. Therefore, in millimeter radioastronomy the Cassegrain arrangement is widely used. The focal ratio is generally in the range 0.3-0.4 as for larger wavelengths, and the secondary focus feed is at or in front of the apex. However, a trend toward more sophisticated optics is presently appearing, with further reflectors conducting the beam on the side of the mount (Nasmyth focus) or in a lower cabin (CoudC focus), as in some antennas for space communication. The advantage is more room for the receivers, but there are some problems in obtaining full efficiency of complicated optics on wide bands, as needed in radioastronomy observation and to enable multibeam operation if necessary. 2. Conventional or Oflset Dishes?

In offset dishes, as shown in Fig. 6 , the beam is unobstructed. There is no side lobe due to spurious reflection on the feed support or on the edge of the prime focus system (Horn or Cassegrain subreflector). It is then possible to minimize efficiently the general side lobe level, and therefore the spillover, and the fraction of ground temperature reaching the receiver feed (Von Hoerner, 1978). Another advantage of offset parabolic dishes is the possibility of easily installing a Cassegrain subreflector on a rigid mount and of having complicated secondary focus optics in accessible locations. These possibilities are indeed used in Bell Laboratories 7-m dish (Chu et al., 1978; Goldsmith, 1977).

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS

@

Ref lector

Fed

-- -

I

135

- - - -- - --

Subrcflec t o r

I

FIG.6. Sketch of the geometry of an offset dish.

A review of the properties of offset paraboloids was published recently (Rudge and Adatia, 1978). The arrangement appears very attractive for millimeter dishes of moderate size; for large dishes-- 10-m diameter or more-the symmetry of conventional dishes probably makes them mechanically superior to offset paraboloids.

3 . Shaped Illumination The aperture efficiency of an antenna is maximized by uniform illumination of the main reflector. This can be approximated by shaping the main reflector, but more easily by shaping the subreflector of a Cassegrain, by using a specially designed focal system, or by a combination of these approaches. Aperture efficiencies up to about 85% have been reported (e.g., Lee et al., 1979) compared to about 60% with conventional shapes and feeds. Offset parabolic dishes appear especially suited for such high efficiencies, because of their inherently low-aperture blocking. It should be noted, however, that increased efficiency outside one beam is not easy to achieve. This may limit the interest of shaped illumination for future millimeter dishes using multibeam feeds. C . Design und Construction of Dishes

1 . Theoretical Background Von Hoerner (1975) has made simple assumptions and has computed a diagram, reproduced in Fig. 7, which shows limits of parabolic dishes. The gravitational limit applies to a rigid design: Under its own weight a parabolic dish changes shape with elevation. When the change is rZ/16, the gravitational

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1000

I

1

I

I

I

STRESS

300

* L

I

1

I -

LIMIT

-

u -,looI:

.-C

t

30-

.a

u

Wavelength in

Millimeters

FIG.7. Natural limits of steerable radio telescopes. [Updated from Von Hoerner (1975).] The limits are based on steel construction. TH.L., thermal limit (see text). Existing dishes are marked by a cross, projects by an open circle. Centimeter and decimeter dishes: 1, 100-m Effelsberg, F.R.G.; 2, 300-ft, NRAO; 3, Mark 1 Jodrell Bank; 4, Parkes, Australia; 5 , Goldstone, J. P. L.; 6 , Algonquin Park, Canada; 7, 140-ft NRAO; 8, 130-ftOwens Valley; 9, Haystack; 10, various 25-m dishes. Millimeter dishes: 11, 22-m Crimea, USSR; 12, Onsala, Sweden; 13, FCRAO, Mass.; 14, 1 I-m NRAO, Kitt Peak; 15, Cal Tech; 16, Bell Tel. Lab.; 17, University of Texas; 18, Aerospace Corp. Millimeterprojects: 19, 45-m Japan; 20, 30-m IRAM; 21, 25-m NRAO; 22, 15-mSRC; 23, Cal Tech Submm.Note: Detailed comparison of dishes should not be made from this figure; the data for wavelength limit is not fully homogenous.

limit is reached. Even if Von Hoerner's model for a dish is simple (octahedron made of steel and held at two corners), its value is proved by the performance of actual dishes, as indicated in the diagram. A step further is the homologous design, where the deformation due to gravity is accepted but controlled, with the dish shape remaining homologous to itself. A parabolic dish stays parabolic, but its focal length changes and its position relative to the elevation drive system tilts. This concept was developed systematically by Von Hoerner (1967a,b, 1969). Considerable improvement from the rigid design has been reached, in particular with the 100-m telescope at Effelsberg (Hachenberg et al., 1975). Figure 7 indicates that these improvementsare limited by another constraint, the thermal limit. However, Von Hoerner assumes temperature differences of 0.8"C at nighttime and 4°C in daytime between parts of the dish structure; circulating air inside a closed dish structure can decrease this differential and push the thermal limit upward in the diagram. Some recent projects take advantage of this idea, but no practical result is available yet.

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2. Mechanical Construction

Relatively small dishes, for instance, 3 m in diameter good to a wavelength of 3 mm, are far below the limits of Fig. 7; in addition the ease of machining and control and the cost are major considerations. Cast metal design or welded rigid structure are frequently used, with the reflecting surface being a part of the structure. Machining and control are possible on a vertical lathe. When the size of dishes with the same design is increased, weight (and cost) increases rapidly, and machining becomes difficult and should be made in a temperature controlled room. Some large vertical lathes are indeed installed in such enclosures. Another difficulty is the local increase of temperature around the cutting tool. One large millimeter dish was built along these methods, the NRAO 11-m dish (Table I). Even if its construction technique is somewhat obsolete now, the 11-m dish is a landmark in the development of large and accurate dishes. There is no clear-cut rule to decide the limiting diameter under which solid construction should be preferred. In the present state of techniques, a diameter of 5 m seems to be a practical maximum with an rms surface accuracy of about 0.1 mm. Structures made of simple metal beams are particularly convenient for computer analysis, because they can use programs based on the finite element method (see,e.g., Mar and Libowitz, 1969). Solid structures are more difficult to optimize for performance and for weight : This is an additional reason to restrict their use in the millimeter range to relatively small diameters. An intermediate design has been used recently by ESSCO to build several dishes with diameters of 14 and 20 m (see ref. on Table 1). In this design, rigidity is achieved by using boxes made of light metal sheets. The boxes are assembled radially and in rings. The reflecting surface is made of sheets fixed on frames attached to the boxes. This gives a light structure requiring a radome for weather protection. Up to this point we have considered the dish structure as a whole including the reflecting surface. This surface may also be independent, and most recent dish designs consist of a back structure onto which the reflecting surface is attached. There are two possibilities. The reflecting surface can be made of a number of independent panels; the panels contribute to the mechanical properties of the structure only by their weight. If, on the contrary, the panels are connected together, the surface forms a skin that participates in the overall mechanical properties. This allows a very light design. The 10.4-m dishes built by R. Leighton at the California Institute of Technology (Leighton, 1978; Wannier el al., 1979) use this technique. The back structure is made of a lattice of tubes, and the reflecting surface consists of aluminum honeycomb panels linked to form a skin. Surface

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accuracy of 25-50 pm is reported. When the panels are independent, as in many projects, the back structure is somewhat heavier, but the surface adjustment or repair is easier. The principle of homology is introduced today for any large symmetrical dish. A structure fully using this principle is faced with some problems: When optimized it has a conical rear shape not convenient for mounting the dish or for locating a receiver cabin at the Cassegrain focus. The resulting compromise is a quasi-homologicstructure, optimized through a cut-and-try computer procedure. 3. Panels

Many models of panels have been tested, and two main types seem to predominate : aluminum honeycomb sandwiches and light cast metal. Both have a good thermal conductivity which minimize the temperature gradient between the faces. Honeycomb is light, but setting and machining its surface is critical. Internal tensions in cast metal make its final surfacing difficult. In both cases control and sometimes final surfacing is made on measuring machines recently introduced in industry. These machines are numerically controlled. Their accuracy varies with size, typically 10 pm on 2 x 1 m, which fits well with the maximum dimension of panels set by their thermal deformation. Simple aluminum sheets shaped by a large number of screws on a frame is another solution for panels, but they require tedious and critical adjustment. The temperature difference between the two faces of the panels is a severe constraint. In daytime, the difference due to sunshine on metallic panels is significant-a few "C. Use of materials with a low-temperature coefficient, like silica, can be envisaged. Infrared reflectors have been built in silica honeycomb, but the cost is high. Solutions using oriented carbon fiber are in development, in particular for the Japanese project (Section VIII,D), but no data are yet available. Reduction of temperature effects can also be obtained by decreasing the size of individual panels, but this means tedious adjustment on the back structure of a large number of panels. Another approach is to decrease the temperature gradient of the panel by an external thermal insulation; but, the insulating material yields some extra loss on the incoming radio waves. Altogether accuracy of about 100 pm on panels of the order of 1 m2 is now attainable with established techniques. Accuracy in the range 25-50 pm is still a challenge in field conditions. D . Adjustment of the Dish Surface

The dish surface must be adjusted with an accuracy compatible with the overall error budget, and equal or better than the panel accuracy: 25 pm

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on 12 m diameter represents a relative error of 2 x lop6. The best results yet reported have been obtained by elaborate template methods (Chu et al., 1978) which are also used for surfacing (Leighton, 1978). Conventional optical methods with angular measurements are accurate to about 10- '. Improved methods are required and some have been proposed. Promising approaches are based on using laser beams to define directions and laser interferometers or modulated lasers to measure distances. For instance, the United Kingdom submillimeter dish 15 m in diameter (Section VIII,D,2) is to be adjusted by the method sketched in Fig. 8. The quantities measured are the distances from the dish axis to the trolley and from the trolley to the probe; a laser interferometer is used for measuring. The angles affecting the result are held fixed by means of an alignment laser and pentaprisms. An overall measuring accuracy of 20 pm rms is expected (Shenton and Hills, 1976). Payne et al. (1976) and Findlay (1979) have proposed a tnethod based on local measurements. A moving cart measures curvature along sections of the dish surface. These measurements are integrated to give the profile of each section. The measurements can be made by a spherometer or by an inclinometer. The method is promising but is still limited because of possible local deformation due to the weight of the cart and because of the discontinuity across the gaps when the surface is made of panels. These methods require the dish to be pointed at the zenith. A completely different approach, called holographic, is based on the Fourier analysis of the diffraction pattern of the dish. The complex Airy disk of the dish, tracking a point source, is Fourier transformed; this gives an image of the dish aperture (Shenton and Hills, 1976; see also Scott and Ryle, 1977). The STIFF .IGHTWEIGHT

A

COUNTER WEtGHT

111 I

/

'

BACK

STRUCTURE

FIG.8. Sketch of dish measurement by a rotating arm. [From Shenton and Hills (1976).]

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EMILE-JACQUES BLUM Casscgrain Astronomical signal !I

Receive-

v

-Receiver

Complex product

FIG.9. Principle of dish measurement by the holographic method. [From Shenton and Hills (1976).]

method is sketched in Fig. 9. The output of the reference horn at the center of the Airy disk is correlated with the output of a second horn, which maps out the focal plane. The number of distinct positions in this plane corresponds to the number of distinct areas in the dish aperture. Satisfactory knowledge of the surface accuracy requires measurements in a large area of the focal plane far from the focus. The method can be used at any position of the dish, but, when used with astronomical sources, it is severely limited by sensitivity and can only be envisaged for large dishes. The same principle can be used for ground-based sources with the dish pointing at the horizon (Anderson et al., 1979), and extension to use in conjunction with transmitters on satellites appears promising.

E. Overall Error Budget The efficiency of a dish is a function of its r m s deviation t as seen in Eq. (6). This deviation is the quadratic sum of the errors on the panels and the adjustment error. When the dish is in operation the gravitational deformation of the structure with elevation, the thermal deformation of the panels and of the structure, and eventually the effect of wind pressure must be added. An overall accuracy of 40 or 120 pm required for efficient operation at a wavelength of 1 or 3 mm allows partial errors on these various

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causes of the order of 20 or 60 pm, respectively. All partial errors should preferably stay in the same range, and efforts to reduce any dominating error to the average level will obviously pay off. Some compromise is at times acceptable; for instance, a limited range of elevation or of temperature gradient may still allow correct operation of a dish at a lower wavelength for a satisfactory fraction of observing time. Such a compromise, however, can seriously reduce the flexibility of the radiotelescope. F. Mount and Pointing There is nothing about mount and pointing peculiar to millimeter antennas except that a figure of the order of the second of arc is desired for pointing accuracy (Section V,B,3). Angular transducers and high-precision servos are industrially available in this range of accuracy. The problem is the accuracy of the antenna structure itself. The temperature gradient is easier to reduce by thermal insulation in the structure than on the reflecting surface, but the wind pressure and the residual deformation (hysteresis) after movements in azimuth or in elevation are the main causes of pointing errors. Reported accuracies for present dishes are in the range 4- 10". Occasionally there is some ambiguity in the reported figures. The figures may correspond to an rms or to a peak accuracy, or they may refer to absolute pointing or to tracking a source. In any case, these figures allow proper operation of the dishes, but their improvement would be valuable to the full utilization of large dishes at the lowest millimeter wavelength. G . Weather Protection

The high precision required in the construction of millimeter dishes, together with the severe climatic conditions found in high mountain sites, led to the use of permanent protection for some antennas. The radome has been adopted for the antennas designed by ESSCO (Sweden, Brazil, etc. ; see Table I). A metallic frame is covered by a thin plastic membrane transparent to the millimeter waves. The antenna is permanently protected from wind and precipitation and can be made lighter; its drives need less power and can be made more accurate. Maintenance and repair can be made regardless of weather conditions. These advantages are balanced by the loss of the radome (screening by metal and loss of the skin gives about 10% loss generally varying with frequency) and the associated radiation temperature. There are also some problems in getting a uniform temperature inside the radome and in minimizing water condensation inside and outside the radome skin. A more satisfactory but more expensive solution is the astrodome, comparable to those used in optical astronomy. The antenna is sheltered by a dome; a large sliding door is open during normal operating conditions,

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with the antenna working in open air. The whole structure must be able to rotate so that the door is always in front of the antenna. This requirement explains the high cost of an astrodome, which represents about half the total cost of an antenna system. On the other hand, the antenna for astrodome-protected structures is lighter (as it is for the radome protected ones) than for open-air antennas. Because of the very small number of existing antennas, comparisons are not well established. The present estimates suggest that for the same cost, there is a decrease of 20%in diameter between antennas in open air and under an astrodome. Overall the two approaches are equally used, and deciding between them is not simple. Streching a skin over a dish protects its surface; this limited solution introduces little loss with dishes of moderate diameter that allow the use of a thin skin (1% loss at 90 GHz for the 6-m-diameter dishes at the Hat Creek interferometer; see Table 11).For antennas on high mountains, an adequate protection should be provided, not only against high winds and snow, but also against icing and sticking snow. Heating is the obvious solution but requires a significant amount of power, in the range 200-400 W/m2. H . Summary

Sizable antennas for millimeter radioastronomy are still in a changing field. Better machining and adjustment of the reflecting surface is required through improvement of existing techniques or perhaps new approaches. A better pointing accuracy would ease operation, especially at the limit of submillimeter waves. An acceptable solution must be a compromise of various requirements: operation over a wide range of frequencies, ability for multibeam operation, low contribution of ground temperature, high aperture efficiency, and easy access to the receivers. The development of sophisticated quasi-optical circuitry may be a step closer to such a compromise, such as the use of offset dishes. More generally the cost of large millimeter antennas, up to about $10 million, will, it is hoped, stimulate some further research work for their optimization.

VII.

RECEIVERS

A. Introduction

The characteristics of the receivers designed for millimeter radioastronomy are similar to those of receivers for centimeter and decimeter

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radioastronomy. The major requirement is sensitivity. Stability is necessary to use the sensitivity fully: gain stability in most observations, and phase stability for interferometry and for polarization measurements. The bandwidth is in most cases not limited by man-made signals and can be made quite wider than at longer wavelengths. Even for line measurements where the bandwidth is fixed by astronomical considerations, it is wider than in centimeter and decimeter radioastronomy, because most natural spectral phenomena are Doppler widened and therefore have a given relative bandwidth : Their absolute bandwidth increases with frequency (see note with Fig. 2). We will focus in the following sections on sensitivity and on some aspects related to bandwidths. For the other characteristics of receivers the reader is referred to texts on radioastronomy or on microwave techniques. B. Bolometer

This device has a resistance that is variable with temperature. An increase of temperature is caused by the power of an incoming electromagnetic wave converted into heat. All information on the phase of such a wave is lost at the output of a bolometer: It is an incoherent detector. At the same time, a bolometer does not require good focusing when installed on an antenna. It is the power receiver on the bolometer surface which heats it, even if the phase of the signal is changing across this surface. Reflector telescopes with poor focusing, sometimes called collectors or “light buckets,” are therefore conveniently associated with bolometers, particularly for far infrared and submillimeter observations. The bolometers are still interesting at the edge of the millimeter region, at least when wideband observations are allowed. A bolometer’s sensitivity is generally characterized by its noise equivalent power, the NEP. If we take the ordinary parameter for sensitivity in iadioasrronomy, the system temperature T,, ,we have’ : NEP = kT,,,,/B

(7)

The loss of absorption efficiency of conventional bolometers in the submillimeter and millimeter region has led to composite bolometers, in which the energy absorption and temperature measuring functions are separated.

’

The NEP is the output noise power on a I-Hzband. Conventional receivers have their output noise determined by ATin Eq. (5). AT corresponds to a noise power of k ATE, where k is the Boltzmann constant and B the receiver bandwidth. We have then: NEP = k ATB = BkT,,/(BO)’/2= kT,,B’/* (as the NEP is defined for 1 Hz, 0 = 1 sec).

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The best among these bolometers (see, e.g., Soifer and Pipher, 1978; Coron, W/Hz’/’. 1976) have a NEP of about 5 x From Eq. (7), the same NEP is obtained by a system with a noise temperature of about 1500 K, on a bandwidth of 1 GHz. As the bolometer receives energy on a much wider bandwidth, its equivalent noise temperature becomes much higher than that of conventional receivers of identical sensitivity. Bolometers can compete with other receivers only for wideband continuum measurements.* It should be noted that bulk InSb bolometers have been used as mixers (Section VII,C,S) and SIS (superconductor-insulator-superconductor) junctions (Section VIII,B, 1) have been proposed (Richards et al., 1980) as photon detectors for the millimeter range.

C. Mixer 1. General The mixer is the basic element of most present receivers in millimeter radioastronomy. After a fast development in the 1940s(Pound, 1948;Torrey and Whitmer, 1948), not much work was done for about 20 years. Then steady progress occurred : the semiconductor material was improved ; the Schottky barrier mixer was introduced, allowing in particular better and more reliable contacting; the mixing process was theoretically studied in more detail; cryogenically cooled mixers were constructed. A review of these matters has been given recently by Schneider (1981). The mixer operation has been known for a long time: A nonlinear resistance, the mixer diode, is pumped by a local oscillator at a frequency VLo. The mixer output at an intermediate frequency KF is sensitive to signals at two frequencies, V, = VLo iKF and Vi = VLo - KF,the signal and image frequencies, respectively. For some types of observations both V , and Vi afford useful information. The receiver sensitivity can be defined in double sideband, TR(DSB). But more frequently, and in particular for line measurements, only one sideband is useful, and TR (SSB) is the relevant parameter. The noise power coming from the other sideband should be minimized. Theory has shown that mixer optimization is possible. The mixer is a multipole with input and output not only at the three main frequencies above, but also at other harmonic combinations of these frequencies. The optimization tends to send back, by proper reactive terminations, all the energy present on the unwanted frequencies to the useful ones.

* Fourier transform spectroscopy (see, e.g., Chamberlain, 1979) with incoherent detectors, such as the bolometer, is considered only when coherent receivers are not available.

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Theoretical studies have been made by Dragone (1968), Van der Ziel (19701, Saleh (1971), and Viola and Mattauch (1973). More recently the work of Held and Kerr (1978) uses a realistic model of mixer with its embedding network and gives results in good agreement with experience. A simplified model (Kerr, 1979) can be used provided the mixer diode has small series resistance and nonlinear capacitance. These assumptions are valid up to about 100 GHz with recent diodes. The mixer can then be considered as a lossy network at a temperature TA,with TA = nT/2, where n is the ideality factor of the diode,g and T its physical temperature. Good diodes have an ideality factor around 1.1. The conversion loss can ideally be 1 (0 dB) for a single sideband mixer, 2 for a double sideband mixer (Kelly, 1977)if the diode has no series resistance. With practical diodes the values of the series resistance and inductance and of the junction capacitance fix the minimum conversion loss and determine the highest usable frequency. Attaining good open or short circuit terminations for all unwanted harmonics is of particular importance in minimizing conversion losses which are typically 5 to 7 dB (see Table VI). 2. Mixer Diodes

The Schottky barrier epitaxial diode made of gallium arsenide is widely used. A number of diodes are prepared on the same chip, and one of them is contacted to be used in the mixer. Since the description of Young and Irvin (1969, efforts have been made to increase the diode cutoff frequency through a lower product of the series resistance R, by the junction capacitance Co (generally defined at zero bias). Typical values are R, 7 SZ, C, N lo-’ pF. For the lower end of the millimeter frequencies, larger diodes are made (diode diameter N 3 pm), which increase C, but decrease R, . At the highest end, the optimum size is of the order of 1 pm (McColl, 1977). The practical fabrication of the chips use the planar diode technique by etching the epitaxied material. In the last few years improvement has been made in several directions. The molecular beam epitaxy (MBE)has allowed Schneider et al. (1977) to obtain diodes with a precise control of the doping profile. This has resulted in better characteristics at ambient temperature The forward current voltage characteristicof a metal semiconductorjunction is described for the case of thermionic emission by: i = i,exp[(u/u,) - I ]

with u,, = nkT/q

where i, is saturation current, n ideality factor, k Boltzmann constant, Tjunction physical temperature, and q charge of an electron.

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and has also allowed the possibility of low doping to obtain “Mott” diodes, which are particularly interesting at low temperature (Linke et al., 1978; Keen et al., 1979) for their low noise and for low requirement of local oscillator power. The notch front diodes (Carlson et al., 1978) allows easy mounting on stripline: The chips are made thicker and are metallized on the side. These high-quality diodes are produced in small quantities for laboratory use and are rarely available commercially. 3. Mixer Assembly Most millimeter wave mixers for radioastronomy are made of a metal block, which is crossed by a reduced height waveguide and terminated by a variable short circuit. The mixer diode is contacted by a thin whisker wire (or sometimes soldered by a beam lead which is more stable, but which introduces parallel capacitance). Several techniques are used to support the diode and its whisker, to couple them to the waveguide, and to connect them through an rf filter to the IF output. One of these techniques is represented in Fig. 10. The diode characteristics are the key parameters, and the various supporting techniques give similar results when used with comparablediodes. The length of waveguide between *themixer and the feed system at the radiotelescope focus should be made as short as possible. Millimeter waveguides are lossy and can significantly degrade the system temperature

INPUT WAV EGU I 0 E

FIG.10. A typical mixer mount. [From Schneider (1981).]

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compared to the receiver temperature, as the atmosphere does to effective system temperature compared to system temperature (Section IV,A,6). The waveguide circuitry in front of the mixer is therefore made as simple and short as possible, and in particular an image frequency rejection filter is generally not used (or a directional coupler for LO injection). Image rejection is, however, possible through proper adjustment of the short circuit behind the diode (Linke et af., 1978). The position is such that the image frequency is short-circuited on the diode (rejection of 18 dB is possible), and a proper impedance is obtained on the signal frequency. Now that mixer construction is well in hand, and the operation of mixers is well understood, some refinements are probably to be expected, in particular optimizing the conversion loss by proper termination at the harmonic frequencies. 4. Mixers in Current Use

The basic mixer indicated previously can be used at room temperature. A typical system is described by Cong et al., (1979). Significant improvement in receiver temperature is obtained when the mixer and the first IF stage are cooled to about 15 K. This is conveniently achieved by commercial closed cycle refrigerators and with established cryogenic techniques. (see, e.g., Linke et af., 1978). The first IF stage is currently a parametric amplifier, well known particularly in centimeter/decimeter radioastronomy. Typical noise temperatures of such amplifiers are 50-100 K at ambient temperature and 15-20 K when cooled. Recently some FET amplifiers have reached similar performances, cooled and uncooled. The IF is selected from a compromise between a high value, which eases image frequency rejection, and a low value, which is better for IF noise. It is commonly around 1 or 4 GHz. The instantaneous bandwidth of the front end of millimeter receivers is limited by various considerations to values of the order of 1 GHz. We will see in the next section that the local oscillator sources and the LO injection in the mixer pose some problems. They are eased when a subharmonicallypumped mixer is used. Two mixer diodes are shunt mounted with opposite polarities. They give similar noise performance as a single ended mixer, but with an LO frequency at half its normal value (Carlson et al., 1978). They still operate (with increased conversion loss) with an LO frequency at one-fourth its normal value. The advantages of the subharmonic mixer are practical : in particular easy separation of LO and signal circuits. These advantages are balanced by the extra difficulty of mounting two diodes. The state of the art in mixer performance is summarized in Table VI.

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TABLE VI MIXERAND RECEIVERPERFORMANCE (SINGLE SIDEBAND)

Frequency (GH4 85 115 115 170 170 230 21OC

300

Mixer loss (dB)

Receiver temperature"

(K)

Mixer temperature (K)

15 300 I5 300 15 300 300 300

100/200b 700 200 1300 2200 1800 2600

817 6 7 8

25O/3OOb 900 300 1600 600 2700 2300 3000

Operating temperature

-

-9 10 -9

(K)

IF temperature is about 50 K for receiver operating at ambient temperature and 20 K for receivers cooled at 15 K. First figures are the best values reported at 85 GHz, second figures are values reported by several laboratories. Subharmonically pumped mixer.

5. Other Types of Mixers Bulk indium antimonide mixers at liquid helium temperatures show low noise and conversion loss properties, but their IF bandwidths are very limited (to about 1 MHz) by the relaxation time of the hot electrons. They are used for isolated line detection at the edge of the submillimeter band (see, e.g., Phillips et al., 1977). Phenomena in superconductive materials have been investigated; the Josephson effect can be used in a mixing process. This has been confirmed by laboratory tests, but the construction of a practical mixer appears extremely difficult. The superconductor-insulatorsuperconductor (SIS)junction appears as a serious alternative as is discussed in Section VIII. D . Local Oscillator 1. General

The klystrons are the most widely used LO source. They are easily tunable, they produce a relatively noise-free signal, and their technique is well established. On the other hand, the millimeter wave klystrons are expensive, and their expected lifetime is relatively short : 1500 hr is an average around 100 GHz. Their delivery time is often long because they are manufactured in small quantities by a few companies. Up to about 100GHz, solid state LO sources are available. The Gunn oscillator delivers enough

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power with limited noise, but its upper frequency limit is about 60 GHz. The impatt oscillator has a higher power output, but is intrinsically noisy. Millimeter wave receiver operation would be eased greatly by improved solid state sources, but the progress on these devices has proved to be slow in recent years. The backward wave tubes (or carcinotrons) are only considered for the upper millimeter frequencies. They have a wide electrical tuning range, sometimes up to one octave, and deliver adequate power level. However, the cost of operation per hour is high-comparable to klystrons-and their production is not well established. Long life is probably possible with low power backward wave oscillators. It is difficult to predict the relative value of these LO sources for radioastronomy in the coming years. It depends much on the industrial efforts in their development and perhaps on the availability of other sources (see, e.g., Button, 1979). An alternative is to use frequency multiplication of some subharmonic LO source. The efficiency of such multiplicators can be relatively high, at least on a limited frequency range. The availability of adequate LO sources is in any case still a problem. For instance, at frequencies over about 150 GHz, mixers have been often operated with degraded performances because of insufficient power level of the LO sources. 2. LO Stability

The frequency stability of klystrons and Gunn oscillators is in principle good enough to allow their use as free oscillators for continuum measurements. In practice most millimeter radioastronomy receivers perform both continuum and line measurements, and therefore require excellent frequency stability. For instance, some natural maser lines have linewidths of the order of kilohertz. This means that the relative error for the frequency of the receiver must be of the order of lo-*. The local oscillator frequency should be controlled by a reference oscillator. This is accomplished by the conventional phase lock method. However, millimeter wave sources show a wider noise spectrum than at lower frequencies. The phase lock loop must have a wide band to react fast enough. Adequate phase lock systems are in operation, but their development and the control of their operation have proved to be somewhat difficult to achieve (see, e.g., Henry, 1976). In the case of millimeter interferometers, phase locking is the only technique that allows production of coherent local oscillators signals on separate antennas. The frequency of a reference oscillator is transmitted to each antenna, where the oscilhtors are phase locked to this reference (Section V,D,3).

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3. LO Injection The injection of the LO in the mixer, without significant losses in the signal line, is easily made in the balanced mixer that uses a magic T or equivalent, and is currently used in microwaves. An added advantage is the cancellation of eventual LO noise within the limit given by the symmetry of the circuits. All these advantages apply to the subharmonically pumped mixer. For single-ended mixers, which are easier to construct on millimeter waves, two methods of LO injection are used. The resonant cavity method is applied for the lower frequencies. A cavity is coupled to the input waveguide of the mixer. It is tuned to the LO frequency and is seen by the signal wave as a reactive element, introducing small losses. In the same time the LO frequency is properly coupled to the cavity and then to the waveguide, and attenuated by a few decibels. The cavity has an additional advantage, because it acts as a high Q filter for the eventual noise sidebands of the LO wave. The injection cavity is a high-precision mechanical piece. Over 100 GHz its construction becomes increasingly difficult. The quasi-optical injection method is therefore preferred (see, e.g., Goldsmith, 1977).

E. Receiver Back Ends for Spectroscopy

The values of bandwidth required for spectroscopy in millimeter radioastronomy lead to spectroscopic systems that are sometimes different than those in radioastronomy at longer wavelength. Radial velocities in an external galaxy or in the galactic center give Doppler shift proportional to frequency and corresponding to about 100 MHz at 100 GHz. The spectrograph should be 1.5 to 2 times wider to be able to measure a line spectrum against a low level continuum background. But a spectrograph should also be able to analyze much narrower bandwidths, down to a few KHz, in the case of maser line emission. Banks of filters are used for wideband observation, with a typical channel width of 0.25- 1 MHz. A spectrograph is made of 100-500 adjacent channels. Most filter spectrographs work as follows: The IF input can be at the first IF, coming from the rf head, or at a lower value, after a second frequency change. Then a number of mixers translate adjacent sections of the whole bandwidth to the same number of groups of filters, all groups being identical, which eases their construction. Stable and reliable spectrographs built along these lines are in current use. However, their cost per channel is relatively high and they are not flexible. For each channel bandwidth a complete bank of filters is necessary. With a spectrum expander (Henry, 1979), however, this is no longer true.

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Basically, the spectrum expander records the signal to be analyzed and plays it back faster than recorded. If a signal on a bandwidth of 3 MHz is speeded up to 10 times, it can be analyzed in a spectrograph havinga 30-MHz bandwidth. A given filter bank can be “adjusted” in this way to any bandwidth narrower than its actual bandwidth. The spectrum expander now in operation on Bell Laboratories 7-m dish uses digital techniques with registers. Its maximum bandwidth is 32 MHz. The bandwidth to be analyzed can be made narrower by steps of 2 MHz from the maximum 32 MHz. The digital correlator, widely used in radioastronomy at longer wavelengths, is presently limited to total bandwidth of the order of 80 MHz, clock frequency at 160 MHz. In principle present digital techniques authorize higher speed and wider bandwidth, but no practical model has yet been built, because of the cost and the difficulty in handling a large number of very high-speed digital circuits synchronously and reliably. A completely different approach is the acoustico-optical spectrograph (AOS) (Cole, 1979), sketched in Fig. 11, which is usable in single-dish observations. An ultrasonic standing wave system is produced in a Bragg cell activated by a transducer, which is driven by the signal to analyze. A laser beam is deflected through the Bragg cell, and the resulting pattern is detected by an array of diodes. This is equivalent to a spectrograph with as many channels as diodes. With the present techniques, a wide total bandwidth, up to about 300 MHz and a large number of channels--1000 or more-are feasible. This is quite satisfactory for the largest bandwidth required in millimeter radioastronomy. AOSs are simple and much cheaper than other spectrographs, but their bandwidth is not adjustable, as for filter banks. Present efforts are concerned with control of the frequency drifts caused by temperature changes and with mechanical instability, which still make the practical use of AOS difficult. There is no spectrograph model that properly answers all the needs of millimeter radioastronomy. The bandwidth range is too large, and hybrid systems are presently used : filters for wide bands associated with digital correlator and spectrum expander for narrower bands. BEAM

BRAGG CELL

PHOTODIODE ARRAY

TELESCOPE

TO A/D CONVERTER FIG.1 I . Principle of the acoustico-optical spectrograph.

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VIII. EVOLUTION AND PROJECTS A . Introduction The rapid and successful development of millimeter radioastronomy has inspired a number of new projects. Some of them will supersede by a large factor the collecting area of the present instruments and/or will have a surface accuracy that allows efficient observations to a wavelength of 1 mm. This development is being made in parallel with improvements in the system temperature of the radiotelescopes through better receivers and observing sites at higher altitudes. Millimeter radioastronomy is still far from the natural limits of sensitivity and resolving power, but with the current progress, this will not remain true for long. Millimeter radioastronomy should reach in the foreseeable future a situation comparable with that of centimeter and decimeter radioastronomy. Large projects should produce a great number of astrophysical results and should be open to use by a wide community of scientists. The organizational and financial effort that these projects imply are additional factors that will tend to slow down the evolution of millimeter radioastronomy after the completion of the present generation of instruments. B. Receivers This essential part of the radiotelescope is currently improving in several directions. 1. Superconducting Mixers Superconducting mixers are being tested in some laboratories. The most promising device appears to be the SIS junction (see, e.g., Dolan et al., 1979; Rudner and Claeson, 1979; BMS, 1980). It uses the sharp quasi-particle nonlinearity of a superconductive tunnel junction in the mixing process which may lead to extremely low conversion loss. Even some gain is possible (Shen et al., 1980; Tucker, 1980). A theory of these junctions has been worked out (Tucker, 1979), and they are potentially more sensitive then the conventional Schottky mixer diodes, particularly because they operate at temperature of a few K, with the correspondingly low thermal noise. The construction of practical SIS mixers faces metallurgical difficulties of realizing the junction, generally between two thin films of lead isolated by an oxide barrier. Another problem is the saturation of the junction which occurs at extremely low power level. This has a favorable counterpart, the

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need of a very low level of local oscillator power, of the order of a microwatt or even less. The dynamic range can be improved by mounting arrays of junctions. Successful tests of SIS mixers have been reported at 36, 76, 115, and 230 GHz,with mixer temperatures of 10,30,60, and 350 K, respectively, and low conversion losses or slight gain.

2. Quasi-Optical Components Quasi-optical components in front of the mixer appear to be the most suitable circuit elements over about 100 GHz, provided that Gaussian beams are available. In particular, dishes with high focal ratio (at the Cassegrain focus) produce in the focal region a beam of quasi-parallel rays along a waist suitable for quasi-optical components. These components have low losses compared with waveguide components and can perform all the needed functions : filtering, diplexing, switching, polarization selection, and calibration. As an example, Fig. 12 shows a local oscillator injection system (Payne and Wordeman, 1978).

3. Local Oscillator Sources Local oscillator sources are shifting to solid state for two main reasons. The SIS mixers just discussed require low LO power levels, as do to a lesser degree the Mott mixer diodes (Keen et al., 1979). Such levels can be obtained

Signal kAlF/4 Mirror

.

4 Local o s c ilia t o r

Mixer

Mirror

FIG. 12. Example of quasi-optical circuit (dual-beam interferometer) at mixer input. The fully reflecting mirrors are set at distance k1,,/4 from half reflecting mirrors, where k is an integer.

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from the frequency of currently available solid state sources, multiplied by harmonic generators. The design of these harmonic generators is also progressing, with a better understanding of the optimization procedure and of possible broadband operation. 4. The First IF Stages The first IF stages following the mixer used to be parametric amplifiers, often cooled to 15 K. Recent results show that cooled FET amplifiers reach comparable sensitivity,i.e., noise temperature of the order of 20 K (Weinreb, 1980) for IFs in the range 1-4 GHz. FET amplifiers are small, simple, and stable, and require only a dc power supply. Their use makes the rf head smaller and lighter. C . Improvements or Extension of Existing Radiotelescopes

Installation of a low-noise SIS mixer is planned to improve sensitivity in particular on the 7-m dish at Bell Laboratories, on the 20-m dish at Onsala, Sweden, and on the 10.4-m dish at Cal Tech. Decrease of system temperature by a factor of at least 2 is expected from this change. The extension of two interferometers is under way at Cal Tech, which is now two 10.4-m dishes, and will be three 10.4-m dishes in 1981 ; and at Hat Creek, which is two 6-m dishes now, and will be three 6-m dishes in 1981. Remember that the addition of a third dish to a single baseline interferometer increases its speed of observation by a factor of 3. A three-antenna interferometer can simultaneously use three independent baselines, compared with one for a simple two-antenna interferometer. The Cal Tech interferometerwill also have its maximum baseline extended to a symmetrical T, 450 m North-South, 400 m East-West. D . Construction of New Millimeter Single Dish Radiotelescopes 1. 10.4-m Dish at the California Institute of Technology

After the successfulconstruction of the 10.4-m dishes to be used mainly in interferometry, the same design pushed to its ultimate accuracy will be used to build a submillimeter dish. Extreme precision in the machining and control of the dish surface is expected to give an accuracy of a few micrometers. This, with the back structure deformation partly controlled by heating, should allow an overall accuracy of about 20 pm, in stable weather conditions. The dish should be excellent for observations at l-mm wavelength

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and usable for observations in the 300-pm atmospheric window. This would only be possible with very low water vapor content, and the plan is to install the dish under an astrodome on Mauna Kea, Hawaii. Completion is expected for 1982-1983.

2. 15-m Dish in the United Kingdom (Science Research Councio This project was approved in mid- 1980 and will be erected in the Canary Islands at Las Palmas, on a site jointly developed by several European countries. The altitude is 2400 m, and the estimated construction cost is close to $10 million, excluding personnel cost. The homologous back structure will be enclosed with an internal circulation of air to limit temperature gradients. The surface panels will be made of aluminum honeycomb formed on templates. The dish will be housed in a shelter, intermediate between a radome and an astrodome; the shelter will be fully closed like a radome, but rotating like an astrodome, with a thin, low loss membrane, always facing the dish. The specified overall accuracy is 50 pm. 3. 25-m Dish Project of NRAO This project is not yet approved. It would be built in Hawaii on Mauna Kea, at an estimated cost of about $25 million. An elaborate astrodome is planned, allowing relatively light construction of the dish itself. The specified overall surface accuracy is 70 pm. 4. 30-mDish at

IRAM

IRAM is a recently established French-German Institute with its headquarters in Grenoble, France. The construction of a 30-m millimeter radiotelescope in southern Spain, near Granada, is in progress. The dish has been designed in West Germany by a consortium of the Krupp and M.A.N. companies, under the responsibility of the Max-Planck-Institut fiir Radioastronomie, in Bonn. The telescope site is at an altitude of 2850 m, latitude 37”N. Since the central hub is rigid, the dish will have quasi-homologous deformations. The receiver cabin will be located under the elevation axis and will not move in elevation (Fig. 13). A quasi-optical system of mirrors will transmit the beam from the Cassegrain subreflector to the receivers through the hub. The dish will be working in the open air with provision for deicing the surface by heating resistors and for equalizing the temperature inside the closed back structure by circulating air. The surface will be made of aluminum honeycomb. The specificationsare 100pm for surfaceaccuracy, and 1” for pointing accuracy, with the ability to operate in winds up to

156

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Cone r e t e

w

FIG.13. Sketch of IRAM 30-m dish. Side view shows the complete insulation of the structure.

14 m/sec. The overall cost of the project is close to $20 million, and completion is planned for 1983.

5 . 45-m Dish in Japan The Tokyo Observatory has the responsibility for this large radiotelescope, which should be completed by 1982 (Plate 3). The site is at an altitude of 1350 m, latitude 36"N (Nobeyama). The structure is homologous

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PLATE3. An artistic view of the 45-m radiotelescope under construction at Nobeyama, Japan. The tube for beam transport is seen in the foreground of the pedestal.

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around a rigid central hub and will be operated in the open air. Temperature effects will be decreased by insulating the back structure, circulating air inside, and using honeycomb sandwich panels with carbon fiber skin in the inner 30 m of the dish. Prime focus operation will be used for centimeter and possibly decimeter observation. For millimeter wave observation, the receivers will be placed in a cabin at ground level. The beam will be transported through a quasi-optical system of mirrors enclosed in tubes, comparable to the Coudt arrangement in optical telescopes. The expected surface accuracy is between 120 and 200 pm, the specified pointing accuracy is 2” for operation in winds up to 7 m/sec. E. Construction of New Millimeter Interferometers

1. Five-Element Interferometer in Japan This instrument is being built at the same site as the 45-m dish mentioned previously. The five dishes will have a diameter of 10m and a surface accuracy of 100 pm. They will be transportable on any of the 30 stations installed on two baselines, one 560 m East-West, the other 520 m, 33O from North-South. The optics are as in the 45-m dish (Cassegrain-Coude). The transmission of the local oscillator reference signal and of the intermediate frequency signal will use cables running through a tunnel. The spectral system will be a digital correlator. Provision is being made to include the 45-m dish as an element of the interferometer. Completion is expected by 1983. 2. Three-Element Interferometer at IRAM The site is on a plateau at an altitude of 2550 m, latitude 44”N, not far from IRAM headquarters in Grenoble. The diameter of the three dishes will be 15 m, and the goal for the surface accuracy is 50 pm. Open air operation with provision for deicing is planned. The surface measurements will be made under a large shelter, where all three dishes could be stored later. In a first stage, the baselines will be 200 m East-West and North-South. Extensions up to 1750 m East-West and 800 m North-South are possible. Completion is expected in 1985-1986, at a cost of about $20 million. F. Conclusion

The main characteristics of these projects are summarized in Table VII. Comparison with Tables I and I1 shows that in about 5 years from now the total available receiving area of the millimeter instruments in the world will

159

RADIOASTRONOMY AT MILLIMETER WAVELENGTHS TABLE VII PROJECTS' MAINMILLIMETER RADIOTELESCOPE

Organization Cal Tech S.R.C. NRAO IRAM IRAM Tokyo Observatory

Antenna diameter (m) 10.4

15 25 30 3 x 15 45 5 x 10

Expected surface accuracy (rm) 20 50 70 100 50

150 100

Site, altitude, latitude Mauna Kea, 4200 m, 19"N

Expected completion

Las Palmas, 2400 m, 28"N

1982-1983 1985

Mauna Kea, 4200 m, 19"N Pic0 Veleta, 2850 m, 37"N Plateau de Bure, 2550 m, 44"N Nobeyama, 1350 m, 36"N Nobeyama, 1350 m, 36"N

1983 1985-1986 1982 1983

b

Extension of the Cal Tech and the Berkeley interferometers (Table 11) by a third dish is underway. Construction not yet approved.

'

go from 1000 mz to 4000 mz for single dishes, and from 350 mz to 1600 m2 for interferometers. These rough figures are not fully comparable; nevertheless they give a correct estimate of the effort of the scientific community in the domain of millimeter radioastronomy. This effort is justified by the astrophysical results obtained in the past 10 years. It is backed by the value of the interaction that exists between astrophysics and other domains of research and development. In millimeter radioastronomy, the fields for this interaction are, for instance, molecular physics and physical chemistry with the analysis of the observation of molecular lines; electronics and physics with the superconducting receivers ; mechanical engineering with the construction and measurement of highly accurate dishes; and atmospheric research with the analysis of atmospheric effects on astronomical observations. From the point of view of the astrophysicist, there is no doubt that with improved receivers now coming from the laboratories, with larger dishes, and better resolving power, millimeter radioastronomy will maintain a high output of new results for many years to come.

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Jennisson, R. C. (1958). Mon. Not. R. Astron. SOC.118, 276. Kardashev, N. S. (1979). Nature (London)278,28. Kaufmann, P., Schaal, R. E., and Raffaelli, J. C. (1978). IEEE Trans. Antennas Propag. AP-26, 854. Kelly, A. J. (1977). IEEE Trans. Microwave Theory Tech. MTT-25, 867. Keen, N. G., Kelly, W. M., and Wrixon, G. T. (1979). Electron. Lett. 15, 689. Kerr, A. R. (1979). IEEE Trans. Microwave Theory Tech. MTT-27, 135. Klemperer, W. (1970). Nature (London) 227, 1230. Kuiper, G. P. (1970). Comm. Lunar Plan. Lab. 8, 121. Lee, T. P., and Burrus, C. A. (1968). IEEE Trans. Microwave Theory Tech. MTT-16,287. Lee, J. J., Parad, L. I., and Chu, R. S. (1979). IEEE Trans. Antennas Propag. AP-27, 165. Leighton, R. B. (1978). Final technical report for NSF Grant AST. 73 04 908. Linke, R. A., Schneider, M. V., and Cho, A. Y. (1978). IEEE Trans. Microwave Theory Tech. MTT-M,935. Lo, L. I., Fanin, B.M., and Straiton, A. W. (1975). IEEE Trans. Antennas Propag. AP-23,782. Lovas, F. J., Johnson, D. K., and Snyder, L. E. (1979). Astrophys. J. Suppl. 41,451. Love, A. W. (1978). “Reflector Antennas.” IEEE Press. McColl, M. (1977). IEEE Trans. Microwave Theory Tech. MTT-25,54. McColl, M., Millea, M. F., Munushian, S., and Kyser, D. F. (1967). Proc. IEEE 55, 2169. Mann, A. P. C., and Williams, D. A. (1980). Nature (London)283,721. Mar, J. W., and Liebowitz, H. (1969). “Structure Technology for Large Radio and Radar Telescopes Systems.” MIT Press, Cambridge, Massachusetts. Meeks, M. L., ed. (1976). “Methods of Experimental Physics,” Vol. 12. Academic Press, New York. Menzel, D. H. (1976). Sky Telex. 52,240. Morris, D. (1978). Astron. Astrophys. 67,221. Payne, J . M., and Wordeman, M. R. (1978). Rev. Sci. Instrum. 49, 1741. Payne, J. M., Hollis, J. M., and Findlay, J. W. (1976). Rev. Sci. Instrum. 47, 50. Penzias, A. A., and Burrus, C. A. (1973). Annu. Rev. Astron. Astrophys. 11,51-72. Penzias, A. A., and Wilson, R. W. (1965). Astrophys. J . 142,419. Phillips, T. G., Huggins, P. J., Neugebauer, G., and Werner, M. W. (1977). Astrophys. J . 217, L 161. Pound, R. V. (1948). “Microwave Mixers.” MIT Rad. Lab. Serie, Vol. 16. McGraw-Hill, New York. Pulkovo Izvestia (1972). Glav. Astron. Obs. Leningrad No. 188. Rank, D. M., Townes, C. H., and Welch, W. J. (1971). Science 174, 1083. Readhead, A. C. S., and Wilkinson, P. N. (1978). Astrophys. J . 223,25. Readhead, A. C. S., Napier, P. J., and Bignell, R. C. (1980a). Astrophys. J. Lett. 237, L 55. Readhead, A. C. S., Walker, R. C., Pearson, T. J., and Cohen, M. H. (1980b). Nature (London) 285, 137. Richards, P. L., Shen, T. M., Harris, R. E., and Lloyd, F. L. (1980). Appl. Phys. Lett. 36,480. Rogers, A. E. E., et al. (1974). Astrophys. J . 193,293. Roosen, R. G., and Angione, R. J. (1977). Publ. Astron. SOC.Pac. 89,814. Rudge, A. W., and Adatia, N. A. (1978). Proc. IEEE66, 1592. Rudner, S., and Claeson, T. (1979). Appl. Phys. Lett. 34,711. Ruze, J. (19661. Proc. IEEE 54,633. Ruze, J. (1978). Preceding paper reprinted with companion papers. In “Reflector Antennas” (A. W. Love, ed.). IEEE press. Ryle, M., and Elsmore, B. (1973). Mon. Nor. R . Astron. SOC.164,223.

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Saleh, A. A. M. (1971).“Theory of Resistive Mixers.” MIT Press, Cambridge Massachusetts. Schneider, M. V. (1981). In “Infrared and Millimeter Waves” (K. J. Button, ed.). Academic Press, New York. Schneider, M. V., Linke, R. A., and Cho, A. Y. (1977).Appl. Phys. Lett. 31,219. Schooneveld,C., van, ed. (1979).“Image Formation from Coherence Functions in Astronomy.” Reidel, Dordrecht. Scott, P., and Ryfe, M. (1977). Mon.Not. R . Astron. SOC.178,539. Shen, T. M., Richards, P. L., Harris, R. E., and Lloyd, F. L. (1980). Appl. Phys. Lett. 36,777. Shenton, D., and Hills, R. (1976).In “A proposal for a U.K. Millimeter Wavelength Astronomy Facility,” SRC report quoted by Von Hoerner (ZEEE Truns. Antennas Propug.AP-26,857). Smoot, G . F., and Lubin, P. M. (1979).Astrophys. J. 234,L83. Snyder, L. E., Hollis, J. M., Lovas, F. J., and Ulich, B. L. (1976).Astrophys. J . 209,67. Soifer, B. T., and Pipher, S.L. (1978).Annu. Reu. Astron. Astrophys. 16, 335. Torrey, H. C.,and Whitmer, C. A. (1948).“Crystal Rectifiers,” MIT Rad. Lab. Serie Vol. 15. McGraw-Hill, New York. Townes, C. H. (1957).Symp. Int. Astron. Union,No. 4,p. 92. Tucker, J. R. (1979).IEEE J. Quantum Electron. QE-15,1234. Tucker, J. R. (1980).Appl. Phys. Lett. 36,477. Ulich, B. L.,and Haas, R. W. (1976).Astrophys. J. Suppl. 30,247. Ulich, B.L.,Davis, J. H., Rhodes, P. L., and Hollis, J. M. (1980).IEEE Trans. Antennas Propag. AP-28,367. Van der Ziel, A. (1970). “Noise: Source Characterisation and Measurements.” Prentice-Hall, New York. Van Vleck, J. H. (1947).Phys. Reu. 71,425. Viola, T. S.,and Mattauch, R. J. (1973).J. Appl. Phys. 44,2805. Von Hoerner, S. (1967a). Astron. J . 72, 35. Von Hoerner, S. (1967b).J. Strucr. Diu. Proc. Am. SOC.Eng. 93,461. Von Hoerner, S. (1969). In “Structures Technology for Large Radio and Radar Telescope Systems” (J. W. Mar and H. Lievowitz, eds.), p. 311. MIT Press, Cambridge, Massachusetts. Von Hoerner, S. (1975).Astron. Astrophys. 41, 301. Von Hoerner, S. (1977). Vistas Astron. 20,411. Von Hoerner, S. (1978). ZEEE Trans. Antennas Propag. AP-26,464. Wannier, P. G.,Leighton, R. B., Knapp, G. R., Redman, R. O., Phillips, T. G., and Huggins, P. J. (1979).Astrophys. J . 230, 149. Waters, J. (1976). Methods Exp. Phys. 12B, 142 Watson, W. D. (1974). In “Atomic and Molecular Physics and the Interstellar Matter” (R. Balian, P. Encrenaz, and J. Lequeux, eds.). North-Holland Publ., Amsterdam. Weinreb, S. (1980).IEEE Trans. Microwaue Theory Tech. MTT-28, 1041. Welch, W. J., Forster, J. R., Dreher, J., Hoffman, W., Thornton, D. D., and Wright, M. C. M. (1977).Astron. Astrophys. 59, 379. Westwater, R. (1978). Radio Sci.13,677. Wilson, R. W., Jefferts, K. B., and Penzias, A. A. (1970).Astrophys. J. 161, L43. Wilson, R. W., Penzias, A. A., Jefferts, K. B., and Solomon, P. M. (1973). Astrophys. J. 179, L107. Wood, P. J. (1980).In “Reflector Antenna Analysis and Design” (p. Pelegrinus, ed.). Woods, R. C., Dixon, T. A., Saykally, R. J., and Szanto, P. G. (1975).Phys. Rev. Lett. 35,1269. Young, D. T., and Irvin, J. C. (1965).Proc. IEEE 53,2130.

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS,VOLUME 56

Pbotovoltaic Effect RICHARD H. BUBE

AND

ALAN L. FAHRENBRUCH

Department of Materials Science and Engineering Stanford University Stanford, California

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

A. Derivation of the Transport Equation . . . .................... B. Solution of the Transport Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Other Contributions to Current Generation . . . . . . . . . . . IV. Junction Currents B. Heterojunctions.. . . . . . . . . . . . . C. Schottky Bamers . . . . . . . . .

163 166 166 171 174 179 189 190 191 193 193 193

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194

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198 198 200 200 201 204 206 208 209 209 210 21 1

V. Examples of Photovoltaic Materials Systems . . . ........... A. Silicon ...............................................................

C. Cu,S/CdS Thin-Film Heterojunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Indium Phosphide.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Cadmium Telluride. . . . . . . , . ..................... F. CuInSe, ............................................................. G. Other Possible Materials of Promise . . . ................. References ..............................................................

I. INTRODUCTION The photovoltaic effect is one of several fundamental photoeffects involving the interaction of light with solid state materials. Other related effects are photoconductivity, photoluminescence, and photoemission. In photoconductivity, the absorption of light that increases the density of free carriers in a material with an applied electric field results in an increase in conductivity. In photoluminescence, the absorption of light that raises electrons to excited states, either free or localized, results in the emission of luminescence when these excited electrons return to their ground state with 163 Copyri ht 0 1981 by Academic Press, Ioc. All rights ofreproduction in any form reserved. ISBN 0-12-014656-8

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the release of their energy as light. In photoemission, the absorption of light that creates free carriers with sufficient energy to pass over a surface or interface barrier results in the emission of electrons from the material into a vacuum (external photoemission) or into a second material (internal photoemission) All three of these phenomena may be observed with only homogeneous materials (although, of course, they may also occur in materials containing internal junction fields), but the photovoltaic effect requires an internal junction field in the material for its observation. The photovoltaic effect is therefore most often associated with the presence of junctions in semiconductor materials, which act to separate the carriers generated by absorption of light in order to produce a conversion of the power from the absorbed light into electric power. In many ways the process of photovoltaic power generation can be thought of as the inverse of the process of electroluminescence; in electroluminescencean applied electric field that forwardbiases a semiconductor junction leads to the generation of luminescence emission, whereas in the photovoltaic effect, absorption of radiation leads to the generation of an electric field, in all but a short-circuit configuration. The photovoltaic effect received relatively little general attention for many years after its initial discovery in the midnineteenth century. The actual origin of the effect should probably be traced back to the work of Bequerel (I), who in 1839 discovered that shining a light on an electrode in an electrolyte solution led to the generation of a photovoltage. Forty years later Adams and Day (2) observed a similar effect in the solid material selenium, within a few years of the date that Willoughby Smith discovered photoconductivity in this material (3). For many years only selenium and cuprous oxide were known to give rise to the effect, and it was not until about 1914 that it was realized that an energy barrier was involved in both types of cell. The selenium photovoltaic cell was used for photographic exposure meters and achieved a conversion efficiency of about 1% for solar radiation. The conversion efficiency of a photovoltaic device is expressed as the ratio of the maximum power generated by the cell to the total radiation power incident on the cell. The outbreak of interest in the space program with the application of photovoltaic cells to power space vehicles gave a fresh impetus to research on photovoltaics. Single crystal silicon was the first material used; in 1954 a solar conversion efficiency of 6% had been reported (4,which was rapidly increased to 14% within four years. Another single crystal cell based on gallium arsenide was reported to have an efficiency of 4% in 1956 (5), and the efficiency of this cell has since been increased to 24% by taking advantage of new technology. Although space applications did not have cost considerations as a primary factor, they did have concerns for weight and flexibility; these considerations led to the investigation of thin-film photovoltaic cells.

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The cuprous sulfide-cadmium sulfide heterojunction cell, first reported with an efficiencyof 6% in 1954 (6),has had its efficiencyincreased by concentrated research to over 9% in 1980 (7). Photovoltaic research suffered a hiatus when the space program ceased to have top priority. Within a few years, however, the realization of the need for new energy sources has given an entire new life to photovoltaics research, in which basic considerations of efficiency, cost, freedom from toxicity, material availability in large quantities, and cell stability for long operating times have all become combined in a complex phenomenon involving the physical sciences, the social sciences, and political considerations. The Department of Energy has founded the Solar Energy Research Institute in Golden, Colorado, and photovoltaic research is a part of the charter of this institute. As a result the number of investigators and the interest in photovoltaics has increased by orders of magnitude over the past decade. As is common in such cases, there has also been an information explosion on photovoltaics, with a proliferation of books, whole journals, and literature, which makes comprehensive review an all but impossible task. The first major book heralding the new interest was Hovel’s research treatise published in 1975 (8).Since then many other books and special journal issues have been added to the growing list of reviews of photovoltaics research (9-24). Because of the magnitude of the task faced by a review in this area, this particular review is limited to solid state semiconductor junctions. Brief notice should be taken, however, of a variety of other photovoltaic effects of interest and/or significance. One of the oldest and most frequently explored effects is the so-called anomalous photovoltaic effect in which the measured open-circuit voltages often exceed the band gap of the material by an order of magnitude or more (25-33); the effect apparently arises from many junctions being present in the material, perhaps from crystallographic defects, adding in series. In the thermophotovoltaic effect, concentrated radiation is used to heat a metallic radiator which in turn illuminates a specially constructed photovoltaic cell (34); the goal is to make a better match between the spectral output of the radiator and the solar cell than exists between the solar spectrum and the solar cell, and to trap photons with energy less than the band gap of the solar cell material in order to help heat the radiator. An idealized model indicates a maximum theoretical efficiency of about 50% for a silicon solar cell and a radiator at 2200 K ; efficiencies of 26% have been achieved to date experimentally. Photoelectrochemical effects, following Becquerel’s initial discovery, are also being investigated; these involve the existence of a junction between a semiconductor and an electrolyte rather than a junction between or within semiconductors ( 3 3 , and are related to the fundamental process that has produced many of our

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traditional energy sources: photosynthesis. There are three major types of photoelectrochemical cells: (a) a photovoltaic cell, in which the chemical system is unchanged and only electrical power is extracted; ( b ) a photoelectrolysis cell, in which energy is extracted in the form of chemical redox reaction products (e.g., photoelectrolysis of water to produce H, and 0,); and (c) a photogalvanic cell (36),in which light absorption takes place in the electrolyte rather than in the semiconductor, and electrical power is subsequently generated by charge transfer to the electrode by a photooxidized or photoreduced molecule diffusing from the electrolyte. 11. AN OVERVIEW OF PHOTOVOLTAIC EFFECTS

In this section we give an overall survey of the types of semiconductor junctions involved in photovoltaic effects and the major processes and mechanisms that control junction currents and cell performance. A . Tjpes of Semiconductor Junctions

It is convenient to distinguish between four types of semiconductor junctions relevant to photovoltaic effects : (a) homojunctions, (/I) heterojunctions, (c) buried or heteroface junctions, and (6,Schottky barriers. 1. Homojunctions A homojunction is a junction formed between two portions of the same semiconductor material, one portion having n-type conductivity and the other p-type conductivity. A representative energy band diagram of a homojunction is given in Fig. 1, where the vacuum level has been included for reference. The electron affinity xs and the band gap EG are the same on both sides of the junction. The diffusion voltage VD,sometimes called the built-in voltage, results from the transfer of charge between n- and p-type portions required to maintain the Fermi level constant across the junction, and is given by the difference between the Fermi energies in the n- and p-type portions far removed from the junction. The drawing in Fig. 1 shows a symmetric distribution of the depletion region between n- and p-type portions, such as would be found if the carrier density in both n- and p-type portions were the same.

2 . Heterojunctions A typical band diagram for a heterojunction is given in Fig. 2. A heterojunction is a junction formed between two different semiconductor materials,

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PHOTOVOLTAIC EFFECT

Ec,\ I_ o-o-o-o-

:

o-o-

o-o-

EC EF

: p type FIG. 1 . Energy band diagram for a p-n homojunction in a semiconductor. Inset shows a typical geometry for a photovoltaic cell, with a narrow n-type region on a wider p-type region.

with different electron affinities and band gaps. One of the semiconductors is usually n-type and the other p-type. The diagram of Fig. 2 has once again been drawn with equal depletion layer widths on the two sides of the junction, for the specific case of equal carrier densities on both sides of the junction. The construction of a band diagram for a heterojunction using only knowledge of bulk properties, such as electron affinity, band gap, and Fenni level position, is a hazardous exercise. Fairly complex processes can occur at the heterojunction interface resulting from interactions specific to the existence of the interface and not reflected in the bulk properties; for example, it is common for there to exist interface dipoles or interface states, the presence and charge of which may considerably change the band profiles at the interface. Figure 2 has been drawn in an idealized fashion following the Anderson abrupt junction model (37) in which interface states and dipoles have been neglected. This model calls for the band diagram to be drawn using only the bulk properties of the semiconductors, in such a way that discontinuities may occur in the conduction band and the valence band because of differences in electron affinity and band gap between the two semiconductors. Figure 2 has been drawn assuming values of these quantities

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

o t o -

0

o-o-oTo-oEF

E

IG2

p type

” type

FIG. 2. Energy band diagram for a p-n heterojunction between two different semiconductors. Energy parameters of the two materials have been chosen so that no energy spike appears in either band. Inset shows two possible modes of operation as photovoltaic cells: (1) front-wall, with illumination incident on the p-type absorber, or (2) back-wall, with illumination incident on the n-type window.

such that these discontinuities do not contribute any “spikes” in the interface band structure. If x1 had been chosen to be larger than xz, on the other hand, the discontinuity in the conduction band would have resulted in an energy spike that would seriously impede electron transport from the p- to n-type portions. The p-type material has also been chosen to have the smaller band gap, a common situation since in general electron diffusion lengths in p-type material are larger than hole diffusion lengths in n-type material. Deviations from an ideal heterojunction structure may arise from at least two other sources. Although it is possible to find two materials with the same lattice constant (e.g., GaAs has a lattice constant of 5.654 A and Ge has a lattice constant of 5.658 A), most heterojunctions consist of two materials with considerable lattice mismatch. Such lattice mismatch produces distortions and dislocations at the interface that give rise to localized interface states, which can play a large role in determining the photovoltaic properties of the junction. The second kind of deviation occurs because of the nature of real surfaces; when ajunction is made by depositing one material on top of another, an intervening layer owing to the oxidized surface

169

PHOTOVOLTAIC EFFECT

of the second material or to chemical interaction or interdiffusion between the two materials may be formed. This intervening layer may control the properties of the junction. In certain cases a thin layer of insulating material, usually an oxide, is deliberately introduced to reduce the junction current; in this case, the junction is sometimes referred to as an SIS (semiconductorinsulator-semiconductor) structure. A basic principle guiding practical heterojunction research is that the properties of the junction may be determined not by the bulk properties of the individual materials, but by the process and interactions involved in junction formation. 3 . Buried or Heteroface Junctions

Figure 3 shows a representative buried p-n junction formed by heterofacing with a p+ material; such a junction consists of a heterojunction and a homojunction. The junction is called “buried” because it is the consequence of a narrow p-type region in the p+-p-n junction illustrated in Fig. 3. The structure retains the advantage of a p-n homojunction and at the same time provides a different kind of front surface to the p-type material to minimize

P+

P

n

FIG.3. Energy band diagram for a pt-p-n heteroface buried junction in which the p+ material acts as a large band-gapwindow and an ohmic contact to the p material. Inset shows the likely orientation of illumination for use as a photovoltaic cell.

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

surface losses. The narrow p-type region in the example of Fig. 3 may be formed before the addition of the p+ heterofacing material, or in many cases it may be formed by diffusion fron the p+ material in the process of junction formation. A heterofaced buried junction is usually preferable to a heterojunction of the two materials, since it moves the junction away from the heterojunction interface. The most efficient example of such a buried junction is the GaAlAs/GaAs cell (38),in which the p-GaAlAs is the heterofacing layer on a p-n GaAs junction; the lattice constant of AlAs is 5.661 A and hence almost the same as that of GaAs, 5.654 A, thus making possible a heteroface contact to the buried junction with minimized density of heteroface interface states. 4. Schottky Barriers

In many ways the Schottky barrier junction, consisting of the junction between a metal and a semiconductor, is the simplest of the junction types. A typical example is given in Fig. 4. It is also a simple model that neglects interface interactions and states and it predicts that a Schottky barrier is

-a4

SEMICONDUCTOR

METAL

METAL n- TYPE SEMICONDUCTOR FIG.4. Energy band diagram for a Schottky barrier on an n-type semiconductor, based on the simple energy parameters of the materials without inclusion of interface interaction effects. Inset shows the normal mode of operation as a photovoltaic cell.

PHOTOVOLTAIC EFFECT

171

formed on an n-type material if the work function of the metal & is larger than the work function of the semiconductor &. Such Schottky barriers are also sometimes prepared with an intervening insulator layer to minimize junction currents; such cells are called MIS (metal-insulator-semiconductor) junctions. Research in recent years has shown that the simple argument advanced above for determining the barrier height of a metal-semiconductor junction does not hold for most materials of interest for photovoltaic cells (39). Evidence favors the conclusion that the location of the Fermi level at the surface of the semiconductor is controlled by interactions with the metal, less than a monolayer being sufficient (40-44). The actual height of a Schottky barrier must most often be determined experimentally. B. Simple Photouoltaic Cell Model

A photovoltaic cell is evaluated in terms of its effectiveness in converting power from radiation into electrical power. A simple equivalent circuit is that of a current generator producing the light current IL = J L A L , where A [ , is the cell area exposed to illumination, which flows in the opposite direction to the forward current of a diode with diode current ID = J D A D , where AD is the total area of the junction. ID = I,[exp(aV) - I ]

(1)

where I , is the reverse saturation current of the diode, and a is a parameter given by a = q/AkT with A = 1 for diffusion currents and A z 2 for recombination currents. For other junction current mechanisms that we discuss later, e.g., tunneling with or without thermal activation, the parameter a does not have the temperature dependence given above and may indeed be virtually temperature independent. In an ideal junction A , may be taken equal to A,, and expressions are commonly written in terms of current densities rather than currents; but in real cells this fundamental geometric difference between light and dark currents must be remembered. Figure 5 shows a typical equivalent circuit, including a series resistance R, and a shunt resistance R, . In an ideal cell with no losses, the light current IL is exactly that corresponding to one electronic charge crossing the junction and being collected in the external circuit for each photon incident on the cell with sufficient energy to be absorbed and create an electron-hole pair, i.e., usually a photon energy larger than the band gap. Since the quantum efficiency is defined as the number of electronic charges collected per incident photon, an ideal cell has a quantum efficiency of unity for photons with sufficient energy to create electron-hole pairs. The diode current IDin such an ideal cell is no larger

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

FIG.5. Simple equivalent circuit for a photovoltaic cell, including a current generator, a diode, a series resistance, and a shunt or parallel resistance.

than the junction current associated either with diffusion of carriers over the junction barrier or with recombination of carriers near the junction. Other characteristics of an ideal cell are: (a) the parameters tl and Zo have the same values under illumination as in the dark; (6) the series resistance R, is zero; and ( c ) the shunt resistance R, is infinite. Since the total current in such an ideal cell is obtained simply by superposing the light-generated and dark currents, the total current is given by

r = ,z =

-

iL

Z,[exp(tlV)

- 13

-

zL

The variation of Z with V in the dark and under illumination corresponding to this model is shown in Fig. 6 . The principle of superposition means that the dark I-V curve is simply lowered by the amount ZL to form the light I-V curve. This curve crosses the voltage axis (I = 0) at the open-circuit voltage V,,,

V,,

=

ct-'

+ I)]

ln[(ZL/Zo

(3)

and it crosses the current axis ( V = 0) at the short-circuit current Z,, , I,, = - I L (4) These two simple results already reveal a basic key to the operation of a photovoltaic cell : The short-circuit current is controlled by the current generation and collection processes only, whereas the open-circuit voltage is controlled also by the magnitude of the diode current expressed through the parameters tl and Zo. The forward current expressed through tl and I, can be considered as a leakage path through which the buildup of the forward-bias voltage of the cell due to illumination can be dissipated; the

PHOTOVOLTAIC EFFECT

173

FIG.6 . Typical idealized light and dark J-V curves for a photovoltaic cell, showing the open-circuit voltage V,,, the short-circuitcurrent density Jsc, and the maximum power point p, ’

short-circuit current, on the other hand, is a current that flows in the reverse direction. To evaluate the power generated by the cell. the shape of the light I-Y curve is as significant as the magnitudes of Yo, and I,, . At a particular point along the I-Y curve, maximum power P, = ImY, is generated by the cell corresponding to a specific maximum power voltage V , and maximum power current I,. It is this maximum power that is used to calculate the efficiency of the cell q,

where Pradis the total radiation power incident on the cell, and ff is called the fill factor and is a measure of the “squareness” of the I-V curve. From Eq. ( 5 ) the fill factor is defined as

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

The coordinates of the maximum power point can be determined by multiplying Eq. (2) by V and then maximizing the power with respect to V. For the ideal cell, the value of V, is readily calculated by iteration from V, = V,, - a-' ln(aV,

+ 1)

(7)

The current for maximum power is then given by Eq. (2) with V = V,. An alternative method of calculating the fill factor of a cell is given by defining a parameter P, This parameter corresponds to the current passing in the forward direction when the diode is biased at V, in the dark, divided by I,; by convention I, is positive and I, is negative. From the maximization of power calculation, an expression for fl can be derived,

from which a value of can be obtained by only a few iterations. For good cells /Ihas a value between 0.04 and 0.10. In terms of P the fill factor can be expressed as

For an ideal cell the fill factor is not a function of the parameter a, but Eqs. (3) and (5) show that the efficiency is directly proportional to l/a through the dependence of V,, on l/a. A desired increase in efficiency cannot be achieved simply by increasing l/a (or A) because a complicated relationship between I , and a exists such that an increase in A usually corresponds to an increase in Zo (45). C . More General Photovoltaic Cell Model A somewhat more general model of a photovoltaic cell can be constructed by adding several nonideal features to the ideal model just discussed: a finite series resistance R, and shunt resistance R,, and allowance for the possibility that only a fraction of the light-generated carriers will actually be collected in the external circuit. The presence of finite R, and R, results in power losses for the cell, which appear through reductions in the fill factor ff. An approximation to these effects can be made by assuming that the cell is operating near the maximum power point and that the loss can be described simply by J:R, for a series

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PHOTOVOLTAIC EFFECT

resistance or Vi/Rp for a shunt resistance. The power loss fraction (PLF) for a series resistance is then (11) PLF = JARJJ,,,V,,, = J,,,R,/V, z JscR,/Voc which corresponds to PLF = 3% for J,, = 40 mA/cm2 and Vo, = 0.6 V if R, = 0.5 $2 per cm2 of cell area. The power loss fraction for a shunt resistance is

(12) PLF = ( Vi/R,)/J,,,V, = V,,,/J,R, x Voc/JscRp which corresponds to PLF = 3% for R , = 500 R per cm2 of cell area. These simple calculations set the scale for the maximum tolerable value of R , and the minimum tolerable value of R , in an efficient cell. For small power losses, the decrease in cell efficiency is almost completely due to decrease in the fill factor, approximately by

w,,R,) = fl(0, a)[1- (JSCRJVOC)- (~oc/J,cR,)l

(13)

Figure 7 shows a typical variation of ff with light-generated current and the effect of finite values of R, and R , on the fill factor. Measurement of this variation can prove a useful analytical aid in interpreting photovoltaic cell phenomena. CONCENTRATION RATIO 1

I

I

10

102

176

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

The I-V relationship corresponding to Eq. (2) when R, and R, are included becomes I = I,{exp[a(V - IR,)] - l}

+ (V - ZR,)/R, - I ,

(14)

The dynamic resistance R, = d V/dI is given by

+

1 R,(1 - R;' + (1

R -

+ R,/R,)- Iocr exp[a(V - IR,)] + RS/Rp)-' Ioaexp[a(V - IR,)]

(15)

For sufficientlyhigh forward voltages, when the second term in the numerator and denominator dominates, R, = R, . For small or negative voltages near or below the I,, point on the curve, R , = R,. Thus both R, and R , can in principle be determined directly from the measured I-V curve. The addition of a simple series resistance to the cell does not change V,,, and decreases I,, only when R, is very large, in which case the I-V curve approaches 1/R, and the ff approaches its minimum value of 0.25. The addition of a simple shunt resistance to the cell does not change the value of I,, ,but may decrease the value of V,, slightly. The other nonideal factor mentioned earlier in this section is the presence of loss mechanisms for the photoexcited carriers to account for the possibility that some of the carriers may not be collected by the junction. A simple way to express this possibility formally is to introduce a collection function H(V), which may also be a function of photon energy. By use of some simple collection functions, insight into the behavior of the cell can be obtained without requiring solution of nonequilibrium transport relations in the cell. Again this approach assumes that dark- and light-generated currents can be superposed, and so is reliable only within the constraints of that limitation. If such a collection function is introduced, Eq. (2) for the I-V relationship becomes I = Io{exp[a(V - IR,)]

- l} + (V - ZR,)/R, - H ( V ) I L

(16)

The function H ( V ) is chosen to express the fraction of the photoexcited carriers that are actually collected. The general effects of a collection function with value less than unity, having a smaller value the higher the forward bias, is again primarily to reduce the fill factor, with only minor reductions in V,, and I,, in efficient cells. Let us consider as an example of the application of this collection function approach the case of a p-n heterojunction where the n-type material is the large band gap material which can be ignored in the photogeneration process, and where the depletion layer is almost totally in the p-type material, since n is larger than p. We make the following reasonable construction of the collection function. We divide the collection function H(V) into two portions

PHOTOVOLTAIC EFFECT

177

so that H ( V ) = g ( V ) h ( V ) ,where g ( V ) describes the loss of carriers to recombination in the bulk of the p-type material beyond the depletion region (those carriers created far from the junction having a higher probability of recombining before diffusing to the junction than carriers generated nearer the junction), and where h(V)describes the loss of carriers to recombination at the junction interface due to interface states. Both g( V) and h( V) may be functions of wavelength as well, but it is expected that g( V) will vary strongly with wavelength because of the variation of absorption constant with wavelength, and that h( V) will be relatively wavelength independent. The collection function g( V) can then be calculated as follows (46,47):

The wavelength dependence enters through the variation of the absorption constant a@). The first term in the numerator of Eq. (17) describes the collection of carriers generated within the depletion layer of width W, under the assumption that all carriers generated within W are collected because of the assisting drift field there. The second term in the numerator of Eq. (17) expresses the loss of carriers generated beyond W if the diffusion length of electrons in the p-type material is L,. Integration of Eq. (17) yields g(V)= 1 -

exp( -aW) 1 UL,

+

The voltage dependence enters through the voltage dependence of the depletion layer width W, W ( V )= (2E/4N*)”2(VD-

V)1’2

(19)

One approach of obtaining an expression for the interface collection function h( V) is to make use of the approximate collection function proposed by Rothwarf (48). Assuming that recombination at the interface can be described by an interface recombination velocity s,, and that the recombination probability could be viewed as a simple competition between crossing the junction without recombination and recombining at the interface, the following interface recombination function is useful:

h ( V ) = (1 + s,/p&)-l

(20)

where p is the mobility of carriers at the interface, and 8 is the electric field at the interface given by 8 = 2( V, - V)/ W(V). If there are N , interface states per cm2at the interface with a capture coefficient of B cm3/sec,then s, = N,B.

178

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

Figure 8 shows the spectral response of quantum efficiency for a CdS/CdTe heterojunction cell, which seems to meet the requirements assumed above for the particular collection functions derived (47).The cell was made by vacuum evaporation of a high-conductivity n-type CdS film onto a p-type single crystal of CdTe. The high and low energy cutoffs of the spectral response curve of Fig. 8 correspond to the band gaps of CdS and CdTe, respectively. Between these two cutoffs, a wavelength-dependent effect is seen in which the quantum efficiency increases with decreasing wavelength, corresponding to increasing absorption constant Q, which can be described by the g ( V ) function with almost negligible dependence on V over the experimental range shown. Also seen is a wavelength-independent effect in which the quantum efficiency at all wavelengths increases with reverse bias, which can be described by the h( V) function with a value of 0.84 at zero bias and 0.89 at a bias of - 1 V. Consistent description with all cell parameters is obtained if s, = 2 x lo6 cm/sec, which is reasonable for this heterojunction in which the two members show a large lattice mismatch of about 9%. Inclusion of the collection function H ( V ) in Eq. (16) means that expres-

IOC

-c

I

l

I

1

1

I

l

I

80

9

*u -

60

u

LL LL

w

5

+ z

40

a

3

0

20

0

1

.m

1

0.80

I 0.70

1

I

0.80

WAVELENGTH ( p m )

FIG.8. Spectral dependence of the quantum efficiency for a CdS/CdTe heterojunction cell prepared by vacuum evaporation of CdS on single crystal CdTe. [From Mitchell el al. (47).]

PHOTOVOLTAIC EFFECT

179

sions for photovoltaic parameters are altered. The open-circuit voltage becomes

and the short-circuit current becomes

I,, = (1 + R,/R,)- ' [ I o exp( -ctl,,R,) - I , - H(O)I,] (22) The dynamic resistance has an additional term added to the denominator of Eq. (15) consisting of - I, dH( V)/dV, so that for small or negative values of voltage near I,, , R,j = [ R p - I , i3H(V)/dV]-1 (23) The observation of a finite slope of the I-V curve through the short-circuit point may be caused, therefore, either by a shunt resistance or by a voltagedependent collection function. Another departure from ideality occurs if the junction parameters vary with illumination. For an ideal cell, elimination of ZL between Eqs. (3) and (4) shows that the relationship between Z,, and V,, is identical to that between Zand V from Eq. (2). The variation of I,, with V,, as the illumination intensity is varied is often measured as a test of the independence of the junction parameters on illumination. If the Z,,-V,, is identical with the I-V dark curve, it is concluded that the junction transport is not affected by light. In the more general case, however, in which R,, R,, and H( Y) effects need to be considered, coincidence between I,,-V,, and dark I-V curves is obtained only if the junction parameters ct and I,, R,,and R, are independent of illumination, if R, is sufficiently small, and if H(0) = H(Kc), as can be seen by eliminating 1, between Eqs. (21) and (22), and comparing with Eq. (16).

D . Major Processes and Mechanisms

A representative diagram of a junction, applicable to any of the junctions described in Section II,A with suitable modifications, is given in Fig. 9. For the sake of the specific discussion that follows, we will consider light being incident on the n-type face of the junction in Fig. 9, this n-type region representing the conditions at the front surface of a homojunction, the front surface of a heterojunction, the n-type region of a buried n-p junction, or the metallic layer of a Schottky barrier. In this section we trace in a qualitative manner the phenomena involved in current generation, current collection, and junction transport.

180

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

0

CONTACT

Q GENERATION DIFFUSION RECOMBINATION

0

DRIFT RECOMBINATION

0 OlFFUSlON

0 CONTACT

FIG.9. Breakdown of the processes taking place in a representative photovoltaic junction. It is assumed that the light is incident on the n-type end.

1. Reflection The first consideration in determining current generation by the light is the proportion of light lost immediately due to reflection from the front surface of the semiconductor. The refractive index of most semiconductors is relatively large, corresponding to reflectivities of 20-40%. Such reflection losses can fortunately be minimized by using a large-band-gap, electrically inert, interference layer, designed in a simple case so that its thickness is a quarter-wavelength within the semiconductor of the radiation wavelength at the maximum of the solar spectrum. Use of a single such layer can reduce the reflectivity most effectively only at one wavelength, of course, but often the improvement achievable is sufficient. Greater reduction in reflection over a wider wavelength range can be achieved by using multiple antireflection layers.

2. Contact Area If opaque contacts cover a fraction of the illuminated surface of the junction, the illuminated area A , useful in current generation is less than the junction area A D active in producing the junction current, as mentioned in Section II,B. Considerable engineering ingenuity is devoted to the task of minimizing the contact area while retaining good current collection by these contacts. One solution that shows promise is to use a high-conductivity degenerate large-band-gap transparent layer (like In,O, , SnO, , CdSnO,,

PHOTOVOLTAIC EFFECT

181

or ZnO) for the contact so that only a minimal area must be obscured by opaque contact to this transparent conducting layer. 3 . Contact Resistance

One of the major contributions to the series resistance R, of the cell sometimes comes from the resistance of the contacts, particularly in novel or experimental cells made with materials not technologically developed. The desirable choice, of course, is to have an ideal ohmic contact that provides the minimum resistance achievable. If metal-semiconductor interaction effects do not dominate, an ohmic contact is provided by a metal with work function less than the work function of an n-type semiconductor, or greater than the work function of a p-type semiconductor. It is usually found beneficial in addition to have a mild heat treatment to diffuse in the metal, which has been chosen to be an n-type impurity (p-type impurity) in an n-type (p-type) semiconductor ;this diffusion increases the carrier density in the semiconductor at the contact interface and reduces the contact resistance, which is relatively strongly dependent on the carrier density at the semiconductor surface. As an example, the ohmic (linear I- V curves in all cases) contact resistance of In contacts on InP crystals has been measured for electron densities in the n-type InP between 5 x 10'' and 5 x 10l5 cm-3; over this range the contact resistance varies from to 10 R * cm2 (49). Any contribution to the total series resistance becomes critical if concentration of sunlight is used, and the total series resistance R.cm2 in AlGaAs/GaAs solar cells, for example, must be of the order of or less for concentrations of the order of lo3. Our estimate in Section II,C of 0.5 R . cm2 for the maximum allowed series resistance for the entire cell indicates that the contribution to R,from any single contact must be much less than this. For some materials of promise for solar cells, e.g., p-type cadmium telluride, no metal exists with an appropriate work function to form an ideal ohmic contact. Another alternative remains in such cases. If the surface of the semiconductor can be made sufficiently conducting, the depletion layer formed by the Schottky barrier of the nonohmic contact in the semiconductor is thin enough to allow tunneling through it. Such a contact may be relatively low resistance and ohmic at one temperature, but may become rectifying and high resistance if the device is cooled appreciably, particularly if the dominant tunneling process is thermally assisted. 4. Collection Resistance

As we continue toward the left in the diagram of Fig. 9, we encounter next the problem of collection resistance. This is to first order simply the

182

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

resistance of the n-type region through which the current must travel to be collected. If the complete area of the semiconductor can be covered with the contact, as with a transparent high-conductivity layer for this n-type region, then the resistance corresponds to the thickness of the semiconductor material; if a contact grid is used, then the resistance involves the lateral flow of current to the grid as well as the flow of current normal to the junction through the semiconductor,If the n-type layer we are considering is a polycrystalline layer rather than a single crystal layer, then the lateral current flow can be impeded still further by the presence of intergrain potential barriers in the layer which reduce the effective carrier mobility p = p o exp( - Eb/kT),where Eb is the height of the intergrain barriers (50). In practical cells, design of the grid structure to minimize the collection resistance has been advanced to a fine art (51) and has been approached analytically using various lumped element equivalent circuits (52-55) and finite element models (56). There is, of course, also a contribution to the collection resistance from the p-type material in Fig. 9, just as there is a contribution from the back contact resistance to the p-type material. Since the n-type region is usually much thinner than the p-type region, however, the resistivity of the n-type layer must usually be several orders of magnitude smaller than that of the p-type region (of the order of tenths or hundredths of an Qacm compared to tens or hundreds of R - cm, respectively).

5 . Optical Absorption In order to create electron-hole pairs the incident light must be absorbed by the semiconductor. For a homojunction there will be contributions to the total current from absorption in both the n-type and p-type regions. For a heterojunction in which the n-type region is a high band gap material, useful absorption may take place primarily in the p-type material. For a Schottky barrier absorption takes place in the p-type material of Fig. 9 after being transmitted through the metallic layer (replacing the n-type layer in Fig. 9), which must be kept very thin therefore to allow maximum transmission to the semiconductor. The major contribution to the optical absorption comes from transitions across the band gap of the semiconductor, caused by photons with energy equal to or greater than this band gap. If the band gap transition is an optical direct transition, i.e., if the extrema of the conduction band and valence band occur at the same value of k, the absorption constant increases very rapidly with photon energy at the band gap energy and quickly reaches values in the 104-105cm-' range. The penetration depth of the light (equal to the reciprocal of the absorption constant) is therefore about a few tenths of a

183

PHOTOVOLTAIC EFFECT

micrometer for a direct-band-gap material, and the required thickness of the material to absorb all the light is only two or three times the penetration depth. If the band gap transition, on the other hand, is an optical indirect transition, i.e., the extrema of conduction and valence bands occur at different values of k, the absorption constant increases more gradually for photon energies greater than the band gap, and thicknesses of about a hundred micrometers are required to absorb all of the light. Among materials used for solar cells, only silicon has an indirect band gap; others such as GaAs, InP, CdTe, etc. all have direct band gaps. If thin-film cells are desired with a total thickness of not more than about 10 pm, only direct-band-gap materials can be used. If a photon flux F&) is incident at x = 0 on the absorbing material, the photon flux F(1,x) at a distance x inside the material is given by

F(1, x) = F&) exp[ -a(l)x]

(24)

where a(1) is the absorption constant of the light. Usually the flux F is measured either in mW/cmz or photons/cm2 sec. Sunlight falls on the earth with a flux of about 100 mW/cm2. The rate of carrier generation because of the absorption of this radiation is given by G(1, X) dx = -dF(1,

X)

=

a(l)F(1,X) dx

(25)

This was the kind of expression used in the calculation of Eq. (17). Two considerations compete with each other. In order to achieve absorption of the largest portion of the solar spectrum, as given in Fig. 10, it is n

E

5

1200-

W V

z

9

9IY

800-

[L A

2

400-

I-

u W a

In I

I

I

I

1

WAVELENGTH ( p m )

FIG.10. Standard AM I .5 solar spectrum, computergenerated from data measured in space. [From Terrestrial Photovoltaic Measurement Procedures, ERDA/NASA/1022-77/16, NASA TM 73702, NASA-Lewis Research Center, Cleveland, Ohio 44135 (1977).]

184

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

desirable to have as small a band gap as possible so that every photon in the solar spectrum has enough energy to create an electron-hole pair. However as the band gap decreases, the magnitude of J , inevitably increases (see Section IV). These competing considerations lead to the conclusion that there is an optimum band gap that will allow the best absorption with the smallest J , . A classic calculation of this type for ideal homojunctions with no surface recombination losses by Loferski (57) indicates that an optimum band gap occurs at about 1.4 eV for recombination-controlled junction currents and at about 1.6eV for diffusion-controlledcurrents.The maximum, however, is broad and suggests that specific circumstances might warrant use of any semiconductor with a band gap in the range between 1.O and 2.0 eV. Loferski's results are shown in Fig. 1 1. Because of these considerations the choice of a specific band gap semiconductor means that all photons with energy less than this band gap do not create electron-hole pairs and therefore contribute to an overall loss of efficiency.The absorption of photons with much larger energy than the band gap also contribute to a loss, since the extra energy of the photons is simply dissipated as phonons as the excited carriers return to thermal equilibrium 26 24 22

-I t-

20

2 W

V E

w

18

t x

2

16

F

14 12

-

10 0.8 0.9 1.0 1.1 12 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

€6 lev)

FIG. 1 1 . Theoretical solar efficiency vs. semiconductor bandgap for ideal homojunction photovoltaiccells with no surface recombinationloss. Curves are calculated for junction current due to injection ( A = 1) and to recombination in the depletion layer ( A = 2). [From Loferski

(mi

PHOTOVOLTAIC EFFECT

185

in the band; it is toward a reduction of this loss that the thermophotovoltaic device described in Section I is directed. If a heterojunction is used, then the number of available photons is reduced still further; for the CdS/CdTe heterojunction with spectral response shown in Fig. 8, only 44% of the solar spectrum is contained in the “window” between the band gaps of CdS and CdTe.

6 . Carrier Collection If Fig. 9 represents a homojunction, then electrons generated by photoabsorption in the p-type material that are able to cross the junction by diffusion and be collected, and holes generated by photoabsorption in the n-type material that are able to cross the junction and be collected, constitute the current. If Fig. 9 represents a heterojunction or a Schottky barrier, then primarily electrons created in the p-type region that cross the junction and are collected constitute the current. Since carriers must be created within about a diffusion length L, = ( p ~ , / k 7 7 ~ of’ the ~ junction (where T, is the electron lifetime in thep-type material) in order to be collected before recombination occurs, only those carriers created within a diffusion length of the junction contribute to the current. This means than an indirect-band-gap material must have much larger values of diffusion length for the minority carriers than a corresponding direct-band-gap material, since optical generation of carriers is spread out over a much larger distance in the indirectband-gap material. Carrier collection can be aided by the presence of electric fields, Carriers generated in the depletion layer, for example, are almost all collected without loss, because of the local field as well as the proximity to the junction. In principle a built-in electric field might be developed across the whole absorbing region of the semiconductor by suitable choice of a gradient of impurity density, but in practice this has not been used for most materials because it is difficult to produce the desired impurity gradient without causing a decrease in minority carrier lifetime, and because such a built-in field automatically reduces the value of V,, that can be obtained owing to its reduction of the diffusion potential of the junction. The existence of such a drift field would probably be essential for the successful operation of lowlifetime materials (58). 1. Surface Recombination

If Fig. 9 represents a homojunction, then carriers generated by light in the n-type region may also diffuse to the surface as well as toward the junction to be collected. Because the surface of most materials consists of a relatively high defect density, the probability for recombination is usually

186

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

larger at the surface than in the bulk. Carriers that diffuse to the surface, therefore, are lost through recombination. Particularly if the material has a direct band gap, the illuminated n-type portion of the junction must be very thin to allow light to penetrate to the junction, but this means that a high density of carriers is generated close to the front surface where they can be lost through surface recombination. For this reason the quantum efficiency of a homojunction usually decreases with increasing photon energy, as the increasing absorption constant associated with the higher photon energies causes carrier creation to occur nearer to the front surface of the n-type material. Losses due to surface recombination can be reduced by incorporation of an electric field at the surface that produces a potential barrier for minority carriers moving toward the surface by suitable impurity doping, by surface passivation in which a specific recipe is developed by which the surface recombination states may be rendered less effective, or by the use of a buried homojunction structure with a suitable heteroface junction at the front surface of the homojunction so that surface states (now interface states) are reduced. In the AlGaAs/GaAs heteroface buried homojunction cell, the front surface of the GaAs p-n junction is converted from a free surface to an AlGaAsIGaAs interface with good lattice matching and few interface states, whereas the free surface of the AlGaAs is not important in the current generation process. 8. Interface Recombination We have already introduced the concept of interface recombination in Section II,C, where the effect was described in terms of the interface recombination velocity of the collection function h( V).If Fig. 9 represents a heterojunction, then the interface between the two different p- and n-type materials is likely to consist of additional localized states that play a role in recombination similar to the one the surface states have on the front surface of the homojunction. Electrons generated in the p-type material may recombine via these interface states and fail to be collected by the junction. Since these states lie in a region of high electric field at the junction, they need not have a major deleterious effect on current collection; indeed, quantum efficiencies close to unity have been achieved in heterojunctions like ZnO/CdTe for which the lattice mismatch is close to 30% (59). On the other hand, such interface states provide a transport path for forward currents and thus lead to a reduction in V,, . 9. Grain Boundaries in Polycrystalline Films

If one or both members of the photovoltaic junction have the form of polycrystalline films rather than single crystals, additional effects may be attributed to the grain boundaries in the polycrystalline films. If the grain

187

PHOTOVOLTAIC EFFECT

size is smaller than the diffusion length of the carriers, there may be appreciable loss of photoexcited carriers by recombination at grain boundaries, thus causing a decrease in the short-circuit current. If the grain boundaries intersect the junction, there may be additional paths for current transport, thus reducing the opencircuit voltage. In Section II,D,4 we have already mentioned the effect of such polycrystalline films on increasing the collection resistance. An example of the effect of polycrystalline vs. single crystal cell behavior is gven by the investigation of CdS/InP junctions prepared on both single crystal (60-62) and polycrystalline InP (60,63).In this case it was possible to obtain almost the same short-circuit current with the polycrystalline InP as with the single crystal InP, but the open-circuit voltage was appreciably reduced by grain-boundary induced leakage currents. Figure 12 compares CdS/InP cell properties (each type of cell was made by chemical vapor deposition of thin-film CdS onto the InP substrate) for the two types of cell; the junction current is about 100 times larger for the cell made with polycrystalline InP, corresponding to a reduction in V,, from 0.79 V in the single crystal cell to 0.46 V in the polycrystalline cell. 10. Back Contact In Section II,D,4 we mentioned the contributions of the collection resistance of the p-type material in Fig. 9, and of the back contact to this p-type material. Since this back contact does not have to be designed to allow light 400

-

N

E

I

1

'

1

04

06

oa

10

10

\

4

E

>

t In z W

l

0

I-

10.

z

W

L

L 3

n

10'

K

s

L

e

10-

10-

o

02

FORWARD VOLTAGE ( V )

FIG. 12. Forward bias current-voltage curves for CdS/InP heterojunctions for singlecrystal (0-0) InP and for polycrystalline thin film (0-0) InP. [From Shay er d.(60).]

188

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

transmission, a large area contact can be used to minimize contact resistance. In cells in which the p-type region thickness is comparable to the diffusion length of photoexcited minority carriers, there may be some loss of carriers due to recombination at the back surface, like the front surface recombination loss described in Section II,D,7. A short diffusion of additional dopant at the back surface can minimize this loss by providing a surface electric field that impedes the flow of carriers to the surface (64); an increase in hole density in the p-type material near the back surface, for example, produces a barrier for minority-carrier electron diffusion to that surface. 11. Junction Current Mechanisms

The final topic in this survey of photovoltaic processes is the origin of the junction current itself, that forward-biased current that reduces the ability of the junction to sustain a forward voltage and hence reduces the opencircuit voltage. The simplified model of Fig. 13 illustrates the principal

--%

@ Injection

fi

@ Recombination

Forward Bias Current Transport

FIG. 13. Simple indication of three major modes of forward junction current: (1) injection over the barrier, (2) recombination in the depletion layer, and (3) tunneling, with or without thermal assistance, through interface or imperfection states, followed by recombination.

189

PHOTOVOLTAIC EFFECT

transport mechanisms, which we describe in somewhat more detail in Section IV. The most ideal behavior and that corresponding to the smallest value of junction current occurs when the junction current is controlled by diffusion over the barrier, which is associated with the injection of electrons from the n-type material to the p-type material in Fig. 13. This ideal behavior corresponds to A = 1 in Eqs. (2) and (16). The second most desirable ideal behavior, corresponding to the next smallest value of junction current. is associated with current transport through the junction by recombination in imperfection states in the depletion region. If these states lie at midgap, then the factor A 2, although it may actually take on values between 1 and 2 in real situations. Additional junction current may result if interface states are present, since it is then possible for junction current to flow via recombination in the interface states. Usually the largest junction currents are the result of tunneling from the n-type material in Fig. 13 either to interface states or to imperfection levels, with subsequent recombination with holes in the p-type material. Such tunneling may occur without thermal activation if the interface barrier is thin enough, or more generally it occurs with thermal activation increasing the electron energy such that tunneling becomes highly probable. When tunneling dominates the junction current the parameter 01 is no longer given by q/AkT, but a varies more slowly with temperature and may indeed be temperature independent altogether. In many real situations in which the measured current-voltage curves of a junction indicate tunneling-dominated transport, the expected depletion layer width at the junction calculated from the known bulk carrier density is simply too wide to allow tunneling (59,637 ; this behavior must then be interpreted as a high density of charge residing near the interface in bulk imperfections or interface states, which reduces the depletion layer width sufficiently to allow tunneling.

-

111. CURRENT GENERATION

In Sections 111 and IV of this review we consider in more detail the specific processes of current generation and junction currents, since these are the two principal contributors to the short-circuit current and the open-circuit voltage, respectively. Current generation is commonly described in terms of what is known as the transport equation for photoexcited carriers. The transport equation correlates carrier generation with recombination, diffusion, and drift of the photoexcited carriers. If the transport equation can be solved with the appropriate boundary conditions, we are able to express the light-generated

190

RICHARD H. BUBE AND ALAN L. FAHREMRUCH

current of the photovoltaic cell. Section II,C has described some of the attempts to circumvent general solution of the transport equation by the use of partially ad hoc collection functions. Even in this more detailed discussion we focus on specific cases of solution of the transport equation, since general solutions are usually so complex as to obscure physical significance. Simple solutions of the transport equation are possible in the case where the dark and light currents of the junction can simply be superposed as in Eq. (2) (66-68). This superposition is valid when the differential equations and the boundary conditions of the system are linear with respect to the carrier densities and their derivatives;it is this linearity that makes it possible to sum directly dark and light currents. The discussion given here is in the form suitable to a p-type absorbing material, for reasons discussed earlier, and is with slight modification equally applicable to either a homojunction, a heterojunction, or a Schottky barrier, since the active region being considered is in the p-type material. A. Derivation of the Transport Equation

Under illumination the time rate of change of minority carriers in the p-type material is described by dn,/dt = G(x) - U ( x ) = a(A)F - (np

- npo)/zn (26) where G(x) is the generation rate given by Eq. (25),and U ( x )is the recombination rate expressible in terms of the thermal equilibrium minority carrier density npo and the lifetime of minority carriers z, . The current density is given by the sum of drift and diffusion components for both electrons and holes: J , = nqp,8

+ qD, V n

(27)

- qD, VP

(28) where p, and p, are the mobilities of electrons and holes, respectively; and D , and D, are the diffusion coefficients for electrons and holes, respectively. The corresponding continuity equations are J, =

PWp8

&/at - V . J , / q = G, -

aplat

+ v - J,/q

= G,

u,

- up

(29)

(30) Since electrons and holes are generated in equal densities by optical transitions across the band gap of the material, G, = G, and U, = Up. Here we

PHOTOVOLTAIC EFFECT

191

neglect departures from charge neutrality, which may occur in transient cases for strong gradients in the generation rate, and carrier trapping effects. Combination of Eqs. (27)-(30) yields the set of one-dimensional transport equations for n and p:

A totally general solution requires that these two equations be solved simultaneously with Poisson’s equation. Under the condition. however, that Gn = G,, p >> n (for our case, or alternatively n >> p for an n-type absorber), and steady state holds (an/& = ap/& = 0), Eqs. (31) and (32) can be uncoupled and a single equation written for the minority carriers np in the p-type material being described here (66,69, 70). d2np D n n+

dn dx

-

np - npo

+ G ( x )= 0

(33)

Tn

This approximation breaks down if the minority carrier density excited by light becomes comparable to the majority carrier density, as is the case, for example, under very high light intensities or at high forward bias (71, 72). B. Solution of the Transport Equation 1. Boundary Conditions A common assumption is that at the edge of the depletion layer in the p-type material the density of minority carriers is equal to the density in thermal equilibrium for zero applied bias, since excess minority carriers will be swept out rapidly by the junction field. Then for a forward-bias voltage V. the carrier density at the edge of the depletion layer in the p-type material is given by

np = npo exp(qI/lW

(34)

2. A Semi-Infinite Absorber If the absorbing material is sufficiently thick that penetration of light to the back of the material can be neglected (i.e,, the thickness is much larger than either the penetration depth of the light or the diffusion length of the minority carriers), a relatively simple solution of Eq. (33) can be obtained. It is further commonly assumed that the electric field in the neutral region

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

of the p-type material away from the depletion layer is zero. Equation (33) becomes

where x is measured positively into the p-type material with origin at the edge of the depletion layer, and F is the light intensity at the edge of the depletion layer. The boundary conditions are given by Eq. (34) at the edge of the depletion layer, and by np going to npo as x goes to infinity. Equation (35) can be solved for n,, and then the diffusion electron current Jn(x)is given by qDn(dnp/dx).The result for the electron current is (24)

The first term represents the dark current density due to diffusion of minority carrier electrons; it is not affected by illumination. Similarly the second term represents the light current density and is not affected by applied voltage. Because of the linearity of the equations in n,, the principle of superposition holds, and dark and light currents simply add; this would not be true, for example, if the lifetime T,, were a function of np, or if generation and recombination in the depletion layer depend on J , (73-75). At the depletion layer edge x = 0, and with V = 0, Eq. (36) yields

for the monochromatic light of wavelength 2.

3. A Finite Absorber with Back Surface Recombination If we need to consider a finite absorber with a surface recombination velocity s at the back surface, we need to add the additional boundary condition that J , = (n, - nPo)qs= -qDn dn,/dx (38) at the back surface. The presence of a back surface field as discussed in Section II,D,lOwould clearly require modifications in the transport equation. Solutions involving the boundary condition given by Eq. (38) show the expected decrease in electron density near the back surface for appreciable magnitudes of s there (8,24).

PHOTOVOLTAIC EFFECT

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C. Other Contributions to Current Generation

Finite contributions to current generation may also be expected in a total p-n junction from the depletion layer and the n-type material as well as the p-type material described earlier. Since all the carriers generated in the depletion layer may be assumed to be collected because of the high junction field, the contribution to the current from absorption in the depletion layer is given by where Fo is the light intensity at the front surface of the n-type side, W is the depletion layer width, and d , is the thickness of the n-type layer from the front surface to the depletion layer edge in the n-type material. Usually contributions to the current generation from the depletion layer and from the n-type material (especially in a heterojunction) are quite small.

IV. JUNCTIONCURRENTS The magnitude of the junction current is, as we have already mentioned, a crucial ingredient in determining the open-circuit voltage and hence the efficiency of a photovoltaic cell. The theory of junction currents in homojunctions is well developed, but this is less true of heterojunctions and MIS or SIS junctions. The subject is so broad that we cannot do more here than give a summary of the major features and mechanisms involved. A . Homojunctions

Under forward bias in the dark, electrons are injected into the p-type region from the n-type region; they pass from the n-type region where they are majority carriers, through the depletion region, and into the p-type quasi-neutral region where they are minority carriers. In the p-type region they recombine with majority carrier holes, and the current flow is completed by a current of holes from the p-type ohmic contact supplied through the external circuit. Similar statements could be made about the current due to holes; it is sufficient, however, for us to consider specifically just the current due to electrons. If recombination in the depletion region is an important process for the total current generation, in addition to the diffusion process just described, diffusion in the depletion layer is commonly neglected, and the current due to recombination may be calculated and added to the current due to diffusion without recombination in the depletion layer.

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

1. Diffkion Currents

If the electron transport is assumed to be controlled solely by diffusion into the p-type quasi-neutral region with recombination there, with the same being true of hole transport, the current density due to diffusion is given by (76) J,j,

= qn”(D,/r,)”’/N..i

+ (D,/z,)”’/N,][eXp(qV/kT)

- 11

(40)

where n, is the intrinsic carrier density, NAis the density of acceptors in the p-type material, and N , is the density of donors in the n-type material.

2. Recombination in the Depletion Layer An approximate treatment of this case starts with the assumption that the quasi-Fermi levels are constant across the depletion layer. The ShockleyRead recombination model (77) indicates that the maximum recombination rate occurs when the intrinsic level lies approximately halfway between the electron and the hole quasi-Fermi levels. The recombination rate U ( x )can be replaced by its maximum value by carrying out an integration over the depletion layer to determine the total current carried by recombination. The following approximate expression is obtained for the recombination-controlled current:

Jrec= [ n i W k T / 2 ( V ~- V)tn,][exp(qV/2kT) - 13

(41)

where W is the depletion layer width, V, is the diffusion potential of the junction, and T , , ~is the minimum lifetimeof electrons when all recombination centers are unoccupied. This approximate calculation is the basis for the common contention that A = 2 for recombination currents, whereas A = 1 for diffusion currents as indicated in Eq. (40).More complete treatments indicate that for recombination currents A is always less than 2 (76), a maximum value of 1.8 being predicted for deep recombination centers falling off to 1.0 for shallow recombination centers. The recombination currents in real junctions usually have a larger magnitude than those predicted by available theories to date (78).It is also possible to envisage recombination processes corresponding to values of A greater than 2 if recombination occurs through more than one level, or if the levels are distributed nonuniformly in space in the depletion layer (79).

B. Heterojunctions The diffusion injection mechanism for junction currents is usually not the dominant mechanism in heterojunctions. This is partially because most heterojunctions of interest have larger band gaps than silicon does, but also because interface phenomena play such a large role in determining hetero-

PHOTOVOLTAIC EFFECT

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junction properties. Several excellent review articles on heterojunctions exist (45,80,81) in addition to the book by Milnes and Feucht (82). Analogous equations to Eqs. (40) or (41) can be written down immediately as approximations to the diffusion or recombination currents expected for a heterojunction with a large-band-gap n-type material on a smallerband-gap p-type absorber. In general, however, much larger currents are measured. The temperature and voltage dependence of experimentally measured J-I/ curves appear to fit a variety of semiempirical forms, e.g.,

J = J,, exp(-AE/kT)[exp(qV/ART) - 11

(42)

where J,, and A may be slowly varying functions of T and/or V, and AE is a measured activation energy for the zero-bias extrapolation of the In J vs. V curves. In other cases the measured slope of the In J vs. V curves is relatively independent of temperature but appears again empirically to correspond to a relationship like where B and IY are constants that are relatively temperature independent, and 4,, = V, (E, - E,),/q, with (E, - Ef), being the energy distance of the Fermi level below the conduction band edge in the n-type material. In many cases In J vs. V curves show more than one well-defined region as a function of I/. We summarize in the following some of the junction current mechanisms proposed for heterojunctions in addition to the diffusion and recombination analogs to homojunctions.

+

1. Direct Recombination through Interface States

One recombination model for heterojunctions pictures the junction as two Schottky barriers back-to-back on either side of an almost metallic layer of interface states where recombination is very high (8484).This model predicts a J vs. V dependence similar to that given by Eq. (42) with a value of A between 1 and 2 depending on the distribution of the depletion layer between the two semiconductors forming the heterojunction. The limiting step in this model is thermal emission of electrons over the barriers at the interface, and hence the model is unable to describe those results found for heterojunctions in which the slope of the In J vs. V curves are nearly or totally temperature independent. 2. Transport Control by Interface States

A similar model has been proposed by Rothwarf (85).The limiting step in this case is interfacial recombination characterized by an interface recombination velocity si .For the intended case of a Cu,S/CdS junction where

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RICHARD H. BUBE A N D ALAN L. FAHRENBRUCH

the Cu,S is sp-type and degenerate, and all of the depletion layer is in the n-type CdS window material, the J vs V relation is given by J(I/)= qSi(nn - nno) = qsjNDexp(-qVD/k7~)[exp(qT//kT)-

11

(44)

A value of A = 1 is predicted in agreement with experimental results for this type of junction at moderate to high bias voltages under illumination. 3. Tunneling Temperature-independent slopes of the In J vs. I/ curves, following Eq. (43), are suggestive of transport by tunneling. Such tunneling is usually appreciable only if the barrier width is less than l o o k The tunneling transmission coefficient for normal incidence through the bottom of a triangular barrier of height E , is (86) T ( E ) = exp[ -4(2rn:)”2El’2/3qhb]

(45)

where m: is the tunneling effective mass (87, 88). Considerable crystallographic anisotropy may be introduced through the dependence of m: on crystallographic orientation in suitable materials (89). If a spike exists a t the interface (because of electron affinity differences, interface dipoles, and the like), tunneling through this spike may be a controlling factor in junction currents (80, 90). On the other hand, tunneling may also be an important process in materials without a spike if tunneling proceeds from the conduction band of the n-type material. for example. to the valence band of the p-type material via interface or depletion layer imperfection states and a recombination step (91). A typical expression for the current resulting from such a combination of tunneling and recombination is given by (91) J ( V ) = B N , exp{[ -4(2m:)1’2( VD - k , V ) ] / 3 h H O }

(46)

+

with H, = ( ~ ~ N A / E Pand ) ” ~k , = 1/(1 cnNA/cPND). Here B is a constant containing N , , the density of tunneling/recombination centers is N , , E , and cp are the dielectric constants of the n- and p-type material. respectively. and k2 expresses the asymmetry of the junction. It may be seen that Eq. (46) is of the same form as Eq. (43) with a small temperature dependence of J, arising from the temperature dependence of the band gaps. 4. Thermally Assisted Tunneling

In many heterojunctions behavior is observed in In J vs. V curves that suggests both tunneling (essentially temperature-independent slope) and thermal activation (current magnitude increasing exponentially with temperature at fixed V ) .This behavior can be interpreted as resulting from the

PHOTOVOLTAIC EFFECT

197

effectsof thermal excitation necessary to raise carriers to an energy sufficient that tunneling becomes highly probable, whereas tunneling at the bottom of the barrier is not probable. This process of thermally assisted tunneling in Schottky barriers has been considered in some detail by Padovani and Stratton (92) and others (93-96). The current through the barrier is the integrated product of the incident electron flux and the tunneling transmission probability, both of which are functions of energy. The product has a maximum value centered around some specific energy Em: For higher energies, the thermal excitation probability decreases exponentially, and for lower energies the tunneling transmission probability decreases exponentially. Integration was achieved approximately in this problem by Padovani and Stratton by assuming a Gaussian distribution of electron energies about Em and then by expanding the tunneling integrand in a Taylor’s series about Em.The result is an approximate forward-bias J-I/ dependence given by with and for the Schottky barrier case, valid over the range of &T/4< E,, < 3kT/2. J o in this expression is given by

Jo =

A*TZ~”2E,!J,2[q(VD- 1/)]1’2 k T cash (Eoo/ k T)

where & is the barrier height, and A* is an adjusted Richardson’s constant. At high temperatures and for thick barriers, J , is thermally activated with an energy approximately &,/A, [if we write Eq. (47) as J ( V ) = J o exp(qV/A,&T)],whereas at low temperatures and for thin barriers, Jo is essentially temperature independent. This treatment has been extended to heterojunctions by Tansley and Owen (99,who did a computer calculation for a parabolic potential barrier, using the WKB approximation for the tunneling transmission probability. Excellent agreement was found for a variety of heterojunctions between p-GaAs and n-Ge, n-Ga,In, -,As, and n-GaAs,P, - y . The simple Schottky barrier form of Padovani’s theory has also been applied with some success to a ZnO/CdTe heterojunction, consisting of a degenerate ZnO n-type layer on a p-type single crystal p-type CdTe substrate (59).In this case electrical measurements as well as the tunneling behavior indicated that a high

198

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

density of charged deep acceptors within the depletion layer reduced the width of a portion of the depletion layer sufficiently to allow thermally assisted tunneling.

C. Schottky Barriers Schottky barriers share many of the same transport mechanisms controlling the junction current in homojunctions and heterojunctions. The forward-biasjunction current mechanisms have been reviewed by Rhoderick (9.5)and Padovani (96),and they include thermionic emission of electrons from the semiconductor into the metal over the Schottky barrier, recombination in the depletion region, tunneling through the barrier, and minority carrier injection and diffusion. The properties of a Schottky barrier can be viewed as the limiting case of a heterojunction when the interface recombination velocity becomes infinite. The usual dominant transport mechanism in Schottky barriers is simple thermionic emission over the barrier. This was treated some years ago by Bethe (98)with the result that J = A*T2 exp( -(P,/kT)[exp(qV/kT - l)] (51) with qt$b = qVD

+ (E, - Ef)"as usual and

A*T2 = 4nqm*k2T2/h3= qN,(kT/2nm*)'I2

(52)

For m* = m, A* is 120 A/cm2 K, the normal Richardson constant for thermionic emission into vacuum. Corrections may be needed for field lowering of the potential barrier for thin barriers (99) and surface state effects (100). The above calculations are based on the assumption that the Fermi level is constant throughout the depletion layer. The Fermi level may be expected to be lowered slightly near the interface if the electron mean free path is less than the depletion layer width, so that transport is limited by the diffusion of the carriers (10Z).Crowell and Sze (99,102)have combined the thermionic emission theory of Bethe and the diffusion theory of Schottky, and to this added electron-phonon interactions, quantum mechanical transmission of the barrier, and image force lowering to form a single model. Their results indicate that with slight modifications Eq. (51) adequately describes the junction current for all except very thin barriers where tunneling cannot be neglected.

D. MIS Junctions Unless Schottky barriers are prepared under the most scrupulous of conditions, the existence of a thin oxide layer between the metal and the

PHOTOVOLTAIC EFFECT

199

semiconductor is a common occurrence. Since this oxide layer can have beneficial results, efforts are sometimes made to grow such layers in a controlled fashion to improve junction performance. An insulating layer between the metal and the semiconductor of an MIS junction may d o the following: ( a ) act as a dielectric separating the metal and semiconductor, thereby decreasing the barrier heights; ( b )limit the flow of carriers, since transport through the insulating layer is either by tunneling or by space-charge-limited currents, thereby reducing the current flow for a given applied voltage; (c) partially sustain the applied voltage, thus leading to variation in barrier height with voltage and diode factors A greater than unity; and ( d )further increase or decrease the effective barrier height because of trapped charge within the insulating layer or at the insulator-semiconductor interface, depending on the sign of the charge. The dark current in an MIS diode is the sum of four components as pictured in Fig. 14: Jth,thermionic emission over the barrier; Jrg,recombination/generation in the depletion layer; Jid,injection and diffusion into the quasi-neutral bulk; and J,, recombination at the semiconductorinsulator interface. All currents, of course, must tunnel through the insulating layer. The presence of the insulating layer can decrease the magnitude of the majority carrier current Jthso that it becomes comparable to the minority carrier currents Jrgand Jid,thus producing a substantial increase in the open-circuit voltage. The maximum thickness of the insulating layer is

FIG.14. Current flow routes in an MISjunction for forward bias of a p-type semiconductor. Quasi-Fermi levels are shown for the dark case.

200

RICHARD H. BUBE AND ALAN

L. FAHRENBRUCH

controlled by the necessity for light-generated carriers to tunnel through this layer also, and an optimum thickness of 20 to 30A is usually found. From Eq. (51) if we generalize slightly to include specifically a diode factor A that need not be exactly unity, the open-circuit voltage for a Schottky barrier controlled by thermionic emission currents is given by

v,, = A& + (AkT/q)hl (J,,/A*T2)

(53)

This expression is still valid for the MIS device, provided that actual values of &, and A are used, and that the insulating layer is thin enough to allow free tunneling. Examination of Eq. (53)shows that the value of V,, can be increased by the insulating layer if its presence serves to increase either +b or A. A variety of models have been proposed that describe such possibilities (103-112).

E. SIS Junctions Because actual heterojunctions often show large values of J , which result in a decreased value of V,, , the inclusion of a thin insulating layer between the two semiconductors may be expected to have the same kind of beneficial effect as such a layer between the metal and semiconductor of a MIS junction. Many systems, especially those in which one of the members of the heterojunction is a conducting oxide, might be expected to have such an oxide layer as a matter of course. Analysis of the situation is complex, and an analysis by DeVisschere and Pauwels (113) indicates that the presence of an insulating layer may be disadvantageous if photogeneration of carriers occurs primarily in the more heavily doped semiconductor, but advantageous if photogeneration occurs primarily in the less heavily doped semiconductor. An SIS model has been proposed to describe the indium-tin oxide heterojunction with silicon (114).

v. EXAMPLES OF PHOTOVOLTAIC MATERIALS SYSTEMS It is an exaggeration (albeit not without considerable truth) to say that a junction between any two materials will show a measurable photovoltaic effect except in very special cases. To show a large enough photovoltaic effect to be of general practical interest, e.g., to have a conversion efficiency for solar radiation of at least lo%, is quite another matter. In fact to date only six materials have produced such high efficiencies: silicon, gallium arsenide, indium phosphide, cuprous sulfide, cadmium telluride, and copper indium selenide. Bucher (1.5) has given an extensive summary of many different types of photovoltaic systems for which basic parameters have been

20 1

PHOTOVOLTAIC EFFECT

reported. In this review we seek only to give a perspective on the types of systems that have shown considerable promise. A . Silicon The Si p-n junction cell is at the present time the only practical solar cell widely available commercially. Reviews of the technological development of the silicon cell have been written by Wolf (115) and Brandhorst (116). These developments have increased the efficiency of single crystal p-n junction silicon cells to values in the range of 15-17%. Improvements have come about by detailed refinements directed toward the solution of particular problems, e.g., an increase in the blue-violet response of the cell by decreasing the thickness of the front n-type layer and increasing its minority carrier diffusion length to produce the “violet cell,’’ (117) and the introduction of a back surface field to decrease loss at the back surface of the cell (118). Standard single crystal growth methods have in recent years been supplemented by methods aimed at reducing the cost of slicing and polishing wafers from grown crystals by producing thin ribbons of Si directly (119-121). 1. Single Crystal p-n Junctions The band diagram of a typical Si single crystal p-n junction is given in Fig. 15. The cell consists of single crystal Si 200-500 pm thick with p-type conductivity. The n-type layer is about 0.1-0.5 pm thick and is produced by diffusion of P or As donor impurities. The back contact typically consists of Al, deposited by vacuum evaporation and heat-treated to produce a p + region capable also of acting as a back surface field. A three layer Ti/Pd/Ag contact is used to the front surface in the form of a suitable grid.

A1

p-Si

”+ FIG. 15. Energy band diagram for a typical Si homojunction p-n junction photovoltaic cell. The thickness of the n-type layer is exaggerated.

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

The 400-A Ti layer acts to produce a strong mechanical bond between Ag and Si, and the 200-A Pd layer inhibits a possible electrochemical reaction between Ti and Ag in the presence of moisture. The front surface grid usually covers about 5-10% of the total area. To reduce the reflectivity of Si (33-54% on a bare surface over the range of 0.35-1.1 pm) antireflection coatings must be used. Materials such as SiO, SiO, ,Si,N,, Al,O, , TiO, ,and Ta,O, have been used as antireflection coatings; one such layer can reduce the reflectivity over the spectral range of interest to lo%, while two layers can reduce it to 3%. Surface texturing has also been used to reduce the reflectivity of silicon (122).

An example of a highly developed cell is the “COMSAT nonreflective” cell, which makes use of a texturized surface to reduce reflection and allow light to travel in paths that are not perpendicular to the junction interface (117).This cell has V,, = 0.59 V, J,, = 46 mA/cmZ,and a fill factor of 0.78 to yield an efficiency of 15.5% for space radiation conditions. The value of Jois 6 x lo-’’ A/cmZ.Under terrestrial radiation conditions, it is expected that this cell will have Jsc= 34 mA/cm2 and an efficiency of about 18%.

2. Polycrystalline Silicon A considerable savings in production cost would be achieved if polycrystalline silicon could be used in place of the single crystalline material just described (21). In general such cells have a lower efficiency but allow many fabrication steps to be eliminated. Polycrystalline silicon can be used in a variety of cell designs, including p-n junction, Schottky barrier, and MIS structures. Large-grain polycrystallineSi cells have been made by directional solidification casting, which produces mm-size grains and a columnar structure with single-crystal-like properties in the direction of the incident light ; efficiencies of the order of 12% have been reported (123). Lindmayer (124) has reported polycrystalline cell efficiencies up to 16%. Diffusion formation of p-n junctions on polycrystalline silicon is complicated by the tendency of the dopant to diffuse rapidly down grain boundaries. Schottky barrier and MIS cells formed by vacuum evaporation of the other layers on polycrystalline silicon or the use of ion implantation doping avoid this difficulty to some extent. 3. Silicon MIS Junction

MIS junction cells on silicon have been developed with efficiency comparable to the best single-crystal p-n junction cells. Such cells with efficiencies between 8 and 12% were made fairly early using Cr/SiO,/p-Si (125, 126), Al/SiO,/p-Si (123, and Au/SiO,/n-Si (128).

PHOTOVOLTAIC EFFECT

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The inversion layer MIS cells is an example of an interesting variation of the MIS structure. The charge in the insulating layer next to the semiconductor interface is strong enough to actually form an inversion layer in the semiconductor surface, thus producing an n-p homojunction via the n-type inversion layer on p-type silicon (129). Godfrey and Green (130) have reported an efficiency of 17.6% for such a cell using either Mg or A1 as the metal. It has been shown that the junction current in this case is minority carrier dominated.

4. Silicon Junctions with Conducting Metal Oxides Efficient cells have been prepared from junctions of silicon with high band gap conducting oxides such as SnO,, In,O, or solid solutions of indium-tin oxides (ITO) as the n-type window material. These oxides are almost completely transparent in the visible portion of the spectrum, while being degenerate semiconductors at the same time. There is considerable evidence that they should be regarded as SIS junctions rather than as simple heterojunctions (II4), especially the observation that equally efficient cells can apparently be made on both p-type and n-type silicon (131, 132). An SnO,/n-Si cell in which the SnOz was deposited by electron beam evaporation and the insulating layer was formed by a subsequent annealing in air showed an efficiency of 10-12% (133). An ITO/p-Si cell that showed an efficiency of 12.8% was analyzed in terms of an SIS model (114, 131). Such oxide/Si junctions have tended to show a degradation in performance with time, presumably owing to the growth in thickness of the insulating oxide layer (134).Overall implications of this degradation mechanism for ultimate practical utility of this type of cell are uncertain.

5 . Amorphous Silicon Amorphous silicon, or more specifically amorphous hydrogenated silicon, a-Si :H, initially prepared by the glow discharge decomposition of silane, SiH, ( 1 3 3 , and containing approximately 20-30% of hydrogen, represents a relatively new form of silicon which is of considerable interest (21). Differences between the a-Si: H and single crystal Si are most evident in the optical absorption spectrum ; the absorption constant is appreciably increased in the a-Si :H material, which exhibits behavior such as a direct band gap at 1.55 eV rather than the indirect band gap at 1.1 eV characteristic of crystalline silicon (136). Hydrogenation apparently decreases the density of localized states by satisfying the broken bonds in the amorphous silicon, thus making possible the doping of the amorphous material n- and p-type (137-14 I).

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

The behavior of a-Si: H as a solar cell material, however, is considerably different from that of single crystal Si, since a-Si:H has a relatively high resistivity and a low carrier mobility. Doping of the a-Si:H to reduce the resistivity produces very short carrier diffusion lengths. Attempts have been made to use the a-Si:H in solar cells using heterojunction, p-i-n, and Schottky barrier structures (136, 142-244b). The following design trade-off is encountered: Since the a-Si:H has short diffusion lengths, it is desirable to have the depletion layer extend over as wide a region as possible, so that the drift field can be used to help collect photogenerated carriers; i.e., it is desirable to have high-resistivity material, but, on the other hand, highresistivity material contributes to the series resistance of the cell. Two other complications arise : (a) since the depletion layer width is a function of forward bias, the width of the field-controlled region changes with voltage; and (b)since a-Si :H is photoconductive, illumination changes the diffusion voltage of the junction. The most efficient cells prepared from a-Si: H have been of the p-i-n barrier type, yielding K, = 0.86 V, J,, = 13.0 mA/cm2, ff = 0.62, and efficiency of 6.9% (144b). Great interest in a-Si: H solar cells persists, since this material provides a way of producing large-area cells at low cost. Although a maximum feasible efficiency of about 15% may be estimated, it remains to be seen whether practical problems can be overcome in real cells to allow the efficiency'to increase appreciably beyond its present values in stable and reproducible cells. B. Gallium Arsenide

The band gap of GaAs at 1.43 eV is near the optimum for solar energy conversion as a photovoltaic material, with a theoretical efficiency of 26-29% for terrestrial use. In addition GaAs has a direct band gap and can absorb 97% of the solar radiation received at the earth's surface within about 2 pm thickness. Although GaAs p-n homojunctions can be prepared (145, 14@, their performance is limited by high front-surface recombination as is typical of a direct band gap homojunction. A major advance occurred when Alferov et al. reported the first p-AlGaAs/n-GaAs heterojunction structure with a space efficiency of 10-1 1% and a strongly increased short-wavelength response compared to a p-n homojunction (147'). A second major increase in efficiency occurred with the introduction of the heteroface p-AlGaAs/ p-GaAs/n-GaAs structure in 1972 fabricated by liquid-phase epitaxy techniques, which had an efficiency of 15.3% for terrestrial radiation and 19.1% in space (148). Although an n+-p homojunction layer with a 0.045-pm thick front n+ layer was reported to have a terrestrial efficiency of 20% after

PHOTOVOLTAIC EFFECT

205

passivation of the front surface by anodization (149), heteroface structures still hold the lead in efficiency, with values of about 21-22% being reported without concentration (150, 151), and a value of 24.7% for a concentration factor of 180 (152). The good performance of the heteroface structure can be traced to the good lattice constant match between AlGaAs and GaAs, producing a low density of interface states at the heteroface interface, corresponding to an interface recombination velocity of less than lo4 cm/sec (153). At the front surface of the AlGaAs the surface recombination velocity is still high, of the order of lo6 cm/sec, but because of the large indirect band gap of AlGaAs, only a small fraction of the light current is generated in the AlGaAs layer. The junction current vs. voltage behavior of GaAs cells is remarkably well described in terms of the basic injection and recombination transport mechanisms. Particularly at high concentration factors for the radiation, most cells show A = 1 with values of Jo reported to be as low as 10- A/cmZ (154).

Because of the high cost of the material itself and because of the precision fabrication processes required to produce these high-efficiency single crystal cells, their major application is in the area of concentrator systems, where concentration of the sunlight by a particular factor allows an increase in cost by roughly the same factor over a cell to be used without concentration (155). Efficiency usually increases with concentration, and concentration factors in excess of lo3 are favored. Under these conditions extreme care must be taken to maximize current collection, since total series resistance values of less than R * cm2 are required. For a typical heteroface cell fabricated for use with concentration, the following parameters are reported for concentration of terrestrial radiation by a factor of lo3: .Is = 23.7 c A/cm2, V,, = 1.19 V, efficiency = 20% (154). Schottky barrier and MIS cells have also been prepared using GaAs single crystals. The presence of an insulating layer plays an important role in improving the performance of Schottky barriers. Figure 16 shows the dramatic effect on the open-circuit voltage of various stages of oxidation on an n-GaAs surface before application of a gold Schottky barrier contact. The effect is not exactly that expected from our previous considerations; increasing insulating layer thickness is actually accompanied by an increase in Jo, but an accompanying increase in A more than compensates for this increase in Jo and produces a net increase in V,, (156).The type of cell shown in Fig. 16 has been called an AMOS cell (antireflection-coated metal-oxidesemiconductor), and efficiencies up to 15% were measured corresponding to these data. As indicated by Eq. (53) two factors play a role in the effect of an oxide layer on the properties of an Au/GaAs MIS junction: increases in

206

RICHARD H. BUBE AND ALAN L. FAHRENBRUCH 1

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I 0.4

VOLTAGE (V)

FIG.16. Light current-voltage curves for Au/GaAs MIS junctions for various treatments of the GaAs surface before application of the metal barrier contact. ( 1 ) “Clean” interface, V., = 0.452 V, q = 8.5%; (2) exposed to air at 300 K for 4 hr, V,, = 0.478 V, 1 = 9.0%; (3) exposed to air at 300 K for 94 hr, V,, = 0.502 V, 1 = 9.8%; and (4) exposed to air at 403 K for 70 hr, V,, = 0.630 V, q = 12.0%.[From Stirn and Yeh (15q.I

barrier height or increases in A, as was the case for the Si MIS devices. The effect is also quite sensitive to the specific crystal orientation of the GaAs face which is oxidized or on which the oxide layer is deposited. The insulating layer in an MIS device need not always be an oxide. Equivalent results have been reported for an Au/n-AlGaAs/n-GaAs cell, in which the n-AlGaAs is a 500-A thick layer made highly resistive by depletion (157). The magnitude of V,, increases with A1 mole fraction x, from 0.53 V for x = 0 to 0.70 V for x = 0.5; a conservative estimate suggests that an efficiency of 19.5% should be possible on an optimized cell of this type. C . Cu,S/CdS Thin-Film Heterojunctions

From the late 1950s and for a period of almost 20 years the only all thinfilm photovoltaic cell available was that formed from a heterojunction between p-type Cu,S and n-CdS, where for the best photovoltaic performance x lies between 1.995 and 2.000, corresponding to the chalcocite structure

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of Cu,S. The p-type Cu,S has a band gap of about 1.2 eV and is the absorber member of the junction; n-type CdS has a band gap of about 2.4 eV and is the large-band-gap window material. The cells of this type have characteristics of the most simple and the most complex of systems. Simplicity lies in the fact that a thin film of CdS deposited, for example, by vacuum evaporation or spray pyrolysis, needs simply to be dipped for a brief period into a warm aqueous solution containing cuprous ions to form a topotaxial layer of Cu,S by a replacement reaction. Other methods may be used, the most popular of which is the vacuum evaporation of CuCl onto CdS, followed by a heat treatment to form the Cu,S and a washing to remove CdC1,. Complexity arises because there is appreciable lattice mismatch between the two materials, Cu diffusion into the CdS occurs near the interface producing the depletion layer in the window material rather than in the absorber, a variety of Cu,S phases exist at room temperature with quite different photovoltaic properties, and the usual grain boundary effects are present owing to the polycrystalline materials. The historical development of the understanding of the mechanisms of the Cu,S/CdS cell had an interesting if tortuous record (6, 158-174). The unified model of the Cu,S/CdS heterojunction has the following general characteristics : (a) light absorption in the Cu,S dominates current generation : (b) the forward junction current flows primarily via recombination through interface states; (c) diffusion of Cu into the CdS widens the depletion layer in the lower carrier-density n-type CdS, giving rise to localized states whose charge can be modulated by illumination; ( d ) low-energy photon response is enhanced by high-energy photon illumination because of the effects on the junction width through modulation of this charge in localized states near the interface ; (e) dark and light forward-bias J- V curves commonly cross owing to effects of illumination on junction current mechanisms; cf, long-term loss of sensitivity may be caused by changes in the Cu,S composition or by additional diffusion of Cu into the CdS; and (9)control of the injection of photoexcited carriers from the Cu,S into the CdS and the injection of carriers from the CdS into the Cu,S under forward bias occurs via recombination or tunneling/recombination through interface states (175, 176) rather than via a series photoconducting layer of insulating CdS :Cu ( I 74) or a small conduction band spike between the Cu,S and the CdS (I77-179). Development of the Cu,S/CdS cell in recent years has been carried forward with some success at the Institute for Energy Conversion of the University of Delaware (7). The heterojunction itself consists of about 20 pm polycrystalline CdS and 0.3 pm of Cu,S. The penetration of Cu,S down grain boundaries in the CdS yields a highly three-dimensional layer; this effect is avoided by using the evaporation of CuCl rather than the dipping

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RICHARD H. BUBE AND ALAN L. FAHRENBRUCH

process to form the Cu,S. Best photovoltaic parameters reported to date are V,, = 0.52 V, Jso = 21.8 mA/cmZ,ff = 0.71, yielding an efficiency of 9.14% for terrestrial radiation. A materials variation that might be expected to improve the performance of Cu,S/CdS cells would be the partial substitution of Zn for Cd to form a Zn,Cdl-,S solid solution (7). Such a substitution would be expected on first principles to produce both a larger V,, because of the electron affinity change and also a larger J,, because of the larger-band-gap window. The bulk resistivity of Zn,Cd, -,,S increases rapidly with increasing y, so that practical values of y are probably limited to less than 0.20 (180-182). Measurements on dipped Cu,S/Zn,.,,Cd,.,,S cells did show an increase in opencircuit voltage V,, = 0.60 V, but a slightly decreased J,, = 15.8 mA/cmZ, yielding an efficiency of 7.4%. Subsequent research has produced a cell with efficiency greater than 10%. D . Indium Phosphide Indium phosphide is in many ways similar to GaAs; it has a direct band gap of 1.34 eV, is limited in homojunction form by surface recombination, and should function well in heterojunctions. As a semiconductor material, however, InP has not received to date the technological development accorded to Si or even to GaAs. A nearly ideal heterojunction is possible with n-CdS and p-InP, since the lattice constant match between these two materials is very close (60-62, 183, 184). Cells with high efficiency up to 15% have been fabricated by vacuum evaporation, chemical vapor deposition, and close-spaced vapor transport deposition of CdS onto single crystal InP substrates. Problems with polycrystalline InP substrates have been described in Section II,D,9. The most efficient CdS/InP cells were made by using a chemical vapor deposition method for depositing CdS on InP using an open-tube H,S/Hz flow system (60-62). Apparently the presence of about 2 mol % of H,S in the gas flow serves to continuously etch the surface of the InP by the formation and sublimation of indium sulfides; thus CdS nucleates on a clean surface and prevents further attack of the InP by the HzS. Cell parameters measured were V,, = 0.79 V, Jsc = 18.7 mA/cm2, ff = 0.74, yielding an efficiency of 15.0%. The largest value of V,, for a CdS/InP heterojunction was produced by the close-spaced vapor transport deposition of CdS (185). An open-circuit voltage of 0.81 V was obtained in a 14.4% efficient cell. In view of this argument that the high efficiencies realized for CdS/InP junctions were the result of good lattice match and clean InP surfaces, it is

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surprising to find that equally efficient cells can be prepared with ITO/InP junctions in which the I T 0 is deposited either by ion-beam deposition methods ( f 8 6 )or by sputtering (187-190). The resolution of this apparent dilemma was given by the realization that in all cases of high-efficiency ITO/InP junctions, it is highly likely that a heteroface buried junction has been formed either by diffusion of a donor like tin from the I T 0 or simply by sputtering-induced damage of the InP surface. E. Cadmium Telluride

Of the six chalcogenide compounds of Zn and Cd, only CdTe can be made highly conducting in both n- and p-type forms. CdTe is the 11-VI analog of the 111-V materials GaAs and InP; it has a direct band gap of about 1S O eV. Like these direct-band-gap materials, homojunctions of CdTe are limited by high front surface recombination losses to values of the order of 8%(291-294). Schottky barrier cells, Pt/n-CdTe, and Au/n-CdTe have been fabricated (195). However, heterojunctions involving CdTe or heteroface buried junctions in CdTe appear to be the most promising. Vacuum evaporation of CdS onto single-crystalCdTe produced a heterojunction with an efficiency of 8% and the spectral response shown in Fig. 8 (196). Chemical vapor deposition of CdS onto single-crystal CdTe was reported to produce cells with efficiency as high as 12% (197,198),although the evidence in this case indicates that a heteroface buried junction has been formed by n-type impurities from the CdS diffusing into the CdTe during deposition. Both CdS/CdTe and ZnCdS/CdTe junctions have been prepared by spray pyrolysis deposition of the CdS or ZnCdS with efficiencies in the 6-8% range (199,200).An efficiency of 8% is also reported for a heteroface CdS/CdTe cell produced by the simple method of screen printing; this cell had the complex structure represented by n-CdS/n-CdTe/p-CdTe :Cu/ p-Cu,Te (201). Large-band-gap conducting oxides such as I T 0 and ZnO are also attractive as window materials for use in heterojunctions. Both of these materials have been used with CdTe. An ITO/CdTe junction formed by sputtering of I T 0 proved to be a heteroface buried junction with an efficiency of 8% (202).On the other hand, a ZnO/CdTe junction formed by spray pyrolysis deposition of ZnO onto single crystal CdTe showed a genuine heterojunction response with an efficiencyof about 9% (59).

F. CuInSe, CuInSe, is the fifth material mentioned at the beginning of Section V that has been made in some form to produce an efficiency of over 10%. It is a struc-

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turally more complex material, belonging to the family of I-III-VI, chalcopyrites. CuInSe, has a direct band gap of 1.04 eV, somewhat smaller than most of the absorbing materials used in solar cells. However, its chalcopyrite structure yields a lattice constant that is a good match with CdS. CdS/ CuInSe, junctions prepared by vacuum evaporation of CdS onto single crystal p-type CuInSe, and fitted with an SiO antireflection coating showed V,, = 0.49 V, J,, = 38 mA/cm2, ff = 0.60, yielding an efficiency of 12% (202,203). All thin-film junctions of CdS/CuInSe, have also been investigated, and = 0.40 V, JSc= the best cells show a heterojunction-like response with 39 mA/cm2, ff = 0.63, and an efficiency of 9.5% (204-206b).

c,

G . Other Possible Materials of Promise

In spite of the promise shown by the major binary compounds of III-V and II-VI types for the production of solar cells, it is still hoped that some other compound might be found that would be structurally simple, composed of abundant elements, capable of inexpensive fabrication into solar cells, and able to display high efficiency for solar energy conversion, which might have some ultimate advantage over the better-known materials. One binary compound that has emerged from such a search is Zn,P, (207). It has a band gap of about 1.4 eV and can readily be prepared in single crystal or thin-film form with p-type conductivity. No isolated n-type form of the material is known to date. Mg/Zn,P, junctions, for which some evidence exists that a buried homojunction has been formed rather than a simple Schottky barrier, have been prepared with an efficiency of 6.0% on bulk polycrystalline ZnJP, (208). The same investigators have produced a 2.7% efficient all thin-film Mg/Zn,P, cell, and a 2% ZnO/Zn,P, cell prepared by sputtering of ZnO. Other materials of exploratory interest are ZnSnP, , ZnSiAs, , and CdSiAs, . Research continues on Cu20, one of the first of the photovoltaic materials, without major improvement in efficiency. Schottky barrier cells of Al/p-WSe, have yielded 5.3% efficiency (209); this material has a direct band gap of 1.35 eV and can be made in either n-or p-type form. If the quest for a simple binary compound is extended to other materials, one may wish to consider the possibility of controlled multielement solid solutions so that both lattice constant match and desirable band gap can be simultaneously achieved (210-212). Polymeric (SN), with a high anisotropic dc conductivity when properly prepared apparently has a larger work function than the elemental metals (213); this material might therefore be of interest as a Schottky barrier

PHOTOVOLTAIC EFFECT

21 1

material with suitable semiconductors, or as an ohmic contact to p-type materials for which no metals exist with large enough work function to provide such contacts. Experimental cells of (SN),/n-GaAs have been prepared with 6%)efficiency (214). Other polymers such as polyacetylene, (CH ) x , may be of interest ;(CH), itself has a band gap of about 1.6 eV and can be doped either n- or p-type, but performance of cells using it appear to be limited by short diffusion lengths for the minority carriers (215). Organic materials can, in principle, be used as the absorber material in a photovoltaic cell, but results to date indicate low efficiencies because of short minority carrier diffusion lengths and high series resistance (216, 21 7).

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141. W. E. Spear, P. G. LeComber, S. Kinmond, and M. H. Brodsky, Appl. P h j x Lett. 28, 105 (1976). 142. D. E. Carlson, IEEE Trans. Electron Devices ED-24,449 (1977). 143. C. R. Wronski, D. E. Carlson, and R. E. Daniel, Appl. Phja. Lett. 29,602 (1976). 144a. C. R. Wronski, IEEE Trans. Electron Devices ED-24,351 (1977). 1446. Y. Kuwano, M. Ohnishi, H. Nishiwaki, S. Tsuda, H. Shibuya, and S. Nakano, 15th IEEE Photovoltaic Specialists Con$, Kissimrnee, Florida, May 1981. 145. D. A. Jenny, J. J. Loferski, and P. Rappaport, Phys. Rev. 101, 1208 (1956). 146. A. R. Cobat, M. F. Lamorte, and C. W. Mclver, IRE Trans. Mil. Electron. 6,20 (1962). 147. Zh. I. Alferov, H. M. Andreev, M. B. Kagen, I. 1. Protasov, and V. G. Trofim, Soo. Phj's. Semicon. 4,2047 (1971). 148 J . M. Woodall and H. J. Hovel, Appl. Phys. Lett. 21, 379 (1972). 149. J. C-C. Fan and C. 0. Bozler, IEEE Phototiolt. Spec. Con& 13th, Proc., p. 953 (1978). 150. L. W. James and R. L Moon, Appl. Phys. Lett. 26,476 (1975). 151. J. M. Woodall and H. J. Hovel, Appl. Phys. Left. 30,492 (1977). 152. R. Sahai, D. D. Edwall, and J. S. Harris, Jr., IEEE Photovolt. Spec. Conf.., 13th, Proc., p. 946 (1978). . 1538 (1976). 153. M. Ettenberg and H. Kressel, J. Appl. P l ~ v47, 154. J. Ewan, R. C. Knechtli, R. Loo, and G. S. Kamath, IEEE Photouolt. Spec. Con$, 13th, Proc., p. 941 (1978). 155. H . Van der Plas, L. W. James, R. L. Moon, and N. J. Nelson, IEEE Photovolt. Spec. Conf., 13th, Proc., p. 934 (1978). 156. R. J . Stirn and Y.C. M. Yeh, Appl. Phys. Lett. 27,95 (1975). 157. Y.D. Shen and G. L. Pearson, Sol. Energy Muter. 2,31 (1979). 158. G. Nadjakov et al., Izv. Bulg. Akad. Nauk. 4, 10 (1954). 159. R. Williams and R. H. Bube, J . Appl. P h j x 31, 968 (1960). 160. E. D. Fabricius, J . Appl. Phys. 33, 1597 (1962). 161. H. G. Grimmeiss and R. Memming, J . Appl. Phys. 33,2217,3596 (1962). 162. J. Woods and J. A. Champion, J. Electronic Control 7, 243 (1960). 163. D. A. Cusano, Solid State Electron. 6, 217 (1963). 164. P. N. Keating, J. Phys. Chem. Solids 24, 1101 (1963). 165. N. Duc Cuong and J. Blair, J. Appl. Phys. 37, 1660 (1966). 166. E. R. Hill and B. G. Kermidas, ZEEE Trans. Electron Deuices ED-14, 22 (19671. 167. B. Selle, W. Ludwig, and R. Mach, Phys. State Solids 24, K145 (1967). 168. A. E. Potter, Jr., and R. L. Schalla, NASA Tech. Note NASA TND-3849 (1967). 169. I. V. Egorova, Sou. Phys. Semicond. 2,226 (1968). 170. R. J. Mytton, Br. J. Appl. Phys. 1, 721 (1968). 171. F. Cabannes, Compt. Rend. 246,257 (1958). 172. H. Moss, Proc. Nut. Aeronaut. Electron. Con/:, p. 47 (1960). 173a. F . A. Shirland and J. R. Hietanen, Proc. Annu. Power Sources Conf. 19th, p. 177 (1965). 173b. F. A. Shirland, Adv. Energy Conv. 6, 201 (1966). 174. L. R. Shiozawa, G. A. Sullivan, and F. Augustine, IEEE Photovolt. Spec. Conf:. 7th Proc., p. 39 (1968). 175. A. L. Fahrenbruchand R. H. Bube, J. Appl. Phys. 45, 1264 (1974). 176. A. Rothwarf, CEC Photovolt. Energy Conv. Con/:,2nd, Berlin, p. 370 (1979). 177. P. F. Lindquist and R. H. Bube, J. Appl. Phvs. 43. 2839 (1972). 178. H. W. Schock, G. Gilger, W. H. Bloss, and F. Pfisterer, Vacuum 27,281 (1977). 179. W. D. Gill and R. H. Bube, J. Appl. Phys. 41,3731 (1970). 180. R. S. Feigelson, A. N'Diaye, S-Y. Yin, and R. H. Bube, J . Appl. Phys. 48,3162 (1977).

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(1979). T. A. Chynoweth and R. H. Bube, J . Appl. Phys. 51, 1844 (1980). S. Wagner, J. L. Shay, K. J. Bachmann, and E. Buehler, Appl. Phys. Lett. 26,229 (1975). J. L. Shay, S. Wagner, K. J. Bachmann, and E. Buehler, J. Appt. Phys. 47,614 (1976). A. Yoshikawa and Y. Sakai, Solid State Electron. 20, 133 (1977). 186. K. S. Sree Harsha, K. J. Bachmann, P. H. Schmidt, E. G. Spencer, and F. A. Thiel, Appl. Phys. Lett. 30,645 (1977). 187. K. J. Bachmann, H.Schreiber, Jr., W.R. Sinclair, P. H. Schmidt, F. A. Thiel, E. G. Spencer, G. Pasteur, W. L. Feldmann, and K. Sree Harsha, J . Appl. Phys. 50,3441 (1979). 188. K. J. Bachmann, T. Bitner, F. A. Thiel, W. R. Sinclair, H. Schreiber, Jr., and P. H. Schmidt, Sol. Energy Muter. 1,249 (1979). 189. H. M. Manasevit, K.L. Hess, P. D. Dapkus, R. P. Ruth, J. J. Yan, A. G. Campbell, R. E. Johnson, L. A. Moudy, R. H. Bube, L. B. Fabick, A. L. Fahrenbruch, and M.-J. Tsai, IEEE Photovolt. Spec. Con$, 13th, Proc., p. 165 (1978). 190. M.-J. Tsai, A. L. Fahrenbruch, and R. H. Bube, J . Appl. Phys. 51,2696 (1980). 191. J. Gu, T. Kitahara, S. Fujita, and T. Sakaguchi, Jpn. J . Appl. Phys. 14,499 (1975). 192. D. Lincot, J . Mimila-Arroyo, R. Triboulet, Y. Marfaing, and M. Bark, CEC Photovolr. Sol. Energy Conf., 2nd, Berlin, p. 424 (1979). 193. J. Mimila-Arroyo, Y . Marfaing, G. Cohen-Solal, and R. Triboulet, Sol. Energy Mutl. 1, 171 (1979). 194. M. Chu, A. L. Fahrenbruch, R. H. Bube, and J. F. Gibbons, J . Appl. Phys. 49,322(1978). 195. J. P. Ponpon and P. Siffert, Rev. Phys. Appl. 12,427 (1977). 196. K. W. Mitchell, A. L. Fahrenbruch, and R. H. Bube, J. Appl. Phys. 48,4365 (1977). 197. K. Yamaguchi, H. Matsumoto, N. Nakayama, and S. Ikegami, Jpn. J. Appl. Phys. 15, 1575 (1976). 198. K. Yamaguchi, N . Nakayama, H. Matsumoto, and S. Ikegami, Jpn. J . Appl. Phys. 16, 1203 (1977). 199. Y. Y. Ma, A. L. Fahrenbruch, and R. H. Bube, Appl. Phys. Lett. 30,423 (1977). 200. S.-Y. Yin, A. L. Fahrenbruch, and R. H. Bube, J. Appl. Phys. 49, 1294 (1978). 201. N. Nakayama, H. Matsumoto, K. Yamaguchi, S. Ikegami, and Y.Hioki, Jpn. J . Appl. Phys. 15,2281 (1976). 202. S. Wagner, J. L. Shay, P. Migliorato, and H. M. Kasper, Appl. Phys. Lett. 25,434 (1974). 203. J. L. Shay, S. Wagner, and H. M. Kasper, Appl. Phys. Lett. 27,89 (1975). 204. L. L. Kazmerski, F. R. White, and G. K. Morgan, Appl. Phys. Lett. 29,268 (1976). 205. L. L. Kazmerski, M. S. Ayyagari, and G. A. Sanborn, 1. Appl. Phys. 46,4865 (19751. 206a. L. L. Kazmerski, 2nd Quarter Rep. to NSF-RANN and ERDA, AER-75-19576-A01, April, NSF/AER-75-19576-2. 2066. R. A. Mickelsen, 15th IEEE Photovoltuic Specialists Conf.,Kissimmee, Florida, May 1981. 207. A. Catalano, V. Dalal, E. A. Fagen, R.B. Hall, J. V. Masi, J. D. Meakin, G. Warfield, and A. M. Barnett, CEC Photovolt. Sol. Energy Conf.. lst, Proc., Luxembourg, p. 644 (1977). 208. A. Catalano, M. Bhushan, and P. S. Noyar, Emerging Materials Contractors In-Depth Review Meeting, August 19-21, 1980, SERI, Golden, Colorado. 209. C. Clemen and E. Bucher, IEEE Photovolt. Spec. Conf., 13th, Proc., p. 1255 (1978). 210. S. Wagner and P. M. Bridenbaugh, J. Cryst. Growth 39,151 (1977). 211. G. H. Chapman, J. Shewchum, B. K. Garside, J. J. Loferski, and R. Beaulieu, Sol. Energy Muter. 1,45 1 (1979). 212. M. Schoijet, Sol. Energy Muter. 1,43 (1979). 182. 183. 184. 185.

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOLUME 56

Spin Polarization in Electron Scattering from Surfaces D. T. PIERCE

AND

R. J. CELOTTA

National Bureau of Standards, Washington, D . C .

I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

219

11. Spin-Dependent Parameters and Interactions

A. Electron Scattering from Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Definitions.. ....................... C. Origin of Spin-Dependent Scattering. . . D. Symmetry Relations of S and P . . . . . . . 111. Experimental Apparatus . . ........................................ A. Measurement of P . . . . ........................................ 5. Measurement of S.. ...................................................

234 234 236

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

240

226

. . . . . . . . . . . . . . . . . . . 252

C. Adsorbates and Phase Transitions

V. Spin-Dependent Scattering from Ferromagnetic Materials. .....................

261

............. C. Scattering from a Ferromagnetic Crystal: Ni( I10 D. Scattering from a Ferromagnetic Metallic Glass: References . . . . . .

...........

I. INTRODUCTION A number of conceptual advances in the physics of the 1920s precipitated attempts to observe spin polarization effects in electron scattering. De Broglie (1924, 1926) postulated the wave nature of particles. The wavelike nature of electrons was observed in electron diffraction at low energies (50-370 eV) from a nickel surface by Davisson and Germer (1927a,b, 1928a) and in diffraction at energies of approximately 20-60 keV first from celluloid (Thomson and Reid, 1927) and subsequently from aluminum, platinum, and gold foils (Thomson, 1928). The concept of electron spin was introduced by Goudsmit and Uhlenbeck (1925, 1926) to explain spectroscopic data. In addition to the spectroscopic evidence, early experimental support for the idea of electron spin came not from measurements of free 219 ISBN 0-12-014656-8

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D. T. PIERCE AND R. J. CELOTTA

electrons but from the observation of the manifestations of the spin of electrons bound in atoms (Gerlach and Stern, 1921, 1924)and in solids (Einstein and de Haas, 1915; Barnett, 1915). With the wave nature of the electron demonstrated, it was natural to look for polarization effects in the scattering of free electrons, analogous to optical polarization experiments or Barkla's (1905, 1906) experiments on the polarization of X rays. It was anticipated that the electron spin might appear as the analog of a transverse electric vector in optical experiments (Cox et al., 1928). To test for the polarization of electron waves, Davisson and Germer (1928b, 1929) performed a double scattering experiment from identical Ni(ll1) crystals. This experiment was similar to a double mirror experiment in which the polarization of light can be demonstrated. The experimental configuration is shown in Fig. 1. Electrons from an electron gun were reflected from the first crystal, the polarizer, and then were reflected again at the same angle of incidence from the second crystal, the analyzer. Only the elastically scattered electrons (in practice those with less than -2 eV energy loss) were collected in the Faraday cup. It was fixed rigidly with respect to the second crystal, and both could be rotated together about an axis coincident with the electron beam between the first and second crystal. The angle between the scattering plane at the first crystal and the second crystal could be varied from O", shown as in the figure (as labeled by Davisson

FIG. 1. Schematic diagram illustrating the principle of the double scattering experiment to test for the polarization of electron waves. [From Davisson and Germer (1929).]

SPIN POLARIZATION IN ELECTRON SCATTERING

22 1

and Germer), to 180" where the Faraday cup was again in the plane of the figure but on the same side of the crystals as the electron gun, to the 90 and 270" positions where the Faraday cup axis was perpendicular to the plane of the figure. In analogy to the optical and X-ray polarization measurements, Davisson and Germer looked for maxima in the intensity at 0 and 1 8 0 and minima at 90 and 270". No such variations of the intensity were found within the experimental uncertainty of one-half of 1%, and they concluded that "electron waves are not polarized by reflection." In their experiment, the electron energy was varied from 10 to 200 eV. The same results were obtained by Joffe and Arsenieva (1929) in a similar experiment using steel mirrors and 10 and 30" angles of incidence over an energy range from 80 eV to 6.4 keV. Double scattering experiments were also carried out at several hundred keV using electrons from a fl source. In these experiments started by Cox et a/. (1928) and continued by Chase (1929), no conclusive evidence was found for the polarization of high-speed p rays by scattering. These early experiments were guided by analogy with optical and X-ray phenomena rather than by a clear theory of spin polarization in electron scattering. [There is a similarity between the mathematical description of light and electron polarization, the basis of which is subtler than was recognized at the time (Fano, 1954; Farago, 1977).] The theory of electron spin was advancing rapidly in those years, first with the nonrelativistic spin theory of Pauli (1927) and then with the relativistic theory of Dirac (1928). Applying the theory of Dirac, Mott (1929, 1932) was the first to provide an understanding of how electrons can be polarized by scattering. The spin dependence is due to the spin-orbit interaction. The orbital motion of the electron as it scatters in the Coulomb field of the nucleus causes the electron to experience a rapidly varying electric field and hence also a magnetic field. The interaction of the electron spin, or equivalently the electron magnetic moment, with this magnetic field produces the spin dependence in the scattering. As emphasized by Tolhoek (19561, it is the inhomogeneous field varying on a microscopic scale that is crucial; a number of theoretical studies showed the impossibility of polarizing an electron beam by interaction with macroscopic fields. With regard to the early double scattering experiments, Mott's theory made it clear that as the Faraday cup was rotated through 360'. only one minimum and one maximum (in the 0 and 180" positions of Fig. 1) were expected, rather than two maxima and two minima as in the optical analogy. This is because the electron spin specifies a direction rather than just an axis of polarization as for light. Thomson ( 1934) mentioned that in fact Davisson and Germer did measure an asymmetry in the 0-180" position, but he attributed it to experimental error. Surprisingly, the negative result of Davisson and Germer was accepted and apparently not further scrutinized

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D. T. PIERCE A N D R. J . CELOTTA

until Kuyatt (1975) pointed out that if Davisson and Germer had analyzed their data for the correct asymmetry, they would have found the polarization on scattering to be as high as 10-15%. Calculations by Feder (1977a) subsequently showed that an apparatus-induced asymmetry of that magnitude could also be caused by an angular error of I”. A test of Davisson and Germer’s conclusion for the Ni( 1 1 1) surface in their experimental geometry has yet to be made using modern techniques. The conditions established by Mott’s theory for significant spin polarization in scattering were that the scattering should be through large angles ( 290”), the scattering nucleus should be of high atomic number Z (the polarization effect increases with 2’1, and the speed of the electrons should be comparable with the speed of light ( E 2 50 keV). With the exception of an experiment by Langstroth (1932) using electrons in the 1-10 keV range, other experiments during this time used high energy electrons. Thomson (1934) and Myers et al. (1934) found no spin polarization in electron scattering and compared their results with the other results of that time, which were usually negative or inconclusive. Shull et al. (1943) reported the first conclusive measurement of a polarization effect in scattering. In their experiment, 400-keV electrons were scattered at 90” from thin gold foils. Special care was taken to have control measurements of apparatus asymmetries and to use very thin foils in order to avoid multiple scattering. This scattering of electrons from high-Z materials at energies in the 100 keV range is known as “Mott scattering” and is widely used as a means of detecting electron spin polarization. The theoretical prediction (Lee and Yang, 1956) and first experimental verification (Wu et al., 1957) of the nonconservation of parity in weak interactions sparked a renewed interest in using Mott scattering to measure the polarization of electrons emitted in fl decay. Sherman (1956) made numerical calculations of spin dependent cross sections for high-energy electron scattering, and the expected intensity asymmetry found on scattering a polarized beam is now known as the “Sherman function.” More recent and refined calculations have been made for Au and Hg by Holzwarth and Meister (1964) for all angles at 30 energies between 200 eV and 290 keV. There have been several double scattering experiments (Apalin et al., 1962; Mikaelyan et al., 1963; Van Klinken, 1966) to test the calculations. Mott scattering in the study of fl decay has been discussed, for example, in reviews by Page (1959) and Frauenfelder and Rossi (1963). As discussed in Section 11, it is the electrons with energies less than a few keV that probe the surface region. A combination of the negative results of Davisson and Germer and of other low-energy experiments, and Mott’s condition of high energy for the occurrence of spin polarization effects appear to have caused the neglect of spin polarization in low-energy electron

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223

scattering experiments until the 1960s. Actually Massey and Mohr (1941) extended Mott’s results down to 100 eV by including the screening effect of the atomic electrons on the Coulomb field of the nucleus and found that polarization effects were still to be expected owing to the spin-orbit interaction. The first evidence of spin polarization in scattering of low-energy electrons was reported by Deichsel (1961) in experiments on a beam of mercury atoms. Since then, spin polarization in electron scattering from atoms has been an active area of research. Maison (1966) suggested that large spin polarization effects should also be expected in electron scattering at low energies from crystals or amorphous solids. He pointed out that Weisskopf (1939, who predicted no significant polarization in electron scattering from the periodic potential in a crystal, approximated the potential by a finite Fourier series and thereby lost the rapidly varying part of the potential with high gradient that gives rise to spin polarization. Spin polarization in low-energy electron scattering from surfaces was first reported by Loth and Eckstein (1966) for solid mercury. Spin polarization was observed in scattering from polycrystalline targets of W, Pt, and Au at 900 eV and scattering angles between 65 and 155”(Loth, 1967). The polarization increased as the sample was heated suggesting the possibility of a reduced polarization due to surface contamination in the lowtemperature measurements. Spin polarization was also observed in scattering from a solid Hg sample at energies between 300 and 900 eV and scattering angles from 65 to 155” (Eckstein, 1967). The surface was kept fresh by continuous evaporation of Hg onto the sample. Theoretical studies of the spin dependence in electron diffraction from single crystals preceded the experimental observations. Starting in 1970 there were several papers investigating spin-dependent scattering in tungsten due to the spin-orbit interaction (Jennings, 1970, 1971a, 1974; Jennings and Sim, 1972; Feder, l971,1972,1973a, 1974,1975,1976).Theseculminated in a joint paper (Feder et af.,1976) which compared the results of the two different computational schemes and, after correcting an error in each of the computer codes, found excellent agreement. In these calculations, the relativistic atomic phase shifts were obtained by solving the Dirac equation with an appropriate potential. These were then used in a dynamical low-energy electron diffraction (LEED) calculation to obtain the spin-averaged and spin-dependent information. A new era in spin polarization in electron scattering from surfaces began when O’Neill et al. (1975) reported the first successful experiment in which polarized low-energy electron diffraction (PLEED) was observed. These experiments on W( 100) showed large polarization effects that depended strongly on diffraction geometry. Soon after, results on Au(ll0) were reported by Muller and Wolf (1976). Both of these groups used Mott scattering

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to detect the spin polarization induced by scattering an initially unpolarized beam. The GaAs spin-polarized electron source was discussed (Pierce et af., 1977;Garwin and Kirby, 1977;Unertl et al., 1978a)as a means of obtaining an intense polarized electron beam for PLEED. An experimental breakthrough occurred with the application of such a polarized electron source (G.-C. Wang et al., 1979); the spin-dependent information could then be obtained simply by measuring scattered intensities rather than polarizations. The types of apparatus that have been used for PLEED measurements will be discussed in Section 111. An introduction to the theory of spin-dependent scattering due to the spin-orbit interaction will be presented in Section IV along with a review of experimental results starting with those of O’Neill et al. So far we have only considered spin dependence in electron scattering due to the spin-orbit interaction. The requirement that the total electron wave function of the target and the incident electron be antisymmetric gives rise to the exchange interaction which can also lead to spin-dependent scattering. Bincer (1957) and Ford and Mullin (1957) extended the electronelectron scattering calculations of Mnrller (1932) to the case of polarized electrons. The calculations, which apply at high incident energies where the binding energy of the polarized target electron is small compared to the energy transfer, show that the cross section for scattering parallel spins is much smaller than for scattering antiparallel spins as expected from the Pauli principle. M~llerscattering is often used as a detector for the longitudinal polarization of high-energy electrons (20.3MeV) and was used to measure electron helicity in j?decay (Frauenfelder and Rossi, 1963).Mnrller scattering has also been tested at 60 keV in a transverse geometry. An electron beam that passed through a thin iron foil magnetized transversely to the beam had ) polarization (Raith and Schliepe, 1962). no observable ( ~ 0 . 3 %spin At low incident energies, the transfer of spin polarization from polarized atoms to electrons by spin-exchange collisions was observed in the electron trapping experiments of Dehmelt (1958)and in later trapping experiments described by Farago and Siegmann (1969). The ratio of the exchange to total electron collision cross section was observed by Rubin et al. (1959, 1960) in elastic electron scattering from a polarized potassium beam and by Lichten ~,~ and Schultz(1959)for inelastic scattering in the excitation of the ~ S ’ S metastable state of hydrogen. Measurements of the individual direct and spinflip amplitudes for electron scattering from polarized potassium atoms have been reported by Hils et al. (1972) and Collins et al. (1971), respectively. The manifestation of the exchange interaction in electron scattering from surfaces was first observed by Palmberg et al. (1968) in a LEED experiment in NiO. Because the length of the magnetic unit cell in antiferromagnetic NiO is twice that of the chemical unit cell, there are half-order

SPIN POLARIZATION IN ELECTRON SCATTERING

225

LEED beams due to the “magnetic” or exchange interaction. Since an antiferromagnet has an equal number of oppositely ordered spins, the halforder beams are neither polarized nor do they reflect a scattering asymmetry if the incident beam is polarized. These experiments are outside the scope of this review and will not be discussed further, although we note that some of the theoretical work on NiO (Wolfram and DeWames, 1974) can be applied to ferromagnets where spin polarization in electron scattering is found. The spin dependence of polarized electron scattering from a ferromagnet was first reported by Celotta et al. (1979) and shown to be a sensitive measure of the surface magnetization. In Section V, spin polarization in electron scattering from magnetic surfaces will be discussed. This introduction clearly has not been limited to spin polarization in scattering from surfaces but has also included fi decay and scattering from atoms and nuclei. Much of the work on electron spin polarization in these fields is applicable in some way to scattering from surfaces. There have been many excellent review articles concerning electron spin polarization. A formal description of spin polarization, methods of producing and detecting polarized electrons, and measurement of the g-factor anomaly are discussed by Tolhoek (1956) and Farago (1965). Some of the reviews of electron spin polarization stimulated by the discovery of parity nonconservation in fi decay are those of Page (1959),Grodzins (1959), McMaster (1961),and Frauenfelder and Rossi (1963). There are several reviews of spin polarization in electronatom collisions (Kessler, 1969; Raith, 1969; Farago, 1971; Bederson, 1973; Lubell, 1977).The book by Kessler (1976)is the most extensive treatment of polarized electrons up to that time; emphasis is on spin polarization in interaction with atoms. There is also a recent review of polarized electron sources (Celotta and Pierce, 1980). A review of spin-polarized LEED, which we expect will give a more detailed discussion of theoretical developments than we do, is currently being prepared by Feder (198 1). This review will be limited in scope to spin polarization in scattering from surfaces which started in earnest experimentally in 1975 and theoretically a few years earlier. Thus it is a rather young field and in this review we have attempted to include all references known to us at the time this was completed (November 1980). 11. SPIN-DEPENDENT PARAMETERS AND INTERACTIONS

In this section we discuss the boundaries of this review implied by limiting it to electron scattering from surfaces. We then consider definitions of the measured quantities, the polarization P and the spin-dependent scattering asymmetry S. The spin-orbit and exchange interactions both give rise to

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D. T. PIERCE AND R. J . CELOTTA

spin-dependent scattering; the scattering geometry can be chosen to enhance one or the other. The relation of S and P implied by symmetry is discussed. A . Electron Scattering,fhomSurjaces

Low-energy electrons can be scattered from solid or liquid surfaces. Whereas there are many studies of solid surfaces, works on liquids, such as the liquid Hg studies of Schilling and Webb (1970), are rare. Of the various types of solid surfaces (e.g., single crystal, polycrystalline, and amorphous), most work has been on single crystals to observe diffraction structure in LEED (Van Hove and Tong, 1979). Scattering from amorphous surfaces can, however, provide information on atom-like properties uncomplicated by variations in scattered intensity due to diffraction (see Section V,D). Metal, semiconductor, and insulator surfaces, both clean or with adsorbates are accessible to studies by low-energy electron scattering, but special techniques must be used for insulators to deal with sample charging. Measurements of the intensity or polarization of elastically scattered electrons are sensitive to the surface region of the sample owing to the high inelastic scattering cross sections for low-energy electrons. The average depth of the surface that is probed is determined by the inelastic mean free path which is about 3-30 A for electron energies in the range 20-2000 eV (Powell, 1974). Only electrons that scatter within roughly a mean free path of the surface contribute to the elastically scattered beam. Inelastically scattered electrons that have undergone a characteristic energy loss are also surface sensitive since electrons from deeper in the solid undergo further collisions and are removed from the characteristic peak. Surface analysis techniques, such as Auger or photoelectron spectroscopy, are sensitive to the outer atomic layers of the sample for these reasons. The definitions that follow are applicable to either an elastically or inelastically scattered electron beam. B. Definitions

If an electron beam is in a pure spin state, it can be described by a single wave function and its polarization is the expectation value of the Pauli spin operator Q

P

= (G)

In a pure spin state, the beam is totally polarized and the degree of polarization /PI = 1. In practice, an electron beam is not in a pure state, but is in a mixed state consisting of an ensemble of different states each described by its own wave function. The polarization is then the ensemble average of the expectation value of the Pauli spin operator. The density matrix p p is useful

227

SPIN POLARIZATION IN ELECTRON SCATTERING

to describe the statistical mixture of spin states of a partially polarized beam, the polarization is then (Tolhoek, 1956; Kessler, 1976)

P = tr(p*o) (2) where we have assumed a normalization such that tr p p = 1. The density matrix can be expressed in terms of the components of the polarization

If the z axis is taken as the direction of polarization, the density matrix is pP = ;(I

'd

1 -O P ) = ( I -PI('

o O+ ) + P ( ' 0

0 0)

(4)

and one sees that an electron beam can be considered as an incoherent sum of a totally polarized part, where for example N , = 0, and a totally unpolarized part ( N , = N , ) in the ratio P/( I - P). N , and N , are the number of electrons with spins, respectively, parallel and antiparallel to the quantization direction, which we have taken to lie in the + z direction. The degree of polarization along this direction can be written

P

=

(Nt - N , ) / ( N r + N , )

(5)

and has the range of values - 1 s P s 1. For example, for P = 0.5 there are three times as many N , as N , or equivalently, half the electrons are lined up in the same direction and the other half are randomly oriented. Strictly speaking, the polarization must be measured in the rest frame of the electron, since P as defined above is not Lorentz invariant. At relativistic energies (Frauenfelder and Rossi, 1963) the transverse polarization in the laboratory frame is smaller than in the rest frame by mc2/(mc2 E ) ; all kinetic energies E of interest in scattering from surfaces are much smaller than the rest energy mc2 = 0.511 MeV. The second quantity we wish to define relates to the asymmetry in the scattering of a polarized beam from a target. We define S as the strength of the spin-dependent scattering, which can be considered the analyzing power of the target. It is the normalized difference in the scattered intensities I , ? ( I , ,) for incident spin polarization parallel (antiparallel) to a quantization axis. S = U T T - IT,)/Utt + IT,) (6)

+

where an incident polarization of unity has been assumed. Equation (6)gives the component of S along the axis of the incident spin polarization. Only if this axis is along S,is the total magnitude of S determined experimentally.

228

D. T. PIERCE AND R. J. CELOTTA

We can also define a density matrix for S (Tolhoek, 1956) p s = j(1

+ s-a)

S = tr(psu) The scattered intensity is

I,,,,,

=

2Ztr(ppps)= Z(l

+ P,*S)

(9)

where Zl.t and I, of Eq. (6) correspond to Po and S being parallel and antiparallel in Eq. (9) and Z = i(Zt + I , , ) .

,

C. Origin of Spin-Dependent Scattering

The scattering from an incident plane wave state with spin s and wave vector k into a final plane wave state with spin s‘ and wave vector k is described by the 2 x 2 scattering matrix, T(k, k’, E, 9, 4), where E is the energy and the scattering geometry is specified by the surface normal fj and the azimuthal orientation 4 (Dunlap, 1980). It is sufficient to consider the two “large” components of the four-component spinor so T is a 2 x 2 matrix (Rose, 1961). The four amplitudes of the matrix T describe the effect of the scattering on the spin: Tll (up-fup), T,, (down-fdown), T12 (down --t up), and T,, (up --t down). The (spin-flip) amplitudes T12and T,, change the spin; the (direct) amplitudes T,, and T,, do not. These amplitudes can only be obtained by a detailed calculation, but symmetry can be used to predict some of their properties as described in Section I1,D. Both the spin-orbit interaction and the exchange interaction can give rise to spin dependent scattering amplitudes. The interaction Hamiltonian contains the spin-independent Coulomb and exchange-correlationpotentials. How to best choose such potentials is the essence of band structure (Morruzzi et al., 1978) and LEED calculations, which are beyond the scope of this review. The spin dependence due to the spin-orbit interaction emerges naturally as a result of solving the Dirac equation for the spin dependent scattering phase shifts. The form of the spin-orbit term from the Dirac equation can be shown to be (Kessler, 1976) 1 1 dV(r - ri) v,, = s.L 2rn2c2 Ir - r,l dr ~

where r is the position of the incident electron with spin s and angular momentum L, and ri is the position of the ith atom. The exchange interaction arising from the required antisymmetrization of the electron wave function is an additional source of spin-dependent scattering from surfaces. In polarized electron scattering from a hydrogen

SPIN POLARIZATION IN ELECTRON SCATTERING

229

atom, there is a difference in the (et + HJ) and (et + H f ) scattering cross sections owing to the antisymmetric nature of the total wave function as required by the Pauli principle. Just as there is exchange scattering from H atoms, there can be exchange scattering from a ferromagnetic surface that has an ordered net spin density ps = pr - p L where p t c l , is the density of majority (minority) spins. However, it is not practical to use antisymmetrized wave functions for the infinite electron system of the incident and surface electrons. To make the problem tractable, the nonlocal exchange potential between the incident electron spin and the surface electrons is approximated by a spin-dependent local potential. What was a problem involving antisymmetrizing wave functions in the case of electronhydrogen atom scattering has been converted in the case of a surface to scattering of electrons from a spin-dependent potential. The potential differs for an incident electron with spin parallel or antiparallel to the excess spin density. The strength of the interaction depends on the orientation of the incident spin given by the unit vector 8 relative to the direction of the ordered spin density 9,a unit vector in the direction of the net surface spins 9. An approximation to this interaction is the linearized Slater (1951) exchange potential, the spin-dependent part V:, of which is proportional to (DeCicco and Kitz, 1967)

+

where use has been made of the fact that ps << p ; p = p , p i is the charge density. Just how to write the spin-dependent exchange of Eq. (11)is an area of current theoretical interest, but it will depend on ps and the orientation of the incident spin relative to the excess spin density. A Slater-type potential was used by Feder (1973b) in PLEED calculations of ferromagnetic Fe. A linearized exchange-correlation potential of von Barth and Hedin (1972)was used in PLEED calculations of ferromagnetic Ni( 110)by S.-W. Wang (1980). From Eqs. (10) and (1 1) it is apparent how to choose the experimental configuration in order to distinguish between the spin-orbit and the exchange interaction. The experimental geometriesare shown in Fig. 2. The spin-orbit interaction is maximum when the incident electron spin s is parallel to its orbital angular momentum L, and zero when it is perpendicular, that is, when s lies in the scattering plane. We measure S or P with respect to the normal of the scattering plane fi = (k x k)/lk x kl. The exchange interaction can be minimized by demagnetizing the sample so that there is no longrange ordered spin density. In the measurement of the exchange scattering, the incident polarization if measuring S (or the induced polarization if measuring P)should lie in the

230

D . T. PIERCE AND R. J . CELOTTA

FIG.2. Experimental geometry to distinguish between the spin-orbit interaction and exchange interaction as the source of the spin dependence. When the electron beam is scattered upward, the effect of the spin-orbit interaction is measured; the scattering plane is vertical in the figure, and the incident spin s is perpendicular to the scattering plane which has a normal ri. In the case of a magnetic surface with magnetization M and majority spin density 9,the deflection of the incident beam to the right defines a scattering plane containing s, so the spinorbit interaction is minimized.

scattering plane so that S O L(or sot?)is zero. The sample is then magnetized in the scattering plane so that j - 9 is maximum. Note that the direction of the surface spin density 9 is opposite to the surface magnetization M, since the electron spin and electron magnetic moment are antiparallel.

D. Symmetry Relations of S and P When an initially unpolarized electron beam is scattered from an unpolarized atom beam, a polarization P is induced perpendicular to the scattering plane by the spin-orbit interaction; this P is equal to the scattering asymmetry S of an incident beam polarized normal to the scattering plane. In scattering from surface, the situation is complicated by multiple scattering and the lower symmetry of the crystal surface, so P and S are no longer always equal.

SPIN POLARIZATION IN ELECTRON SCATTERING

+.I

23 1

w (100) (00) BEAM

,

60

.

I

.

'

*

.

,

100

.

.

A

160

INCIDENT ENERGY (aV)

FIG.3. Measurements of S by G.-C.Wang rt al. (1979) (solid line) are compared to measurements of P by Kalisvaart el at. (19781 (crosses) for a W(100) surface at angles of incidence from 10 to 17". The scattering plane is the (010) plane, a mirror symmetry plane of the crystal, so S = P. [From G.-C.Wang er al. (1979).]

G.-C. Wang et al. (1979) showed experimentally and theoretically that

P = S in specular scattering from a W(100) surface when the scattering plane was a mirror symmetry plane of the crystal, in that case the (010) plane. The comparison between S and P is illustrated in Fig. 3 for eight different angles of incidence. The crosses are the polarization measurements of Kalisvaart et al. (1978) using a Mott detector. The solid lines are the S measurements of G.-C. Wang et al. (1979) using a polarized incident beam. The magnitude of the S curve was normalized to the P curve at 13" thereby determining the polarization of the incident beam. The rest of the curves then show remarkable agreement. The angles of incidence in Fig. 3 are those of Kalisvaart et al. (1978) and are 1" less than those determined in the recent work of G.-C. Wang et al. (1981a).

232

D. T. PIERCE AND R. 3. CELOTTA

The symmetry properties of S and P have been studied further by Dunlap (1980) and Feder (1980a) to determine a general relationship between S and P and to find special cases where they are equal in addition to the mirror plane case. The discussion here follows closely those of Dunlap and of Feder. The 2 x 2 scattering matrix can be written in terms of the Pauli spin matrices T = A1 BOG (12)

+

where 1 is the unit matrix. The determination of the complex coefficients A and B requires a multiple scattering calculation, but this is not necessary to make symmetry arguments. It is assumed that the symmetry of the manyelectron wave function of the solid is the same before and after the scattering process; in particular, this holds for elastic scattering. S and P can be written

+ A*B - ZBx B*)/(AA* + B.B*) P = (AB* + A*B + ZBx B*)/(AA* + B.B*) S = (AB*

(13) (14)

Note that while in general S and P are different owing to the different signs of the last term in Eqs. (13) and (14), their lengths are equal, S . S * = Pap*, i.e., the total magnitudes of polarization and asymmetry are equal. In this notation, the intensity of the scattered beam for incident polarization Po is Z(P0) = (IAJ2 lBI2)(1 S.P,) (1 5 )

+

+

The symmetry properties of T and hence of S and P are determined by the total Hamiltonian of the electron and the crystal plus the asymptotic form of the wave function at large distance. If the crystal is time reversal invariant (or, in the case of a magnetic crystal, if the magnetic fields are reversed) then Eq. (12) must be unchanged under time reversal. Since under time reversal u+ -u, k+ - k’, and k’-t -k , this implies A(k, k ,E, Q, 4 ) - t A ( - k , -k, E, Q, 4) and B(k, k‘,E, Q, +)+ - B ( - k , -k, E, Q, 4). Hence under time reversal S(k, k’, E, Q, 4) + -P(-k, -k, E, Q, #),andP(k, k’, E, 4, 4)+-S(-k’, -k, E , 4 , 4).Thus the original S equals the negative of the time-reversed P and vice versa. The length of the vector remains the same. Time reversal invariance alone is not sufficient to ensure that S = P. Consider now the intensity of Eq. (15). For the usual spin-averaged LEED case Po = 0, and then I@, k’) = Z( -k, -k’). This is just the usual reciprocity theorem (Woodruff and Holland, 1970; Lagally et al., 1971a). If Po # 0, the intensity is still time reversal invariant since Sapo is a scalar. However the time reversed case is more complicated, since Po changes on scattering to some P,, which would be the initial polarization in the time reversed case; S would also be different.

SPIN POLARIZATION IN ELECTRON SCATTERING

233

Dunlap and Feder have pointed out that the difference between S and P could be observed in specular scattering from a threefold symmetric surface such as the (1 11) surface of an fcc or bcc crystal. As a function of azimuthal angle 4 for a fixed angle of incidence, the intensity will show a sixfold symmetry, while S will display a threefold symmetry rotated 60" with respect to the threefold symmetry of P.Note that it is the vectors S and P that will show the threefold symmetry; the magnitudes, IS/and /PI, will show a sixfold symmetry. The axial vectors S and P transform as vectors under rotations. Under reflections, in contrast to a normal vector, the components of an axial vector that are in the mirror plane rather than perpendicular to it change sign. Dunlap (1980) has worked out the relationship of S and P under rotations and reflections for elastic PLEED from surface symmetries characterized by any of the six point groups: C2, C,, , C , , C,,, C,, C4".With regard to specular scattering from W(100) as discussed above, time reversal and a 180" rotation about the surface normal (which leaves the crystal unchanged) interchange S and P;that is, in this case S = P for all 4, not only for the mirror plane tested by G.-C. Wang et al. (1979). As discussed by Kessler (1 976) the polarization induced in an unpolarized electron beam scattering from a spherically symmetric atom is along the normal to the scattering plane. No projection of S or P is expected along an axis given by k, since P k and S k are pseudoscalars, and as Lee and Yang (1956) pointed out, the observation of a pseudoscalar implies nonconservation of parity. However, a parity operation does not leave a semi-infinite crystal invariant, and scattering from such a target can produce a longitudinal polarization Pk. A recent PLEED experiment by Bauer et al. (1980a) provides a nice illustration of this phenomenon and how multiple scattering effectively samples the symmetry of the crystal. Figure 4 shows the longitudinal component of the polarization vector as a function of azimuthal angle d, in

.

30°

60"

90'

120°

150°

180°

Azimuthal Angle 4 FIG.4. A rotation diagram of the component Pkof the specular beam lying in the scattering plane. The incoming beam was incident on the Pt( 1 1 I ) surface at an angle of incidence of 43.5" and an energy of 60 eV. Mirror planes at 60, 120, 180",etc., separated by 60", correspond to the threefold rotational symmetry of the crystal. [From Bauer et al. (1980a).]

234

D. T. PIERCE AND R. J. CELOTTA

specular scattering from Pt( 111) at an angle of incidenceof 43.5"and incident energy of 60 eV. P , vanishes for r) = 60, 120, 180", etc., which are mirror planes of the crystal; that is, P is normal to the scattering plane if the scattering plane is a mirror plane. pk ,which is parallel to the mirror plane, changes sign on either side of the mirror plane as expected for an axial vector. Mirror planes separated by 60" imply a threefold rotational symmetry. Note that 90 and 150" do not correspond to mirror planes. Thus Pk reflects the true threefold rotational symmetry of the crystal rather than the sixfold symmetry of the specularly reflected intensity. The PLEED quantities S and P are sensitive to the symmetry of the surface, and a specific relationship between S and P is expected for a given surface structure. A comparison of the two quantities when measured together will allow one to place restrictions on possible models of the surface structure. A preliminary report of such a comparison has been given by Reihl et al. (1980). With regard to scattering from magnetic surfaces, we note that the magnetization M transforms under rotations and reflections like S and P and under time reversal M + - M. For elastic magnetic scattering, in the absence of spin-orbit coupling, the spin is conserved and S and P are equal and lie along the magnetization axis (Feder, 1981). Spin-flip scattering from a ferromagnetic surface is inelastic due to magnon excitation, and in general S # P in that case. 111. EXPERIMENTAL APPARATUS A . Meusurement oj'P

Since LEED apparatus are inherently intensity measuring devices, and as such are ill-equipped for electron polarization determinations, it is in some ways surprising that the first successful polarized LEED experiments used Mott detection at high energies to measure the polarization of the scattered beam. It would appear that a simpler tactic would be the addition of an electron source which was capable of modulating the polarization direction. The apparatus would be otherwise unchanged and could be used in the mode for which it was designed, that is, to make intensity measurements. This seeming contradiction can be explained by the fact that the extensive use of Mott detection in nuclear physics has given us a well-developed, if inefficient, procedure for polarization determination, whereas polarized electron sources (Celotta and Pierce, 1980) only recently have reached the stage where they can be considered as an alternative to a conventional electron gun in a LEED experiment. In LEED experiments that measure spin dependence by determining P , the parameters of the incident electron beam are free to vary over a wide

SPIN POLARIZATION IN ELECTRON SCATTERING

235

range. Beams are formed with energies of a few electron volts to over 1000 electron volts with typical currents of a few hundred nanoamperes. In order to preserve the angular information in the diffraction process, beam divergences are kept below 1". The cathode is usually a directly heated tungsten filament with an energy spread in the beam of the order of 0.5 eV. We show in Fig. 5 the polarized LEED apparatus of Kalisvaart et uf. (1978) as one example of the Mott detector type of apparatus. Apparatus of this variety have also been constructed by Miiller ez ul. (1978) and Calvert et a/. (1977). The two functions, the LEED experiment and the polarization measurement, are physically separated, each occupying its own vacuum chamber . The experimental realization of the Mott technique requires accelerating the electrons to 2 100 keV, scattering them from a thin gold foil, and detecting the small backscattered current in wide-aperture detectors. Kessler (1976) gives a good description of the design, application, and possible sources of error in Mott detection. The need to accelerate the electrons to 2 100 keV has some definite experimental drawbacks. The Mott analysis system tends to be large (due to diffuse backscattering and voltage standoff considerations) and usually dwarfs the LEED chamber. Also, the entire Mott analysis chamber, with associated pumps and electronics, is generally floated at 100 keV above ground, requiring a shielding arrangement. In the experimental apparatus shown in Fig. 5 the Mott detection system is fixed in space, and angular variations in the PLEED scattering geometry are accomplished by rotating either the crystal or the electron gun-LEED

LEED CHAMBER

MOTT ANALYSIS CHAMBER

FIG. 5. A schematic view of a PLEED apparatus that uses Mott detection. The electron gun, LEED grids, and crystal can be rotated. The polarization of the diffracted beam is determined by a second scattering at 100 keV from a thin gold target, resulting in asymmetric count rates at the surface barrier detectors. [From Kalisvaart e / al. (1978).]

236

D. T. PIERCE AND R. J. CELOTTA

screen assembly. A slot has been cut in the LEED system fluorescent screen so that the spot to be analyzed may be extracted, accelerated to 100 keV, and scattered from the gold foil. The LEED grids are used to remove electrons from the beam which have undergone an energy loss of more than 2 eV. Measurements of both specular and nonspecular diffraction have been obtained using this apparatus. An attractive alternative to high-energy scattering is to use the spin-orbit interaction present in PLEED as the basis of a low-energy polarization detector. Recently, Kirschner and Feder (1979a) and Wang et al. (1981a) have described PLEED detectors that make use of the nonspecular beams from WlIOOl. We discuss the practicality of PLEED detectors in Section IV,E. B. Measurement of S Determinations of S quantify the spin dependence of the scattering event by measuring the scattered intensity for each of two possible incident spin orientations. Recall that S is the ratio of the difference in scattered intensity for the two orientations to the sum of the intensities,

s = ( l / p o I u , ~- I,,WITT + I , , ) .

(16)

This equation differs from Eq. (6) by the factor l/IPol which corrects for the fact that the source has a polarization of lPol < I . Note that only intensity measurements are made, and the apparatus resembles a conventional LEED apparatus except for the substitution of a polarized electron gun. The polarized electron gun selected should have all the characteristics of the normal LEED electron gun described earlier. In addition it should produce as highly polarized a beam as possible, since the numerator of Eq. (16) will vary linearly with the polarization. On the other hand, it is usually possible to achieve the same level of precision in the measurement of S with a source of lower polarization if the statistical noise is reduced by a higher current at the lower polarization. A figure of merit, which takes into account the advantage gained both by high intensity and high polarization, is P i 1 (Kessler, 1976); a source with 50% polarization is therefore equivalent to a source with lOOo/, polarization if it produces four times as much current. Of great importance are the characteristics of the source with regard to reversal of the preferred spin direction. Since intensity differences are measured, polarization reversal should cause no change in the incident beam current and should be achievable at a rate that can be adjusted to optimize the signal-to-noise ratio, given the noise spectrum of the apparatus. Since the spin-dependent effects may be very small, as in the case of exchange

SPIN POLARIZATION IN ELECTRON SCATTERING

237

scattering, the use of a polarization modulation technique coupled with phase-sensitive detection becomes an essential part of the source requirements. There is no strong need for long-term stability in the source intensity because S is independent of the incident current. Measurement of quantities such as reflection coefficients are easier with a stable incident flux, and, of course, decreased intensity implies a poorer signal-to-noise ratio in the measurement of S . It is useful if the source polarization does not vary with either time or intensity so that it need not be simultaneously monitored. The characteristics of each of the currently utilized sources of polarized electrons has been enumerated and compared in a recent review of polarized electron source technology (Celotta and Pierce, 1980). A source based on photoemission from negative electron affinity GaAs (Pierce et al., 1980b)has exceptionally good characteristics, in general, and is well matched to polarized LEED. It makes use of angular momentum selection rules to convert the circular polarization of incident radiation into a polarization of the photoemitted electrons. The polarization achieved is k43%. The sign of the polarization is varied by modulating from 'rc to 0 - radiation, typically via the combination of a linear polarizer and a rotating quarter-wave plate or a Pockels cell, the latter offering a wid5 frequency range. The 8000-A radiation is conveniently produced by a GaAlAs diode laser, although other techniques (Reihl et al., 1979; Conrath et al., 1979) have been used that permit the use of a HeNe laser as the photon source. The electron current produced is high; a few percent quantum efficiency results in a yield of 20 pA/mW of incident light. This 20-pA current emerges from a 0.5-mm-diameter spot in the apparatus of Fig. 6 with a kinetic energy of approximately 0.25 eV, giving an electron-optically bright source. In addition, the GaAs source has a narrower energy distribution than that available from conventional guns; its energy width (FWHM) is 0.13 eV. The degree of polarization obtainable is stable in time and does not depend on current. There is a slow decay in intensity with constant use, with the intensity typically falling to l/e of its initial value in 4-12 hr. A surface treatment with cesium rejuvenates the photocathode in a few minutes. Figure 6 shows the PLEED apparatus used by Wang et al. (1979) and Celotta et al. (1979) to measure S for the respective cases of spin-orbit and exchange interactions. An isolation valve separates a conventional (commercial) LEED apparatus from the polarized source chamber. Aside from a single internal magnetic shield and a small electromagnet at the target which is used to align the domains of a magnetic sample, the scattering chamber is typical of many surface chambers. A small optical bench focuses light of a suitable wavelength, modulated between a+ and (r- polarization with a frequency of 159 Hz, onto the surface of a GaAs wafer. Optical

238

D. T. PIERCE AND R. J . CELOTTA

fl*45 a + , LCP

Source SurfaceChamber FIG.6. A schematic view of a PLEED apparatus that uses a GaAs source. Circularly polarized light incident on the GaAs photocathode produces electrons with spin polarization along the light axis. A modulation of the circular polarization from u t to u - will result in a modulated incident spin polarization and, if the scattering is spin dependent, in a modulation of the scattered intensity collected in the Faraday cup. The Faraday cup can be positioned at all azimuthal scattering angles and at polar scattering angles 0 < 166".The inset shows the arrangement of optical elements to produce a particular spin polarization of photoemitted electrons. Light from a source (*) passes through a linear polarizer defining the plane of vibration of the electric vector at 45" to the fast axis (for the electric vector) of a quarter-wave plate (double arrow). The electric vector of the resultant circularly polarized light, as observed at a fixed point on the light axis, moves in the direction of the curved arrow. This is called u + light and corresponds to the light angular momentum in the direction of light propagation. It is also called fefi circularly polarized light in traditional optics. The polarization of electrons emitted from the GaAs is always antiparallel to the incident photon angular momentum. For u+ light, the electron spin polarization is parallel to the electron momentum. If the fast axis of the quarterwave plate is rotated 90", one obtains u - light for which the photon angular momentum is antiparallel to the light propagation direction. Then the electron spin polarization is in the direction of light propagation and antiparallel to the electron momentum.

elements to obtain 0' light and the resulting electron spin polarization are shown in the inset of Fig. 6 . The wafer is cleaned by heating and treated with Cs and 0, to produce a negative electron affinity. Emitted electrons pass through a sector of a spherical energy analyzer which serves to bend the beam 90" without changing the spin direction. The electron polarization is thus changed from longitudinal to transverse to the electron's momentum. This is important because, as discussed earlier, a transverse polarization is needed to observe the effect of the spin-orbit interaction. The electron beam is accelerated to 1 keV in order to transport it through the isolation valve to the scattering chamber, where the LEED gun optics focuses it on the sample. The Faraday cup assembly, which includes an einzel lens to retard inelastically scattered electrons, can be positioned at any azimuthal angle and all but the largest polar scattering angles. For the cup position shown in Fig. 6 , the electron spin is in the scattering plane, as is appropriate to suppress

SPIN POLARIZATION IN ELECTRON SCATTERING

239

the effect of the spin-orbit interaction while the effect of the exchange interaction is being observed. By a 90" azimuthal rotation of the cup to a position out of the plane of the figure, the effect of the spin-orbit interaction is observed. The current collected by the Faraday cup has an ac component at the modulation frequency imposed on the spin-averaged dc current. The peak-to-peak amplitude of the ac component is I , - I , 1, the numerator of Eq. (16), and the constant level is ( I , , I , )/2, or half the denominator of Eq. (16). A sensitive lock-in amplifier is used to measure the ac component, while a slow electrometer simultaneously measures the average or dc level. The spin dependent part of the scattering is thus separated from the spin averaged part, and the two magnitudes are displayed on adjacent instruments. A computer records both signals and displays the calculated S and the intensity as a function, for example, of the incident energy. Since the GaAs polarized electron gun has an intensity equal to that of conventional electron guns, measurements of S can be made in the same time and simultaneously with measurements of the intensity alone. The results of one such measurement, S(E), for the (01) and (01) nonspecular beams of W(OO1) are

+

80

90

100 110 E (OW

,

120

130

FIG.7 . The value of S as a function of energy for the W( 100) (Or) beam ( x ) and (01) beam ( 0 )following the labeling convention and in the scattering geometry shown. The data points are at 2-eV intervals. The good agreement for the two beams is a sensitive test for normal incidence. [From Wang el a / . (1981a).]

240

D. T. PIERCE AND R. J. CELOTTA

shown in Fig. 7 by 0and x , respectively. Each curve represents data points taken at 2-eV intervals; each point had an integration time of 1 sec. This high degree of overlap is obtainable only when the electron beam hits the crystal at normal incidence, and it allows a determination of normal incidence to better than 0.2". Although the choice of measuring P or S places the experimental complexity, respectively, at the detector or the source, there are some clear reasons why S is preferred. First, since polarization detectors are not yet movable devices, the apparatus must allow for the electron source to move in order to obtain angular distributions or to track nonspecular beams. Second, since all P measurements involve two scatterings, initially from the sample and then from the detector, the strength of the final signal to be measured will be lower and the chance for spurious asymmetries are higher than those for an S measurement where only one scattering occurs. This is only true, of course, now that polarized electron guns are as intense as conventional LEED electron guns. Indeed, the modulation technique used in the S determinations can lead to extraordinary sensitivity. In some of the work to be discussed later the noise level in the measured value of S was less than 0.0001.

SCATTERING DUETO THE SPIN-ORBIT INTERACTION IV. SPIN-DEPENDENT A . Theory

Over the past decade, the theoretical development of spin-polarized

LEED has been rapid, owing mostly to the work of P. J. Jennings (1970, 1971a,b, 1974;Jennings and Sim, 1972;Jennings and Read, 1975;Jennings and Jones, 1978) and R. Feder (1971, 1972, 1973a, 1974, 1975, 1976, 1977a-c; Feder et al., 1976, 1977). It is not our goal to elucidate fully the complexities of the relativistic LEED calculations that have been developed to predict spin-dependent behavior, but rather to extract a few of the basic principles that have emerged and to summarize the underlying assumptions. A more detailed review of the theory is available (Feder, 1981). At first glance, a difference in cross sections for a polarized beam of electrons scattered to opposite sides of a spherically symmetric charge distribution may seem difficult to explain. How can a symmetric central field have a preferred direction along which the spin polarization can be gauged, and what is the effective energy term in the Hamiltonian? The necessary perspective is gained from a vantage point of the rest frame of the incident electron. The radial electrostatic field of the approaching ion core is transformed to appear as a magnetic field perpendicular to the scattering plane of the electron. The interaction of this B field with the magnetic moment of the electron

SPIN POLARIZATION IN ELECTRON SCATTERING

24 1

p gives rise to an energy -p B which has a small, but sometimes dominant, effect on the electron trajectory. The spin -orbit interaction energy can be written as (1/2m2c2)(1/r)(dV/dr)(s. L), where V is the electrostatic potential, s is the incident electron spin, and L is the angular momentum associated with the collision. Thus, the central field obligingly provides a magnetic field perpendicular to the scattering plane upon which the electron spin can be projected and from which the energy necessary for a spin dependence in scattering arises. For scattering from a single scattering center, the maximum spin dependent effect occurs when the incident spin and the scattering plane normal are aligned. The size of the spin-dependent term is most conveniently measured by reversing the relative orientation of the spin direction and the scattering plane normal. Although the spin-orbit interaction term may be added in an ad hoc fashion to the nonrelativistic Schrodinger equation, it occurs naturally in the Dirac formalism that has been generally adopted for treating these problems. One of the possible statements of the Dirac equation for this problem is given by Jennings (1970) as,

-Vz

+ V ( r ) - -a2 [E 4

- V(r)]’

+ -U8V2 2 V ( r ) + 4(r)L*a $(r) = E$(r)

(17)

with L = - i(r x V) and 4 ( r ) = - (u2/4)(l/r)(aV/dr). We see that in addition to the spin-orbit term, the third and fourth terms serve to correct the nonrelativistic Hamiltonian. Generally (Feder et al., 1976; Feder and Kirschner, 1981), the relativistic LEED calculations assume plane waves incident on the crystal, perfect crystal structure within each layer, and a “muffin-tin” potential within the solid. This type of potential distribution consists of nonoverlapping spherically symmetric potentials centered at each atom site with the remaining space held at a constant potential. The potential within the solid is connected to the vacuum level by assuming a form for the surface potential barrier. Electrons are removed from the beam by inelastic processes, and this is incorporated into the calculations by adding an imaginary component to the potential within the solid and matching it to zero in vacuum by means of the surface potential barrier. Within the crystal the imaginary component may be taken to be uniform or dependent on position or electron energy. In the first stage of the calculation the spin-dependent scattering is calculated for electrons scattered from a muffin-tin potential of a single atom. As suggested by the presence of the dV/dr factor present in the scattering Hamiltonian of Eq. (17) and as we shall see later, the exact form of the potential is important in relativistic calculations of the polarization. The spin-up and spin-down phase shifts are calculated by a direct numerical

242

D. T. PIERCE AND R. J . CELOTTA

solution (Bunyan and Schoenfelder, 1965) of the Dirac equation with the chosen potential. These types of calculations are described and many representative results are presented in a review by Walker (1971). Typically five to eight phase shifts are retained in the calculations. Next the scattering of the electrons within a single layer is considered. The objective is to calculate a transfer matrix that will completely characterize the spin dependent scattering of that layer on the incident flux. This matrix would have dimensions of 2 N x 2N for a nonrelativistic calculation, where 2N is the number of backscattered and forward-scattered beams retained in the calculation, typically N = 20 or more. The necessity of keeping track of two spinor amplitudes increases the dimensionality to 4 N x 4N. Different techniques have been used (Jennings, 1970; Feder, 1976) to calculate the layer transfer matrix. Finally, the effects of interlayer scattering are obtained either by successive application of the one-layer transfer matrix or through its direct diagonalization (Feder et al., 1976). The calculations have been for elastic scattering and inelastic scattering is included as a parameter to account for attenuation of the beam. The higher dimensionality of the matrices used in the computation to carry the spin information lengthens the computer time required considerably. All things being equal, a factor of 8 increase in total computation is required over spin-averaged LEED calculations (Pendry, 1974; Van Hove and Tong, 1979). Two scattering amplitudes are generated in a polarized LEED calculation. Although a complete multiple scattering calculation is required for quantitative information, we can gain some understanding of the physics of the situation by considering the expressions that result (Jennings and Sim, 1972) under the kinematic approximation, F(E, K ) =

1 J;(E,K ) exp(iK

r,l

(18)

i

G ( E , K)

g,(E, K ) exp(iK r,)

=

(19)

i

Here/, and g, are the direct and spin-flip scattering amplitudes for the jth atom, and F and G are the summed amplitudes. The factor, exp(iK.r,), where K is the momentum transfer, describes the effect of the structural arrangement of the individual atoms on the sum. The spin-dependent scattering asymmetry as expressed in terms of these amplitudes is (Jennings and Sim, 1972) S(E, K) = -

(21)

SPIN POLARIZATION IN ELECTRON SCATTERING

243

For the case of identical atoms, Eq. (21 ) becomes,

[Note that i(jg* - f * g ) is real; it can also be written as 2 1mf"g.l From Eq. (22) we can see that the exponential factor that gives rise to the diffraction condition cancels out in this special case, leaving an interference term between the direct and spin-flip amplitudes, normalized by I f ) ' + )g)', which is just the scattered intensity. Hence, in the single scattering approximation, we should see Bragg diffraction features due to the long-range crystalline order in the intensity profiles but not in the spin-dependent parameter S . In Fig. 8 we show a measurement of both the intensity and S taken by scanning a Faraday cup detector across the specularly diffracted beam from W( 100) at an energy of 112 eV and angle of incidence of 9'. The strength of the interference effect in the intensity profile is to be contrasted with the relative insensitivity of the S parameter. Surface structure determinations are made in LEED by comparison of the results of detailed calculations, which are based upon assumed structures, and experimental data taken under carefully controlled conditions. Implicit

-3 -2

-1 0 1 Angle (deg)

2

FIG.8. Spin dependence S (top) and intensity (bottom) measured by scanning the Faraday cut detector across the beam which is specularly reflected from W(100)at an angle of incidence of 9" and an energy of I I3 eV.

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D. T. PIERCE AND R. J . CELOTTA

in this procedure is the assumption that approximations made for the nonstructural parts of the theoretical construct do not significantly affect the structural conclusions. It is, therefore, of considerable importance to know how this extension of LEED theory, which accommodates the spin parameter, is sensitive to structural and nonstructural variations. For example, the orderly termination of the bulk structure (i.e., the absence of surface reconstruction) is frequently accompanied by a change in the interlayer spacing; this type of structural information should be available from the procedure. On the other hand, it is important to choose the best potential for the scattering centers to improve the final comparison of experiment and theory. The question is, how does PLEED help, .and does it offer advantages over ordinary LEED? Feder (1976) has stressed the advantages of PLEED in determining top layer spacing changes. In Fig. 9 we see theoretical predictions (Feder and Kirschner, 1981) for both the intensity and polarization as a function of incident energy calculated for the (10) beam from W(OO1). The three curves depict the results for an assumed contraction of the top layer spacing of 0, 5 , or 10% of the bulk value. The point is that the intensity profiles are reasonably similar, and yet the predicted polarization features change dramatically

Energy (eV)

FIG.9. Results of calculations of the polarization and intensity for W( 100) (10) beam with assumed top layer spacing contractions of 0 (solid), 5 (dotted), and 10% (dashed). [From Feder and Kirschner (1981).]

SPIN POLARIZATION IN ELECTRON SCATTERING

245

over the range of spacing variation considered. The structures between 75 and 100 eV are a fine example; in going from 0 to 10% contraction the intensity feature shifts slowly to higher energy, whereas the associated polarization first changes by a factor of 2 and then reverses sign. Making use of this type of enhanced sensitivity, Feder and Kirschner (1981) were able to determine that the top layer spacing is contracted by 7 f 1.5%. The exact form of the potential used has been shown (Walker, 1971) to be of great importance in obtaining accurate predictions of polarization effects in electron-atom scattering. For scattering below 100 eV, the effects of exchange and the distortion of the atomic orbitals due to electric field of the incident electron can be seen. Walker found that the form of the exchange potential used was important at low energies. In particular, the Slater (1951) potential, V,, = 3 ( 3 p / 8 n ) l i 3proved to be too large at distances far from the nucleus. For the PLEED case, Feder and Kirschner (1981 ) examined the sensitivity to assumed potential, including the effects of inelastic processes. They considered four different potentials made up of combinations of relativistic and nonrelativistic band structure potentials and different variations of the Slater exchange potential, including one with an explicit energy dependence. The calculated polarizations and intensities as a function of energy both showed some regions where the structures were strongly dependent on either the assumed potential or geometry, but not both. Through comparison with measured specular and nonspecular data for W(100) they find best agreement with a potential incorporating an exchange interaction that decreases with increasing energy and an imaginary term in the ion core potential contribution to account for the local nature of the 4f excitation. A second aspect of the choice of potential is the selection of a shape for the surface barrier potential. The interference between the decay of quasibound surface states and direct scattering from a surface can produce a series of rapid intensity variations with incident energy, i.e., resonances (McRae, 1979). In the case of electron-atom scattering, large polarizations are associated with small cross sections, where the rather small absolute difference in cross section between spin parallel and antiparallel can still result in a large ratio of the two cross sections (Kessler, 1976). In theory, resonance scattering in LEED presents a similar situation, where small energy shifts in the intensity curves could give rise to large polarization features (Jennings, 1971a,b;Jennings and Sim 1972;Jennings and Jones, 1978; Feder et al., 1976; Feder, 1977a,b). In particular, the polarizations at surface resonances have been shown theoretically to be much more sensitive than the corresponding intensities to both the real (Feder et a/., 1976) and imaginary (Feder, 1977a) components of the assumed surface potential barrier.

246

D. T. PIERCE AND R. J. CELOTTA

As in electron-atom scattering, the general magnitude of polarization features that result from the spin-orbit interaction increases with increasing atomic number, although Feder ( 1977a) shows that in specific cases, e.g., resonances, a low-Z material may still exhibit relatively large polarization features. In contrast with the atomic case, large polarization features need not occur only when the cross sections for one spin direction approaches zero, and the other remains finite. They may occur (Jennings and Sim, 1972) as a result of the large degree of multiple scattering present. However, the calculated PLEED polarization features remain very sensitive in regions of low intensity, and therefore a calculation that does not include a sufficient number of phase shifts in the analysis may not determine the intensities at minima sufficiently well and, as a consequence, produce prominent spurious polarization features. 8. E.lcperimentsj o r Structure Determination In surface structure determination, polarized low-energy electron dif1981a) not available with fraction has some significant benefits (Pierce et d., ordinary LEED. First, the experimental results consist of two parameters rather than one. The second quantity, the spin-dependence parameter P or S, provides qualitatively different information from that obtainable in conventional LEED. As seen in the discussion of the previous section, the spindependent quantity depends on assumed structures and potentials in different ways than the spin-averaged intensity does. Since S (or P ) is fundamentally the difference between two quantities, it tends to exhibit sharp, very structure sensitive peaks, rather than slowly changing features. This facilitates the process of comparison of the predictions of theoretical models with experimental results. Second, the fact that S (or P ) is a unitless ratio of measured or calculated quantities is itself significant. It means that a correct calculation should be expected to do a good job of fitting the magnitude of the polarization, along with the shape of the curve. Further, it simplifies the experimental process, since such factors as beam current variations with time or energy or possible energy dependent collection efficiencies do not affect the measurement of S (or P ) . This is at least partially responsible for the remarkable agreement exhibited between the results in Fig. 3. An additional, less obvious, reason to expect a higher degree of consistency in PLEED measurements of S (or PI can be understood by considering the measurement process in terms of an instrument response function (Park et af., 1971 ;Wang et al., 1978). Since the instrument response function does not depend on spin, it does not, in a reasonable approximation, (Wang et d.,1981a) enter into measurements of S (or PI. Hence, quite different experimental arrangements can be expected

SPIN POLARIZATION IN ELECTRON SCATTERING

247

to produce accurate determinations of S (or P),as shown in Fig. 3, without allowances being made for differences in instrument response. This results in better agreement between experiments, and the comparison of experiment and theory should be more meaningful. The expected reproducibility of PLEED data should help in situations where the variation within the available experimental data precludes structural determination to the desired degree of accuracy (Read and Russell, 1979). Experimentally, the most studied surface has been W( loo), for a number of reasons. Tungsten is both a high-Z metal and is readily cleaned using a well-developed procedure. Most important, however, was the existence of a body of theoretical knowledge about this system, as described in Section IV,A previously. The only possible disadvantage that W( 100)has is a surface reconstruction which could cause difficulty if the experimental procedure does not ensure the correct phase. The specuiar scattering data for an unreconstructed W( 100) ( 1 x 1) crystal as shown in Fig. 3 illustrates two of the basic features of PLEED from high-Z samples. First, very large polarization effects are possible. Values of S of - 70% can be seen; this means that, under these diffraction conditions, the cross section for an incident down-spin electron is six times that for an incident up-spin electron. Hence, from an unpolarized incident beam, six down-spin electrons will be scattered at the prescribed energy and angle for every up-spin electron producing a roughly - 70% polarized beam. Similarly, a fully polarized incident beam produces, under the same diffraction conditions, a signal six times larger for down-spin incident electrons than for up-spin incident electrons. A second basic feature of such measurements is that the size, shape, and position of the major polarization features are very sensitive to diffraction conditions. Changes of 0.5" in the angle of incidence can make a substantial change. Scattering asymmetries of greater than 40"/, have been seen to change sign with a 1" change in angle of incidence (Wang et al., 1981a). In Fig. 10 we show a set of S curves (Wang et al., 1981a) measured for nonspecular scattering from W(100). For the (02) and (1 curves a comparison is made to the calculation of Feder assuming a 7% contraction of the surface layer spacing (Feder and Kirschner, 1981). The agreement between experiment and the theory using a potential derived from a selfconsistent charge density and an energy-dependent exchange term is encouraging. The features of the intensity curves are in agreement with Debe and King's (1977) nonpolarized measurements, with the exception of the (12) beam. [A shift of energy scale of 5 eV is necessary to achieve agreement in this case (Wang el al., 1981a).] Another method of collecting PLEED data is to observe the specular beam at a fixed incident energy and polar scattering angle while the azimuthal

r)

248

D. T. PIERCE AND R. J . CELOTTA

0.4 0

-0.4

0.3 0.2 0,l 0

FIG. 10. Measured values of S and fir,, for five nonspecular beams of W(IOO), where I and I,,are the scattered and incident currents, respectively (Wang er al., 1981a). Data were taken at 2-eV intervals except for the (On beam, where higher resolution and correction for the diffuse background intensity were employed in the region of the sharp peaks in S. The dashed curves are the calculations of Feder and Kirschner (1981) assuming a 7% contraction of the topmost layer spacing.

scattering angle is varied. Such a “rotation diagram,” obtained by Kirschner and Feder (1979a),is presented in Fig. 1 1. This type of data accumulation is usually used to isolate the effects of single and multiple scattering (Lagally et al., 1973, since for single scattering the specular beam is expected to give rise to only a uniform intensity as a function of azimuthal angle. There are a number of experimental advantages to such a data accumulation scheme, and it has recently been argued that contrary to previous conclusions, rotation diagrams can be useful in obtaining surface structure information (Kirschner and Feder, 1979b3. The modulation of the polarization with angle comes solely from multiple scattering effects. Such diagrams have been used in discriminating among model potentials and in corroborating an assumed contraction of the top layer in W(OO1) (Feder and Kirschner, 1981). In an attempt to reduce the complexity of the theory required to extract structural information from LEED data, the constant momentum transfer averaging (CMTA) technique has been developed (Lagally et a/., 1975). It simplifies the scattering calculation by averaging all the experimental data

SPIN POLARIZATION IN ELECTRON SCATTERING

t

20

249

(b’

FIG. I I . A comparison of theory and measurement for the rotation diagram for specular reflection from W(100) at an energy of 100 eV and an angle of incidence of 47.S. (a) The calculated reflection coefficient J,,/Jo, where Jo0 and Jo are the scattered and incident currents, respectively, compared with measured values of J , , over a 70 range of azimuthal angle. (b) A comparison between the calculated and measured polarization over the same conditions. (The polarization scale has been expanded about 509, for the experiment relative to the theory.) [From Kirschner and Feder (1979a).]

taken for a specific momentum transfer, independent of the value of ko and k. This has the effect of averaging out the multiple scattering contribution (Lagally et al., 1971b1, and thus permits kinematic theory to be applied. It is possible (Wang et al., 1981~)to apply the same concept to PLEED studies, and Fig. 12 shows the results. In Fig. 12a the intensity average shows the expected Bragg peaks at values of K/Ko = 2 and 3. Here the vertical momentum transfer K is expressed in terms of the momentum transfer associated with a Bragg feature, K O .Figure 12b presents the results of applying the same formalism to the “difference function,” which is just the

250

D. T. PIERCE AND R. J. CELOTTA

2

3

KIK,

3

2

KIK,

FIG. 12. Results of applying a constant momentum transfer averaging (CMTA) procedure to specular data collected for W(100). (a) Averaged intensity data vs. reduced momentum transfer, where K / K o equals an integer for a Bragg peak. (b) The averaged difference between [he intensities for incident spin-up and -down relative to the scattering plane normal plotted versus reduced momentum transfer. [From Wang ei a/. (1981c).]

numerator of Eq. ( 6 ) .The averaged difference function also exhibits strong Bragg peaks. These data have been used to estimate the top layer contraction in W(100) (Wang et al., 1981~). While the averaged difference function provides an alternative set of data for this type of determination, there appears to be no advantage to using it instead of the averaged intensity data. So far we have discussed systems in which both the structural and nonstructural parts of a model PLEED calculation were being determined ; we knew neither the exact form of the potential nor the exact geometry in the surface region of the crystal. In order to separate these two classes of parameters, Bauer et al. (1980b) chose to study Pt( 11 l), a system that is free from the complications of a surface reconstruction and that has essentially the same interlayer spacing at the surface as in the bulk. Their results are shown in Fig. 13. The (10) beam is shown, with data taken in the format of a fixed incident energy with the polar scattering angle varied. The experimental data points, represented by short vertical lines, were measured on an apparatus using a conventional electron gun and a Mott detector to measure P. With the structure part assumed to be well in hand, this experiment focused

SPIN POLARIZATION IN ELECTRON SCATTERING

25 1

Polar Angle e (*)

FIG. 13. The measured spin polarization of the (10) beam of Pt(lI1). Experimental data points are presented as vertical dashes. The calculations plotted for comparison are based on a potential constructed from a self-consistent charge density with energy-dependent exchange barrier as well as a band structure potential and a nonreflecting (--.--.) or exponential (-) with an exponential barrier (....) . [From Bauer et a/. (1980b).]

on comparisons made using various potentials. The calculations shown in Fig. 13 are based, for the case of one curve, on a band structure potential with exchange constant as a function of energy with an exponentially smooth surface potential barrier, and for two other curves, on a potential generated from a self-consistent charge density with an energy dependent exchange contribution and either a nonreflecting or an exponentially smooth surface potential barrier. Best results are obtained with the energy dependent exchange term included, and, except near surface resonance conditions, it makes little difference which surface potential barrier is chosen. The effect of finite temperature is usually included in LEED structure determinations by means of the Debye-Waller factor. There have been several investigations on the effect of finite temperature in PLEED. Unertl (1978b) contrasted the temperature-dependent polarization effects expected in electron scattering from atoms, crystals, polycrystals, and liquids. In a study of W( IOO), Calvert et al. (1977) found no change in the specular beam polarization with temperature, although changes in the intensity curve were readily visible. They did their experiments at an angle of incidence of 47.5 and an azimuthal angle o f 4 = 50”. Riddle et a/. (1978) also studied W(100) specular reflection, but at an angle of incidence of 13” and for 4 = 0’, an azimuth in the [OlO] direction. They measured the polarization at a fixed incident energy as the temperature was varied and found large changes. They concluded that small shifts in the energy position of sharply peaked polarization features could explain the observed results. These shifts are also observed in the intensity features and are explained by the thermal expansion of the lattice.

252

D. T. PIERCE AND R. J. CELOTTA

Kirschner and Feder (1980) have studied the question from both a theoretical and an experimental viewpoint. They find that the effects are measurable but very weak under the conditions of the experiment of Calvert et al. They conclude from their calculations that the effect of the thermally induced lattice expansion is an energy shift of a polarization peak, whereas the shape of the peak is changed because of the temperature dependence of the multiple scattering. In addition, the anharmonic vibrational potential well of the surface atoms could cause the contraction of the top layer to be temperature dependent. They find evidence for a relaxation of the surface contraction in their analysis of the spin-dependent data. C . Adsorbates and Phase Transitions

Polarized LEED has been used to study surface reconstruction. Muller et al. (1978) have studied the structural phase change in Au( 100) as a function of temperature. A (1 x 2) room temperature superstructure in Au(ll0) goes over into the (1 x 1) bulk structure for temperatures above -720 K. In Fig. 14, measurements of P for specular reflection are displayed as a function of scattering angle, for different temperatures, The constant incident energy was 50 eV, and Mott detection was used. A continuous and dramatic

e FIG. 14. Values of polarization vs. polar scattering angle for different temperatures as measured for specular scattering of 50 eV electrons from Au( 110). The reversal in the ordering of peak heights as a function of temperature is due to a reconstruction of the crystal surface. [From Miiller et al. (197W.l

SPIN POLARIZATION IN ELECTRON SCATTERING

253

change in the polarization profiles is observed as the temperature is varied from 320 to 830 K, and the phase change occurs. The features are large, sharp, and very sensitive to the surface structure and should provide a good basis for comparison with PLEED calculations. The polarization of the (@) beam of the low-temperature phase has also been measured as a function of temperature (Muller, 1977). Wang et af. (1981b) have studied both the temperature-induced and hydrogen-induced reconstruction of W( 100). The transition between the lower temperature ( 8 x $)R45' phase and the high-temperature (1 x 1) phase of the W(100) surface has been the subject of many recent papers [see Wang et al. (1981b) and references therein]. The phase change, thought to occur near 370 K, is detected via the additional half-order spots that appear at lower temperatures. A similar pattern is created by hydrogen adsorption which gives rise to a C(2 x 2)-H superstructure. In Fig. 15 both the S curves and intensities are shown for the case of the high-temperature (1 x 1) phase, the low-temperature (,h x fi)R45' phase, the hydrogen covered C(2 x 2)-H phase, and the (1 x 1)-H phase at saturation hydrogen coverage, Although the intensity curves are similar with small differences, the polarization curves exhibit clear changes. For example, just between 90 and 100eV, a major positive polarization peak for the (1 x 1)and ($ x $)R45' phases becomes a strong negative peak for the hydrogen reconstructed phase.

-0.8

03 0.0 -0.2 -0.4 -0.6

0.2 0.0 -0.2 -0.4

FIG.15. Measured values for the spin dependence S (left) and the intensity I (right) for the (01) beam of W(100) under four different conditions: (1) crystal in the high-temperature (1 x I ) phase; (2) crystal in the low-temperature ( $ x ,'Z)R45 phase; (3) crystal with C(2 x 2) hydrogen overlayer at a coverage 0 = 0.1; and (4) crystal with saturation hydrogen coverage to give a ( 1 x 1) pattern. [From Wang et al. (1981b).]

254

D. T. PIERCE AND R. J. CELOTTA

At saturation hydrogen coverage the (1 x 1) pattern returns, but the S curve shows that the structure must be different from the clean high-temperature (1 x 1) phase. A complete treatment of the adsorbate-substrate interactions is possible only through a full PLEED calculation. However, some measure of understanding of the hydrogen reconstruction can be gained by viewing the scattering by a single atom as having Coulomb term and spin-orbit contributions. The numerator of the S function of Eq. (21) is seen to depend on the cross terms between the direct and spin-flip amplitudes, f and g, respectively. This interference could arise from scattering from the top substrate layer, the absorbate layer, or even between the absorbate and substrate layer. Hence, if the absorbate and substrate have very different nuclear charges, then general arguments can be made as to the source of the polarization effect (Pierce et al., 1981a). For the hydrogen on W(lOO), the adsorbate layer will not produce a polarization effect through its own spin-orbit coupling; one possibility would be an interference between the Coulomb scattering amplitude of the hydrogen and the scattering amplitude of the tungsten substrate. However, since the hydrogen Coulomb scattering amplitude is small, we attribute the change in the polarization profile upon hydrogen adsorption to a change in the position of the tungsten atoms and therefore to changes in the tungsten coulomb and spin-orbit scattering, Hence, the changes in the polarization profiles alone point toward the conclusion that hydrogen causes a reconstruction of the tungsten surface that is different from that of the low-temperature phase. A study of the changes in the polarization of electrons scattered from W( 100) with adsorption of disordered CO and 0, overlayers was performed by Riddle et al. (1979a). Both adsorbates greatly reduced the magnitude of the most prominent (-75%) polarization feature for exposures of 1 langmuir (L). Each caused a positive polarization feature to grow with exposure at an energy just below the negative peak. The change in polarization from - 75 to 0% is accompanied by only a very small change in intensity. Alternatively, there are energies at which the adsorption process causes large changes in the intensity with only small changes in the polarization. Ordered overlayers of CO (Riddle et al., 1979b) adsorbed on W(100) produced interesting changes as seen in Fig. 16, which shows the specular beam at an angle of incidence of 13" for three cases : clean, after 20 L of CO exposure, and following an anneal to 875°C. The 20 L exposure to CO is seen to reduce dramatically the major polarization feature while maintaining moderate polarizations throughout. With an 875°C anneal, a major positive feature appears at 71 eV, and half-order spots are detected. The authors conclude that the heating causes partial desorption of the CO B phases, and the ordered c(2 x 2) structure consists of fi3 CO. The sharp positive polariza-

-

SPIN POLARIZATION IN ELECTRON SCATTERING

255

tion feature is therefore thought to be an indicator of the tightly bound p3 phase. An additional CO exposure of 2 L causes the +60% peak at 71 eV to become a broad - 50% feature. This is accompanied by the loss of halforder beams and, since the p3 phase is thought to correspond to half-monolayer coverage, represents the filling in of the remaining empty lattice sites (Riddle et al., 1979b3. For nitrogen on W(lOO), Mahan et a / . (1980) found that the major polarization feature at 71 eV exhibits large changes in magnitude and changes sign with different exposures to N,. Annealing to 1050°C after a 3-L exposure also causes dramatic polarization changes, but the specular intensity profiles remain essentially the same. The similarity between some of

-40.

FIG.16. Effect of exposure to CO on measured polarization for specular scattering of electrons from W(100) at an angle of incidence of 13'. (a) Measured polarization as a function of energy for the clean surface. (b)Polarization after exposure of 20 L of CO. (c) Polarization after exposure of 20 L of CO and annealing to 875°C. [From Riddle el a/. (l979bl.l

256

D. T. PIERCE AND R. J. CELOTTA

the polarization features in the nitrogen and CO overlayer work suggested that they both may be responsible for a reconstruction of the W(100) surface (Mahan et al., 1980). D . Surface Barrier Resonances

A great deal of interest has been generated by the subject of electronic surface resonances in crystals. A review of the theoretical and experimental work has been presented by McRae (1979). In Section IV,A, we saw that theoretical treatments of the effects of surface resonances led to the prediction that large and rapidly varying polarizations may be associated with the observed rapid intensity variations. Muller (1977) has associated some of the sharp polarization variations he observed in PLEED from Au( 1 10) with surface resonance phenomena. The surface resonance condition can be visualized by considering what happens to a nonspecular beam as the incident energy of a nonnormal incident beam is decreased. Since, for the first nonspecular beam, the momentum parallel to the crystal surface is changed by a fixed amount g. the nonspecular beam will move away from the specular beam when the energy is decreased. At a particular energy, called the beam emergence threshold, this beam will be traveling parallel to the crystal surface. Under these conditions we can visualize an electron traveling along the crystal in its own image charge potential. This image charge potential can support bound states, whose energies are given by the well-known Rydberg formula, where n = 1,2, . . . ,and a is the quantum defect. A surface resonance occurs when

h2k2 - h2 2m lkll 2m

+ gI2 + 6"

where k and k,, are the initial total momentum and momentum parallel to the surface, respectively. Hence the energy for the motion along the surface comes from the initial energy plus the energy gained from the image potential. Figure 17a shows schematically the potential and the bound state wave functions for the first two Rydberg levels. Since the total energy is positive, and the electron is not really in a bound state, it can escape by interacting with the ion cores to transfer a momentum quantum g and return to the specular beam, its history having been recorded as a phase shift. Figure 17b shows two possible paths for an incident electron. Path 1 is direct specular reflection, but in path 2 the electron undergoes multiple reflections from the substrate and surface potential barrier before being diffracted back into the specular beam. The total reflection amplitude can be written in terms of

SPIN POLARIZATION IN ELECTRON SCATTERING

257

-1 -2

-3 -4

(b)

FIG.17. (a) Sketch of the surface potential barrier; the solid is located in the + z direction to the right of the energy axis. Electron probability density is shown schematically for each of the first two Rydberg-like states supported by the image potential. (b) Diagram showing the (1) direct and (2) indirect path for specular eleastic scattering and the associated reflection amplitudes. [From Pierce el al. (1981b).]

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D. T. PIERCE AND R. J. CELOTTA

From Eq. (26) it can be seen that rapid changes in the reflection cross section for the specular beam can come either from an interference between the direct and indirect terms or from zeros in the denominator of the indirect term. The reflectivity variations seen experimentally in W( 1001 (Pierce et al., 1980c, 1981b) are shown in Fig. 18. Here the specular intensity is given as a function of energy for different angles of incidence. The polarization data have been used to give two sets of intensity curves, one for a spin-up incident beam, and a second for spin-down. A characteristic Rydberg series of three peaks converging on the (10) beam threshold, indicated by a large arrow, can be seen in the top curve of Fig. 18. Spin-independent studies at higher energy resolution (Adnot and Carette, 1977) resolve an additional peak.

FIG. 18. The measured specularly reflected elastic intensity in the low energy, surface resonance region of W(100)for four different angles of incidence. The solid curves represent the intensities for incident electrons with spin parallel to the scattering plane normal, and the dashed curves for those with spin antiparallel. The large arrows mark the (01) beam emergence threshold energy. [From Pierce et al. (1981b).]

SPIN POLARIZATION IN ELECTRON SCATTERING

259

The most immediately evident result that can be seen in, for example, the 37 or 26“ curves, is that the spin-orbit interaction produces a shift in the features or a splitting of the Rydberg levels. The splitting is greatest for the lowest lying state, n = 1, and is least for the highest Rydberg level seen, n = 3. In fact, both the spin splitting and the peak width are seen to decrease in going from the n = I to n = 3 levels. This can be understood by considering the peak width dependence on the decay probability of the state, and thereby on the electron’s overlap with the solid. The spin-orbit effect also depends on the electron sampling the effects of the high-Z ion cores, so it is reasonable that the spin splittings and half-widths are proportional. Detailed treatments (Pierce et al., 1981b; McRae et al., 1981) have shown that above 26‘ the ratio of the spin splittings of peaks n = 1 and n = 2 to the full widths at half maximum of these peaks is nearly constant. At smaller angles a double peaked feature emerges in the spin-up curve. The “extra” low energy spin-up peak seen in the 15- curve may be explained (McRae et d., 1981) by allowing the phase of rggto be spin dependent. The use of the PLEED techniques in the study of the W(100) surface resonances has greatly facilitated the modeling of electron reflection from this surface at low energies. The origin of the lowest energy peak has been clarified, and our understanding of surface resonances has been modified (McRae et al., 1981).

E. PLEED Polarization Detectors

Although high-energy Mott detection has proved reliable, its inefficiency, coupled with the cumbersome nature of a 100-kV device, argues for the development of an alternative method for many applications. The spin sensitivity of electron diffraction from high-Z materials has been suggested on many occasions as a possible basis for an alternative technique (Jennings and Sim, 1972; Feder, 1974, 1975, 1977b; Pierce et a/., 1977). A detector has been constructed along these lines by Kirschner and Feder (1979a). It is shown schematically in Fig. 19. Incident electrons pass through a cylindrical mirror energy analyzer and lens system which limits the energy and angular distribution ofthe beam and prepares it for normal incidence on the crystal at the preselected energy. Separate detectors monitor the (20)and (20) nonspecular beams, which will have the opposite spin dependence. A measurement of the left-right asymmetry in count rate, coupled with a known value of S for the scattering conditions, permits the polarization of the beam to be measured. A PLEED detector is therefore conceptually very similar to the highenergy Mott technique. Both detectors rely on the spin-orbit interaction to give rise to a spin dependence. In the high-energy version the Sherman

260

D. T. PIERCE AND R. J. CELOTTA I

counter 2

AN A LY Z ER FIG.19. A schematic representation of a PLEED detector. The cylindrical mirror analyzer (CMA) provides energy analysis, and the laser beam is used for alignment purposes. [From Kirschner and Feder (1979a).]

function is less sensitive to the exact atomic potential and can be calculated with high accuracy; a PLEED detector requires an experimental determination of S. Both techniques measure a left-right asymmetry in count rate, but whereas a Mott detector must collect its signal within a large solid angle, the outgoing beams in the PLEED detector are formed by diffraction and all of the signal is concentrated into two well-defined beams. The Mott technique is sensitive to small changes in the scattering geometry, and for some choices of diffraction conditions, the PLEED detector may also be sensitive to the angular width of the beam around normal incidence. Hence, a determination of the angular sensitivity is an important part of establishing a particular device like a PLEED detector. Wang et al. (1981a) present a discussion of the angular acceptance question for PLEED detectors. They also present angular data for the W(100)(02) beam selected for a PLEED detector by Kirschner and Feder (1979a) and an alternative, the (11) beam. The measured angular variation suggest limiting the angular acceptance to - 1 O at 105 eV and k 2" at 70 eV for the (02)and (IT) beams, respectively. The figure of merit for the efficiency of polarization detection is usually taken as S21/Io,where I/Iois the ratio ofdetected to incident current (Kessler, whereas 1976).The figure of merit for the (02) beam at 105 eV is -8 x that of the (11)beam at 70 eV in W(100) is slightly higher at 1.2 x (Wang et al., 1981a).These efficiencies are a factor of 10 larger than those of a typical Mott detector, although a fully optimized Mott system would be comparable. Omitted from such comparisons is the issue of the characteristics of the incident electron beam acceptable to the detector. Since the product E * A * R

+

-

SPIN POLARIZATION IN ELECTRON SCATTERING

26 1

is conserved in electron optics, where E is energy, A is cross-sectional area, and Q is the solid angle of the beam, two scattering geometries with comparable limits on area and angular acceptance will have very different beam acceptances if they operate at widely different energies. For this reason, the high-energy Mott detector is particularly useful (Pierce et a/., 1979) in those situations in which the beam has a high emittance, for example, in spinpolarized photoemission in a longitudinal magnetic field. For beams where the emittance is more nearly like that of a PLEED detector, the efficiency, compactness, and convenience of such a device may be the overriding concern. A clean vacuum system with pressures in the low lo-” Torr range is necessary for a PLEED detector using a W crystal, although it may be possible to find crystals that are tolerant of higher pressures. Several materials are currently being tested for ‘detector performance. The development of PLEED as a spin polarization detection scheme is just beginning, and we should expect refinements and improvements over the next few years.

v. SPIN-DEPENDENT SCATTERING FROM FERROMAGNETIC MATERIALS A . 771oo rj *

The magnetic properties at a surface can be expected to be different from those in the bulk owing to the reduced number of neighboring atoms, the absence of translational invariance, or the possibility of a surface reconstruction. The size of the surface magnetic moments, the thermal behavior, or even the type of magnetic ordering can differ at the surface. The magnetic properties of the surface have been described by a number of theoretical models using mean field theory (Mills, 1971 ; Wolfram ef a/., 1971 ; Kumar, 1974), scaling theories (Fisher, 1973), and these approaches plus numerical techniques (Hohenberg and Binder, 1974; Binder and Hohenberg, 1976). An experimental determination of surface magnetic properties is difficult, and only a few methods have been tried (Gradmann, 1974; Alvarado, 1979; Rau, 1980).There have been few experimental tests of the theoretical models on well-characterized surfaces. Polarized electron scattering provides a sensitive way to probe surface magnetic properties. In this section we will discuss theoretical work on spin polarization in electron scattering from magnetic surfaces. The theories are needed to understand the origin of the spin dependence of the experimentally measured parameters and hence how these parameters relate to surface magnetic properties. Vredevoe and DeWames ( 1968) considered four spin-dependent terms in the Hamiltonian for electron scattering from a ferromagnetic target with

262

D. T. PIERCE AND R. J . CELOTTA

a net ordered spin density: the term for the spin-orbit interaction of the scattering electron, the exchange term, the dipoie-dipole term, and the host spin-orbit term. The latter three terms are magnetic terms, i.e., they are only nonzero when there is a net ordered spin density. The last two terms are negligible in surface scattering where the electron kinetic energy is much less than its rest energy. Neglecting the spin-orbit interaction, which can be minimized by the choice of experimental geometry, the Hamiltonian is

where V(r - r,i) includes the Coulomb term and that part of the exchange potential independent of the direction of the incident spin, J(r - rj) is the rest of the exchange potential, s is the spin of the incident electron at r, and 9, is the net spin at site rj. By using the Born approximation and the kinematic (single) scattering model and neglecting the excitation of magnons, the scattering amplitude can be written (Lu and Wang, 1981) A(K)

=

[V(K)

(rn/2nh2) i

+ J(K)S-Y’~]exp(-iK.rj)

(28 1

where V(K) and J(K) are the Fourier transforms of the spin-independent and spin-dependent parts of the potentials, and K is the momentum transfer. The intensity is

where the effects of the thermal motion of the atoms or the attenuation of the electrons have not been included. The average spin at site . j is (9:) where . z is the majority spin direction, and (9;YPf) is the spin-spin correlation function. The first two terms are independent of the incident spin orientation, whereas the two interference terms are linear in the spin-dependent potential and change sign if the orientation of the incident spin is reversed. The scattering asymmetry of Eq. (6) for incident spin parallel and antiparallel to the majority spin direction is then

The numerator shows the interference between the spin-independent scattering and the exchange scattering and contains the average magnetization per site M: = - g p B ( 9 ; ) .

SPIN POLARIZATION IN ELECTRON SCATTERING

263

are the same at each With the approximation that C(K), J , ( K ) , and 9, site in the surface and in each layer, Eq. (30),simplifies to the following result like that derived by SaldaTia and Helman (1977) S(K)

=

- J ( K ) M ' ( T ) / Q ~V(K) ,

(31 1

Note that in the kinematic approximation the exponential factor (the interference function of LEED) cancels out. The term in IJl2 in Eq. (30) has been omitted in Eq. (31 ) since (JI2<< 1 VI2. It is interesting to note, however, that this small term which is proportional to the spin-spin correlation function produced the half-order LEED spots for NiO observed by Palmberg rt ul. (1968). Saldaiia and Helman evaluated Eq. (3 1 ) as a function of momentum transfer using the self-consistent Hartree-Fock-Slater potentials for majority electrons VT(r)and minority electrons V,(Y)which have been calculated by Wakoh (1965). The spin-dependent potential is then J = VT(r)- VL(u).They find that the largest spin dependence is expected for small momentum transfer as did Vredevoe and DeWames with their approximation to J . In order to obtain Eq. (31),it was assumed that Vj(K) and Y jare the same in the different layers probed by the electron beam. If there is a layer-dependent magnetization, there are, in principle, complicated interference terms in Eq. (30), and it is not possible to obtain the simple form of Eq. (31). In practice, owing to the very short electron inelastic mean free path, theelectron scattering probes primarily the magnetic behavior of the outer layer or two at electron energies of 100 eV, and interference terms with deeper layers can to first order be neglected. Saldaiia and Helman included the effect of magnon absorption or emission in their analysis, but pointed out that this gives another term of order ]JI2and therefore neglected it in Eq. (31 ). The main contribution to the spin dependence is from scattering processes in which the spin is conserved. At the energy resolution of current experiments ( 100 meV), electrons that lose energy to surface magnons (a few tens of meV) would still be measured as part of the elastically scattered intensity, but the momentum transfer is such as to scatter them out of the elastic beam. With sufficient energy and angular resolution, the surface spin wave dispersion could be measured. This possibility was discussed a number of years ago by Mills (1967) and DeWames and Vredevoe (1 967) in their calculations of spin-dependent inelastic scattering from magnons. Both calculations used the Born approximation with an effective local exchange potential. These authors suggest separating the electron-magnon and electron-phonon scattering by means of temperatureand angle-dependent measurements. Magnon scattering can be unambiguously identified by measuring the change of the polarization of the incident beam on scattering. The electron-magnon scattering cross sections can be expressed in terms of the surface spin-spin correlation functions. Future high-resolution inelastic polarized electron scattering measurements

-

264

D. T. PIERCE AND R. J. CELOTTA

with spin analysiswill yield detailed information on the dynamical properties of surface spins and test the predictions of these calculations. For the energies and angles of interest in surface scattering, it is well known that both the Born approximation and the kinematic picture are inadequate to obtain quantitative results. A partial wave analysis is required, and the effects of multiple scattering must also be taken into account. The first calculation of this type for a ferromagnet was reported by Feder (1973b, 1975) for Fe( 100). Since then, there have been more extensive calculations of Fe(ll0) (Feder, 1979), Ni(ll0) (Wang 1980, 1981a,b; Davis, 1981), and even NiO(ll1) (S.-W. Wang et al., 1979). (Although we mentioned in Section I that in general no spin-dependent scattering is expected from an antiferromagnet, a surface of NiO was chosen in which the NiZ+spins in the surface layer were all oriented in one direction and those of the next NiZ+ layer below in the opposite direction. Because of attenuation of the electrons, the scattering from the Ni2+layer nearest the surface is strongest, and a net spin-dependent scattering was calculated.) Dynamical PLEED calculations typically employ a muffin-tin approximation for the potential. That is, the electron density is assumed to be spherically symmetric inside nonoverlapping spheres centered on the nuclei and constant between the spheres. Exchange is added in the Slater (1951) approximation, or a more refined exchange-correlation potential can be calculated in the local spin-dependent density functional formalism. In the dynamical PLEED calculations for Ni( 1 lo), Wang (1980,198la,b) and Davis (1981) employed the band structure potential that was used by Moruzzi et al. (1978) which included the muffin-tin approximation and an exchange correlation potential suggested by von Barth and Hedin (1972). The exchange potential can be written as a shifted and rescaled Slater potential in the form

vp

+

= ~(p)(2p~,,/p)1/3 ~

( p )

(32)

where p is the electron density as in Eq. (1 11, and A ( p ) and B(pt are the potentials used by Hedin and Lundqvist (1971) in the spinless case. This equation can be written in the form of Eq. (1 1) by expanding to first order in the difference between the majority and minority spin densities,p s = p t - pL,

v,, = A ( p ) + B(p) + $4(p)(p,/p)s^*9

(33)

The last term in Eq. (33) is the spin-dependent part of the exchange-correlation potential which depends on the orientation of the spin of the incident electron relative to the majority spin direction in the surface. Two sets of phase shifts, one for parallel and the other for antiparallel incident spin, are required for the PLEED calculation and can be obtained using Eq. (32) or (33). The scattered intensity for each incident spin orientation is then found from two LEED calculations, one with each set of phase shifts.

265

SPIN POLARIZATION IN ELECTRON SCATTERING

In their calculations of S for Ni(l101, Wang (1981b) and Davis (1981) found that S was sensitive to the scattering geometry and the potential. Calculations were also made using the less sophisticated Wakoh (1965) potential and compared to the results using Eq. (33). Calculations of I and S were made as a function of energy at the angle of incidence 0 = 12" and azimuthal 4 = 35.26" in the [lTl] direction corresponding to the experimental data available (Celotta et af., 1979). The results of such a calculation are shown in Fig. 20 (Wang, 1980). The calculated value of S is only a few percent except for a large resonance-like structure at an intensity minimum near 70 eV. The experimental data, which have been reported only for the region around 20 and 125 eV, have the same sign and approximately the same magnitude as the calculation. Figure 20 shows a curve where a temperature-dependent variation of the magnetization per layer is included ; in this case the temperature-dependent 60

50

0.01 5

40

-

0.010

>

L

0 c

20 0.005

-K

0

0

Ni(ll0)

8=12'

(001Beam +=35.26'

0

t 00

50

150

E

FIG.20. The calculated spin-dependent scattering asymmetry S and reflection coefficient I / l o are shown as a function of energy for Ni( 110)at a polar angle of incidence of 12" and azimuthal angle in the 11i l l direction. The solid curve is I vs. E, the dashed curve, S vs. E (surface magnetization); and the dotted curve, S vs. E (bulk magnetization). The solid arrows indicate Bragg peaks. The dashed arrows indicate energies at which calculations were made as a function of temperature. [From Wang (1980).]

266

D. T. PIERCE AND R . J. CELOTTA

surface magnetization is found to be less than that of the bulk. Such layerdependent magnetization causes S to differ from the calculation for the bulk particularly in the energy range 100- 150 eV. Self-consistent calculations of the surface layer magnetic moments have predicted an enhancement with respect to the bulk (Jepsen et al., 1980) or a decrease with oscillations into the bulk (Wang and Freeman, 1980a,b). By varying layer-dependent magnetic moments in a PLEED calculation and comparing the calculated and measured S , it will be possible to determine the surface magnetic moment and test the predictions of the self-consistent theories. The temperature dependence of the surface magnetization provides an interesting problem for theoretical and experimental investigation. For an itinerant ferromagnet like Ni, a consistent theoretical explanation of the temperature dependence of the magnetization has only recently become available for the bulk (Koreman et al., 1977; Hubbard, 1979). Most theories of surface magnetization are appropriate for' localized spins (Hohenberg and Binder, 1974).The mean field theory, which applies best to a Heisenberg local spin system, predicts a temperature dependence of the bulk magnetization near the Curie temperature of M , cc [l - (T/T,)]1'2, but a linear dependence of the surface magnetization of M , oc 1 - (T/T,).The distance over which the surface magnetization differs from the bulk magnetization is characterized by a correlation length 5 that also has a critical temperature dependence 5 oc [ 1 - (T/T,)]-'I2. Therefore, in probing surface magnetization by elastic electron scattering, the surface magnetization is observed when the inelastic mean free path is less than <. The surface magnetization relative to that of the bulk is enhanced at higher temperatures as has been pointed out (Alvarado, 1979)in a discussion of spin-polarized photoemission. As the temperature increases, there is a smearing of the Fermi surface. In the case of Ni, even though the temperature dependence of the Fermi occupation number changes the filling of the majority and minority spin subbands, the effective magnetic moment per site decreases only about 10% as T+ T, (Cook, 1981). The orientation of the magnetic moments changes, however, because the energy required to rotate spins is small. This is the main mechanism for the disappearance of long-range spin order as the temperature increases to the Curie temperature. The temperature dependence of the spin-dependent scattering asymmetry can be calculated using Eq. ( 3 3 ) if the thermal average of the projection of the direction of the surface spins onto the direction of the incident electron spin is known. The calculation of this thermal average is not straightforward and remains unsolved in the itinerant band model. Wang (1980, 1981a) used a local Heisenberg model and mean field theory for Ni, as Wolfram et al. (1971) did for NiO, to calculate a layer-dependent magnetization as a function of temperature. This was then used in the PLEED calculation to obtain

SPIN POLARIZATION IN ELECTRON SCATTERING

267

the temperature dependence of S at 125, 124, 21, and 20 eV for Ni(l10) at an angle of incidence of 12". At energies of 125,124, and 21 eV, the curvature of the temperature dependence of the bulk magnetization is calculated to be greater than that of the surface. Near 125 eV, the surface magnetization near T is approximately linear, in agreement with experiment and the predictions of mean field theory using the kinematic approximation. However, at E = 20 eV, the result is very nonkinematic; the multiple scattering actually caused the curvature of the surface magnetization curve to be greater than that of the bulk. Although this result has not yet been experimentally tested, it cautions against applying simplified kinematic approximations, especially in regions where S(E, 8 ) or I(E, 8 ) are rapidly varying. The use of a Heisenberg local spin model and mean field theory in a temperature-dependent dynamical PLEED calculation is a first step; it is expected that the availability of more experimental data in the future will stimulate theoretical work on the temperature dependence of the surface magnetization of itinerant systems. A constant complex potential V, = V, 5 is used in LEED calculations outside the muffin-tin spheres. The imaginary part of the potential describes the absorption or attenuation of the electrons due to inelastic scattering. Feder (1979) has argued that can be spin dependent and in fact is the dominant cause of the spin dependence in his calculations of electron scattering from Fe(l10). Inelastic scattering can be caused by electron-phonon scattering, electron-magnon scattering, electron-hole pair creation, and plasmon excitation. Electron-phonon scattering is weak and spin independent, and according to Kleinman (19781, the potential for electronmagnon scattering above 10 eV is an order of magnitude smaller than that for electron-hole pair or plasmon excitation. Helman and Baltensperger (1980) recently calculated that the spin dependence in the excitation of plasmons by polarized electrons is very small, less than 0.4% for plasmons in Ni. Feder (1979) postulated that in the energy range of interest ( E < 100 eV), the triplet scattering amplitude vanishes, that is, there is only scattering between electrons with opposite spin orientation. This leads to

+

-

V!.eh/v/,ch

=

1 7 h t

(34)

where n t and nJ are, respectively, the number of majority and minority valence electrons per atom. The average electron-hole excitation potential is Yeh = 3Vifeh+ V/,eh). Using this approximation for the spin-dependent part of V [ * l ,Feder compared the spin-dependent scattering due to V!.'(v) inside the muffin-tin sphere and in a dynamical PLEED calculation for specular scattering up to 100 eV from Fe( 110 at an angle of incidence of 45". The absorption-induced spin dependence due to the imaginary part of the potential is more than twice as large as that due to the real part. Calculations V / y l

268

D. T. PIERCE AND R. J. CELOTTA

using this model have also been carried out for Ni(ll0) (Wang, 1981b; Davis, 1981). There is, however, little experimental evidence to justify the assumption of Eq. (34) that the triplet scattering cross section is zero. In polarized electron-polarized H atom scattering, the triplet scattering cross section is calculated to be zero only at ionization threshold (Klar and Schlecht, 1976). Experimentally,at energies a few eV above threshold, the ratio of the triplet to singlet scattering cross section was found to be one-third and increased to two-thirds 100 eV above threshold (Alguard et af., 1977). Although the model of Eq. (34) was used to interpret the spin-polarized photoemission data of Bringer et al. (1979), the precision of the data and the indirect interpretation did not provide any clear justification of the model. Polarized electron scattering measurements discussed in Section V,D argue against this model which allows only scattering between antiparallel spins. Recently Rendell and Penn (1980) have calculated the spin-dependent which is inversely related to the spin-dependent inelastic mean free path

- 2 0-

I

I

I

I

1

FIG. 21. The normalized asymmetry in the spin-dependent inelastic cross section d = + u/)shown as a function of energy for Fe, Co, and Ni. [From Rendell and Penn

(u] - u / ) / ( u /

(1980).]

SPIN POLARIZATION IN ELECTRON SCATTERING

269

scattering cross section ot.1,for Fe, Co, and Ni using the statistical approximation (Lindhard et al., 1963).The asymmetry, d = (at - al)/(a' + a!) = (1;' - A T 1 ) / ( l r l + Ail), for Fe and Co goes from 0.11 and 0.025 at the Fermi energy to 0.047 and 0.016 at 20 eV above EF as shown in Fig. 21. Rendell and Penn find I d 1 for Ni is always less than 0.007. In contrast, the model of Feder predicts negative values of d for Fe, Co, and Ni independent of energy. The difference in the sign of .a? in the two calculations in the lowenergy region is due to phase space effects, which were included by Rendell and Penn but not by Feder. These effects cause the scattering of low-density minority spin electrons to dominate at low energies. At high energies, the scattering depends essentially on the number of electrons available to scatter from, and the two calculations give the same sign for d. B. Special Experimental Considerations

So far, our discussion has assumed a homogeneously magnetized sample. A ferromagnet actually has small regions known as Weiss domains which are spontaneously magnetized below the Curie temperature. The orientation of the domains is such as to minimize the free energy which depends on such factors as the magnetization energy due to an applied field and the magnetic anisotropy energy. One might consider trying to probe a single domain with the electron beam. However, it is difficult to obtain an intense wellfocused electron beam at low energy, where the exchange interaction is largest. In addition, the orientation of a domain, which depends on its thermal and magnetic history, is generally unknown. If the electron beam averages over several domains, the net spin-dependent effect can be anything between zero and the saturation value. In practice, it is desirable to apply a sufficiently large magnetic field to remove the domain structure and align the Weiss domains in the field direction. What constitutes a sufficient field depends on such factors as the crystalline anisotropy, the geometry and consequent demagnetizing field, and the magnetic susceptibility. The magnetization can cause a stray magnetic field which can deflect the electron beam owing to the Lorentz force or can cause a depolarization owing to precession of the electron spins in the stray field. In order to obtain a homogeneously magnetized surface and to minimize the stray magnetic field, it is desirable to magnetize the sample parallel to the surface and provide a closed path for the magnetic flux. The ideal configuration is a toroid as pictured in the paper by Saldaiia and Helman (1977) on the theory of spindependent electron scattering from ferromagnets. Such a parallel configuration was analyzed in connection with spin, energy, and angle resolved photoemission (Pierce et al., 1979) and found to offer many advantages over the configuration where the field is perpendicular to the surface, which is most

270

D. T. PIERCE AND R. J. CELOTTA

often used in polarized photoemission experiments. This parallel configuration was subsequently tested for photoemission by Kisker et al. (1980). In the case of electron scattering in a configuration in which the field is perpendicular to the surface, a longitudinally polarized electron beam and normal incidence and exit from the sample would be required. Since a toroid of the sample material, although ideal, is usually impractical, a C- or horseshoe-shaped electromagnet with a soft iron core is used to hold the sample. The basic arrangement used in the first measurements (Celotta et al., 1979) is shown in Fig. 6 . An air gap between the Ni sample and the core of the electromagnet facilitated sample heating and cleaning. With a gap, however, the stray field is larger, a larger current in the electromagnet is required to achieve saturation, the remanent magnetization is lower, and the relationship between the electromagnet current and the field inside the sample is very complicated. An air gap was avoided in the measurements of the ferromagnetic metallic glass discussed in Section V,D. When the electromagnet core is far from saturation, the hysteresis loop of the core is of the Rayleigh type (Bozorth, 1951)for which the induction has a roughly linear relationship to the electromagnet current. In the absence of an air gap, the applied field in the sample is then also roughly linear in the electromagnet current. The stray field outside and parallel to the surface is a result of the failure of the sample to close completely the magnetic circuit and screen the field of the electromagnet. High-susceptibilitysample materials are most suitable, such as well-annealed single crystals magnetized in an easy direction or metallic glasses that have low anisotropy. It is advantageous to have the sample near saturation, but in saturation a sample cannot screen any additional stray field. There is a trade-off between optimum screening and maximum sample magnetization. Also, there is no screening of the field above the sample Curie temperature. The electromagnet sets up a stray field that decreases as the area of the poles and the distance between them decreases. In this regard a small sample and magnet are advantageous. However, there must be sufficient separation of the poles that the electron beam does not pass near a pole where the stray field can be perpendicular and cause rapid precession of the electron spin. A stray field can deflect the beam and change the scattering geometry causing not only angular uncertainty, but also changing the true scattering plane from the nominal scattering plane, The polarization that lies in the nominal scattering plane may then have a component perpendicular to the true scattering plane giving rise to a spin-orbit contribution to the spindependent scattering. Ordinarily, the spin-orbit interaction depends on the spin of the incident electron and not on the magnetization of the surface. However, the deflection of the electron beam in a stray field depends on the

SPIN POLARIZATION IN ELECTRON SCATTERING

27 1

magnetization, and the resultant spin-orbit contribution changes sign on reversing the magnetization just as the exchange contribution does. As the applied field is increased beyond the point of sample saturation, the exchange scattering remains constant but the stray field and hence the spin-orbit contribution increases. Therefore, measurements as a function of magnetic field beyond saturation allow one to test for a stray field induced spin-orbit contribution. C . Scattering from a Ferromagiretic Crystal: N i ( l I 0 )

The first measurements of the spin dependence in electron scattering from a ferromagnet were carried out on Ni(l10) by Celotta et af. (1979).The sample was magnetized along the [ I l l ] easy axis by an electromagnet, as in Fig. 6 . An air gap allowed the crystal to be heated by passing current through it. A combination of Ar' ion sputtering and heating were used to clean the surface. Because of the air gap, it is not likely that the sample was uniformly magnetized, but there was a single-domain region at least a few millimeters in diameter near the center of the crystal. This was established before attempting the electron scattering by measurements of hysteresis curves using the magneto-optic Kerr effect (Pierce et id., 1980a). The measurements (Celotta et al., 1979) of the spin-dependent scattering were all for the case of elastic specular scattering at an angle of incidence of 12". A measurement of the spin-dependent scattering as a function of applied field showed a hysteresis curve, Fig. 22, as expected for an effect that depends on the surface magnetization. At maximum applied field S reaches a saturation value of approximately 1.5%. The measurement was at a nominal incident energy of I25 eV ( 122 eV when corrected

A

I

* --t.02

e l

_ I I

'H

FIG.22. A surface hysteresis curve S ( H )for Ni( 1 10) at room temperature obtained by polarized electron scattering at an angle of incidence of 12 and energy of 122 eV. The data points ha, 3 been connected by straight lines. The magnetic field applied in the sample was not calibrated owi-g to the air gap between the crystal and electromagnet. [From Celotta et al. (1979).]

272

D. T. PIERCE AND R. J. CELOTTA

for the contact potential difference between GaAs photocathode and Ni crystal). The inelastic mean free path of electrons in Ni at this energy is about 5 A (Demuth et al., 1975) so an electron on the average penetrates and returns through two atomic layers. In order to display a hysteresis curve, the definition of S has to be changed from those of Eq. (6) or Eqs. (30) and (311. In these equations, I,, and I, are the scattered intensities for the incident spin, respectively, parallel and antiparallel to the net spin density in the surface. When the applied field is reversed, the directions of the surface spins are reversed, but the sign of I , , - Z t f is the same, and hence S is unchanged. In order to measure a hysteresis curve, a preferred direction is established in the laboratory, for example, to distinguish between + H and - H. If I, and I, are defined with respect to this preferred axis, the sign of I , - I,, will change on reversing the magnetic field. For an incident electron energy of 19 eV, S as defined by Eqs. ( 6 ) ,(30), and (31) did have the opposite sign from that at E = 122 eV. In that case, the hysteresis curve was reflected about the vertical axis in Fig. 22. The abscissa scale of Fig. 22 is difficult to establish. Experimentally, S is measured as a function of the current in the electromagnet. The field applied to the sample with an air gap is a complicated function of the current. Even in the absence of an air gap, the resultant hysteresis curve is a combination of the sample hysteresis and the hysteresis of the core of the electromagnet. Careful analysis is required for the interpretation of such curves. For example, in the case of an easily magnetized sample, the width of the hysteresis curve will be determined by the width of the core hysteresis curve. The temperature dependence of S measured by Celotta et al. (1979) over the limited temperature range 0.5 < T / T , 0.8 is shown in Fig. 23. The upper curve is the result of measurements of the temperature dependence for three different positive saturation fields as denoted by the three different symbols. The lower curve is the same measurement for negative fields. There was no provision for control of the sample temperature in this first experiment ;the sample was heated to 1.35T,, and measurements were made while it cooled. The cooling rate for T > 0.8T, was too rapid for precise measurement. In the temperature range measured, S decreasesapproximately linearly with temperature by a factor of 3 from S(OST,) = 0.015 to S(0.87J = 0.005. This is in sharp contrast to the functional form of the temperature dependence of the bulk magnetization, where there is a decrease of only about 30% in this interval. In the low-temperature limit, surface spin waves are expected to give a linear temperature dependence. Near the Curie temperature, existing theories predict a critical exponent from *, which is the bulk value, up to

,

-=

SPIN POLARIZATION IN ELECTRON SCATTERING

-.O?s

.8

.7 .8 .9 TEMPERATURE (TITc)

273

10

FIG.23. The temperature dependence S(T) is shown in the range 0.5 < T/T, < 0.8 for the same scattering conditions as in Fig. 22. The three different types of points represent three different applied fields in the positive and negative regions of saturation of the hysteresis curve. [From Celotta el at. (1979).]

1. Attempts are being made to extend the temperature range to test existing theories (Felcher et al., 1980). In the experiments of Celotta et al. (1979) it was noticed that the hysteresis curves were very sensitive to sulfur contamination. In subsequent work (Celotta et al., 1980),measurements were reported of the change in the spin-dependent scattering S on deliberate chemisorption of a surface species. Figure 24 shows the decrease in S as a function of oxygen exposure in Torr sec). This increase in the oxygen Auger signal langmuirs (1 L = relative to the Ni signal with oxygen exposure is also shown. The spindependent scattering decreases monotonically to a small value with increasing exposure to oxygen. As is well known, ferromagnetic metals are also widely used as catalysts. Magnetic measurements can be used to monitor changes that occur in catalytic reactions under realistic temperature and pressure conditions where electron spectroscopies cannot be used (Selwood, 1975). Electron spectroscopies,on the other hand, are used in ultra-high-vacuum conditions on well-characterized surfaces to obtain a microscopic understanding of the chemical bonding. In addition to the various electron spectroscopies, it is

274

D. T. PIERCE AND R. J. CELOTTA

.010

S

.005

Exporuro (L)

FIG. 24. The effect of chemisorption of oxygen as a function of exposure ( I L = Torr sec) on the surface magnetization as reflected in the spin-dependent asymmetry S is shown in relation to the ratio of the 0 to Ni Auger peak heights at 503 and 848 eV, respectively. [From Celotta et af.(1980).]

now possible with polarized electron scattering to investigate changes in surface magnetization induced by chemisorption. An understanding can be gained of how a change in surface magnetization associated with a particular chemical change measured in the ultra-high-vacuum environment might be manifested in macroscopic magnetic measurements under reaction conditions. Polarized electron scattering measurements will thus make macroscopic magnetic measurements more informative monitors of catalytic processes.

D . Scattering from a Ferromagnetic Metallic Glass: Ni4,Fe4,B,, In previous sections we have discussed spin-dependent scattering from single crystals where the electrons are diffracted into well-collimated beams. In this section we review work in which the polarized electron scattering technique was extended to an amorphous material where the scattering is diffuse. This work demonstrates the wide application of polarized electron scattering to measure surface magnetic properties; such scattering provides a versatile surface magnetometer. The preparation of metallic glasses and their magnetic properties have been widely investigated (Luborsky, 1980; Chen, 1980). The amorphous ferromagnets are produced by rapid quenching from the melt, for example, onto a cooled rotating drum. The metalloid boron in Ni40Fe40B20 stabilizes

SPIN POLARIZATION IN ELECTRON SCATTERING 0.04

I

N140F040B20

O.O1 0 .o

e=1

w

E=90OV

t i

0

275

15

1I 30

ANQLE OF INCIDENCE, a (dog)

FIG.25. In the case of scattering from an amorphous ferromagnet. S is seen to be independent of the angle of incidence a, that is, the relative orientation of the sample surface and incident electron beam. For thedata shown. thescattering angle was 166 and the incident electron energy was 90 eV. [From Pierce ri al. (1981c).]

the amorphous phase. Properties of ferromagnetic glasses, such as low anisotropy and high susceptibility, facilitate the electron scattering experiment. The effect of structural disorder on the scattering is apparent from measurements of the angular dependence of Iand S. Provision was made to rotate the sample through an angle a, about an axis in the sample surface normal to the scattering plane, from normal incidence c1 = 0 to about a = 30 . The scattering asymmetry S was approximately independent of the orientation of the surface relative to the electron beam as seen in Fig. 25 for a scattering angle 8 = 166' (Pierce er al., 1981~).The initial polarization Po was corrected to Po cos a, since only a component is parallel to the surface spins. On the other hand, both S a n d the spin-averaged intensity Iwere functions of the scattering angle 19.Both S and I were larger for scattering near the backward direction, 8 = 166', and both decreased as the scattering angle decreased to 90"; the curves were roughly independent of a for 0" I a I 30". It is apparent that in the absence of crystallinity, there is no special angular dependence relative to the surface of the sample; only the total scattering angle in the scattering from the atoms in the surface is of consequence. A theory of the mechanism of this spin-dependent scattering should explain the higher S observed at larger 8. For scattering from an amorphous ferromagnet, S(K) in Eq. (30) depends only on the atomic scattering factors. The elimination of diffraction effects allows the measurement of the energy and angle dependence of the magnetic scattering alone without complicated interference structure. The spindependent asymmetry in the elastic scattering S(E,) is shown in Fig. 26 as a function of incident electron energy Eo from 2 to 300 eV (Pierce et ul., 1981~).(In this section only, we use S(Eo) and S(E) to distinguish elastic

276

D. T. PIERCE AND R. J. CELOTTA

.05

.

*

-

*

.

-

.

.

"

*

.04.

.03.

:?\

.02 . .01 b

** ++%+++++*

#

*+++++tt*+,t

O -.01.

+++g*

$.+

-.02.

-.03. -.04.

- . 0 5 - " '

*

"

"

"

'

FIG.26. The spin-dependent asymmetry in elastic scattering from Ni40Fe40B,oshown as a function of incident electron energy from 2 to 300 eV at a scattering angle of 166". [From Pierce et al. (1981c).]

and inelastic scattering.) S(Eo)is positive below 12 eV, becomes negative, and then is positive again above 50 eV. It remains small and does not change sign from 300 to 500 eV. From Fig. 26 we see that parallel spins scatter more strongly below Eo = 12 eV and above Eo = 50 eV. The fact that S changes sign as a function of energy argues against this structure being due to the spin dependence of the imaginary part of the potential (Feder, 1979). In that model, the cross section for inelastic scattering of electrons with spins oriented antiparallel to the majority spins is larger than for those antiparallel to minority spins; the former are more rapidly attenuated, so the elastically scattered current I , is expected to be larger than I , leading to an energyindependent positive S contrary to observation. The spin-dependent asymmetry of inelastically scattered electrons and secondary electrons was first measured by Siegmann et al. (1981), also on Ni,oFe40B,o. The result for an incident energy Eo = 97 eV is shown in Fig. 27. The right-hand scale is for the spin-averaged scattered current N(E). The elastic peak is seen at 97 eV, some damped surface plasmon structure 5-10 eV below this, and the large peak below 20 eV of true secondary electrons created primarily by electron-hole pair production. The other curve shown is S [ N ( E ) ] ,the spin asymmetry in the scattering or production of those electrons that make up N ( E ) .

,

StE)

f

S"(E)I

=

"(E)ft-NtE)t1I/"(E)lt

+ N(E)tll

(35)

N(E)tT(fJ) are the number of electrons scattered into the Faraday cup at

SPIN POLARIZATION IN ELECTRON SCATTERING

0

20

40 60 ELECTRON ENERGY (eV)

80

277

100

FIG. 27. The number N ( E ) of electrons scattered from the amorphous ferromagnet Ni,,Fe,,B2, at an energy Eand scattering angle of 166".The elastic peak at the incident energy 97 eV, some loss structure, and part of a large peak of true secondaries can be seen. The spindependent asymmetry S ( E ) of inelastically scattered electrons is shown as a function of their energy E after scattering. [From Siegmann er a/. (1981 ).]

an energy E when the spin of the primary beam is parallel (antiparallel) to majority spins in the sample. S(E) is largest for the elastic scattering, decreases and becomes negative at about 40 eV, and goes to zero at low energies where true secondaries dominate the spectrum. The small wiggles in N ( E ) and S ( E ) are generated by noise and do not have physical meaning. A detailed theory of S(E) is not yet available. However, it is known that for E 2 E,,/2, N ( E )is predominantly due to inelastically scattered primaries, that true secondaries dominate the spectrum at E < E0/4,and that most inelastic collisions are followed or preceded by an elastic collision which redirects the electron to the surface so it can escape. Siegmann et al. (1981) point out that S ( E ) changes sign near where S(Eo) changes sign and suggest that the primary electrons retain their spin in inelastic collisions and are redirected to the surface by spin-dependent elastic events. There is also no particular spin dependence in S(E)at a loss energy of 5-10 eV, in agreement with Helman and Baltensperger (19801, who predict a very small spin dependence in plasmon production. The fact that S(E)+0 as E -t 0 indicates that the production of secondary electrons is not spin dependent. This is in contrast to the model in which the imaginary part of the potential responsible for electron-hole pair production is assumed spin dependent (Feder, 1979). In that model, the ratio of the cross sections for electron-hole pair production is rst/al = n l / n t , where n t ( l ) is the number of majority (minority) spins per site. The model makes a prediction for S ( E ) of the true secondary electrons: S ( E ) = ( n l - n t ) /

278

D. T. PIERCE AND R. J. CELOTTA

+

(nJ nT) r -0.1 since n t - nl = nB = 2.2 is the experimental value for the Bohr magneton number at room temperature and nl nl = 19 is the total number of valence electrons per formula unit (NiFeB,,,). Siegmann et al. (1981) also found that the current absorbed by a ferromagnet, when a polarized electron beam is incident on it, depends on the relative orientation of the incident polarization and the net surface spin density. The spin-dependent asymmetry in the net absorbed electron current (number of electrons per second) i, is defined as

+

A = (l/lPo[)(iaT~ - i,Tl!/ci,TT

+ ij,Tl)

(36)

where Tt(TJ)means the polarization of the incident beam is parallel (antiparallel) to the majority spin direction in the sample. The spin-averaged absorbed current is I, = $(i,tT iaTJ). The spin-dependent asymmetry of the absorbed current is shown as a function of primary electron energy in Fig. 28. Below 100 eV, A is less than 1%. Before considering the divergent behavior at higher energy (Section V,E), it is interesting to note that A is negative below 9 eV, becomes positive, and then becomes negative again at about 50 eV. Note that the energies where A changes sign are very near to those where S(E,) changes sign. At very low energies where more antiparallel than parallel spins are absorbed, there are more parallel spins elastically scattered. The energy dependence of A, together with the observation that secondary electron production is not spin

+

1.

I

I

.5

-.5

-1

0

25

50 75 100 125 150 INCIDENT ELECTRON ENERGY (eV)

+

175

FIG.28. The spin-dependent asymmetry A = (i,fT - iafJ)/(iaTT i J J ) in the net absorbed electron current in Ni40Fe40B,oas a function of incident electron energy is shown by the solid line, which is magnified by 100 below 100 eV (shown by + ). The spin-averaged absorbed current I, is shown (0) near the energy where it changes sign. [From Siegmann el a / . (1981 ).]

SPIN POLARIZATION IN ELECTRON SCATTERING

279

dependent led Siegmann et a/. (1981) to suggest that the spin dependent absorption of electrons is due to the spin dependence of the elastic scattering. I t should be noted that the measurement of A is particularly simple. A lock-in amplifier is connected to the sample to measure the ac spin dependent signal, and an electrometer is used to measure the spin-averaged current. There is no need for LEED optics or a Faraday cup to make this measurement. Hysteresis curves have also been obtained by measuring the absorbed current; moreover, such measurements are even easier at higher energy where there is an enhancement of A , as we discuss in the next section.

E. Spin Detection from Enhuiiced Absorbed Curretit Asj3mmetrqt

The measurements of Siegmann et ul. ( 198 1 ) displayed in Fig. 28 are also exciting because of their potential importance as the basis for a new detector of spin polarization. As seen in Fig. 28 there is an energy range where A changes very rapidly to A = - 1 at E, = EoTT = 148.9 eV, where i,TT = 0,and then reversessign to becomeA = + 1 at E, = EoTJ = 150.2eV. Thespin-averaged current I , is seen to go through zero at En Z i ( E n f f + EoTJ 1. At this energy, the current of elastically and inelastically scattered primary electrons and true secondary electrons that leave the sample just equals the current of the beam incident on the sample. For the case of polarized electrons incident on a ferromagnet, there are two energies where the current leaving the sample and that incident on it are equal, one for parallel spins E,(TT) and one for antiparallel spins E,(fJ) as shown in Fig. 29. At Eo(TT)where i,TT = 0, only antiparallel spins induce a net absorbed current and i,tJ is measured, giving A = -1. At EotT and

FIG.29. The absorbed currents with the incident spin parallel i.tt and antiparallel i,tl to the majority spin direction shown near the energy where I, = 0. The currents i,tl and zaTT pass through zero at two different energies, where A = + 1 and A = - 1, respectively.The difference between these two energies and their sensitivity to angle of incidence of the beam are important parameters for a spin detector.

280

D. T. PIERCE AND R. J. CELOTTA

E,Tl, the absorbed current is still 0.6% of the incident current. Because I, changes sign, a very small spin asymmetry is increased to 100% in a very convenient energy range. The zero intercept depends on the angle cc between the incident beam and the surface; however, the shift is less than k0.3 eV for an angle change of k4' which provides a satisfactory angular acceptance (Celotta et al., 1981). Some ways in which this spin-dependent absorption effect can be used as a spin detector are apparent by considering Fig. 29. The absorbed current curve I(l3 for an incident electron beam of unknown spin polarization P would lie between the curves z,tt and i,tJ which correspond to P = 1 and - 1, respectively. For example, for P = -0.5, the line /(El lies between the line I, (corresponding to P = 0 ) and idtJ,and, to the extent i,tt and i,TJ are linear, the zero intercept would be halfway between the zero intercepts of /, and i,fJ. Linearity is not necessary, since as long as a calibration measurement of i,tt and i,tl has been made, P can be determined from the zero intercept. P can also be determined by measuring the current /(E,fJ) at EotJwhere A = 1 and I ( E o f f )at E o f t where A = - 1 and using the expression P = (/Z(E,tJ)l - ~ ( E o ~ ~ ) ~ ) / ( ~ Z /Z(Eoff)/). ( E o ~ J )Alternatively, ~ if the polarization of the incident beam can be reversed, or if the magnetization of the detector is reversed with respect to the incident beam polarization, the currents required in the expression for P can be measured without varying the incident beam energy. As discussed at length in Section IV, the spin-orbit interaction is the source of large spin-dependent effects and could be expected to cause a large spin-dependent asymmetry in the absorbed current. The asymmetry in the absorbed current is shown in Fig. 30 for a polarized beam incident on a W(100) surface at angles of incidence a = 0.4, 1.5, 6.5, and 14" (Celotta et d.,1981). The definition of A remains the same, but in this case TT and J. correspond to incident electron spin, respectively, parallel and antiparallel to the scattering plane normal defined by the wave vectors of the specularly scattered beam. At normal incidence A = 0, and the sensitivity of A to angle of incidence allows a precise determination of a = 0. At cc = 6.5", A is already greater than in the case of Ni40Fe40B,oshown in Fig. 28. At a = 14" the spin dependence is large as seen from the slow variation of A at E o t t and Eof J and from the large energy separation A = 4.1 eV between A = + 1 and - 1. The normalized scattered intensity Ia/I,,at Eo?t or E,tJ is 0.008 (Celotta et ul., 1981). Spin-dependent absorption due to the spin-orbit interaction has also been observed for Au( 110) with an ZJZ, as high as 0.01 at ct = 57" and 4 = 90" where A = 2.5 eV (Erbudak and Miiller, 1981). A detector based on this spin-dependent absorption has the advantage of being simple, compact, and efficient. Such a detector operates in an analog mode, but because of the high figure of merit, its inability to count single

+

+

28 1

SPIN POLARIZATION IN ELECTRON SCATTERING

A

Op

-0.6

-1.0'

-4

'

' -3

'

'

-2

'

'

' 0

-1

E-E,

1

2

3

4

(EV)

FIG.30. An illustration of the spin-dependent absorption of an electron beam by a W(100) crystal at angles of incidence of 0.4, 1.5, 6.5, and 14". The separation A between the energies where A = + 1 and A = - 1 is 0.1,0.38, 2.1, and 4.1 eV, respectively.The zero intercept Eo of I, is 206, 206.5, 216.9, and 222.5 eV, respectively.[From Celotta et al. (1981).]

electrons is a disadvantage only for the weakest signals. Both the exchange and spin-orbit interaction provide the required spin dependence;the choice of detector material depends on its ease of preparation, stability, and efficiency over the required electron-optical acceptance phase space. This new type of detector is expected to find wide application.

VI. OUTLOOK Spin polarization in electron scattering from surfaces is a field in its infancy, and we anticipate rapid development. Throughout this article we have indicated many of the directions of future work; we enumerate them in this section along with a few additional ones. The use of PLEED for surface structure determination will benefit from the close coupling between theory and experiment as in the recent work on W( 100)of Feder and Kirschner (1981). In suitable energy or angular ranges, information on surface geometry or on the details of the scattering potential

282

D. T. PIERCE AND R. J. CELOTTA

could be obtained. The good agreement obtained between theory and experiment provides a foundation for future use of PLEED in surface structure analysis. Future theoretical developments may include treatment of adsorbate structures and reconstruction at surfaces. The advantageous features of PLEED discussed in Section IV provide motivation for further work in this area. A compact, movable, efficient spin polarization detector would allow a number of new measurements of spin polarization effects in electron scattering from surfaces, and PLEED could be the basis of such a detector. With such a detector, the change in the polarization of a polarized beam scattered from a sample could be measured. This would allow the identification of processes in which a spin-flip or a depolarization has occurred. Such a detector would also be useful where the source of the electrons scattered in the surface region is not an incident beam but is internal to the sample, such as photoexcited electrons or secondary electrons regardless of how generated. Angle-resolved photoemission measurements show intensity variations related to diffraction of the photoelectrons. Feder (1977d) has suggested that measurements of the spin polarization of electrons excited in an adsorbate atom, diffracted from a high-2 substrate, and subsequently emitted in a particular direction will show spin-dependent effects related to adsorbate site symmetry. [This spin dependence is independent of the polarization that has been observed (Heinzmann et al., 1979) for angledependent emission of photoelectrons from atoms by unpolarized light.] Since LEED and secondary electron emission are related (Willis, 1977), spin polarization effects can be expected (Feder and Pendry, 1978) for nonnormal secondary emission, particularly in the region of surface resonances. In the case of a ferromagnetic surface, the secondary electron emission may be polarized even when the emission is normal to the surface. An experiment in this direction has been the measurement of the polarization of secondary electron emission from ferromagnetic EuO (Chrobok and Hofmann, 1976). We note in passing that spin dependence is also expected in the diffraction of low-energypositrons from high-Z surfaces (Feder, 1980b). Even with new intense sources of low-energy positrons (Mills, 1979), which are known to have a polarization of approximately 22% (Zitzewitz et al., 1979), polarized low-energy positron diffraction will be very difficult to investigate. We believe that a very promising direction of future development is spin polarization in electron scattering from magnetic surfaces. By modulating the polarization of the incident beam, it is possible to detect the spindependent exchange scattering on a background of spin-averaged Coulomb scattering. In this sense, the polarized electrons can be thought of as “surface neutrons” in that they “see” surface magnetic effects just as neutrons sense

SPIN POLARIZATION IN ELECTRON SCATTERING

283

bulk magnetic effects. Many of the experiments with polarized electrons which can be contemplated have their analogs in neutron scattering. Further experimental and theoretical work is required to understand the mechanism of spin-dependent electron scattering from magnetic surfaces. Many questions remain unanswered. Does the spin dependence arise only in elastic scattering via the exchange interaction? Can the energy and angular dependence of the spin-dependent scattering be predicted theoretically? Experiments on a number of different materials, crystalline vs. amorphous, itinerant vs. localized spin systems, will provide the facts to guide and test the theories. From PLEED measurements of magnetic crystals coupled with dynamical PLEED theories it may be possible to extract the layer dependent magnetic moment near the surface. The temperature dependence of the surface magnetization as compared to that of the bulk, particularly in the region of the critical temperature, is of great interest. The calculation of that temperature dependence, especially for an itinerant ferromagnet, is a challenge. We have discussed how the spin-dependent scattering can be used to measure changes in surface magnetization during chemisorption on the magnetic surface. This change can be correlated with changes in the electronic structure and chemical bonding of the surface species as determined by other spectroscopies available in an ultra-high-vacuum environment. An understanding of how changes in the surface magnetism reflect microscopic changes will facilitate the interpretation of macroscopic magnetic measurements used to monitor catalytic processes. Such measurements under reaction conditions are nominally of the bulk magnetization, but actually measure surface magnetization in the case of highly dispersed catalysts. The understanding of surface magnetism gained by spin-dependent scattering can therefore provide insight into the microscopic changes that are correlated with the macroscopic magnetization measurements. It is apparent that polarized electron scattering has practical applications and will be useful in addressing some technological problems in an industrial laboratory. Its use in relation to the study of chemical reactions on surfaces is an obvious example. In addition, as magnetic storage and recording devices are made thinner, the surface magnetization and its behavior increases in importance. Spin polarization in electron scattering may also provide a means of measuring submicron-sized magnetic storage structures. The first inelastic spin-dependent electron scattering measurements of Siegmann et al. (1981) suggest another new direction of future investigation. Already, an absence of a spin dependence was found in plasmon and true secondary electron production for the ferromagnetic metallic glass, Ni40Fe40B20.The measurement of the change in the spin polarization

284

D. T. PIERCE AND

R. J.

CELOTTA

of the inelastically scattered electron beam will give additional information about the magnetic character of the initial and final electron states involved in an excitation associated with the inelastic loss. As discussed in Section V, high-resolution measurement of polarized electron energy loss and spin analysis after scattering will allow the determination of surface magnon dispersion curves. In the itinerant electromagnet, surface spin waves are predicted (Griffin and Gumbs, 1976) to be higher in energy than those of the bulk, an advantageous experimental situation. Since the electron magnon cross section can be expressed in terms of the spin-spin correlation function, measurements of this type will provide information on the dynamical behavior of surface spins. At the other extreme, for large energy losses, there may also be a spin dependence in the inelastic scattering; there is a question as to the size and consequent observability of this spin dependence. In principle, appearance potential spectroscopy and other spectroscopies could exhibit a spin dependence for ferromagnetic materials. By measuring large angle scattering and large energy loss (10 keV for a 20 keV incident energy, for example) Vriens (1971) has suggested that it might be possible to measure the spindependent electronic momentum density distribution of a ferromagnet. An analogous measurement has been proposed (Platzman and Tzoar, 1970) employing Compton scattering of circularly polarized X rays. If the scattered electron and the excited electron are collected in coincidence, an (e, 2e) experiment, then the spin- and energy-dependent momentum distribution can be obtained (Vriens, 1971). At lower energy the measurements would be surface sensitive. Such polarized (e, 2e) measurements at surfaces are extremely difficult, but are not to be ruled out in the coming years. As we look ahead, it is clear that there are many new and exciting directions to be investigated. The measurement of spin polarization effects in electron scattering from surfaces is a powerful technique that can be used to address many questions; the future of this field looks very promising. ACKNOWLEDGMENTS We are grateful to many of our colleagues in the field of spin polarization in electron scattering from surfaces for helpful discussions, sending preprints, and constructive criticism of this review. This work was supported in part by the Office of Naval Research.

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Jennings, P. J., and Jones, R. 0. (1978). Surf. Sci. 71, 101. Jennings, P. J., and Read, M. N. (1975). J . Phys. C 8, L285. Jennings, P. J., and Sim, B. K., (1972). Surf. Sci. 33, I . Jepsen, O., Madsen, J., and Anderson, 0. K. (1980). J . Mugn. Magn. Muter. 15-18,867. Joffe, A. F., and Arsenieva, A. N. (1929). Compres Rendus 188, 152. Kalisvaart, M., ONeill, M. R., Riddle, T. W., Dunning, F. B., and Walters, G. K. (1978). Phys. Rev. B 17, 1570. Kessler. J. (1969). Rev. Mod. Phys. 41, 3. Kessler, J. (1976). “Polarized Electrons.” Springer-Verlag, Berlin and New York. Kirschner, J., and Feder, R. (1979a). Phys. Rer. Lerf. 42, 1008. Kirschner, J., and Feder, R. (1979b). Surf: Sci. 79, 176. Kirschner, J., and Feder, R. (1980). Proc. I n f . Con/: Solid SurJ, 4th, ECOSS, 3rd, Cunnes 11, 1104. Kisker, E., Gudat, W., Kuhlmann, E., Clauberg, R., and Campagna, M. (1980). Phys. Rev. Lett. 45,2053. Klar, H., and Schlecht, W. (1976). J . Phys. B 9, 1699. Kleinman, L. (1978). Phys. Rev. B 17,3666. Koreman, V., Murray, J. L., and Prange, R. E. (1977). Phys. Rev. B 16,4032,4048,4058. Kumar, P. (1974). Phys. Rer. B 10,2928. Kuyatt, C. E. (1975). Phys. Rev. B 12,4581. Lagally, M. G., Ngoc, T. C., and Webb, M. B. (1971a). Surf Sci. 25,444. Lagally, M. G., Ngoc, T. C., and Webb, M. B. (1971b). Phys. Reu. Lerr. 26, 1557. Lagally, M. G., Buchholz, J. C., and Wang, G.-C. (1975). J . Vuc. Sri. Techno/. 12, 213. Langstroth. G. 0. (1932). Proc. R . Soc. (London), Ser. A 136,558. Lee, T. D., and Yang, C. N. (1956). Phys. Rev. 104, 254. Lichten, W., and Schultz, S. (1959). Phys. Rev. 116, 1132. Lindhard, J., Scharff, M., and SchUtt, H. E. (1963). K . Dun. Vindensk. Selsk. Mar. Fvs. Medd. 33, (14).

Loth, R. (1967). Z. Phys. 203,66. Loth, R., and Eckstein, W. (1966). Phys. Lett. 20, 390. Lu, T.-M., and Wang, G.-C. (1981), unpublished. Lubell, M. S. (19771. In “Atomic Physics 5” (R. Marcus, M. Prior, and H. Shugart, eds.), p. 325. Plenum, New York. Luborsky, F. E. (1980). In “Ferromagnetic Materials” (E. P. Wohlfarth, ed.), Vol. 1. NorthHolland Publ., Amsterdam. McMaster, W. H. (1961). Reti. Mod. Phys. 33, 8. McRae, E. G. (1979). Rei>.Mod. Phys. 51, 541. McRae, E. G., Pierce, D. T., Wang,G.-C., and Celotta. R. J. (1981). Phys. Rev. (in press). Mahan, A. H., Riddle, T. W., Dunning, F. B., and Walters, G. K. ( 1980). Surf. Sci. 93, 550. Maison, D. (1966). Phys. Lett. 19,654. Massey, H. S. W., and Mohr, C. B. 0. (1941). Proc. R. Soc. (London), Ser. A 177,341. Mikaelyan, L., Borovoi, A,, and Denisov, E. (1963). Nucl. Phys. 47,328. Mills, A. P. (1979). Appl. Phys. Lelt. 35,427. Mills, D. L. (1967). J. Phys. Chem. Solids 28, 2245. Mills, D. L. (1971). Phys. Rev. B 3, 3887. M#ller, C. (1932). Ann. Physik 14,531. Morruzzi, V. L.. Janak, J. F., and Williams, A. R. (1978). “Calculated Electronic Properties of Metals.” Pergamon, Oxford. Mott, N. F. (1929). Proc. R. Soc. (London), Ser. A 124,425. Mott, N. F. (1932). Proc. R. Soc. (London), Ser. A 135,429.

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Miiller, N. (1977). Ph.D. Dissertation, Ludwig-Maximilians-Universitat, Munich. Miiller, N., and Wolf, D. (1976). Bull. Am. Phys. Soc. II21, 944. Miiller, N., Wolf, D., and Feder, R. (19781. In “Electron Diffraction 1927-1977” (P. J. Dobson, J. B. Pendry, and A. J. Humphreys, eds.). Inst. of Physics Conf. Ser. No. 41, p. 281. Myers, F. E., Byrne, J. F., and Cox, R. T. (1934). Phys. Rev. 46,777. ONeill, M. R., Kalisvaart, M., Dunning, F. B., and Walters, G. K. (1975). Phys. Rev. Lett. 34, 1167. Page, L. A. (1959). Rev. Mod. Phys. 31,759. Palmberg, P. W., DeWames, R. E., and Vredevoe, L. A. (1968). Phys. Rev. Lett. 21,682. Park, R. L., Houston, J. E., and Schreiner, D. G. (1971). Rev. Sci. Instrum. 42,60. Pauli, W. (1927). Z. Phys. 43,601. Pendry, J . B. (1974). “Low Energy Electron Diffraction.” Academic Press, New York. Pierce, D. T., Celotta, R. J., and Unertl, W. N. (1977). Proc. In?. Vac. Congr., 7th, int. Conf Solid Surf, 3rd., Vienna p. 2399. Pierce, D. T., Kuyatt, C. E., and Celotta, R. J. (19791. Rev. Sci. Instrum. 50, 1467. Pierce, D. T., Celotta, R. J., Wang, G.-C., Felcher, G. P., Bader, S. D., and Miyano, K. (1980a). J . Magn. Magn. Muter. 15-18, 1583. Pierce, D. T., Celotta, R. J., Wang, G.-C.. Unertl, W. N., Galejs, A., Kuyatt, C. E., and Mielczarek, S . R. (1980b). Rev. Sci. Instrum. 51,478. Pierce, D. T., Celotta, R. J., and Wang. G.-C. (1980~).Proc. Int. Conf. Solidsurf., 4rh, ECOSS, 3rd, Cannes 11, 1060. Pierce, D. T., Celotta, R. J., and Wang, G.-C. (1981a). Conf. Determin. Surf. Strucl. LEED. Pierce, D. T., Celotta, R. J., Wang, G.-C., and McRae, E. G. (1981b). Solid State Commun. (in press). Pierce, D. T., Celotta, R. J., Siegmann, H. C., Unguris, J., and Wang, S.-W. (1981~)(in press). Platzman, P. M., and Tzoar, N. (1970). Phys. Rev. B 2, 3556. Powell, C. J. (1974). Surf. Sci. 44,29. Raith, W. (1969). In “Atomic Physics 1” (V. W. Hughes, B. Bederson, V. W. Cohen, and F. M. J. Pichanick, eds.), p. 389. Plenum, New York. Raith, W., and Schliepe, R. (1962) Z , Phys. 170, 185. Rau, C. (1980). Comments Solid State Phys. 9, 177. Read, M. N., and Russell, G. J. (1979). Surf: Sci. 88,95. Reihl, B., Erbudak, M., and Campbell, D. M. (1979). Phys. Reu. B 19, 6358. Reihl, B., Miiller, N., Dunlap, R. I., and Pierce, D. T. (1980). Bull. Am. Phys. Soc. / I 25, 329. Rendell, R. W., and Penn, D.R. (1980). Phys. Reo. Lett. 45, 2057. Riddle, T. W., Mahan, A. H., Dunning, F. B., and Walters, G. K. (1978). J . Vac. Scr. Technol. 15, 1686. Riddle, T. W., Mahan, A. H., Dunning, F. B., and Walters, G. K. (1979a). Surf: Sci. 82, 511. Riddle, T. W., Mahan, A. H., Dunning, F. B., and Walters. G. K. (1979b). Surf: Sci. 82, 517. Rose, M. E. (1961). In “Relativistic Electron Theory.” Wiley, New York. Rubin, K., Perel, J., and Bederson, B. (1959). BUN. Am. P h p . SOC. 114,234. Rubin, K., Perel, J., and Bederson, B. (1960). Phys. Rev. 117, 151. Saldaiia. X.I., and Helman. J. S. (1977). Phys. Rev. B 16,4978. Schilling, J. S., and Webb, M. B. (1970). Phys. Rev. B 2, 1665. Selwood, P. W. (1975). “Chemisorption and Magnetization.” Academic Press, New York. Sherman, N. (1956). Phys. Rev. 103, 1601. Shull, C. G., Chase, C. T., and Myers, F. E. (1943). Phys. Rev. 63,29. Siegmann, H. C., Pierce, D. T., and Celotta, R. J. (1980). Phys. Rev. Lett. 46,452. Slater, J. C. (1951). Phys. Rev. 81,385. Thomson, G. P. (1928). Proc. R. Soc. (London), Ser. A 117,600, and 119,651.

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Thomson, G. P. (1934). Phil. Mag. 17, 1058. Thomson, G. P., and Reid, A. (1927). Nature (London) 119,890. Tolhoek, H. A. (1956). Reo. Mod. Phys. 28,277. Unertl, W. N. (1978b). J . Vac. Sci.Technol. 15, 591. Unertl, W. N., Celotta, R. J., and Pierce, D. T. (1978a). Inst. fhys. Cot$ Ser. 41, 287. Van Hove, M. A., and Tong, S. Y. (1979). “Surface Crystallography by LEED.” SpringerVerlag, Berlin and New York. Van Klinken, J. (1966). Nucl. Phys. 75, 161. von Barth, U., and Hedin, L. (1972). J . Phys. C 5, 1629. Vredevoe, L. A., and DeWames, R.E. (1968). f h y s . Rev. 176,684. Vriens, L. (1971). f h y s . Rev. 84,3088. Wakoh, S . (1965). J. Phys. Sor. Jpn. 20, 1894. Walker, D. W. (1 97 I). Rdu. Phys. 20,257. Wang, C. S., and Freeman, A. J. (1980a). J. Mugn. Magn. Muter. 15-18,869. Wang, C. S., and Freeman, A. J. (1980b). f h y s . Rev. 8 21,4585. Wang, G.-C., Lu, T.-M., and Legally, M. G. (1978). J. Chem. fhys. 69,479. Wang, G.-C., Dunlap, B. I., Celotta, R. J., and Pierce, D. T. (1979). Phys. Rev. Lett. 42, 1349. Wang, G.-C., Celotta, R. J., and Pierce, D. T. (1981a). f h y s . Reo. E 23, 1761. Wang, G.-C., Unguris, J., Pierce, D. T., and Celotta, R. J. (1981b). Surf. Sci. (in press). Wang, G.-C., Celotta, R. J., and Pierce, D. T. (1981~).Surf. Sci. (in press). Wang, S.-W. (1980). Solid State Commun. 36, 847. Wang, S.-W. (1981a). Conf. Surf.Struct. Determin. LEED. Wang, S.-W. (1981b). J . Appl. fhys. (in press). Wang, S.-W., Kirby, R. E., and Garwin, E. L. (1979). Solid State Commun. 32,993. Weisskopf, V. (1935). 2.Phys. 93,561. Willis, R. F. (1977). Inst. Phys. Conf. Ser. 41, 233. Wolfram, T., and DeWames, R. E. (1974). frog. Surj. Sci. 2, 233. Wolfram, T., DeWames, R. E., Hall, W. F., and Palmberg, P. W. (1971). Surf. Sci. 28,45. Woodruff, D. P., and Holland, B. W. (1970). fhys. Lett. A 31,207. Wu, C. S., Ambler, E., Hayward, R. W., Hoppes, D. D., and Hudson, R. P. (1957). f h y s . Rev. 105, 1413. Zitzewitz, P. W., Van House, J. C., Rich, A,, and Gidley, D. W. (1979). fhys. Rev. Len. 43, 1281.

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ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS, VOLUME 56

Solid Surfaces Analysis" MICHAEL J. HIGATSBERGER Instirure of Experimental Physics University of Vienna, Vienna, Austria

A. B. C. D. E.

Electrons Incident to the Surface. . . . . . . . . . . . . . Ions Incident to the Surface . . . . . . . . . . . . . . . . . . Neutral Particles Incident to the Surface . . . . . . . Photons Incident to the Surface.. . . . . . . . . . . . . . Atomic Surface Waves.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

............................. .................... H. Magnetic Field . ... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

350 351 352 354 356

I. INTRODUCTION Experimental methods for studying solid surfaces are numerous. Many new and novel methods to investigate solid surfaces have become available, especially in the last two decades. On the other hand, some of the basic principles were already known and well understood in the nineteenth century. Matter may occur in a solid, liquid, gaseous, or plasma phase. The boundary between two of these phases can be designated as surface phases. The importance of the interfaces ranges from pure fundamental aspects as surface states to applied technical processes, such as sintering, catalysis, and corrosion phenomena. Extensive experimental data are available as a result of the rapid progress in semiconductor development, but a complete theoretical picture of surfaces is still missing. One step toward improving a theoretical understanding of solid surfaces is the use of atomically clean surfaces of single crystals in surface analysis. When enough experimental data for a welldefined geometrical solid structure are on hand, it will be much easier to find a satisfactory theoretical model. The forces acting in crystals are of a periodic nature in contrast to those in noncrystals, where such a periodicity is in general missing. Inside the solid body forces act in all directions. The wellknown cutoff of the crystal forces at the surface creates energy states that are

* Work supported by the Austrian Science Research Fund, Project 4088. 29 I Copyri ht C 198 I by Academic Press. Inc All rights o%rep&luction in any form reserved.

ISBN 0-12414656-8

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MICHAEL J . HICATSBERGER

very different from the energy states inside the crystal. Only when ultra-highvacuum technology and gas pressures below lo-' Pa were made available could atomically clean surfaces be studied, and experimental technology has accelerated so fast that it is practically impossible to keep track of the vast amount of work. A crystal used as a target for probing a surface is immediately contaminated by hydrocarbons and oxygen when exposed to air. Sulfur is also in many cases an unwanted contaminant. When the gas pressure is Pa, within 1 sec a monatomic adsorption layer is formed if the adsorption probability is near to the factor 1. Only when the adsorption probability is much less than 1, which sometimes is the case for technical surfaces, will gas presPa be acceptable. sures larger than Special care must be given to the choice of crystal mounting, because the probe may become contaminated despite the ultra-high-vacuum environment by surface diffusion from the surrounding vacuum components and sample holders. Some authors recommend that the mounting consist of the same high-purity substances as those of the crystals. Alternatively, high-melting materials such as tungsten or molybdenum are recommended if they have been fabricated and heat-treated under ultra-high-vacuum (uhv) conditions; but tantalum mountings have been found to give rise to surface contamination by diffusion. To maintain clean conditions once they are achieved, devices have been built in which the samples are prepared under uhv conditions, heat-treated, and transported over a uhv sluice lock to the uhv analyzing chamber. Even when the preparation chamber and analyzing chamber maintain a uhv environment and precautions are taken to avoid surface diffusion to the sample from the sample mount, contamination is still sometimes found as a result of the cleaning procedure used on the sample in the preparation chamber. Several cleaning procedures have a tendency to deposit contaminants from the surrounding structure or from the surface layers that were removed by sputtering processes; thus a memory effect may occur. The simplest means of cleaning a surface of adsorbed layers is thermal heat treatment or the thermoflash technique. The idea behind it is to remove loosely bonded adsorbed layers from the surface under uhv conditions; and its effectiveness is seen in the pressure change when desorption takes place. The heating regimes may be constant, linearly increasing with time, or on a short flashlike, repeating sequence. In general these methods are applicable for removing contaminants from refractory materials, but they have their limitations, particularly when samples must be exposed to temperatures that lead to thermal etching. Another accepted cleaning process for single crystals is cleavage in uhv. In this process also only certain materials are suitable. Best results are achieved by fracturing the sample along a defined orientation. Other cleavage

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293

processes normally lead to surface irregularities. One that is used widely is the solid surface reaction with certain gases. Surface contaminants can only be removed by specific reactive gases; therefore it is necessary to know the contaminants’ constituents. This method is widely used in industrial semiconductor production processes. Often heating and gas solid surface reactions are combined. For example, the introduction of hydrogen at the proper temperature may solve the problem of removing carbon from a surface. Other cleaning processes include electron impact phenomena, photodesorption, field desorption, and pulsed laser bombardment. Desorption processes by electron bombardment were investigated considerably. The desorption is selective for certain contaminants, but the bombardment may break up compounds or may form compounds at the surface. Photodesorption works either by low-energy electrons produced by the photoeffect or by desorbing chemisorbed species by photogenerated minority carriers. Field desorption is only achieved at the field emission tip. Even when the first field emission microscope was being developed it was already seen that positive barium ions were desorbed from the needle tip. The pulsed laser bombardment needs a high-power laser of short pulse length. This method has several advantages: There are no foreign atoms introduced to the surface, and because of the short pulse length, migration and diffusion processes are minimal. On the other hand, surface disorder and local melting may occur. The most universal method of cleaning surfaces is still by ion bombardment. In order to avoid chemical reactions with the surface, noble gas ions are normally used. The ion current density and the ion energy must be chosen to avoid thermal etching and damage of the crystal structure. As a rule of thumb, A/cm2 remove one monolayer every second. The homogeneous removal or sputtering of surface layers depends on the present state of the art of available ion sources, in particular the uniformity and cross section of the ion beam and the ion current density. For an effective cleaning procedure several of the techniques mentioned are normally used in combination. In order to achieve very clean surfaces, substances are often deposited on substrates by chemical or electrochemical methods. Cathode electrolytic depositions and electrodeless or anode electrolytic depositions are some well-known processes. Liquid-phase epitaxial growth is used to form semiconducting epitaxial films, based on crystallization of semiconductors desolved in a suitable metal. Chemical vapor deposition is an accepted process in semiconductor technology and it allows the production of thin and pure monocrystalline films. The production of pure Si and GaAs, for instance, is done by chemical vapor deposition. The two most important physical methods of preparing high-purity layers are cathode sputtering and vacuum evaporation. The physical foundation of vacuum evaporation includes the following stages : transformation of the

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material to be deposited into the gaseous phase, transfer of the evaporated atoms to the substrate, deposition at the substrate and rearrangement of the deposited atoms with respect to the surface atoms and each other. Deposited surface layers are called crystalline surfaces when they exhibit a two-dimensional periodicity in the surface plane. To such pure and welldefined surface layers atoms or molecules may be added as impurities, and changes of the surface structure result. Physical adsorption is due to van der Waals forces, whereas chemisorption has either a covalent, ionic, or metallic bond force. Normally the adsorption heat of chemical bonds is much larger than the adsorption heat of physical bonds. Physical adsorption was mainly studied with the noble gases, and to achieve measurable effects low temperatures were required. Work on chemisorption is very extensive, and the most important results are tabulated in a few review articles. The chemisorbed particles may form a coherent layer on the substrate and thus form a kind of overlayer. There also exists the possibility that the adsorbed atoms will interact with the substrate and form an alloyed type structure. Crystallographic studies must tell us what the periodic structure is like. In the case of several monolayers, as it happens on alloy structures, it is also important to know if the periodicity of the new surface changes from layer t o layer.

11. SURFACE ANALYTICAL TECHNIQUES AND METHODS

Before the modern experimental techniques for surface analytical studies became available, spectrophotometric optical absorption instruments were in use as well as polarography and flame spectrometry. The physical basis of polarography rests on the current-voltage relation ; in flame spectrometry the emission spectrum was used. The sensitivity of these methods ranges from several monolayers in spectrophotometry to about 10 monolayers in polarography t o about one-tenth of a monolayer in flame spectrometry. The three methods are all of a destructive nature and require approximately gm minimum amount of substance under investigation. The destructive character of the methods mentioned and their relative insensitivity led to the search for new surface analysis techniques. The requirements of surface studies are primarily the analysis of surface structure and surface composition. Along with surface composition and structure, other surface properties like the electronic behavior, the surface atom motion, and the adsorption of atoms and molecules are of particular interest. In Table I a summary of the most important analytical techniques is classified by incident versus emitted radiation. A short description of each individual analytical technique follows. The techniques have been divided into groups by their incident radiation, following the classification used in

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TABLE I SUMMARY OF SURFACE ANALYTICAL TECHNIQUES CLASSIFIED BY INCIDENTAND EMITTED RADIATION Radiation Incident to surface Electrons

Ions

Emitted from surface

Surface analytical techniques

Auger electron appearance potential spectroscopy or Incident energy modulation method Augei-electron spectroscopy Electron energy loss spectroscopy or Characteristic energy loss spectroscopy High energy electron diffraction or Transmission electron diffraction High energy electron impact spectroscopy Inelastic low energy electron diffraction Low energy electron diffraction or Elastic low energy electron diffraction Reflected high energy electron diffraction Scanning electron microscopy and Transmission electron microscopy Electron impact ion desorption Ions or Electron probe surface mass spectrometry Electron stimulated desorption of ions by angular distribution Neutral particles Electron induced (impact) desorption or Electron stimulated desorption Surface desorption molecule microscopy Appearance potential spectroscopy Photons or Soft X-ray appearance potential spectroscopy Characteristic isochromat spectroscopy Electron probe microanalysis or X-Ray microanalysis Disappearance potential spectroscopy Ion neutralization spectroscopy Electrons Ion microprobe mass analysis Ionometry Electrons

Abbreviations AEAPS

IEMM AES ELS CELS HEED TED HEEIS ILEED LEED ELEED RHEED or RED SEM TEM EIID EPSMS ESDIAD EID ESD SDMM APS SXAPS CIS EPMA XMA DAPS INS IMMA (continued )

TABLE I (continued) Radiation Incident to surface

Emitted from surface

Ions

Neutral particles Photons

Neutral particles Electrons Ions Neutral particles

Photons

Photons Electrons

Ions Neutral particles Photons

Acoustic surface waves

Neutral particles

Thermal heat

Electrons Ions Neutral particles

Electric field

Electrons Ions

Magnetic field

Surface analytical techniques Ion scattering spectroscopy or Low energy ion scattering spectroscopy or Medium energy ion scattering spectroscopy Secondary ion mass spectrometry Sputtering Ion induced optical emission or Ion induced X-ray analysis Ion microprobe X-ray analysis Proton induced X-ray analysis or Surface composition by analysis of neutral and ion impact radiation Thin layer activation analysis Secondary electron emission Sputtering Low energy molecular beam scattering Sputtering Neutron activation analysis Electron spectroscopy for chemical analysis or X-Ray photoelectron spectroscopy and Ultraviolet photoelectron spectroscopy Laser microprobe mass analysis Photodesorption by an intrinsic photoeffect Photostimulated desorption Ellipsometry Laser Raman spectroscopy Mossbauer spectroscopy X-Ray fluorescence Desorption induced by surface acoustic waves Ionization pressure gauge Rest gas mass spectroscopy Thermionic emission Surface ionization Infrared absorption Thermal cleaning (pressure gauge) Themoflash technique (Flash filamentrest gas mass spectrometer) Inelastic electron tunneling spectroscopy Field emission microscopy Field ion microscopy Nuclear magnetic resonance Change of magnetization by adsorption Electron paramagnetic resonance

Abbreviations ISS

LEISS MEISS SIMS

IIX IMXA PIX SCANIIR

LEMS NAA ESCA XPS UPS LAMMA PSD

XRF

IETS FEM FIM NMR EPR

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Table I. The reader is, however, referred to the relevant review articles or original papers listed in the References. A . Electrons Incident to the Surface 1. Auger Electron Appearance Potential Spectroscopy (AEAPS)

The methods of excited core level spectroscopies have been grouped in Auger electron appearance potential spectroscopy (AEAPS), Auger electron spectroscopy (AES), disappearance potential spectroscopy (DAPS), ionization loss spectroscopy (ILS), soft X-ray appearance potential spectroscopy (SXAPS), electron microprobe analysis (EMA), and X-ray excited electron appearance potential spectroscopy (XEAPS). In Auger electron appearance potential spectroscopy, electrons from a filament of modulated energy irradiate a target. The energy modulation is achieved by adding a sinusoidal varying voltage to a dc accelerating voltage. As seen in the schematic diagram of Fig. 1 the target current, which is made up of the the primary electrons less the secondary electrons leaving the sample, is fed into a phase lock amplifier. ELECTRON GUN ANODES

+X

PROGRAMMABLE 0-2000 V DC

Y

x-Y RECORDER

I

REF.

I

PHASE-LOCK AMPL I F I E R

FIG.1. Layout of Auger electron appearance potential spectroscopy.

MICHAEL J . HIGATSBERGER

298

In order to avoid intensity modulations by the energy modulation voltage, part of the modulating voltage is applied to the focusing electrodes. The measured current intensity decreases at the thresholds. It is customary not to measure the target current, but instead the current to a nearby positively biased collector. There exist also other possible methods of measurements, for instance, suppressing the secondary electrons by a broadband energy filter supplied with a retarding field. In this case the high-energy Auger electrons are measured only. First and secondary derivatives of the secondary electron yield as a function of the primary electron bombardment energy are the usual graphical representations, which can be recorded on a X - Y recorder. In AEAPS electrons in the energy range between 100 and 2000 eV are used as bombarding particles. The angle of incidence is normally near 0" and the incidence energy resolution required is around 500 meV. The primary current should be on the order of 100 PA. The beam diameter, when hitting the target, is about 10 mm. The emitted particles are electrons of an energy range between 50 and 1400 eV. The current from the excited core levels is by 100-vA incident current on the order of 10 nA. The peak-to-background ratio depends on the detection system, but is in general 10-'-10-2. 2. Auger Electron Spectroscopy ( A E S ) The mechanisms involved in AES are ionization of atom core levels by incident electrons followed by radiationless Auger transition and the escape of an Auger electron. With the help of an electron spectrometer the ejected Auger electrons are registered as a function of their energy. If an electron with the energy E , ionizes a core level, the vacancy is immediately filled by another electron as seen in Fig. 2. The transition L, K releases the energy E , - EL,either in the form of characteristic X rays or in the form of an Auger --+

V

V

E L2,3 E

L1 EK

n ( L2,3

m:

FIG.2. Energy level diagram of AES.

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SOLID SURFACES ANALYSIS

electron, which is ejected from the L, level. According to Fig. 2 the process is called KL,L, Auger transition. However, a number of other transitions are possible. The most prominent Auger transitions are the KLL, LMM, and MNN transitions. These transitions are tabulated for the electron energy as a function of atomic number for all elements. Three electrons are involved at two energy states at least; hydrogen and helium therefore cannot eject Auger electrons. The principles of an Auger spectrometer are sketched in Fig. 3. Since the Auger electrons, which are ejected from the sample after electron bombardment with the electron gun. have an energy below 2400 eV, the coaxial cylindrical mirror analyzer must be magnetically shielded to avoid an adverse effect on the energy analysis due to penetrating magnetic fields. Inspection of Fig. 2 leads to the equation of the energy of Auger electrons E = E , EL, - Q A . Careful examination of the observed Auger lines shows that this relation is not exactly true. A correct energy of an Auger line cannot be expressed by the difference of the three binding energies as obtained from X-Y RECORDER OR OSCILLOSCOPE

LOCK-IN AMPLIFIER

I SWEEP SUPPLY

--

I

/

TARGET

L--I

-_ELECTRON GUN

I

r\

MAGNETIC S H I E L D

FIG.3. Diagram of an Auger spectrometer with cylindrical mirror analyzer.

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MICHAEL J. HIGATSBERGER

X-ray photoelectron spectroscopy (XPS). As soon as the L, electron has filled the hole in the K-shell, the binding energy of the L2,3 electron is increased, since the Coulomb repulsion of an L, electron has been removed. The hole-to-hole interaction depends on whether the holes are both in core shells, one is in a core shell and one is in a band, or both are in a band. If one or both of the final state holes are in the conduction band of a metallic sample, the notation V is used for these holes. An L,,,VV Auger transition involves an initial state hole in L2,3 and two final state holes in the conduction band. Experimentally accuracies of less than 5 eV can be obtained, and in the light of these data the energy of the Auger transition involving the three levels WXY reads wwx, = EWG) - SCEXCZ) + E dZ

+ l)] - +[Edz) +

+ l)] - @A

where OA is the work function of the analyzer material, and 2 is the atomic number of the atom involved. The number of Auger electrons depends on the incident electron current, the number of contributing atoms, and the cross section for Auger emission back into the vacuum. In no known apparatus can all Auger current emitted be collected. Only the fraction 0/4n will arrive at the detector, with being the solid angle accepted by the analyzer. Since the incident electrons partly ionize atoms at the surface and produce secondary electron emission, which in turn may have enough energy to ionize other surface atoms, a certain factor must be allowed for to take into account the effective increase of the incident electron current. For light elements the Auger emission has a higher probability than X-ray fluorescence. The Auger cross section is defined as gA = (1 - w)@,where w is the portion attributable to characteristic X-ray emission, and (D is the cross section for ionization by an incident electron. Reasonable Auger currents are on the order of 10-12-10-'4 A. But this current is superimposed on a background due to secondary electrons, which may well be an order of magnitude larger, In order to measure the Auger signals in the presence of the large background, the differential d[N(E)]/dE is usually measured instead of N ( E ) .The function d [ N ( E ) ] / d E can be obtained directly from the electronic recording on the X - Y recorder. If the energy analyzer voltage is slowly changed and a high-frequency sinoidal voltage of small amplitude is superimposed, the differentiated signal on the electron multiplier will be recorded (Fig. 4), provided the electron multiplier is connected with a phasesensitive amplifier as indicated in Fig. 3. Auger electron spectroscopy has reached a high level of sophistication and is in widespread use. Quantitative Auger analysis involves the determination of the relevant physical parameters entering the calculation and data recording, and the manipulation to extract the Auger intensities from the measured curves.

301

SOLID SURFACES ANALYSIS

tI

0

E

P

Ag

200

400

ev

= 1000

-

TARGET

600

800

1000

ELECTRON ENERGY ( e l ' )

FIG.4. Number of Auger electrons and dN(El/dE as a function of energy.

Besides the mirror-type cylindrical energy analyzer a 127" cylindrical analyzer has also been used, but because of the better signal-to-noise ratio the cylindrical mirror analyzer (CMA) is almost exclusively used at the present time. If a CMA is combined with a scanning electron microscope, elemental mapping with submicron spatial resolution is possible. Initial applications of AES were restricted to fundamental surface studies. Lately the applicability of AES to many practical problems has been demonstrated, such as the identification of anomalous structures. adsorption and desorption studies, surface segregation, surface reactions, mechanical surface properties, corrosion and oxidation, adhesion, friction and wear, embrittlement, intergranular corrosion, stability of grain structures, catalytic activity, and semiconductor technology.

3. Electron Energy Loss Spectroscopy ( E L S ) Electron energy loss spectroscopy is concerned with the study of energy loss at the surface of the reflected electrons. For the reflection from a surface the wave number conservation is valid only parallel to the surface, and because of the cutoff of the periodicity not normal to the surface. A complete theory of electron scattering should cover all measurable effects of electron scattering. So far no complete theory exists. The concept of the so-called dielectric theory has been treated in the classical way, but a full quantum mechanical treatment has also been published. Experimentally the excitation of optical surface phonons in infrared-active material as well as in noninfrared-active substrates has been observed. Also the excitation of plasma waves and electronic surface transitions have been found. Nonisotropic p f f p r t c frnm c i i r f s r e c

nf nnnicntrnnir matprialc w m r m

a l f n rerontlw A m t p r m i n m A

302

MICHAEL J. HIGATSBERGER

In order to perform experiments of scattering of low-energy electrons from surface optical phonons, high-resolution spectrometers are required. In principle five different dispersion devices for electron energy analysis are available as depicted in Fig. 5. 1. The hemispherical electrostatic filter has a capacity

C =

4nc0 * riro ro - ri

where E,, is the electrical permittivity of free space, and ri and T o , respectively, the inner radius and the outer radius of the spherical condenser. The resolution is varied by changing the voltage difference between the inner and the outer hemispheres. Slits are arranged at the entrance as well as at the exit of the condenser. Energy resolutions of 1% can easily be obtained. 2. The cylindrical energy filter has a capacity

c = - 2n€,

1

ln(ro/ri 1

with I standing for the cylinder's length. The 127" system angle is used for electron optical reasons.

1

I

I

I

I

r

1 (5)

- +

(5)

FIG.5. Typical electron energy analyzers. See text for explanation.

SOLID SURFACES ANALYSIS

303

3. The parallel plate energy filter has been used previously in time-offlight spectrometers. The device can be built simply, but the energy resolution is usually lower than with a cylindrical or hemispherical condenser. The analyzer is often also called plane mirror analyzer (PMA). The main idea of this energy selector is that electrons entering through the grounded plate leave the condensor with the same energy again. The plane mirror analyzer is entered normally at an angle of 45", since in this configuration small beam divergences cancel out. 4, The cylindrical mirror analyzer (CMA) is the most commonly used electron energy analyzer. The cross section of the CMA looks like that of PMA, but at the cylindrical mirror the deflection is caused by a potential difference between the inner and the outer cylinder as seen in Fig. 5. The outer cylinder is negatively charged and the smaller inner cylinder positively charged. The maximum apogee of the beam into the deflecting region is given by

r,

=

ri exp[+v

In

()'

sin2 93

The cylindrical mirror energy filter accepts electrons which come from a point on the cylinder axis and enter at an angle of 42.3" with the axis for second-order focusing. Large signals with high-energy resolutions are obtainable. 5. The Wien filter and similarly the trochoidal filter use mutually perpendicular electrostatic and magnetostatic fields'. Such filters are well suited for high-energy electrons, and in the case of the Wien filter the electric and magnetic forces exerted on the moving electron balance. The information ELS can give is comparable to that which is possible by optical methods, but it is often easier to undertake ELS. Vibrational spectra of adsorbed gases can be measured, and many other types of information already mentioned can be obtained. The method, which is in many respects novel, has been cross-checked and supported by low-energy electron diffraction (LEED), AES, flash filament, and mass spectroscopy. As a matter of fact, all these different surface analytical systems were combined in one experimental setup. In ELS the incoming electrons interact mainly with the longer range fields set up by the oscillating dipole. It depends on whether the dipole is oriented parallel or perpendicular to the surface. Only those vibrations can be excited that have a component perpendicular to the surface. For adsorption systems ELS can yield information on the microscopic structure of the adsorbate. It also contains information on the type of adsorption and on the binding potential. A kinetic study is possible if intensity is measured versus coverage. Because of the high resolution of the spectrometer contact potentials are also measurable.

304

MICHAEL J . HIGATSBERGER

4. High-Energy Electron Diffraction (HEED) Electron diffraction is the result of the wave character of electrons having a mass of me and moving with the velocity u. For relativistic electrons of the energy quothe de Broglie wavelength is

A=[

h2

I”’

2qme uo(1 + quo/2mec2)

Electrons with an energy of 104-106 eV vary their de Broglie wavelength from 1.22 x lo-’’ m to 0.9 x lo-’’ m. The difference between X-ray diffraction and electron diffraction lies mainly in the fact that X rays are diffracted at shell electrons, whereas electrons as incident radiation are diffracted besides at the shell electrons at the potential wall of the nucleons. In order to describe geometrically the diffraction phenomena of fast electrons reciprocal lattice vectors bi are used instead of the real characteristic vectors of the crystal lattice. If a plane wave with the direction so is diffracted by a crystal, the refracted wave s obeys according to Fig. 6(1) the condition (s - s0)/A = h

with

lsoI = Is1 = 1

+

The vector h can be written ash = h , b , h2b2 + h,b,. The relation between the coordinates and the Miller indices ( h k l ) is with n = 1 , 2 , 3 , . . . Ihl = dh;iZh,= nd;: A solution for the refracted waves can be shown using the Ewald construction of the reciprocal space. From Fig. 6 one can deduce the well-known Bragg condition which reads: Sin

8 = d / 2 d h , , = A/2dh,hlh3

Since high-energy electrons are mainly diffracted in the forward direction, two possible versions of the system are in use. namely. transmission electron

(1I

(2)

6. Ewald construction for different wavelengths determines graphically the Laue diffraction spots. ( I ) S,/i. = h ; ( 2 ) So/). >> h . FIG.

305

SOLID SURFACES ANALYSIS L

SCREEN

SCREEN

(1)

(2)

TIo 1 t

t

t

)

*t

--I* t

*

*

t (4)

(3)

FIG. 7. Schematic diagram and Ewald construction, respectively, of TED (1 and 3) and RED (2 and 4).

diffraction (TED) and reflection electron diffraction (RED, often also called RHEED). The principle of the system may be seen in Fig. 7. A typical experimental system for high-energy electron diffraction is shown in Fig. 8. Pa, sharp reflections can be If the vacuum conditions are kept below obtained even with a simple experimental unit. The sharpness of the reflection

ELECTRON GUN

1

I D IAPHRAGH

LENS PHOTOGRAPHIC PLATE

FIG.8. Experimental setup of an HEED system.

306

MICHAEL J. HIGATSBERGER

spots depends on the electron beam cross section and on the focal length of the condenser lens. With the help of an additional condenser lens a further reduction of the image points is possible, and higher resolutions are consequently achieved. If the electron beam is focused not at the screen but at the object, object areas with a diameter as low as lo-' m can be investigated. RED works quite similarly to TED except that in TED the object must be movable by a special manipulator in two perpendicular directions, whereas RED needs in addition a tilting action to change the glancing angle of incident electrons. The diffraction image shows therefore the dots as elongated lines. HEED is well suited for fine structure investigations on thin films and surfaces. For HEED investigations the minimum mass of samples may be as low as 10- gm and the time for registration of the refracted beam is below 1 min. If transmission electron diffraction is not possible because of a bulk sample, reflected high energy electron diffraction may be alternatively used. The accuracy of lattice constants determination is about 1% by RED, but with TED it may be two orders of magnitude lower.

5. High-Energy Electron Impact Spectroscopy (HEEZS) High-energy electron impact spectroscopy was born out of the application of the first Born approximation. The energy range is usually limited to 50 keV, because up to this energy the experimental results can be integrated by means of nonrelativistic theory, applying low-order corrections for relativistic effects. HEEIS is different from HEED because it uses a low grazing incidence scattering from surfaces. The HEEIS experimental setup consists of an electron gun, from which an electron beam confined with small apertures is incident onto a target. Scattered electrons arrive after passing through an energy analyzer at a proper detector. Often particles other than the scattered electrons, such as ions produced by striking the target or photons emitted therefrom, are measured. Current experiments in the HEEIS domain cover elastic electron scattering, inelastic electron scattering, scattered electron ion coincidence studies, and scattered electron, ion, and fluorescent photon triple coincidence. In the case of elastic scattering experiments, the measured scattered intensity as a function of angle and energy loss yields a function proportional to the cross section differential with respect to the scattered solid angle

do/dR = (~U/~R),IFO,(K))~ The differential cross section is expressed in Rydberg atomic units. Fo,(K) is the elastic form factor with K designating the momentum transfer. For inelastic processes d20/dR dE, must be used with E , standing for the energy

SOLID SURFACES ANALYSIS

307

loss. A survey of the experimental results includes data from outer or valenceshell spectroscopy, inner shell spectroscopy, and coincidence experiments. A particularly unique application of HEEIS is angular dependence spectroscopy which permits charge and momentum density measurements. One of the main applications of low-energy electron impact spectroscopy is the search for and the characterization of optically forbidden transitions, but high-energy electron impact spectroscopy also allows the observation of some forbidden transitions from their anomalous angular dependence. These transitions were not found with low-energy electrons. 6. Inelastic Low-Energy Electron Diffraction (ILEED)

Inelastic low-energy electron diffraction is the spatial analysis of scattered electrons which have lost specific amounts of energy. ILEED has been used mainly for the study of plasmon dispersion. ILEED analyzes electrons that have undergone one or more elastic and inelastic scattering processes. The theoretical treatment and the explanation of such complicated scattering processes are difficult, and therefore ILEED has not found as yet broad application. Electron loss spectroscopy can be considered as the aspect of ILEED that is widely used. Experimental ILEED systems are considerably more complex than other comparable analytical systems and require skilled and experienced experimentalists. 7. Low-Energy Electron Diflraction (LEED) Slow electrons with energies from about 5 to 500 eV interact very strongly with matter. Low-energy electron diffraction (LEED) is therefore one of the most suitable methods for surface examinations. The low-energy electrons have a very small penetration depth into the solid surface, as schematically shown in Fig. 9. The electrons impinge upon the surface of the sample, and the diffracted electrons penetrate the very fine grids G I , G,, and G, and arrive at the fluorescent screen, which is biased at about 5 kV positively with respect to the sample. Grid G, is grounded as are the sample and the anode of the electron gun. The hot filament acting as electron source is at a temperature of approximately 2500 K if it is made of tungsten or about 1000 K if it is made of bariated material. The primary electron beam current required is of the order of 1 PA. Electron optical lenses between cathode and anode produce a parallel beam with a diameter of less than 1 mm. For the microscopic structure of the crystal under investigation the cross section of the electron beam is quite large, and the beam can be described as an incident plane wave. Experimental investigations using LEED have reached a very high standard and are widely used. Because of the high atomic scattering cross sections of low energy electrons, the diffracted electrons are very

308

MICHAEL J. HIGATSBERGER

-__--.

> FILAMENT

-vP INCIDENT

OPT I CAL WINDOW

- v p *v I VACUUM VESSEL

FIG.9. Schematic diagram of an LEED apparatus.

sensitive to the surface atomic structure. The coverage of the sample surface with fractional monolayers can quite easily be seen. For the investigation of clean surfaces or single crystals it is thus necessary to operate the probe under uhv conditions, preferably in the region of lo-’ Pa. The diffracted electron pattern can be described by the Ewald sphere construction as shown in Fig. 6. From this construction the lattice parameter of a crystal reads a=

+

(h2 k2)112A 2 sin 8 cos(8 + 4)

and if the incident electrons are normal to the sample, then lattice parameter reduces to a=

(h2

4

= 0 and the

+ k2)”21 sin 28

Since low-energy electrons have a wavelength of a few nanometers, they are comparable to the wavelength of soft X rays. If sin 28 is plotted vs. A, the slope of the curve will give the mesh side a. Surfaces are defined by the planes of the bulk crystal to which they are parallel. The unit cell is repeated to build up the whole surface. Five two-dimensional lattices exist ;they are called Bravais lattices. If a monoenergetic beam of electrons is incident on a perfectly clean

SOLID SURFACES ANALYSIS

309

surface of a single crystal, the elastically scattered electrons will produce a diffraction pattern similar to the structure of the single crystal. The diffraction pattern can be calculated by applying the Schrodinger equation. The diffracted beam spots give the unit surface cell of the crystal, but no information about the disposition of the cell contents. Therefore it is not possible from the location of the beams to know the location of adsorbates relative to the substrate. This information is, however, contained in the intensities of the elastically scattered electrons measured as a function of energy. Intensity energy curves are the usual form of information. LEED studies give information about surface structures of pure crystalline substances, but also about reaction processes on the surface. It is possible to investigate adsorption and desorption processes, chemisorption processes, epitaxy processes, and so on. The reference structure to a surface structure is always the substrate. The symmetry of the atomic arrangement at a surface can be obtained immediately in an LEED experiment without the necessity of varying the diffraction geometry. Thus LEED permits observation of the surface dynamics. The surface sensitivity of LEED is very high and was experimentally determined by measuring the buildup of monolayers on metals, the growing rate of which was known. For all diffraction phenomena coherence conditions are important. The primary beam divergence in a typical LEED system is about lo-' rad, and the energy spread of the electrons is about 0.5 eV. For this condition 100-eV primary electrons will give a coherence zone diameter of roughly 10 nm. In summary LEED permits one to determine the direction and the location of the diffracted electrons, and the intensity of the diffracted spots as a function of the incident electron energy and as a function of the target temperature. From these data the lateral periodicity at the surface or the location of the atoms in the unit cell, the vibrational amplitudes of surface atoms, and the deviations from lateral periodicity can be derived. 8. ReJected High-Energy Electron Dijraction ( R H E E D or R E D )

The theoretical treatment of reflected high-energy electron diffraction follows the same pattern as that for LEED. If electrons from intermediate to high energies are incident-almost grazing to a flat surface, the diffraction pattern will reproduce the surface atomic structure, since the incident electron momentum normal to the surface will be small. At 100 keV the wavelength I = 3.7 x m and lkol = 1700 nm-'. Compared to the reciprocal lattice, the Ewald sphere as shown in Fig. 7(2) and (4) is very large. In RHEED the diffraction pattern will consist of long streaks at the fluorescent screen spaced by a distance determined by the lattice parameter, the wavelength, and the distance of the sample to the fluorescent screen. Because of the large

310

MICHAEL J. HIGATSBERGER

size of the Ewald sphere in a RHEED experiment, it is necessary to change thediffraction geometry in order to find the structure of the reciprocal lattice rods in three dimensions. Experimentally one can achieve this by rocking the sample about an axis in its surface or by rotating it about its surface normal. Surface roughness will influence the sensitivity of RHEED. In RHEED the inconvenience to an experiment of varying the primary energy is that intensity data are usually in the form of rocking curves or rotation diagrams. The scattering cross sections in RHEED are smaller than in LEED, and multiple scattering is therefore of less importance. Many workers prefer LEED to RHEED, but some instruments incorporate the capabilities of both methods. On an atomically clean surface the RHEED patterns will be streaks. Small surface roughness is indicated as spots and lines on the fluorescent screen, whereas larger surface inhomogeneities yield spot patterns only. Electrons must pass through the irregularities, and consequently transmission patterns in the form of individual points are the result. One of the reasons that the diffraction patterns produce less accurate results than the transmission data lies in the fact that the distance between sample and scizen cannot be precisely defined when the electrons are incident under a glancing angle. It is either possible to focus the electron beam onto the sample with a diverging reflected beam as a consequence or to use a parallel but broader beam on the sample and produce a sharp RHEED pattern on the screen. By transmission electron diffraction a single crystal will produce spot patterns, whereas a polycrystalline sample will show diffraction rings owing to the individual crystallites which are randomly oriented with respect to the impinging electrons. The radii of the rings correspond to the distances of the individual spots of a single crystal pattern. Diffuse patterns indicate the presence of amorphous substances. Good results with high-energy electron diffraction (HEED), which includes transmission electron diffraction (TED), and reflected high-energy electron diffraction (RHEED) are obtained when thin surface films are investigated. In general high-energy electron diffraction is more representative for the bulk material than for the outermost surface layer. 9. Scanning Electron Microscopy ( S E M ) and Transmission Electron Microscopy ( T E M )

The scanning electron microscope was developed by adding scan coils to the transmission electron microscope. Figure 10 shows the basic components of the scanning electron microscope: the electron gun, two focusing lenses and a final reduction lens, and a collector for measuring the reflected and secondary electrons coming from the specimen. These electrons are amplified, and the signal modulates the brightness of a viewing tube such as an oscillo-

SOLID SURFACES ANALYSIS

31 1

FINAL LENS

VACUUM SYSTEM

FIG.10. Basic components of a scanning electron microscope.

scope. By means of a scan generator the well-focused electron beam is scanned over the specimen. The scanning generator and the electron beam of the oscillograph must operate in synchronous mode. The magnification of the oscilloscope picture can be set by simple electronic means with the magnification control. When the primary electrons in the scanning electron microscope interact with the specimen surface, elastically scattered and reflected primary particles are found in addition to low-energy secondary electrons, Auger electrons, characteristic X rays, and cathodoluminescence. It is also possible to observe induced currents and/or voltages in the specimen. Through thin films transmitted primary electrons may also be found. The scanning electron microscope is used for surface topography, material analysis, and for the measurement of thickness and electrical properties of a specimen. In semiconductors the primary electrons can also produce an electron-hole pair, and in crystalline objects electron channeling effects have been observed. In comparison with the optical microscope SEM has more than an order of magnitude better resolution. The depth of focus is very high, and a large specimen area can be scanned. Transmission and diffraction mode operations like the normal TEM are applied, but the two most frequently used operating modes are the emissive and the reflective modes. Schematic diagrams are shown in Fig. 1l a and 1lb.

312

MICHAEL J . HIGATSBERGER (UC+AU) 0

GLASS

__

ELECTRON GUN

(1)

(b)

FIG.1 1 . (a) Emissive and (b) reflective modes for SEM.

In the emissive mode the specimen is acting as a cathode upon which electrons, ions, or UV radiation are impinging. The reflected mode is sometimes also called the mirror mode. The object specimen is held at a slightly more negative potential than the electron gun potential, and thus electrons come very near to reaching the object and are reflected back and accelerated through a diaphragm onto the fluorescent screen. The equipotential line of reflection for the electrons is close to the surface under investigation, and therefore local geometrical and potential variations of the samples can be determined. Two glass windows permit the visual observation of the fluorescent screen. A mirror is used so that the screen may be viewed from the rear. The detector can be as simple as a Faraday cage. The most widely used detector, however, is a scintillating photomultiplier, in which the light is created by accelerating the secondary electrons to an energy of 10-15 keV. Of all the kinds of information that can be gained by SEM, topographical studies rank on top. Because of the wide depth of focus, SEM pictures are very impressive and show details of surface topography not detectable by other methods. 10. Electron Impact Ion Desorption ( E I I D )

or Electron Probe Surjace Mass Spectrometry (EPSMS)

In ELS, LEED, and AES low-energy electrons are probing the surface, When these surface analytical tools were used, some disturbing effects were noticed which are due to electron impact desorption (EID). Neutral and

SOLID SURFACES ANALYSIS

313

ionic particle desorption have already been found from the operation of ion gauges and ion sources which are used in mass spectrometers. In a number of subsequent investigations it became apparent that there exists a proportionality between electron current impinging on a surface and the electron induced desorbed ion signal. For example, 40-eV electrons of lop5 A which struck a CO layer on a molybdenum substrate produced an O + ion current of A. If the same primary electron current had an energy of 85 eV, the oxygen ion current increased by 13 orders of magnitude. Experimental studies for other desorbed layers such as hydrogen or oxygen confirmed the linear relation between incoming electron current and collected desorbed ions over a wide range. Basically two different methods are used to investigate electron impact desorption. The first uses high primary electron current densities by which adsorbed layers are removed as a function of time. The second one uses very low electron current densities to study other desorption processes like thermal desorption or even to look for dynamical adsorption or desorption processes. The vast amount of work has been concerned with investigating adsorption layers on metals. In this case the impinging electrons liberate ions and neutrals from the top adsorbed particles. Most of the desorbed particles were neutrals, some of them in an excited state. The contribution of ions is of the order of a few percent only. The neutral particles can be ionized and analyzed by mass spectrometers. Other work was concerned with the EID induced work function determination using tips of thin wires of field emission microscopes. Electron impact desorption investigations permitted the characterization of different binding states for adsorbed particles. But since primary electrons can also break up the molecular structure of adsorbates or can convert one adsorbate into another, these aspects found wider applications. What can happen in the EID process is indicated in the potential energy diagram of Fig. 12. EID may not at this stage have as wide applicability as an independent surface analytical E (ENERGY)

1 E X C I T A T I O N ENERGY I N METAL)

ITED STATE OF ADSORBATE)

OUND STATE)

1

(DISTANCE FROM SURFACE)

FIG.12. Potential energy diagram of an adsorbate system.

314

MICHAEL J. HIGATSBERGER

method, but it is important to the understanding of what happens in uhv systems and machines in which electron impact desorption phenomena occur. 11. Electron Stimulated Desorption of Ions by Angular Distribution (ESDIAD) A typical electron impact ion desorption system consists of an electron gun producing electrons of some 100-eV kinetic energy bombarding the specimen and a mass spectrometer like a quadrupole instrument analyzing the desorbed ions according to their mass and intensity. Residual pressures should be below 3 x lo-* Pa during desorption studies. If the instrument is modified in such a way that the sample can be rotated around an axis in its surface and around its normal (in order to vary the azimuthal and polar angles on which the quadrupole mass spectrometer views the specimen), mass discriminating measurements of the angular distributions of electron stimulated ion desorption are possible. Studies were undertaken of CO adsorbed on W(100) and coadsorbed with carbon and oxygen. The experimental data indicate that low-temperature layers contain vertical and nonvertical CO whose proportions vary with the adsorbed CO thickness. If the substrate was precovered with carbon, vertical CO species could not be observed, and adding oxygen eliminated the nonvertical species. Pictures could be constructed showing the geometrical position of CO with respect to the wolfram substrate crystal. ESDIAD investigation is in its beginning stages, but it seems t o be a powerful tool to explain the bonding arrangements of adsorbed gas layers to a solid surface. In a number of measurements using different combinations of adsorbate-substrate, it was shown that 0' ions have an energy of about 8 eV. The energy distribution is approximately of Gaussian type with half-widths between 2 and 4 eV. The H + ions have a half-width of about 1.7 eV. It is interesting to observe that ions which are produced onto a surface of a solid body by laser irradiation show similar energy half-widths. The desorption process is strongly dependent on the specimen's temperature, but the W(100) surface also changes the form and intensity of the fluorescent screen pictures characteristically with temperature.

12. Electron Induced Desorption (EID) or Electron Stimulated Desorption (ESD) Depending on the kind of gas adsorbed to a metal surface, low-energy electron induced desorption processes produce one to four ions and about 100 neutral particles leaving the surface. The desorption rate may reach such values that a low-pressure-indicating gauge registers some pressure increase. Normally the desorbed number of particles is, however, small, and other methods for measuring them must be chosen. With the help of proper electrodes ions can be directed to the registering detector with high collection

SOLID SURFACES ANALYSIS

315

efficiency. The desorbed neutral particles, which may leave the surface also in an excited state, are difficult to collect as they spread out in all directions. The efficiency of passing these neutral particles through an ionization chamber may be as low as l o v 3or even In practical cases extremely low ion currents must be measured, but any good analyzing technique of electron induced neutral particles is bound to provide interesting information about the adsorbed layers. In addition to atoms, the EID process produces molecules. It was shown that the measurement of the total desorption cross section 6,may be derived from recording the surface ion current as a function of time, while holding the electron current density and energy as well as the temperature of the sample constant. The total desorption cross section is

where q is the electronic charge, i / F is the electron current density, and z the time constant of the exponential ion current decay. When the sample temperature, the electron energy, and the current density are held constant, then the ion current of the desorbed particles decays as a function of time, since the adsorbed gas particles are constantly removed. Therefore, if the time dependence of the current produced by the desorbed ions is determined for several values of electron current densities and an exponential dependence is found for all values i / F , it follows that 17,is a constant and the ion current is linearly related to the adsorbed gas. If for different values of in the product i , , ~is constant, then it is possible to calculate the maximum permissible value of i / F for which T is large compared to the measuring time. For different gases 0, is available from literature and can be compared with 6,determined by the above equation. Out of the neutral desorption studies a new technique evolved which the authors called the molecule microscope. 13. Surjace Desorption Molecule Microscopy ( S D M M )

The electron surface desorption phenomenon for neutral particles can be used to produce molecule micrographs. The experimental equipment required is sketched in Fig. 13. Neutral atoms or molecules, which are desorbed from the sample. pass through a fine pinhole and reach a field ionization detector built in the form of a fine field emitting needle. The positively biased needle ionizes the neutral particles in its vicinity by field ionization. The ionized particles reach an electron multiplier either directly or after passing through a mass filter. Scanning is achieved by moving the pinhole foil in a raster-like manner, or the sample itself is scanned by a beam of electrons so that the neutral particles are stimulated to leave the sample surface from a small area that is defined by thediameter of the electron beam. The resolution of this microscope is defined by the pinhole diameter, the geometrical dis-

316

MICHAEL J. HIGATSBERGER FIELD IDNIZA~lON DETECTOR

CI

7 -

PINHOLE FOIL

SHIELD

SAMPLE

FIG.13. Schematic diagram of a molecule microscope.

tance of the sample to the pinhole foil, and the distance of the pinhole foil to the field ionization detector. Two metal shielding plates, which are usually cooled to liquid air or liquid helium temperature, prevent the field produced by the ionization detector from reaching the sample surface and furthermore reducing the residual gas pressure that may exist around the specimen. Whenever the desorbed molecules are ionized they are accelerated toward the detector system, and the output pulses from the electron multiplier are further amplified to produce a voltage proportional to the neutral particle flux from the sample. A raster signal drives the scanning system and the oscilloscope synchronously, thus varying the brightness of the oscilloscope spot signals and giving an image of the desorbed sample surface. If the desorbed neutrals pass instead through a pinhole foil onto a cold plate, these particles adhere to the surface and freeze there. Taking a micrograph from the cold plate later would reveal what kind of desorbed particles had been adsorbed to the cold plate. Molecule microscopy is at an early stage, but it has the potential to map surfaces according to spatial variations in emission of neutral particles in particular molecules. From the recorded signal it is possible to obtain direct information about the spatial distribution of surface regions that contain, transport, or preferentially bind various species of neutral particles. Resolutions of the order of 1 pm are obtainable with a focused desorbing electron beam. With mechanical scanning of the pinhole foil resolutions of the order of 100pm are possible. The vacuum conditions especially in the region of the specimen should be below Pa in order to improve the signal-to-noise ratio, Adding a mass spectrometer to the molecule microscope permits identification of the desorbed particles. 14. Appearance Potential Spectroscopy ( A P S ) or Sofi X-Ray Appearance Potential Spectroscopy (SXAPS)

Electrons impinging on a surface can excite core levels and produce secondary electrons. They also can produce ions and neutral particles de-

317

SOLID SURFACES ANALYSIS

sorbed from the surface. From Auger spectroscopy it is known that core excitation can lead to either Auger electrons or to characteristic soft X-ray fluorescence. The technique that uses soft X-ray measurements is therefore called soft X-ray appearance potential spectroscopy (SXAPS) or simply appearance potential spectroscopy (APS). A possible experimental arrangement is shown in Fig. 14. The operation of such a spectrometer is straightforward. The electrons from the filament, which have a variable energy from 0 to lo00 eV imposed with a ramp power supply, impinge onto the specimen surface. As the potential difference between filament and sample is continuously increased, the electron energy reaches a value that is equal to one of the thresholds for core level excitation. Soft X-rays of the excited surface atoms are emitted when the threshold energy is reached. These created X rays appear superimposed on the already existing large background due to bremsstrahlung. The total number of quanta takes a sharp step up at the threshold energy. In order to measure the X rays they are allowed to pass through a grid that is electronrepellent. In the chamber separated by the grid the X-ray quanta produce photoelectrons which are drawn to the collector by a positive potential. If the photoelectron yield is registered as a function of primary electron energy, the diagram of Fig. 15 is obtained. Since the appearance potential soft X-ray electron signal is small compared to the background, a differentiation by modulation is advantageous. In Fig. 15 therefore the yield per volt is seen as a function of the potential applied between the filament and the sample. If Ep is the minimum primary

OUT

+350 V

FIG.14. Experimental setup of a soft X-ray appearance potential spectrometer.

318

MICHAEL J. HIGATSBERGER

0

’

I

POTENTIAL

I

1

400

I

800

(VOLTS>

FIG. 15. Typical SXAPS spectra of chromium.

electron energy at which a core electron is excited to the lowest unoccupied state above the Fermi level, then the equation

E , = EB - @C holds, where EB = hf’, the soft X-ray energy, and Oc is the work function of the cathode. When the primary electron energy is increased above threshold, then the final states can include all combinations of energies of the scattered primary electron and the excited core electron allowed by the conservation law. SXAPS records the excitation probabilities rather than the energies of ejected electrons. All allowed unoccupied states near the Fermi level can be probed. APS has one disadvantage which is resolution. In order to get enough X-ray photons, high electron currents must be used and the spatial resolution is only of the order of some tenths of a cm2. The soft X rays are emitted from the sample over the whole solid angle, and therefore the method with grid and adjacent chamber for soft X-ray photoelectron emission must be used. Since relatively low-energy electrons are used, the method is sensitive to one or two of the outermost layers. SXAPS is in fact a possibility for looking at the structure of the valence band just above the Fermi level, and it is therefore a valuable tool in situations where the structure is changing, as in catalysis or corrosion. It is, of course, also possible to use Auger electrons in appearance potential measurements; in that case the signal is normally much larger.

15. Characteristic lsochromat Spectroscopy ( C I S ) Using the experimental equipment for APS it is also possible to measure the soft X rays with a dispersive analyzer directly. A grating spectrometer, for instance, is adjusted to pass the characteristic emission line associated with the recombination of a particular core hole. This is in principle the characteristic isochromat spectroscopy (CIS). CIS has the advantage that it reduces the background, and its resolution is only dependent on the energy spread of the primary electrons. The characteristic isochromat of nickel L, is

319

SOLID SURFACES ANALYSIS

shown in Fig. 16. Despite the progress made in the development of energy dispersive X-ray analysis, CIS has so far only found limited application as a surface analysis technique. 16. Electron Probe Microanalysis ( E P M A ) or X - R a y Microanalysis ( X M A )

Electron probe microanalysis (EPMA), sometimes also called X-ray microanalysis (XMA) uses a finely focused electron beam of a diameter less than 1 pm, which is directed onto the surface of a specimen. Characteristic X-ray lines emerge from the small volume under investigation and are representative of the chemical constitution of the sample volume. In advanced systems the electron microprobe analysis is combined with the features of a scanning electron microscope by adding to the detector side a wavelength dispersive or energy dispersive X-ray detector system. The schematic layout of a combined SEM-EPMA is sketched in Fig. 17. The emitted electrons and photons from the specimen provide information about the surface topography and its composition in small regions. If the instrument scans, the information can be expanded over a larger sample area. The main components of a combined SEM-EPMA unit are the hot cathode with Wehnelt cylinder and anode; one or two magnetic condenser systems, the final objective lens, in which double deflection coils are incorporated for scanning purposes; the scan generator and the magnification control. The detector system is twofold and includes a secondary electron detector with photomultiplier and a display tube. The X rays, which are emitted from the sample spot, are analyzed by a wave dispersive and/or energy dispersive X-ray detector system. Ultrahigh vacuum is required, which is achieved either by diffusion or by turbomolecular pumps. Ultimate pressures below lo-' Pa are required. The energy of the electron probe is usually around 30 keV, while the electron current is between and lop9A. With special

d..... 840 POTENTIAL

.

I 850

I 860 (VOLTS)

FIG.16. Characteristic isochromat spectrum of nickel L,

320

MICHAEL J. HIGATSBERGER

m l p

SECOND CONDENSER LENS DOUBLE DEFLECTION C O I L AND OBJECTIVE LENS WAVE D I S P E R S I V E AND/OR ENERGY D I S P E R S I V E DETECTOR

SPEcIHEN w a , F S C A N

GENERATOR

SECONDARY ELECTRON DETECTOR TO O W B L E A DEFLECTION C O I L

CONTROL

FIG. 17, Schematic drawing of the electron and X-ray optics of a combined SEM-EPMA.

beam-reducing electron optical lenses a beam diameter as low as m can be obtained at the expense of the electron current. The scanning mechanism is similar to the SEM system. The X-ray emission distribution is represented by brightness modulation of a synchronously operated cathode ray display tube. The magnification is determined by the magnification control unit and is related to the proportion of scanning length to the size of the cathode ray tube. The precision of the measurements is furthermore dependent on the constancy of electron accelerating voltage and electron current. Stabilization for both voltage and current should be better than lo-' over several minutes. A good representation of the surface is obtained only when lens distortions are avoided. In the specimen region a light microscope with magnification around 300 is normally also used to preselect roughly the surface area to be investigated. For the X-ray analysis either wave dispersive or energy dispersive units are available. In the wave dispersive mode single crystals are used with lattice parameters similar to the wavelength of the investigated X rays. X Rays emitted from the surface area are subject to Bragg reflections, when falling onto the single crystal. The Bragg condition is given by

2d sine = nL It is possible to focus the X rays after they are reflected from the crystal, either fully or at least partly, as can be seen in Fig. 18. The final X-ray detector may be a Geiger or a proportional counter usually containing 90% argon and 10%methane. In case the single crystal is built from lithium fluoride, X-ray wavelengths between 0.8 and 3.6 x lo-'' m can be measured. Other crystal substances exist that permit analysis of wavelengths up to lo-' m. The registration of longer wavelengths than lo-' m is especially suited for the light

SOLID SURFACES ANALYSIS

32 1

elements above helium. In the energy dispersive mode of operation semiconductors of silicon or germanium are widely used. Silicon is normally doped with lithium, but germanium is available already in the pure form. To avoid backdiffusion of lithium from the silicon crystal, the detector must always be held at a low temperature; whereas the new pure germanium semiconductor detector can be raised to room temperature at any time and needs only to be cooled to liquid air temperature to reach good resolving power. The resolving power of good semiconductor crystals for the Mn K, line (5.9 keV) is slightly above 100 eV. which is already close to the theoretical value. The setup for an energy dispersive X-ray detecting system is composed of a liquid air cooled semiconductor connected to a preamplifier. followed by a linear amplifier. and an analog-digital converter (ADC). The ADC signal is fed to a multichannel analyzer (MCA) which may be computer controlled. The accumulated and stored MCA data are finally displayed by a cathode ray tube. The combined SEM-EPMA is one of the most powerful techniques for surface analysis and microanalysis of solids. Thin film analyses are undertaken with the films either free or deposited onto the substrate. Through such studies the technique also became accepted for the investigation of biological samples. 17. Disappearance Potential Spectroscopy ( D A P S )

In measuring the threshold excitation one either observes the secondary particles emitted during de-excitation, which may be characteristic X rays or Auger electrons, or analyzes the exciting beam itself. In the latter case beam variations near the threshold are the result. The observations of characteristic X rays and Auger electrons have been classed as SXAPS and AEAPS, while the beam variation method is called disappearance potential spectros-

322

MICHAEL J. HIGATSBERGER

copy (DAPS). With the experimental equipment used in the simple lowenergy electron diffraction system both AEAPS and DPS can be undertaken, with the difference that in AES the collector is on a fixed potential, whereas in the DAPS operation the potential is programmed. The DAPS measurement makes use of the fact that those electrons which create a core hole lose their energy and are not reflected from the specimen and thus have disappeared from the reflected beam. All the electrons that contribute to the production of a core hole are lost. The reflected electron current must decrease sharply when an excitation threshold is reached. The method is of particular interest, because it is a direct measurement with no interference or influence from the core decay process, which is of the order of sec. Unfortunately, the change in the reflected electron number is small. Differentiation of the reflected current with respect to the primary energy is therefore required to suppress the large background. A typical disappearance potential spectrum for the L3 shell excitation of a clean polycrystalline vanadium surface indicates a variation of the number of reflected electrons of one per mill only, whereas dR(E)/dE shows clearly the L,, L2, and the L, shell excitation. DAPS compares quite well with other methods using similar electronic transitions. X-Ray absorption spectroscopy has the same general spectrum form but with a better fine structure resolution, and ionization loss spectroscopy (ILS) shows an energy resolution that is not as good as the one from DAPS. B. Ions Incident to the Surface 1. Ion Neutralization Spectroscopy ( I N S )

Electron ejection processes by impinging ions can be divided into two categories: the kinetic ejection and the potential ejection. For ions with an

Attnc;

\

-

RESONANCE NEUTRALIZATION

RESONANCE IONIZATION

-

A*t(n-l)ei

/

A t ( n-2)citc'

FIG.19. Ion neutralizationspectroscopy electronic transitions.

SOLID SURFACES ANALYSIS

323

energy above several hundred eV the secondary emission factor y increases with increasing bombarding ion energy. The kinetic process ejects electrons by transfer of kinetic energy despite the disparity of ion and electron masses. Ions with low energies can eject electrons by Auger neutralization or by a two-step resonance neutralization and Auger de-excitation process as depicted in Fig. 19. The direct process of Auger neutralization can be written as A+

+ ne,

-P

A

+ (n - 2 ) e i + e -

The other two-stage resonance neutralization process with A+

+ ne,

+A*

+ (n - 1)e;

+A

+ (n - 2)e; + e-

and A*

+ (n - 1)e;

has a much lower probability compared to Auger neutralization. INS therefore is mainly concerned with the Auger neutralization transition. In the Auger neutralization process two electrons are involved which initially lie energetically at c1 and c2 below the vacuum level. The energy diagram of Auger neutralization is shown in Fig. 20. When the slow-moving ion approaches the metal surface at a distance s, the neutralization energy, which is equal to the ionization energy, will be supplied by two electrons coming from the conduction band of the metal. Electron 1 from level c1 is tunneling

VL

FL

I ON

FIG.20. Energy diagram of Auger neutralization.

324

MICHAEL J. HIGATSBERGER

to neutralize the ion, and electron 2 from level e2 is ejected beyond the Fermi and vacuum levels to the energy E . The whole process is radiationless, and therefore it must obey the following energy relation : &(S)

- CD - (1

=E

+@ +

~2

and thus E = E ~ ( s) (€1

+ 0)- + 0) ( ~ 2

Ifel and c2 are symmetricwith respect to c, then the equation can be written as

E

+

= E ~ ( s) 2 ( ~ @)

The experimental setup for INS must include an ion source for generating a well-focused slowly moving ion beam of a kinetic energy normally between 5 and 10 eV and a device to measure the kinetic energy distribution of the ejected electrons. The ejected electrons are analyzed in the simplest way, by a gridded retarding spherical potential analyzer. A more complex instrument has been developed which incorporates in addition to the INS spectrometer, LEED, ultraviolet photoelectron spectroscopy (UPS), XPS, and AES equipment. Sample processing means are also provided in the uhv system. In INS the role of the slow surface approaching ion is to provide the lowlying vacant electronic state that permits Auger neutralization to proceed. Only the effective neutralization energy of the ion near the surface enters as a parameter. The sensitive volume of INS was experimentally found to lie almost entirely outside the solid, but definitely not deeper than the first monolayer. Therefore INS is probing the adsorbate electronic structure. The probability of a spatial neutralization process in which the electrons of the conduction band are involved must be proportionai to the product of the initial density levels N ~ ( c A)NJc - A)

+

as indicated in Fig. 20. The total probability F(c) for the production of excited electrons is the integral of the above product F(c) =

[:

U(c

+ A)U(c - A)dd

The inner energy distribution F(E) multiplied with the ejection probability P(E) as seen in Fig. 21 leads to the measurable energy distribution D(E). So far most of the INS investigations have been of a methodical nature. TKe method is very sensitive, but the interpretation of data is complicated and requires some mathematical processing. Interesting results were obtained when INS was used together with another surface analytical technique such as UPS.

SOLID SURFACES ANALYSIS

325

I

FIG.21. Energy level diagram of INS.

2. Ion Microprobe Mass Analysis ( I M M A ) Ion microprobe mass analysis emerged as a special category of secondary ion mass spectroscopy (SIMS). A beam of primary ions is produced in a duoplasmatron ion source and is accelerated to an energy of about 20 keV. The ions pass through a primary magnet where isotopic mass selection is achieved and, after passing a focusing lens and the X-Y-beam scanning plates, impinge well focused by another electrostatic lens system onto the sample surface. The beam diameter can be varied between 1 and 300 pm, and the scanning length and mode are dependent on the potential applied to the scanning plates. Secondary ions emerge from the spot where the primary ions hit the sample and are accelerated by an electrostatic lens to the entrance slit of an electrostatic analyzer followed by a magnetic analyzer, which is essentially a double-focusing mass spectrometer. The mass resolution M / A M is about lOOO, but with special electrical condensers and magnetic sector fields the resolution may be as high as 10,OOO. The well-resolved isotopic masses, after passing a final slit, impinge on an ion electron converter, and the secondary electrons are multiplied by an electron multiplier. The final electron signal is fed to a counter, a recorder, or the X-Y-plates of a cathode ray tube, whose electron beam is being rastered in synchronism with the primary ion beam. The method of image formation is identical to that in an SEM or EPMA instrument. When the primary ion beam is scanned over the specimen surface, the secondary ions from the sample are used to modulate the intensity of the

326

MICHAEL J. HIGATSBERGER

cathode ray tube. Figure 22 gives an overview of a typical microprobe mass analyzer. Some instruments use negative primary ions for the secondary ion production, since there are two distinct processes involved in eroding the specimen surface. One process is of kinetic origin. The impinging ions penetrate the solid surface and are scattered inside the solid; they break lattice bonds, eject electrons, atoms, and ions, and come to rest at some depth. Experimental studies reveal that the secondary ions are either positive or negative ions. But the majority of secondary particles are neutrals which are apparently neutralized ions by recombination with conduction band electrons. The kinetic process is dominant if inert primary ions are used as impinging particles. If chemically reactive ions are the primary particles, the erosion process may be of a chemical nature combined, of course, with the existing kinetic type. Oxygen or nitrogen are typical chemically reactive species. The chemical erosion process may also be present if chemically reactive atoms or molecules are on or within the sample surface. To avoid unwanted surface effects, it is necessary to operate the IMMA under uhv conditions at pressures below low8Pa. If the surface work function through chemical reactions of the surface layer is increased, then electrons from the solid must overcome a higher energy to neutralize a positive secondary ion. Therefore this is a way to increase the positive secondary ion current. On the other hand, if the specimen is bombarded with ions of electropositive elements, the work function is reduced and the elements with high electron affinities will produce a high negative ion yield. A qualitative microprobe analysis is achieved by collecting the particles passing through the doublefocusing mass spectrometer system. A typical spectrum reproduces the count

6AS COUNTER

+ PO

RECORDER

kV

-I'

+30 kV

@ I: I

}

X-Y

BEAM DEfLECTION PLATES

MAGNETIC ANALYZER -150

v -1,5

kV

+1,5

kV

SAMPLE

FIG.22. Scheme of an ion microprobe mass analyzer.

SOLID SURFACES ANALYSIS

327

rate as a function of m/q. Such a spectrum is normally not a quantitative description of the isotopic masses present in the small volume under investigation. A step in the direction of quantitative analysis is the use of oxygen as a primary ion source gas. High and stable ion yields are obtained with oxygen, but further investigations seem necessary. Problems that make the qualitative analysis difficult at this stage are caused by the complex sputtering process itself. The sputtered yield varies with the atomic number of the material and is, of course, a function of the incident ion type and energy. The sputtering yield varies also with the angle of primary ion incidence. Further problems in getting quantitative data are encountered with the mass resolving power when two different ions have the same mass number, as the case of 12CH, and I4N. In order to help resolve these problems defined surface layers are produced by deposition processes of extremely pure materials and in-depth profiling is applied. IMMA has broad applications in a variety of fields, such as semiconductor technology, nuclear fuel technology, metallurgy, and many others. Even more applications for IMMA will result as soon as the instrument is computer controlled and operated. The ion probe is a destructive method by nature, but depending on the primary energy of the bombarding ions it is able to probe the constituents of a few outermost surface layers.

3. ionometry In the last few years special conferences dealt with the subject of “ion beams for surface analysis” and near surface regions of matter through Rutherford backscattering (RBS), channeling, nuclear reactions, and ion induced X rays. Such investigations have been called ionometric studies. In ionometry high-energy ions coming from van de Graaff generators or other electrostatic accelerators are used as probing particles. The ions have an energy range between 0.1 and 5 MeV, are isotopically selected, and are energy stabilized better than 1 per mill. The samples are crystals, which can be rotated in two directions. The detector used for the reflected ions is the surface barrier detector. To register particles that have been produced by nuclear reactions detectors with large surface areas are required. Ring detectors placed near the target are a possibility. In addition to Rutherford backscattering and nuclear reactions, ion channeling became an interesting subject. If ions enter below a critical angle to the crystal plane, such ions are bound to travel between two lattice planes in a channeled manner. In such a channeled mode because of repulsive potentials the ions cannot come closer than about 0.1 or 0.2 A to the crystal atoms. Thus Rutherford backscattering, nuclear reactions, characteristic X-ray emissions, and similar processes are not possible. The inverse of channeling is the blocking of an ion. The ion yield of the channeled ions depends on the length of travel inside the crystal,

328

MICHAEL J. HIGATSBERGER

because some of the channeled ions are dechannelized and belong then to the so-called “random” beam. The dechannelizing processes have their origin in the interaction of ion with the crystal electrons and lattice vibration. Impurity atoms contained in crystals also contribute to dechanneling. The energy spectra of “random” and channelized ions are distinctly different, and it is therefore possible to localize impurity atoms and other crystal defects. 4. Ion Scattering Spectroscopy (ISS),

Low-Energy Ion Scattering Spectroscopy (LEISS), or Medium-Energy Ion Scattering Spectroscopy (MEISS) Interactions of ions with solid surfaces cause sputtering of the substrate surface or elastic or inelastic scattering of the impinging ions. The extent to which the processes occur depends on the atomic composition of the solid substrate and the energy and mass of the bombarding ions. At medium or low impinging ion energies ion scattering becomes dominant. For elastic binary collisions of incoming ions with Ei, and mass m, , the energy of the reflected primary ions Eref,will be determined by the laws of conservation of energy and momentum as ‘follows:

where m2 is the mass of the target atom, and 8 the scattering angle in the laboratory system. Figure 23 is a schematic representation ofan ion scattering

ION SOURCE

ENERGY A N A l

L

TARGET OF

1

’EREFL-

FIG.23. Schematic layout of an ISS system.

SOLID SURFACES ANALYSIS

329

system. The equation holds for a single collision proctss and is independent of the angIe of the incoming ions. For the elastically scattered target atom the equation after collision can be written as:

5 - 4m2 Ein

m1

[+

1'

~ 0 ~ 0 '

1

(m2Im1)

It is more difficult to measure the energy of the target masses, and therefore the majority of ISS systems use the measurement of primary reflected ion count rate as a function of energy. Since the energy of the reflected ion can be measured and the angle is fixed and predetermined, m, can be deduced. The experimental equipment contains an ion source, a beam forming system, an energy analyzer, and a detector. The ion source must produce a parallel ion beam with small energy spread. The current density of the primary beam should not exceed A/cm2, or else within the required measuring time of about 100 sec one surface monolayer will be sputtered off. Sometimes ISS is classed in low-energy ion scattering spectroscopy (LEISS)and in mediumenergy ion scattering spectroscopy (MEISS). The low-energy interval is usually defined as 0.1-5 keV, and the medium energy extends to about 100 keV. The scattered ion yield is the product of the surface density of the constituent atoms, the primary ion current, the analyzer transmittance, the analyzer acceptance angle, the detector sensitivity, the differential cross section, and the probability that the primary ions remain ionized after scattering. The quantities for differential scattering cross section and the probability which refers to the remaining scattered ions are unfortunately not well known. These quantities must be measured for each particular case for quantitative analysis. The differential cross section as a function of ion energy turns out to be a monotonically decreasing function with respect to primary ion energy. On the other hand, the probability as a function of primary ion energy turns out to be monotonically increasing. For 0 = 90" the mass resolving power for m , c m2 is

For the noble gas argon as bombarding particle a resolving power of AmJm, I 1/100

can easily be obtained. ISS is applicable for analysis of the top monolayer. The scattering method allows surface quantities to be detected which are as little as of a monolayer. The sensitivity for heavy masses is higher than for light masses. Ions of higher energies penetrate deeper into the sample and can therefore detect spurious foreign atoms located there. For quantitative

330

MICHAEL J. HIGATSBERGER

analysis, calibrating the instrument with a sample of known constituent concentration is advisable. 5. Secondary Ion Mass Spectrometry ( S I M S )

The aim of SIMS analysis is the determination of the isotopic concentration of surface elements. The measurement of the amount of secondary ions leaving the surface after primary ion bombardment is the principle behind SIMS. The secondary isotopic ion current I , is a function of the primary ion current I , , the number of particles sputtered divided by the number of impinging primary ions ( S ) ,the number of particles sputtered as ions divided by the total number of sputtered particles ( R * ) , the isotopic fractional concentration C , and the mass spectrometer transmission 7: The basic SIMS formula therefore reads

I , = I,SR*CT = I,S*CT SR' is the ratio of the number of sputtered ions divided by the number of impinging ions. This quantity is called ion yield S * . Presently several models exist that relate experimental and theoretical results via the ionization process. No complete theory exists as yet for all processes that occur in surface sputtering. Some of the models are good approximations for given situations, and therefore a general theory probably must deal with all the models, even if for a special case a particular model is predominant. The autoionization model is valid when noble gas ions are used as primary particles. An inner shell excitation process leads to an autoionization state and relaxation over an Auger process giving an Auger electron and a secondary ion. The kinetic model is applicable for secondary ions with energies above 30 eV. This model also works for noble gas ions as bombarding particle only. The guiding process is a collision cascade. If it is assumed that all processes relevant to the ion creation take place in a region near the surface, the so-called surface effect model must be used to approximate experiment and theory. Other models are the bond breaking model, the thermodynamic model, the local thermodynamic equilibrium (LTE), and some quantum mechanical models. Good agreement between theory and experiment is found in the quantum mechanical adiabatic surface ionization model and the LTE model. The LTE model assumes a local thermodynamic equilibrium zone of a few angstroms diameter, where the concentration of particles in two successive ionization processes ni and n , , + , , are expressed by the Saha-Eggert equation. The ionization probability R

+

n+

P + (2nm,kT)3'2 AE - I n,h3 "'(7)

=--no - P o

SOLID SURFACES ANALYSIS

33 1

where n, is the electron concentration at the surface, me the electron mass, and I the ionization energy. P + and Po relate to the ionization stage. If the Saha-Eggert equation is applied for the positive ions and the neutral particles that have been sputtered, the ion concentration of two elements A and B in the plasma zone can be written

If values or standards for the A and B concentrations are available, all the other particle concentrations can be deduced using T . If the measurements show single- and double-charged ions of element A and element B. the plasma temperature can be calculated from the equation

In case single-charged, double-charged. and triple-charged currents for element A have been measured, it is possible to calculate the plasma temperature and thus the concentration of all other elements by the equation

Originally the SIMS system used magnetic sector field type instruments for mass analysis. With ion optical lens systems it is possible to get reasonable transmissions through such instruments, since the electrical fields accelerating the secondary ions can be made quite high. Lately quadrupole mass spectrometers are also being used for SIMS at the cost of secondary ion transmissions, but with the advantage of being magnetic-field-free. In principle SIMS units consist of a primary ion source with electron-optical lenses, a chamber for specimen manipulation and/or preparation, a secondary ion mass spectrometer (magnetic sector or quadrupole), and a secondary ion current measurement unit. The system in which the primary and secondary ions travel must be uhv compatible with pressures in the range of Pa. An advanced SIMS system with a special sample preparation chamber is shown in Fig. 24. A typical mass spectrum for an aluminum tantalic target which was covered with hemoglobin and measured at room temperature is shown in Fig. 25. Quantities that are important for SIMS are the erosion rate, the lowest detectable concentration, and the sputtering process itself. With the help of sputtering, depth analysis and depth profiling are possible. SIMS can be operated in a dynamic fashion when the current density is of the order of A/cm2, which roughly gives a sputtering rate of one monolayer every

332

MICHAEL J. HIGATSBERGER

FIG.24. Ultra-high-vacuum specimen preparation and analyzing chamber. 1, uhv pumping systems; 2, specimen storage tube unit; 3, analyzing chamber spindle drive; 4, “spindle nut”; 5 , specimen carrier; 6, specimen (target); 7, specimen carrier coupling screw driver; 8, UHV sluice lock; 9, target preparation chamber spindle drive; 10, specimen heater (electron bombardment); 11, cooling jaws; 12, thermocouples; 13, electron beam evaporation gun; 14, wide beam ion etching gun; 15, quartz crystal thickness gauge; 16, impurity gas inlet; 17, residual gas analyzer; 18, primary ion gun; 19, secondary ion quadrupole mass spectrometer; and 20, viewing port.

second. Operating the primary ion source at values around lo-’’ A impinging on a sample of one-tenth of a cm2 requires tens of hours for one monolayer to be removed, and therefore this mode is particularly nondestructive. It is called static SIMS. The sputtering process is depicted in Fig. 26. The penetration depth is the depth of implanted primary particles. The information depth is concentrated practically on a few uppermost surface layers and depends on the impinging mass and energy and on the target mass and recoil energy. For primary noble gas ions between 5 and 10 keV most solid surfaces have a mean escape depth of 5 A. The state of excited particles can be ground state, excited, and positive or negative ionized. It is possible that chemical bonds of molecules at the surface are broken, but it is

333

SOLID SURFACES ANALYSIS

Negative 51

FIG.25. Typical mass spectrum for AlTa target covered with hemoglobin, 15th layer. I,,,, = 5 x lo-* A/cmz, Ar+ = 3-keV primary ions,p,,, = 2 x lo-' Pa.

also possible that clusters of several atoms or molecules are sputtered off as a consequence of cascade collisions. Besides the kinetic emission process of secondary ions and neutrals, a chemical ion emission may exist. Chemical emission is due to adsorption of reactive gases. For oxide covered surfaces the ion yield S' is for many elements more than two orders of magnitude larger as compared with a chemically pure metal surface. Chemical ion emission can also be obtained when surfaces are bombarded with positive oxygen ions or negative oxygen

I

ION DEPTH

PENETRATION (EXCITATION) ---DEPTH

s o L --T y IMPLANTED PRIMARY PARTICLE

FIG.26. Sputteringprocess by elastic collisions.

334

MICHAEL J. HlGATSBERGER

molecules. Neutral particles or ions impinging on a surface can be elastically backscattered, or their elastic collisions with surface particles can lead to a secondary emission of surface atoms or surface clusters in a neutral, positive, or negative manner. Inelastic processes lead to emissions of secondary electrons, photons, or X-ray quanta. If the region inside the solid is considered one can speak of implanted primary particles or of physical or chemical surface erosions through sputtering or blistering, Structure variations are the result of damages of the solid body by swelling and trapping. If neutrons are the impinging particles to a solid. radioactivity through neutron capture results. 6. Ion Induced Optical Emission or Ion Induced X-Ray Analysis ( I I X ) , Including Proton Induced X-Ray Analysis ( P I X ) and Ion Microprobe X - R a y Analysis ( I M X A ) , or Surface Composition by Analysis of Neutral and Ion Impact Radiation (SCANIIR)

Optical radiation from infrared to ultraviolet is emitted from a surface when ions in the energy range from 30 eV to 100 keV impinge on a solid. The photon radiation is due to inelastic processes involving the outer shell electrons. Direct information on the identity and quantum state of both sputtered and reflected particles can be gained. The incoming ions collide with surface particles leading to the effect of sputtering. Most of the sputtered particles are in excited states which decay by emission of optical quanta. Thus discrete atomic and ionic emission lines can be measured. Excited molecules give emission bands. Doppler broadening is observed since the sputtered particles have kinetic energy. Reflected primary beam particles may also produce ionic emission lines. Their excitation is produced by the violent momentum change on the surface of the solid sample. Experimentally two kinds of broadband continuum radiation are observed in the sequence of the collision process. The solid itself gives an intrinsic continuum luminescence due to electron excitations in the solid or radiative recombination of electron-hole pairs. Another type of broadband emission is assigned to the sputtered molecules. The spectral characteristics are element specific. The experimental apparatus required must consist of a monoenergetic ion beam with energies between 30 eV and 100 keV. It is advantageous to build the ion source in such a way that both ions and neutral beams can be produced. The neutral particles are useful in comparing corresponding ion impact measurements and are an elegant means for investigating electrical insulating materials. A detecting system must incorporate means to measure monochromatic photons between 2000 and 9000 A. The vacuum in which the target is contained should be of the order of Pa or better. Ion induced optical

335

SOLID SURFACES ANALYSIS

emission provides a fundamental insight to the sputtering process. The method is a sensitive and simple technique for elemental surface composition analysis. The sensitivity may be as high as if the background radiation is suppressed. The method permits the multielement analysis over the whole periodic system including hydrogen. If simultaneous measurements of photon and secondary ion emissions are carried out. it is possible to measure the temperature for the local thermal equilibrium model of secondary ion emission by the optical method. The LTE model was verified quantitatively with a high precision. If ions of higher energy are used. ion induced X-ray emission is observed. Of particular interest is the proton induced X-ray emission. The high-energy protons coming from an accelerator impinge on the target. where characteristic X rays are produced. The X rays after collimation reach a proper detector which, in the modern version. is a highresolution semiconductor detector. In order to relate the characteristic X rays to the impinging primary ions, means like a Faraday cup are provided to measure the ion current. &-Particlescan also be used as high-energy ions. The experimental setup is seen in Fig. 27. An annular 241Am source of approximately 10 mCi consisting of a ceramic active component in a welded steel capsule with a tungsten alloy rear shielding is directed toward the surface film under investigation. The a-particles impinge on the specimen surface and excite X rays characteristic of the target surface material. The X rays are emitted through an aperture and measured with a pure germanium semiconductor detector. The X-ray

-

FIG.27. Experimental setup for 241Ama-induced X-ray spectroscopy.

336

MICHAEL J . HIGATSBERGER

emission spectrum from a metal alloy target is shown in Fig. 28. In an applications test a similar system was used to analyze the surface and color composition of bank notes of different origins. Typical measuring times are of the order of 10 sec. Considerable effort in the use of X-ray analysis has been devoted to devices such as the ion microprobe. Such systems are called ion microprobe X-ray analysis (IMXA). In this system the compositional information of the sample volume under investigation is obtained by X-ray analysis rather than by mass analysis. UtilIzing the X-ray analysis means less surface sensitivity, since the X rays are coming from a much greater depth in the materials under study. 7. Thin-Layer Activarion Analysis The neutron activation technique is used as a sensitive technique in multielement analysis. but the activation process usually includes the whole sample volume. Recently another activation technique for sensitive surface studies and for measurements of wear and corrosion was introduced. With this method a thin radioactive layer is produced within a small surface area of the material which is subject to wear studies. The activation is achieved by a beam of protons or deuterons from a linear accelerator. Since the high energy ions are stopped within a relatively short distance in the bulk material, the radioactivity produced by such reactions extends from roughly 10 to 1000 pm.If some of the surface is lost by wear. the total activity is reduced.

Target:Cu Rb

Mo

Ag Ea Tb- Alloy

FIG.28. X-Ray emission by 10-mCi 241Amu bombardment.

SOLID SURFACES ANALYSIS

337

The total activitiy is direct proportional to the surface loss. and thus a highly sensitive surface wear determination is possible. Other general activation methods take advantage of the fact that a number of ions are capable of inducing in many elements nuclear reactions in which the reaction products can be used for analysis. 6Li is a candidate for nuclear reactions with surface elements, and because of the weakly bound lithium nucleons, all reactions between Li and Ne have positive Q values. The reactions "C(d, p)I3C and I60(d,p)' '0 have been used successfully to profile carbon and oxygen in solids. On the other hand. low concentration oxygen depth profiling was carried out by the reaction "O(d, a)I4N. Depth resolutions of about 100 A are achievable. Other nuclear reaction methods analyzed the nuclear reaction products. which are particularly easy to measure when their energy is high compared to the energy of the incoming ion.

C. Neutral Particles Incident to the Surface 1. Low-Energy Molecular Beam Scattering ( L E M S )

Neutral particles of several keV energy eject in solid surface collision processes sputtered particles in the form of neutral, positive, or negative secondary particles. As in ion bombardment part of the impinging neutral particles are reflected from the surface. Inelastic collisions lead to secondary electron emission; but photons are also observed due to luminescence of the solid or from excited, reflected, or secondary emitted particules. A particular method of surface composition analysis of neutral impact radiation has been discussed in connection with SCANIIR. Neutral N, or Ar are obtained by charge exchange of a beam of fast ions in collision with a molecular beam crossing the ion beam. The kinetic energy of the neutralized ions remains nearly unchanged, and the sputter yield of such neutrals is practically the same as the sputter yield of the same ionized particles. Since neutral particles eject also positive and negative charged ions, systems of this kind have been named sputter ion mass spectrometry. The instrumental components are the same as with SIMS except that the neutral particle forming element with the molecular beam crossing is added to the primary SIMS ion source. Sputter ion mass spectrometry is mainly used for the analysis of insulators. Insufficient secondary ion production as a consequence of the neutral particle collision cascades can be improved by postionization of the sputtered neutral particles with the help of a transverse electron beam. The production of a plasma in argon gas where the neutral particles pass through led also to ionization of the sputtered neutrals which can then be analyzed by magnetic or quadrupole mass spectrometers. Beams of neutrals and ions impinging on a metallic surface produce photons from the sputtered excited secondaries

338

MICHAEL J. HIGATSBERGER

of equal efficiency. It has been verified that the radiations that result from sputtering for primary ion or neutral beams at the same kinetic energy are equal. In low-energy molecular beam scattering (LEMS) neutral particles with energies below 1 eV are used. If low-energy monoenergetic neutral particles are on hand, surface structure diffraction experiments can be performed in an apparatus similar to conventional low-energy electron diffraction or ion scattering systems. With such neutral beams the gas surface interaction potential, the cross sections for energy transfer between gas and surface, as well as the kinetics of adsorbed gas reactions on the surface can be measured. LEMS instruments are more complicated than other similar surface analytical systems. The main problems are the production of the monoenergetic low-energy molecular beam and the measurement of the scattered, reflected, or secondary neutral particles. A molecular beam can be produced with a high-pressure nozzle expansion apparatus. Expansion of a noble gas from a container that is under a pressure of lo5 Pa to about Pa leads to a monoenergetic beam with about 5% energy variation. If gas mixtures are used in the nozzle beam, the velocity of the diluent can be manipulated over a wide range. Combination of a heavy and a light gas component in such a system will result in equal speeds for both gas components, and consequently the heavier gas will have a higher kinetic energy. Energies in the range from 0.005 up to 15 eV have been achieved. Beam modulation is possible by rotating choppers. Time of flight measurements can then be performed for a velocity analysis. Other detector systems may employ ionization gauges or a detector which is similar to a Pitot tube. In such a system the neutral beam reaches a small ionization gauge after passing through a long channel. The directed beam can pass through the channel, whereas the trapped gas cannot pass, which leads to a pressure increase proportional to the beam flux. LEMS units need vacuum systems with high pumping speeds. Ultrahigh vacuum is a requirement to reduce the disturbing background effect. Diffraction studies employ the Bragg diffraction principle with the requirement that the wavelength of the neutral particle is of the same order of magnitude as the lattice under study. If a neutral atom or molecule collides with a surface, a number of reaction processes occur and can be measured. An interesting possibility is the gas surface interaction potential measurement. LEMS is especially suited for investigating adsorbed layers. The low energy molecular particles react only with the top surface layer. Specularly reflected neutral particles give a hint of fine surface roughness of the specimen. Inelastic collisions between gas and solid give rise to single phonon excitation. In this connection it is necessary to measure the speed distribution of the scattered monoenergetic incident beam. Since phonon energies are of the order of eV, the relative effect on the final beam energy will be high if low-energy neutrals

SOLID SURFACES ANALYSIS

339

are impinging. In some cases LEMS was combined with other surface analytical tools like LEED and Auger. LEMS opens a new and powerful avenue for surface analysis for the cost of a rather complicated and involved experimental technology.

2. Neutron Activation Analysis ( N A A ) In neutron activation analysis a sample of unknown elemental composition is irradiated with neutrons. The neutrons are captured and the atoms become radioactive. They disintegrate with the emission of high energy electromagnetic radiation. The radioactive nuclei have characteristic halflives and characteristic y-ray energies. Besides a (n, y ) nuclear reaction, (p, 7). (M, n), and (y, n) reactions are used in general activation analysis. The neutron activation analysis experimental setup consists of a vacuum chamber connected to a neutron source. Mostly thermal neutrons are used, because they have a larger cross section compared with fast neutrons. Thermal neutron fluxes of up to 10l3 n/cm’ sec are in use. The neutrons may come from a nuclear reactor or from an isotopic neutron source of an (a, n) or (7, nf type. The specimens are placed in the neutron beam, directly facing a solid state detector. The detecting system with surface barrier detector and multichannel analyzer is depicted in Fig. 27. For the absolute determination of a particular element a well-defined layer is produced by vapor deposition. The layer thickness is monitored with an oscillating quartz thickness gauge. Thickness accuracies of 5 1 A can be obtained. The known thickness and the density of the layer allow one to calculate the number of atoms present per cm’. The y count rate is directly proportional to the elemental concentration (atomsjcm’), the neutron flux density, the detector efficiency, and the neutron cross section. Nuclear activation analysis experiments were undertaken to analyze oil refinery feeds, detect pesticides and residues, measure impurities in semiconductors, determine the composition of lunar and planetary surfaces, measure trace impurities in metallurgy, identify gun powder in criminology, analyze minerals, and trace metals in biological samples, just to name a few fields of application. NAA is particularly suited for multielement analysis. If a thermal neutron flux density of 1013 n/cm2 sec is available and the irradiation time is about 5 hr, then the lower limits of detection are about gm for the very sensitive elements and about gm for rather insensitive elements using a 1 gm sample. The median sensitivity element has a lower limit of detection of about lo-’’ gm for the same sample quantity. Neutrons are particularly suitable for inducing nuclear reactions, since they have no electric charge and therefore can penetrate the nucleus without having to overcome electrostatic repulsion. This advantage is a drawback for surface sensitivity, and therefore neutron activation analysis cannot be considered to be very surface sensitive.

340

MICHAEL J. HIGATSBERGER

D. Photons Incident to the Surface 1. Electron Spectroscopy for Chemical Analysis (ESCA), or X-Ray Photoelectron Spectroscopy ( X P S ) , and Ultraviolet Photoelectron Spectroscopy ( U P S )

The interaction of photons with solid surfaces and the resulting electron ejection was originally called electron spectroscopy for chemical analysis (ESCA). If the quanta are produced by an X-ray source, the method is called X-ray photoelectron spectroscopy (XPS). The name ultraviolet photoelectron spectroscopy (UPS) was coined for the case in which the quanta came from an ultraviolet light source. ESCA has become a powerful surface analytical technique. It is nondestructive and is applicable to metals as well as to other inorganic and organic substances. The photoemitted electron spectra are the result of UV or X-ray excitations. The exciting quantum energy hf removes a shell electron from a surface atom, and the kinetic energy of the ejected electron is measured with an energy dispersive detector. The principle of the process is sketched in Fig. 29. Energy conservation requires that the following equation holds: hf = E k i n

+ EZC + @sp- 0 s

where asp is the work function of the spectrometer, and Qs the work function of the sample. If the binding energy is related to the Fermi level, then, as can be seen in Fig. 29. E F = E F m i + QS

The equation can therefore also be written as

hf = Erin

+ E F m i + Qsp

SAMPLE

'

I

SPECTROMETER

FIG.29. Electron kinetic energy as a function of the photon radiation energy.

34 1

SOLID SURFACES ANALYSIS

In the photoelectron spectrum the intensity of the emitted electrons are measured as a function of their energy. The basic elements of ESCA are shown in Fig. 30. For experimental reasons ESCA has developed in three different directions characterized by the energy of the exciting radiation. In the low energy photon region, ultraviolet radiation is used with a cutoff photon energy at 11.8 eV. If higher photon energies are required, X-ray sources with anodes of Mg, Al, Cr, or Cu with their characteristic radiation are in use. Lately synchrotron radiation became established as a spectrometer source, which, after appropriate monochromatization, covers the range from the visible light all the way to hard X rays. The components depicted in Fig. 30 are standard experimental equipment. Quantum radiation impinging on the sample produces photoelectrons of specifickinetic energy. The electron kinetic energy is analyzed by an energy dispersive system. Any of the electron energy analyzers as shown in Fig. 5 can be used. The electron intensity measurement can be performed with a special charge sensitive electrometer or an electron multiplier. The sample, energy analyzer, and detector are part of an uhv system; and the X-ray or UV source as well as the data recording unit may be kept outside the vacuum system. In XPS the X-ray anode normally has an annular geometry to produce an intensive radiation. If the X-ray anode is located at the Rowland circle and the radiation is diffracted from a spherical crystal approximately opposite the anode but also on the Rowland circle, the diffracted radiation can be concentrated onto the sample giving high photoelectron efficiency. Since the electron energies can be measured quite accurately, it is possible to determine all electronic levels provided the excitation energy is high enough. The core level energy is element specific, and therefore a UPS or XPS spectrum contains all the information about the elementary composition of the surface layers. The electron intensity is a function of the material present in the surface, but ESCA intensities depend on the mean free path of the ejected electron in the

SPEClME

n

- _ _PHOTOEJECTED - - - _ - - - - - _ - -ELECTRON ENERGY ELECTRONS

ANALY LER

I

DETECTOR (ELECTRON X-RAY OR U SOURCE OR

FIG.30. Basic elements of ESCA.

342

MICHAEL J . HIGATSBERGER

sample. Another aspect that must be taken into consideration is the absorption cross section of the exciting radiation in the specimen. The mean free path of the electrons varies with the kinetic energy of the electron and is a function of the matrix composition itself. The mean free path of electrons in the energy range from 10 to 2000 eV leads to an escape depth of 5-30 A.The exact knowledge of core level cross sections is a prerequisite for quantitative surface analysis. Most of the core level cross sections have been measured experimentally with respect to specific element 1s shell cross sections. XPS spectra contain peaks originating from other transitions, like Auger. The energies of Auger lines depend only on the energy levels of the specimen and are independent of the incident photon energy. Unfortunately bremsstrahlung gives rise to a high background, which can be eliminated by using an X-ray monochromator. Other surface phenomena besides the valence electron energy levels of solids can be studied with XPS and UPS. Chemical shifts of the ESCA spectra are due to changes in the chemical structure and the oxidation state of chemical compounds. But chemical shifts are also related to a given molecular structure. Spectra from fluorinated polymers showed chemical shifts in carbon 1s induced by fluorine substitution. Inorganic structural and chemical information also can be obtained when analyzing the energy spectrum. This method found application in catalytic studies and in a number of other technical surface studies. The atomic intensity of the elements with the ESCA technique is almost uniform over the entire periodic table. For UPS electrons are coming mostly from the outermost layer, whereas the XPS region extends typically between 20 and 30 A. From organic substances the XPS range extends to almost 100 A. The element sensitivity can reach 10-5.

2. Laser Microprobe Mass Analysis ( L A M M A ) Because of space charge effects electron and ion microprobe instruments have a limit of power density. Laser light, on the other hand, has been concentrated to a power density up to 1014 W/cm2. The laser-amplified and -stimulated radiation is available for periods as low as sec. It is easy to focus the parallel laser beam to a diameter below m. If light from a high power laser is concentrated onto a solid surface. the solid state matter is instantaneously converted into an ionized plasma. This principle has been used in building a laser microprobe mass analyzer (LAMMA). A schematic view is shown in Fig. 31. A frequency-quadrupled YAG Nd-power laser of about J together with a small He-Ne laser is used as a primary source. The He-Ne laser permits easier alignment. The laser radiation is focused onto the target after passing a quartz window. The target is inside the vacuum system; the parallel axis microscope and the two laser systems are outside of it. When the short-pulsed laser ionizes the specimen area under investigation,

343

SOLID SURFACES ANALYSIS

a

He-Ne LASER

MULTIPLIER

II ACHROWT

CATHODE RAY TUBE

SPECIMEN

]OK

PHoToD1oDE

D E S I ECTnD

VACUUM PUMPS

U FIG.31. Schematic representation of LAMMA.

these ions are accelerated and then focused by an appropriate lens system; they then travel along a field-free tube for about 1.2 m and after reflection reach a multiplier. The electron multiplier signal is amplified, and via a transient recorder it reaches a cathode ray tube or an X - Y plotter. Since all the ions present in the laser induced microplasma are formed at the same time, a time-of-flight mass spectrometer is used for mass analysis. The accelerating voltage is around 3 keV. The traveling time is proportional to the length of the flight path multiplied by the square root of the mass. The time-of-flight spectrometer consists therefore of a device to accelerate the microplasma ions to a constant energy, the drift tube, in which the ions are separated in packages according to their mass and the secondary electron multiplier. The time-of-flight instrument has a higher transmission than quadrupole or magnetic sector field mass spectrometers, and therefore LAMMA has a higher sensitivity. With proper ion lenses the transmission can be made as high as 50%. The detection limit of LAMMA was found to be as low as gm for a volume of 3 x lo-’” gm organic material. So far work has been concentrated on the analysis of biological samples, but results have also been reported on the constitution of atmospheric aerosol particles; coal mine particles, which were found in human lymphocytes; and impurity analysis in particulate residues of solvents and crystalline organic particles. Analytic data of UF, and UO2F2 have also been reported. The samples are normally deposited in powder form on copper grids similar to the grids used in electron microscopy. LAMMA like the electron or ion microprobe is a destructive analytical method. 3. Photodesorption by an Intrinsic Photoefiect

Several metal alloys when irradiated with photons of 1-50 keV showed ionic desorption phenomena. It was known already that neutral molecules

344

MICHAEL J . HIGATSBERGER

U < R A Y

SOURCE

COLLIMATOR TARGET MASS SPECTROMETER

FIG.32. Basic photodesorptioncomponents.

are desorbed from surfaces with a yield of about 1 molecule per lo00 photons. The experimental equipment used for studying the ionic desorption process is shown in Fig. 32. The components are enclosed within a uhv Pa. The X rays are system having an ultimate pressure below 5 x produced in the same way as in an XPS system. With a photon flux of 5 x 10" photons/cm2 sec, ionic desorption products were measured at mass 23 (Na' ), 27,39-40 (K' ), 52, and 55 with a quadrupole mass spectrometer. The target was stainless steel. The intensities of desorbing ions varied from 10- to lo-' ions/photon. Heating the target reduced the desorbed ion intensity markedly. The effect of ion desorption of X rays is questioned by some researchers. According to their findings the desorbed ion intensity is less than ions/ photon for other stainless steel samples.

4. P ~ o r o s f i ~ ~ l Desorption ute~ (PSD) Photodesorption of neutral particles from solid surfaces is either the result of photon interaction with the production of thermal energy or due to an electronic excitation which is a quantum effect. If photons of sufficiently high flux are absorbed in a solid sample, local thermal heating produces a phonon excitation and thermal desorption. The electronic photoexcitation is restricted to the adsorbed gas layers and somewhat to the substrate. Substrate excitation depends on the lifetime of the excited electronic state, which is small for a metal surface. but larger for a semiconductor. Direct measurements of photodesorption from metal surfaces covered with adsorbed gas layers are difficult, since the thermal effect normally supersedes the quantum effect by several orders of magnitude. Polycrystalline pure Ni surfaces have a yield smaller than l o v 9 molecule/photon, whereas a yield from a stainless steel sample of 5 x molecule/photon at 1850A was observed. True excited electronic photodesorption is experimentally obtained when the photon flux density is very low and thus the thermal effect negligible. To measure the thermal effect requires means to measure the local temperature of the surface, which. for a few monolayers, has practical limitations. It is possible, however, to calculate with the help of the StefanBoltzmann law upper temperature limits. and therefore experimental con-

SOLID SURFACES ANALYSIS

345

ditions can be chosen for which the thermal desorption effects are negligible. The equipment to measure photodesorption requires uhv compatible conditions. Pressures below lo-' Pa must exist in the target area, and the desorption of neutral particles is measured as partial pressure increases in a mass spectrometer of either a magnetic sector residual gas analyzer or a quadrupole instrument. Partial pressure changes of the order of lo-'' Pa must be measured. Electronic excited photodesorption has only been found with ultraviolet light below 3000 A, whereas with a hundredfold photon density no desorption was measured at 3650 A. Photodesorption efficiency varies with wavelength. A sharp rise in efficiency was measured at about 2000 A. Photodesorption processes have a theoretical and a practical value. Comparison with the electron induced desorption phenomenon indicate that the photon induced desorption is basically the same process. High-energy photodesorption produces neutral and ionic particles. Lately synchrotron radiation has been used to study the process. The practical applications include electron accelerators, plasma machines. and fusion reactor systems. General applications for use as a surface analytical tool are not yet at hand. 5. Ellipsometry

Light is only propagated with the same velocity in all directions in isotropic media. There are certain crystals such as calcite and quartz that split up light passing through them into two perpendicularly polarized rays called the ordinary and the extraordinary ray. The refractive indices of these nonisotropic crystals are different for the ordinary and the extraordinary ray. Natural light is unpolarized, with the electric field vector E randomly changing in direction. The vector E can always be resolved into two mutually perpendicular components E, and E , . E , stands for the parallel component, and E , stands for the perpendicular component. In general a polarizer attenuates one component and lets the other through. When the phase difference between two mutually perpendicular. linearly polarized waves is n/2, the superposition of the two waves gives elliptically polarized light. If elliptically polarized light exists, insertion of a quartz 1/4platelet produces linearly polarized light again, as the following equation shows: where A 4 is the phase difference of the extraordinary to the ordinary ray after passing the quartz plate, d is the platelet's thickness, neo and no are the refractive indices of the extraordinary and the ordinary rays, respectively, and A is the light wavelength. Insertion of the phase difference leads to

346

MICHAEL J. HIGATSBERGER

When polarized light is reflected from a film covered substrate, its magnitude and polarization are altered by the optical refractive index n and the extinction coefficient k. Therefore analysis of the reflected polarized beam permits computation of these physical properties. Substrates may be metals, dielectrics, or semiconductors. The surface layers may be transparent or absorbing if purely polarized monochromatic light is incident onto a surface. Their respective electric components must satisfy the wave equation E,*,(t) = Ep*sexp i[wr - W ( Z / V )

+

where 01, z, and v are the angular frequency, the propagation direction, and the linear velocity of light. ap - a, represents the phase difference between the p and s component. When reflection takes place, the amplitudes can be attenuated and the incident electric field components can be altered in phase. Thus the reflected components must also satisfy the above equation. The reflection coefficients pp,sare defined as Pp.s

where Rp,s is the amplitude. If coefficient finally reads Pp,s

= Rp,s(t)/Ep,s@)

PP,,are the respective phases, the reflection

= (Rp,s/Ep,s) exp

up,s -

ap,s)

The phase difference /?p,s - up,s is not directly measurable. but the ratio p p / p sis. The functions Rp/Rs and /? can be determined when measuring the inclination of the major axis from the plane of incidence, and the tangent of the ellipticity is the ratio of the minor to the major axis of the reflected beam. The same holds for E p / E s and a. tan $ = RpE,/RsEp A=P-CI which finally leads to p = tan $ exp id

Ellipsometry therefore requires the measurement of tan $ and the change of phase difference upon reflection. As shown $ and A are functions of n and k. A typical arrangement used for ellipsometric measurements is shown in Fig. 33. There are several ways to measure the required quantities, but the most common equipment is the null ellipsometer. As seen in Fig. 33 the electron-optical instrument consists of two telescopes, whose axes lie in one plane. The telescope with the polarizer is fixed, and the telescope with the analyzer rotates around a central axis, which passes through the point where both optical arms intersect. At this position the sample is mounted. The

SOLID SURFACES ANALYSIS w

347

SUBSTRATE

U

K

!?

FIG.33. Schematic representation of an ellipsometer.

operation requires rotation of the polarizer and the analyzer around their telescope axis until the light flux passing the analyzer is a minimum. If a laser instead of a light lamp is used, collimators are not required. But narrowband filters are also advantageous in order to suppress other wavelengths or background radiation. Lasers are used when low reflectance samples are investigated. The polarization angle can usually be measured with a precision of degrees. With ellipsometric measurements it is possible to detect adsorbed particles of about 10' atoms/cm2. The thickness measurement extends from a few A to several pm if the layer is transparent. Absorbed film thicknesses around 500 A can be measured with a precision of 1 A. The optical constants of surface films can be determined with a precision of 1 per mill. Ellipsometers have been used in combination with other surface analytical instruments and have proved their potential value. 6. Laser Raman Spectroscopy

Light quanta absorbed in a solid, liquid, or gas can give rise to an excited fluorescence emission. According to the rule of Stokes the absorbed radiation has a shorter wavelength than the emitted one. This is evident from the equation of conservation of energy, where hf', the emitted quantum energy, must be smaller or equal to hf,, the absorbed quantum energy. The small difference in energy and frequency is called Raman effect and is due to an inelastic light scattering process. The inelastic contribution may come from molecular vibration. rotational vibration, or an electronic transition. If radiation of the frequency fo shows a Raman effect. the scattered radiation will be either fb - f' or fb j". The frequency f o - f ' is called Stokes radiation, and the frequency f b f ' has the name anti-Stokes radiation. f" is the vibration frequency of the molecular system under investigation. f o is the monochromatic exciting radiation. Raman lines always occur together with

+

+

348

MICHAEL J. HIGATSBERGER

elastically scattered radiation. The vibrations of molecules are responsible for the inelastic scattering and the weak absorption effect. The intensity of the Raman spectrum is usually of the source intensity, whereas scattered radiation is 4-5 orders of magnitude larger. The wavelengths of the incoming radiation most used are around 5000 A, and a Raman line may deviate by about 10 A only. The experimental equipment used for measuring the Raman effect must take this into account. The recorded spectrum displays intensity of scatter with respect to frequency shift. If the sample is not transparent, the intensity problem will be even greater. To cope with this, welldefined monochromatic high-intensity laser light is used. Luminous flux densities between lo4 and lo6 W/cm2 are required. In experiments linearly polarized light is used, and the depolarization effect is measured. For analysis of the scattered radiation, monochromator systems with up to three optically fast grating monochromators are used together. Photomultipliers are used as detectors. In the Raman experiment the laser beam must be focused onto the sample, and the subsequent light must be collected efficiently. Sophisticated cells and sample tube designs have been published, which enhance the performance of the whole system. Samples studied were of the hydrogen bonded type. The method lends itself to studying adsorbed species at solid surfaces and is in many respects superior to infrared absorption measurements. Further progress in the course of development can be expected in the future. 7. Mossbauer Spectroscopy The nuclear excitation process. called the Mossbauer effect, is a recoilfree pray nuclear resonance fluorescence phenomenon. The Mossbauer effect is based on the fact that nuclei of the same kind can reabsorb y rays only if the nuclear energy levels of the emitting y quanta are narrow and sharply defined. A Mossbauer spectrum is produced by moving the y-emitting source relative to the absorber. Then the resulting Doppler broadening modulates the y-ray energy slightly. Only those y rays with the proper energy experience resonance absorption thus producing an absorption dip. The absorption process is possible only if the natural linewidth r of the source emission or the absorption lines are small. Because of Heisenberg’s uncertainty principle A E A t 2 ti it follows that

AE = r

=

h/At

If the excited state has a mean lifetime T, then

r = ti/r = ( h In 2 ) / t I i r

SOLID SURFACES ANALYSIS

349

MC - ANALYZER lNPUrO MS START

MSAZOO

EHT

RATTEME

III

FORM

M U F&$.E VIBRATOR

PROP,

COUNTER

FIG.34. Block diagram of the Harwell Mossbauer spectrometer

For the half-life x see, the natural linewidth will be of the order of 5 x eV. The accuracy of the measurements is determined by the ratio of the natural linewidth and they quantum energy TIE,. For r = 5 x eV and E , = 14 keV ("Co) the ratio T I E , is about 3 x The experimental layout is shown in Fig. 34. The use of the Mossbauer spectrometer for analysis work is restricted to those isotopes for which the Mossbauer effect has been observed. So far more than 40 elements can be identified. In principle isomer shift, quadrupole splitting, and magnetic splitting can be measured with the Mossbauer instrument. The Mossbauer method is highly sensitive. It is possible, for instance, to measure the surface stress of a sample. A change in the metal density causes a change in electron density, which shows up in an isomeric shift. Isomeric shifts, however, are small and can also be caused by the presence of impurities. I t was found that stress also gives rise to a local electric field gradient and thus a quadrupole splitting, which can easily be measured. 8. X - R a y Fluorescence ( X R F )

In X-ray fluorescence analysis atoms or ions are excited by a primary radiation and give up a fluorescence radiation characteristic for the elements under investigation. The primary radiation may be a radioactive source or X-ray radiation coming from an X-ray tube. The registration system is identical with the X-ray spectrometer sketched in Fig. 27 except that the

350

MICHAEL J. HIGATSBERGER

241Am-asourcemust be replaced by an X-ray source. To excite fluorescence radiation X-ray sources are operated with voltages between 20 and 100 kV with an electrical power up to 4 kW. Both anode voltage and anode current must be well stabilized to at least 1 per mill. If the sample contains elements with 2 > 20, tungsten anodes are used, which have a high-intensity bremsstrahlung spectrum. For the analysis of elements with Z < 20, Cr, Mo, or Au anodes or mixed anodes like Pt-Rh are in use. X-Ray fluorescence analysis has found a wide spectrum of application in metallurgy, chemistry, and medicine. XRF is not very surface specific, and quantitative analysis requires standards for comparison and an efficiency library for the elements of the periodic table. E . Atomic Surface Waves

Desorption Induced by Surface Acoustic Waves Gas-solid interaction, particularly the desorption of gases from solid surfaces, can be studied by applying surface acoustic waves to the specimen. Desorption of adsorbed residual gases from a quartz substrate at room temperature can be performed, when applying a surface acoustic wave of approximately 20 MHz to the sample. The desorbed constituents are measured with a mass spectrometer and the change in the total pressure of the uhv system is indicated by an ionizing gauge. The desorption is strongly dependent on the applied peak acoustic power. The desorbed constituents include methane. carbon monoxide, and carbon dioxide. A linear dependence of the desorption on the average acoustic power was found, when the peak acoustic power was constant. Under controlled conditions it is possible to study the fundamental problems involved in acoustic wave induced desorption processes. Since there are no charging-up effects involved desorption rates from insulators can be investigated. Lately optoacoustic effects were used in solid and liquid sample surface analysis. The optoacoustic effect is produced by absorption of a modulated electromagnetic radiation of 2020,000 Hz incident on the specimen. Part of the incident energy is absorbed and converted into heat energy. As a consequence the sample temperature varies locally and produces a pressure change. A microphone functions as a detector. By placing a monochromator between source and sample and monitoring the microphone signal as a function of the wavelength of the incident radiation, an absorption spectrum similar to that achieved by an optical spectrometric technique is obtained. Optoacoustic spectrometry may use any wavelength of the electromagnetic spectrum. A schematic sketch of an optoacoustic cell is seen in Fig. 35. The optoacoustic signal is a function of the radiant power absorbed by the sample. The signal amplitude is inversely proportional to the modulation

35 1

SOLID SURFACES ANALYSIS

MICROPHONE

-

RADIATION

WINDOW

FIG.35. Optoacoustic cell

frequency. The absorption of the radiation energy and the subsequent deexcitation by the sample happens within a few nanoseconds. On the other hand, the heat transfer mechanism through the sample is about 6 orders of magnitude larger and is of the same order as the modulation period of the incident electromagnetic wave. Optoacoustic spectra have been obtained in the visible and in the U V region as well as in the infrared. In contrast to conventional optical absorption or reflectance spectroscopy, in optoacoustical spectroscopy only the absorbed photons contribute to the signal. No scattering effects exist. The signals can be obtained from shallow surface layers. The depth is determined by the optical absorption coefficient and the thermal characteristics of the sample. The optoacoustic effect is based on the radiationless energy conversion of the absorbed electromagnetic wave. The signal magnitude is identical for fluorescent materials and nonfluorescent materials. The combination of calorimetric and optical effects allows surface analysis and depth profiling. F. Thermal Heat Infrared Absorption

Infrared absorption spectroscopy can be used to study the vibrational frequencies of molecules adsorbed on solid surfaces. If surface structural information is available, it can be correlated with the vibrational behavior of the adsorbed particles. Even more information is obtainable if infrared absorption is measured together with reflection. This method is called reflection absorption spectroscopy and is distinct from transmission and

352

MICHAEL J. HIGATSBERGER

reflection spectroscopy. In reflection absorption spectroscopy the attenuated reflected signal from the solid surface is determined. It must be kept in mind that large absorption energy by the surface layers are found only in the component polarized parallel to the plane of incidence. At large angles of incidence the parallel polarized component leads to an elliptical standing wave with the major component normal to the surface. and vibrations involving a change of dipole moment normal to the surface can absorb the radiation. Monolayer and submonolayer amounts of chemisorbed substances at metal surfaces can be determined. If surfaces are cooled, infrared spectroscopy can be combined with other surface analytical techniques and more detailed information will be available. So far the bulk of work has been concentrated on the study of CO layers adsorbed on metal.

G. Electric Field 1. Inelastic Electron Tunneling Spectroscopy ( I E T S )

Field emission is a quantum mechanical tunneling process. A tunneling electron may lose energy by inelastically scattering at the scattering center. When an atom or molecule is chemisorbed to a surface, the energy levels of the metal as well as of the adsorbate will shift. A tunneling electron can experience an inelastic collision with the adsorbed particles. As a result the inelastically scattered electron will have a different energy compared to the elastically scattered electron. The vibrational mode of the adsorbate is responsible for the inelastic tunneling electron. The electron energy distribution must be measured experimentally. Since the inelastic effect is small compared to the background current, it is necessary to measure the second derivative as is done in other electron spectroscopy methods. In contrast the inelastic signal from large organic molecules adsorbed on a field emitter may be of the same order of magnitude as the primary signal. Inelastic electron tunneling spectroscopy may also be applied to metal-oxide-metal tunneling junction sandwich structures. Here the current is monitored against voltage, and it is thus possible to find the steps in which the inelastic collisions occur. From such data it is possible to determine the molecular structure of the adsorbate. Oxide layers of the order of 20 A thickness were measured.

2. Field Emission Microscopy ( F E M ) and Field Ion Microscopy ( F I M ) High electric fields applied to the surface of metals produce several typical surface effects. In FEM a negative potential is applied to the metal, whereas in FIM the metal under investigation is on a positive potential. The

SOLID SURFACES ANALYSIS

353

field emitting electrode is a tip of conducting material with a radius of curvature of about 10-6-10-8 m. The positive electrode is in its simplest form a fluorescent screen. Both electrodes are contained in a highly evacuated glass or metal container. Normally the emitting tip is mounted to two insulated wires, which penetrate the vacuum vessel. The tip extends only a few millimeters at the end of the wires. Means are also provided for the thermal evaporation of the substances to be investigated onto the tip. Applying an electric potential between tip and fluorescence screen produces a high electric field gradient, and if the negative potential is at the tip, a reduction of the tip work function occurs together with field electron emission. Electric forces may also induce movements to surface atoms. Since the current density of field emitted electrons is correlated to the surface properties, the current density angular distribution can be seen on the screen. The electron current density in the field emission regime is j,,

=

A ( E 2 / @ exp( ) -I?@~’~/E)

where A and B are constants which contain the electron charge, the Planck constant, the electron mass, and numerical factors; E is the electric field strength, and 0 the work function. The work function is material dependent and the electric field is surface structure dependent. When a positive potential is applied to the tip, field ionization of the rest gas atoms or molecules in the region of the highest field strength occurs together with field desorption of ionized surface particles. The field ionization current density j,, shows a different proportionality, namely, j,,

-

exp(V3I2/E)

where V is the ionization potential. FIM permits fine details of the surface relief to be revealed, and both j,, and j,, are sensitive to the electric field strength. Surface steps down to 2.5 x lo-’’ m can be resolved with FEM and down to 8 x 10- m with FIM. Despite this simple experimental arrangement magnifications as high as lo7 can be achieved. With field emitting instruments the mobility of the adsorbate, two-dimensional condensation and sublimation, atomic interactions, surface chemical reactions, catalyses, physical electronics problems, and other surface problems can be studied. The magnification is given by V

=

1//3r,

where I is the distance between tip and fluorescence screen, Y, the radius of the tip, and B a geometrical image compression factor. Mass analysis of the desorbed particles can be done by conventional mass spectroscopic methods by time-of-flight measurements or when a short-pulsed potential is applied to the tip. It has been found advantageous to operate a field emission unit in

3 54

MICHAEL J. HIGATSBERGER

both FEM and FIM modes. Information from the two regime operations are complementary and permit more insight to a given surface situation. At the author’s institute several liquid metal field emitting ion sources have been developed based on the principle that liquid metal by capillary action reaches the emitting tip, from where the ions are desorbed. In another version the liquid metal is fed to a hollow cylinder of about 1 mm inside diameter. A highintensity ion source with an efficiency up to 80% and a current density of several hundred ,uA/cm2 were obtained. In a third version field emission of liquid metals was obtained along a line of several centimeters when razorblade-like metal sheets were put together having an opening of about mm at the top. Numerous emission centers were found with this system. Photographic inspection revealed that the liquid metal forms fine tips, from which field emission takes place. Ion emission by electric fields has the advantage in that it forms the ions under ultra-high-vacuum conditions and with an extremely high current density. Indications exist that liquid metal field emitting ion sources can also be built with two-dimensional extended surfaces.

+

H . Magnetic Field Nuclear Magnetic Resonance ( N M R ) and Electron Paramagnetic Resonance (EPR)

In nuclear magnetic resonance spectroscopy the amount of energy absorbed from an rf coil surrounding the sample permits the quantitative detection of certain chemical elements. Elements and their isotopes, whose nuclei posses a magnetic moment, can be measured when the experiment is carried out in a strong magnetic field. If the magnetic field is held constant and the radiofrequency is varied, small shifts in the absorption peaks can be observed. The splitting of some of the peaks into multiplets occurs owing to interactions between various magnetic nuclei within molecules, and this gives further information regarding the structural relationships of the atoms to one another. So far more than 60 chemical elements have been investigated by nuclear magnetic resonance. Elements with an odd number of nucleons will have a net spin of angular momentum that will be some multiple of ih. Nuclei in a magnetic field with have two possible energy states. The magnetic momentum can align parallel or antiparallel to the field. The parallel orientation is the more stable one. A nucleus can remain in one energy state for a long time without being dis-

355

SOLID SURFACES ANALYSIS

turbed. It can either absorb energy going from the parallel to the antiparallel state or give up energy with the reverse transition. For proton nuclei in a magnetic flux of 1.4092 T at room temperature, there are 1,O00,010 nuclei parallel to the field for every 1,000,000 antiparallel. The 10 nuclei out of 2,000,010 are responsible for the weak magnetic polarization of the sample. The energies corresponding to the parallel and the antiparallel orientation of the nuclei differ by 2pB. The frequency for which absorption occurs is therefore

f

= 2pB/h

where p is the magnetic dipole moment of the nuclei (,u = 1.4106 x J/T). For a magnetic flux of 1.4 T, f is approximately 60 MHz. A typical nuclear magnetic resonance spectrometer is shown in Fig. 36. Quantitative studies by nuclear magnetic resonance can be undertaken if the rf level and the sweep rate are fixed. Then the areas under the absorption peaks are proportional only to the concentration of those nuclei in the sample. In structural studies the relative intensities of N M R absorption peaks give the ralative numbers of nuclei in a pure substance or the relative numbers of molecules in each type of a mixture. Some instruments operate with a fixed resonance frequency and a changing magnetic flux. Electron paramagnetic resonance is principally similar to nuclear magnetic resonance. Here the sample in a magnetic field also receives an rf signal which is partly absorbed. The absorbed signal frequency corresponds to the frequency of the magnetic resonance induced by the applied magnetic field on the electrons. The problem is to obtain a measurable signal and to keep the noise low. This is particularly important for studying an adsorbed monolayer. Electron paramagnetic resonance is often also

DISPLAY

SOURCE

RECORDER

RF TRANSMITTER

FIG.36. Diagram of a typical nuclear resonance spectrometer.

356

MICHAEL J . HIGATSBERGER

called electron spin resonance. The frequency for resonance condition is much higher compared with NMR. If measured in gigahertz (10’ Hz), one finds

f

=

288

where B is measured in tesla. Thus for electron spin resonance frequencies are required that are in the millimeter range, and therefore microwave technology must be applied. Masers and lasers are suitable electromagnetic wave generators. The population difference of the upper to the lower level is to be measured experimentally. The best absorption signal is obtained if the population density between the upper and the lower level is a maximum. Besides paramagnetic point defects, nuclear quadrupole resonance, ferromagnetic and antiferromagnetic resonance, as well as spin wave resonance can be measured in particular cases.

REFERENCES Azzam, R. M. A., and Bashara, N. M. (1977). “Ellipsometry and Polarized Light.” NorthHolland Publ., Amsterdam. Backx, C., and Van der Wiel, M. J. (1974). Proc. In(. Con$ Vacuum. Uttruciolet Radiut. Phys., 4th. Behrisch, R., ed. (1980). Sputtering by Particle Bombardment. In “Topics in Applied Physics.” Springer-Verlag, Berlin and New York. Benninghoven, A. (1975). Surface Investigation of Solids by Secondary Ion Mass Spectrometry (SIMS). DECHEMA Monogr. 78, 197. Benninghoven, A., Evans, C. A., Jr., Powell, R. A,, Shimizu, R., and Storms, H. A., eds. (1979). “Secondary Ion Mass Spectrometry SIMS 11.” Springer-Verlag, Berlin and New York. Blakely, J. M., ed. (1975). “Surface Physics of Materials,” Vol. 1. Academic Press, New York. Block, J. H. (1975). Field Ion Microscopy and Mass Spectrometer and Field Induced Ion Desorption. DECHEMA Monogr. 78, 215. Bonham, R. A., and Fink, M. (1974). “High Energy Electron Scattering.” ACS Monograph No. 169, Van Nostrand-Reinhold, Princeton, New Jersey. Brenner, S. S., and McKinney, J. T. (1970). Construction and Performance of an FIM Atom Probe. Surf. Sci. 23 ( l ) , 88. Briggs, D., ed. (1977). “Handbook of X-Ray and Ultraviolet Photoelectron Spectroscopy.” Heyden, London. Brongersma, H. H., Meijer, F., and Werner, H. W. (1974/75). Oberflachenanalyse Methoden zur Untersuchung der ausseren Atomschichten von Festkorpern. Phitips Tech. Rundsch. 34, (1 1/12), 362. Briimmer, O., Heidenreich, J., Krebs, K. H., and Schneider, H. G. eds. (1980). “Festkorperanalyse mit Elektronen, Ionen und Rontgenstrahlen.” VEB Deutscher Verlag der Wissenschaften, Berlin. Brundle, C. R., and Baker, A. D., eds. (1979). “Electron Spectroscopy: Theory, Techniques and Applications,” Vol. 3. Academic Press, New York. Cadenhead, D. A., and Danielli, J. F. (1979). “Progress in Surface and Membrane Science,” Vol. 13. Academic Press, New York. , Cardona, M., and Ley, L., eds. (1978).Photoemission in Solids I. In “Topics in Applied Physics.” Vol. 26. Springer-Verlag, Berlin and New York.

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Castaing, R.(1960). Electron Probe Microanalysis. Adt.. Electron. Electron Phys. 13, 31 7. Czanderna, A. W., ed.( 1975). “Methods of Surface Analysis.” Elsevier, Amsterdam. Daly, N. R.,ed. (1978). “Advances in Mass Spectrometry,” Vol. 7A. Heyden, London. Davison. S. G., ed. (1973). “Progress in Surface Science,” Vol. 3. Pergamon, Oxford. Dearnaley, G. H., Freeman, J. H., Nelson, R. S., and Stephen, J. (1973). “Ion Implanation.” North-Holland, Amsterdam. Derouane. E. G., and Lucas, A. A., eds. (1976). “Electronic Structure and Reactivity of Metal Surfaces.” Plenum. New York. Dupuy, C. H. S., and Cachard, A., eds. (1976). “Physics of Nonmetallic Thin Films.” Plenum, New York. Eckertova, L. (1977). “Physics of Thin Films.” Plenum, New York. Fabel, G. W., Cox, S. M., and Lichtman, D. (1973). Photodesorption from 304 Stainless Steel. Surf. Sci. 40,57 I . Farnsworth. H. E. (1975). Atomically Clean Surfaces. DECHEMA Monogr. 78,9. Feuerbacher, B. et al., eds. (1978). “Photoemission and the Electronic Properties of Surfaces.” Wiley, New York. Fiermans, L., Vennik, J.. and DeKeyser. W. eds. (1978). “Electron and Ion Spectroscopy of Solids.’’ Plenum, New York. Franchy, R.,and Menzel, D. (1977). Photodesorption at High Photon Energies. Proc. Int. Vacuum Congr., 7th: Int. Conf. Solid Surjaces, 3rd, Vienna 11, 1209; Phys. Re($.Lett. 43,865 (1979). Goldstein, J. I., and Yakowitz, H., eds. (1975). “Practical Scanning Electron Microscopy.” Plenum, New York. Gomer, R.,ed. (1975). Interaction on Metal Surfaces. In “Topics in Applied Physics.” Vol. 4. Springer-Verlag. Berlin and New York. Hamann, C. (1978). “Organische Festkorper und organische dunne Schichten.” Geest 8t Portig, Leipzig. Hass, G., Francombe, M.H., and Hoffman, R. L. eds. (1973). “Physics of Thin Films” Vol. 7. Academic Press, New York. Heiland, W. (1975). Ion Scattering and Surface Analysis. DECHEMA Monagr. 78, 181. Hendra, P. J., McQuillad, A. J., and Turner, I. D. M. J. (1975). Laser Raman Spectra of Species Adsorbed at Solid-Gas and Solid-Liquid Interfaces. DECHEMA Monogr. 78,27 I , Higatsberger, M. J. (1969). Meth. Exp. Phys. 8, 169. Higatsberger, M. J. (1977). “Physik in 700 Experimenten.” Verlag Blick in die Welt, Frankfurt. Higatsberger, M. J. (1979). Proc. Natl. Conf. Interact. At. Particles Solids, 51h, Minsk, 1978, 111, 3. Higatsberger, M. J., and Klaus, N. (1975). Ein Beitrag zum Verstandnis und zur Anwendung des Sekundarionen Erzeugung an Oberflachen. Acta Phys. Austr. 41, 269. Higatsberger, M. J., and Klaus, N. (1979). A New Specimen Preparation Chamber for Solid Surface Analysis with Sample Transport Mechanism over a UHV-Sluice Lock to a SIMSApparatus. Proc. Int. Vacuum Congr., 7th: Int. Con$ Solid Surfaces, 3rd, Vienna, 1977 HI, 2597. Ibach, H., ed. (1977). “Electron Spectroscopy for Surfaces Analysis.” Springer-Verlag, Berlin and New York. Int. Atomic Energy Agency (IAEA). (1975). “Surface Science,” Vols. 1 and 11, IAEA, Vienna. Journal de Physique (1 980). Int. Conf Mossbauer Spectros., Portoroz, Yugoslavia, I979 49, Suppl. 1, c-I. Kaufmann, R., Hillenkamp, F., and Wechsung, R. (1978). Laser Microprobe Mass Analysis. Eur. Spectros. News No. 20. Kaufmann. R.,Hillenkamp, F., and Wechsung, R. (1979). The Laser Microprobe Mass Analyzer (LAMMA). Med. Prog. Technol. 6, 109-121.

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Kirkbright, G . F., and Adams, M. J. (1977). Optoacoustic Spectrometry. Eur. Spectros. News 14, 22. Kistemaker, J. (1962). Proc. Int. Con$ Ionizat. Phenomena Gases, Sth, Munich, 1961. Krischer, C., and Lichtman, D. (1973). Observation of Desorption from Quartz Induced by Surface Acoustic Waves. Phys. Lett. MA, (2), 99. Lax, M. (1974). “Symmetry Principles in Solid State and Molecular Physics.” Wiley, New York. Liebl, H. (1975). Secondary-Ion Mass Spectrometry and Its Use in Depth Profiling. J. Vac. Sci. Technof. 12, (l), 385-391. Mayer, H. (1972). “Physics of Thin Films,’’ Vols. I and 11. Wissenschaftl. Verlagsgesellschaft, Stuttgart. Menzel, D. (1975). Desorption Phenomena. In “Topics in Applied Physics” (R. Gomer, ed.), Vol. 4, pp. 101-142. Springer-Verlag, Berlin and New York. Menzel, D., and Fuggle, J. C. (1978). SI Units: A Proposal for the Replacement of Langmuirs and Exposure, Surf. Sci. 74,321-322. Meyer, 0.. Linker, G., and Kappeler, F., eds. (1976). “Ion Beam Surface Layer Analysis,” Vol. I. Plenum, New York. Parilis, E. S . (1980). Electron Emission and Sputtering under Multiple Charged Ion Bombardment of Solid Surfaces. Proc. Symp. Sputter. Vienna p. 664. Park, R. L., and Houston, J. L. (1973). The Electronic Structure of Solid Surfaces: Core Level Excitation Techniques. Vac. Sci. Technol. 10, (I), 176-182. Pritchard, J. (1975). Infrared Reflection Absorption Spectroscopy. DECHEMA Monogr. 78, 231. Prutton, M. (1975). “Surface Physics.” Clarendon, Oxford. Riviere, J. C. (1975). Ionization Spectroscopy and Appearance Potential Spectroscopy. DECHEMA Monogr. 78,83. Roth, J. (1980). Sputtering with Light Ions. Proc. Symp. Sputter. Vienna, I980 p. 773. Ryssel, H., and Ruge, I. (1978). “Ionenimplantation.” Teubner, Stuttgart. Rzhanov, A. V., and Svitashev, K. K. (1979). Ellipsometric Techniques to Study Surfaces and Thin Films. Ado. Electron. Electron Phys. 49, 1. Saltsburg, H., Smith, J. M., Jr., and Rogers, M., eds. (1967). “Fundamentals of Gas-Surface Interactions.” Academic Press, New York. Seraphin, B. O., ed. (1976). “Optical Properties of Solids-New Developments.” NorthHolland Publ., Amsterdam. Sparnaay, M. J. (1975). Ellipsometry. Dechema Monogr. 78, 247. Toennis, J. P. (1975). Streuung von Molekularstrahlen an Festkorperoberllachen. Dechma Monogr. 78, 133. Toennis, J. P. (1977). Scattering of Molecular Beams from Surfaces. Vak. Tech. 22, (6), 185. Tolk, N. H., Tull:., J. C., Heiland, W., and White, C. W., eds. (1977). “Inelastic Ion-Surface Collisions.” Academic Press, New York. Van Hove, M. A., and Tong, S . Y. (1979). “Surface Crystallography by LEED.” SpringerVerlag, Berlin and New York. Vossen, J. L., and Kern, W., eds. (1978). “Thin Film Processes.” Academic Press, New York. Weaver, J. C., and King, J. G. (1973). The Molecule Microscope. Proc. Natl. Acad. Sci. U.S.A. 70, (lo), 2781. White, C. W., Simms, D. L., and Tolk, N. H. (1972). Surface Composition Determined by Analysis if Impact Radiation. Science, 177,481. Wolicki, E. A., Butler, J. W., and Treado, P. A., eds. (1978). Proc. Int. Con$ Ion Beam Anal., 3rd, Washington, 1977, Nucl. Instr. Methods 149 (1-3).

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOLUME 56

The Inverse Discrete Radon Transform with Applications to Tomographic Imaging Using Projection Data ALLEN G. LINDGREN

AND

PAUL A. RATTEY

Department of Electrical Engineering University of Rhode Island Kingston, Rhode Island

I. Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Introduction ..... ... 111. The Continuous Radon Transform Pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. The Bu-Coordinatization of the Radon Transform (Parallel-Beam Geometry). B. The Fourier Transform-Radon Transform Relationship . . . . . . , . . . . . . . . . . . C. The Inverse Bu-Coordinatized Radon Transform . . . . . . . . . . . . . . . . . . . . . . . . . D. The Bu-Coordinatized E. The By-Coordinatization of the Radon Transform (Fan-Beam Geometry) . . . . IV. Applications of the Radon Transform in Imaging. A. Radiographic or Tran B. Radionuclide or Emission Imaging C . Radio Astronomy . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Refractive Index Tomography . . . E. Reflectivity Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Electron Microscopy. G . Pollution Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . H. Miscellaneous Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Historical Background and Review of Reconstruction Algorithms . . . . A. Early Theoretical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . B. The Modem Era of Tomography . . . . . ............................. VI. Properties of the Radon Transform.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Sampling the Radon Transform with Parallel-Beam Projections . . . . .... A. Continuous Projections at Equispaced Angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . .... B. Sampled Projections at Equispaced Angles . . VIII. Sampling the Radon Transform with Fan-Beam Projections. . . . . . . . . . . . . . . . . . . . A. Continuous Projections at Equispaced Angles B. Sampled Projections at Equispaced Angles . . IX. The Inverse Discrete Radon Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Theoretical IDRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Practical IDRT.. . . . . . . . . . . . . . . . . . . . . . . X. Effects of Nonideal Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI. Conclusion .... XII. Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...................... I

360 360 362 362 363 364 366 367 368 368 368 370 370 370 37 1 37 I 37 1 372 372 372 376 380 380 385 388 388 392 394 394 399 40 1 406 407 408

359 Copyright c> 1981 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-014656-8

360

ALLEN G . LINDGREN AND PAUL A. RATTEY

I. PROLOGUE

An image of an unknown object can instantly transform ignorance to understanding. An image is one of the most efficient means of displaying data derived from measurements and of conveying vast amounts of information. The molecular structure of matter, the internal state of the human body, and the surface detail of a neighboring planet or star are dramatic examples of areas where an image has affected our understanding of nature and the universe from a microscopic to a macroscopic scale. The convergence of communication theory, Fourier optics, and digital signal processing in the last half of the twentieth century, along with the ready availability of powerful and specialized computer systems and displays, has led to the creation of novel imaging schemes. Computed tomography has produced a revolution in areas where the instrument of imaging was previously unavailable to the clue-seeking sleuths of science. The theoretical foundation of this imaging technique was discovered in 1917 by the mathematician Johann Radon when he determined that the “cross section function” of an object can be reconstructed from measurements that are integrals of the “cross section function” over lines. The function defined by a complete set of line integral measurements has been appropriately named the Radon transform of the cross section runction. The practical tomographic imaging problem is how to obtain the inverse Radon transform from only a limited number of Radon transform samples (i.e., line integral measurements).

11. INTRODUCTION We begin with the important example of X-ray transmission tomography illustrated in Fig. 1. In this application, the objective is to determine “non-

IZ

FIG.1 . In X-ray transmission tomography, a three-dimensionalobject is decomposed into a set of parallel slices or cross sections. An X-ray beam is passed through a particular slice, and the attenuated beam intensity is measured as it exits the body. Each measurement, defined by the coordinates 0 and u, is exponentiallyrelated to the integral of the slice (crosssection) attenuation function over the line defined by the beam path.

INVERSE DISCRETE RADON TRANSFORM

36 I

invasively” the attenuation function of a subject’s head. Since the amount of absorption differs in various tissues, an image of the internal brain structure is indirectly obtained from the attenuation function. Conventional imaging techniques (e.g., optics) are useless in this situation, and an alternate and nonconventional imaging scheme must be employed. Tomographic imaging is such a scheme. With tomographic imaging a three-dimensional object is viewed as a set of parallel two-dimensional slices. Each slice is imaged separately, and the three-dimensional problem is solved by stacking reconstructed two-dimensional slices. In this illustration each slice is imaged by passing pencil-like X-ray beams through the slice at various scan angles (see Fig. 2), measuring the exiting attenuated beam intensity, and then using these measurements to determine the attenuation cross section function. Each attenuated intensity measurement is exponentially related to the integral of the slice attenuation function over the line defined by the beam path. This line integral measurement is a sample of the Radon transform of the slice attenuation function. In practice only a finite set of these samples is measured, and hence the necessity for inverting the sampled or discrete Radon transform arises. The inverse continuous Radon transform is well known (e.g., see Radon, 1917; Gel’fand et al., 1966; Brooks and DiChiro, 1976a; Herman and Naparstek, 1977; Scudder, 1978; Horn, 1978; Kak, 1979; Rowland, 1979). However, the theory for defining and inverting the discrete Radon transform has been less than complete. This article deals with the situation when the Radon transform samples are on a “regular” grid. By viewing the Radon transform as a bivariate function, rather than as a parameterized univariate function as is usually done, the power of twodimensional signal theory is applied to Radon transform theory. This ap-

/:

AD’

, SCeNZ ,

DETECTOR

FIG.2. Illustration of scanning sequence in which data are gathered as described in Fig. 1 at M equispaced viewing angles.

362

ALLEN G. LINDGREN A N D PAUL A . RATTEY

proach permits the story of tomographic imaging, told by the varied and vast body of literature, to be unified and simplified. In this article, we review and clarify the requirements for a set of regularly spaced measurements to specify adequately the Radon transform. With that viewpoint taken, it is possible to place past efforts (regarding parallel- and fan-beam geometry sampling) in perspective. Existing questions regarding the amount of information in a finite number of projections are addressed, and the processing required to extract this information is identified. It is shown (to within standard approximations employed in sampling theory) that, for Radon transforms adequately sampled on a rectangular grid, an exact inverse discrete Radon transform exists. The effects of finite detector (source) size and motion are reviewed, and a systematic approach is again show to be available through the unifying viewpoint provided by the application of two-dimensional signal processing techniques. The ultimate purpose of this review is to establish a firm theoretical foundation for tomographic imaging systems where the measurements are regularly spaced. 111. THECONTINUOUS RADONTRANSFORM PAIR A . The Bu-Coordinatization of the Radon Transjorm (Parallel-Beam Geometry)

With f ( x , y) a function defined on two-dimensional Euclidean space

(R’),a sample of the Radon transform off is the integral off over a line in the xy plane. The manner in which the line is defined determines the “COordinatization” of the Radon transform. The most common coordinatization (which arises naturally in parallel-beam geometry; see Fig. 3) results from defining the line of integration as a function of the variables 0 and u in the following way: x cos B

+ y sin 8 = u

(1)

If fe(u, u) is the representation of J’ with respect to the uu-coordinate system, which is rotated by the angle B in the counterclockwise direction relative to the original xy coordinate (see Fig. 3), then the Bu-coordinatized Radon transform p(B, u ) is the integral of f&u, u) with respect to u ; i.e.,

where

INVERSE DISCRETE RADON TRANSFORM

363

COLLIMATED X-RAY SOURCE

SUPPORT OF

k

+ I DETECTOR ARRAY

FIG.3. In parallel-beam geometry, for a fixed orientation angle O,, X rays from a collimated source (which translates in the u direction) are attenuated as they pass through a cross section of an object [characterized by S(x, y)]. This gives rise to the attenuated intensity measurement function 1(8,, u). for all u. The (logarithmic) transformed measurement function, p(Bo, u), a parallel-beam projection, is then computed. This provides samples of the Bu-coordinatized Radon transform for a particular 8 = Bo : P(O0, u )

=

s

x

J ( x , Y) do EOS

go+

y sin B u = u

The disk support of f ( x , y), which is centered on the origin and of radius R , , is called an “RM disk.”

Traditionally, rather than being treated as a function of the two variables 8 and u, the Radon transform p(& u ) has been viewed as a function of the single variable u with B being a parameter (Scudder, 1978; Rowland, 1979; Bracewell and Riddle, 1967; Mersereau and Oppenheim, 1974). This function of one variable is called the parallel-beam “projection” o f f at the angle 8. One reason for this one-dimensional viewpoint is the projection slice theorem. This theorem is often used as the basis for developing the inverse Radon transform.

B. The Fourier Transjorm-Radon liansform Relationship It is well known that a function f’(x, y), which meets certain mathematical constraints, can be equivalently represented by its Fourier transform F(w,, QJ, where

Fb,, m y ) =

jm{Im

f ( x , y ) exp[ -j(w,x

--m

+ wyy)]dx d y

(3a)

364

ALLEN C. LINPGREN A N D PAUL A. RATTEY

FIG.4. Pictorial view of the projection-slice theorem. The one-dimensional Fourier transform of a projection of the cross section function represents a slice of the two-dimensional Fourier transform of the cross section function [see Eq. (4)]. Equispaced views (A0 apart) provide the additional slices illustrated by the dashed lines.

The function .f’(x, y) is related to its Fourier transform by

-:1 @:I

f(x, Y ) = (2:)’

F(L~).~, o)).) expu(w,x

+ w,y)] d w , dw,

(3b)

By changing variables in (3a), using (2), and evaluating F(w,,w,) at ( w x , w y= ) (ocos8,wsinO) [i.e., along the line 0, sin 0 - w,cos8 = 0 at a (signed) distance w from the origin], it is easy to find that the Fourier transform of the cross section function is related to the Radon transform of the cross section function in the following way:

I

,11,=,1)

s,. m

F ( w , oY) ,,,,=lr,conO Sl”N

-

p ( 0 , U ) exp( -W)du

(4)

Equation (4) is a mathematical statement of the projection slice theorem. In words, Eq. (4) states that the one-dimensional Fourier transform of the projection at the angle 8 is the slice of the two-dimensional Fourier transform of the cross section function at the angle 0 relative to the Q, axis. This is illustrated in Fig. 4.

C. 7he Inverse 8u-Coordinatized Radon lransform

Because of the close relationship that the Radon transform has with the Fourier transform (4), the Radon inversion formula is easily developed.

365

INVERSE DISCRETE RADON TRANSFORM

Rewriting (3b) in terms of polar coordinates in both the space and frequency domain yields

fp(r, 4) = f ( x 9 Y ) ~ x = , c o s 4 y=rsinO

F,(o>, 8)expDmr cos(8 - 4)}1wI do d6

(5a)

where

Because of the link between Fp(o,0) and p ( 6 , u) provided by (4),Eq. ( 5 ) can be viewed as the inverse Radon transform. That is, the cross section function f (x, y ) can be obtained by first generating F,(o, 8) by one-dimensionally Fourier transforming all projections from 8 = 0 to 8 = n [using (4)]and then inverse Fourier transforming Fp(o,6) [using ( 5 ) ] . This is the principle behind the Fourier domain technique of tomographic image reconstruction. An alternate and more popular form of the inverse Radon transform algorithm is set in the space domain and is obtained by regrouping (5a) in the following way:

where

Equation (6b) expresses " p tilde" as the one-dimensional inverse Fourier transform of the product function Fp(oU, 8 ) . loul.By invoking the convolution theorem of Fourier analysis and using (4),Eq. (6b) can be rewritten as

p(6, u) = p(6, u) * h ( u ) =

p(8, u')h(u - u') du'

for all

BE

[O, n[ (7a)

where

The inverse Radon transform algorithm specified by (6a) and (7a) has been called the convolution technique of tomographic image reconstruction. Equation (7a) specifies that each projection must be convolved with a

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ALLEN G. LINDGREN AND PAUL A. RATTEY

“magnitude-omega’’ filter, and (6a) specifies that each convolved projection be “backprojected” and then the backprojected function, $0, r cos(8 - 4)], be “averaged” over 8. In practice, windowed magnitude-omega filters are employed in the convolution step (Scudder, 1978;Rowland, 1979; Bracewell and Riddle, 1967; Ramachandran and Lakshminarayanan, 1971; Shepp and Logan, 1974; Kwoh et al., 1977).

D . The Bu-Coordinatized Radon Transform Pair

In writing (8b), it was convenient for the development that follows to integrate p ( 0 , u)over a 271interval rather than a n interval: the only compensation necessary to maintain identity is a scale factor of 5 which has been added. It is emphasized at this point that just as the cross section function f ( x , y ) is uniquely represented by its Fourier transform, so also is it uniquely represented by its Radon transform. And just as (3b) is a prescription for relating the Fourier transform to f , so also do (8b)-(8d) provide a method for relating the Radon transform to f . Furthermore, in just the same way that the Fourier transform F(wx,m y )is treated as a function on R2, so also should the Radon transform p(0, u ) be treated as a function on RZ.In applications, it has become customary to treat the Radon transform as the parameterized function pe(u)on R ’ rather than as the function p(8, u) on R2. This limited point of view has prevented the proper development and unification of Radon transform theory in general and of a sampling theory for tomographic imaging systems in particular.

INVERSE DISCRETE RADON TRANSFORM

367

E. The By-Coordinatization of the Radon Transform (Fan-Beam Geometry) A different coordinatization of the Radon transform arises in fan-beam geometry. In this situation each line, over which the cross section function is integrated, is naturally defined in terms of the coordinates B and y which are defined in Fig. 5. This gives rise to the By-coordinatized Radon transform: P“B9 Y ) =

s

x cos(/l+ y ) + ysin(/l+ y ) = D sin y

f (x, Y) do

(9)

This states that p’(B, y), the By-coordinatized Radon transform, is the integral of f ( x , y ) over the line x cos(B + y) + y sin(B + y) = D sin y in the xy plane. For a fixed angle /? = Bo, the one-dimensional function p’(Bo, y) which is a line sample of p’(B, y ) , is called the “fan-beam projection” of f at the angle Po. This is further detailed in Fig. 5. By comparing the Bu-coordinatized Radon transform defined in (2) [see also (l)] with the By-coordinatized Radon transform defined in (9), it can be found that

FIG.5. In fan-beam geometry, for a fixed orientation angle Po, X rays from a point source are attenuated as they pass through a cross section of an object [characterized by J ( x , y ) ] . This gives rise to the attenuated X-ray measurement function I’(Bo, y), for ally. The (logarithmic) transformed measurement function #(Po, y), a fan-beam projection, is then computed. This , = Po: provides samples of the By-coordinatized Radon transform for a particular 8 P V O > Y) =

s

x

S(x, Y ) do ( P o + ? ) t y sin(#” t Y I = D sin y

M(I

368

ALLEN G. LINDGREN AND PAUL A. RATTEY

In view of the coordinate relationships defined in (10) and because of properties that the Radon transform enjoys, knowing p’(p, y) is equivalent to knowing p(O, u) and vice versa. Consequently, if the continuous by-coordinatized Radon transform is known, so also is the continuous Ou-coordinatized Radon transform, and therefore, the cross section function can be obtained by inverting p(8, u) as discussed previously. Alternatively, an inversion formula, which can be directly applied to p’(B, y), can be obtained from (8b)-(8d) by a transformation on the variables of integration (Herman and Naparstek, 1977: Scudder, 1978: Kak, 1979: Horn, 1979).

Iv. APPLICATIONS OF THE RADONTRANSFORM IN IMAGING In order to provide insight into potential areas of application, several areas where imaging is achieved from projection data are reviewed. A. Radiographic or Transmission Imaging (Cormack, 1963, 1964; Houndsjieid, 1973; Brooks and DiChiro, 1976a; Scudder, 1978)

This important application was mentioned in the Introduction. It should be clear from that discussion and Fig. 1 that each (logarithmic) transformed attenuated X-ray beam measurement in X-ray transmission computerassisted tomography (TCAT) provides a sample of the Radon transform of the cross section attenuation function. These samples are usually collected either with a parallel-beam geometry (Fig. 3) or a fan-beam geometry (Fig. 5). Because of the time required to scan the beam for each parallel-beam projection, most fast modern scanners use a fan-beam geometry where measurements in a given view (projection) can be obtained simultaneously. These systems lead naturally to different coordinatizations of the Radon transform as discubsed previously. Alternatively, each system can be viewed as one that samples p(8, u) on a different “regular” sampling grid in the Ou plane. B. Radionuclide or Emission Imaging (Kuhl and Edwards, 1963; Budinger et al., 1979)

In emission computer-assisted tomography (ECAT), determination of the spatial distribution of a radiolabeled pharmaceutical (tracer) that has been introduced into internal body organs is desired. By using y-ray ab-

INVERSE DISCRETE RADON TRANSFORM

369

sorbing collimators which restrict the field of view of measuring detectors, various types of measurement geometries arise. If spreading and attenuation losses are negligible (or can be compensated for), measurements made using parallel-hole (Fig. 6a) and pinhole (Fig. 6b) collimators provide samples of the du- and By-coordinatized Radon transform of the cross section radioactivity emission function.

DETECTOR ARRA

(a)

FIG.6. Emission computer-assisted tomography. In nuclear medicine, there is a need to image the distribution of a y-ray emitting (radiolabeled) pharmaceutical introduced into a patient in order to identify a specific biological function or abnormality. (a) Parallel-hole collimator gathers photons from narrow strips within the plane of interest to form a “parallelbeam” projection. (bl Pinhole collimator gathers photons from a plane in a “fan-beam” geometry.

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ALLEN G. LINDGREN AND PAUL A. RATTEY

C. Radio Astronomy (Bracewell and Riddle, 1967; Bracewell, 1979) A classical problem is the reconstruction of a two-dimensional “brightness” distribution of a radio-emitting body from “strip scans.” Radio telescopes which have a long, narrow viewing aperture receive radiation from a narrow strip of the sky. When this strip passes through or near a radio source at a (signed) distance u from the origin of the radio emission function and at a direction 8 (similar to the parallel-hole collimator tube in Fig. 6a which “sees” only radiation from a narrow strip), a measurement is obtained that is a sample of the (smoothed)Radon transform of the radio emission function. As the earth rotates or as the reception beam is steered, a set of strip sums in the same direction is obtained, and a strip scan or projection results.

D . Refractive Index Tomography (Greenleajet al., 1975; Kak, 1979)

Refractive index tomography is based on a transmission geometry similar to Fig. 3 or Fig. 5, except that the propagation delay (or phase shift) of an ultrasound (or other) signal in passing through the object is the measurement of interest. The delay of the “normalized” received signal is proportional to the integral of the object’s (complementary) refractive index function over the ultrasound transmission path which is approximately a straight line under certain conditions.

E . Reflectivity Tomography (Norton and Linzer, 1979) In reflectivity tomography the reflectivity cross section function is of interest. A slice of an object is interrogated with a pulsed (ultrasound) signal and the reflected signal recorded. As illustrated in Fig. 7, the value of the returned signal at any instant of time is proportional to the integral of the reflectivity function along the corresponding location of the wave front.

F.

kq

ANSMTTER

RECEIVER

~

I

I

,

,

I

.

,

j

jp(e,u)

, , ,

U

FIG.7. Reflectivity tomography. A pulsed ultrasound signal is reflected from discontinuities in the object density. The received signal at a given instant in time is proportional to the integral of the reflectivity function along the corresponding wave front. The receiver waveform represents a projection of the reflectivity cross section function.

INVERSE DISCRETE RADON TRANSFORM

37 1

Thus, to the extent that the wave front can be approximated by a straight line within the object, the received signal (in time) represents a “parallelbeam” projection of the reflectivity function. F. Electron Microscopy (DeRosier and Klug, 1968; Crowther et al., 1970; Mueller et ul.. 1979)

In an electron microscope, a three-dimensional object receives electron radiation from parallel electron beams. An attenuated radiation pattern is recorded on an electron micrograph in much the same way that a diagnostic X-ray picture is recorded on film. Hence, this micrograph is a two-dimensional projection of a three-dimensional structure. By rotating the object around a single axis, a set of two-dimensional projections is obtained. By isolating the density distribution along corresponding lines in this set of projections, a set of parallel-beam projections of a particular plane are isolated. This provides samples of the Radon transform of the molecular structure function. G. Pollutioil Monitoring (Stuck, 1977)

When a narrowband laser beam is passed through atmosphere contaminated by pollutants, light energy at various wavelengths is absorbed by the pollutants so that the beam intensity diminishes exponentially with the integral of the airborne pollution function.

H . Miscellaneous Applications In addition to the preceding applications, other imaging examples involving samples of the Radon transform exist, e.g., holographic interferometry (Rowley, 1969), phase-contrast microscopy (Berry and Gibbs, 1970), and geophysical exploration (Dines and Lytle, 1979). The Radon transform also has application as a vehicle for solving linear hyperbolic partial differential equations (John, 1955, 1978; Courant and Hilbert, 1966), as a mechanism for proving Galin’s theorem which is used in theoretical stress analysis (Willis, 1970), and as a basis for generalizing certain onedimensional proofs to n dimensions (Cramer and Wold, 1936). It should be stressed that in those applications, where the Radon transform (or samples of it) is measured, interest is almost always in the inverse Radon transform, i.e., the cross section function. Hence the problem is to invert the Radon transform. One notable application in which the Radon transform itself is of interest is in image edge detection. In this application, a picture is processed

372

ALLEN G . LINDGREN AND PAUL A. RATTEY

so that only edge information is retained. By taking the Radon transform [or the Hough transform in image analysis (Duda and Hart, 1972; Pratt, 1978)] of this processed image a “line spectrum” results. From this spectrum, it is a simple matter to extract the dominant picture edges. V. HISTORICAL BACKGROUND AND REVIEW OF

RECONSTRUCTIONALGORITHMS A. Early Theoretical Work

The analytical foundation for reconstructive tomography was established in 1917 by Johann Radon, an Austrian mathematician concerned with gravitational theory (Radon, 1917). For the next 50 years, though his result found application in theoretical mathematics, it apparently remained unknown to the practicing scientific community. For example (as related by John, 1955), in 1931 G. Herglotz found a connection between Radon’s inversion formulas and the solution of hyperbolic partial differential equations with constant coefficients. Later John (1955, 1978) and Courant and Hilbert (1966) solved the initial-value problem of the wave equation by representing the solution in terms of its Radon transform. Gel’fand et al. (1966) applied the Radon transform to integral geometry and representation theory. For their purposes, the Radon transform had an advantage over the Fourier transform and this allowed them to construct (at least in part) an operational calculus based on the Radon transform. In addition to Radon’s result, the tool for inverting the Radon transform was available (although perhaps not generally recognized as such) in the form of the projection slice theorem for quite some time. Cramer and Wold (1936) made use of this theorem to obtain simple proofs of theorems on n-dimensional probability distributions from corresponding theorems known in one dimension. 3. The Modern Era of Tomography

A renaissance in reconstructing functions from line-integral measurements occurred in the second half of this century when, independently in several disciplines, the “inverse Radon transform” was rediscovered. This rediscovery was motivated by significant advances in technology which had occurred in the elapsed period of time. Included in these advances is the evolution of new and sophisticated measurement devices and the widespread availability of powerful computers. In radio astronomy, a series of papers

INVERSE DISCRETE RADON TRANSFORM

373

(Bracewell and Roberts, 1954; Bracewell, 1956; and Bracewell and Riddle, 1967) showed that a radio “brightness” function could be reconstructed from strip scans. In medical applications, Olendorf (1961) described a method of imaging transverse sections of the head attenuation function from X-ray transmission data. Kuhl and Edwards (1963) applied the principles of stereoradiography and body-section radiography to radioisotope scanning and reconstructed transverse sections from emission data. However, Olendorf and Kuhl and Edwards used only simple backprojection of the data which yielded blurred approximations of the desired image. It was Cormack (1963) who precisely stated the medical radiology problem in mathematical terms and presented an exact method of finding the original cross section function given its line integrals. In electron microscopy, De Rosier and Klug (1968) and Crowther er al. (1970) presented the general principles behind reconstructing a three-dimensional object from a set of electron microscope images (two-dimensional projections). The basic methodology for determining Radon transform sampling requirements was set by Bracewell and Riddle (1967) and Crowther er a/. (1970). They used (one-dimensional) Fourier methods to determine the number of “views” required to reconstruct a band-limited cross section function of finite size. From (4), they recognized that (discrete) Fourier transformed projection data represent samples (on a polar grid) of the (twodimensional) Fourier transform of the cross section function (see Fig. 4). Basically, their sampling criterion required that the maximum spacing (in arc length) between Fourier transformed projections be less than n/RM, i.e., Am = WMA0 In/RM or

A e 5 n/WMR,

( 1 1)

where RM is the object radius (see Fig. 3), and WMis the largest spatial frequency in the spectrum of the object. Sample spacing within each projection (sampling in u ) was simply determined from one-dimensional sampling theory to be AM = n/WM(Mersereau, 1976). The basis for modern cross section reconstruction algorithms was established in a remarkable pair of papers by Bracewell (1956) and Bracewell and Riddle (1967). They recognized the need for (and proposed) the convolution of the projection data with a band-limited function, and they proposed a solution to the inverse Radon transform that makes use of numerical operations on the projection data and that does not require the computation of two-dimensional Fourier transforms. This technique was refined (and independently arrived at) by Ramachandran and Lakshminarayanan ( 1971). Basically, this technique numerically performs the convolution in (7a) where h(u) is derived from a band-limited (windowed) version of

374

ALLEN G . LINDGREN AND PAUL A. RATTEY

the filter defined by (7b). With a finite number of equispaced views, (6a) is approximated by the summation

This summation is referred to as backprojection averaging (Brooks and DiChiro, 1976a). Since the convolved projections are defined only at a finite number of(discrete) sample points, the evaluation of$@, r cos($ - O,)] at each ei requires an interpolation. Simplified filter functions, h(u), and interpolation schemes that reduce the computational burden and provide “robust” reconstructions were proposed by Shepp and Logan (1974). The steps required in the convolution-backprojection method are (a)convolution (may be performed by use of the one-dimensional FFT) and (b)interpolation and summation (backprojection averaging). Lakshimarayanan (1975) was the first to modify this reconstruction method to handle directly data from fan-beam geometries. Gordon et a / . (1970) proposed an alternate (and perhaps more intuitive) reconstruction method called the algebraic reconstruction technique (ART). Basically this approach and modified versions of it [ e g , simultaneous iterative reconstruction technique (SIRT) (Gilbert, 1972; Herman and Lent, 1976)] assumed a model that partitions the object into pixels whose values are to be determined. By geometry, the vector F representing the unknown cell values can be related to the measurements via a linear transformation

P

=

AF

(134

where P is the vector of all projection measurements, A is (generally) a nonsquare matrix, and F is (generally) of smaller dimension than P. With this modeling, the reconstructed image E is given by

E = AttP

(13b)

where the generalized inverse (Dahlquist and Bjorck, 1974) is defined by A t ? = [ATA]-’AT, or (when decomposition methods are used, i.e., A = USVT) by At? = VSttUT. Direct computation of E from (13b) even when the square matrix ATA is well conditioned is not reasonable because of the enormous computational requirements (Scudder, 1978). Reconstructions were achieved, however, by iteration methods (Dahlquist and Bjorck, 1974) that refine trial values of E to minimize a metric of the residual

E = [ P - AE]

(14)

under constraints. The flexibility to impose constraints (e.g., positivity, where it is required that all the elements of the reconstruction satisfy Pi 2 0) is an advantage often cited for ART style algorithms. However, the ability to

INVERSE DISCRETE RADON TRANSFORM

375

impose a priori information is only significant when (13a)is underdetermined (i,e., det[ATA] = 0). Under these conditions the solution to (13) is not unique, and additional information must be used to select one of the reconstructions from the family of solutions. The solution generated by (13b), where the generalized inverse is now A t t = [ATA]ttAT, is the solution that has minimum norm (Dahlquist and Bjorck, 1974).This is generally not the preferred solution since, for example, it may violate positivity. It has also been reported (Katz, 1978) that the pixel model used by ART permits more detail to be extracted from a given set of data than could be achieved with the convolution-backprojection method. This advantage is mainly due to the a priori knowledge that the object is composed in a specific way. However, if the resulting system of equations is ill conditioned (i.e., the condition number of the matrix ATA is not close to unity), then the solution will be sensitive to measurement errors (noise) and modeling errors (pixel location, shape and size, and mismatch between pixel model and actual structure of the cross section) (Dahlquist and Bjorck, 1974: Lawson and Hanson, 1974). If the measurement data do not meet the sampling requirements (imposed on convolution-backprojection algorithms), then one must be concerned about the sensitivity (stability) of the resulting ART solution. Since the introduction of ART in 1970, various refinements and extensions have been made [ART 1, ART 2, ARTIST, SIRT (Herman and Lent 1976; Katz, 1978)], and these algorithms seem to offer advantages over the convolution-backprojection method under certain conditions. Early claims of superiority were quickly disputed [see Crowther and Klug (1971) vs. Bellman et a/. (1971)], and certain aspects still remain largely unresolved. However, it has been reported by all comparative studies that reconstruction quality generally varies with the algorithm selected. It is usually agreed (Katz, 1978: Herman and Rowland, 1973) that an ART style algorithm has an advantage when: (a) fewer projections than required are available; (b)the projections are taken only over a limited (narrow) range of angles (i.e., Om,, - Omin << n); and (c) the samples within each projection are noisy. However, most modern scanners, which obtain data at regularly spaced intervals, employ reconstruction algorithms based on convolution-backprojection, because it is inherently much faster than ART-like methods and performs well when adequately sampled (Katz, 1978; Tretiak, 1978). Despite the advances in the convolution-backprojection method, the sampling requirements are still not well understood, and the approaches currently taken do little to provide insight into the processing required to extract all available information from the data. Yet the efforts to date have been substantial, and the mathematical tools necessary to provide a more complete understanding of this are available. By combining two-dimensional signal theory with the theoretical advances on tomographic reconstruction

376

ALLEN G. LINDGREN AND PAUL A. RATTEY

methods (inversion of projection data), it is possible to unify the theory of tomographic imaging. To this end, it is necessary to view the Radon transform as a bivariate function rather than as a parameterized univariate function as is done in the projection slice theorem approach. This will be shown to provide insight not available via the Fourier methods, which with few exceptions (e.g., ART) have dominated the modern era for systems with regularly spaced data. From this point on, this article concentrates on the special case where projection data and sampling points are regularly spaced. We begin by reviewing the properties of the Radon transform.

VI.

PROPERTIES OF THE U D o N

TRANSFORM

Selected properties of the 8u-coordinatized Radon transform are summarized and illustrated in Fig. 8. The periodic (with period 2 4 nature of p ( 8 , u) is obvious from Fig. 3. The Fourier transform of p ( 0 , u), as a consequence of this periodicity, is defined only for discrete values of coo. That is,

p ( o h o4,) =m:j reduces to

SP,

p ( 8 , U) exp[ -j(o,e

+ oj,u)]

du d8

(15)

'u

p(oio,q,) =

C m=

Pdm, ~ , , ) 8 ( 0-1 m) ~

( 16 4

-m

e (a)

FIG.8. Space and frequency domain support of the continuous Radon transform and some corresponding properties. (a) p(0, u ) is supported on an infinite-length "RM strip" and has the following properties: (1) periodicity, p(O + 2n, u ) = p ( 0 , u ) ; (2) symmetry, p(O + n, - u ) = p ( 0 , u); (3) realness, p*(0, u) = p ( 0 , u). (b) P(w,, 0,)is supported on an infinite-length "RM bowtie" and has the following properties: ( 1 ) P(w,,w,) = 0 for wonot an integer; (2) P( -rn,w,) = (- l)'"P*(m,m u ) ;(3) P ( - m , -mu) = PYm, mu).

INVERSE DISCRETE RADON TRANSFORM

377

where

POh,

=

p ( 0 , u ) exp[ -j(m#

+ oj,u)] du d0

(16b)

Because of the projection slice theorem (4),Eq. (16b) can be written as Po(m,ol,) =

jO2‘

Fp(o>,, 0) exp( -jrno)

do

(17)

where Fp(w,,0) is the polar coordinate representation of the Fourier transform of the cross section function f ( x , y). Equation (17)shows that Po(rn,w,,), i.e., the line-mass density of P(o,,oj,,), represents the Fourier series coefficients of the &periodic function FP(w,,,0). By using the same bandwidth approximation made in F M communication theory* (Taub and Schilling, 1971), along with the fact that f ( x , y) has compact support on an RM disk (see Fig. 3), it can be shown (Rattey, 1980) that

P0(m,w,) E 0 for Im( > 1RMoj,,)+ 1 (18) This means that the band region of the Radon transform [i.e., the support of P(o,, w.)] has the shape of a bowtie (see Fig. 8b). This approximation (18) is in some sense a bound on the band region of the Radon transform of f ( x , y). For certain special functions, this band region boundary is pessimistically large (Rattey and Lindgren, 1981). For instance, the Radon transform of a circularly symmetric function (i.e., the Abel transform) has a band region confined solely to the o, axis, ie., Po(m,w,J = 0 form # 0. However, concern here is for arbitrary cross section functions whose band region is supported over the entire RM bowtie: this represents the general tomographic imaging problem. Because the cross section functions dealt with here are compact on an RM disk, it follows that the Radon transform p(0, u ) is zero for 1ul > RM. This space domain property has two important consequences in the frequency domain. First, it means that P(w,, o,)is “band limited” with respect to o, to RM and consequently it can be uniquely represented by its samples Po(m, n Amu) where Amu I x/RM. Second, it means that theoretically p ( 0 , u ) cannot be exactly band-limited in the o,, direction (Papoulis, 1977). Hence the bowtie-like band region is infinite in length (Fig. 8b) and is termed for obvious reasons an R, bowtie. In spite of this theoretical bandwidth limitation, the “character” of most practical compactly supported cross section functions causes the cross section function Fourier transform [and hence

* This amounts to approximating J,(R,w,), the mth-order Bessel function of the first kind, by zero for Iml > IR,w,J + 1. See also Crowther et al. (1970) and for a different viewpoint, see Pridham and Lindgren (1978).

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ALLEN G . LINDGREN A N D PAUL A. RATTEY

I FIG.9. “RYWMbowtie” band region of the Radon transform p ( 0 , u) of the cross section functionf(x, y) supported on an R, disk.f(x, y ) is also assumed to be effectively band-limited to a W, disk.

P(w,, 0,) with respect to w,] to be “effectively zero” at “high” frequencies. In this situation [or when p(& u) is low-pass filtered in the u direction], the band region of p(8, u ) is a finite-length RM W, bowtie (see Fig. 9). Another important property of the Radon transform, which can be deduced from Fig. 3, is the symmetry property

p ( e + 7t, -u) = P(B, U)

(19)

This manifests itself in the frequency domain as Po(-m,

0,) =

( - 1)”P8(m,

(20)

Equation (19) means that p ( 8 , u ) can be thought of as being defined on a Mobius strip connected at 8 = 0 and 7t (Beattie, 1975). This property, as characterized by (20), along with the fact that p ( 8 , u) is real [meaning that Po(-m, -w,) = Pa(rn, wJ], implies that P(s,, wl,)is completely defined whenever it is known over any single quadrant. In fact, in view of the band region of P(w,, w,) (as pointed out in the last paragraph), P(oI,, w,) is completely defined whenever it is known on a grid of points Po(rn,n Am,,) in any single quadrant with Am, = 7t/RM. An example of a Radon transform pair, which emphasizes the properties just discussed and also provides insight into Radon transform theory, is the Radon transform of a two-dimensional impulse function located somewhere within the RM support disk at (xo,yo) (see Fig. 10). It is a simple matter to show that the Radon transform of this impulse function is a line mass along a sinusoid in the 8u plane and that the Fourier transform of this Radon transform is the Bessel function of the first kind:

.@{6(x- xo, y - yo))

=

p(8, u ) = S[u - (xo cos e

+ yo sin e)]

(21a)

,m

F{P(&u ) } = P(W,, OIL,)=

1

m= - m

P,(m, o,)S(w, - m)

(21b)

INVERSE DISCRETE RADON TRANSFORM

379

I

lo)

e (bl

FIG. 10. An example of a Radon transform pair. (a) A two-dimensional impulse (point source) at (xo, yo). (b) Radon transform of a two-dimensional impulse function.

where

+ n/2)]J(rn, roo>,)

(21c)

exp[j(mO - w,r0 sin e)] dB

(214

Po(rn, o~,)= 2n exp[ -jrn(@

and

J ( m , roo>,)= -

2n l s -' n

Figure 11 illustrates (21) without the phase factor and dramatically shows several of the properties discussed previously, especially the bowtie-like band region. In fact by constructing an arbitrary cross section function as a superposition of impulse functions a simple proof of the bowtie-like band region of p(0, u) immediately follows (Rattey and Lindgren, 1981). By using the properties of the Radon transform discussed previously and exemplified by (21), it is easy to understand the implications of sampling the Radon transform and its impact on the performance of tomographic imaging systems.

380

ALLEN G . LINDGREN AND PAUL A. RATTEY

we FIG. 1 1 . Fourier transform of the Radon transform in Fig. lob [see Eq. (21)]. Note that J,,,(o,) = J(m, mu),J,,,(-u,)= (-IY’””m(~u), and J-,(mu) = (-l)”’Jm(mJ.

VII. SAMPLING THE RADONTRANSFORM WITH PARALLEL-BEAM PROJECTIONS A . Continuous Projections at Equispaced Angles

A set of M equispaced parallel-beam projections, continuous in u, samples the Radon transform on a vertical line array as shown in Fig. 12. Because of the periodicity of p(8, u), projections taken over the interval 8 E [0,2n[ equivalently sample p ( 8 , u) on a vertical line array extending from 8 = - 00 to 8 = co. In addition to this “principal image” sampling set, the Mobius strip property leads to a second set of vertical line samples. The effective sampling array produced by combining the principal image samp-

FIG.12. Support of “vertical-line” sampled Radon transform generated from M = 2n/AO equispaced parallel-beam projections.

lNVERSE DISCRETE RADON TRANSFORM

38 1

ling set with the Mobius image sampling set is illustrated in Fig. 13 for both M odd and M even. Clearly when M is odd and p ( 0 , u ) is sampled from 0 to 2n, an effective sampling array is generated which has twice as many ( 2 M ) equispaced vertical line samples. When M is even and p ( 8 , u ) is sampled from 0 to 211, the effective sampling array remains at M vertical line samples, since the Mobius strip symmetric line samples duplicate the principal image set. Nonetheless, it is possible to effectively generate 2M equispaced line samples when M is even. This is achieved by sampling p ( 6 , u ) at M equispaced projections from 0 to n and effectively sampling from n to 2n by the symmetry property (see Fig. 14). It should be noted that with this sampling strategy, M can be odd or even and still generate an effective 2M line samples. This sampling scheme is used in practical scanners and is used here to achieve an effective spacing between vertical line samples of A6

=

n/M

(22)

The ideal sampling operator defined by the (effective 2 M ) vertical line array just described produces a new function pJ8, uf given by the product of the Radon transform p ( 0 , u ) and the sampling function u(6, u): i.e., p , ( & u ) = P(6,u)u(H,u )

(23a)

I b)

FIG.13. Effective vertical-line sampling arrays (from parallel-beam projections) generated by the symmetry propertyp(0, u ) = p ( 0 + n, - u ) . ( a ) The effective vertical-line sampling array that occurs when M = 2n/AO is an odd integer and p ( 8 , u ) is sampled at M equispaced angular positions from 0 to 2n. This is generated by using the Mobius strip symmetry property of the Radon transform and reflecting the line samples for O E [0, n( into the region O E [n,2n[, and vice versa. This results in an effective sampling array with M’ = 2M equispaced projections from 0 to 2n with spacing AO’ = AOi2. (b) The effective vertical-line sampling array that occurs when M = 2xiAfl is an even integer. This results in an effective sampling array with M’ = M equispaced projections from 0 to 2n with spacing AO’ = AO.

382

ALLEN G. LINDGREN AND PAUL A. RATTEY

FIG. 14. The effective vertical-line sampling array that occurs when M = n/AB is an odd or even integer and p(B, u ) is sampled at M equispaced angular positions from 0 to n. This is generated by using the Mobius strip symmetry of the Radon transform and reflecting the line samples for OelO, n[ into the region B ~ l n2, 4 . This results in an effective sampling array (which uniformly spans the Ou plane) with M' = 2M equispaced projections from 0 to 271 and spacing A 6 = AO.

where

The Fourier transform of the sampled function, Pv(We, uu), is then simply a The line-mass scaled sum of translates of the Fourier transform, P ( O 8 , uu). density [denoted by the subscript 0 as in (16)] for this Fourier transform is given by

and represents a periodic replication of the R , bowtie in the direction (me, 0,) = (1, 0). The band region associated with Pv(Qe,8,) is shown in

Fig. 15.

FIG.15. Support of PJw,, mu),the Fourier transform of the effective vertical-line sampled Radon transform [PJB, u)] generated from M odd (even) equispaced parallel-beam projections from 0 to 2x (0 to n). This band region represents a periodic replication of the R, bowtit of Fig. 8b. Overlapping of translated bowtie band regions produces aliasing.

INVERSE DISCRETE RADON TRANSFORM

383

The fundamental tomographic imaging system limitations due to aliasing from undersampling in 0 is revealed in Fig. 15. It is immediately obvious that the nonaliased portion of the (presampled) band region of p ( 0 , u ) recoverable from p,(& u ) is contained in a "pointed-end bowtie." This region is isolated = in Fig. 16 for clarity, and the bowtie boundary is approximated by loo( IRMw,I for simplicity. From this figure the number of nonaliased, independent, real pieces of information that can be extracted from M equispaced views or projections of f ( x , y) in the absence of noise can be determined. The total area of the pointed-end bowtie is 4 M 2 / R , . However, as pointed out in the last section, independent information exists only on a grid of points within any quadrant. In order that samples within the quadrant be independent, it is necessary that Aw, = n / R M .Hence, since Amo = 1, an "information cell" of area 1 . n/RM is obtained. If the (quadrant) bowtie area is normalized by the information cell area and if one accounts for the fact that generally each sample of P(oo, 0,) is complex valued, the total number of pieces of information that can be extracted from Pv(wo,w,) [and hence from pV(&u ) ] is found to be

N , = (2/x)M2

(25)

This amount of nonaliased information [concerning the Radon transform, p ( 0 , u ) ] can be obtained by passing p,(B, u ) through a low-pass filter that has a pointed-end bowtie band region like that shown in Fig. 16. The inverse Radon transform operator can then be applied to this filtered Radon transform to yield an artifact-free, but smoothed estimate, f,,of the cross section function f. This smoothing roughly corresponds to a space-variant filtering that causes f , to be twice as smooth at r = RM as at the origin

t""

t

-2M

2n

FIG.16. Band region of the vertical-line sampled Radon transform that has been filtered to reject all aliased information. The band region required for uniform resolution is indicated by dashed lines. I t is assumed in this figure thatp(8, u ) is sampled with M equispaced projections over the interval [O, n[ or 10, 2 4 if M is odd, or [0, n[ if M is even.

384

ALLEN G. LINDGREN A N D PAUL A. RATTEY

(Rattey and Lindgren. 1981). This has been called a nonuniform reconstruction by Klug and Crowther (1972). A uniform reconstruction can be generated from p,(& u) by extracting only one-half the available information with a low-pass filter whose band region preserves the “flat-end’’ bowtie shown by the dashed line at Iw,I = M / R , in Fig. 16. This filter may, alternatively, have a simple rectangular passband with boundaries defined by )o,I= M / R , and Iool= M . The number of nonaliased, real, independent pieces of “uniform resolution information” that can be extracted from M parallel-beam projections is

N,, = (1/n)M2

(26)

Such a reconstruction produces a uniform resolution frequency in the cross section of wvu

=

(27)

Equation (26) implies that the amount of uniform resolution information is independent of object size (nRL) and dependent only on the number of equispaced views. It can be inferred from this that the number ofindependent cross section reconstruction “resolution cells” is fixed at N,, and each cell has an area of (nR,/M)’. The band region (shown in Fig. 16) of the Radon transform which has. been.filtered to reject all aliased information, combined with Eqs. (25), (26),and (27), is a summary of sampling the Radon transform with continuous parallelbeam projections. The sampling (and aliasing-rejection filtering) operation has taken the original continuous Radon transform whose band region is shown in Fig. 8b and reduced it to a filtered continuous Radon transform whose band region is shown in Fig. 16. This figure clearly illustrates the limitations of parallel-beam geometry and indicates the information content of these projections. For undersampled situations this analysis also identifies the need for and the effect of windowing the Fourier transform of the convolution operator in (8). Practical implementations employing simplified algorithms are discussed in Section IX,B. This unifying two-dimensional signal theory viewpoint also permits questions on the information content of parallel-beam projections which were raised by Klug and Crowther (1972), and more recently by Cormack (1978), to be clearly answered. Our results also have something practical to say about the theorem of Smith et al. (1977), which in their own words is “a finite set of radiographs (projections) tells nothing at all (about the cross section function).” In view of the success of practical reconstructions from a finite set of projections, Katz (1978), who calls this theorem the first theoretical result with practical significance, insists that more a priori information must be accounted for and that some change in the mathematical model is

INVERSE DISCRETE RADON TRANSFORM

385

needed in order for theory to agree with practice. To better understand Smith’s theorem (1977), it is beneficial to consider his mathematically precise statement of it, which we paraphrase as “Given M projections of a compactly supported, infinitely differentiable cross section function, there is another infinitely differentiable cross section function that has the same support, the same M projections, and that is completely arbitrary on the interior of the support of the cross section function.” From this, one must conclude that the cross section function cannot be uniquely recovered within the region of support. Because of the need for both theoretical results and practical reconstructions (algorithms), this result is examined in detail to focus attention on the very real problem of extracting whatever information exists from the data. First, Smith’s phrase “tells nothing at all” (for which he means “is completely arbitrary”) does not properly describe his mathematically exact results. If nothing else, one can exactly extract the average value of the cross section function from these projections (even if M = 1). Furthermore, we show that practically (to within perhaps a small amount of aliasing due to the inexactness of the bowtie band region approximation in the general imaging problem) N , pieces of information can be obtained concerning this cross section function. From Figs. 15 and 16, this means that even though a reconstruction estimate off’ [made from p,(B, u)] is lacking in high-frequency information (and hence is completely arbitrary there), it is nevertheless “uniquely” defined at the low frequencies by these N , pieces of information and hence is not “completely arbitrary.” Consequently, even though f ’ ( x ,y) may belong to an infinite-dimensional vector space (as Smith assumes), it can be “uniquely” reconstructed from M projections on a finite-dimensional subspace. Certainly other cross section functions with the same low-frequency information will have the same finite-dimensional reconstruction, i.e., the same “projection” into a finite-dimensional subspace. This however does not detract from the usefulness of the reconstruction so long as M has been selected large enough to maintain the degree of resolution necessary for the purpose at hand. Perhaps Smith means that relative to an infinite-dimensional vector space, a finite-dimensional subspace is “nothing at all.” We might summarize our viewpoint by saying that a finite set of M equispaced projections from 0 to n says (almost) everything there is to know (uniformly) about a cross section function f’(x, y) for 0,’ 01,’ 5 (M/Rm)’ and says twice as much about it (nonuniformly) for OJ: 0,” s ( 2 M / R M ) ’ .

+

+

B. Sampled Projections at Equispaced Angles In this section the point sampling requirements for the Radon transform of “effectively band-limited” cross section functions are derived. I t is assumed that the Fourier transform of the cross section function is zero outside a disk

386

ALLEN G . LINDGREN A N D PAUL A. RATTEY

of radius W, in the o,oyplane, yielding an RMWM bowtie as the band region of the Radon transform (see Fig. 9). This situation also results when continuous projection data are filtered to achieve a uniform resolution reconstruction as indicated in the previous section. Standard approaches to the development of point sampling requirements for the Radon transform give rise to a rectangular sampling grid in the du plane (Brooks and Di Chiro, 1976a; Mersereau, 1976; Brooks et al., 1978; Rattey and Lindgren, 1981). From the two-dimensional viewpoint advocated in this article, “Nyquist sampling” of the Radon transform is easily obtained by noting how the frequency plane is utilized by the Fourier transform of the rectangularly sampled Radon transform. Figure 17a and b shows the relationship between the rectangularly sampled Radon transform and its Fourier transform for the situation where Ad and Au are made as large as possible without permitting aliasing to occur. Here it is seen that

AU = n/WM

(284

and

Ad producing a rectangular grid of

Z

n/RM WM

(28b)

min(N,) z (2/n)(R,WM)2 = (2/n)M2

(29)

nonzero Radon transform samples. Equation (29) takes into account the Mobius strip symmetry property. It is observed that (29) is larger than the number of pieces of uniform resolution information given in (26) by a factor of 2. However, from a two-dimensional signal theory viewpoint, it is obvious from Fig. 17b that the rectangular sampling grid is not efficient, since nearly one-half of the woo,plane is unused. By packing these bowties in a more efficient way, an optimal sampling grid for the Radon transform can be

4

i

t t

* t

*

b

* -+

J

2l-T .-

nu ...

t

t

b

4

b

* t

Ibl

Fig. 17. (a) Support of rectangularly sampled Radon transform of Fig. 9 with A 0 = 2n/[2(RMWM) 31 and Au = n/WM;and (b) its Fourier transform.

+

INVERSE DISCRETE RADON TRANSFORM

lb) la1

387

L I I

A 0

FIG. 18. (a) Support of hexagonally sampled Radon transform of Fig. 9 with A 0 = 61 and Au = n/WM;and (b) its Fourier transform.

2x/[2(&WM)

+

generated. If the unused regions of the frequency plane are covered by RM W, bowties as shown in Fig. 18b, then the optimal point sampling grid of Fig. 18a results. Such a grid is achieved, for example, by sampling each parallel-beam projection half as often. This type of sampling has been called “hexagonal sampling” by Mersereau (1979) and is a particular kind of “minimum sampling lattice” as defined by Peterson and Middleton (1962). This result, which gives a sampling requirement half that of rectangular sampling, could not have been achieved with the traditional viewpoint, where sampling in u and 0 are treated separately rather than simultaneously. Furthermore, this hexagonal sampling of p ( 0 , u ) is approximately as efficient a representation of f , the original cross section function, as rectangular sampling of f is. That is, if the isotropic function [i.e., one whose band region is an WMdisk (Peterson and Middleton, 1962)l f ( x , y) is represented on a rectangular grid, then by direct application of two-dimensional sampling theory it can be found that sample spacing must satisfy Ax In/W, and Ay 5 n/WM.Therefore, iff is contained in an RM disk, then it is adequately sampled on a rectangular grid by as few as nRi/(Ax)(Ay) = M 2 / n samples.* This says that the number of measurements and the number of unknowns can be (approximately) equal. Brooks and DiChiro (1976a,b) argue that this must be true but assume that the samples are on a rectangular grid. Our viewpoint clarifies the required distribution of the M 2 / n samples in the Radon transform plane and requires a different distribution between the number of projections and the number of samples within each projection from their result (Rattey and Lindgren, 1981).

* The most efficient packing of the circular band region off’in the wxwyplane for the sampled function is achieved by samplingfitselfon a hexagonal grid which involves 13.4%fewer samples than a rectangular grid (Mersereau, 1979).

388

ALLEN G. LINDGREN AND PAUL A. RATTEY

VIII. SAMPLING THE RADONTRANSFORM WITH FAN-BEAM PROJECTIONS A . Continuous Projections at Equispaced Angles

The By-coordinatization of the Radon transform (see Fig. 5 ) is natural for Radon transform samples taken with the fan-beam geometries used in most modern CT scanners (Kak, 1979). From the relationship between the fly- and Bu-coordinatization given in (lo), it is easy to see that a fan-beam projection, i.e., p’(& y) for a particular p, specifies p ( 8 , u ) along the sine wave u = Dsin(8

- j?)

(30)

in the Ou plane. Although an exact analysis regarding the implications of this “sine wave” sampling for a set of M equispaced projections is possible (Rattey and Lindgren, 1980), it is more instructive to examine a linearization of the principal image sampling set of M projections shown in Fig. 19. From this figure, it is apparent that the portion of any sine wave segment that samples p ( 8 , u) over its support ((ul I RM) is nearly linear for reasonable fan-beam geometries (i.e., D/RM 2 2). The simplified analysis presented here approximates each sine wave segment by

u = D(6 - j?)

(31)

Since p(8, u) = 0 for Iu) I RM, these sampling lines may be assumed to extend from - 00 to + 00, producing the skewed line sampling array shown in Fig. 20. Corresponding to Figs. 13 and 14 for the parallel-beam case, effective sampling arrays due to the Mobius strip symmetry property are shown in Figs. 21 and 22 for fan-beam geometry. For reasons not detailed here (see,

FIG. 19. “Curvilinear” sampling of the Bu-coordinatized Radon transform generated by sampling the By-coordinatized Radon transform with equispaced (in 8) fan-beam projections. This is shown here for D = 2RM.The solid portion of each sinewave segment indicates the portion of the line sample that is nonzero.

INVERSE DISCRETE RADON TRANSFORM

389

M SKEWED-LINE SAMPI.ES

FIG.20. Support of “skewed-line” sampled Radon transform generated from M = 2n/AB equispaced fan-beam projections.

(b)

FIG.21. Effective skewed-line sampling arrays (from fan-beam projections) generated by the symmetry property p ( 8 , u ) = p ( 8 ?I, - u ) or equivalently p‘(p, y ) = p ’ ( p + A + 2 y , - y). (a) The effective (doubly) skewed-line sampling array that occurs when M = 2 x / A p is an odd integer and p ’ ( p , 7 ) is sampled at M equispaced ”8” positions from 0 to 2 x . This is generated by using the Mobius strip symmetry property of the Radon transform and reflecting the line samples for p E [0, n[ into the region fl E [ A . 2 4 , and vice versa. (b) The effective (doubly) skewedline sampling array that occurs when M = 2x/A/3 is an even integer

+

FIG.22. The effective skewed-line sampling array that occurs when M = x/AP is an odd or even integer and p’@, y ) is sampled at M equispaced *‘/?’* positions from 0 to x . This is generated by using the Mobius strip symmetry property of the Radon transform and reflecting the line samples for ~ E [ OA, [ into the region PE[x, 2 x [ . This result is an effective sampling array that does not uniformly span the 8u plane.

390

ALLEN G. LINDGREN AND PAUL A. RATTEY

however, Rattey and Lindgren, 1980), these effective sampling arrays do not derive the same benefits as they did in the parallel-beam case. Consequently the most important case, involving only the principal image set shown in Fig. 20, is analyzed. Following the development of the previous sections, it is now a simple matter to understand the effect of sampling the Radon transform with fan-beam projections. The set of M equispaced fanbeam projections, continuous in y, samples the Radon transform to produce the new function

and

A P = 2z/M

(324

is given by The line-mass density of the Fourier transform P,(o>,,q,)

P,dm, Q,)

1

“

=-

AP

k=-m

Po m

- Mk,

+

o,, Dk

)

(33)

and represents a periodic replication of the R M bowtie in the direction (wo, 0,) = (1, - l/D). This band region is illustrated in Fig. 23, and the fundamental tomographic imaging system limitations due to aliasing from undersampling in P are revealed. The upper half-plane is viewed in greater detail in Fig. 24, where the (presampled) band region of the continuous Radon transform is highlighted and the number of aliased components within subregions is indicated. It is immediately clear that the subregion with “ 0 aliasing is recoverable. In addition, because of the Mobius strip

FIG. 23. Band region of p,@, ul. For fan-beam sampling the band region is a periodic replication, in the direction ( 1 , - l/D), of the R , bowtie of Fig. 8b. Overlapping of the translated bowtie band regions produces aliasing.

INVERSE DISCRETE RADON TRANSFORM

39 1

FIG. 24. The upper half of Fig. 23 viewed in greater detail. The number of aliased components within various regions of the bowtie-like baseband region of the (presampled) Radon transform is illustrated.

symmetry property, it is possible to effectively invert some of this aliasing. For example, by directly invoking the symmetry property Po( - m , w,) = (- l)"'P~(m,at,), a new function A(m@,mu)can be formed from P,(w,, 0,) which has less severe aliasing of the original function P(w,, a,,)i.e., , Ao(m, 0,)

=i

(-l)"'P,*o(-m,o>,) P,o(m, w,)

for m > O , o , > O and m < O , w , c O (34) for m _< 0, Q,, 2 0 and m 2 0, w, I 0

The support of A(wo, w,) is illustrated in Fig. 25. This band region [of ,l(O,u)] applies whether M is odd or even (D < a),and the nonaliased portion of the band region of p(8, u ) that can be extracted from A(0, u ) is a region resembling a double-pointed bowtie. As in Section VII,A, the information content of M fan-beam projections can be determined from this region. For finite.D to R , ratios, it is found (Rattey and Lindgren, 1980) that the amount of nonuniform resolution information N , , the amount of

FIG. 25. The number of noninvertible aliased components within various regions of the bowtie-like band region of the (presampled) Radon transform is illustrated for the situation where M is odd or even. This figure illustrates the band region of the function A(0, u), whose Fourier transform is defined by Eq. (34). and equivalently represents Fig. 24 after all invertible aliasing has been eliminated.

392

ALLEN G. LINDGREN AND PAUL A. RATTEY

uniform resolution information N,, and its associated uniform bandwidth W,, are all maximized for D/RM = 3 (see Fig. 26). For this situation N , = f(2/n)M2 N,, = $ ( l / n ) M 2

and w s u

= +(M/RM)

(37)

The band region (shown in Fig. 26), which has been processed to reject all aliased information, combined with Eqs. (3-9, (36),and (37), is a summary of sampling the Radon transform with continuous fan-beam projections. By comparing these values to those obtained with parallel-beam geometry [(25), (26), and (27)], it is observed that: ( a ) in order to obtain the same amount (but different kind) of nonuniform resolution information, fan-beam geometry must sample the Radon transform with f l times more continuous projections: and ( b )in order to obtain the same amount of uni$ororm resolution information (and bandwidth) fan-beam geometry must sample the Radon transform with 1i times more continuous projections. Thus, with regard to information content, M equispaced fan-beam projections are inferior to M equispaced parallel-beam projections.

B. Sampled Projections at Equispaced Angles In this section, the rectangular grid sampling requirements in the B y plane are derived. As in Section VII,B, it is assumed that the cross section function is effectively band-limited to W,.

FIG.26. Band region of the skewed-line sampled Radon transform that has been processed and filtered to reject all aliased information. The band region required for uniform resolution is indicated by dashed lines. This figure is drawn for D = 3 4 , . which yields optimal performance for fan-beam systems when D < co.It is assumed in this figure that p'@, y ) is sampled with M equispaced projections spaced over the interval [O, 274.

INVERSE DISCRETE RADON TRANSFORM

393

A popular method of determining how p ’ ( p , y) should be sampled has been to force parallel-beam geometry samples out of fan-beam geometry. These parallel-beam geometry samples, i.e., samples on a rectangular grid in the Ou plane, are produced by sorting the available fan-beam samples. Unfortunately, the samples obtained from fan-beam measurements do not generally produce a rectangular sampling grid in the Ou plane. However, Dreike and Boyd(l976),Wang(1977),and Peters and Lewitt (1977)examined methods for achieving this goal and described approximations and interpolation schemes that they employed to obtain a sufficient set of parallelbeam samples. Generally, these schemes require that Afl (the angle spacing between fan-beam projections) be an integer multiple (mostly 1 or 2) of Ay (the angle spacing between samples within each fan-beam projection). This requirement tends to produce an oversampled rectangular grid in the Ou plane. Furthermore, by employing these schemes, that sidestep basic issues, a fundamental understanding of fan-beam geometry sampling is not obtained. Two-dimensional signal theory again provides a unifying framework from which the desired insight can be obtained. A rectangular sampling grid in the B y plane [i.e., one where p’(& y) is sampled at (p, y) = ( k Afl, IAy) for all integers k and I ] defines via (10) the Ou-coordinatized Radon transform, p(O, u), on a skewed sampling raster as illustrated in Fig. 27a. This point sampling is easily shown (Rattey and Lindgren, 1980) to produce a band region that is a skew-periodic replication of the RMWM bowtie as shown in Fig. 27b. By applying simple geometry to this band region, the fly-plane rectangular grid sampling requirements can be established so that no “noninvertible aliasing” occurs in the WgO, plane. If it is desired to sample p’(fl, 7 ) so that no aliasing (invertible or not) occurs (see Fig. 28), the minimum number of views is found (for D/R, = 3) to be I t times larger than that required in parallel-beam geometry.

FIG.27. (a) Support of skew-sampled Radon transform of Fig. 9 generated by applying the linear approximation [Eq. (31)] to the curvilinear-sampling raster in the 6u plane (produced by a rectangular-sampling raster in the B y plane); (b) its Fourier transform.

394

ALLEN

G.

LINDGREN AND PAUL

A.

RATTEY

FIG.28. Position of bowties when fan-beam sample spacing A/3 and Ay are made as large as possible while avoiding both invertible and noninvertible aliasing (D= 3R,).

IX. THEINVERSE DISCRETE RADONTRANSFORM A . Theoretical I D R T

If the Radon transform is adequately sampled on a "regular" grid in accordance with the requirements developed in previous sections, then the resultant discrete Radon transform (DRT) can (in principle) be low-pass filtered to reproduce the continuous Radon transform (CRT). In most applications, however, it is ultimately desired to reconstruct the crosssection function. In theory, this can be obtained by inverting the CRT using, for instance, (8b)-(8d). In practice, samples of the inverse continuous Radon transform (ICRT) suffice, and an inverse discrete Radon transform (IDRT) is sought to process directly the Radon transform samples defined on a regular measurement grid. Since recovery of the CRT is not practical, and the integrations required in the ICRT cannot be exactly performed, approximate forms of the ICRT have been devised and implemented (Herman and Naparstek, 1977; Scudder, 1978; Rowland, 1979; Mersereau and Oppenheim, 1974; Shepp and Logan, 1974; Shepp and Kruskal, 1978).These forms are based on the methodology of replacing the ICRT integrals by sums and applying the resultant discrete inversion formula to the DRT. In this section the unifying mechanism of two-dimensional signal theory again is used to show that, to within the finite-length R , W , bowtie approximation and provided the sampling requirements are met and certain processing performed (adjustments made to the data), the approximate Ou-coordinatized ICRT is, in fact, an appropriate approach. That is, to within standard signal processing approximations, when a DRT (defined on a rectangular grid in the Bu plane) is known and the

INVERSE DISCRETE RADON TRANSFORM

395

sampling requirements [which can be obtained from (28)] are met, an “exact” IDRT exists. The processing required to invert the CRT involves a set of one-dimensional operations. The one-dimensional operation in (8c) is the magnitudeomega filtering operation, and the one-dimensional operation defined by (8b) is the backprojection-averaging operation. To facilitate the development of the IDRT (while simultaneously gaining a deeper understanding of the ICRT) it is beneficial to view these steps as two-dimensional rather than one-dimensional operations. This permits the implications of magnitudeomega filtering and backprojection-averaging to be viewed and interpreted in the o ~ Qplane, ,, resulting in the straightforward development of an IDRT. A partitioning of the ICRT into a set of two-dimensional operations, equivalent to the set of one-dimensional operations defined by (8b) and (8c), is given in Fig. 29. Here the backprojection-averaging operation, which requires an integration of the magnitude-omega filtered Radon transform over the curve u = x cos 8 y sin 8 for reconstruction at (x, y ) , is achieved in three two-dimensional steps: ( a ) a distortion in u [defined by u’ = u (x cos 8 + y sin 8)] which shifts the path of integration to the 8 axis; (b) a low-pass filtering [convolution with the line mass 6(u)] which produces a smoothed function fid(x,y)(8ru) with variation only in the u direction; and finally ( c ) a sampling of the low-pass-filtered distorted function jd(x,y)(8, u) at(8,u) = (0,O)toproduce thesampleoffat(x,y).Theeffectofeachoperator on the bowtie-like band region of the CRT is also illustrated in this figure. Of particular importance later are the spreading effect the distortion step has on the bowtie band region and the fact that only the information along the w,, axis survives the low-pass filtering operation. It should be noted that the band region at each stage of the processing in Fig. 29 is compact. This is the key to the development of the IDRT. The starting point in developing an IDRT, which is “equivalent” to the ICRT just described (see Fig. 29), is an adequately sampled DRT defined on a rectangular grid in the 8u plane. The Fourier transform of the point sampled CRT (i.e., the DRT) was shown in Fig. 17. The baseband image of this periodic band region uniquely specifies the Fourier transform of the Radon transform p(8, u). Figure 29 defines the processing that must be performed on p ( 8 , uj, and hence P(oI,, q , j , to obtain a sample [at the point (x, y)] of the reconstructed cross section function. By demanding that “equivalent” processing be performed on the baseband image of the Fourier transform of the DRT, an IDRT results. Formally, the IDRT algorithm is obtained by deriving the discrete counterparts for each two-dimensional operator (step) in the ICRT algorithm illustrated in Fig. 29. This development, detailed by Rattey (1980), is straightforward, and only the main

+

+

396

ALLEN G . LINDGREN AND PAUL A . RATTEY Frequency Domain 1r.terpretation

Space Domain Interpretation

~d(x,y)(e,~)@ where h L ( Q , u ) =

*

hL(Q,u)

.

filtering

where H L ( m , u l U )

= {~:~t~e~wise

6(uf O.WM-bowtie 'd(xvy)(O'u)

f(x,y) = f(rcos0.rsin0) =

f

bandregiun

D D ( D

sampling

Td(x,y)(o*o) f(X?Y)

f(x ,y)=$.'-

(r?n)'--

--J$d(x,

y) ( ae P o,,)dugddu

INVERSE DXSCRETE RADON TRANSFORM

397

features are reviewed here to show the limitations and to provide insight into the behavior of the IDRT. The first processing operation to be discretized is the magnitude-omega filtering operation. Since the band region of the CRT is finite (an RM W, bowtie), the result is unaltered if filtering is performed with a rectangularly windowed magnitude-omega filter which cuts off at Iq,l = n/Au 2 W,. Equivalently, the continuous magnitude-omega filtered function p”(8,u ) can be obtained filtering the DRT with a (low-pass)windowed magnitude-omega filter with cutoff at I o ~ , , ~ = n/Au and I Q ~ ) = rc/Atl. If the resultant continuous function is resampled on the original rectangular grid, then a discretized version of the magnitude-omega filtering operation is obtained. The band region of the sampled magnitude-omega filtered function is identical to that shown in Fig. 17. The consolidation of all the steps taken to achieve this result yields a discrete two-dimensional convolution operation which (for implementation) reduces to the following set of one-dimensional convolutions: 00

C

p”(k Ad, I Au) =

~ ( AO, k I’ Au)h,,[(I - 1’) Au]

(3W

for all I E Z , k E [O, M [ where

To reconstruct the value ofthe cross section function at the point (x, y), the distorted function &x,y)(Or u ) is required. If the discrete function p”(kAO, I Au) is low-pass filtered with a filter whose Fourier transform is a known nonzero constant within the rectangle [ - n/A& n/AO] x [ - n/Au, n/Au] and zero elsewhere, then p”(0,u ) is retrieved. The continuous function p(O, u ) can then be distorted to produce &x,y)(O, u ) whose bowtie band region suffers a spreading (see Fig. 29). By resampling @d(x,y,(fl, u ) on the original rectangular grid, the discretized distorted function whose band region is shown in Fig. 30 j

1%

I

t-!

.

n ’

5%

FIG.30. Periodic band region of the rectangularly sampled distorted function ,Ed,x,y,(O, u).

398

ALLEN G. LINDGREN AND PAUL A. RATTEY

is obtained. It is apparent from the figure that this sampled function is aliased, and hence the ability to regenerate fi',(x,J)(8, u ) continuously has been lost. However, because of the low-pass filtering operation that follows, only the information along the OI,,axis is ultimately required for reconstruction at the point (x, y) (see Fig. 29). So long as (J-)'/* < M/WM - RM, then the bowtie spreading (to within the original bowtie approximation) does not alias the information along the oil,axis, and so the reconstruction sample is not affected. By processing the discretized distorted function in a manner that retains only the information along the oil, axis from -n/Au to n/Au, a continuous, low-pass-filtered,distorted function is produced which "exactly" equals p"d(,,,)(d, u). To maintain the discrete nature of the problem, &x,y)(8, u ) can be resampled on the original rectangular grid and a sampled version obtained whose periodic band region is shown in Fig. 31. Finally the sample f(x, y) is obtained by simply sampling j d ( , , , ) ( k A8, I Au) at (k,I ) = (0, 0) and accounting for a known scale factor (Rattey, 1980). By consolidating all the steps discussed, the following discrete backprojection-averaging operation which is "exactly" equivalent to the continuous backprqiection-averaging operation given by (8b) is found: 1

1M-1

where 'x

bd(x,y)(k

Ad, 0) =

1

,

p"(k

I Au)

I=-a,

sin{n[(r/Au) cos(k Ad - 4 ) - I]} n[(r/Au) cos(k A8 - 4 ) - I]

(39b,

r2 = x2 + y2 and

4

= arctan(y/x)

In words, the IDRT algorithm defined by (38) and (39) requires that: first, each sampled projection be digitally filtered [(38a)] with a windowed

FIG.31. Periodic band region of the rectangularly sampled low-pass-filtered distorted function h,x,yl(ft u).

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399

magnitude-omega filter [(38b)]; second, each filtered projection be interpolated to provide the required backprojected sample [(39b)] ; and finally all backprojected samples must be summed [(39a)] to provide the sample f ( x , y). It is important to reiterate that although the IDRT was obtained by viewing the ICRT as a sequence of two-dimensional operations, the practical algorithm defined by (38) and (39) has been reduced to a set of one-dimensional operations. The two-dimensional viewpoint was necessary only for the theoretical development of the IDRT, and by eliminating unnecessary steps the actual realization produces an algorithm with minimal computational requirements. In view of different approaches to inverting the DRT which are found in the literature, it is worth reflecting on the IDRT algorithm just derived. A discrete Radon inversion formula is commonly developed by simply approximating the continuous inversion integrals by sums (see, for example, Herman and Naparstek, 1977; Scudder, 1978; or Horn, 1979).The development presented here has shown that this is essentially correct provided that certain adjustments are made and certain demands are met. Foremost, it is necessary that A0 and Au be chosen to satisfy the requirements of the sampling theorem. It is also required that the magnitude-omega filter be modified to a bandlimited (or sufficiently windowed) magnitude-omega filter, or else aliasing will result. Finally, it is seen that when the backprojection integral is replaced by a sum, an exact reconstruction is obtained so long as backprojection of each filtered projection is achieved by an exact interpolation process. It should be noted that the frequency domain viewpoint can also be used to determine what adjustments must be made if the spacing of the measurements (A0 or Au) does not meet the sampling requirements; i.e., it shows how filter band regions must be modified to achieve an artifact-free reconstruction. The price paid for this is a “smoothed” reconstruction.

B. Practical IDRT The IDRT algorithm just presented is a theoretical procedure for inverting the DRT defined on a rectangular grid. In practice, situations exist where simpler algorithms have been reported to yield better reconstructions than the “exact” IDRT. Among the reasons to seek an alternative are: (a) the measured samples of the Radon transform are noise contaminated and blurred; and (b) the computational burdens need to be minimized. For example, the infinite sum in (39) must be approximated if a finite amount of computation is to be realized. Achieving a viable reconstruction then requires a trade-off among the deterministic reconstruction accuracy, the statistical reliability of the reconstruction, and computational cost and time. The realization of the magnitude-omega filter and the type of interpolation

400

ALLEN G. LINDGREN AND PAUL A. RATTEY

employed are the variables in the reconstruction algorithm in which one can affect these factors. The immediate impact of these factors on the “exact” IDRT is (a)abandonment of the rectangularly windowed magnitude-omega filter in favor of a filter that emphasizes (amplifies) the high-frequency signals (primarily noise) less; and (b) replacement of the ideal interpolator by one that is computationally simpler. Modified magnitude-omega filters have been obtained by either multiplying 10) by a tapered window (e.g., Hamming or Butterworth) rather than a rectangular window or directly approximating IwI at low frequencies by an analytical function. The application of modified magnitude-omega filters which attenuate high frequencies (relative to the rectangularly windowed magnitude-omega filter) not only reduce noise, but also virtually eliminate Gibb’s phenomenon type of reconstruction artifacts. Early reconstructions (Bracewell and Riddle, 1967; Ramachandran and Lakshminarayanan, 1971) used the rectangularly windowed magnitude-omega filter and, as a consequence, tended to be noisy and oscillatory. Shepp and Logan (1974) found a rectified sine wave (in place of the periodic triangle waveform which results when the impulse response of the rectangularly windowed magnitudeomega filter is sampled) provided better reconstructions of the head. They also made further modifications and approximations that reduced the computational burdens and provided additional smoothing. Kwoh et al. (1977) extended this class of filters to a “generalized Iwl-filter” which they reported achieved simultaneously good reconstruction accuracy, considerable reduction in X-ray dosage (because of improved noise performance), and improved processing time. Lewitt et al. (1978) have shown that it is computationally advantageous to perform the discrete lo(-filtering operation using the onedimensional FFT. They also examined the performance of finite-length filters which were optimized to a least mean square criterion. An approximation to the optimal Weiner filter was developed by Levitan et al. (1979). A performance comparison of various modified Iw)-filtersis given by Budinger et al. (1979). The interpolation that is required in the backprojection-averaging operation is most simply achieved by a nearest-neighbor or a linear interpolator (e.g., see Lewitt e l al., 1978; or Rowland, 1979). Because of deterministic and statistical tradeoffs, such simple schemes have even been preferred. For example, Herman et al. (1979) compare the performance of a linear interpolator with that of the modified cubic spline interpolator. Based on experiments, their conclusion favored linear interpolation, since both methods behaved similarly and the linear interpolator was less expensive computationally. A summary of performance trade-offs one can expect with various modified magnitude-omega filters and interpolators is given by Rowland (1979).

INVERSE DISCRETE RADON TRANSFORM

40 1

He presents and evaluates the performance of the convolution reconstruction algorithm using four tests with ten different magnitude-omega filters and six different interpolators. Generally, based on experimental reconstruction, he found linear interpolation to be best but was not able to offer a clear-cut preference for a magnitude-omega filter. A theoretical approach to these tradeoffs involves analysis of one-dimensional projection data, the onedimensional convolved projection data, and their one-dimensional Fourier transforms. The overall impact of these approaches and others can all be put into perspective by the unifying two-dimensional viewpoint of this article.

x. EFFECTS OF NONIDEAL SAMPLING In Sections VII and VIII, the implications of sampling the Radon transform were discussed under the assumption of “ideal” impulse sampling. In practice, these ideal measurements cannot be made. The basic reason that “nonideal” sampling occurs is because measuring devices have a finite resolution. For instance, blurring occurs in TCAT measurements owing to the finite (rather than infinitesimal) width of the X-ray beam and detectors. This results both because of mechanical constraints and because of the need to collect a significant number of photons in each measurement to reduce statistical fluctuations. Another. factor contributing to the production of nonideal measurements is radiation source or measurement detector motion over the measurement time interval. In parallel-beam geometry (Fig. 3), this may be due to a translation in u and/or a rotation in 0 ; whereas in fan-beam geometry (Fig. 5) this may be due to source motion around the circumscribing circle of radius D.It is important to recognize that the descriptor “nonideal” in this discussion does not necessarily mean undesirable. Averaging performed by the measurement process has been termed as “nonideal” sampling only in the sense that “ideal” impulse sampling has not occurred. In general, filtering produced by finite-width detectors and source/detector motion (and other mechanisms such as a noncollimated X-ray source in parallelbeam geometry or a finite-size point source of X rays in fan-beam geometry) is the only vehicle by which the Radon transform may be filtered prior to the sampling operation. It may, therefore, be important to use effectively all these “smoothing devices” to reduce measurement noise and to limit the band region of the Radon transform as much as possible in order to prevent aliasing of the information that is of interest. Filtering effects that give rise to nonideal measurements may be simply understood from the two-dimensional signal processing viewpoint. Specifically, the nonideal sampling process may be modeled as a sequence of two operations: The first operation models the “nonideal” effect on the exact continuous Radon transform, and the second operation models the “ideal”

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ALLEN G . LINDGREN AND PAUL A. RATTEY

sampling process on the “modified”Radon transform. Because of the analysis done on ideal sampling in Sections VII and VIII, we will consider only the first operation in this section. In some applications, such as ECAT (for a nonattenuating medium) or radio astronomy, nonideal effects directly give rise to measurements that are averages of p(B, u) [or p’(& y ) ] over regions in the Bu (or by) plane. In other applications, such as TCAT, nonideal effects indirectly lead to a consideration of measurements that are averages of p(0, u) [or p’(P, y ) ] over regions in the Bu (or b y ) plane. A complication in the latter case (TCAT) arises, since the radiation intensity that exits the cross section function is exponentially related to the Radon transform: hence the nonideal effects directly give rise to measurements that are averages of exp( - p(& u)) [or exp( - p‘(& y))] over regions in the &(or by) plane. However, by expanding these exponentials in a Taylor series about the average value of the Radon transform and then ignoring terms of order two or larger, this averaging effect reduces to a consideration of (logarithmic) transformed measurements that are averages of p(0, u) [or p’(p, y ) ] over regions in the Bu (or B y ) plane.* Consequently, in either case, the “nonideal” measurement effects give rise to a smoothing process which can be described as

where c is a scale factor not significant to the analysis presented here. If the region of integration R shifts uniformly as a function of 0 and u, then (40)reduces to the convolution

ss

p a p , u) = c’

R

p ( e - e’, - u’)do’ du’

(41)

Because of (31) this convolution holds for both parallel- and fan-beam geometry. In (41), the region of integration R distinguishes between these cases. Equation (41)shows that the “nonideal” eflects give rise to a measurement process p,(B,u) which is a convolution of the ideal Radon transform with a Jitter whose impulse response is a constant over some region R in the Bu plane. With a simple modification, (41) can be generalized to handle a nonuniform, shift-invariant weighting of the Radon transform.

* More exactly, this approximationgives rise to measurements that are averages of a normaly)]. Verly and Bracewell (1979) discuss this approximation in detail. izedp(f3,u) ”@,

INVERSE DISCRETE RADON TRANSFORM

+

403

By periodically extending the measurement process for all 6 from - co to Eq. (41)can be written as the following periodic/aperiodic convolution:

00,

pa(&4 = P(& u)@*h(B, U) =

Jo2n

p ( 6 - O',u - u')h(6',u')du' d6'

(42)

In parallel-beam geometry, a model for the averaging window corresponding to finite detector width and uniform source/detector rotation is a uniformly weighted rectangle [ -00/2, 6,/2] x [ -u0/2, uo/2] in the 6u plane. This gives rise to a filter whose impulse response is (to within a scale factor) 1

h(6, u ) = h,(8, u) = -

"

where rect[x] =

1 0

for 1x1 c otherwise

1

Similarly in fan-beam geometry, the analogous model for the averaging window corresponding to finite detector width and uniform source/detector rotation is the uniformly weighted rectangle [ -p0/2, bo/2] x [ - y0/2, y0/2] in the by plane. This is equivalent by (31) to a parallelogram in the 8u plane and gives rise to a filter whose impulse response is (to within a scale factor)

1

h(6,u) = h,,(O,u) = 1 "

rect[(0

-; -

2nk)i].&rect[u.&]

PO k=-m

(45) The effect of these filters is most clearly seen in the frequency domain (i.e., the o,q, plane) where they serve to attenuate spectral components of p(6, u). The associated line-mass densities for the Fourier transform of these impulse responses are

and

Two particular examples of this filtering are considered in Figs. 32 and 33. In Fig. 32a and b, the integration window in the space domain is super-

404

ALLEN G . LINDGREN AND PAUL A. RATTEY

.\q&

.\@ \

.-

\

I \

I

'

\ \

-

. .

I \

,

w,

- ....

lc)

~__., Id1

FIG.32. Space and frequency domain interpretation of Radon transform smoothing due to both finite detector width (defined by uo in parallel-beam geometry and yo in fan-beam geometry) and source/detector rotation (defined by Bo in parallel-beam geometry and Pa in fan-beam geometry). (a) Integration region for parallel-beam geometry sample p,(Oi,u j ) when 0, = n/RMWM 1) = At9 and uo = n/WM= Au in Eq. (43). (b) Integration region for fan-beam geometry samplep,(Bi,u,) when D = 3R,, Po = x/(RMWM+ I) = AO, and yo = n/DW, = Ay in Eq. (45). (c) 3-dB band region of smoothing filter obtained by applying (a) to Eq. (46). (d) 3-dB band region of smoothing filter obtained by applying (b) to Eq. (47).

+

lb)

lo)

'

x -

, ...

.

....

(Cl

FIG. 33. Space and frequency domain interpretation of Radon transform smoothing due to finite detector width (defined by uo in parallel-beam geometry and yo in fan-beam geometry). (a) Integration interval for parallel-beam geometry sample p,(Oi,u,) when 0, = 0 and uo = n/WM= Au in Eq. (43). (b) Integration interval for fan-beam geometry sample pa(Bi,u,)when D = 3RM, = 0, and yo = n/DWM= Ay in Eq. (45). (c) 3-dB band region of smoothing filter obtained by applying (a) to Eq. (46). (d) 3-dB band region of smoothing filter obtained by applying (b) to Eq. (47).

so

INVERSE DISCRETE RADON TRANSFORM

405

imposed on the Radon transform in a manner that indicates how the averaged and sampled Radon transform is obtained for the case where 8, = flo = A0 = n/(R,W, l), uo = Dy, = Au = n/W,, and D = 3R,. Figure 32c and d illustrate the effect these filters have on the bowtie-like band region of the Radon transform. This filtering represents the degradation in the measured Radon transform due to a smearing (averaging) in both the 8 and u directions caused by finite detector width and source/detector rotation. Figure 33 illustrates the same effects for a lesser amount of filtering due to finite detector width but no source/detector motion [i.e., O0 = flo = 0 in (46)and (47)l.From these figures, it is clear that the filtering effect in fan-beam geometry is not symmetric with respect to the coordinate axes. However, if desired, this filtering effect can be made symmetric by simply averaging the symmetric samples p:(fl, y ) and p’,(B + n + 2y,-y) if they are available. Because of the symmetry property of the Radon transform, this averaging process produces an effective filter impulse response whose symmetric averaging window in the 8u plane is the superposition of two oppositely skewed parallelograms, one due to the original fan-beam integration window defined by pi(fl, y) and the other due to the Mobius strip image p:(fl n 2y, - y ) . This sort of averaging increases the filtering of p(8, u). An alternate way to “symmetrize” the filtering of p(8, u ) is to use directly the Mobius strip symmetry property in the frequency domain and generate the function A(8,u) whose Fourier transform is defined by (34). The effects of measurement blurring on the Radon transform are clear from the previous discussion. In fact, in a noise-free environment, it is also clear what shape a compensation (equalization) filter must take in order to restore the original Radon transform. However, in the presence of white measurement noise, the amount of restoration that should be performed involves a trade-off between “statistical” and “deterministic” accuracy. In any circumstance, the restoration of’the blurred Radon transform requires a linear space-invariant jiltering of the measured Radon transform itself. Based on the preceding systematic and unified approach to analyzing “nonideal” measurement effects, past efforts in this area are now reviewed and put into perspective. In 1977, Bracewell (who was interested in the effect of “finite-beam width” in radio astronomy as early as 1956) applied the concept of “strip integrals” (of which line integration is the limiting ideal case) to the TCAT problem. He shows that (after making a suitable approximation) the degradation due to finite beamwidth gives rise to a reconstruction in which the original cross section function is convolved (two-dimensionally) with a circularly symmetric function (Bracewell, 1977). Unfortunately because of his approximation, this result was correct only for “small central features” in the reconstruction. Later, Verly and Bracewell (1979) eliminated this approximation and provided a description of the smearing process that

+

+ +

406

ALLEN G. LINDGREN AND PAUL A. RATTEY

is accurate over the entire reconstruction. To accomplish this, they introduced the notion of a “generalized Radon transform” and showed in a very complicated development that application of the inverse Radon transform operator to the “generalized Radon transform” gives rise to a space-variant impulse response. Based on their analysis, they obtained a relatively complex method for restoring the blurred tomographic image. By comparison, analysis of the effect of nonideal measurements on the Radon transform itself with the viewpoint just given leads to a much simpler (and just as general) restoration scheme. Cormack (1978)discussed the effect of beams of finite width with the goal of computing how much information can be obtained from M projections. He employed an averaging model which in terms of our viewpoint gives rise to a smoothing filter whose impulse response is a constant over a diamondshaped region in the 8u plane. Clearly, the implications of this averaging filter can be easily assessed by Fourier transforming the impulse response. By incorrectly treating the variables 8 and u in polar form, Cormack showed in a mathematical development (which is relatively complicated) that beams of finite width give rise to measurements that are averages of ‘‘~(0, u)” over “diamond-like’’ regions which increase in size as a function of the “radius u.” With this (incorrect) viewpoint, he computes that “as much as” M 2 f z independent pieces of information can be extracted from M “smoothed” projections [compared to the result in (25) for M “nonsmoothed” projections]. Even if Cormack’s polar coordinate interpretation were valid, because of the space-variant nature of his averaging model which arises in his “polar coordinate” representation, it is impossible to obtain as simple a frequency domain interpretation as that given previously through the twodimensional signal theory viewpoint. Beattie (1975) correctly recognized that in fan-beam geometry the effect of finite source and detector averaging gives rise to measurements that are averages of the Radon transform over “diamond-like” regions in the (rectangular) 8u plane. However, the all-important step into the frequency domain was never taken, and the discovery of the simple mechanism for restoration was missed.

XI. CONCLUSION This review was directed at providing a unifying framework for tomographic imaging systems that would permit contributions to this field to be viewed and evaluated with some perspective. Its intent is to improve the insight into the factors affecting image quality and to provide the theoretical foundations for imaging systems involving “regular” sampling of the Radon

INVERSE DISCRETE RADON TRANSFORM

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transform and digitally processed reconstructions. Two-dimensional signal theory provides the analytical thread that weaves this together into a unified story. The purpose of this review is not to provide detailed processing algorithms but rather to review past efforts in a way that brings out the underlying theory and establishes the basic principles on which advanced processing and measurement schemes can be developed. Finally, it is hoped that, this work may permit workers in other areas to recognize places where Radon transform theory may make a contribution and then immediately to apply this theory in a systematic way without the necessity of repeating history.

X11. EPIL(K;UE Undoubtedly the single most important application of tomographic imaging has been X-ray transmission computer-assisted tomography. Since it was introduced clinically in 1971, it has caused a revolution in diagnostic medicine. Initially, because of the high cost of X-ray scanners, it was feared that general use of this equipment would escalate the already soaring cost of health care. Currently, the TCAT scanner is acknowledged as being not only a cost effective, but also a significant part of diagnostic radiology. The importance of TCAT as a technological breakthrough is attested to by the fact that the 1979 Nobel Prize in Physiology or Medicine was jointly awarded to Alan Cormack and Godfrey Houndsfield for their key contributions in this area (see Susskind, 1980). Cormack’s path to this award began in 1955 when, as a nuclear physicist and lecturer at the University of Capetown, he was asked to spend l $ days a week at the affiliated Groote Shuur Hospital to supervise the administration of radioactive isotopes. While he was observing the planning of radiotherapy treatments, it occurred to him that in order to improve treatment planning, it is necessary to know the distribution of the attenuation coefficient of tissues in the body. He also realized that knowledge of this internal structure, obtained by X-ray measurements made outside the body, would be useful for diagnostic purposes. To this end, in 1957 he performed an experiment that measured the attenuation of an X-ray beam passing through a simple circularly symmetric object consisting of aluminum surrounded by an annulus of wood. By applying a mathematical theory for image reconstruction (which he developed) to a set of such measurements, he successfully determined the attenuation coefficient function of this object. Later he revised his mathematical approach so that it was better suited for calculation, repeated his experiment with an asymmetrical object, and published his results. In Cormack’s words: “Publications took place in 1963 and 1964. There was virtually no response” (Cormack, 1980).

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A.

RATTEY

Houndsfield, an electrical engineer at the Central Research Laboratory for Electric and Music Industries, Ltd. (now called EMI), began his (totally independent) early work about 10 years after Cormack’s. Like Cormack, he felt that practical reconstruction of a three-dimensional object should be done a slice at a time, hence reducing a three-dimensional problem to a twodimensional one. To determine the ultimate utility of this approach, Houndsfield calculated its potential accuracy and concluded that it could be nearly 100 times more sensitive than conventional X-ray analysis. After a number of successful and encouraging experiments, Houndsfield coupled his experience in pattern recognition (which led to an ART-like reconstruction algorithm) with his ability to integrate the required technology into a working system and produced the first clinical head scanner in 1971. In 1972, when the first patient with a suspected brain lesion was scanned, an image ofa dark circular cyst in the brain was clearly detailed. Houndsfield, who holds the basic patent on computed tomography (1968) and for whom the unit of measure in quantitative CT reconstruction was named (Houndsfield number), states: “From that moment o n . . . it became evident that the machine was going to be sensitive enough to distinguish the difference between normal and diseased tissue” (Houndsfield, 1980). Clearly, computed tomography was an idea whose time had come. “It is no exaggeration to state that no other method within X-ray diagnostics has led within such a short period of time to such advances in research and a multiple of applications” [statement of Nobel Selection Institute (see Susskind, 1980)]. More remains to be done. REFERENCES Beattie, J. W. (1975). IEEE Trans. Nuclear Sci. NS-22 (I), 359-363. Bellman, S. H., Bender, R., Gordon, R., and Rowe, J. E., Jr. (1971). J . Theor. Biol. 32,205-216. Berry, M. V., and Gibbs, D. F. (1970). Proc. R. SOC.A 314, 143-152. Bracewell, R. N. (1 956). Aust. J. Phys. 9, 198-21 7. Bracewell, R. N. (1977). J . Comput. Assist. Tomog. 1 (I), 6-15. Bracewell, R. N. (1979). In “Image Reconstruction from Projections” (G. T. Herman, ed.), p. 81. Springer-Verlag, Berlin and New York. Bracewell, R. N., and Riddle, A. C. (1967). Astrophys. J . 150,427-434. Bracewell, R. N., and Roberts, J. A. (1954). Ausr. J. Phys. 7 , 615-640. Brooks, R. A., and DiChiro, G . (1976a). Phys. Med. Biol. 21,689-732. Brooks, R. A., and DiChiro, G. (1976b). Med. Phys. 3,237-240. Brooks, R. A., Weiss, G. H., and Talbert, A. J. (1978). J . Comput. Assisr. Tomog. 2, 577-585. Budinger, T. F., Gullberg, G. T., and Huesman, R. H. (1979). In “Image Reconstruction from Projections” (G. T. Herman, ed.), p. 147. Springer-Verlag, Berlin and New York. Cormack, A. M. (1963). J . Appl. Phys. 34,2722-2727. Cormack, A. M. (1964). J . Appl. Phys. 35,2908-2913. Cormack, A. M. (1978). Phys. Med. Biol. 23 (6), 1141-1 148.

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Cormack, A. M. (1980). Med. fhys. 7 (4), 277-282. Courant, R., and Hilbert, D. (1966). “Methods of Mathematical Physics, Vol. 11.” Wiley (Interscience), New York. Cramer, H., and Wold, H. (1936). J. Math. Soc. (London) 11,290-294. Crowther, R. A,, and Klug, A. (1971). J. Theor. Biol. 32, 199-203. Crowther, R. A., De Rosier, D. J., and Klug, A. (1970). Proc. R . SOC.A 317,319-340. Dahlquist, G., and Bjorck, A. (1974). “Numerical Methods,” (N. Anderson, transl.). PrenticeHall, New York. De Rosier, D. J., and Klug, A. (1968). Nature (London) 217, 130-134. Dines, K. A., and Lytle, R. J. (1979). Proc. IEEE67 (7), 1065-1073. Dreike, P., and Boyd, D. P. (1976). Comput. Graph. Image Process. 5,459-469. Duda, R. O., and Hart, P. E. (1972). Commun. Assoc. Compur. Mach. 15, 11-15. Gel’fand, I. M., Graev, M. I., and Vilenkin, N. (1966). “Generalized Functions: Vol. 5 , Integral Geometry and Representation Theory.” Academic Press, New York. Gilbert, P. F. C. (1972). 1.Theor. Biol. 36, 105-117. Gordon, R., Bender, R., and Herman, G. T. (1970). J . Theor. Biol. 29,471-481. Greenleaf, J. F., Johnson, S. A., Samayoa, W. F., and Duck, F. A. (1975). In “Acoustical Holography” (N. Booth, ed.), Vol. 6, p. 71. Plenum, New York. Herman, G. T., and Lent, A. (1976). Compuf. Biol. Med. 6, 273-294. Herman, G. T., and Naparstek, A. (1977). S I A M J . Appl. Math. 23, 511-533. Herman, G. T., and Rowland, S. (1973). Compuf. Graphics Image Process. 2, 151-178. Herman, G. T., Rowland, S., and Yau, M. (1979). IEEE Trans. Nuclear Sci. NS-26(2), 28792894. Horn, B. K. P. (1978). Proc. ZEEE66 ( S ) , 551-562. Horn, B. K. P. (1979). Proc. ZEEE 67 (12), 1616-1623. Houndsfield, G. N. (1973). Br. J. Radiol. 46, 1016-1022. Houndsfield, G. N. (1980). Med. Phys. 7 (4), 283-290. John, F. (1955). “Plane Waves and Spherical Means Applied to Partial Differential Equations.” Wiley (Interscience), New York. John, F. (1978). “Partial Differential Equations” (3rd Ed.). Springer-Verlag, Berlin and New York. Kak, A. C. (1979). Proc. IEEE67 (9), 1245-1272. Katz, M. B. (1978). “Questions of Uniqueness and Resolution in Reconstruction from Projections” (Lecture Notes in Biomathematics, No. 26). Springer-Verlag, Berlin and New York. Klug, A,, and Crowther, R. A. (1972). Nature (London) 238,435-440. Kuhl, D. E., and Edwards, R. Q. (1963). Radiology 80,653-661. Kwoh, Y. S., Reed, I. S . , and Truong, T. K. (1977). IEEE Trans. Nuclear Sci. NS-24(S), 19901997. Lakshimarayanan, A. V. (1975). Reconstruction from Divergent Ray Data. Tech. Rep. 92, Dept. Comput. Sci., State Univ., New York, Buffalo. Lawson, C. L., and Hanson, R. J. (1974). “Solving Least Squares Problems.” Prentice-Hall, New York. Levitan, E., Degani, J., and Zak, J. (1979). IEEE Trans. Nuclear Sci. NS-26 (3). 4327-4329. Lewitt, R. M., Bates, R. H. T., and Peters, T. M. (1978). Optik 50 (2), 85-109. Mersereau, R. M. (1976). Comput. Biol. Men. 6, 247-258. Mersereau, R. M. (1979). Proc. IEEE 67 (6), 930-949. Mersereau, R. M., and Oppenheim, A. V. (1974). Proc. IEEE62 (lo), 1319-1338. Mueller, R. K., Kaveh, M.,and Wade, G. (1979). Proc. IEEE 67 (4), 567-586. Norton, S. J., and Linzer, M. (1979). Ulfrasonic Imaging 1 (2), 154-184.

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Olendorf, W. H. (1961). IRE Trans. Bio-Med. Electron. BME-8,68-72. Papoulis, A. (1977). “Signal Analysis.” Wiley, New York. Peters, T. M., and Lewitt, R. M. (1977). J . Comput. Assist. Tomog. 1, 429-436. Peterson, D. P., and Middleton, D. (1962). In$ Control 5,279-323. Pratt, W. K. (1978). “Digital Image Processing.” Wiley, New York. Pridham, R. G . , and Lindgren, A. G. (1978). IEEE Trans. Nuclear Sci. NS-25 (I), 866-874. Radon, J . (1917). Ber. Verh. Saechs. Akad. Wiss. 69, 262-277. Ramachandran, G . N., and Lakshminarayanan, A. V. (1971). Proc. Nail. Acad. Sci. U.S.A. 68,2236-2240. Rattey, P. A. (1980). Two-Dimensional Signal Processing and the Radon Transform. M.S. Dissertation, Univ. Rhode Island, Kingston. Rattey, P. A., and Lindgren, A. G . (1980). Sampling the 2-D Radon transform with paralleland fan-beam projections. Tech. Rep. Dept. Electrical Engineering, Univ. Rhode Island, Kingston. Rattey, P. A., and Lindgren, A. G. (1981). IEEE Trans. Acoust., Speech, Signal Processing ASSP-29 (5). Rowland, S. W. (1979). In “Image Reconstruction from Projections” (G. T. Herman, ed.), p. 9. Springer-Verlag, Berlin and New York. Rowley, P. D. (1969). J . Opt. SOC.Am. 59, 1496-1498. Scudder, H. J. (1978). Proc. IEEE 66 (6), 628-637. Shepp, L. A,, and Kruskal, J. B. (1978). Am. Math. Mon. 85 (6), 420-439. Shepp, L. A,, and Logan, B. F. (1974). IEEE Trans. Nuclear Sci. NS-21 (3). 21-43. Smith, K. T., Solomon, D. C., and Wagner, S. L. (1977). Bull. Am. Math. Soc. 83 (6), 12271270. Stuck, B. W. (1977). J . Opt. SOC.Am. 67 (9,668-678. Susskind, C. (1980). Proc. IEEE 68 (I), 3. Taub, H., and Schilling, D. L. (1971). “Principles of Communication Systems.” McGraw-Hill, New York. Tretiak, 0. J. (1978). J . Comput. Assist. Tomog. 2,477-480. Verly, J.G., and Bracewell, R. N. (1979). J . Comput. Assist. Tomog. 3 (5). 662-678. Wang, L. (1977). IEEE Trans. Comput. C-26,264-268. Willis, J. R. (1970). Inf. J . Eng. Sci. 8, 559-574.

ADVANCES I N ELECTRONICS A N D ELECTRON PHYSICS. VOLUME 56

Spectroscopy of Electrons from High-Energy Ion-Atom Collisions D. BERENYI Insrirure of Nuclear Reseclrch of rhr Hungarian Acudemy of Srienrrs (ATOMKO),Debrewn, Hunguri.

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 A. Scope and Significance of the Field . . , , . . . . . . . . . . . . . 411

B. Subject of the Present Review . . . . . . . . .

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

11. A Brief Survey of Instrumentation and Basic Concepts of Collision Mechanism . . . A. Instruments and Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B. Basic Concepts of Collision Interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Projectiles of Intermediate Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Light Projectiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. Heavy Projectiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

IV. High-Energy Projectiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Closing Remarks . . . . . . . ....................... ......... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

413 414 414 41 5 41 7 418 428 432

431 438

I . INTRODUCTION A . Scope and Significance of the Field

The field of ion-atom collisions is very broad. The bombarding energy itself can range from several eV up to the GeV region, and the projectiles can be electrons or ions ranging from the lightest elements (proton, deuteron, etc.) up to multiply ionized uranium. In order to study the collision process. several parameters can be measured in principle: the energy, charge state, and excitation state of the projectiles; the energy, charge state, excitation state, and angular distribution of the scattered projectile and those of the recoil target atom; and the electrons and electromagnetic quanta emitted during the collision process itself and after the collision in the rearrangement of the electron cloud of ions or atoms (X rays, light photons, Auger electrons). Coincidence relations between these particles may also be observed in studying collision processes. Research activity is also very intensive with regard to these phenomena, which is exemplified by the size of the series of International Conferences on Physics of Electronic and Atomic Collisions (ICPEAC) first held in New 41 1 Copyright mi" 1981 by Academic Presb. Inc All rights or reproduction in any form reserved.

ISBN 0-12-014h5~-X

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York (1958). Figure 1 shows the number of papers that have been presented at these meetings. Such interest in these phenomena is quite understandable if we bear in mind that, as far as we know, the majority of the matter in the universe exists in the form of ions. Research in the medium and the high energy regions of impact particles is prompted by several basic and applied reasons. It is impossible to understand a number of phenomena in astrophysics, in the upper atmosphere, without the knowledge of ion-atom collision processes. One can also expect important fundamental information, e.g., on the validity of quantum electrodynamics in strong fields, from the collision of ions and atoms of very high atomic number. At the same time, it is essential to know the ion-atom collision processes, e.g., in plasma physics and controlled thermonuclear research (the importance of high-energy ion-atom collisions is increasing here; see e.g., Gilbody, 1979; and Godlove, 1979), in energy deposition phenomena, and the issues of stopping power, dosimetry, and radiation damage of biological systems, as well as in various contemporary analytical applications. At any rate, in the first decades of this century, the phenomena and changes in the domain of valence electrons or those in the domain of an atom with at most one vacancy in the inner shells were regarded as atomic physics.

i

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n 5 W v) In Q: L

! Z

w

3

v)

E P Y FIG.1. The number of papers presented at the series of ICPEAC meetings [data from Barat and Reinhardt (1977); and Takayanagi and Oda (1979)l.

SPECTROSCOPY OF ELECTRONS

41 3

Now, by using all the techniques of nuclear physics, it is possible to study multiply ionized and highly excited atoms (e.g., hydrogen-like Ne, i.e., a neon nucleus with one electron around it, or lithium-like Ar, an argon nucleus with three electrons in its atomic cloud). It is also possible to observe transitions and processes in atoms which could not be observed before. At the same time, one can investigate the collision mechanism in the various energy regions. This is the present-day atomic physics which has become once again one of the most flourishing fields in physics.

B. Subject o j t h e Present Review

It is impossible to survey the whole field in the limits of the present review. We will focus on the light and heavy ion projectiles of higher (medium and high) energy (roughly greater than 10 keV/amu in order of magnitude) and on the investigation of the spectra of electrons being emitted from the collision (continuous spectrum) or during the rearrangement in the electron clouds just after the collision (Auger and autoionization lines). That is to say, we will limit ourselves to the study of electrons from ion-atom collisions. The study of electrons from solids at ion impact is also a very broad field which will not be regarded in the present survey (for high-energy projectiles see, e.g., Folkman, 1975; Groeneveld, 1976; Pferdekamper and Clerc, 1977). It should also be mentioned that the range of bombarding energies from about 10 to 100 keV is sometimes classified as the medium energy region. The beam-foil phenomena, however, will be not included. If some early works are disregarded, the investigation of ion-atom collisions began with the study of X rays in the early 1960s (see. e.g.. in Kessel and Fastrup, 1973; or Richard, 1975). Just after that the study of the electrons from these collision processes also began (Kuyatt and Jorgensen, 1963; Rudd and Jorgensen, 1963). In these first works, however, the energy of the impact protons was relatively low (from 50 to 150 keV). Similar experiments with heavy ions were carried out first at the University of Connecticut (Kessel and Everhart, 1966)with an argon projectile up to 400 keV and at the University of Nebraska (Rudd et al., 1966) with argon in the region from 100 to 300 keV. The study of electron spectra from collisions with projectiles of higher energies became a topic of research only in the 1970s, for example, with protons up to 1.7 MeV by Toburen (1971) and with heavy ions (0”) of 30 MeV by Burch et a/. (1972). See details in the original papers and in earlier surveys on the study of electrons from ion-atom collisions (Rudd and Macek, 1973; Rudd, 1975; Stolterfoht, 1976a,b, 1978; Berenyi, 1979; and Toburen, 1979a).

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It is worthwhile to mention here the advantages of studying electrons from ion-atom collisions, because the techniques of electron spectroscopy are more difficult than those of X-ray spectroscopy in general. 1. It is possible to study prompt electrons directly from the collision (ejected electrons) and thereby to have direct information on the collision process. 2. Selection rules for transitions by Auger electrons are different from those for transitions by X rays. 3. The Auger transitions are more sensitive for vacancies in outer shells than are X-ray transitions (satellite structure !). 4. In the cases when fluorescence yield is low (at low atomic number or outer shells at higher atomic number), the investigation of Auger electrons is practically the only way to study the ionization process. 5 . In some cases the resolving power in Auger spectrum is much higher in general than that in X-ray spectrum, sometimes by orders of magnitude.

Thus, the importance of this field within the whole field of ion-atom collision physics is quite understandable. In the present review Section I1 is devoted to a brief survey of the instruments and techniques as well as the basic concepts ofthe collision mechanism. The results in the field will be treated in two main sections : Section I11 for projectiles in the intermediate energy region (from about 10 to 100 keV/amu) and Section IV for the higher energy (greater than about 100 keV/amu) projectiles. OF INSTRUMENTATION AND BASICCONCEPTS 11. A BRIEFSURVEY OF COLLISION MECHANISM

A . Instruments and Techniques

To investigate electrons from ion-atom collisions with high energy projectiles, two instruments are essential. These are the accelerator, which provides the beam of projectiles, and an electron spectrometer to observe the spectrum of electrons emitted from the individual collision events. In the energy range of the projectiles of interest here the source of the beam is a nuclear accelerator: Van de Graaff, tandem, and, e.g., the UNILAC in Darmstadt, or at the lower domain only, some type of ion source or heavy ion accelerator of low energy. The range of the spectrum of the electrons studied is mostly in the region from several eV to several keV [the higher energy spectrum up to several

SPECTROSCOPY OF ELECTRONS

415

hundred keV was studied only in a few cases (e.g., Kozhuharov et al., 1977; Bosch et al., 1978; McClintock et al., 1979) using magnetic spectrometers]. In this spectrum range, electrostatic electron spectrometers were used practically without exception. These spectrometers are more flexible, and shielding them from a disturbing magnetic field is rather simple. There are several types of electrostatic spectrometers, e.g., the spherical condenser, the cylindrical mirror analyzer and its different versions (see some details, e.g., in Berknyi, 1976), and the frequently used parallel-plate analyzer, which was first constructed by Harrower (1955) with a rather broad variance of precision and resolving power (from about 1 to 0.01% in orders of magnitude). Differentiallypumped gas-scattering cells or gas beams ejected from a gas jet (with target gas pressures of about 10-2-10-3 Torr) were used as targets. The base pressure in the system and in the analyzer chamber was about 3-4 orders of magnitude lower than that in the target region. In some studies, however, solid foil targets were used (e.g., Musket and Bauer, 1973;Groeneveld, 1976; Schumann et al., 1979). Magnetic fields inside the apparatus are reduced to a few milligauss by Helmholtz coil systems or more frequently by shielding with soft magnetic material. To operate the apparatus and to carry out measurements, power supplies and different electronic units are necessary to form, record, and evaluate the data. The control and evaluation of the measurements are usually performed with an appropriate computer. The energy and efficiency calibration of the system (including the determination of the numbers of atoms or molecules in the target region) is very important for accurate measurements. Different calibration procedures were employed, e.g., the use of a monoenergetic electron source with known emission rate per solid angle (Stolterfoht, 1971a), normalization to elastic scattering measurements (McKnight and Rains, 1976a,b), comparing the continuous electron spectrum at p-H, collisions with “standard” spectrum (Matthews and Hopkins, 1978), and using absolute KLL or LMM Auger yields for comparison (Matthews et al., 1974b; Stolterfoht et al., 1975). B. Basic Concepts of Collision Interaction

In the above-mentioned surveys and in several other papers (e.g., Bell and Kingston, 1974; Madison and Merzbacher, 1975; Hansteen, 1975; Moiseiewitsch, 1977; Briggs and Taulbjerg, 1978) fairly detailed reports are available on the theoretical interpretation of the excitation-ionization mechanism during ion-atom collisions. Here only the main types of excitation (ionization) will be outlined.

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First, the direct Coulomb excitation is an interaction between the Coulomb field of the projectile and one of the electrons of the target atom. In this approximation only one electron of the atom takes part in the collision, with the rest of the atom (the other electrons and the nucleus) supplying only the binding energy of the electron concerned. The three most important approximate calculations, according to this model, are PWBA (plane-wave Born approximation ; see e.g., Merzbacher and Lewis, 1958), SCA (semiclassical approximation; Bang and Hansteen, 1959), and BEA (binary encounter approximation ;e.g., Gryzinski, 1965). The validity of the models depends on the velocity of the projectile up and the atomic number of the projectile 2, and the target atom 2,. The cross section data for excitation can be interpreted by the direct Coulomb mechanism if the projectile is relatively fast (its velocity is high enough to that of the orbiting atomic electron in question, i.e., A = up/z), 2 1) and/or the Z,/Z, ratio is small (see Fig. 2). In the lower velocity region, 1 c 1, and for heavy ion projectiles, however, the molecular orbital (MO)description (quasi-molecular concept) of the collision mechanism is in operation. According to this model a temporary molecule forms as the projectile and the target atom approach each other. Here the ionization-excitation is produced owing to electron promotion via the MO model (see Fano and Lichten, 1965). Figure 2 shows schematically the regions of validity for the PWBA, SCA, and MO models in the case of K-shell ionization.

’P “K

FIG.2. The approximate regions of validity for the direct Coulomb interaction and for the molecular promotion model of the collision mechanism. For the designations in the figure see the text. [After Madison and Merzbacher (1973.1

SPECTROSCOPY OF ELECTRONS

41 7

Multiple ionization is an important and frequently used process especially in heavy ion collisions, and much experimental data have been obtained on this phenomenon. Theoretical works about this subject, however, are rather sparse (McGuire and Richard, 1973; Hansteen and Mosebekk, 1972). For protons and especially for bare heavy projectiles (but also for nearly stripped impinging ions), the ionization of target atoms by electron capture mechanism becomes important. The higher the projectile atomic number is, the more important this capture mechanism becomes (Lapicki and Losonsky, 1977). If the projectile itself has electrons, the projectile will be partially screened by them. As a result, an effective charge will be produced for the projectile, which, however, will depend on the impact parameter, the collision energy, etc. At the same time, the same models will be valid for the excitation of the projectile as for the target, in the frame of reference of the projectile. Thus, e.g., the electron spectrum taken in the laboratory frame will be the superposition of the electrons from the target and from the projectile (including the ejected electrons and the Auger electrons in both cases), taking into consideration the kinematic and velocity transformation effects for the electrons from the moving projectile ion (Drepper and Briggs, 1976). To study the ionic-atomic states produced in the collision processes, theories and models for de-excitation mechanisms including those for multiply ionized atoms and various complex mechanisms (e.g., double Auger process) should be used. For information in this regard for radiative transitions (X rays) see, e.g., Scofield (1975); and for Auger, CosterKronig, as well as autoionization transitions see, e.g., McGuire (1975) and Mehlhorn (1978).

111.

PROJECTILES OF

INTERMEDIATE ENERGY

The results for projectiles in the medium energy region will be surveyed in two subsections. In one subsection the processes brought about by light bombarding ions (various hydrogen and helium ions) are dealt with, and in the other those by ions with atomic number Z 2 3. Light projectiles are regarded here to be in the medium (intermediate) energy region if their energy is in the interval from about 100 keV to several MeV, which is the range of the smaller accelerators for nuclear physics. Otherwise, in this whole interval the direct Coulomb interaction mechanism is prevalent (see Section 11,B).At the same time, however, electrons from ion-atom processes with light projectiles have not been studied at bombarding energies higher than 10 MeV to my knowledge. In the higher impact energy region, studies were carried out only with detection of X rays (e.g., Jarvis et al., 1972;

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Anholt et al., 1976; Ishimaru et al., 1979).For heavy ions the medium energy region means the energy region very approximately from 10 to 100 keV/amu, that is, e.g., for lithium from about 100 keV to 1 MeV, for neon from about 200 keV to 2 MeV, and for argon from about 400 keV to 4 MeV. It is also the region of the smaller nuclear accelerators, and the interaction mechanism is described here in general by the quasi-molecular concept. A . Light Projectiles

There are electrons from ion-atom collisions which are promptly ejected in the collision process itself. They have a continuous spectral distribution with a rough structure with broad peak(s) and valley(s). The monoenergetic Auger (autoionization) peaks are emitted after the collision process when the vacancies produced in the collision are being filled. In spite of the fact that the electrons of two different origins appear in the same spectrum, the results for the two phenomena will be treated here in two separate subsections. 1. Prompt Electrons The first measurements for the electrons of continuous spectrum from a light ion impact on atom (molecule) process were published in 1963 from the University of Nebraska (Kuyatt and Jorgensen, 1963; Rudd and Jorgensen, 1963), where H, and He gas targets were bombarded by protons of 50-150 keV. The differential cross sections (based on the energy spectra of the electrons at different emission angles)were measured at angles of 10-160”. Such studies have been carried out more intensively from the early 1970s up to the present. These measurements are shown in Table I. A double differential (in energy and angle) spectrum has, first of all, a broad peak (BEP = binary encounter peak) at an energy EBEp= 4(Ep/1)COS’ 9

(where Ep is the projectile energy, I the projectile mass in electron mass units, 9 the electron emission angle relative to the projectile direction) that is produced by direct binary encounter between the projectile and one electron (mostly outer; see, e.g., Toburen and Manson, 1979) of the target atom (Fig. 3). Collisions of larger impact parameters, however, produce a continuous tail up to the increase of the intensity at the lowest energies (“soft” collision). In the case of the simplest collision systems where helium targets are bombarded by protons, the most thorough studies were performed. With the collaboration of four different laboratories the double differential cross

SPECTROSCOPY OF ELECTRONS

419

FIG.3. Spectra of electrons emitted for relatively simple collision systems, at 42.3" emission angle.

sections (DDCS) were measured in a rather broad energy range (from 5 keV to 5 MeV) of the incident protons at nine emission angles of the electrons in the energy range from 1 to 8600 eV (Manson et al., 1975; Rudd et al., 1976). (A similar collection of data was published recently for p-Ar collision by Rudd et al., 1980b.) It was found that the electron spectra measured at different laboratories were in good agreement except in the lowest energy region, below about 10 eV. Here some deviations from the theory (relativistic PWBA) for DDCS (observed in other cases also) were confirmed, e.g., for small angles of electron ejection. If the projectile also has electrons ( H i and He' are the most simple cases of this type), a new broad peak, the so-called electron loss peak (ELP), will appear in the electron spectrum (see Fig. 3). This peak, which centers on the electron energy, corresponding to the projectile velocity (u, = up), originates from the ejection of the projectile electrons by collision with the target. (It is the same process in the projectile frame which caused the BEP in the target frame, i.e., a binary encounter between the target nucleus and one of the electrons of the projectile.)

TABLE I

STUDIESON PROMPTELECTRONS AT LIGHTPROJECTILEIMPAC? Emitted electrons

Projectile

8

H+ H+ H+ H+ H+ H+ H+ H+ H:

H+ H+

Preliminary energy 50-100 keV 50- 150 keV 100-300 keV 200-500 keV 200-500 keV 0.3-1.7 MeV 50-300 keV 0.3-1.5 MeV 0.6-1.5 MeV 0.3-2.0 MeV 0.3-2.0 MeV

Target

Angle(s) of observation Spectrum (degrees) range (eV) 23-152 10-160 10-160 18-155

20- 150 20- 130 10-160 20- 130 20- 125 20-1 30 20- 130

4-250 1-500 2-700 1-loo0 1-1300 5-4O00 1.5-1057 5-1500 5-1700 3- 1500 4-5000

References Kuyatt and Jorgensen, 1963 Rudd and Jorgensen, 1963 Rudd et al., 1966 Stolterfoht, 1971a Stolterfoht, 1971b Toburen, 1971 Crooks and Rudd, 1971 Toburen and Wilson, 1972 Wilson and Toburen, 1973 Toburen, 1974 Wilson and Toburen, 1975

H+ H+ H’ H+ H+ H + , H:, He+, He2+ H+ H+ H + , He+, HeZ+ H+ H+ H i , He+ H+ H+ He+, He2+ He+, He2+ H + , H:, He+ H0

0.25-2.0 MeV 0.1-5.0 MeV 5 keV-5.0 MeV 5- 100 keV 5- 1500 keV 0.75 MeV/amu 0.25-2.0 MeV 0.3- 1.5 MeV 0.3 Meviamu 1.0 MeV 0.1-1.5 MeV 1.O MeV/amu 5-100 keV 4.2 MeV 0.3-2.0 MeV 0.3-2.0 MeV 0.8 Meviamu 15- 150 keV

N 2 , Ne, Ar, Xe He He He Ar

N2 CH,, NH,, CH,, NHZ, (CH3)zNH Hz 0 2 , HzO He, Ne, Ar Kr He, Ne, A r H 2 , He Hz, Nz Kr Ar H2O H 2 , He He 9

30-150 10-160 10-160 10-160 30- I45 90 15-125 15-125 15-125 15, 90 15-125 30-140 10-160 30 15- 125 15-125 42.3 10-160

0.3-250 0.3-1 166 1-8600 1.5-300 1-1600 20-520 1-2500 5-5000 2-600 1-3000 I -600 20-1000 1.5-300 100-500 I .5-1500 4- 1500 50-2000 1.5-300 ~

Toburen and Wilson, 1975 Manson et al., 1975 Rudd et al., 1976 Rudd and Madison, 1976 Criswell et al., 1976 McKnight and Rains, 1976a Lynch et al., 1976 Toburen and Wilson, 1977a Toburen and Wilson, 1977b Manson and Toburen, 1977 Toburen et al., 1978 Oda and Nishimura, 1979 Rudd, 1979 Toburen, 1979b Toburen and Wilson, 1979 Toburen et al., 1980 Kovkr et al., 1980 Rudd et al., 1980a _________

Papers especially devoted to the investigation of the “cusp” in the electron spectrum around zero degree (see Section III,A,l) are not included.

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The ELP was observed for the first time in H i -H, collisions by Wilson and Toburen ( I 973) and in the same year by Burch et al. (I 973) in heavy ion collision processes. Corresponding theoretical considerations were published by Drepper and Briggs (1976). Very few further studies on ELP were carried out even when heavy ion bombardments were regarded (see Section IILB, 1). Recently, the main characteristics of ELP were measured and compared with theoretical calculations for H: and He’ projectiles at Atomki, Debrecen (KovCr et al., 1980). In the above and in some other measurements (e.g., McKnight and Rains, 1976a; Toburen and Wilson, 1977a,b; Oda and Nishimura, 1979; Toburen et al., 1980) the so-called 2’ rule (the electron spectrum intensity and the DDCS, respectively, changes as Z z of the charge of projectile 2, according to Coulomb ionization) and the screening conditions brought about by the electrons carried by the projectile on ionization (i.e., DDCS) were studied (see, e.g., Fig. 4). Finally, the “cusp” at around zero-degree electron emission angle should be mentioned in connection with the prompt electron spectra. At these spectra in a forward direction a very intensive and pronounced peak has appeared at electron energies corresponding to the projectile velocities UH; -

T

dH+

Hf-He H+-He

.... .... .*

ZOO

400

600

800

ENERGY OF E M I T T E D

.-me-.

I

1000

--

1200

1400

E(eb

ELECTRONS

FIG.4. Check of the so-called 2’ scaling rule on ionization in ion-atom collisions. It can be seen in the figure that the 2’ rule is not valid for Hi.This projectile may be regarded as two protons.

SPECTROSCOPY OF ELECTRONS

423

(u, = up), even in the case of incident protons or other bare nuclei. Although

there have been relatively numerous studies on this cusp, only a qualitative and not quantitative interpretation has been attained by “charge transfer to continuum states” (CTC) theory (Macek, 1970), according to which the projectile carries along an electron captured in its continuum states for a time and then emits it in the projectile frame. Recent surveys have dealt with the cusp problem (Sellin, 1979a,b),and there have been some recent experimental and theoretical studies (Duncan and Menendez, 1979; Sellin e f al., 1979; Vane et al., 1979; Menendez and Duncan, 1979; Garibotti and Miraglia, 1980).

2. Auger Electrons The monoenergetic lines in the spectrum of electrons (superimposed on the continuous distribution of prompt electrons in general) from ion-atom collisions originate from the rearrangement of the excited (ionized) atoms 10-’3-10-16 sec after the encounter by Auger and autoionization processes. In the case of light ions of higher energy, the structure of the spectrum is the same as that for electron impact; i.e., it consists of diagram lines and shake-off as well as shake-up satellites (Fig. 5 ) if the projectile velocity is large relative to the orbital velocity of the electronic shell concerned. The diagram lines indicate that there is only a single vacancy in the excited atom. The shake-off (or -up) satellites are produced when an atomic electron is excited into one of the upper unfilled levels (or into the continuum) in addi-

ELECTRON ENERGY

(eV1

FIG.5. K-shell Auger electron spectrum of Ne at 4.2-MeV proton impact. The diagram

(D)and satellite lines are indicated in the figure. [After Stolterfoht er al. (1973b).]

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d.2

' 0.5'

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I 2 ENERGY/MASS (MeV/amu) I

I 10

I

-

l

l

5

I 10

VELOCITY

FIG.6. Relative satellite line intensities for Ar and Ne at proton ( 0 )and electron impact ( 0 ) .[From Schneider el al. (1976ab.l

tion to the inner shell vacancy (for details see, e.g., Mehlhorn, 1974, 1976; Stolterfoht, 1976a). The relative intensity of the satellite to the diagram lines, however, at light ion impact depends on the bombarding energy. If the impact energy is relatively low, then a richer satellite structure (i.e., not only shake-off and -up satellites) will be produced because of the multiple ionization. Figure 6 shows, e.g., that the satellite-to-total ratio (the total is the sum of the intensities of the satellite and diagram lines) for protons has the same low value as that for electrons only at the higher impact energy region. As can be seen in the figure, at the same projectile velocity the satellite intensity depends on the target atom species, and similarly on the projectile (e.g., p, H i , or He+, etc.) species as well. The fluorescent yield mi,which gives the probability that a vacancy will be filled by an X-ray transition (i.e., wi = N,/(N, + N,), where N A and N , are the number of transitions with Auger electron and X-ray emission, respectively, if the vacancy is on shell i), also depends on the species of the projectile having the same velocity (i.e., impact energy per nucleon = keV/amu; see Fig. 7). Since the fluorescence yield for the K-shell of the light elements ( Z 10) and for L-shell of the somewhat heavier elements (ca. Z < 40) is less than 2% (e.g., Bambynek et al., 1972), i.e., vacancies are filled by Auger transition to nearly loo%, the ionization cross section can be determined in these cases with the help of the Auger spectra if we neglect the small correction for the X-ray emission. Therefore, numerous measurements were carried out for the determination of the total ionization cross section for the K-shell of the light elements and for the L-shell of the somewhat heavier elements by integrating the con-

-=

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0 A

w> W

V Z

yj

10

u) W

a

0

3

lL

H+

I

50

I I I 100 2 00 500 ION ENERGY /AMU (keV/amu)

00

FIG.7. Mean fluorescence yield a,. as a function of the projectile velocity for different projectiles (Stolterfoht er d.,1973a).

cerned region of the Auger spectra (see Table 11). The determination of these cross sections in this way is based on the isotropic emission of K-shell Auger electrons and the nearly isotropic emission of L-shell Auger electrons (Stolterfoht, 1973; Stolterfoht et al., 1974a; Kobayashi et al., 1979a).At the same time, the intensity of the continuous spectra of prompt electrons decreases with an increase of emission angle, especially for angles higher than 90". For that reason Auger spectra are measured at 90" or at higher angles. I should mention in connection with the cross section measurements that in general the agreement with theory (BEA, corrected PWBA, e.g., Basbas et al., 1973) is not satisfactory. By studying ionization cross sections their projectile Z 2 dependence can be checked. Figure 8 shows the deviation from the Z z rule, and it also shows that these deviations are not explained by the theoretical calculations of Basbas and associates (1973). Otherwise, the molecular effects, i.e., the dependence of the cross sections on chemical species of the target, have also been verified (Chaturvedi et al., 1977; Matthews and Hopkins, 1978). Finally, Cocke and associates' (1977) experiment is worthwhile mentioning, in which Auger electrons from proton on 0, , N, , and Ne processes at

TABLE I1

STUDEXON AUGER(AUTOIONIZATION) ELECTRONS AT LIGHTIONIMPACT ~____

~

~

Projectile

H+

ft H + , H e t m

H+, H : H+ D', He2+ H + , H:, He+ H+ H', H:, He, He+ H+, D', H:, He+ H+ H+ H+

Primary energy

Target

Angle(s) of observation (degrees)

75-200 keV

Ar

160

150-25OkeV

Ne

160

125-300 keV 0.3-2.0 MeV 0.15-0.5 MeV/amu 30-600 keV 4.2 MeV 20- 150 keV 50-600 keV 50-500 keV 0.3-2.0 MeV 0.15-6.0 MeV

10-160 90 125

150

10-160 150 18-155 -

90

Measured region of electron spectrum L-shell Auger lines, autoionization lines K-shell Auger lines, autoionization lines L-shell Auger lines K-shell Auger lines K-, L-shell Auger lines L-shell Auger lines K-shell Auger lines Autoionization lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines

References Rudd et al., 1966 Edwards and Rudd, 1968 Volz and Rudd, 1970 Toburen, 1972 Watson and Toburen, 1973 Stolterfoht et al., 1973a Stolterfoht et al., 1973b Schowengerdt et al., 1973 Stolterfoht et al., 1973c Stolterfoht et al., 1974d Toburen, 1973 Matthews et al., 1974a,b

H+ H + , D + , HZ, He' H+,H e + H ' , He+ H ' , He2+

0.3-2.0 MeV 50-600 keV 50-600 keV 100-400 keV 0.5-2.6 MeV

H+

H', He'

0.5-10 MeV 0.3-2.6 MeV 0.4-4.0 MeV 1-5 MeV 2.0,4.0 MeV 4.0 MeV 4.0 MeV 50-300 keV

Xe Ar CH,, N,, Ne Li vapor CO, , N 2 , NO, 0 2 , CCl,, F,, Ne Ne CC1, , F, , Ar Ar N,, SF,, Ne Ar Ar He Li, Na vapor

H+

0.75-5.0 MeV

N,, O,, Ne

H+

0.5, 1.5 MeV

H+

0.5- 1.5 MeV

BF,, CF,, C,F,, SF,, TeF, SF,, CF,. CCl,, H,S, SO2 > CH4

H+,He'+ H+

H+,He' & H+ H' H+

-

150 -

M-, N-shell Auger lines L-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines

Toburen, 1974 Stolterfoht ef al., 1974a Stolterfoht and Schneider, 1975 Ziem et al., 1975 Kobayashi et al., 1976

K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines Autoionization lines 90, 150 K-, L-Auger, and autoionization lines 95-174 ang. range K-shell Auger lines in coincidence, Ho 125 K-shell Auger lines

Woods et a/., 1976 Maeda et al., 1976 Schneider ef al., 1976a McKnight and Rains, 1976b Schneider el al., 1976b Schneider et al., 1976c Burch et al.. 1976 Stolterfoht. 1976a,b

160 (90)

Matthews and Hopkins, 1978

90- 174 ang. range 90 90 90 90 90

K-, L-shell Auger lines

Cocke et al., 1977 Chaturvedi et al., 1977

428

D.

-,,

1.0

BERBNYI

--------__

c

Z theoretical

N

-

./

v

b

-

2

-

U

N

I1

N

b

0.2I

I

I

I

I

I

RED. PROJECTILE VELOCITY

1

I

PARAMETER

-! 3.0

FIG. 8. Ratios for K-shell ionization cross section after Stolterfoht and Schneider (1975). ' , and with Z = 2: He+, He2+.The The projectiles with nuclear charge Z = 1 are H', D dashed curve is indicated only as a guide. The theoretical calculations were carried out for N, and CH, (the curves for these nearly coincide) by Basbas et af. (1973). The reduced projectile velocity parameter is defined in the latter paper also.

0.75-5 MeV impact energy were detected in coincidence with charge-neutralized projectiles. It was found that the K-shell fraction of total electron capture by protons amounts to about 100% at 5-MeV impact energy (at 1 MeV it is much less, largely depending on the target: 7% for Ne, 39% for N). B. Heavy Projectiles

1. Prompt Electrons There are only a few measurements in which the continuous spectrum of electrons ejected in intermediate energy heavy ion on atom collisions were studied. The earliest and more detailed study was carried out by Cacak and Jorgensen (1970). They investigated the electron spectra from several eV to about 300 eV at eight angles (10-160") in Ne+-Ne and Ar+-Ar collisions (50-300 keV impact energy). After a relatively long interval, investigations into this field have started again just recently in two laboratories (Hahn-Meitner Institute, Berlin, and Battelle, Pacific Northwest Laboratory, Richland). In Berlin argon targets ' projectiles in the energy region from 50 were bombarded by N + and 0 to 500 keV, and the electron spectra (from 5 to 500 eV) were measured at several angles from 16 to 160"(Stolterfoht and Schneider, 1979). In Richland, however, the spectra of emitted electrons were studied (for angles from 15 to 130" in the 10-800 eV region) for different targets (He, CH,, Ne, Ar) at 1.2-MeV C+ ion impact (Toburen, 1979b; see also the survey of Toburen, 1979a, where a measurement on the effect of different charge state projectile-C+, C3+-on continuous spectra is mentioned).

SPECTROSCOPY OF ELECTRONS

429

At these projectiles in the intermediate energy region the different structures in the continuous electron spectrum (BE and EL peaks; see Section III,A,l) are not so prominent, and sometimes it is difficult to recognize them. At the same time, some new unexpected structures (bumps) above where the BE peak occurs were observed. The position of these structures is the same at different observation angles, and their intensity increases as a function of the emission angle from 90 to 165" (Stolterfoht and Schneider, 1979). It is quite clear that additional experimental and theoretical investigations are still needed in this field. Above all, detailed systematic studies are lacking. 2. Auger Electrons Around the time when some works were being conducted in which Auger electrons from intermediate energy heavy ion impact on atoms were observed (Kessel et al., 1966, 1967; McCoughey et al., 1968), Rudd and associates carried out the first more detailed studies on Auger and autoionization spectra from intermediate energy Ar', Ne' on Ar, Ne collisions (Rudd et al., 1966; Edwards and Rudd, 1968). In the 1970s a number of works dealt with the study of Auger electrons originated from ion-atom collisions in the intermediate energy heavy ion impact region (see Table 111). The main characteristic of the Auger spectrum in the collisions observed is the presence of Auger lines both from the projectile and the target. At the same time, multiple vacancy production is highly probable under these conditions. In addition, line broadening is also rather large here (larger than it is for light impact ions of intermediate energy and for high-energy light and heavy projectiles) because of kinematic and instrumental reasons (for details see Rudd and Macek, 1973; Stolterfoht et al., 1975; Dahl et al., 1976). As a result of all these effects, broadened and shifted Auger lines will be observed in the spectrum, and in the case of the electrons emitted by the scattered projectile, the value of the shift depends on the angle of emission (Fig. 9). Total ionization cross sections have been determined on the basis of the Auger electron spectra mainly for the K-shell (see Table 111). For the case under study there are, however, two K-shells (those for the same atom in homonuclear-or symmetric-collisions as, e.g., Ne+-Ne or those for different atoms in heteronuclear-or asymmetric-collisions as, e.g., C+-O,). In this way a vacancy sharing ratio can be defined S = odh)/aK(O

where aK(k)and oK(f)are the total K-shell ionization cross sections for the higher and lower Z atom (ion), respectively (for the symmetric case one

TABLE I11 STUDIESON AUGER(AUTOIONIZATION) ELECTRONS AT HEAVYIONIMPACT OF INTERMEDIATE ENERGY"

Projectile

Primary energy

Target

hgle(s) of observation (degrees)

Art

100-300 keV

Ar

160

Ne+

150-250keV

Ne

160

50-300 keV 200-500 keV 45-2250 keV 3.0 MeV 35-600 keV "-3+ ~ ~ 1 - 4 + 50-500 keV ~ ~ 1 - 4 + 50- I200 keV B+, C + , N + , 0 +Ne+ , 40-600 keV N2 2.0 MeV C z + ,N2+,0 2 + 0.75-2.5 MeV c1-3+ Nl-3+ ,0 2 + 0.5-5.0 MeV c1-3+ N1-3+ 0 1 - 3 + 0 4 2 . 5 MeV Li+, Be+, B+, C + 100-500 keV

Ne, Ar Na, Ne, O , , N, Ne He Ar , CH4, N 2 , 0 2 Ne Ne CH,, N,, 02,Ne N2, CO2 BF3 CO2, N2,02 CO2, N2,02 H2 , He, Li, CH,, N,, Ne

10-160 90, 150 30-150 90 20- 160 90 90 30- 160 45-135 90 45-135 0-150

Li '

Ne

I25

Ar+, Ne+ Ne+ Ne', Ne+, Ne2+ CI2 C', N + , 0 ' +

+

15-70 keV 10-100 keV/amu.

-

Measured region of electron spectrum L-shell Auger lines, autoionization lines K-shell Auger lines, autoionization lines K- and L-shell Auger lines K-shell Auger lines K-shell Auger lines Autoionization lines K- and L-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines K-shell Auger lines, autoionization lines Autoionization lines

References Rudd et al.. 1966 Edwards and Rudd, 1968 Cacak and Jorgensen, 1970 Stolterfoht et al., 1974b Stolterfoht el al., 1975 Burch el al., 1976 Stolterfoht et al., 1977a Fortner et al., 1917 Hoogkamer et al., 1977 Schneider and Stolterfoht, 1979 Kobayashi et al., 1979a Kobayashi et al., 1979b Sakisakai et al., 1979 Kobayashi et al., 1979c Redbro et al., 1979 Bisgaard et al., 1980

43 1

SPECTROSCOPY OF ELECTRONS

I

150° p - N e 500

600

700 800 900 1000 ELECTRON ENERGY (eV)

1 1100

FIG.9. K-shell Auger electron spectra of Ne for 500-keV Ne+ projectile and 1.2-MeV H+ at different angles. T indicates the Auger electrons from the target, and P those from the projectile. The instrumental full width at half-maximum (FWHM) is different in the case of the spectra obtained at Ne+ impact from that at p impact. Their contribution to the observed linewidths, however, is negligible in both cases. [After Stolterfoht et d.(1975).]

is the cross section for the projectile and the other is that for the target). For the Ne+-Ne case it was found that the sharing ratio is equal to unity (Stolterfoht eta].,1975). For the general case Fig. 10 shows a very regular behavior for ratio S on a scaled plot. A similar sharing can be defined and studied for the K-and the L-shells of the projectile and the target, respectively (see Stolterfoht et al., 1977a). There are several investigations on charge state dependence of the cross sections (e.g., Stolterfoht et al., 1975; Fortner et al., 1977; Hoogkamer et al., 1977; Sakisaka et al., 1979). Proportionality of the K-shell ionization cross section with the charge state of the projectile was found in agreement with the quasi-molecular theory (Fano and Lichten, 1965; Lichten, 1967). There are, however, serious deviations mainly at relatively higher impact energies

432

D.

$1

BERBNYI

K

-

shell

1

Q

= 10-2

nAZlv (a.u.1

FIG.10. Scaling plot for the K-shell vacancy sharing ratio for different heavy ion projectiles of intermediate energy (O', Ne', NeZ+,F'+) and different targets (Ne, BF,, 0 2 ,CH,). In the plot A 2 is the difference in the atomic numbers of the collision partners, and u is the projectile velocity. A straight line is obtained according to the formalism of Meyerhof (1973). [Plot is taken from Schneider and Stolterfoht (1979).]

(2500 keV) and, e.g., for N + + 0, collision system even at lower impact energies. According to the measurements, the fluorescence yield depends on the projectile energy (Stolterfoht et al., 1975) and the projectile charge state (Hoogkamer et al., 1977), as well as the actual species (2 number) of the impact ion. Finally another work should be mentioned. For N 2 + ion (1.5,2.0 MeV) impact on N, and CO, ,no anisotropy was observed in a broad angle region in the case of K-shell Auger electrons from carbon, nitrogen, and oxygen (Kobayashi et al., 1979a).

IV. HIGH-ENERGY PROJECTILES As indicated in Section I, the projectiles are regarded here as high-energy projectiles if their kinetic energy is higher than about 100 keV/amu. In the following subsections the field of electron emission at high-energy heavy ion impact will be surveyed. In the studies cited, the projectile energy is mostly in the 1-2 MeV/amu region (see Table IV). 1. Prompt Electrons

The general pattern of the electron spectrum is given even here by the continuous energy distribution of the electrons ejected in the collision

TABLE IV. STUDIESON AUGER(AUTOIONIZATION) ELECTRONS AT HEAVY ION IMPACT OF HIGHEN ERG^

Primary energy

Projectile

Target

(-15-151

30 MeV 33 MeV 30 MeV 33 MeV 50 MeV

Ne Ne Ne Ne Ne

0 5 +

33 MeV

Ne

07+ 0 5

+

OS'b

0 6 +

0 5

+

04-8+

1.5 MeV/amu Ne

p-9+

3-35MeV

F3-9+

~

~

1 ~2 ~+ 2

u44 + C2

+

a

xe31+ 5 + ,

Ne

1.4 MeV/amu CH,, CO,, CO, NH,. N,, 0, 18.75MeV Ar

At least 100 keV/amu.

Angle(s) of observation (degrees) 90 90 90 90 90

What was measured

K-shell fluorescence yield K-Auger satellite structure Comp. satellite structure for O6+, 08+ Comp. satellite structure for p. 05+ Fluorescence yield dependence on projectile charge state 90 Satellite structure, satellite to total ratio 90-175 K-shell Auger-electron production cross section 90- 175 K-shell Auger-electron production cross section 90 Autoionization lines 90- 174 Satellite structure hypersatellite production cross section Satellite structure fluorescence yield 90 K-shell Auger-electron production 90-174 cross section Molecular efficiency in K-Auger 155 spectra 90, 128, 155 Satellite structure angular distribution

References (Location) Burch et a/., 1972 (Seattle) Matthews ef a/., 1973 (Austin) Moore er a/., 1974 (Austin) Bhalla et a/., 1974 (Austin) Burch et a/., 1974 (Seattle) Matthews el al., 1974 (Austin) Woods e t a l . , 1974 (Manhattan) Woods etal., 3975b (Manhattan) Burch et a/., 1975b (Seattle-Austin) Woods et a / . , 1975a (Manhattan) Schneider e t a / . , 1976d (Austin) Woods ei a/., 1976 (Manhattan)

Mann efa/., 1976 (FrankfurtDarmstadt) Stolterfoht et al., 1977a,b (BerlinDarmstadt) 120,60- 145 Molecular efficiency in K-shell Auger Mann etal., 1978 (Frankfurtspectra Darmstadt) 1 L Auger spectra in coincident scattered Suter et a/., 1979 (Knoxville-Oak ion Ridge)

434

D. B E R ~ N Y I

process itself. This general picture can be seen in Fig. 1 I with BE and EL peaks (discovered independently by Wilson and Toburen (1973) and by Burch et al. (1973) in the case of light projectiles and 03-*+ impact at energies of 17-41 MeV, respectively; see also Section III,A,l) and with the Auger lines from the target and the projectile. Relatively few papers, however, have been published on this continuous component of the electron spectrum. Stolterfoht and associates (1974a-c) investigated this continuous spectrum and its dependence on angle, projectile charge state, impact energy, and target species (see also Stolterfoht, 1978; and Burch et al., 1975a). All of these studies, however, were carried out only at oxygen ion impact and they are rather qualitative in character. At light ion impact the continuous spectrum above the BE peak has not been studied. At heavy ion bombardment, however, there are some investigations of the high-energy region of the spectrum. In three papers the spectrum was measured from 36 to 400 keV for oxygen, sulfur, nickel, and bromine projectiles of high energy in a broad Z region of targets and partly in a broad angular range, using the techniques of magnetic spectroscopy (Kozhuharov et al., 1977; Bosch et al., 1978; McClintock et al., 1979). Relatively the best agreement seems to be with the relativistic Born calculations, but considerable deviations also have been found.

FIG. 11. Electron spectra (cross section x electron energy) at 30-MeV 0 ' ' impact at different emission angles (Stolterfoht et al., 1974).

SPECTROSCOPY OF ELECTRONS

435

Some of the recent works on the “cusp” in the electron continuous spectrum in forward direction (see Section III,A,l) were carried out (including coincidence measurements between the scattered projectile of different charge state and the electrons) by fast heavy bare or highly ionized projectile impact (e.g., Vane et al., 1978, 1979; Sellin etal., 1979). A complete interpretation and explanation of the phenomenon, however, is still lacking. 2. Auger Electrons First of all because of the multiple ionization, a very dense satellite structure characterizes the Auger spectrum from collisions with high-energy heavy ion impact. This and the kinematic effect result in a broader distribution in addition to a series of discrete K Auger lines (see Fig. 12). The mean energy to be assigned to this distribution (centroid) decreases as the number of vacancies increases in the higher shell (L-shell). From the measurement of

-. .

7-p-7-p~I

7

Ne AUGER SPECTRA F *’

(25 MeV1

FIG. 12. Ne K-shell Auger electron spectra at F impact of different charge states and at proton impact. [After Woods et al. (1975a).]

436

D.

BERBNYI

the centroid energy, the mean number of L vacancies, simultaneously produced with the K vacancy, can be determined (Matthews et al., 1974a; Stolterfoht et af.,1974d; see also Stolterfoht, 1976a,b). For sufficiently heavy projectiles of high enough velocity, the line broadening effects are avoided (i.e., the energy transfer to the target atom by recoil is sufficiently low). Under these conditions, the outer shells are largely stripped and so the number of states will be limited. As a result of the above two effects, the Auger spectrum is composed of relatively few lines, i.e., the spectrum will have a relatively simple structure again. This was demonstrated in the collision of 200-MeV Xe31+ with an Ne target (Stolterfoht et al., 1977b). In this measurement a significant anisotropy was also observed in the emission of Auger electrons, showing the alignment of the target atom in the collision process (i.e., the different populations of the magnetic quantum sublevels). A number of published papers deal with the satellite structure of the Auger spectrum, showing first of all the changes of the general pattern (shift) of the spectrum depending on the species of the impact ion (Schneider et al., 1976a-d) or its charge state (Moore et al., 1974). In other works the energy of the lines (mostly satellites) and their relative intensities also were determined with configuration assignment (Matthews et al., 1973, 1974b; Bhalla et al., 1974). Woods and associates (1975a) studied the dependence of satellite structure on the charge state of the projectile (Fig. 12). If the projectile is a bare nucleus (F”), a new peak, the so-called hypersatellite can be observed here at about 910 eV, originating from Auger transitions in Ne with double K-shell vacancies in the initial state. The cross sections for the production of these hypersatellites were also determined. This amounts to about 5% of the corresponding total K-shell Auger electron production cross section. In these measurements and in most of the following, Ne atoms were used as targets (see Table IV). Burch et al. (1975b), however, studied the autoionization lines of He in 30-MeV 0 5 +on He collisions (Burch et al., 1975a,b). There are several papers on fluorescence yield (all for the K-shell of Ne) which changes with the species, energy, and charge state of the projectile. An especially drastic increase can be observed in wK as a function of the charge state of the impact ion because of the increasing probability for higher-grade multiple ionization (more outer shell electrons will be ejected). So, the wK which is less than 2% for single vacancy in the K-shell of Ne will increase, e.g., to about 40% for Cl15+ impact (see Burch et al., 1972, 1974; Matthews et af., 1974a; Stolterfoht et af.,1974d). Some works were carried out directly for Ne K-shell Auger electron and vacancy production cross section measurements and the study of the dependence of the cross section on projectile energy and charge state (Woods

43 7

SPECTROSCOPY OF ELECTRONS

et al., 1974, 1975a,b). The most detailed study on these cross sections on vacancy sharing was published in 1976 (Woods et al., 1976) for N4-’+, 0 4 - 8 i F3-9+ , C17 - 1 3 + on Ne. The calculations on molecular orbital theory predict the results here fairly well. Groeneveld and associates (Mann ef al., 1976, 1978) bombarded different molecules (CH4, C2HZ,CO,, et al.) with heavy ions (Ar’”, Kr’”, xe31+ u44i ) for the first time. In the case of N, , C,H, ,and similar mole, cules a “Coulomb explosion” was observed with a substantial increase in the corresponding Auger linewidth owing to the nuclear repulsion between the atoms of nearly the same mass of the target molecule which are highly ionized in the collision process (Mann et al., 1976, 1978). Finally, it should be mentioned that the measurement were made of the K-Auger spectra in coincidence with the scattered projectiles (Cqi, Oq+) of different charge state. Experiments of these types can yield direct information on the cross sections of a number of single and multiple electron excitation and ionization processes (Sellin, 1979b; Suter er al., 1979). 3

V. CLOSING REMARKS

In the earlier sections, an important part of the continually growing field of ion-atom collisions was briefly surveyed, namely, the investigations on electrons from these processes. On the basis of the present survey, it seems to be quite clear how open the field is and how many problems there still are to be investigated. There are, e.g., relatively few measurements on the continuous spectra of prompt electrons ejected in heavy ion projectile on atom collisions, and practically no systematic quantitative study has been carried out on the features of the electron loss peak in this continuous spectrum. Even for light ion projectiles, the highest impact energy for which measurements were published is 10 MeV. In regard to the theoretical interpretation of the phenomena, substantial disagreements are reported for medium-energy relatively light heavy ion (Cz+,N z + ,etc.) impact K-shell excitation cross sections or in the identification of the lines in fast heavy ion impact collisions (200 MeV Xe3 on Ne), to name only a few concrete problems. Further experimental and theoretical efforts in this field are necessary and well justified. +

ACKNOWLEDGMENTS The author wishes to thank Dr. T. Mukoyama, Kyoto, for his valuable comments in reviewing the manuscript during his stay at Atomki, Debrecen.

438

D.

BERBNYI

The author is also indebted to the following copyright owners for permission to reproduce certain diagrams or some part of them: Academic Press, New York (Fig. 2); The American Physical Society, New York (Figs. 7-12); North Holland Publ. Co., Amsterdam (Figs. 3-6); and to the authors of the corresponding papers.

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SPECTROSCOPY OF ELECTRONS

439

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442

D. BERBNYI

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Author Index Numbers in parentheses are reference numbers and indicate that an author’s work is referred to although his name is not cited in the text. Numbers in italics show the page on which the complete reference is listed.

A

Arsenieva, A. N., 221,287 Arthurs, E. G., 40, 42,89, 90 Ashkin, A,, 70, 90 Audouze, J . , 113, I59 Augustine, F., 207(174), 215 Ausschnitt, C. P., 40, 47,48, 92 Ayyagari, M. S., 210(205), 216 Azzam, R. M. A,, 356

Aagaard, B., 415,429,430,431,432,441 Abakumov, G. A., 20,73,89 Adams, M. J., 358 Adams, W. C., 164, 168(2), 206(2), 211 Adatia, N. A., 135, 161 Adnot, A., 258,284 Adrain, R. S., 40,42,89 Aegerter, M. A,, 55, 89 Akaruma, S., 425,430,432,439 B Akhmanov, S. A., 71, 90 Albercht, A. C., 211(216), 217 Bachmann, K. J., 187(60, 61, 62, 63), 208(60, Alcock, A. J., 43, 52, 94, 96 61, 62, 183, 184), 209(186, 187, 188), 212, Alexander, J. H., 203(125), 214 216 Alferov, Zh. I., 204(147), 215 B a c k , C., 356 Alguard, M. J., 268, 284 Bader, S. D., 272,285,286,288 Allain, J. Y., 12, 14, 62, 90, 92, 94 Baker, A. D., 356 Allison, J. F., 201(117), 202(117, 122), 214 Baltakov, F. N., 16, 90 Alton, G. D., 423,433,435, 437, 441, 442 Baltensperger, W., 267,277,286 Alvarado, S. F., 261,266,284 Bambynek, W., 424,438 Ambler, E., 222, 289 Bang, J., 416, 438 Andersen, N., 430,438 Bannon, J. K., 119,159 Anderson, A. P., 140, 159 Barat, M., 412, 438 Anderson, 0. K., 266,287 Barber, H. D., 196(87), 213 Anderson, R. L., 167(37), 212,214 Barikhin, B. A,, 16, 90 Anderson, W. A,, 202(125), 214 Barker, D. L., 78, 93 Anderson, W. W., 196(89), 213 Barkla, C. G., 220, 285 Andreev, H. M., 204(147), 215 Barnett, 0. M., 165(7), 207(7), 208(7), 210 Angelov, D. A,, 41, 53, 90 (207), 211, 216 Angione, R. J., 119, 161 Barnett, S. J., 220, 285 Anholt, R., 418, 438 Basbas, G . , 425,428,438 Antes, L. L., 165(6), 207(6), 211 Bashara, N. M., 356 Apalin, V. A., 222, 285 Bass, M., 6, 74, 90, 96 Appt, W.. 74, 95 Bates, H. E., 201(120), 214 Aranovich, J., 174(45), 186(59), 189(59), 195 Bates, R. H. T., 400,409 ( 4 9 , 197(59), 209(59), 212 Bauer, P., 233,250,251,285 Arguello, C. A., 10, 94 Bauer, W., 415, 440 Ariotedja, A.P., 165(21),202(21), 203(21),211 Baumgartner, R. A,, 71, 72,90 Arndt, R. A., 202(122). 214 Beattie, J. W., 378, 406, 408 Amy, T., 106, I59 Beaulieu, R., 210(211), 216 443

444

AUTHOR INDEX

Becquerel, E., 164, 168(1), 206(1), 211 Bederson, B., 224,225,285,288 Behrisch, R.,356 Beigang, R., 59,93 Belanger, P. A,, 43, 90 Bell, K. L., 415,438 Bellman, S . H., 375, 408 Bender, R., 374,375,408,409 Benedict, G., 40,45,91 Bennett, J. C., 140, 159 Benninghoven, A., 356 Bertnyi, D., 413,415, 422, 438,439 Berlaga, R. Y., 165(28), 212 Berry, M. V., 371,408 Berry, S. D., 423,435,442 Best, J. S., 210(213b), 217 Bethe, H. A., 198,213 Bettini, M., 187(60, 61, 62), 208(60, 61, 62), 212 Bhalla, C. P., 433,436,438 Bhushan, M., 210(208), 216 Bierry, M., 4, 24, 25, 90 Bigio, I. J., 17, 90 Bignell, R. C., 131,161 Bincer, A. M., 224,285 Binder, K., 261, 266,285, 286 Bischel, W. K., 79, 80, 81, 90, 93 Bisgaard, P., 430,438,440 Bitner, T., 209(188), 216 Bjorck, A., 374,375, 409 Bjorkholm, J. E., 70,90 Bjorklund, G. C., 84,90 Blair, J., 207(165), 215 Blakely, J. M., 356 Blamont, J. E., 62, 94 Blit, S., 36,48,49, 50, 73, 74, 90, 95 Block, J. H., 356 Bloembergen, N., 63,90 Bloom, D. M., 38,41,51, 52,55, 56, 90, 94 Bloss, W. H., 207(178), 215 Blum, E. J., 104, 107, 131, 160 Boivin, J., 43, 90 Bolger, J. E., 427, 430, 433,436, 438,440 Bonham, R. A., 356 Boring, E., 415,429,430,431,432,441 Borisevich, N. A., 36, 90 Borovoi, A., 222,287 Bortfield, D. P., 23, 95 Bos, F., 4,22,23, 93 Bosch, F., 415,434,438

Bourkoff, E., 47,90 Bowman, H., 418,438 Boyd, D. P., 393,409 Bozler, C. O., 205(149), 215 Bozorth, R. M., 270,285 Bracewell, R. N., 363, 366,370,373,400,402, 405,408,410 Bradley, D. J., 39,40,42,45, 61, 84,90, 95 Brandhorst, H. W., 165(11), 201, 211,214 Brandt, D., 430,431,433,441 Brandt, W., 425,428,438 Brashears, H. C., 79, 90 Bratton, T., 425,427,438 Braverman, L. W., 52,91 Brenner, S. S.,356 Bridenbaugh, P. M., 210(210), 216 Brienza, M. J., 39, 92 Briggs, D., 356 Briggs, J. S., 415,417,422,438 Bringer, A., 268,285 Brodsky, M. H., 203(141), 215 Broglie, L. de., 219, 285 Brongersma, H. H., 356 Brooks, R. A., 361,368,374,386,387,408 Browell. E. V., 4, 25, 26, 90 Bruch, R., 427,430,440,442 Briimmer, O., 356 Brundle, C. R., 356 Bube, R. H., 165(24), 177(47), 178(47), 181 (49), 186(59), 189(59, 65), 192(24), 197 (59), 207(159, 175, 177, 179), 208(180, 182), 209(59,189,190,194,196,199,200), 211,212,213,215,216 Bucher, E., 165(15), 200,210(209), 211,216 Buchholz, J. C., 248, 287 Budinger, T. F., 368, 400, 408 Buehler, E., 187(60,61), 208(60, 61, 183, 184), 212,216 Buhl, D., 110, 160 Bukin, G. V., 85,90 Bunkenburg, J., 14, 90 Bunyan, P. J., 242,285 Burch, D., 415, 422, 427, 429, 430, 431, 432, 433,434,436,438,441 Burgess, E. L., 191(72), 192(73), 213 Burk, D. E., 203(131), 214 Burlamacchi, P., 11, 19, 90 Burnham, R., 78,80, 82,90,91 Burrus, C. A., 99, 100, 129,161 Burton, W. B., 114, 149,160

AUTHOR INDEX Button, K. H., 149,160 Buzzenda, Kh., 73,89 Byer, R. L., 29, 68, 69,70, 71,72, 91, 92 Byrne, J. F., 222, 288 C

Cabannes, F., 207(171), 215 Cacak, R. K., 428,430,438 Cachard, A., 357 Cadenhead, D. A,, 356 Calvert, R. L., 235, 251, 285 Campagna, M., 268,269,285,287 Campbell, A. G., 209(189), 216 Campbell, D. M., 237,288 Carboni, G., 18, 91 Card, H. C., 200(103, 106), 213,214 Cardona, M., 356 Carette, J. D., 258. 284 Carlson, D. E., 203(136), 204(136, 142, 143), 214,215 Carlson, E. R., 146, 147,160 Carney, E. R., 36,91 Caron, N., 144,160 Castaing, R., 357 Catalano, A,, 210(207, 208), 216 Ceccon, H. L., 8, 14,92 Celotta, R. J., 224, 225, 231, 233, 234, 236, 237, 239, 246, 247, 248, 249, 250, 253, 254, 257, 258, 259, 260, 261, 265, 269, 271,272,273,274,275,276,277,278,279, 280,281,283,285,286,287,288,289 Celto, J. E., 82, 83, 95 Center, R.E., 80, 92 Chamberlain, J., 144, 160 Champion, J. A,, 207(162), 215 Chan, C. K., 38,40,47, 91 Chandra, A., 58,91 Chang, C. Y., 197(93), 213 Chang, R. S. F., 82, 91 Chanin, M. L., 62, 94 Chapin, D. M., 211 Chapman, G. H., 210(211), 216 Charles, H. K., Jr., 165(21),202(21), 203(21), 211 Charlson, E. J., 202(127), 214 Chase, C. T., 221, 222, 285, 288 Chaturvedi, R. P., 425,427,438 Chen, H. S., 274,285 Cherednichenko, 0. B., 73,91

445

Cheroff, G., 165(32), 212 Chittick, R. C., 203(125), 214 Cho, A. Y., 145, 146, 147,161,162 Chrisman, R. W., 40,47, 92 Christiansen, W. N., 99, 124, 160 Christman, S. B., 171(42,43,44), 212 Chrobok, G., 282, 285 Chu, M., 209(194), 216 Chu, R. S., 135, 161 Chu, T. L., 182(54), 212 Chu, T. S . , 102, 106, 134, 139, 160 Chye, P. W., 171(39,40), 212 Chynoweth, T. A,, 208(182), 216 Ciamanque, L., 119,160 Claeson, T., 152, 166 Clark, F. D., 109. 160 Clark, W. D. K., 166(36), 212 Clauberg, R.,269,287 Clemen, C., 210(209), 216 Clerc, H.-G., 413,440 Cline, C. F., 85, 94 Coates, R. J., 100, 160 Cobat, A. R., 204(146), 215 Cocke, C. L., 425,427,433,436,437,438,442 Coffou, E., 185(58), 212 Cogdell, J. R., 100, 106, 160 Cohen, M. H., 131,161 Cohen, M. J., 21 1(214), 217 Cohen-Solal, G., 209(193), 216 Cole, T. W., 151, 160 Collins, R. E., 224, 285 Cong, H. I., 147, 160 Conrath, D., 237,285 Cook, J., 266,285 Corbett, H. H., 100, 160 Cordray, R., 37,38, 94 Corkurn, P. B., 43,91, 94 Cormack, A. M., 368,373,384,406,407,408, 409 Cotter, D., 19, 84, 90, 91 Courant, R., 371, 372,409 Coutts, T., 165(20), 211 Cox, A. J., 43,45, 91 Cox, R.T., 220,221,222,285,288 Cramer, H., 37 I , 372, 409 Crasemann, B., 424,438 Cristensen, C. P., 52, 91 Criswell, T. L., 421, 438 Crooks, J. B., 420,438 Crowell, C. R., 196(88), 197(94), 198, 213

446

AUTHOR INDEX

Crowther, R. A., 371, 373, 375, 377,384, 409 Curnutte, B., 425,427,438 Cusano, D. A., 207(163), 215 Czanderna, A. W., 357

D Dahl, E. D., 73, 74, 96 Dahl, P., 429, 438 Dahlquist, G., 374, 375, 409 Dalal, V. L., 191(71), 210(207), 213, 216 Daly, N. R., 357 Daly, T., 40, 47, 92 Daniel, R. E., 204(143), 215 Danielli, J. F., 356 Dapkus, P. D., 209(189), 216 Davis, H. L., 264, 265,268, 285 Davis, J . H., 129, 160, 162 Davison, S. G., 357 Davisson, C. J., 219, 220, 285 Day, R. E., 164, 168(2), 206(2), 211 Dearnaley, G., 357 Debe, M. K., 247,285 De Cicco, P.D., 229,285 Degani, J . , 400,409 de Hass, W. J., 220, 285 de Heer, F. J., 425,426,427,441 Dehmelt, H. G., 224, 285 Deichsel, H., 223, 285 Del Gaudis, A. M., 38, 52, 55, 56, 57, 90, 94 Delahoy, A. E., 202(125, 126), 214 Delannoy, J., 104, 107, 131, 160 De Maria, A. J., 38, 39, 91,92 Demuth, J. E., 271,272,285 Denisov, E., 222, 287 Derkacheva, L. D., 31, 91 De Rosier, D. J., 371, 373, 377, 409 Derouane, E. G., 357 Derr, V. E., 10, 94 Desnica, U. V., 185(58), 212 Deutsch, T. F., 74, 90 de Visschere, P., 200, 214 DeWames, R. E., 224,225,261,263,266,285, 288,289 Dewey, C. F., Jr., 74, 91 Dibene, A., 18, 91 Di Chiro, G., 361,368, 374,386, 387,408 Diels, J.-C., 38, 40, 45, 91 Dienes, A,, 39, 43,47, 64,90, 92,93, 96 Dietz, R. E., 87, 93

Dimitriev, V. G., 64, 91 Dines, K. A., 371, 409 Dirac, P. A. M., 221,285 Dixon, T. A., 110, 162 Djeu, N., 78,90, 91 Dolan, G. J., 152, 160 Dolega, U., 195(83), 213 Donnelly, J. P., 177(46), 212 Doorn, S., 430,431,438 Dorr, F., 42,93 Dorsenvil, R., 73,89 Dragone, C., 145, 160 Dreher, J., 104, 107, 162 Dreike, P., 393,409 Drepper, F., 417,422,438 Dubow, J., 200(114), 203(114, 131), 214 Duc Cuong, N., 207(165), 215 Duck, F. A., 370,409 Ducuing, J., 60,92 Duda, R. O., 372,409 Dudina, N. S., 73,91 Duncan, M. M., 423,438,440 Dunlap, B. I., 224,228,23 1,232,233,285,289 Dunlap, R. I., 234, 288 Dunn, M. H., 33,64, 65, 66, 67,68, 91, 96 Dunning, F. B., 61,73,74,90,91,95,223,231, 235,251,254,255, 256,287, 288 Dunning, T. H., Jr., 79, 91 Dupuy, C. H. S., 357 Dyadyusha, G. G., 31, 91

E Eckert, J. A,, 166(36),212 Eckertova, L., 357 Eckstein, J. N., 48, 49, 92 Eckstein, W., 223, 285, 287 Eckstrom, D. J., 80, 90 Economou, N. P., 41, 54,91 Eden, J. G., 82, 91 Edwall, D. D., 205(152), 215 Edwards, A. K., 426,429,430,438 Edwards, R. Q., 366,373,409 Egorova, J . V., 207(169), 215 Ehrenreich, H., 165(17), 211 Ehrlich, D. J., 88, 89, 91 Einstein, A., 220, 285 Ellis, S. G., 165(31), 212 Elsmore, B., 130, 132, 161 Elston, S. B., 423, 433, 435, 437, 441,442

AUTHOR INDEX

Emerson, D. T., 127,160 England, R. W., 102, 106, 134, 139, 160 Erickson, L. E., 36,91 Erbudak, M., 237, 280,285,288 Ernst, W. E., 80, 81, 91, 96 Ettenberg, M., 205(153), 215 Everhart, E., 413, 429,439 Ewan, J., 205(154), 215 F

447

Fisher, C. H., 80, 92 Fisher, M. E., 261, 286 Fishman, C., 203(133), 211(217), 214,217 Foley, R. J., 11, 92 Folkmann, F., 413,433,436,437,438,439,441 Fonash, S. J., 165(23), 200(107), 211, 214 Ford, G. W., 224,286 Forster, J. R., 104, 107, 162 Fortner, R. J., 430,431,432, 438,439 Fossum, J. G., 191(72), 192(73), 213 Fourikis, W., 133, 160 Fowler, W. B., 55, 92 Franchy, R., 357 Francombe, M. H., 357 Franken, P.A,, 60, 92 Frauenfelder, H., 222, 224, 225, 227, 286 Freeman, A. J., 266,289 Freeman, R. R., 41, 54, 91 French, W. G., 78,93 Frey, R., 4, 24,25,60, 90, 92 Frigo, N. J., 40, 47, 92 Frische, B., 415, 440 Frolich, D., 32, 33,64, 92, 95 Fryar, J., 421,440 Fugger, B., 32, 95 Fuggle, J. C., 358 Fujita, S., 209(191), 216 Fuller, C. S., 211 Furumoto, H. W., 8, 14, 15, 16, 92, 93

Fabel, G. W., 357 Fabick, L. B., 209(189), 216 Fabricius, E. D., 207(160), 215 Fagen, E. A., 210(207), 216 Fahey, D. W., 36, 91 Fahrenbruch, A. L., 165(24), 174(45), I77(47), 178(47), 186(59), 189(59), 192(24), 195 (45), 197(59), 207(175), 209(59, 189, 190, 194, 196, 199, 200), 211,212, 215,216 Fan, B., 9, 10, 45. 91, 96 Fan, J. C.-C.,205(149), 215 Fang, C. R., 182(53), 212 Fanin, B. M., 116, 161 Fano, U.,221,286,416,431,438 Farago, P. S., 221, 224,225,286 Farnsworth, H. E., 357 Fastrup, B., 413,415, 429, 430, 431, 432,438, 439,441 Faure, J., 18, 92 Fedeev, V. V., 20, ?3,89 G Feder, R., 222, 223, 225, 229, 232, 234, 235, 236,240,241,242,244,245,246,247,248, Gabler, H., 423,426,441 249,250,251,252,259,260,264,267,268, Gacoin, P.,19, 93 276,277, 281,282,285,286,287,288 Galejs, A., 237, 288 Fedosejevs, R., 52, 96 Ganiel, U., 36, 74, 90 Feigelson, R. S., 208(180), 215 Gardner, R. K., 425,427,438 Felcher, G. P., 225, 237, 265, 270, 271, 272, Garibotti, C. R., 423,439 273,274,285,286,288 Gamer, C. M., 171(39,40), 212 Feldmann, W. L., 209(187), 216 Garside, B. K., 210(211), 216 Feng, T., 203(133), 211(217), 214,217 Garwin, E. L., 224,264,286,289 Ferguson, A. I., 48,49,64,65,66,67,68,91,92 Gary, B. L., 104, 107, 160 Ferrar, C. M., 8, 92 Gel’fand, I. M., 361, 372, 409 Feucht, D. L., 195(82,91a,b), 213 Gerischer, H., 165(35),212 Feuerbacher, B., 357 Gerlach, W., 220, 286 Findlay, J. W., 139, 160, 161 German, K. R., 41,51, 92 Fiermans, L., 357 Germer, L. H., 219,220,285 Fink, M., 356 Ghosh, A. K., 203(133), 211(217), 214,217 Fink, R. W., 424,438 Gibbons, J. F., 209(194), 216 Fischer, H., 202(123a,b), 214 Gibbs, D. F., 371,408

448

AUTHOR INDEX

Gibson, A. J., 36,92 Gibson, J. E., 100, 160 Gidley, D. W., 282, 289 Gilbert, P. F. C., 374, 409 Gilbody, H. B., 412,439 Gilger, G., 207(178), 215 Gill, W. D., 207(179), 215 Giordmaine, J. A., 60, 92 Glass, A. M., 40,42, 94 Glass, G. A,, 423,435,442 Glenn, W. H., 9, 39,92, 94 Godfrey, R. B., 203,214 Godlewski, M. P., 165(11),211 Godlove, T. F., 412,439 Goldberg, L. S.,43, 73, 92, 94 Goldsmith, P. F., 130, 134, 150,160 Goldstein, B., 165(29b, 30), 212 Goldstein, J. I., 357 Goldstein, M., 224,285 Goldstein, R.,8.92 Goldwin, M. P., 140, 159 Golmayo, D., 186(59), 189(59), 197(59), 209 (59), 212 Gomer, R., 357 Gordon, M. A,, 114,160 Gordon, R., 374,375,408,409 Goudsmit, S.A., 219,286 Goujon, P., 40, 42, 94 Gradmann, U., 261,286 Graev, M. I., 361, 372,409 Grahl, B. H., 136, 160 Grant, C. R., 100, 160 Grasiuk, A. Z., 74, 92 Gray, D. A., 102, 106, 134, 139,160 Green, M. A., 200(112), 203,214 Greenleaf, J. F., 370, 409 Greiter, L., 42, 93 Griffin, A., 284,286 Griffin, J. E., 418,439 Griffin, P. M., 435,441 Grimmeiss, H. G., 207(161), 215 Gringorten, I. I., 119, 160 Grodzins, L., 225,286 Groeneveld, K.-O., 413, 415, 433, 437, 439, 440

Gryzinski, M., 416, 439 Gu, J., 209(191), 2f6 Gudat, W., 268, 269,285,287 Guelin, M., 113, 160 Guggenheim, H. I., 87,93

Gulkis, S.,104, 107, I60 Gullberg, G. T., 368, 400, 408 Gumbs, G., 284,286 Gurzadyan, G. G., 41,53, 90 Gusev, Yu.L., 59,92 Gustafson, T. K., 9, 10,43, 45, 91, 93, 96 H Hass, G., 357 Haas, R. W., 128,162 Hachenberg, O., 160 Hansch, T. W., 26,48,49,59, 92 Hanch, T. W., 26,96 Hagen, J. P., 99, 100,160 Haines, W. G., 189(65), 213 Hall, R. B., 208(181), 210(207), 215,216 Hall, W. F., 261, 266, 289 Hamadani, S.M., 61, 92 Hamann, C., 357 Hammaker, J. P., 130,160 Haneman, D., 235, 251,285 Hanna, D. C., 64,92 Hansch, T. W., 26, 92,96 Hansen, 0. L., 119, 160 Hanson, R. J., 375,409 Hansteen, J. M., 415,416,417, 438,439 Hargrave, P. J., 130, 160 Harris, J. M., 40, 47, 92 Harris, J. S., Jr., 205(152), 211(214), 215, 217 Harris, R.E., 144, 152, 161, 162 Harris, S.E., 68,92 Harrison, K. G., 426, 441 Harrower, G. A., 415,439 Hart, P. E., 372,409 Haslam, C. G. T., 127,160 Hauser, J. R., 182(53), 212 Hay, P. J., 79, 91 Hayden, H. C., 429,439 Haynos, J. C., 202(122), 214 Hayward, R. W., 222,289 Hedin, L., 229,264,286,289 Heeger, A., 211(215), 217 Heffner, R., 433,436,438 Heiland, W., 357, 358 Heindorff, T., 237,285 Heinzmann, U., 282,286 Heizer, K. W., 182(54), 212 Held, D. N., 145, 160 Helman, J. S.,263,267,269, 277, 286, 288

449

AUTHOR INDEX

Hench, T. L., 208(181), 215 Hendra, P. J., 357 Henry, P. S., 149, 150,160 Herbst, E., 112, 160 Herbst, R. L., 29,69, 70, 91, 92 Heritage, J. P., 40,41, 47, 54, 91, 92 Herman, F., 165(31),212 Herman, G . T., 361, 368, 374, 375, 394, 399, 400,409 Hermanni, A., 237,285 Hess, K. L., 209(189), 216 Heynau, H., 38,91 Higatsberger, M. J., 357 Hietanen, J. R., 207(173), 215 Hilbert, D., 371, 372,409 Hildebrandt, G. F., 73, 74,96 Hill, A. E., 60, 92 Hill, E. R., 207(166), 215 Hill, K. O., 78, 92, 93 Hill, R. M., 79,80, 90, 92, 93 Hillenkamp, F., 357 Hills, R., 139, 140, 162 Hils, D., 224, 286 Hinder, R.,160 Hiramatsu, S., 418, 439 Hirsch, M. D., 40,47, 93 Hirth, A,, 18, 62, 92 Ho, J. C. T., 201(120), 214 Hocker, L. O., 74,91 Hodge, W., 415,424,426,427,436,440 Hogbom, J. A., 99, 124, 160 Hoffman, D., 198(100), 213 Hoffman, R. L., 357 Hoffman, W., 104, 107,162 Hofmann, M., 282,285 Hogg, D. C., 119,160 Hohenberg, P. C., 261,266,286 Hohenberg, P. E., 261,285 Holcomb, D. F., 58,91 Holland, B. W., 232,289 Hollis, J. M., 110, 129, 139, 161, 162 Holzwarth, G., 222, 286 Hoogkamer, Th. P., 430,431,432,438,439 Hopkjns, F., 415, 425, 427, 440 Hoppes, D. D., 222,289 Hori, H., 427, 431,439, 440 Horn, B. K. P., 361,368,399,409 Houndsfield, G. N., 368,408,409 Houston, J. E., 246,288 Houston, J . L., 358

Hovel, H. J., 165,170(38), 192(8), 194(78), 204 (148), 205(151), 211, 212, 213,215 Howard, W. E., 170(38), 212 Hubbard, J., 266,286 Hudson, R. P., 222,289 Huesman, R. H., 368,400,408 Huestis, D. L., 79, 80, 81, 90, 92, 93, 96 Huggins, P. J., 106, 137, 148,161,162 Hughs, V. W., 268,284 Huijser, A., 171(41), 212 Huppert, D., 40,43, 44,45,46, 92 Hutchinson, M. H. R., 84,90 I Iback, H., 357 Igarashi, Z., 418,439 Ikegami, S., 209(197, 198), 216 Ingalls, W. B., 422,433,434,436,438 Inokuti, M., 418, 439 Ippen, E. P., 38, 39,40,41,42,45,48,64, 92, 93, 95 Irie, T., 425,430, 432,439 Irvin, J. C., 100, 145, 162 Isganitis, L., 41, 51, 92 Ishimaru, H., 418,439 Itskhoki, I. Ya., 64, 91 Iverson, M. V., 88, 92

J Jackson, D. J., 59, 92 Jaeger, T., 2, 94 Jain, R. K., 40,47,48,78, 92,93, 96 Jakubassa, D. H., 415,434,439 James, L. W., 205(150, 155), 215 Jamison, K . A., 427,433,435,436,437,442 Janak, J. F., 228, 264,287 Janssen, M. A., 104, 107,160 Janiz, W., 74,93 Jarrett, S. M., 33, 93 Jarvis, 0. N., 417, 439 Jefferts, K. B., 100, 113, 160, 162 Jennings, D. A,, 61, 93 Jennings, P. J., 223, 240, 241, 242, 245, 246, 259,286,287 Jennisson, R. C., 131, 160 Jenny, D. A., 204(145), 211,215 Jensen, H. P., 85, 96 Jepsen, D. W., 271,272,285

450

AUTHOR INDEX

Jepsen, O., 266,287 Jewett, D. N., 201(120), 224 Joffe, A. F., 221,287 John, F., 371, 372,409 Johnson, B. M., 415,426,427,433,436,440 Johnson, D. C., 78,92,93 Johnson, D. K., 102,161 Johnson, L. F., 78, 87,93 Johnson, R. E., 209(189), 216 Johnson, S. A., 370,409 Johnston, T. F., Jr., 33,34,93 Johnston, W. D., 32, 93 Jones, R. O., 223,240,241,242,245,286,287 Jonscher, A. K., 191(69), 213 Jorgensen, T., Jr., 413,418,420,426,428,429, 430,438,439,440

K Kabelka, V., 71, 93 Kagen, M. B., 204(147), 215 Kaiser, P., 78, 93 Kaiser, W., 42, 72, 93, 95 Kak, A. C., 361, 368,370,388,409 Kalisvaart, M., 223, 231, 235, 287, 288 Kamarinos, G., 200(11 l), 214 Kamath, G. S., 205(154), 215 Kanasaki, B. S., 78,92 Kar, S., 200(110), 214 Kardashev, N. S., 116,161 Karpenko, S. G., 64, 96 Kasper, H. M., 209(202), 210(203), 216 Kato, D., 78, 93 Kato, K., 31,93 Katz, M. B., 375, 384,409 Kaufmann, K. J., 33, 38, 94, 95 Kaufmann, P., 106, 161 Kaufmann, R., 357 Kauffman, R. L., 427,433,435,436,437,441, 442 Kaveh, M., 371,409 Kawasaki, B. S., 78,93 Kazmerski, L. L., 165(20), 210(204, 205, 206a), 211,216 Keating, P. N., 207(164), 215 Keen, N. G., 146, 153, 161 Kellhr, S. P., 165(32), 212 Kelly, A. J., 145, 161 Kelly, W. M., 146, 153, 161 Kermidas, B. G., 207(166), 215

Kern, W., 358 Kerr, A. R., 145, 147, 160, 161 Kessel, Q. C., 413,429,439 Kessler, J., 225, 227, 228, 233, 235, 236, 245, 260,282,286,287 Keto, J. W., 37, 38, 94 Kharitonov, L. A,, 20,89 Khokhlov, R. V., 20,89 Kholodnykh, A. I., 71,90 Kienle, P., 415,434,439 Kim, J. K., 202(126), 214 Kim, Y. K., 421,441 King, D. A., 247,285 King, F. D., 200(112), 214 King, J. G., 358 Kingstone, A. E., 415, 438 Kinmond, S., 203(141), 215 Kirby, R. E., 224,264,286,289 Kirkbright, G. F., 358 Kirpichnikov, A. V., 59, 92 Kirschner, J., 236, 241, 244, 245, 247, 248, 249,252,259,260,281,286,287 Kisker, E., 268,269,285,287 Kistemaker, J., 358 Kitahara, T., 209(191), 216 Kitz, A., 229, 285 Klar, H., 268, 287 Klaus, N., 357 Kleber, M., 415,434,439 Klein, V., 127, 160 Kleinman, L., 267,287 Kleinpoppen, H., 224,286 Klemperer, W., 110, 112, 160, 161 Kligler, D., 79, 93 Klimpke, C., 200(108a,b), 214 Klug, A,, 371,373, 375, 377, 384,409 Knapp, G. R., 106, 137,162 Knechtli, R. C., 205(154), 215 Knystautas, E. J., 429,439 Kobayashi, N., 425, 427, 430, 431, 432, 439, 440 Koch, K.-P., 59,93 Kover, A., 422,439 Kogelnik, H. W., 64, 93 Koidl, P., 74, 93 Kojima, H., 425,430, 432,439 Koltay, E., 422,439 Komine, H., 29, 70, 76, 82, 92, 93 Konoplin, S . N., 59,92 Koo, Ja.-Y., 38, 95

AUTHOR INDEX

Koopman, D. W., 83,93 Kopylov, S. M., 73, 91 Koreman, V., 266,287 Komienko, N. E., 64,91, 96 Kovrigin, A. I., 71, 90 Kozhuharov, C., 415,434,439 Kressel, H., 205(153), 215 Krimm, H., 415,434,438 Krischer, C., 358 Krupke, W., 54, 93 Kruskal, J. B., 394,410 Krylov, V. N., 64, 96 Krymova, A. I., 31,91 Kryukov, P. G., 20, 31, 72, 93, 96 Kuhl, D. E., 366, 373,409 Kuhl, J., 40,47, 61, 63, 93 Kuhlmann, E., 268,269,285,287 Kuiper, G . P., 123, 161 Kukio, T. C., 1I , 92 Kumar, P., 261,287 Kuprishov, V. F., 20,31,96 Kurrelmeyer, B., 220,221,285 Kutikov, I. Y., 222, 285 Kutla, A., 71, 93 Kuwano, Y., 204(144b), 215 Kuyatt, C. E., 222, 237, 261, 269, 287, 288. 413,418,420,439 Kuznetsov, V. I., 71, 90 Kwoh, Y. S., 366,400,409 L LaBelle. H. E., Jr., 201(119), 214 Lacroix, J., 104, 107, 131, 160 Lagally, M. G . ,232,248,249,287 Lakshimarayanan, A. V., 366, 373, 374, 409, 410 Lambrich, R., 40,47, 93 Lamneck, J. H., Jr., 201(118), 214 Lamorte, M. F., 204(146), 215 Landsberg, P. T., 190(67), 200( 108a,b), 213, 214 Langstroth, G. O., 222, 287 Lankard, J. R., 3, 4, 21, 60, 95 Lapicki, G., 417,439 Laubereau, A., 42, 72, 93, 95 Laubert, R., 425,428,438 Lawler, J. E., 59, 92 Lawson, C. L., 375,409 Lax, M., 358

45 1

Le Comber, P. G., 203(132, 138, 140, 141), 214,215 Lee, J. J., 135, 161 Lee, T. P., 100, 161,222,233,287 Lee, Y. K., 415,434,439 Legally, M. G., 246, 289 Legg, W. E., 102, 106, 134, 139, 160 Leheny, R. F., 78, 96 Leies, G., 165(6), 207(6), 211 Leighton, R. B., 106, 137, 139,161, 162 Leithauser, U., 423,426,441 Lent, A., 374, 375,409 Leopold, K. E., 52, 96 Lequeux, J., 113, 159,160 Letokhov, V. S., 72, 93 Levitan, E., 400,409 Lewis, H. W., 416,440 Lewitt, R. M., 393,400,409,410 Ley, L., 356 Liao, P. F., 36, 37,41, 54, 91, 95 Lichman, D., 358 Lichten, W., 131, 224, 287,416, 431, 438,439 Liebl, H., 358 Liebowitz, H., 137, 161 Lien, J. C., 202(127), 214 Lill, E., 42, 93 Lillington, D. R., 200(105), 214 Lin, C., 36,38,43,52,78,90, 93,95, 96 Lincot, D., 209(192), 216 Lindau, I., 171(39,40), 212 Lindgren, A. G . ,377, 379, 384. 386, 387, 388, 390,391,393,410 Lindhard, J., 269,287 Lindholm, F. A., 165(19), 192(73), 211,213 Lindmayer, J., 201(117), 202(117, 124), 214 Lindquist, P. F., 207(177), 215 Ling, C. C., 84, 90 Linke, R. A,, 145, 146, 147,161, 162 Linn, J. W., 43,95 Littin, G., 59,93 Linzer, M., 370,409 Lloyd, F. L., 144, 152, 161, 162 Lo, L. I., 116, 161 Loannon-Yannon, J. G., 418,438 Loebner, E. E., 165(31),212 Loferski, J. J., 184, 204(145), 210(21 I), 211, 212,215,216 Logan, B. F., 366, 374,394,400,410 Loo, R., 205(154), 215 Loree, T. R., 78, 93

452

AUTHOR INDEX

Lorents, D. C., 79, 80, 90, 92, 96 Losonsky, W., 417,439 Loth, C., 4, 19,22,23,93 Loth, R., 223,287 Lougnot, D., 18,92 Lovas, F. J., 102, 110,161,162 Love, A. W., 134,161 Lu, T.-M., 246,262,287,289 Lubell, M. S., 225,268,284, 287 Lubin, P. M., 115,162 Luborsky, F. E., 274,287 Lucas, A. A., 357 Lucatorto, T. B., 15, 16,93 Ludwig, N., 237,285 Ludwig, W., 207(167), 215 Liity, F., 5 5 8 9 Lukashevich, I. I., 222,285 Lundqvist, B. I., 264, 286 Lynch, D. J., 421,425,427,438,439 Lytle, F. E., 40,47,92 Lytle, R. J., 371, 409

M Ma, Y. Y.,209(199), 216 McCaldin, J. O., 210(213a,b), 216,217 McClintock, J. A., 415,434, 439 McColl, M., 100, 145, 161 McCoughey, M. P., 429,439 McCusker, M. V., 224,286 McDaniel, J. P.,80, 92 Macek, J. H., 413,423,429,439,440 McGil1,T. C., 198(100),210(213a,b),213,216, 217 McGuire, E. J., 417, 439 McGuire, J. H., 417,439 Mach, R., 207(167), 215 McIlrath, T. J., 4, 15, 16, 25, 26,83, 90.93 McIlwraith, C. G., 220, 221, 285 McIver, C. W., 204(146), 215 Mack, M. E., 9,93 McKee, T. J., 84, 93 Mackey, J. J., 415,426,433,436,440 McKnight, R. H., 415,421,422,427,439 McKinney, J. T., 356 McMaster, T. F., 146, 147, 160 McMaster, W. H., 225,287 McOuat, R. F., 200(109), 214 McRae, E. G., 245,256,257,258,259,287,288

Madansky, L., 415,434,439 Madison, D. H., 415,416,419,421,439,440 Madsen, J., 266,287 Maeda, N., 18,36,41,52,53,93,94,425,427, 430,43 1,432,439,440 Magyar, G., 61,92 Mahan, A. H., 251,254,255,256,287,288 Mahr, H., 40,47,92,93 Mairnan, T. H., 2,94 Maison, D., 223,287 Maitland, A., 64, 92 Marker, P. D., 63,96 Malone, T. G., 78,93 Maloney, P. J., 36, 37, 95 Malysev, V. I., 31, 91 Manasevit, H. M., 209(189), 216 Mandelkorn, J., 201(118), 214 Manifacier, J. C., 203(132), 214 Man'ko, A. A., 64,96 Mann, A. P. C., 108,161 Mann, R., 433,436,437,439,441 Manson, S. T., 418,419,421,439,440,441 Mar, J. W., 137, 161 Marburger, R. E., 165(6), 207(6), 211 Marcus, P. M., 271,272,285 Marennikov, S. I., 59,92 Marfaing, Y., 209(192, 193), 216 Margaritondo, G., 171(42,43,44), 212 Markin, A. S., 31, 91 Marotta, A., 10,94 Marowsky, G., 33,37, 38,81,94, 96 Marrone, M. J., 57, 95 Martin, B., 415,434, 438 Masi, J. V., 210(207), 216 Massey, H. S., 223,287 Mastrup, F. N., 8, 92 Matrosov, V. N., 85,90 Matsurnoto, H., 209(197, 198, 201), 216 Matsutani, K., 19, 94 Mattauch, R. J., 145, 162 Matthews, D. L., 415,425,426,427,433,436, 438,440 Matveets, Yu. A., 40,47,72,93,94 Mayer, H., 358 Mayo, S., 15, 16,93 Mead, C. A., 198(100), 210(213a,b), 213,216, 217 Meakin, J. D., 210(207), 216 Medvedeva, A. M., 73,89 Meeks, M. L., 99, 161

453

AUTHOR INDEX

Megie, G., 62, 94 Mehlhom, W., 417,424,440 Meister, H. J., 222, 286 Memming, R., 207(161), 215 Menendez, M. G., 423,438,440 Menzel, D. H., 102, 106, 161,357,358 Merrigan, J. A., 165(10), 211 Mersereau, R. M., 363,373,386,387,394,409 Merz, W. J., 165(31),212 Merzbacher, E., 415,416,439,440 Meulenberg, A., Jr., 202(122), 214 Meyer, O., 358 Meyer, Y.H., 4,22,23,93 Meyerhof, W. E., 432,440 Mialocq, J. C., 40.42, 94 Mickelsen, R. A., 210(206b), 216 Middleton, D., 387,410 Midwinter, J. E., 72, 94 Mielczarek, S. R., 237,288 Migliorato, P., 209(202), 216 Mikaelyan, L. A., 222,285,287 Mikhailov, L. K., 73, 91 Milano, R. A., 202(125), 214 Miller, R. C., 60, 92 Mills, A. P.,282, 287 Mills, D. L., 261, 263, 287 Milnes, A. G., 177(46), 195(82,84), 212,213 Mimila-Arroyo, J., 209(192, 193), 216 Minck, R. W., 76,94 Miraglia, J. E., 423,439 Mitchell, K. W., 177(47), 182(56), 209(196), 212,216 Miyano, K., 271,288 Miyazoe, Y., 18, 36,41, 52, 53, 93, 94 Mizunami, T., 41, 52, 53, 93 Mlavsky, A. I., 201(119), 214 Mohr, C. B. O., 223,287 Moiseiwitsch, B. L., 415, 440 Molhotra, A. K., 203(139), 214 Mollenauer, L. F., 38,41,52,55,56,57,58,59, 90,94 Meller, C., 224, 287 Moon, R. L., 205(150, 155), 215 Mooradian, A,, 2, 87, 88, 94 Mooney, J. B., 210(213a,b), 216, 217 Moore, C. A., 43, 73, 92, 94, 191(71), 213 Moore, C. F.,415,424,426,427,430,433,436, 438,440 Morel, D. L., 21 1(217), 217 Morey, W. W., 9,94

Morgan, G. K., 210(204), 216 Morris, D., 129, 161 Morris, R. C., 85, 94, 96 Morrison, A. D., 201(120), 214 Morrison, H. D., 43, 94 Morruzzi, V. L., 228,264,287 Mosebekk, 0. P., 417,439 Moses, E. I., 41,42,43, 94 Moss, H., 207(172), 215 Mostovnikov, V. A,, 23, 95 Mott, N. F., 221,287 Moudy, L. A., 209(189), 216 Moulton, P. F., 87, 88, 89, 91, 94 Miiller, N., 233, 234, 235, 240, 250, 251, 252, 253,256,280,285,288 Mueller, R. K., 371, 409 Mullaney, C. J., 80, 92 Mullin, C. J., 224, 286 Murray, J. L., 266, 287 Musket, R. G., 415,440 Muto, K., 418,439 Muttauch, R. J., 147, 160 Myers, F. E., 222,288 Myerscough, V. P., 83, 93 Myszlowski, A., 200(114), 203(114), 214 Mytton, R. J., 207(107), 215

N Nadjakov, G., 207( 158), 215 Nagamiya, S., 418, 438 Nahum, J., 56,94 Nakano, H. H., 79, 80,90,93 Nakano, S., 204(144b), 215 Nakayama, N., 209(197, 198,201), 216 Naparstek, A., 361, 368, 394, 399, 409 Napier, P. J., 131, 161 Nash, T. R., 214 Navon, D. H., 182(55), 212 Nayer, P. S., 210(208), 216 Negran, T. J., 40,42,94 Nelson, N. J., 2 0 3 155), 215 Neudeck, G. W., 203(139), 214 Neugebauer, G., 148,161 Neumark, C. F., 165(33), 212 Neville, R. C., 165(12), 211 New, G. H. C., 42, 84,90, 94,96 N’Diaye, A. N., 208(180), 215 Ng, W. K., 74, 96 Ngoc, T. C., 232,249,287

454 Nicholas, J. V.,61, 90 Nighan, W. L., 82,94 Nikogosyan, D. N., 41, 53, 72,90,93 Nishimura, F., 421,422,440 Nishiwaki, H., 204(144b), 215 Nolte, G., 415,440 Nordheim, L., 196(86), 213 Norton, S. J., 370, 409 Noyce, R. N., 194(76), 213

AUTHOR INDEX

Perel, J., 224,288 Perez-Albuerne, E. A., 165(22), 211 Pershin, S. M., 71, 90 Peters, C. W., 60, 92 Peters, T. M., 393,400,409, 410 Peterson, D. P., 387, 410 Peterson, 0. G., 4,7, 1 I , 32,85,86,87,92,94, 96 Peterson, R. S., 433,437,439 Petritz, R. L., 182(50),212 Pferdekamper, K. E., 413,440 0 msterer, F., 207(178), 215 Pheibel, W., 78, 93 Oda, N., 412,421,422,440,441 Phillips, T. G., 106, 137, 148, 152, 160, 161, O’Dell, E. W., 85, 96 162 Ohnishi, M., 204(144b), 215 Pianetta, P., 171(39,40), 212 Okada, T., 36,94 Pierce, D. T., 224,225,231,233,234,236,237, Oldham, W. G., 195(84), 213 239,246,247,248,249,250,253,254,257, Olendorf, W. H., 373,409 258,259,260,261,265,269,270,271,272, Olsen, E. T., 104, 107,160 273,274,275,276,277,27a, 279,280,281, Olsen, J. 0.,430,438 283,285,286,287,288,289 Olson, D. H., 59, 94 Pine, A. S., 74,94 O’Neill, M. R., 223, 231, 235,287,288 Pipher, S. L., 144,162 Oppenheim, A. V., 363,394,409 Piskarskas, A,, 71, 93 Ornstein, M. H., 10, 94 Piwkowski, T., 165(25),211 Osgood, P. M., Jr., 88, 89, 91 Platzman, P. M., 284,288 Owen, S. J. T., 197,213 Plourde, B. E., 18, 96 Polloni, R., 64, 94 Ponpon, J . P., 202(128), 209(195), 214,216 P Popowich, R. J., 421,422,441 Padovani, F. O., 197, 198, 213 Potter, A. E., Jr., 207(168), 215 Page, L. A., 222,225,288 Pound, R. V., 144,161 Palmberg, P. W., 224,261,263,266,288,289 Povh, B., 415,434,438 Palz, W., 165(13), 211 Powell, C. J., 226, 288 Papoulis, A., 377, 409 Pradere, F., 4,24, 25, 60, 90, 92 Parad, L. I., 135, 161 Prange, R. E., 266,287 Parilis, E. S., 358 Pratesi, R., 11, 12, 90, 94 Park, R. L., 246,288, 358 Pratt, W. K., 372,410 Parker, G. H., 198(100), 213 Pridham, R. G., 377,410 Pasteur, G., 209(187), 216 Prince, M., 190(68b),213 Pauli, W., 221,288 Pritchard, J., 358 Pauwels, H., 200, 214 Proffitt, W., 33, 34, 93 Payne, J. M., 139, 153,161 Protasov, I. I., 204(147), 215 Pearson, G. L., 206(157), 211,215 Prutton, M., 358 Pearson, T. J., 131, 161 Pschunder, W., 202(123b), 214 Pendry, J. B., 242, 282,286, 288 Pucci, D., 11, 12, 94 Penn, D. R., 268,288 Pulfrey, D. L., 165(14), 192(74), 200(104a,b, Pensak, L.,165(29a, 30), 212 109), 211,213,214 Penzias,A.A.,99,100,113,115,129,160,161, Pulkovo, Izvestia, 102, 161 162 Purwin, P. E., 211(217), 217

455

AUTHOR INDEX

Q Queisser, H. J., 194(79), 213

R Rado, W. G., 76, 94 Radon, J., 360,361,372,410 Raffaelli, J. C., 106, 161 Rains, R. G., 415,421,422,427,439 Raith, W., 224,225,288 Ramachandran, G. N., 366,373,400,410 Rank, D. M., 100,161 Rappaport, P., 165(19), 204(145), 211,215 Rasmussen, J. O., 418,438 Rao, P. V., 424,438 Rattey, P. A., 377, 379, 384, 386, 387, 388, 390,391,393,395,398,410 Rau, C., 261,288 Rauschenbach, H., 182(52), 212 Rauscher, E., 418,438 Ravi, K. V., 201(120), 214 Read, M. N., 240,247,287,288 Read, W. T., 194,213 Readhead,A. C. S., 130, 131, 161 Rediker, R. H., 196(90), 213 Redman, R. O., 106, 137, 162 Reed, I. S., 366,400, 409 Reed, T. B., 87, 94 Reichert, E., 237, 285 Reid, A,, 219, 289 Reihl, B., 234, 237,288 Reinhardt, J., 412,438 Reintzes. J., 85, 94 Rendell, R. W., 268, 288 Rentzepis, P. M., 40,43,44,45, 46, 92 Reynolds, D. C., 165(6), 207(6), 211 Rhoderick, E. H., 197(95), 198,200(103), 213 Rhodes, C. K., 79, 93 Rhodes, P. L., 129, 162 Riben, A. R., 196(91a,b), 213 Rich, A,, 282,289 Richard, P., 413,417,427,433,435,436,437, 439,440,441,442 Richards, P. L., 144, 152, 161,162 Richardson, M. C., 52,96 Ricz, S., 422,439 Ridder, D., 430,441 Riddle, A. C., 363, 366, 370, 373, 400, 408 Riddle, T. W., 231, 235, 251, 254, 255, 256, 287,288

Rideout, V. L., 197(94), 213 Riel, R. K., 201(121), 214 Riemer, D. E., 182(51), 212 Risley, J. S., 421, 433, 434, 436, 438, 440,441 Riviere, J. C., 358 Roberts, J. A., 373, 408 Roberts, K., 424, 427,436, 440 Redbro, M., 429,430,438,440 Roddie, A. G., 40,42,89, 90 Rohr, H., 96 Rogers, A. E. E., 131,161 Rogers, M., 358 Rohr, H., 85.96 Rolfes, R. G., 421, 440 Ronchi, L., 11,90 Roosen, R. G., 119, 161 Rose, M. E., 228,288 Rossi, A., 222,224,225,227,286 Roth, J., 358 Rothwarf, A., 165(7), 177(48), 192(75), 195, 207(7, 176). 208(7), 211,212,213,215 Rowe, J. E., 171(42,43,44), 212 Rowe, J. E., Jr., 375, 408 Rowland, S. W., 361, 363, 366,375, 394,400, 409,410 Rowley, P. D., 371,410 Rubin, K., 224, 288 Rubinov, A. N., 23, 95 Rudd, M. E.,413,418,419,420,421,426,429, 430,438,440,442 Ruddock, 1. S., 39,41,95 Rudge, A. W., 135,161 Rudner, S., 152, 161 Ruge, I., 358 Runge, P. K., 32, 93 Russell, G. J., 235, 247, 251,285, 288 Ruth, R. P., 209(189), 216 Ruze, J., 125,166 Ryan, J. P., 38, 45, 90, 95 Ryle, M., 130, 132, 139, 160, 161, 162 Ryssel, H., 358 Ryzhkov, A. I., 64,91 Rzhanov, A. V., 358

S Sah, C-T., 194(76),213 Sahai, R., 205(152), 215 Sakaguchi, T., 209(191), 216 Sakai, Y., 208(185), 216

456

AUTHOR INDEX

Sakisakai, M.,425,427,430,431,432,439,440 Saldafia, X. I., 263,269,288 Salimbeni, R., 1 I , 90 Sallaba, H., 38,40, 45, 91 Salmela, H. A,, 119, I60 Salter, G. C., 203(129), 214 Saltsburg, H., 358 Samayoa, W. F., 370,409 Sanborn, G. A., 210(205), 216 Sari, S.O., 40, 47, 91 Saris, F. W., 430,431,432,438,439 Sarjeant, W. J., 52, 96 Sato, A., 41, 52, 53, 93 Saykally, R. J., 110, 162 Saylor, T. K., 425,427,438 Sceats, M., 41, 51,92 Schaal, R. E., 106,161 Schafer, F. P., 3,4, 11, 13, 23, 32, 36, 37, 38, 39, 61, 94, 95 Schalla, R. L., 207(168), 215 Scharff, M., 269,287 Schearer, L. D., 36, 91 Schilling, D. L., 377,410 Schilling, J. S.,226,288 Schimitschek, E. J., 82,83,95 Schiett, H. E., 269,287 Schlecht, W., 268,287 Schliepe, R., 224, 288 Schmidt, A. J., 42, 95 Schmidt, P. H., 209(186, 187, 188), 216 Schmidt, W., 3,23,39,74, 75, 76,95, 96 Schneider, D., 415, 424, 425, 427, 428, 429, 430,43 1,432,433,434,436,438,440,441 Schneider, I., 57, 95 Schneider, M. V., 144,145,146, 147,160,161, 162 Schneider, S.,42, 93 Schock, H. W., 207(178), 215 Schonhense, G., 282,286 Schoijet, M., 210(212), 216 Schonfelder, J. L., 242,285 Schooneveld, C., van., 131, 162 Schotland, R. M., 17, 62, 95 Schottky, W., 198(101), 213 Schowengerdt, F. D., 426,440 Schreiber, H., Jr., 209(187, 188), 216 Schreiner, D. G., 246,288 Schroder, H. W., 32,64, 92, 95 Schultz, S.,224, 287 Schumann, S.,415,440

Schwabe, G., 165(26), 211 Scofield, J. H., 417,440 Scott, G. W., 43,45, 91 Scott, P., 139, 162 Scoville, N. Z., 130, I60 Scranton, R. A., 210(213a), 216 Scudder, H. J., 361, 363, 366, 368, 374, 394, 399,410 Sebekina, N. N., 73,89 Seigman, A., 29, 95 Seilmeir, A., 42, 95 Selah, A. A. M., 145, 161 Selbin, I. A,, 423, 433, 435, 437, 441,442 Selle, B., 207(167), 215 Sellin, I. A,, 423, 435, 437, 440, 441 Selwood, P. W., 273,288 Semchishen, V. A., 40,47,94 Senatskii, Yu.V., 20, 31,96 Seraphin, B. O., 165(18), 211,358 Serreze, H. E., 201(120), 214 Setser, D. W., 79, 90 Sevast’yanov, B. K., 85, 90 Seymour, R. J., 74,95 Shah, M., 417,439 Shalaev, E. A., 64, 91 Shank, C. V., 36,38,39,40,41,42,45,48,64, 92, 93, 95 Shapiro, S.L., 38,40, 95 Sharkov, A. V., 72,93 Sharp, J., 119,160 Shaw, J. R. D., 61,90 Shaw, L. J., 130,160 Shaw, R. F., 211(217), 217 Shay, J. L., 187, 208(60, 61, 62, 63, 183, 184), 209(202), 210(203), 212,216 Shen,T. M., 144, 152,161,162 Shen, Y. D., 206(157), 215 Shenton, D., 139, 140,162 Shepp, L. A,, 366,374,394,400,410 Sherman, N., 222,288 Shewchum, J., 200(112, 114), 203(114), 210 (21 I), 214, 216 Shibata, S.,418,439 Shibuya, H., 204(144b), 215 Shiozawa, L. R., 207(174), 215 Shirland, F. A., 207(173a,b), 215 Shizheviskii, V. L., 64, 91 Shockley, W., 194, 213 Shpak, M. T., 31,91 Shull, C. G., 222, 288

457

AUTHOR INDEX

Shuster, G. B., 38, 95 Sibley, W. A,, 88, 92 Siegmann, H. C., 224,275,276,277,278,279, 280,281,283, 285,286,288 Siffert, P., 202(128), 209(195), 214, 216 Sim, B. K., 223,240,242,245,246,259,287 Simonov, A. P., 20, 79,89 Simpson, O., 165(27), 212 Sinclair, W. R.,209(187, 188), 216 Singh, R.,200(114), 203(114), 214 Singh, S., 63,95 Sites, J. R-, 203(121), 214 Slater, J. C., 229,245, 264,288 Smart, S. R.,426,440 Smiley, V. N., 19, 96 Smil’gyavichyus, V., 71, 93 Smirnov, G. V., 222,285 Smith, J. M., Jr., 358 Smith, K. K., 38, 95 Smith, K. T., 384, 385, 410 Smith, L. E., 415,424,426,427,433,436,440 Smith, P. W., 36,37,95 Smith, R. A., 190(66), 191(66), 213 Smith, R. G., 64, 68, 70, 90, 95 Smith, S. J., 224,286 Smith, W., 164(3), 206(3), 211 Smoot, G. F., 115,162 Snavely, B. B., 4, 32, 94, 95 Snyder, L. E., 102, 110, 160, 161, 162 Soffer, B. H., 43, 95 Soifer, B. T., 144, 162 Solomon, D. C., 384, 385,410 Solomon, I., 119, 160 Solomon, P. M., 113, 162 S o h , F. S., 104, 107, I60 Sorokin, P. P., 3,4, 21, 60, 95 Sosnowski, L., 165(27), 212 Spaderna, D. W., 182(55), 212 Spaeth, M. L., 23, 95 Spanner, K., 42,72, 95 Sparnaay, M. J., 358 Spear, W. E.,203(132,138,140,141), 214,215 Spencer, E. G., 209(186, 187), 216 Spicer, W. E., 171(39.40). 212 Spitschan, H., 61, 63, 93 Spivak, P. Y.,222,285 SreeHarsha, K. S., 209(186, 187), 216 Stappaerts, E. A., 76, 82, 93 Starkiewicz, J., 165(27), 212 Stebbings, R. F., 61, 91

Steele, L. P., 119, 159 Steier, W. H., 52, 91 Stein, L., 32,64, 92, 95 Stepanov, B. I., 23, 95 Sterling, H. F., 203(125), 214 Stern, O., 220,286 Stetser, D. A., 38, 91 Steuer, K.-H., 85. 96 Steyer, B., 36, 95 Stickel, R. E., 81, 96 Stickel, R. E., Jr., 73,74, 95, 96 Stirn, R.J., 205(156), 206, 215 Stogryn, P. E., 21 1(217), 217 Stoicheff, B. P., 84,93 Stokes, E. D., 61, 91 Stokseth, P., 2, 94 Stolen, R.H., 78, 93, 96 Stolterfoht, N., 413, 415, 419, 420, 421, 423, 424,425,426.421,428,429,430,43I, 432, 433,434,435,436,437,438,440,441,442 Stopek, S., 196(90), 213 Straiton, A. W., 116, 161 Strakhov, L. P., 165(28), 212 Stratton, R.,197,213 Strizhevskii, V. L., 64,96 Struck, C. W., 165(31), 212 Stuck, B. W., 371,410 Su, C. Y., I71(39), 212 Sukhanov, L. V., 16,90 Sullivan, G. A., 207(174), 215 Susskind, C., 407, 408, 410 Suter, M., 423,433, 435,437, 441, 442 Svelto, O., 64, 94 Svitashev, K. K., 358 Swanson, R. M., 165(34), 212 Szabo, A., 36,91 Szabo, Gy., 422,433,437,439 Szanto, P. G., 110, 162 Sze, R.C., 78, 93 Sze, S. M., 197(93), 198,213 Szepessy, L., 203(132), 214

T Takayanagi, K., 412,441 Talbert, A. J., 386, 408 Talley, L. D., 43, 45, 91 Tang, C. L., 41,42,43,48,49, 50, 90,94 Tang, C. W., 211(216), 217 Tang, K. Y.,81,96

458

AUTHOR INDEX

Tansley, T. L., 195(80), 196(80), 197,213 Tarr, N. G., 192(74), 213 Taub, H., 377,410 Taulbjerg, K., 415, 438 Taylor, D. W., 38, 52, 90 Taylor, J. R., 40, 42,89 Tdomachev, A. I., 31.91 Terhune, R. W., 63, 76,94,96 Thiel, F. A., 209(186, 187, 188), 216 Thoe, R. S., 423,433,435,437,441,442 Thomas, L., 36, 92 Thomas, R. A., 87, 93 Thomas, R. E., 203(129), 214 Thomson, G. P., 219,221, 222,289 Thornton, D. D., 104, 107,162 Tikhonov, E. A., 31, 91 Timoshechkin, M. I., 85, 90 Tittel, F. K., 37,38,73,74,80,81,90,91,94,96 Toburen, L. H., 413, 418, 419, 420, 421, 422, 425,426,427,428,434,438,439,440,441, 442 Toennis, J. P., 358 Tolhoek, H. A., 221, 225, 227, 228, 289 Tolk, N. H., 358 Tomov, I. V., 52, 96 Tong, S. Y., 226,242,289, 358 Torrey, H. C., 144, 162 Townes, C. H., 100, 161,162 Townsend, W. G., 200(105), 214 Traxel, K., 415,434,438 Tretiak, 0. J., 375, 410 Treves, D., 36, 74, 90 Trevor, P. L., 79, 92 Trias, J. A., 82, 83, 95 Triboulet, R., 209(192, 193), 216 Trofim, V. G., 204(147), 215 Truong, T. K., 366,400,409 Tsai, M.-J., 181(49), 209(189, 190), 212, 216 Tsuda, S., 204(144b), 215 Tuccio, S. A,, 32,94 Tucker, J. S.,152, 162 Tully, J. C., 358 Turner, J. J., 41,42,43, 94 Tyan, Y.-S., 165(22), 211 Tzoar, N., 284,288

U Uchino, Q., 41,52, 53,93 Uhlenbeck, G. E., 219,286

Ulich, B. L., 110, 128, 129, 162 Unertl, W. N., 224,237,251,259,288,289 Unguris, J., 253, 275, 276, 280, 281,285, 289, 288 Urli, N. B., 185(58), 212

V Valeriani, G., 106, 159 Van den Bout, P., 129, 160 Van der Plas, H., 205(155), 215 Van der Wed, M. J., 356 Van der Ziel, A., 145, 162 Vane, C. R., 423,433,435,437,441,442 van Eck, J., 425,426,427,441 Van House, J. C., 282, 289 Van Hove, M. A., 226,242,289,358 Van Klinken, J., 222,289 van Laar, J., 171(41),212 Vanni, U., 11, 12, 90, 94 Van Roosbroeck, W., 191(70), 213 Van Ruyven, L. J., 195(81), 213 Van Stryland, E., 40,45, 91 Van Vleck, J. H., 117, 162 Varga, A. V., 61, 93 Varga, P., 20,31, 96 VCgh, J., 422,439 Verly, J. G., 402,405, 410 Vigroux, L., 113, 159 Viktorovitch, P., 200(11 I), 214 Vilenkin, N., 361, 372, 409 Viola, T. S., 145, 162 Volkov, S. Yu.,85, 90 Vollrath, K., 62, 92 Volosov, V. D., 64, 96 Volz, D. J., 413,420, 426, 429, 430, 440, 442 Volze, J., 3, 23, 95 von Barth, U., 229,264,289 von der Linde, D., 40,47, 93 Von Hoerner, S., 134, 135, 136, 162 von Roos, O., 188(64),212 Vossen, J. L., 358 Vredeool, L. A., 224, 261,263, 285,288,289 Vriens, L., 284,289

W Wade, G., 371,409 Wagner, S., 165(20), 187(60, 61, 63), 208(60, 61, 183, 184), 209(202), 210(203, 210), 211,212,216

459

AUTHOR INDEX

Wagner, S. L., 384, 385,410 Wagstaff, C. E., 33, 66, 68, 96 Wainwright, P. F., 268,284 Wakoh. S., 263, 265, 289 Walcher, T., 415,434, 438 Walker, D. W., 242, 245, 289 Walker, R. C., 131, I61 Wallace, S. C., 84, 93 Wallenstein, R., 26, 96 Walling, J. C., 85, 86, 87, 96 Walters, G. K., 223, 231, 235, 251, 254, 255, 256,287,288 Wang, C. S., 266,289 Wang, G.-C., 224, 225, 231, 233, 236, 237, 239, 246, 247, 248, 249, 250, 253, 254, 257, 258, 259, 260, 261, 262, 265, 270, 271,272,273,274,285,286,287,288,289 Wang, L., 393,410 Wang, S.-W., 229, 264,265,266,268,289 Wannier, P. G., 106, 137, 162 Ward, J. F., 84,96 Ward, J. H. R., 196(90),213 Warfield, G., 210(207), 216 Warner, J., 72, 74, 94, 96 Waters, J., 117, 118, 162 Watson, R. L.,426,442 Watson, W. D.. 112, 162 Waynant, R. W., 82, 91 Weaver, E. G., 73, 90 Weaver, J. C., 358 Webb, J. P., 18,96 Webb, M. B., 226,232,249,287,288 Weber, M. J., 6, 96 Webster, F. G., 18, 96 Wechsung, R., 357 Weinreb, S., 154, 162 Weinreich, G., 60, 92 Weiss, G. H., 386, 408 Weisskopf, V., 223, 289 Welch, W. J., 100, 104, 107, 161, 162 Welling, H., 32, 59, 64, 92, 93, 95 Werner, M. W., 148, 161 Westwater, R., 119, 162 Whinnery, J. R., 47, 90, 96 Whitaker, A. J. T., 140, 159 Whitcomb, B. M., 19, 96 White, C. W., 358 White, F. R., 210(204), 216 White, J. G., 165(31), 212 Whitehead, C., 417,439

Whitenton, J., 424, 427, 436, 440 Whitmer, C. A,, 144, 162 Wielebiniski, R., 136. 160 Wieman, H., 422,433,434,436,438,441 Wilke, V., 75, 76, 96 Wilkerson, T. D., 4, 25, 26, 90 Wilkinson, P. N., 130, 161 Williams, A. R., 228, 264, 287 Williams, D. A,, 108, 161 Williams, E. W., 165(16), 211 Williams, R., 207(159), 215 Willis, J. R., 371, 410 Willis, R. F., 282, 289 Wilson, W. L., 37,38,81,94,96, 100, 102, 106, 113, 115, 134, 139, 160, 161, 162, 420, 421,422,425,427,434,438,439,441,442 Windscheif, J. C., 88, 92 Wittig, C., 52, 91 Woerlee, P. H., 430,431,432,438,439 Wold, H., 371, 372,409 Wolf, D., 223, 235, 240, 252, 286, 288 Wolf, M., 182(52), 190(68a,b), 201. 212, 213, 214 Wolfram, T., 225, 261, 266, 289 Wolicki, E. A., 358 Wood, P. J., 134, 162 Woodall, J. M., 170(38), 204(148), 205(151), 212,215 Woodbury, E. J., 74, 96 Woodruff, D. P., 232,289 Woods, C. W., 427,433,435,436,437,442 Woods, J., 207(162), 215 Woods, R. C., 110,162 Woody, D. P., 152, 160 Wordeman, M. R., 153, 161 Wright, M. C. M., 104, 107, I62 Wrixon, G. T., 146, 153, 161 Wrobel, W.-G., 85, 96 Wronski, C. R., 203(136), 204(136, 143, 144a). 214,215 Wu, C. S., 222,289 Wynne, J. J., 60, 95

Y Yakowitz, H., 357 Yamada, S., 430,439 Yamaguchi, K., 209(197, 198,201), 216 Yamane, N. I., 104, 107,160 Yan, J. J., 209(189), 216

460

AUTHOR INDEX

Yang, C. N., 222,233,287 Yang, E. S., 200(106), 214 Yariv, A., 39, 63, 96 Yasa, Z. A,, 47, 96 Yasevichyute, Ya., 71, 93 Yau, M., 400,409 Yee, T. K., 9, 10, 96 Yeh, Y. C. M., 205(156), 206,215 Yin, S.-Y., 208(180), 209(200), 215, 216 Yoshikawa, A., 208(185), 226 Young, D. T., 100, 145,162

Young, J. F., 33, 93 Young, M., 47, 96 "

L

Zak, J., 400, 409 Zernike, F., 60,68, 74,95,96 Zhdanov, B. V., 71,90 Ziem, P., 425,427,430,434,441,442 Zitzewitz, P. W., 282, 289 Zubarev, I. G., 74, 92

Subject Index

A

Ablating flashlamp, 8-9 Absorption, crystal, in resonant cavity, 65 Absorption spectrum, of atmosphere, 117, 119-121 Accelerator, 414 Acoustico-optical spectrograph (AOS), 15 1 Active mode-locking, 39 ADA, see Ammonium dihydrogen arsenate ADP, frequency doubling of cw dye laser, 63-64 Adsorbate-substrate interaction. 252-256 Adsorption, physical, 294 AEAPS, see Auger electron appearance potential spectroscopy AES, see Auger electron spectroscopy AHP, see N-amino-homopiperidine Alexandrite laser, 85-87 Alexandrite laser-pumped dye laser, 5 Algebraic reconstruction technique (ART), 374-376,408 Alkali halides, cw color center lasers in, 55-59 Aluminum arsenide, lattice constant, 170 Aluminum gallium arsenide/gallium arsenide heteroface buried homojunction cell, 186 Aluminum gallium arsenide/gallium arsenide heterojunction, 204 N-amino-homopiperidine (AHP), 19 Ammonium dihydrogen arsenate (ADA), frequency doubling in cw dye laser, 63-65 Amorphous silicon, 203-204 Amorphous solid electron scattering from surfaces, 226 spin polarization in electron scattering, 223 AMOS cell, 205 Amplifier, see also Oscillator-amplifier excimer lasers, 52-53 millimeter radiotelescope, 147 optical parametric, 71 -72 picosecond pulses, amplification of, 43 pulsed laser-pumped, 43 46 1

Anomalous photovoltaic effect, 165 Antenna millimeter radiotelescope, 100, 102, 124, 133-142 adjustment of dish surface, 138-140 atmospheric effects, 126 baseline ripple, 129- 130 beam switching, 127-128 calibration, 128-129 design and construction, 135- 138 frequency switching, 128 geometry and optics, 134- 135 interferometer, 130 lower limit of wavelength, 125-126 mount and pointing, 141 overall error budget, 140-141 pointing accuracy, 126 sensitivity, 124- 125 weather protection, 141-142 Antiferromagnet, 225 Antireflection coating, photovoltaic cell, 202 Anti-Stokes radiation, 75, 347 AOS, see Acoustico-optical spectrograph Appearance potential spectroscopy (APS), 316-318 APT, see Algebraic reconstruction technique Argon as buffer gas, in vapor phase dye laser, 3738 relative satellite line intensities, from ionatom collisions, 424 target, ion-atom collisions, 428,430, 433 Argon laser, 32, 35, 47, 49, 64, 84-85 Astigmatism, in laser, 64 Astrodome, for radiotelescope protection, 100,141-142 Atmosphere absorption spectrum, 119-121 effects, in millimeter radioastronomy, 116123, 126, 130-131 radiation temperature, 128-129 remote sensing of gases, 25

462

SUBJECT INDEX

Atomic number of projectile, in ion-atom collisions, 416417 and spin polarization, 246 Atomic physics, 412-413 Attenuation, atmospheric, in millimeter radioastronomy, 116-1 17, 119-121, 128-129 Auger electron, in ion-atom collisions, 423433,435-437 Auger electron appearance potential spectroscopy (AEAPS), 297-298 Auger electron spectroscopy (AES), 298-301 Auger spectrum, satellite structure, 436

B Back contact, photovoltaic cell, 187-188, 192 Backprojection averaging, 374, 395, 398, 400 Backscatter method, of remote sensing of atmospheric gases, 25 Backward wave oscillator, 149 Backward-wave Raman pulse compression, 54 Band gap transition, photovoltaic cell, 182183 BEA, see Binary encounter approximation Beam switching, millimeter radiotelescope, 127-128 BEP, see Binary encounter peak Binary encounter approximation (BEA), in direct Coulomb excitation, 416 Binary encounter peak (BEP), from ion-atom collision, 418-419,429, 434 Blackbody radiation, in millimeter radioastronomy, 115 Blue-green laser, 79-83 Bolometer, millimeter radioastronomy, 143144 Brewster-angled element, of laser, 64 Buried junction, see Heteroface junction C

Cadmium sulfide/cadmium telluride junction, 178 Cadmium sulflde/indium phosphide junction, 187 Cadmium telluride photovoltaic cell, 209

Calcite, ellipsometry, 345 Carbon monoxide, energy levels, 108-109 Carcinotron, 149 Carrier collection photovoltaic cell, 185 Cassegrain arrangement, parabolic dish antennas, 134- 135 Cathode sputtering, in surface cleaning, 293 Cavity-dumped laser, 47,49-50 Characteristic isochromat spectroscopy (CIS), 318-319 Charge state dependence, of ionization cross section, 43 1,436 Charge transfer to continuum states (CTC) theory, in ion-atom collisions, 423 Chemical vapor deposition, in surface cleaning, 293 Chemisorption, 294 Chloroaluminum phthalocyanine, 3,21 CIS, see Characteristic isochromat spectrosCOPY Clouds, effects of, in millimeter radioastronomy, 116 CMA, see Cylindrical mirror analyzer CMTA, see Constant momentum transfer averaging Coaxial flashlamp, 8 Coaxial flashlamp-pumped dye laser, 4, 14- 17 Cobalt, spin-dependent scattering, 268-269 Collection function, photovoltaic cell, 176I79 Collection resistance, photovoltaic cell, 181182 Color center laser, 54-59 tunable picosecond and subpicosecond sources, 39,41, 51-52 Coma, in laser, 64 COMSAT nonreflective cell, 202 Constant momentum transfer averaging (CMTA), 248-249 Contact area, photovoltaic cell, 180-181 Contact resistance, photovoltaic cell, 181 Continuous Radon transform (CRT), 394395,397 Continuous wave color center laser, 55-59 Continuous wave dye laser, 32-35 injection-locking, 36 intracavity frequency-doubled, 63-68 mode-locking, 39,41 tunable picosecond and subpicosecond sources, 39-40,45-51

SUBJECT INDEX

Convolution-backprojection method, of reconstruction algorithms, 374-375 Convolution technique of tomographic image recontruction, 365 Copper indium selenide photovoltaic cell, 209-210 Copper vapor-pumped dye laser, 5 Coudk focus, 134 Coumarin dyes, 45-46 Cresyl violet perchlorate, 46 CRT, see Continuous Radon transform Cryptocyanine, 19 Crystal cleaning of surfaces, 292-293 electron scattering, 232-233 mounting, 292 spin polarization in electron scattering, 223 surface analysis, 291-292 surface resonances, 256-259 Crystalline surface, 294 CTC theory, see Charge transfer to continuum states theory Cuprous oxide, photovoltaic effect, 164 Cuprous sulfide-cadmium sulfide heterojunction photovoltaic cell, 165,195-196,206-

208 Current generation, photovoltaic cell, 189-

193 Curved planar dye cell, 1 1 - 12 Cyanine dye, 3 Cyclohexane, 20 Cylindrical energy filter, 302 Cylindrical mirror analyzer (CMA), 303 ion-atom collision studies, 415

D DAPS, see Disappearance potential spectrosCOPY Dark current MIS diode, 199 photovoltaic cell, 171-172,176,190,192 De-excitation mechanisms, in ion-atom collision studies, 417 Degenerate parametric generation, 68 Delay line dye laser, 50-51 Density matrix, in spin polarization, 226-228 Depletion layer of homojunction, recombination in, 194

463

Desorption induced by surface acoustic waves, 350-351 in surface cleaning, 293 DIAL, see Differential absorption lidar Dicarbocyanine dye, 18-19 3,3’-DiethyL2,2’-0xyatricarbocyanineiodide (DOTC), 19,23,25,47 3,3’-Diethyltricarbocyanine,3 Differential absorption lidar (DIAL), 25,71 Diffusion current, photovoltaic cell, 171,194 Dimethylsulfoxide (DMSO), 18-19,23,47 Diode, mixer, 145-146 Diode current, photovoltaic cell, 171 Dirac equation, 228,241-242 Dirac’s theory of electron spin, 221 Direct Coulomb excitation, 416 Disappearance potential spectroscopy (DAPS), 321-322 Discrete Radon transform (DRT), 394-395,

397,399 DMSO, see Dimethylsulfoxide DODCI (dye), 39,42,45,47, 53 DOTC, see 3,3’-DiethyL2,2’-0xyatricarbocyanine iodide Double differential cross section (DDCS), in ion-atom collisions, 418-419,422 Double-pass optical parametric oscillator, 70 DRT, see Discrete Radon transform Dry air, effects of, in millimeter radioastronomy, 116-117,121-122 Dye, for usein dye lasers, 3,17-19,31-32,42,

46-47 chemical names of IR dyes, 25 energy level, 5-6 relative output energy tuning curves, 28 tuning curves, 35 tuning efficiencies, 29 vapors, 36-38 Dye laser, 3-38 cw dye lasers, 32-35.45-51 flashlamp-pumped, 7-19,42-43 harmonic generation in, 60-63 injection-locked, 35-36 intracavity frequency-doubled, 63-68 laser-pumped, 20-32 Lyman-a source, 84 mode-locking, 39,41 Nd: YAG-pumped, 27-32 nitrogen laser-pumped, 25-27 principles and limitations, 5-7

464

SUBJECT INDEX

pulsed laser-pumped, 43-45 ruby laser-pumped, 21-25 SRS sources, 74-77 sum-frequency mixing, 73-74 synchronous pumping, 39,41 vapor phase, 36-38 Dye laser mirror, 20

E ECAT, see Emission computer-assisted tomography EID, see Electron induced desorption EIID, see Electron impact ion desorption Elastic scattering, 226, 232 Electroluminescence, 164 Electron-atom scattering, 245 Electron bombardment, in surface cleaning, 293 Electron capture mechanism, 417 Electron diffraction, 304 Electron energy loss spectroscopy (ELS), 301-303 Electron gun, 235-236,238 Electron-hole pair creation, inelastic scattering, 267 Electron impact ion desorption (EIID), 3123 14 Electron induced desorption (EID), 314-315 Electron loss peak (ELP), in ion-atom collisions, 419,422,429,434 Electron-magnon scattering, 263, 267 Electron microscopy, Radon transform, 371, 373 Electron paramagnetic resonance (EPR), 354356 Electron-phonon scattering, 267 Electron probe microanalysis (EPMA), 31932 1 Electron probe surface mass spectrometry (EPSMS), 312-314 Electron scattering spin polarization, 219-289 from surfaces, 226 Electron spectrometer, 414-41 5 Electron spectroscopy, from high-energy ionatom collisions, 41 1-442 Electron spectroscopy for chemical analysis (ESCA), 340-342

Electron stimulated desorption (ESD), 314315 Electron stimulated desorption of ions by angular distribution (ESDIAD), 314 Electrostatic electron spectrometer, 41 5 Ellipsometry, 345-347 ELP, see Electron loss peak ELS, see Electron energy loss spectroscopy Emission computer-assisted tomography (ECAT), 368-369,373,402 Energy level of interstellar molecules, 108- 109, 111 of organic dye, 5-6 Epitaxial film formation, in surface cleaning, 293 EPMA, set! Electron probe microanalysis EPR, see Electron paramagnetic resonance EPSMS, see Electron probe surface mass spectrometry Equivalent circuit, photovoltaic cell, 171-172 ESCA, see Electron spectroscopy for chemical analysis ESD, see Electron stimulated desorption ESDIAD, see Electron stimulated desorption of ions by angular distribution Ethanol, 20 Exchange interaction, spin-dependent scattering due to, 224,228-230,236-237,239 Excimer laser, 76,79-82 tunable picosecond and subpicosecond sources, 39,41, 52-53 Excitation-ionization mechanisms, in ionatom collisions, 415-417 Extraordinary ray, of polarized light, 345

F Fabry-Perot interferometer, in pumped dye laser, 26 Fan-beam geometry, 367-369, 374, 388-394, 401,403-406 Faraday cup assembly, 238-239 FEM, see Field emission microscopy Ferromagnetic materials, spin polarization in electron scattering, 225, 261-281 Ferromagnetic surface, exchange scattering, 229 FET amplifier, 147, 154 Field desorption, in surface cleaning. 293

465

SUBJECT INDEX

Field-effect transistor amplifier, see FET amplifer Field emission microscopy (FEM), 352-354 Field ion microscopy (FIM), 352-354 Filled aperture radiotelescope, see Single dish radiotelescope Fill factor, photovoltaic cell, 173- 176 Filter spectrograph, 150 FIM, see Field ion microscopy Flame spectrometry, 294 Flashlamp-pumped dye laser, 4,7-19 coaxial flashlamp dye laser, 14-17 frequency doubling, 63 infrared flashlamp, 17-19 injection-locking, 36 linear cells with linear flashlamps, 7-14 mode-locking, 39,4243 tunable picosecond and subpicosecond sources, 39-40,42-43 W radiation, 61-62 Fluorescent yield, in ion-atom collisions. 424-425,432,436 Foil target, ion-atom collision studies, 415 Folded cavity, three-mirror, 32-33, 48 Folded path optical delay line cavity, 5 1 Formaldehyde, energy levels, 108-109 Fourier domain technique of tomographic image reconstruction, 365 Fourier transform-Radon transform relationship, 363-364, 373 Four-wave mixing, picosecond tunable source, 41 Frequency band allocation, for remote sensing, 115 Frequency-conversion devices, tunable picosecond sources, 39 Frequency-doubling cw dye laser, 63-68 KDP crystal, 62-63 pulsed dye lasers, 60-62 Frequency switching, millimeter radiotelescope, 128 G

Galactic structure and evolution, 113-1 14 Gallium arsenide lattice constant, 168 photovoltaic cell, 164, 204-206 polarized electron source, 237-239

Gallium aluminum arsenide/gallium arsemide cell, 170 Gallium aluminum arsenide-pumped dye laser, 5 Gas-solid interaction, 350 Gas target, ion-atom collision studies, 41 5, 4 18-42 1 Germanium, lattice constant, 168 Gold phase change as function of temperature, 252-253 spin polarization in electron scattering, 223 Gunn oscillator, 148-149

H Hansch cell, for dye laser, 26 Harmonic generation, in pulsed dye lasers, 60-63 Heavy projectiles, from ion-atom collisions, 428-432 HEED, see High-energy electron diffraction HEEIS, see High-energy electron impact spectroscopy Helium-neon laser, 342 Helium target, in ion-atom collisions, 418421,428,430,433,436 Hemispherical electrostatic filter, 302 Heteroface junction, 169-170 p-AIGaAs/p-GaAs/n-GaAs, 204-205 CdS/CdTe, 209 surface recombination, 186 Heterojunction, 166-169 p-AlGaAsln-GaAs, 204 carrier collection, 185 n-CdS/p-InP, 208 CdTe, 209 Cu,S/CdS, 206-208 junction current, 194-198 optical absorption, 182 photovoltaic cell, 178 Hexagonal sampling, of Radon transform, 387 I ,3,3,1’,3’,3’-Hexamethyl-2,2’-indotricarbocyanine iodide (HITC), 19,25,47 High-energy electron diffraction (HEED), 304-306,3 10 High-energy electron impact spectroscopy (HEEIS), 306-307 High-energy ion-atom collisions, 41 1-442

466

SUBJECT INDEX

HITC, see 1,3,3,1’,3’,3’-Hexamethyl-2,2’indotricarbocyanine iodide Holographic method, of parabolic dish measurement, 139-140 Homojunction, 166,169 band gap, 184 carrier collection, 185 CdTe, 209 GaAs, 204 junction current, 193-194 optical absorption, 182 quantum efficiency, 186 surface recombination, 185-186 Houndsfield number, 408 Hydrogen polarized electron scattering, 228-229 target, in ion-atom collisions, 418-421 Hypersatellite, in Auger spectrum, 436

I ICRT, see Inverse continuous Radon transform IDRT, see Inverse discrete Radon transform Image edge detection, 371 IMMA, see Ion microprobe mass analysis Impatt oscillator, 149 IMXA, see Ion microprobe X-ray analysis Indium antimonide mixer, 148 Indium phosphide photovoltaic cell, 208-209 Inelastic electron tunneling spectroscopy (IETS), 352 Inelastic low-energy electron diffraction (ILEED), 307 Inelastic scattering, 226,263,267,283-284 metallic glass, 275-277 Infrared absorption spectroscopy, 351-352 Infrared dye, 18-19,25,42 Infrared dye laser, 20 Infrared flashlamp-pumped dye lasers, 17-19 Infrared radiation sum-frequency mixing, 74 tunable sources, 60 Injection-locked dye laser, 35-36,43 INS, see Ion neutralization spectroscopy Insulator, electron scattering from surfaces,

226 Integrated precipitable water vapor (IPWV),

118-119

Interface collection function, photovoltaic cell, 177-178 Interface recombination heterojunction, 195 photovoltaic cell, 186 Interface state of heterojunction, 195-196 Interferometer calibration, 132-133 data reduction and phase fluctuation, 131 millimeter radioastronomy, 102, 104,107,

124,130-133,149,158 phase stability, 131 scaling down, 132 Interstellar chemistry, 112-113 Interstellar maser, 111 Interstellar molecules, 108-1 10 Intracavity frequency-doubled cw dye laser,

63-68 Invar, 100 Inverse continuous Radon transform (ICRT),

394-395,399 Inverse discrete Radon transform (IDRT),

394-401 Inverse layer MIS cell, 203 Inverse Radon transform, 364-366.372-376 Ion accelerator, 414 Ion-atom collisions, 411-442 high-energy projectiles, 432-437 instrumentation and basic concepts, 414417 intermediate-energy projectiles, 417-432 Ion bombardment, in surface cleaning, 293 Ion induced optical emission, 334-336 Ion induced X-ray analysis (IIX), 334-336 Ionization cross section, 424-425,428-429,

431 Ionization mechanisms, in ion-atom collisions, 415-417 Ion laser-pumped dye laser, 5 Ion microprobe mass anaIysis (IMMA), 325-

327 Ion microprobe X-ray analysis (IMXA), 334-

336 Ion neutralization spectroscopy (INS), 322-

324 Ionometry, 327-328 Ion scattering spectroscopy (ISS), 328-330 IPWV, see Integrated precipitable water vapor ITO/InP junction, 209

467

SUBJECT INDEX

J Junction current inversion layer MIS cell, 203 photovoltaic cell, 171-172, 188-189, 193200

K KDP crystal, 61 -63, 71,73 KF: Fi laser, 55 Kiton Red 5 (dye), 17 Klystron local oscillator source, 148-149 Krypton laser, 32,47, 5 1, 55-56, 58 K-shell Auger electron production cross section, 436-437 ionization, 416 ionization cross section, 424-425,428-429, 43 1 vacancy sharing ratio, 43 1-432

Lithium, nuclear reactions with surface elements, 337 Lithium fluoride:F,+ laser, 55, 57-58 Lithium niobate, 63 Local oscillator (LO), millimeter radiotelescope, 131, 147-150, 153-154 Low-energy electron diffraction (LEED), 223, 226,232,240-246,248,264, 267 experimental apparatus, 234-238 NiO, 224-225 surface analysis, 307-309 Low-energy ion scattering spectroscopy (LEISS), 328-330 Low-energy molecular beam scattering (LEMS), 337-339 L-shell ionization cross section, 424-425 vacancy sharing ratio, 431 Lyman-a sources, tunable UV, 83-85

M

L LAMMA, see Laser microprobe mass analysis Laser, 2; see also specific lasers Laser microprobe mass analysis (LAMMA), 342-343 Laser-pumped dye laser, 4-5, 20-32 frequency doubling, 61 Laser Raman spectroscopy, 347-348 Lattice matching AIGaAsiGaAs, 205 heterojunction, 168 photovoltaic cell, 178 LEED, see Low-energy electron diffraction LEISS, see Low-energy ion scattering spectroscopy LEMS, see Low-energy molecular beam scattering Light bucket, 143 Light current, photovoltaiccell, 171-172,176, 189-190, 192 Light projectiles, from ion-atom collisions, 417-428 Linear cavity, cw dye laser, 50 Linear dye cell with linear flashlamp, 10-1 1 Linear flashlamp-pumped dye laser, 4, 7-14

MacDonald Observatory, Texas, 100, 102, 105-106, 123 Magnesiumizinc phosphide junction, 210 Magnetic spectrometer, 415 Magnetic spectroscopy, 434 Magnetic storage and recording, 283 Magnetic surface, electron scattering from, 234 Magnon scattering, 263, 267, 284 MBE, see Millimeter beam epitaxy Medium-energy ion-atom collisions, 41 3, 417-432 Medium-energy ion scattering spectroscopy (MEISS), 328-330 Mercuric halide laser, 82-83 Mercury, spin polarization in electron scattering, 223 Metal, electron scattering from surfaces, 226 Metal-doped solid state laser, 85-89 Metal-insulator-semiconductor (MIS) junction, 171 gallium arsenide, 205-206 junction currents, 198-200 silicon, 202-203 Metallic glass, spin-dependent scattering, 274-279,283

468

SUBJECT INDEX

Metal oxide, silicon junctions with, 203 Millimeter radioastronomy, 97-162 achievement and prospects, 107-1 14 antennas, 133-142 development, 99-107 evolution and projects, 152-159 observing conditions and sites, 114-123 radiotelescope fundamentals, 124-130 receivers, 142-154 Mirror, intracavity frequency-doubled laser, 64-65 MIS junction, see Metal-insulator-semiconductor junction Mixer local oscillator injection, 150 millimeter radioastronomy, 100, 104, 144148, 152-153 Mode-locking, 39-42 cw dye lasers, 45,47-49 excimer lasers, 52-53 flashlamppumped dye lasers, 42-43 picosecond lasers, 45 MO description, of ion-atom collision, see Molecular orbital description Molecular beam epitaxy, mixer diodes, 145 Molecular clouds, 107, 110-1 12 Molecular orbital (MO) description, of ionatom collision, 416 Molecule microscope, 316 Meller scattering, 224 Mossbauer spectroscopy, 348-349 Mott detection, 234-235,259-261 Mott diode, 146 Mott scattering, 221 -223 Muffin-tin potential, 241, 264 Multiple-flashlamp arrangement, for pumping dye lasers, 11- I4 Multiple ionization, 417,436

N

NAA, see Neutron activation analysis Nasmyth focus, 134 National Radio Astronomy Observatory, Arizona, 100-102,105-106, 122,137 Neodymium:glass laser, 20, 44-45, 52, 61 Neodymium:YAG laser, 43, 55-57, 61, 73, 76-79 OPA pump, 71

OPO pump, 68-70 UV pulses, 53 Neodymium: YAG laser-pumped dye laser, 4, 25,27-32 Neon K-shell Auger electron spectrum, 423, 431, 435-436 relative satellite line intensities, from ionatom collisions, 424 target, ion-atom collisions, 428, 430, 432433,436-437 NEP, see Noise equivalent power Neutron activation analysis (NAA), 339 Nickel, spin-dependent scattering, 264-269, 271-274 Nickel oxide, electron scattering, 224-225,264 Nitrogen laser-pumped dye laser, 4,20,25-28, 36,45 NMR, see Nuclear magnetic resonance Noise, millimeter radiotelescope receiver, 100, 102 Noise equivalent power (NEP), bolometer, 143-144 Noise temperature millimeter receivers, 125 parametric amplifier, 147 Nonideal sampling, Radon transform, 401406 Nonlinear coherent optical sources, 60-79 harmonic generation in pulsed dye lasers, 60-63 intracavity frequency-doubled cw dye laser, 63-68 optical parametric oscillators and amplifiers, 68-72 Raman generation, 74-79 sum-frequency mixing, 72-74 Notch front diode, 146 Nuclear accelerator, 414 Nuclear magnetic resonance (NMR), 354-356 Nuclear reaction methods of surface analysis, 337 Nyquist sampling, of Radon transform, 386 0

Offset parabolic dish antenna, millimeter radioastronomy, 102- 103, 133- 135 Ohmic contact, 181 OPA, see Optical parametric amplifier

SUBJECT INDEX

OPO, see Optical parametric oscillator Optical absorption, photovoltaic cell, 182-

469

Photoelectrochemical effect, 165-166 Photoelectrolysis cell, 166 185 Photoemission, 164 Optical delay line cavity, 51 Photogalvanic cell, 166 Optical diode, ring dye laser, 34-35 Photoluminescence, 163 Optical parametric amplifier (OPA), 71-72 Photostimulated desorption (PSD), 344-345 Optical parametric oscillator (OPO), 68-70 Photovoltaic cell, 171-179 Optical-pumped dye laser, 5 back contact, 187-188 Optoacoustic spectrometry, 350-351 carrier collection, 185 Ordinary ray, of polarized light, 345 collection resistance, 181- 182 Oscillator contact area, 180-181 millimeter radioastronomy, 148-150,153contact resistance, 181 154 efficiency, 173-I74 mode-locked, 42-43 interface recombination, 186 optical parametric, 68-70 junction current, 188-189 Oscillator-amplifier system optical absorption, 182-185 flashlamp-pumped dye laser, 17,62 polycrystalline films, 186-187 Nd: YAG-pumped dye laser, 29-30 reflection, I80 nitrogen laser-pumped dye laser, 26-27 surface recombination, 185-1 86 pulsed laser-pumped, 44 Photovoltaic effect, 163-217 ruby laser-pumped dye laser, 22-26 cell models, 171-179 Oxazine-I-perchlorate, 47 conversion efficiency, 164 Oxazine-170-perchlorate, 42 current generation, 189-193 Oxygen depth profiling. in surface analysis, junction current, 193-200 337 major processes and mechanisms, 179-189 photovoltaic materials systems, 200-211 P semiconductor junctions, 166-I71 Parabolic dish antenna, radiotelescope, 100, Picosecond and subpicosecond tunable laser 102,133-142 sources, 38-54 Parallel-beam geometry, 362-363, 368-369, color center lasers, 51-52 401,403-404 cw dye lasers, 45-51 sampling the Radon transform, 380-387, excimer lasers, 52-53 393 flashlamp-pumped dye lasers, 42-43 Parallel-plate analyzer, ion-atom collision pulsed laser-pumped dye lasers, 43-45 studies, 415 vacuum UV sources, 53-54 Parallel-plate energy filter, 303 PIX, see Proton induced X-ray analysis Parametric amplifier, 71-72 Plane mirror analyzer (PMA), 303 Parametric oscillator, 68-70 Plane-wave Born approximation (PWBA), in Passive mode-locking, 39,45,47 direct Coulomb excitation, 416 Pauli spin operator, 226 Planoconvex lens, for unfolded cavity of cw Pauli’s theory of electron spin, 221 dye laser, 47 Phase closure relation, in interferometer ra- Plasmon excitation, inelastic scattering, 267 diotelescope, 131 Platinum, spin polarization in electron scatterPhase transition, 252-256 ing, 250-25I p-Phenylene-bis(5-phenyl-2-oxazole) PLEED, see Polarized low-energy electron (POPOP), 36-38 diffraction Photoconductivity, 163 PMA, see Plane mirror analyzer Photodesorption p-n heterojunction, 168 by an intrinsic photoeffect, 343-344 collection function, 176-I77 in surface cleaning, 293 p-n homojunction, 167

470

SUBJECT INDEX

p-n junction, polycrystalline silicon, 202 p-n junction silicon cell, 201 Pockel's cell, 42, 237 Polarized low-energy electron diffraction (PLEED), 223-224, 229, 233-234, 244254,264,266-267,281-282 experimental apparatus, 235-238 polarization detector, 259-261 Polarography, 294 Pollution detection lidar, 71 Pollution monitoring, 371 Polycrystalline film collection resistance, 182 grain boundaries in, 186-187 Polycrystalline silicon, 202 Polymeric (SN), photovoltaic cell, 210-21 1 Polymethine dye, 20 POPOP, see p-Phenylene-bis(5-phenyl-2oxazole) Potassium, spin polarization in electron scattering, 224 PPD (dye), 46 pt-p-n heteroface buried junction, 169 Projection-slice theorem, of inverse Radon transform, 363-364, 372 Prompt electrons, from ion-atom collisions, 418-423,428-429,432-435 Proton induced x-ray analysis (PIX), 334-336 PSD, see Photostimulated desorption Pulse compression, 54 Pulsed dye laser, 20-32 harmonic generation in, 60-63 Pulsed laser bombardment, in surface cleaning, 293 Pulsed laser-pumped dye laser, 43-45 frequency doubling, 63 PWBA, see Plane-wave Born approximation

Q Quadraxial dye cell, 19 Quantum efficiency homojunction, 186 photovoltaic cell, 171 spectral dependency, 178 Quartz, ellipsometry, 345 Quasi-optical components, millimeter radioastronomy, 153

R Radioastronomy, Radon transform, 370,372373,402,405 Radioastronomy at millimeter wavelengths, see Millimeter radioastronomy Radiographic imaging, 368 Radionuclide imaging, 368-369,373 Radiotelescope, millimeter, 100-103, 124130, 154-159 Radon transform, 359-410 applications in imaging, 368-372 continuous Radon transform pair, 362-368 historical background and review, 372-376 inverse discrete Radon transform, 394-401 properties of, 376-379 sampling nonideal, 401-406 with fan-beam projections, 388-394 with parallel-beam projections, 380-387 Radon transform pair, 366 Rain, effects of, in millimeter radioastronomy, 1I6 Raman effect, 347-348 nonlinear coherent optical sources, 74-79 ruby laser-pumped dye laser, 24 Rare-earth-doped laser, 88-89 RATAN, millimeter radiotelescope, 102 Receiver, millimeter radioastronomy, 100, 102, 104, 125, 142-154 back ends for spectroscopy, 150-151 bolometers, 143-144 local oscillator, 148-150 mixer, 144-148, 152-153 noise, and baseline ripple, 129 quasi-optical components, I53 Recombination current, photovoltaic cell, 171 Reconstruction algorithms, 372-376 RED, see Reflected high-energy electron diffraction Reflected high-energy electron diffraction (RHEED or RED), 305-306,309-310 Reflection-absorption spectroscopy, 35 1-352 Reflectivity tomography, 370-371 Reflector telescope, 143 Refraction effects, in millimeter radioastronomy, 121 Refractive index tomography, 370 Remote sensing, tunable W sources, 61-62

SUBJECT INDEX

Resolving power, millimeter radioastronomy, 102 Resonance scattering, in LEED, 245 Resonator, Nd:YAG lasers, 27.29 RHEED, see Reflected high-energy electron diffraction Rhodamine B, 46,53 Rhodamine6G, 6-7,10,13,16-17,42,46-49, 53 Rhodamine 6G laser, 61, 63-64, 66 Rhodamine 640,42 Ring laser, 32-36,49-50 Ring laser cavity, frequency doubling, 66-68 Ruby laser-pumped dye laser. 4,21-26 Rydberg formula, 256

S Satellite, in ion-atom collisions, 423-424,436 Satellite-to-submarine laser communication project, 79 SCA, see Semiclassical approximation SCANIIR, see Surface composition by analysis of neutral and ion impact radiation Scanning electron microscopy (SEM), 310312, 319-321 Schottky barrier, thermally assisted tunneling, 197 Schottky barrier cell, 210 gallium arsenide, 205 Schottky barrier epitaxial diode, millimeter radiotelescope mixer, 145 Schottky barrier junction, 170-171 carrier collection, 185 junction currents, 198 optical absorption, 182 SDMM, see Surface desorption molecule microscopy Secondary ion mass spectroscopy (SIMS), 325,330-334 Second harmonic generation (SHG), 60 tlashlamp-pumped device, 62 Selenium, photovoltaic effect, 164 Self-mode locking, 39 SEM, see Scanning electron microscopy Semiclassical approximation (SCA), in direct Coulomb excitation, 416 Semiconductor band gap, 182-184

47 1

electron scattering from surfaces, 226 reflection, 180 Semiconductor-insulator-semiconductor structure heterojunction, 169 junction currents, 200 Semiconductor junction, photovoltaic effects 166- 171 Series resistance, photovoltaic cell, 174-1 76, 181 SFG, see Sum-frequency mixing Shake-off (or -up) satellite, from ion-atom collisions, 423-424 Sherman function, 222 SHG, see Second harmonic generation Shunt resistance, photovoltaic cell, 174-176 Silica, fused, pulsed tunable SRS sources, 78 Silicon indirect band gap, 183 photovoltaic cell, 164, 201-204 solar cell, 165 Simmer-enhanced flashlamp, 9- 10 SIMS,see Secondary ion mass spectroscopy Simultaneous iterative reconstruction technique (SIRT), 374-375 Single crystal p-n junction, 201-202 Single dish radiotelescope, 104-106, 124-125, 154-1 58 SIRT, see Simultaneous iterative reconstruction technique SIS structure, see Semiconductor-insulatorsemiconductor structure Sky background, in millimeter radioastronomy, 115-116 Slater exchange potential, 229, 245 Soft X-ray appearance potential spectroscopy (SXAPS), 316-318 Solar cell, 201, 210 amorphous silicon, 204 band gap, 183 contact resistance, 181 Solar spectrum, absorption, 183-185 Solid surface, 291-358 electron scattering, 226 Solid state laser, 85-89 intracavity frequency doubling, 64 Solid state local oscillator, 153-154 Spectrograph, millimeter radioastronomy, 104, 150-151

472

SUBJECT INDEX

Spectrophotometry, 294 Spectrum expander, 150- 151 Spherical condenser, 415 Spin detector, absorption effect as, 279-281 Spin-orbit interaction, 280-281 electron scattering due to, 221, 224, 228230,237-239 ferromagnetic materials, 270 Spin polarization in electron scattering, 219289 definitions, 226-228 experimental apparatus, 234-240 ferromagnetic materials, 261 -28 1 origin of spin-dependent scattering, 228230 outlook, 281-284 scattering due to spin-orbit interaction, 240-261 spin-dependent parameters and interactions, 225-234 symmetry relations, 230-234 SRS, see Stimulated Raman scattering; Stimulated Raman spectroscopy Standing wave laser, 33 Star formation, 113 Stimulated Raman scattering, 74-79, 82 Stimulated Raman spectroscopy (SRS), 60 W pulses, 53-54 Stokes radiation, 347 Stokes Raman shifted radiation, 75 Sum-mixing, 41, 53,72-74 Superconducting mixer, 152-153 Superconductor-insulator-superconductor junction, 152-153 Surface analysis, 291-358 by atomic surface waves, 350-351 by electric field method, 352-354 by electrons incident to surface, 297-322 by ions incident to the surface, 322-337 by magnetic field methods, 354-356 by neutral particles incident to the surface, 337-339 by photons incident to the surface, 340350 by thermal heat, 351-352 classification of techniques, 295-296 contamination and cleaning, 292-293

electron scattering, 226,230-231, 233-234, 245 exchange scattering, 229 magnetic properties, 261-283 PLEED studies, 252-253 structure-determination experiments, 246252,281-282 temperature-dependent magnetization, 266-267,283 Surface acoustic waves, 350-351 Surface barrier potential, 245 Surface barrier resonances, 256-259 Surface composition by analysis of neutral and ion impact radiation (SCANIIR), 334-336 Surface desorption molecule microscopy (SDMM), 315-316 Surface phase, 291 Surface potential barrier, 257 Surface recombination, photovoltaic cell, 185-186 SXAPS, see Soft X-ray appearance potential spectroscopy Synchronous pumping, 39,41,47-49,51

T Tandem accelerator, 414 Target, ion-atom collision studies, 415-421, 428,430,433 TCAT, see X-ray transmission computerassisted tomography TED, see Transmission electron diffraction TEM, see Transmission electron microscopy Temperature polarization effects in electron scattering, 251-253 spin-dependent scattering, 272 and surface magnetization, 265-267,283 P-Terphenyl, 20,46 Thermal desorption effects, 344-345 Thermal effects in nonlinear crystal, 65 on parabolic dish antennas, 136, 138, 140 Thermophotovoltaic effect, 165 Thin-layer activation surface analysis, 336337 Three-mirror folded cavity, 32-33,48

473

SUBJECT INDEX Time-of-Bight spectrometer, 343 Tomography convolution technique of image reconstruction, 365-366 Fourier domain technique of image reconstruction, 365 Radon-transform applications, 360-362, 368-376,407-408 Total ionization cross section, 424-425,429 Transition-metal-doped laser, 87-88 Transmission electron diffraction (TED), 304306 Transmission electron microscopy (TEM), 310-3 12 Transport equation, for photoexcited carriers, 189-192 Traveling wave ring dye laser, 33-34 Triaxial dye cell, 19 Triaxial flashlamp-pumped dye laser, 17 Tricarbocyanine dye, 18- 19 Trochoidal filter, 303 Tunable lasers, 1-96 blue-green lasers, 79-83 color center lasers, 54-59 dye lasers, 3-38 Lyman-cc sources, 83-85 metal-doped solid state, 85-89 nonlinear coherent sources, 60-79 picosecond and subpicosecond tunable sources, 38-54 Tungsten, spin polarization in electron scattering, 223, 247-249,251, 253-255,258259 Tunneling, 196-198,352

U Ultraviolet photoelectron spectroscopy (UPS), 340-342 Ultraviolet radiation, sources, 53-54, 60-67, 72-75,83-85 Unfolded cavity, planoconvex lenses, of cw dye laser, 47 UNILAC, nuclear accelerator, 414 Unstable resonator cavity, for Nd:YAG laser, 69 UPS, see Ultraviolet photoelectron spectrosCOPY

V

Vacancy sharing, Auger electron, 437 Vacancy sharing ratio, in ion-atom collisions, 429,43 1 Vacuum evaporation, in surface cleaning, 293-294 Vacuum W sources, 53-54 Van de Graaff accelerator, 414 Vapor phase dye laser, 36-38 Vortex-stabilized flashlamp, 9

W

Water vapor, effect of, in millimeter radioastronomy, 117-1 19, 121 Water vapor measurements, atmospheric, 25 Waveguide switch, 127 Weiss domain, of ferromagnet, 269 White light subpicosecond tunable laser source, 39, 41 Wien filter, 303

X Xan thine dye, 23 XeCl excimer laser, 52-53 Xe,CI laser, 79,81-82 XeF amplifier, 52 XeF laser, 79-81 XMA, see X-ray microanalysis XPS, see X-ray photoelectron spectroscopy X-ray diffraction, 304 X-ray fluorescence (XRF), 349-350 X-ray microanalysis (XMA), 3 19-321 X-ray photoelectron spectroscopy (XPS), 340-342 X-ray transition, 424 X-ray transmission computer-assisted tomography (TCAT), 360-362, 368, 373, 401402.405-407 Z

Zinc oxide/cadmium telluride heterojunction, 197 Zinc phosphide, 210 Z z scaling rule, in ion-atom collisions, 422

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