Advances in Electronics and Electron Physics, Volume 71 (Advances in Imaging and Electron Physics)

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 71

EDITOR-IN-CHIEF

PETER W. HAWKES Laboratoire d’Optique Electronique du Centre National de la Recherche Scientifique Toulouse, France

ASSOCIATE EDITOR

BENJAMIN KAZAN Xerox Corporation Palo Alto Research Center Palo Alto, California

Advances in

Electronics and Electron Physics EDITED BY PETER W. HAWKES Laboratoire d’Optique Electronique du Centre National de la Recherche Scientifique Toulouse, France

VOLUME 71

ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers

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COPYRIGHT 0 1988

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CONTENTS CONTRIBUTORS VOLUME 71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PREFACE ..........................................................

vii ix

Scanning Electron Acoustic Microscopy LUDWIG JOSEFBALK

I. 11. 111. IV. V.

Introduction . ......................... Signal Generation and Contrast Mechanisms . . . . . . . Instrumentation . . . . . . . .............................. Applications . Conclusions . . . . . . . . . . . . . . . . . . . ................

26

69

Recent Progress in Particle Accelerators F. T. COLEand F. E. MILLS

I. 11. 111. IV. V. VI. VII.

Introduction . . . . . . . . . . . . . . . . . . . . . .................. Inventions and Developments . . . . . . . . . . . . . . . . . . Beam Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistical Methods and Qualit ntrol ......................... Superconducting Technology .............................. New Kinds of Accelerators . . . . . . . . . . ............. Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75 79 87 90 92 98 105 105

Foundations of Environmental Scanning Electron Microscopy G . D. DANILATOS

.... ..... I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 11. State of Gas in the ESEM . . . . . . . . . . . . ............. 111. Outline of General Interactions in the ESEM . . . . . . . . . . . . . . . . . . . . IV. Electron Beam Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. The Electron Beam and Gas System . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Detection . . . . . . . . . . . . . . . . . . . . . .............. VII. Contrast and Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Beam Radiation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

110 115 134 138 178 193 217 223

vi

CONTENTS

IX . Operation and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

238 248 248

Optical and Acoustic Device Applications of Ferroelastic Crystals STEVEN W . MEEKSand B . A . AULD I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Periodic Domain Walls and Ferroelastic Bubbles in NPP . . . . . . . . . . . 111. Interaction of Optical and Acoustic Waves with Ferroelastic Domain Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV . Optical and Acoustic Devices Using NPP Periodic Domain Wall Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Conclusions and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

251 256 292 327 350 354

Applications of Scanning Electron Microscopy in Archaeology SANDRA L . OLSON I. I1. I11. IV .

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preparation Methods for Archaeological Specimens . . . . . . . . . . . . . . Applications of SEM to Archaeological Materials . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

357 359 361 375 375

381

CONTRIBUTORS The numbers in parentheses indicate the pages on which the authors’ contributions begin.

B. A. AULD(4), Edward L. Ginston Laboratory, Stanford University, Stanford, California 94305 LUDWIG JOSEF BALK(l),Universitat Duisburg, Fachgebiet Werkstoffe der Elektrotechnik, Soriderforschungsbereich 254, Kommandantenstrasse 60, D-4100 Duisburg 1, Federal Republic of Germany

F. T. COLE(2), Fermi National Accelerator Laboratory, Batavia, Illinois 60510 ( 3 ) , ESEM Research Laboratory, 98 Brighton BouleG. D. DANILATOS varde, North Bondi (Sydney), NSW 2026, Australia

W. MEEKS(4), IBM Research, Almaden Research Center, 650 STEVEN Harry Road, San Jose, California 95120-6099

F. E. MILLS(2), Fermi National Accelerator Laboratory, Batavia, Illinois 60510 L. OLSEN( 5 ) , Department of Cell Biology and Anatomy, The Johns SANDRA Hopkins School of Medicine, Baltimore, Maryland 21205

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PREFACE The present volume has more of a common theme than many of its companions in the serial for three of the five chapters are devoted to one aspect or another of scanning electron microscopy, while a fourth is again concerned with charged particles, though in accelerators rather than in microscopes. The remaining chapter, by S. W. Meeks and B. A . Auld, is an extremely informative survey of applications of ferroelastic crystals in optical and acoustic devices. The authors cover the physics of ferroelastics, the interaction between waves propagating in the material and the domain walls and the devices themselves. Particle accelerators were the subject of a chapter in this serial many years ago, by J. P. Blewett. That review, much used for many years, is now out of date and I am delighted that F. T. Cole and F. E. Mills have agreed to provide an account of the present situation and, in particular, of the likely directions of future accelerator development. The chapters in the field of scanning electron microscopy cover scanning electron acoustic microscopy (SEAM), environmental microscopy, and an important but not very well known domain of applications of the instrument. The first SEM chapter, by L. J. Balk, gives an account of the instrumental modifications required to perform SEAM and the nature of the information provided. The second, by G . D. Danilatos, likewise covers both the microscope itself and the uses to which the technique can be put. The last of the three, by Sandra Olsen, is devoted not to a mode of operation but to the whole field of applications involved in archaeology. The author first explains which operating modes are suitable for the various types of specimen (thus “Auger electron spectroscopy was used to anaiyse the constituents of Greek bronze arrow tips”). She then considers a wide range of SEM studies: hair, fingernails, and blood, for example, in the case of animal materials (“the SEM has been used to observe the external surfaces of hairs from mummified Egyptian cats”) and glass, ceramics, and metalwork. Although the SEM is the common theme, the studies described are placed in context; thus we are told that the cut ends of Lindow man’s hair resemble those of modern scissor-cut hair though no Iron Age scissors have been found. Finally, we give the usual list of forthcoming chapters. Peter W. Hawkes ix

J. K. Aggarwal

Parallel Image Processing Methodologies H. H. Arsenault Image Processing with Signal-Dependent Noise

G. Bastard et u1. Electronic and Optical Properties of Two-Dimensional Semiconductor Heterostructures M. Bertero Inverse Problems H. Bley Pattern Recognition and Line Drawings A. Bratenahl and P. J. Baum Magnetic Reconnection

J. L. Brown Sampling Theory J. F. Carinena and M. Santander Dimensional Analysis J. M. Churchill and F. E. Holmstrom Electrons in a Periodic Lattice Potential

J . M. Coggins The Artificial Visual System Concept H. G. Craighead High-Resolution Electron Beam Lithography R. L. Dalglish Corrected Lenses for Charged Particles G. Donelli The Development of Electron Microscopy in Italy

J. Fink Energy-Loss Spectroscopy W. Fuhs Amorphous Semiconductors N. C. Gallagher and E. Coyle Median Filters x

S. and D. Geman Bayesian Image Analysis

J. D. Gibson and K. Sayood Vector Quantization and Lattices E. Hahn Aberration Theory D. Ioanoviciu Ion Optics

M. Kaiser Systems Theory and Electromagnetic Waves K. Kano et al. Phosphor Materials for CRTs H. Van Kempen The Scanning Tunnelling Microscope H. Kobayashi and S. Tanaka Multi-Colour A C Electroluminescent Thin-Film Devices

K. Koike Spin-Polarized SEM J. S. C. Mc Kee and C. R. Smith

Proton Microprobes S. Morozumi Active-Matrix TFT Liquid Crystal Displays C. Mory and C. Colliex Image Formation in STEM

J. Pawley Low-Voltage SEM R. H. Perrott Languages for Vector Computers

G . A. Peterson Electron Scattering and Nuclear Structure F. H. Read and I. W. Drummond Electrostatic Lenses

xi

J . H. Reisner Historical Development of Electron Microscopy in the USA

T. Sakurai Atom-Probe FIM G. Schmahl X-Ray Microscopy

J. Serra Applications of Mathematical Morphology T. Soma et al.

Focus-Deflection Systems and Their Applications Y. Uchikawa Electron Gun Optics K. Ura Electron Beam Testing

xii

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOL. 71

Scanning Electron Acoustic Microscopy LUDWIG JOSEF BALK Universitat Duisburg Fachgebiet Werkstoffe der Elektrotechnik Duisburg, Federal Republic of Germany

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

11. Signal Generation and Contrast Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Contrast Mechanisms . . . . . ........................................ 111. Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

A . Detection of SEAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Electron Beam Current Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Experimental SEAM Arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ListofSyrnbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 21 26 27 32 34

39 40 56 66 68

69 70 70 71

I. INTRODUCTION The scanning electron microscope (SEM) is one of the most widely spread scientific instruments of today’s research. Its high importance is due to a number of advantages associated with this technique which make the SEM a newly universal tool for characterization of materials. Two of these advantages are of extreme importance: the ease with which this instrument can be used for nearly any material problem, without the need for extensive specimen preparation or a very skilled experimentalist. The other advantage is given by the enormous amount of information to be gained from the examined specimen location. Because of these advantages, the SEM is frequently applied in nearly every area of materials I Copyright 0 1988 by Academic Press lnc All rights of reproductlon in any form reserved ISBN 0-12-014671-1

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research and engineering technology, but similarly in many fields of biological and medical applications, too. The high number of attainable information on a sample by means of an SEM is mainly caused by a versatile interaction of high energetic electrons, as delivered by the SEM electron gun, with the solid. This electron-solid interaction takes place within a precisely defined volume close to the electron beam entry point into the specimen. It is determined in its nature and magnitude by both the primary electron beam parameters and the locally existing specimen properties. Depending on the interaction product to be used for achieving information about the sample, which often results in the production of a corresponding SEM micrograph, various modes of SEM applications arise; or, if the SEM is strongly layed out just to deliver one desired information, special types of SEM or SEM-like instruments are developed. In this manner, detection of X-rays has led to the introduction of the electron microprobe and analysis of the Auger electron yield has caused the development of the scanning Auger microscope. The conventional SEM, however, not being optimized for a special mode has the advantage that many of the different possible interaction products can be analysed simultaneously within a single experiment as a spatially resolved correlation of various specimen parameters. In this sense, scanning electron acoustic microscopy (SEAM) is just another SEM mode. Up to date, all SEAM experiments have been carried out using a commercial SEM as a basic instrument. In SEAM, the interaction product detected is a sound or ultrasound wave generated by the primary electron beam within the sample. Whereas most other SEM modes are carried out with a steady-state primary electron beam intensity, the generation of an acoustic wave inherently necessitates a modulation of the primary electron beam, the modulation frequency being strongly correlated to the frequency of the sound wave, often being identical to it. Therefore, in most SEAM experiments, an electron beam chopping (or blanking) system has to be installed within the SEM electron column. The interaction mechanisms responsible for the acoustic sample response, in the following denoted as SEAM signal, are quite manifold. Any property of the primary electron beam itself or of any of its other interaction products that may cause a mechanical deformation of the sample can cause an SEAM signal. These properties include specimen heating due to energy dissipation of the primary electron energy in any material with non-vanishing thermal expansion coefficient, piezoelectric or electrostrictive effects in dielectric materials due to the space charge generated by the impinging electrons, magnetostrictive coupling of the magnetic field of the beam in magnetic materials, direct coupling of excess

SCANNING ELECTRON ACOUSTIC MICROSCOPY

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charge carriers generated by the primary beam within semiconductors, and finally, a heat contribution of these excess carriers during their recombination process. Beside these signal generation processes, even more complex SEAM contrast mechanisms have to be considered when interpreting SEAM micrographs. Part I1 gives an introduction into this complicated field of SEAM signal interpretation without attempting to cover any theory which might be related to this technique. A s will be pointed out in this part, the complexity of SEAM signal generation and contrast mechanisms successfully allows the microscopical detection of many material parameters by SEAM, such as thermal and elastic properties, ferroelectric and ferromagnetic domains, semi-conductor properties like doping concentrations, and pn-junctions. Since the introduction of SEAM by Brandis and Rosencwaig (1980) and by Cargill (1980), its applicability to materials research has been extended considerably. The reason for this is to be seen in an improved system design. Beside more versatile detectors, new amplication techniques have been developed resulting in various modes of SEAM operation. Whereas the first SEAM experiments utilized a harmonically modulated primary electron beam intensity and a subsequent amplification of the attained SEAM signal at the frequency of electron beam modulation, today’s SEAM arrangements employ much more detailed signal analysis. The various operation modes of SEAM will be explained in Part I11 in a relatively simple manner, omiting any unnecessary detailed information both in the text and in the block diagrams. Their usefulness for different applications and the special modifications necessary will be pointed out. The operation and principle of a standard SEM will not be explained in this paper, however, the uninitiated reader is referred to the according literature. Applications of SEAM are covering a large number of aspects of materials research and device engineering. Therefore, many different materials have already been analyzed by means of SEAM. The main applications up to date are covering the investigation of metals and semiconductors, but others like ceramics or even organic materials like polymers have been explored. In Part IV, most of the typical SEAM applications will be discussed. It is not the aim of this part to give a complete almanac of all published results; rather it is attempted to point out which of the various SEAM operation modes has to be chosen to reveal a certain specimen property best. Therefore only some crucial results, mainly from metals and semiconductor research are discussed explicitly. For further information, the reader is again referred to the reference literature.

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11. SIGNALGENERATION AND CONTRAST MECHANISMS

In SEAM, a temporally varying primary electron beam current l ( t ) of a scanning electron microscope is used to generate an acoustic signal within the sample. This variation of the electron beam can be done in different manners. The most common variation is a harmonic modulation of the beam intensity by means of a so-called beam blanking or chopping device. The wave form used here is typically a square wave, as this is more easily achieved experimentally than a sinusoidal electron beam variation. Another variation is pulsed SEAM excitation using short primary electron beam pulses with such low repetition rates that after one cycle no SEAM signal remains from the preceding pulse. Finally, an I(t)-variation can be achieved at a fixed specimen location even with a temporally constant primary electron beam current by controlled movement of the beam on the sample. In any case, the same properties of the materials will be determining the generation of SEAM signals. The point of origin of these signals then will be close to the beam entry point into the sample and the overall volume for the SEAM signal generation will be determined by the generation mechanism and by the energy dissipation volume of the primary electron beam. As this dissipation is strongly inhomogeneous, inhomogeneities and nonlinearities may govern the SEAM signal behaviour. In the first section of this chapter, SEAM signal generation will be discussed taking into account primary electron energy dissipation. Furthermore, the various ways to create an acoustic signal by means of highly energetic electrons will be mentioned. While the most familiar mechanism, the generation of heat and by this of thermal waves during the energy dissipation process, has been discussed in detail by many authors. other mechanisms are possible as well; in more recent work these are treated in first theories and already proven by crucial experiments. Mechanisms in this context are piezoelectric, excess carrier of or electrostrictive and magnetostrictive coupling between primary electron beam and acoustic signal. In addition, all of these mechanisms have been shown to allow harmonic signal generation in case of a square wave excitation. Therefore, this nonlinear signal generation is also addressed in the first section. The second section of this chapter tries to explain how contrast may arise within SEAM micrographs, whereby parts of this section will only indicate how much mechanisms could be treated quantitatively. First of all, one will assume that those material parameters influencing the dominant signal generation will be responsible for a contrast. But additionally, other material properties may contribute to the SEAM constrast. Contrast may

SCANNING ELECTRON ACOUSTIC MICROSCOPY

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not only be due to a variation of the SEAM magnitude, but also due to time delays or phase shifts of the signal. Finally, it is possible that the generated acoustic wave is disturbed in its propagation towards the transducer, which means that propagation properties such as acoustic absorption may form part of SEAM contrast.

A . Signal Generation

As the frequencies of SEAM signals are often below the MHz regime, the corresponding acoustic wavelength is in the order of the specimen thickness or quite often even longer. Thus attenuation of sound does not dominate the SEAM micrographs, unless the propagation of sound is strongly influenced by large imperfections such as a delamination. Therefore, in a first approximation, primary electron energy dissipation can be treated as the source of SEAM signals. As will be seen moreover, many contrast mechanisms within the SEAM images are directly coupled with the SEAM generation process. Therefore, it is important to understand two issues: where is this SEAM signal generated, and what are the physical reasons for this generation?

1. Electron Energy Dissipation in a Solid Acoustic microscopes using the generation of sound within the sample by an incident primary flux of particles or electromagnetic radiation distinguish mainly the penetration of the primary probe into the material and its interaction with the solid. The penetration properties limit the attainable spatial (along the investigated specimen surface) and the axial (along the probe direction and perpendicular to specimen surface) resolution. Whereas this penetration can easily be calculated in the case of laser or ion excitation of sound, it is very complicated for a high energy electron beam. Furthermore, the penetration depth of the electron probe is often much larger than for photons or ions. This fact is frequently a reason for misinterpretation of SEAM images, concerning information depth or origin of influencing parameters. The primary electron dissipates its energy gradually on its way through the solid, until it is stopped down. As this stopping down procedure is not a precisely known sequence of scattering processes, access to this phenomenon can only be gained by Monte Carlo calculations, which yield reasonable agreement with the experiment (Shimizu el al., 1975). The shape and the size of the energy dissipation volume is strongly dependent

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LUDWIG JOSEF BALK

on the primary electron energy W,, although quite often this volume is approximated by a hemisphere of an energy dependent radius being proportional to W;" (Reimer, 1979). Other approximations use a sphere located directly below the surface or, even worse, a point source at the beam entry point. As will be seen in this chapter, the density of energy dissipation is an important clue to the understanding of SEAM micrographs. This statement becomes more important as the electron beam penetrates more deeply. This is especially the case for semiconductors and ceramics. To give an estimate of the statistical penetration of a primary electron into a semiconductor, the primary electron dissipation function D(r, z ) is plotted in cylindrical coordinates, r being the distance to the beam entry point at the surface and z the penetration depth (Fig. 1). The primary electron energy is 30 keV, the material is gallium arsenide. This result is obtained by taking the calculations of Shimizu et al. (1975) and modifying them numerically with material parameters relevant to electron scattering, such as atomic number or mass density (Balk, 1976). The curves shown in Fig. 1 indicate how much energy in eV is dissipated into the solid by one primary electron within a cubic micrometer at the site of the curve. Obviously these data are normalized by JJ D ( r , z ) r dr dz = 30 keV. One can see by the data given, that the primary electron energy dissipation is strongly inhomogeneous. Unfortunately this energy dissipation can occur by various means. Main processes are X-ray production and Auger electron generation, ionization processes, excess carrier production in semiconductors and generation of heat. As no reliable information is achievable at present on the dependence of the distribution of these products on the actual electron energy, for the low energy products, such

-radlus

durn)-

-5N f Q D C

0

z

c

1

a C,

a I

FIG. 1: Primary electron energy dissipation function of a 30 keV electron in gallium arsenide.

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7

as excess carriers or heat, a proportionality to D ( z , r ) is assumed. In the same sense, the primary coupling of the electron beam to a sound signal is assumed to be determined by this function. As will be discussed in the following section, both thermal heating and excess carrier generation are sources for SEAM signals in a semiconductor. Therefore, one has to consider the actual distribution of the excess carriers as they undergo a diffusion process. As a result, they both carry electrical charge away from their original production site and recombine after the diffusion process under heat production due to nonradiative recombination mechanisms. Therefore, the spatial distribution of SEAM generation is not only affected by the D ( r , 2)-function but also by the diffusion of the minority carriers. The distribution of Fig. 2 is shown for an example of a material with a minority carrier diffusion length of L = 1 pm. The calculation has been carried out by applying the diffusion equation to any volume increment and by neglecting surface recombination (Balk, 1976). This diffusion corrected dissipation function D*(r, z ) shows neither such a strong inhomogeneity like the original D(r, z ) nor is it that strongly centered to the beam entry point. Though one would hope that by this smoothing effect the SEAM distribution is more easily calculated, the situation becomes even worse. One important reason is that heat is generated both directly by the primary electron and by the excess carriers produced by the same primary electron. Thus heat production, as an example, has contributions from both D(r, 2 ) and D*(r, z ) as D*(r,z) determines the local distribution of the excess carrier recombination. If one wants to determine the mean depth of SEAM signal origin, the theoretical situation is somewhat easier. The depth dependence of SEAM can be gained by integration of D(r, z ) and D * ( r , z ) over r dr assuming

0

7

5

1

3

2

-

radius r (pm) 1 0 1 2

~aAs,30keV,L=lpm ' J ' j '

3

L

5

e~ vm-3 dec trot

I

FIG.2: Diffusion corrected electron energy dissipation function for a 30 keV electron in GaAs with an assumed 1 pm minority carrier diffusion length.

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LUDWIG JOSEF BALK 10

Y

0

2

1

6

8

penetration depth lpml

FIG.3: Depth dose function in GaAs for 30 keV electrons with and without diffusion correction.

that both contributions affect SEAM. The results are the corresponding depth dose functions of Fig. 3, showing that the maximum of energy dissipation is only slightly shifted by the diffusion process. In the example given it is located at about 2 pm below the surface, though even at 5 p m depth an SEAM generation is still possible. It is a special feature of SEAM compared to the other acoustic microscopes that the signal generation is widely spread within the solid, if high energies such as 30 keV are used. On the other hand, the penetration depth zD of the primary electrons, corresponding to the maximum of the depth dose function, can be varied strongly with the primary electron energy due to an approximate zD Wgdependence. This enables, as discussed in Part IV, a semi-quantitative depth profiling without specimen destruction.

-

2. S E A M Coupling Mechanisms

When a primary electron is injected into a solid, various possibilities are given to generate an acoustic signal. Principally, any physical interaction mechanism can be used that is related to the electron's properties and that finally results in a mechanical or elastic change within the sample. In this respect, various means of SEAM signal generation are already discussed. These are: thermal wave coupling, which is a general coupling mechanism, as heating due to electron impact occurs in any material, and as nearly any material has a non-vanishing thermal expansion coefficient;

SCANNING ELECTRON ACOUSTIC MICROSCOPY

9

piezoelectric coupling, which is possible in any dielectric material with piezoelectric properties due to the generation of a local space charge in or close to the primary electron energy dissipation volume; excess carrier or electrostrictive coupling, which in principle occurs in any dielectric and which is amplified in a semiconductor by the large amount of excess carriers generated by the primary electron; magnetic coupling, which can be given by the existence of a magnetic field associated with the primary electron beam and which can have magnetostriction as coupling property. Though there is experimental evidence for only these four mechanisms at present, there may be other evidence for direct sound generation by direct momentum transfer. The stages of theoretical treatment of the mentioned mechanisms vary in quality. The most well-treated mechanism is thermal wave coupling, as it has been discovered first and has been treated extensively for photoacoustic excitation. Excess carrier coupling has been treated theoretically by various authors and has already been proven experimentally. Somewhat poorer is the situation for the other mechanisms, especially for magnetic contrast. In the following, a comparative description will be given for the mechanisms mentioned (with the exception of magnetic coupling) according to a discussion by Kultscher and Balk (1986). The relative magnitudes of the various coupling mechanisms to each other are not yet known, the reason being that it is difficult to vary one of the material properties without changing the other. But, according to Stearns and Kino (1985) a significant contribution of two mechanisms to the SEAM signal can occur at one time; in their experiment, thermal wave coupling was a factor of 2.6 smaller than excess carrier coupling (see subsubsection c). Beside the relative magnitudes of the various mechanisms, the temporal response needs further analysis as this response can cause a phase shift of the SEAM signal in the case of a harmonic excitation. Although the experimental arrangement for SEAM will be discussed in detail in Part 111, a basic sketch for SEAM instrumentation shall be given here. to ensure readability of the following few sections. The main component for SEAM is a commercial scanning electron microscope (SEM) which has to be modified to allow modulation of the primary electron beam intensity. As an example, a square wave generator is indicated in Fig 4 which drives a pair of condensor plates mounted parallel to the electron beam’s direction. Due to this, the primary electron beam is blanked away from its original axis and is absorbed by shielding apertures or Faraday cages before reaching the sample. Thus, the primary electron beam modulation results in a square wave function for the electron beam current Z ( t ) . The four indicated lenses are used to optimize the electron

10

LUDWIG JOSEF BALK electron beam

FIG.4: Principal experimental arrangement for SEAM.

beam parameters and to focus the beam onto the sample surface. By means of scan coils, the beam position is controlled via the usual scan generator of the SEM. As already pointed out, the temporarily varying I ( t ) causes the excitation of a sound wave within the specimen. This wave propagates from the beam entry point at the upper surface of the specimen to the lower surface which has to be in acoustically tight contact with an acoustic transducer, typically a piezoelectric material. Due to this piezoelectricity, the acoustic signal u(t) is linearly transferred into an electric signal which can then be amplified and processed by electronic instrumentation. The final SEAM signal is used to control the display screen of the SEM via a video amplifier. a. Thermal Wave Coupling Thermal wave generation due to harmonic electron beam modulation as an intermediate mechanism for sound generation in a specimen has been the first mechanism to be discussed as a signal source for SEAM (Rosencwaig and Gersho, 1976; Opsal and Rosencwaig, 1982). The first model used to calculate this effect was simplified in the manner that only one-dimensional calculations were carried out and only the excitation of longitudinal modes were assumed. A widely used sketch for the thermal wave coupling is presented in Fig. 5 . The modulated electron beam looses its energy within the primary electron energy dissipation volume D ( z , r ) , z being the beam axis. z = 0 corresponds to the upper specimen surface and z = d to the interface between specimen and transducer. Due to I ( t ) and the energy dissipation, a

SCANNING ELECTRON ACOUSTIC MICROSCOPY

11

electron beam I

dissipation

.--- __ _ - - .’ ~

I

acoustic waves, H’

transducer

/

/’

I

FIG.5: Thermal wave model.

temperature variation T ( z , r , t ) arises which, to a first approximation, is directly proportional to D ( z , I) Z ( t ) . Outgoing from this and using only a one-dimensional and linear treatment, one gets as the equation of motion

-

d2U dt2

v2.

d2U - ~. a - E,, -

dt2

Pcr

dT(z, t) ~

dZ

(1)

where u = u ( z , t ) is the z-component of the particle displacement within the sample, (Y is the linear thermal expansion coefficient, T ( z , t) is the temperature rise starting from an arbitrary temperature To, Eel is the (one-dimensional) elastic modulus, pcr the material density and v the longitudinal sound velocity. As can be seen by Eq. (l),the thermal gradient dT(z, t ) / d z is the driving force which generates the sound signal. Figure 6 schematically summarizes the result. If the two material parameters a and E,, change, a contrast in the SEAM micrograph will arise. Because the typical velocity of the thermal waves, that is the propagation of the thermal temperature variation, is of the order of meters per second for typical operational conditions, the thermal wavelength At,, is in the range of micrometers and thus much smaller than the acoustic wavelength Aac. Furthermore, the

LUDWIG JOSEF BALK

12

T; t, material parameters

I

1

thermal expansion coefficient elastic modulus

thickness d thermal coupling

'/electric

aTlz.t) az

generated property heat driving force thermal gradient

CL

-

acoustic signal u1d.t)

signal -u(d.tl

FIG.6: Parameters relevant to thermal wave coupling.

thermal waves are exponentially damped with a l/e-decay of

with K the thermal conductivity of the material, C t h its specific heat and w = 2f where is the modulation frequency of Z ( t ) . dT is often called the thermal diffusion length. It determines the region in which a conversion of thermal into elastic waves occurs. Thus, the volume contributing to the SEAM signal generation is determined by dT. In this manner, only thermal properties and the modulation frequency f determine the spatial resolution attainable with SEAM when thermal heating is its main signal source. This can be experimentally proven (see Balk et al., 1984a) for an alloy of Cu-Zn-A1 within a large frequency range. As shown in Fig. 7, the result is a clearfp''2 law for the spatial resolution attained, the absolute values being in perfect agreement with the thermal properties of the material examined. For higher frequencies than shown in Fig. 7. a further increase of spatial resolution still can be measured, but with the frequencies no longer following this law due to a limitation of the spatial resolution by the primary electron dissipation volume D ( z , I ) . The one-dimensional treatment only gives a first estimate of the SEAM signal situation. Taking into account the more complex problem, threedimensional calculations have already been carried out (Davies 1983; Holstein, 1985; Favro et at., 1987). These calculations and the following theories explain the importance of elastic properties for the contrast within the SEAM micrographs. Favro et al. emphasize the fact that the conversion of thermal into elastic waves necessitates the presence of a scatterer. which can be any imperfection or interruption of the ideal crystal, one possibility being the top surface of the sample itself. Such mode conversions can

SCANNING ELECTRON ACOUSTIC MICROSCOPY

13

-E 300 - 100 3

C

0

c

2 30

s

2

- 10

c

c

0

a

*

3 0.05

5 50 chopping frequency flkHzl

500

05

FIG.7: Spatial resolution versus frequency for a Cu-Zn-A1 alloy and linear SEAM operation, W,, = 30 keV.

explain the appearance of shear or transversal waves. Furthermore, they can explain different results in spatial resolution, as the distance of a mode converting scatterer to the original beam entry point determines resolution, if it is smaller than the thermal wavelength. Ikoma et al. (1984) calculated the SEAM signal as a function of the modulation frequency f for aluminum. Their result is given by two separate equations for the SEAM signal u = u ( f ) : V,,'(Y'W

1

with V , = const. and W = U,. J Z ( t ) dt as the absorbed energy: Uo = l/e W,. For both low and high modulation frequencies (dT f - ' / * ) , a proportionality of the SEAM magnitude is given, but its phase is relative to the exciting waveform changes by 180". This theoretical result is varified by the authors for a 1.1 mm thick aluminum plate and a frequency range from 5Hz to 100kHz, the result being shown in Fig. 8. The thermal wave model as discussed here yields reliable results for metals and failing for semiconducting materials. This is mainly caused by the fact that heat generation cannot directly be correlated to the primary dissipation function D ( z , r ) . As Sablikov and Sandomirskii (1983) have pointed out, there are two different means of heat generation: one is the primary electron energy dissipation, the other one being the non-radiative recombination of excess carriers generated by the primary electron beam. As this typically is a huge number (about lo4 electron-hole pairs for

-

14

LUDWIG JOSEF BALK

I

"

I

chopping frequency fikHz)

~~

0.001 0.01 01 1 10 100 chopping frequency fikHz)

~

FIG. 8: Linear SEAM magnitude and phase response as a function of frequency (after Ikoma

et

al., 1984).

Wo = 30 keV in silicon per each single primary electron), this second contribution to a heat production cannot be neglected, but has to be considered for the overall SEAM signal, its temporal response and the achieved spatial resolution. Clearly, the spatial distribution of heat generation in the case of a semiconductor is affected by both D ( z , r ) and the dissipation function D*(z, r ) after the excess carrier diffusion process. A precise calculation of the spatial resolution is very difficult: for the carrier diffusion length L > dT, the apparent resolution becomes independent of dT and thus of the modulation frequency. This is the case for higher f - values. Furthermore, there are two different time shifts involved for the heat production: a first maximum for the primary process and a second maximum which is delayed by the excess carrier lifetime 7 correlating to the heat generation due to excess carrier recombination. By photothermal investigations, Fournier et al. (1986) proved this both theoretically and experimentally. As can be seen by Fig. 9, they showed that both contributions add up to a sum curve and that excess carrier contribution becomes dominant for the low kHz regime. As both signal contributions have different time-responses, they are shifted by their relative phase, which causes the sum curve to show a dip at the frequency where the direct thermal wave component and the excess carrier component are of about equal magnitude. The location of this dip on the frequency axis is given approximately by the reciprocal minority carrier lifetime. b. Piezoelectric Coupling Many dielectric materials exhibit piezoelectric properties. Materials like this may be ceramics, semiconductors or

SCANNING ELECTRON ACOUSTIC MICROSCOPY

15

0

-5

-1

6

-2

-

I

excess carrier component sum of both components

X

U

n

-3

I

-

0)

O

-6

-

0

111

;-100 - -200 0

U a,

111

Jz 0

a -300

even plastics. As soon as there is an electric field E acting on these materials, they suffer a change in their physical dimensions. If the electric field is varying with time, elastic waves are generated. Such a generation of an electric field can be achieved by the impact of the primary electron beam in two different manners. One is the direct generation of a field by the charge built up by the primary electrons stopped down within the dissipation volume D ( z , r).This is a well known effect, which is especially of importance when investigating insulating materials. A general treatment of the local field induced by the electron beam is given by Cazaux (1986) for various operational conditions. H e shows that significant fields can be generated in any case. Even more pronounced is this phenomenon in the case of semiconducting materials, as the original space charge is amplified by the excess electron-hole pairs. As minority and majority carriers have different lifetimes and mobilities, local net charges arise. Sasaki et al. (1986) explain this effect for n-doped silicon: the minority carriers (holes) are trapped by the locally fixed donors and form together with these a locally stable concentration of charged donors. The excess electrons, which are thermally excited, especially for high electron energy impact, diffuse

16

LUDWIG JOSEF BALK

away. Combined with the fixed charge donors, this diffusion causes the generation of an internal electric field. This simple explanation shows a very important feature: as soon as this field generation is disturbed, the SEAM signal changes. An important disturbance in this respect is the u priori existence of electric fields, like at the location of a pn-junction. As no additional mechanism, such as heat production, is needed for this coupling mechanism between electron beam and acoustic wave, the local extension of sound origin is solely given by the electron energy dissipation. For typical insulators, the primary dissipation function D(r, z ) will determine the distribution of the local electric field, whereas for semiconductors the D * ( r , z ) distribution after diffusion will be dominant. In this manner, the spatial resolution should be widely independent of thermal properties and not in the same sense frequency dependent like the thermal wave component within the SEAM signal. As piezoelectric coupling occurs directly, no additional scatterer is needed. In this sense, much higher spatial resolutions are to be expected, especially for the lower frequency range. If one has determined the actual local field by integration of the created space charge distribution , one can again deduce an equation of motion for this coupling mechanism. In a simplified model (Kultscher and Balk, 1986), one gets

where e is the piezoelectric stress constant. A main assumption for this calculation is a solely linear dependence of the elastic wave magnitude on the electric field. Figure 10 summarizes the result of Eq. (4), the elastic stiffness constant c being implicitly given by d 2 u / d t 2 . One can further deduce from the result that the density of energy dissipation determines the SEAM magnitude in this approach and not the totally deposited energy into the solid. This is in consistency with the I

modulated electron beom current Ilt)

I

FIG.10: Parameters relevant to piezoelectric coupling

SCANNING ELECTRON ACOUSTIC MICROSCOPY

17

results for the thermal wave model too, and means that high beam current densities are more important than the total beam current. As the piezoelectric coupling has been discussed in this subsection as a linear effect, a change in electrical polarities, like for differently orientated pn-junctions, should cause a phase shift of the acoustic wave because of harmonic excitation and a 180" polarity inversion. c . Excess Carrier o r Electrostrictive Coupling Excess carrier coupling can be discussed in a similar manner to piezoelectric coupling. It relies on the sound generation due to a deformation dependent permittivity tensor. Though this effect is a general mechanism for all dielectric materials, it should only result in a reasonable contribution to SEAM signals for semiconductors, as only for these a significant space charge can be generated (due to excess carrier generation). If one introduces a stress dependent permittivity by F = E~ + as, with E~ being the permittivity of vacuum, a a constant and s the local strain, one gets the equation of motion (Kultscher and Balk, 1986): d2u dz2

d2U

- = v 2 . -

dt2

E()

-

(Y

+--87r - pcr

dE2(z,t ) dz2

(5)

This result is sketched in Fig. 11. Compared to Fig. 10, the charge density is replaced by the excess carrier density, as this is the dominating quantity. As the permittivity correlates mechanical elongation to a local electric field by a clean square law, the electric field gradient is replaced by the electric square field gradient. This means that for harmonic electron beam modulation at a frequency f, a SEAM signal due to this coupling mechanism should be expected only at the frequency 2f. The spatial distribution of SEAM signal generation should be solely given by the D * ( z , r ) function, as this is the maximum extension for the excess carrier

I

modulated electron beam current I(t1 energy dissipation volume generated property

a~~(z.t)driving force

1I

:,?':?t

'-I d17

material parameters

az

permittivity

E

electric square field gradient

elastic stiffness const

specimen

excess carrier coupling

transducer e -'lcirt

- gg''tiL(d,tl signal -u(d.t)

FIG. 11: Parameters relevant to electrostrictive coupling.

18

LUDWIG JOSEF BALK

density. Thus, the spatial resolution should be comparable to the one achievable by piezoelectric coupling. In a somewhat different calculation, Stearns and Kino (1985) show that a periodic fluctuation of an excess carrier density causes a periodic mechanical strain. Though they discuss excitation by means of photons, their situation is very similar to SEAM. For silicon, they deduce a dependence of strain due to the excess carrier fluctuation by selectronrc = -9.5 lo-'' cm3 An, with An being the excess carrier density, and a dependence of strain on thermal wave theory by sthermal = 3 10-6K AT, with AT being the local temperature rise. Their results show that depending on the density of electron energy dissipation and on the achieved thermal heating, one of the two coupling mechanisms may be dominant. They further show that both signal contributions are inversed in sign consequently leading to a phase change of 180" between the two signals. Stearns and Kino (1985) proved their theory by a crucial experiment. They covered a thermally oxidized silicon wafer with a 100 nm thick chromium metallization. The doping of the wafer was very low, 3 1013 ~ m - The ~ . sound generation source was a laser whose light could not penetrate the chromium layer. In this manner, they could separate a mere thermal wave signal generation for the specimen surface covered by the chromium from signal generation due to both thermal and electronic strain at the uncovered specimen region. Their experimental set-up and the results obtained with it are sketched in Fig. 12. Although they use a laser beam, an electron beam as indicated at the top of Fig, 12 would act equivalently on the sample. The signal in the uncovered sample area is somewhat higher, and phase changes as expected by about 180" at the beginning of the metal layer. By a detailed calculation the authors show that for this example the following relation results: total photacoustic signal == - 1.6 ' Stherma1 - Stherma1 + Selectronlc, thus the magnitude of Selectromc = 2.6 magnitude of Sthermal. Although this experiment does not explain the various contrasts within photoaconstic and electron acoustic images, it clearly shows that a mere thermal wave treatment is not valid for signal generation within a semiconductor.

-

-

-

d . Magnetic Coupling In ferromagnetic materials, SEAM contrasts have been observed which are not explainable by means of the mechanisms discussed thus far. Balk et al. (1984b) clearly demonstrated the ability to image ferromagnetic domains within Si-Fe transformer steel sheets. The domain contrast could be observed for both uncoated and coated material. Furthermore, this domain imaging has only been possible for a harmonic

SCANNING ELECTRON ACOUSTIC MICROSCOPY

metallization

soecimen

I a-

-2 3.e

19

transducer

I

3 2

'E ?

ge E'

1

0

-60 0 60 120 distance from edge (pml

I

-120

I

-120 -60 0 60 120 distance from edge (pm)

FIG.12: Experimental separation of thermal wave and excess carrier coupling for silicon (after Stearns and Kino, 1985).

electron beam modulation and a subsequent amplification of the attained signal at an even harmonic of the modulation frequency, preferably at the second harmonic. No contrast could be observed at the fundamental SEAM signal, when proper electron beam duty cycles were established; if the signal wave form is not a clean sine or square wave, other frequencies like harmonics and subharmonics may falsify the signal response. Coupling mechanisms yielding a pure square law are in this respect: magnetoinductive coupling, coupling via magnetohydrodynamic waves, or magnetostrictive coupling. From the material properties of Si-Fe and from the chosen geometry, the first two effects seem to be very unlikely, whereas magnetostriction is well pronounced in this material. A coupling between sound and magnetic configuration seems very likely, as has been already discussed for sound fields in antiferromagnets (Koirakh and Preobrazhenskii, 1984). Further, it is known that mechanical stress induces in steel reversible and irreversible changes of the magnetization. Atherton and Szpunar (1986) assume that stress changes the arrangement of the easy axes and, accordingly the domain structure. As the magnetic field associated with the

20

LUDWIG JOSEF BALK

primary electron beam current is fairly low and as form anisotropy should govern the effect to be discussed here, a pure square law should result between magnetic field and magnetostriction. The quantitative treatment of this effect has not been undertaken yet, one reason being that the calculation has not been done inherently in three dimensions. 3. Nonlinear SEAM Signal Generation

Generation of nonlinear SEAM signals could be used for the production of SEAM micrographs in a large variety of materials (Balk and . indicates that there are various Kultscher, 1984; Balk et al., 1 9 8 4 ~ )This possibilities for nonlinear signals. In principle, three different mechanisms are understood at present: nonlinear signal generation due to high excitation, inherent nonlinear coupling mechanisms, and sound generation by means of hysteretic material properties. Though nonlinear signal generation due to high excitation conditions seems to be unlikely within SEAM at the first sight, even for thermal wave coupling, this cannot be excluded. Ferrieu and Auvert (1983) show that for a precise calculation, a three-dimensional treatment has to include a solution of the nonlinear heat diffusion equation. Similarly, Yamada et al. (1985) showed for a silicon-onsilicon dioxide layer that an inclusion of nonlinear contributions into the heat calculation yields significantly different heat levels, especially close to the surface. Their result is shown in Fig. 13 for a 1.7 Watt electron beam into a surface area of 50 pm2. This power density is comparable to the operational conditions used in SEAM, as the typical parameters are given by W , = 30 keV, 1, = lop7 A and an electron beam diameter of less than 1 pm. 1300

- 1100 Y +

900

? p 700

1

m

e

a, 500 300 0

5

10 15 depth zlFm)

20

25

FIG.13: On the difference between linear and nonlinear treatment of heating due to an electron beam power of 1.7 watts into a 50 pmZ surface area (after Yamada ef al., 1985).

SCANNING ELECTRON ACOUSTIC MICROSCOPY

21

In semiconductors, a nonlinear signal generation seems to be a general effect, no matter which theory is discussed. Sablikov and Sandomirskii (1983) emphasize that the photoacoustic effect (and electron acoustic signal generation) may become nonlinear with strong excitation, as soon as the excess carrier transport properties become nonlinear. This typically occurs if the excess carrier density exceeds the equilibrium carrier density. Although the excitation conditions are Iow enough in this case not to change the thermal properties of the material, the authors assume a generation of harmonic signals, even if an inhomogeneous excess carrier density is neglected and all thermal properties are treated in a linear manner. As already pointed out in the previous subsection, sound generation may occur due to an inherently nonlinear coupling. Two of these effects are the electrostrictive and the magnetostrictive coupling, as both obey a pure square law. Electrostriction is proportional to the square of the electric field induced locally at the beam entry point, whereas magnetostriction would correlate to the square of the magnetic field of the primary electron beam. Thus a harmonic modulation of the primary electron beam generates an SEAM signal at the second harmonic of the modulation frequency. It is important to mention that these nonlinearities are widely insensitive to the level of energy dissipation and that nonlinear SEAM micrographs could be recorded for low beam currents and voltages. As already mentioned, a mode conversion from thermal into elastic waves should occur at a scatterer site. Independent of the excitation level, a nonlinear signal results, if the scatterer shows a hysteretic behaviour due to the exposure of temperature variation. This, for instance, is the case for monoclinic martensite platelets within a cubic Cu-Zn-A1 alloy. The martensites exhibit a hysteretic growth and shrinkage due to a temperature change which overlaps the usual SEAM signal generation (Balk et al., 1 9 8 4 ~ )Accordingly, . harmonic signal levels are added to the linear thermal signal close to mode conversion sites of temperature dependent size. B. Contrast Mechanisms

At the beginning of SEAM, the contrasts within micrographs were only explained by physical mechanisms like the SEAM signal generation. As only thermal waves were assumed to be responsible for a signal generation, merely thermal material parameters were assumed to govern the SEAM contrast. According to the previous section, various signal generation mechanisms are possible within a sample, and consequently various contrasts may arise being of the same nature as the signal generation.

22

LUDWIG JOSEF BALK

Other contrasts may be due to parameters influencing the SEAM signal during its generation process, although not primarily related to the generation process. Finally, most SEAM theories assume that the acoustic wave is not disturbed during its propagation towards the detector. As can be seen in more recent research, this assumption is not always valid, especially for high modulation frequencies. Furthermore, it should be emphasized here that contrast has been thought of merely as the magnitude variation of a harmonic signal generation. As will be shown, variations in the phase position of the signal or corresponding time delays may form contrast as well, and yield additional information about the sample properties. Unfortunately, contrasts in SEAM are not treated like signal generation. Therefore this section will mainly give some phenomenological explanations.

1. Contrasts of the Same Nature As Signal Generation Depending on the dominating signal generation mechanism, any parameters which are included in the corresponding equation of motion can contribute to a contrast. For the thermal wave model, certainly any change of a thermal material parameter, such as thermal conductivity, will cause a contrast, preferably in an SEAM magnitude image. But, as can be shown by many experiments, elastic properties have to be considered too. If the thermal properties are constant, the elastic properties dominate the SEAM contrast. Concerning their influence on the resulting SEAM magnitude, Hildebrand (1986) developed a three-dimensional theory. He showed that an anisotropic behaviour can be expected even for cubic material. Parts of his results are presented in Table 1, indicating that the crystal orientation of highest magnitude in cubic material is the (100)-direction, a result which is in agreement with calculations by Davies (1985). Due to this anisotropic behaviour, a crystallographic contrast is also observed for an isotropic heat TABLE 1

THERMOACOUSTIC GENERATION FACTORS (IN ARBITRARY UNITS) (AFTERHILDEBRAND, 1986).

Material Aluminum GaAs InP Silicon

Crystalline Directions (loo) (110)

(111)

2.14 1.91 2.13 1.77

2.01 1.46 1.62 1.44

2.04

1.55 1.73 1.51

SCANNING ELECTRON ACOUSTIC MICROSCOPY

23

production as the usual detection techniques are designed to detect the sound propagating in one direction only. Additionally, the temporal SEAM response should be different for materials or directions of different stiffness. Therefore, regions of different stiffness should show contrast in phase or time-delay SEAM micrographs. As these contrasts can be handled more quantitatively in practice, they should allow a quantitative determination of the local stiffness at the specimen location under test. In semiconductors or for piezoelectric and electrostrictive coupling, the interpretation of contrasts is even more complicated. Here any parameter influencing the generation of an internal field, such as the excess carrier generation rate, will form an SEAM contrast. Then in the same sense for thermal wave coupling, the elastic properties and the anisotropy of the stiffness contribute to the contrast formation. Additional to this, a significant thermal signal generation and thus a thermal contrast may form part of the contrast, too. Thus it is very difficult to decide why a certain semiconductor feature is measured. A dislocation may be visible both due to higher heating as a consequence of increased nonradiative excess carrier recombination and to a changed excess carrier concentration due to a higher recombination rate. Doped areas may be visible not only due to changed thermal or electronic properties, but they may be seen also by a change in the elastic stiffness. Averkiev et al. (1984) proved by theory and experiment a strong change of the elastic moduli with the free charge carriers. Thus a quite complicated network of contrast mechanisms has to be considered for a semiconductor, the problem being that none of the relevant parameters varies without changing the others. Reliable understanding of the magnetic contrast has not yet been attained due to a lack of experimentation on magnetic coupling.

2. Other Contrasts Originating within the Generation Volume The SEAM level may be affected by parameters or specimen features not correlated with the original SEAM signal generation. One general parameter in this respect is the backscattering coefficient for highly energetic electrons. Other possibilities are given by special sample features like the temperature dependent physical dimensions of a structure that may superimpose a contrast onto the regular SEAM image, like previously discussed for the growth and shrinkage of martensites due to a thermal wave. In the case of semiconductors or other dielectrics, contrast that originates from the presence of internal electric fields, which may separate the excess carrier and by this, impair the attained signal level may be important. Balk and Kultscher (1983) and Ikoma et al. (1984) were the first ones to express the strong influence of pn-junctions onto the SEAM signal.

24

LUDWIG JOSEF BALK

Balk and Kultscher (1983) showed that within the space charge region of a pn-junction (for low enough frequencies), a very low SEAM magnitude results, as all excess charge carriers are separated by the electric field and contribute to an electron beam induced current (EBIC), no matter whether this EBIC signal is measured or not. This means that any EBIC contrast will be introduced into the SEAM contrast, though inverted in its magnitude. A separation of this EBIC contribution from the SEAM image can only be done by reducing the modulation frequency so much that only thermal properties determine the signal (compare Fig. 9). Similarly, internal magnetic fields may influence the magnetic contrast, although there is no experimental evidence for this. 3. Contrasts due to Propagation of the Acoustic Wave

SEAM contrasts have been assumed to be directly associated with the SEAM signal generation or at least with the generation volume. As has turned out, however, this assumption is only valid if strong enough SEAM contrasts arise by these means. Otherwise, the propagation of the acoustic waves, their attenuation or scattering, has to be considered. A first evidence could be seen in the creation of vibrational mode patterns in thin metal sheets. Depending on the sample geometry. these patterns exhibit chess board or ring-like structures which are directly correlated to the length of the SEAM sound wave. Their origin has been treated theoretically by Holstein (1985) within a three-dimensional theory which accounts for both signal generation and sound wave propagation, and is sketched in Fig. 14. Assuming that only the upper surface of a foil is heated, a bending of the sample should be the consequence. Under harmonic excitation conditions, this causes a flexural wave which is reflected at the boundaries of the sample and then can interfere with previous waves to give the patterns mentioned above.

electron beam

I

bl

electron beam

inhomoaenecuslv

surface

surface during heating /

FIG. 14: On the origin of vibrational mode patterns.

SCANNING ELECTRON ACOUSTIC MICROSCOPY

25

If severe imperfections like cracks or delaminations hinder the acoustic waves in their path from the SEAM generation volume towards the transducer, contrasts arise due to a phase shift of the signal, as the wave has to bypass this disturbed region (Begnoche and Holstein, 1984). Thus, phase SEAM images may directly determine such subsurface imperfections. In a similar manner, Ringermacher and Jackman (1986) were able to image a subsurface cut by means of SEAM within metals, although the distance of this cut to the beam entry point was more then twenty times the thermal wavelength. Favro et al. (1984) have described this contrast mechanism theoretically for thermal excitation. If one wants to compare in this respect SEAM with conventional scanning acoustic microscopy, one could make the following statements: at low modulation frequencies the main information is given by the SEAM signal generation itself; at high frequencies one has to consider both signal generation and sound propagation. If the modulation frequency of SEAM is about the same as for a conventional acoustic microscope, say about 1 GHz, the achieved micrographs should be distinguishable solely by the contribution of the signal generation (compare Fig. 15). Assuming a homogenous surface, easily achieved for high quality semiconducting materials, one can use the propagation of the sound wave to measure the location of subsurface defects quantitatively. In order to establish such a technique, Huebener and Metzger (1985) cooled down the sample to liquid helium temperature. Then, they attached micron-sized electron beam chopped below MHz

electron beam chopped with several GHz

wavelength ot sound -1mm

wavelength of sound lpm

main information by signal generotbon

information by signal generation and sound propagation

-

ultrasound GHz 1 generator

pGFl information by sound propagation

FIG.15: Contrast mechanisms in SEAM compared to conventional scanning acoustic microscopy.

26

LUDWIG JOSEF BALK electron beam modulated at GHz frequencies

diameter at (x1 .y1 1

I

beam position1

1

I

beam posihon 2

I

I

at Lxd.yd,zdl d detector position2 at Ix;.yi )

detector position 1 otIx,.y,)

FIG. 16: Three-dimensional defect tomography by use of micron sized sound detectors.

detectors (bolometers) at the bottom surface. As shown in the upper part of Fig. 16, this is equivalent to a conventional scanning acoustic microscope, if contrasts due to signal generation can be neglected. Already, the use of two such detectors has allowed the determination of all three components of a subsurface defect as indicated in the lower part of Fig. 16. For two primary beam positions ( x o , yo) and (&, y b ) and two detector positions (xl, y l ) and ( x i , y i ) , the defect location (xd , yd , zd) is uneqivocally determined. Although this tomographic technique seems only to be applicable for single crystals, it is at present the best possibility for a nondestructive and quantitative evaluation of subsurface structures. 111. INSTRUMENTATION In all SEAM work published to date, a modification of a commercial scanning electron microscope (SEM) has been undertaken to set up an SEAM experiment (Cargill, 1980; Brandis and Rosencwaig, 1980; Morizuka et al. 1982; Balk and Kultscher, 1983). As there is easy access to an SEM instrument in most any scientific laboratory, such a modification allows for

SCANNING ELECTRON ACOUSTIC MICROSCOPY

27

an SEAM set-up with moderate financial costs compared to other acoustic microscopes. This fact should allow SEAM to become more common, especially if one considers that many of the additional components are quite often standard laboratory equipment. The use of an appropriate detector in SEAM is certainly important. Such a detector can be directly contacted to the sample to measure the sound or heat generated in the sample. Other detectors can be used which operate without a direct contact to the specimen. These are mainly optical or electrical detection techniques. The first section of this part, will present those techniques which are already established or which seem to be most promising for future developments without tending to give a complete view of possible detectors. As already described in Part 11, SEAM signal generation necessarily implies modulation of the primary electron beam current at a fixed specimen location. Two modulation techniques are explained in the second section: modulation by means of electron beam chopping and variation of the actual energy deposition into the examined specimen location by modification of the beam position itself. In the third section, several arrangements for SEAM will be introduced, both for general purpose experiments and for special applications. The various instrumentations are sketched in according block diagrams which all are designed in similarly to Fig. 4 which was used previously to explain SEAM signal generation. A . Detection of SEAM Detection of SEAM signals is very similar to photoacoustic sensing techniques which are extensively discussed by Tam (1986). However, any of these techniques relying on the presence of air or any similar surrounding at the specimen surface cannot be used in vacuum equipment, like the mirage effect or a gas cell. Furthermore, one will tend to use such detectors which are easily mounted in the SEM specimen chamber. Therefore, laser beam deflection as an acoustic sensor has not been used. Possible detectors can be classified into those contacting the sample mechanically and others operating without any contact. 1. Contacting Detectors These are detectors which are brought into direct contact to the sample, in most cases at the bottom surface of the specimen. They have to transduce at least one of the properties determining the SEAM signal or

28

LUDWIG JOSEF BALK

SEAM contrast into an electric signal, which then can be amplified by subsequent preamplifier. Two properties are most important, as we have seen in Part 11: the sound signal itself and, if thermal wave coupling occurs, the heat wave production. The task of sound detection is done best by piezoelectric transducers, whereas heat detection can be achieved by pyroelectric transducers. a. Piezoelectric Transducers The most common material used with SEAM for piezoelectric transduction is a lead zirconate titanate (PZT) ceramic. Usually it is clamped or glued to the bottom surface of the specimen. If one wants to use common SEM specimen holders, only very simple arrangements can be used, which leads typically to a poor acoustic response. The main disadvantage due to this is a pronounced frequency response of the detector system and by this of the overall SEAM set-up (Davies, 1985). To achieve a flat band response of the detection system that allows for tuning of the SEAM signal to any frequency of interest, a detector design has to avoid reflexion of acoustic waves from the back side of the transducer. A very good design for this purpose has been described by Proctor (1982). He proposes a transducer system like the one indicated in Fig. 17; with such a device, a flat response within 3 dB can be achieved from 50 kHz up to 1 MHz. According to this, Balk and Kultscher (1983) have designed a simple detection unit with a PZT ceramic as shown schematically in Fig. 18. Some additional remarks should be given which might help setting up a suitable detection unit. One important feature is that perfect electrical signal shielding is necessary to avoid intrusion o f SEAM signais by other

vibrating surface active tronsducer element

-

'

/

,

I\

lOmm

7

electrode 1

-brass

electrode

1

FIG. 17: Optimized PZT detector design for flat band response (after Proctor, 1982).

SCANNING ELECTRON ACOUSTIC MICROSCOPY

29

electron beam electrical

transducer

I

sDecimen

brass

electrode oiiminium block

11csatvll i

t o SMA vacuum feedthr ough FIG. 18: SEAM detection unit.

signals within the instrumentation. Therefore coaxial connectors, cables and feedthroughs are to be used already inside the vacuum. Furthermore, no open structure is allowed on top of the transducer, as otherwise a signal measured can essentially be a secondary electron (SE) signal. The SE signal is amplified by means of a photomultiplier. As it is modulated with the same frequency as the primary electron beam (in case of beam chopping), a high frequency electron beam current of high intensity results inside the photomultiplier giving rise to an electromagnetic wave which penetrates back into the specimen chamber via the glass window the photomultiplier is mounted to. Then the PZT ceramic, which is nothing but an electric condensor, acts like an antenna for SE signals. This effect can easily be checked by turning down the SE photomultiplier voltage. To avoid such spurious signals, one can encapsulate the transducer, but this may give a somewhat poorer acoustic coupling to the sample. A signal reduction can also be seen when using coupling fluids, like diffusion pump oil, instead of a direct contact. As PZT is limited in its bandwidth, it seems desirable to replace it for high frequency applications with other piezoelectric ceramics, one possible material being barium titanate (Tronconi et al., 1984). Instead of ceramics, one can use single crystal material and, additionally, interdigital transducers on piezoelectric crystals. Though they force a fixed operation frequency, they should exhibit a better resolution than usual detectors. Veith (1982) has used such an arrangement for photoacoustic microscopy by depositing the sample onto an LiNbO, crystal with an interdigital transducer on the same crystal surface. It is important to

30

LUDWIG JOSEF BALK

mention here that many samples may be already piezoelectric on their own. Under certain precautions, the voltages measurable at their bottom surface will deliver the same SEAM information as those detected by an extra transducer. That means they can act as their own transducer. It is quite understandable that such a detection is preferable, as any signal falsification due to a poor acoustic coupling between sample and transducer is omitted. In this respect, many semiconductors could be directly used as their own transducer. This is especially true for most 111-V compounds. So far arrangements have been discussed for coupling the transducer to the bottom surface, which necessitates a propagation of the sound wave through the bulk of the specimen. Alternatively, one could adapt a transducer to the upper surface which is probed by the electron beam. Then those sound waves are detected traveling along the surface of the sample. Such a surface acoustic wave detection has been published by Yamanouchi et al. (1984) who deposited a circular interdigital transducer structure onto a piezoelectric sample. From theory, they concluded that this arrangement should give a strongly improved quality of SEAM micrographs. b. Pyroelectric Transducers Thermal wave generation is one of the possible SEAM signal generation mechanisms. Therefore it might be useful to detect these waves directly. By comparing their signal behaviour with the total SEAM signal as detected by a piezoelectric transducer, one should be able to separate various possible SEAM generation mechanisms. In Part 11, it was shown that thermal waves decay within the thermal diffusion length. Therefore pyroelectric detection is only possible at the bottom surface of a sample, if the sample thickness is of the order of the thermal diffusion length d,. As dT is a function of frequency, such an arrangement is possible either by use of low beam modulation frequencies or by thinning the sample to an appropriate thickness. Baumann er al. (1983) performed some first principal experiments by use of an LiTa0,detector. Another detection material could be polyvinylidendiflouride (PVDF), which is already used for photothermal experiments (Coufal, 1984), a material having very good frequency response up to about 1 GHz. 2. Non-Contacting Detectors Though most SEAM work uses contacting detectors, it is a great advantage to use detection techniques which do not have the need of disturbing the mechanical properties by pressing o r gluing it to a transducer. This is especially of importance, if fragile samples are to be examined. Presently, there are two different groups of non-contacting detectors, those using optical detection and other which rely on electrical parameters.

SCANNING ELECTRON ACOUSTIC MICROSCOPY

I

31

electron beam IR-radiation

/ ellipsoidal mirror

turn

HgCdTe detector

FIG.19: Infrared detection of thermal heating (after Dacol et al., 1985).

Again, various techniques may determine either the SEAM signal or the thermal wave only. a. Optical Detectors Like in photoacoustics, the deflection of a probing laser with glancing incidence to the examined specimen surface could be used to determine the acoustic wave at the upper surface due to its distortion. This has not yet been done, probably because this introduces a difficult design of the SEM specimen chamber. Another optical detection utilizes the thermal heating of the sample. Due to this thermal modulation, a modulated infrared signal is emitted. Dacol et al. (1985) have used a cathodoluminescence detection system to measure the infrared intensity emitted from the electron beam entry point at the specimen surface (Fig. 19). Using a cooled CdHgTe detector, they produced thermal images of a Si,N,-sample. In their set-up, the total intensity of the infrared emission, integrated over all wavelengths accepted by the detector, has been used for image construction. In a more sophisticated experiment, one could think about using an infrared spectrometer and monitoring rhe wavelength of maximum intensity. b. Electrical Detection In ion acoustic experiments, Sieger and Lefevre (1985) have been able to show that capacitive detectors can be used with high frequency response. These detectors are based on the change of a capacitance between the bottom specimen surface and a reference electrode. Though probably of lower sensitivity than PZT transducers, they should be used for fragile samples. Furthermore, they should allow a calibration of other transducers, as their properties are not determined by any material parameters. Specimens already having piezoelectric properties exhibit significant surface acoustic waves due to an electron impact. These surface waves are associated with a corresponding variation of the local surface potential. This surface potential travels along

32

LUDWIG JOSEF BALK

the surface with the same speed like the sound wave itself. By means of stroboscopic voltage contrast of the secondary electrons, a direct SEAM detection at the surface is possible, as already accomplished for acoustic waves generated by a transducer (Eberharter and Feuerbaum, 1980).

B. Electron Beam Current Modulation To obtain an SEAM signal, a variation of the primary electron beam current at the examined specimen location must be achieved. This is usually done by blanking of the electron beam within the electron optical column. Though there are various ways to realize a beam blanking. in the following subsection the system introduced has been used by the author and shows all features necessary for reliable SEAM work. Instead of a direct beam current modulation, an indirect modulation can be gained with a steady state beam, if its position is modulated with high enough frequency to move forth and back at a centre position. This technique does not have the need of introducing a beam blanker into the electron optics. 1. Electron Beam Chopping

Though many of today’s SEM are already commercially equipped with a beam blanking or chopping unit, it is worthwhile to mention some necessities with respect to SEAM instrumentation. Three properties are important: (i) high beam blanking sensitivity, (ii) variable frequency response up to the GHz regime, and (iii) neglectable chopping degradation. All these three requirements can be met by an electrostatic beam blanker (chopper) consisting of a pair of condensor plates which are mounted parallel to the electron beam direction. To attain high sensitivity, that is, a high beam deflection out of its axis due to an electric signal supplied to the plates, it is important to use a small blanking aperture beyond the condensor plates which prevents the deflected beam from reaching the sample. Usually mechanical apertures have the disadvantages that they are too large in diameter and that they contaminate during operation. Menzel and Kubalek (1979) have shown by theory and experiment that it is more convenient to use an additional electromagnetic lens (prelens) beyond the electron beam gun and to position the chopper at the crossover of this lens. As this crossover has to be an image point within the whole electron optical column, only those electrons can pass towards the sample which are within

SCANNING ELECTRON ACOUSTIC MICROSCOPY

33

the image of the final aperture at this crossover position. Accordingly, very small deviations from the axis result in blanking of the primary electron beam. Thus a maximum blanking sensitivity can be achieved. Due to this, beam chopping can be realized even for primary energies of 30 keV and more with less than 5 volts (quite often even less than 1 volt.) This fact has two significant advantages: one is that at high frequencies signal generators very rarely deliver more than 5 volts into a 50 ohm impedance. More important is that the signal to drive the condensor plates of the chopper is of the same frequency and phase as the SEAM signal to be measured. As SEAM signals can be very low, depending on operational conditions and specimen properties down to 1 p V , any unnecessarily high voltage supplied to the chopper will cause a crosstalk into the SEAM detection and preamplification circuitry and makes signal processing more difficult, if not impossible. A variable high frequency response of the chopper is inevitable, as the operator has to find an SEAM frequency fitting to the specimen properties to be measured. This can be any frequency from, say, some Hz up to the GHz range. The only system to do this is a pair of condensors with very small physical dimensions and layed out in a manner that a 50 ohm impedance is achieved at any connection. For pulsed experiments, precise rise and fall times of the electric field between the plates are necessary to allow accurate temporal SEAM analysis. High quality signal synthezisers should be used to get clean square wave response for harmonic signal excitation. Use of sine wave excitation is not recommended, as it is nearly impossible to create a clean sine wave modulation of the primary beam current at the specimen surface without a large amount of spurious signals. A sinusoidal current modulation by the chopper described above cannot be used with SEAM for yet another reason. It would generate a significant chopping degradation which is a periodical movement of the electron beam close to its location without chopping operation. This degradation causes a reduced spatial resolution and, more importantly, generates an additional beam current modulation (compare next subsection). Because of this, no correct results would be obtained. 2. Modulation of Electron Beam Position Rather than by a chopper, the primary electron current at the beam entry point can be modulated by an oscillatory movement of the beam at a fixed central position. If this movement is small enough compared to the total scan distance for a micrograph and if the modulation is of much higher frequency than the saw tooth used to scan the electron beam (for analog scan generators), the SEAM signal achieved should deliver the first

34

LUDWIG JOSEF BALK

derivative of the original SEAM signal with respect to the coordinate of beam movement (compare Balk and Kubalek, 1973). The advantage of such a procedure is that no modifications of the electron beam column have to be done.

C . Experimental Arrangements In the following, the SEAM set-up’s used to date are presented in a comparative manner so as to not confuse the reader. Therefore all block diagrams of this section are of identical structure though showing different systems. In the first two sections, the general purpose arrangements are shown, whereas the third section addresses the question of how to gain SEAM micrographs with additional specimen treatment. 1. General Purpose Arrangements with Beam Chopping There are two main ways to analyze SEAM signals. One is given by a harmonic signal generation and its analysis by means of a lock-in amplifier concerning frequency, magnitude and phase. The alternative is the use of a pulsed electron beam and the temporal analysis of the signal by means of a boxcar integrator or signal averaging system.

a . Set-Up for Lock-in Amplification Figure 20 shows schematically all necessary components for harmonic SEAM signal generation and analysis. The reader’s knowledge of the function of an SEM is assumed. The electron beam

f--

generator

1 frequency standard

-i scan COllS

IxI

1 oenerator

-

specimen transducer

amplifier lock-in amplifier

6 A

A sin 6 A cos 6

I

l

l

yzi f

p

2f

Lf

amplifier

FIG.20: SEAM arrangement for linear and nonlinear experiments

SCANNING ELECTRON ACOUSTIC MICROSCOPY

35

electron beam is chopped by a pair of condensor plates and a square wave generator. It is essential to determine the preciseness of the achieved duty cycle of the beam modulation, as otherwise signals may be generated at any harmonic of the modulation frequency f. As already discussed in Part 11, it is possible to generate nonlinear SEAM signals at even harmonics of the fundamental frequency f,preferably the second harmonic at 2f. To allow detailed analysis of such nonlinear signals, a triggering circuitry consisting of a frequency standard and a programmable word generator is used. The word generator delivers square waves at frequencies f , 2f, 4f and so on with no relative phase shift between these waveforms. The lock-in amplifier used has to be adapted to the frequency of interest. The maximum bandwidth of commercially available instruments is presently 50 MHz. Though A sin c$ and A cos 4, with A the magnitude and c$ the phase angle of SEAM relative to the electron beam waveform, are the direct lock-in amplifier outputs, instruments should be preferred which deliver magnitude A and phase 4 separately, as these quantities give different information on the sample’s properties. A differential amplifier is used to optimize the final signal level to the video system of the SEM. The centre of the SEAM set-up, the specimen-transducer-assembly , is usually connected to a preamplifier which can avoid spurious signal pick-up in the cables such as low signals or high frequencies.

b. Set-Ups for Temporal Analysis Using Boxcar Integration The main change of Fig. 21 from Fig. 20 is the substitution of the lock-in amplifier by a boxcar integrator. This can be simply an analog instrument or a more electron beam

b-

pulse nerator I

scan

-

IxI

COIIS [XI

Y

frequency

-

scan generator

specimen

sampling amplifier

FIG.21: Experimental set-up for time-resolved SEAM micrographs.

LUDWIG JOSEF BALK

36

* sampling head

preamplifier boxcar integrator

different 101 amplifier

1

FIG.22: SEAM arrangement to record “time delay versus linescan” images

sophisticated digitized and programmable signal averager. The electron beam waveform can be controlled either by a square wave or a pulse generator. If a square wave generator is used at higher frequencies, a frequency divider may be necessary for triggering of the sampling heads incorporated within the boxcar integrator. In any case, it is inevitable for a reliable temporal SEAM analysis to achieve very short electron beam decay times with typical values in the order of 100 ps pulses down to the nanosecond regime are possible. If the time delay of the input gate or sampling head within the boxcar is fixed, its output can be used to produce time-resolved SEAM micrographs, the brightness of these directly indicating the signal magnitude for the chosen delay time. If the electron beam position is fixed to a certain spot at the specimen surface, scanning of the delay time allows complete analysis of the temporal SEAM response at this spot by recording the boxcar integrator output onto an oscilloscope or any other recording equipment. Quite often it is not convenient to record a series of SEAM micrographs of different time delay for comparison. In the same sense, it is an awkward task to compare sets of oscilloscope traces for various specimen locations. To avoid these problems, a set-up like the one in Fig. 22 can be used as a compromise between these two alternatives. It still uses one ramp generator of the scan generator to produce a linescan. Another ramp generator is added to the system which drives the y-axis of the display screen and simultaneously controls the delay time of the sampling input of the boxcar integrator. In this manner, micrograph-like pictures are generated which have the x-axis as a local coordinate and the y-axis as a time

SCANNING ELECTRON ACOUSTIC MICROSCOPY

37

electron beam

-

specimen

FIG.23: Set-up for scan modulation SEAM.

axis. These time delay versus linescan images can give an easy and quantitative comparison of specimen features at different locations. An additional marker pulse can be used to ensure that synchronization is undistorted. By means of such a set-up, it has been possible to separate surface defects from grain boundaries in polycrystalline silicon (Balk, 1986). 2. Scan Modulation S E A M Set-Up Scan modulation techniques have already been applied in SEM for derivation of EBIC signal within laser diodes (Balk et al., 1975). The arrangement for such an SEAM experiment is shown in Fig. 23. The main differences to the preceding diagrams are that the chopping assembly consisting of a prelens and a pair of condensor plates is omitted and that the scan of one axis, as indicated for the x-axis, is modulated with a sine wave of much higher frequency f i than the saw tooth used for scanning and with much lower amplitude A , as well. The x-axis of the display screen is not modulated. In this manner, grain boundaries in silicon and in metals could be detected (Balk, 1986). 3. Special Purpose Instrumentation

Most SEAM experiments are done without any in situ specimen treatment or without simultaneous recording of other SEM signals rather than the SE yield. But, both specimen treatment and comparison to other

38

LUDWIG JOSEF BALK

t

micro-

,

electrc 7

X

y z

4

-L

multi-

computer network

storage drsplay

zl I

scan coils

H

7

ponlzssor /prober

needle

/

. electrometer amplifier

EBIC

system vol tmet er

.~ lock-in

amplifier 1

4

SEAM system voltmeter Ah

FIG.24: Arrangement for simultaneous EBIC and SEAM experiments.

SEM techniques can help to separate SEAM signal generation and to understand SEAM contrasts. Two SEAM instrumentations in this respect are explained in the following. a. Set-Up for Simultaneous SEAM and EBIC Experiments As already discussed in Part 11, in a semiconducting sample, any EBIC signal necessarily has to have its complemental SEAM signal (with inversed magnitude contrast). Simultaneous EBIC and SEAM recording therefore can help to separate those contrasts out of an SEAM micrograph which are determined by EBIC features. A set-up for this purpose has been introduced by Balk et al. (1985) and is shown in Fig. 24. Needle probers, which can be positioned at any arbitrary location on top of the sample, are used to measure the EBIC signal that is detected by an electrometer. The SEAM part corresponds to Fig. 20. To ensure quantitative comparisons, the whole system is completely automatized. Digital scanning is needed to make sure that the EBIC versus SEAM comparison is not falsified by different signal delays in the amplifying electronics. b. SEAM Arrangement for Magnetic Materials Although the magnetic contrast of SEAM is not yet understood in detail, it delivers very clear images of ferromagnetic domains in silicon-iron sheets. Thus, one can use SEAM to analyse the response of such sheets to varying magnetic fields. In order to do this, a magnetic SEAM has been developed (Balk, 1986), which at the same time contacts the sample by the PZT transducer and by four magnetic coils. To enable tight contact of all components, both

SCANNING ELECTRON ACOUSTIC MICROSCOPY

39

electron beam square generatar

7 scan

coils [XI

-

Y

generator

video amplifier

f

I

magnetic coils

I

a&bf,er

2f

I

FIG.25: SEAM experiment with variable magnetic fields applied to the sample.

transducer and coils are spring suspended and pressed carefully against the sample. The electron beam itself is shielded from the magnetic fields by a mu-metal aperture. Quantitative magnetic field alignment is achieved by separate control of all (four) magnetic coils. Figure 25 shows this set-up combined with lock-in amplification.

IV. APPLICATIONS

A large variety of materials and devices has been investigated by means of SEAM already. The main groups which have been examined are metals and semiconducting materials and devices, but ceramics, glasses and polymers have been tested by SEAM, too. In the following it is not attempted to give a complete view of all published applications, as this would lead to numerous separate items. Instead, it is the aim of the following to show by a few examples how different signal generation mechanisms deliver information about the sample and how the various operation modes of SEAM contribute to these applications. Though most of the examples shown are taken from work of the author’s group, it should be clarified that there is a lot of other good applications published in literature. This restriction is solely made to point out certain SEAM image features of the various SEAM modes without introducing any additional system differences. To allow intelligible classification of the various operation modes, images taken by harmonic beam chopping operation are

40

LUDWIG JOSEF BALK

distinguished by the terms “linear” and “nonlinear”. Linear means amplification at the fundamental frequency f which is identical to the chopping frequency. Nonlinear refers to images taken at the second harmonic frequency 2f. Both terms are used for magnitude and phase images in the same manner. Images taken by means of a boxcar integrator are referred to as “time-resolved”. A . Metals

Three different metals have been investigated intensively to date. These are aluminum, a Cu-Zn-Al-alloy, and Si-Fe transformer steel. As aluminum only showed linear contrast images, it is not discussed here. Contrasts in aluminum are well understood, as regular thermal wave heating is the only relevant signal mechanism in it. This has been proven by depth profiling measurements (Alpern et al., 1987), grain boundary investigations (Murphy et al., 1987) and generation of vibrational mode patterns (Holstein, 1985). Cu-Zn-A1 will be discussed here, as it shows in addition to regular thermal wave images nonlinear contrasts due to the change of the physical dimensions of a mode converting scatterer (compare subsection 1I.B .2). Si-Fe transformer steel shows not only linear thermal wave signal generation, but also nonlinear magnetic contrast at the second harmonic. 1. Cu-Zn-Al-Alloy Though Cu-Zn-Al alloys have been examined in a very early stage of SEAM development (Cargill, 1981), they exhibit many unexpected properties. Furthermore, due to extensive experiments (Balk et al., 1984; 1984b; Davies, 1985; Balk 1986a), most of all properties relevant to metals can be shown in this subsection. Figure 26 shows a secondary electron (SE) micrograph of a polished Cu-Zn-A1 specimen. Aside from a few inclusions, no structure can be seen. The polycrystalline structure is not visible at all.

a. Linear S E A M Figure 27 demonstrates the great difference of information gained by linear SEAM compared to the SE micrograph. Figures 27a and b are taken at a frequency of 10 kHz, Figs. 27c and d at 190 kHz, Figs. a and c are magnitude images, Figs. b and d phase images. Without going into detail, one can make the following statements: the polycrystalline structure is clearly visible in any of these micrographs. Not only the large cubic grains can be recognized, but additionally narrow needle-like structures which correlate to monoclinic martensite platelets (compare Balk et a f . , 1984a). Furthermore, one can see that the spatial

SCANNING ELECTRON ACOUSTIC MICROSCOPY

41

FIG.26: Secondary electron micrograph of a polished Cu-Zn-A1 alloy

resolution increases with frequency. From a series of such images taken between 50 Hz and 200 kHz, the plot of Fig. 7 was deduced by visual estimation of the attained resolution. The values correspond very well with the theoretical frequency behaviour of the thermal diffusion length d T . As the cubic grains and the martensites are of identical chemical composition, their thermal properties should be the same, too. Therefore the contrast is solely due to a change of the elastic properties in the direction the sound has to propagate towards the transducer. Not only do the cubic grains exhibit an anisotropic elastic behaviour, the contrast of the martensite platelets is even more pronounced in both magnitude and phase images. If one increases the frequency to obtain further resolution gain, the primary electron energy dissipation will be a limiting factor. Furthermore, intrusions into the original contrast will arise due to standing wave patterns, so-called vibrational modes (compare subsection II.B.3). In Fig. 28b, these vibrational mode patterns, visible by a periodic black and white contrast, show to be independent for the grains and the martensite. Davies (1983) has discussed the effect of such patterns in narrow structures in

FIG.27: Linear SEAM micrographs of same sample area as in Fig. 26: (a) Magnitude at f = 10 kHz; (b) Phase at f = 10 kHz; (c) Magnitude at f = 190 kHz; (d) Phase at f = 190 kHz.

(b)

FIG.28: Cu-Zn-Al-alloy, W, = 30 keV: (a) Secondary electron micrograph; (b) Linear SEAM image in the A sin +-mode at 5 MHz.

44

LUDWIG JOSEF BALK

detail. The corresponding SE micrograph taken after a preferential etching shows very vaguely some of the structure of the SEAM image. One can see by comparison that a set of parallel martensite platelets at the left side of the picture is confined to a single grain. In order to get a more quantitative measure of the dependence of spatial resolution on the modulation frequency f, linescans have been taken across a grain boundary. They were recorded by means of a digital storage oscilloscope that allows derivation of the recorded waveform with respect to the scanning coordinate. Typical results are shown in Fig. 29 for four different frequencies (Davies, 1985). For both magnitude A and phase d, one can see that the resolution seems to increase with frequency. But unfortunately the waveform’s attitude changes drastically. This is one reason why grain boundary contrast is not yet completely understood in

boundary r p m l

boundary $m)

FIG.29: Linescans of linear magnitude and phase SEAM and their spatial derivatives across a grain boundary in Cu-Zn-A1 alloy for various frequencies, W,, = 30 keV (after Davies, 1985).

SCANNING ELECTRON ACOUSTIC MICROSCOPY

45

-

I -

10

100 1000 chapping frequency f(kHz)

10000

FIG.30: Comparison of resolution results at grain boundaries (after Davies, 1985; and after Murphy et al., 1987).

spite of many theoretical approaches (Murphy et al., 1987). In order to get a reasonable estimate for the achieved resolution, the first derivatives of magnitude and phase angle have been calculated. Although still of different shape, all of these curves show a clear maximum. Davies has taken the full width of these maxima to calculate the resolution dependence on frequency. His result is plotted in Fig. 30. A computer fit to his values shows afp”.3s -dependence of the spatial resolution. Fits with -0.3 and -0.4 slope in the double logarithmic plot showed to be of significant error. The lower values of Fig. 30 are taken from Murphy et al. (1987) and are experimental results for aluminum. The dashed line is the variation of dT for aluminum. At first sight, this curve seems to fit the results with reasonable accuracy. But again a -0.35 slope gives a better approximation. If one further shifts the values of Murphy et al. into the data obtained by Davies (by multiplying any value by 52), one can see that all values together meet perfectly the -0.35 slope. This result indicates that a fp”3-law governs spatial resolution in grain contrast rather than the originally assumed inverse square root law. However, both the grain boundary contrast and its frequency dependence are not yet understood in detail.

b. Nonlinear SEAM Going back to the specimen area as displayed in Figs. 26 and 27, in the centre of the linear SEAM images martensite structures could be seen very clearly. Figure 31 is a slightly larger magnification of this area imaged in the nonlinear mode at f = 98 kHz.

46

LUDWIG JOSEF BALK

FIG.31: Nonlinear SEAM magnitude micrograph at 2f of Cu-Zn-A1 alloy, black lines indicate grain boundaries visible in linear SEAM (compare Fig. 27); f = 98 kHz, W,, = 30 keV.

The original contrast has completely vanished. The grain boundary position is indicated by ink drawings. The only reasonable signal level arises at or around the martensite platelets. As will be discussed in more detail in the following subsection, the oval structures are due to a hysteretic shrinkage of growth of the martensites with temperature (Balk et a l . , 1984b). However, from nonlinear experiments an explanation of this contrast is very difficult, unlike explanation from time-resolved experiments. c. Time-Resolved SEAM According to Fig. 21, time-resolved SEAM images can be taken by use of both periodic and pulsed primary excitation. By setting the input gate (or sampling head) of the boxcar integrator to a fixed time delay, images are recorded directly correlating to this delay time. The difference between square wave and single pulse excitation is that in the first case a harmonic behaviour of the sample’s response results, whereas in the pulsed mode, the propagation of a single wave can be

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analyzed. Figure 32 shows the results of time-resolved SEAM for a square wave excitation for three different time delays. All three images (Figs. 32b to 32d) exhibit the martensite structures, which are not visible by SE contrasts (Fig. 32a). But contrary to the linear SEAM magnitude images, they change their relative contrasts. Comparing the two sets of martensites in Fig. 32, those having a 45" angle with the picture frame and others having an approximate angle of about the 70" with the horizontal axis, one can see that for 30 ps delay only the 45" martensites show clear (bright) contrast, that at the 35 ps delay image both groups of martensites are of good dark contrast on a bright background, and that at 40 ps delay the 70" martensites appear very bright, whereas the others are dark on a grey background. This situation correlates with results of linear SEAM phase images, though the quantification in the time-resolved mode can be done more reliably. The contrast inversions are due to a phase shift of the signals excited in the various martensites. As these have monoclinic crystalline structure, they show anisotropic elastic properties. Assuming various stiffness values, one can deduce from the present results that different crystalline directions should mode convert heat production into sound with a different temporal response. The contrast should not be affected by the velocity of either sound or thermal wave. Thus the contrast correlates to different crystalline orientations of the martensites, the 45" group having a uniform orientation, the 70" group having another one. A different situation results for single pulse excitation, which is demonstrated by Fig. 33. The sequence of time-resolved SEAM micrographs (a-d) is taken at the same delay range as in Fig. 32. The 30 ps delay image shows again a martensite by dark contrast which has a 35" angle to the horizontal axis. The signal to noise is lower compared to Fig. 32, as a low power dissipation occurs due to a low repetition rate and thus a high duty cycle. (Only a quasi-single pulse situation can be achieved, as signal averaging is necessary due to the low signal levels involved.) Variation of the time delay by 5 ps steps up to 45 ps, for Fig. 33d exhibits the same contrast inversion of this martensite as discussed before. But in addition to this regular martensite contrast, a ring or oval-like structure is superimposed on the image. This structure is fixed with its centre for all four images, but its effective diameter is linearly growing with time delay. It should be emphasized here that the images are not taken in the same sequence by the operator as arranged here, which excludes a priori experimental artefacts due to an overall heating of the sample, for instance. The only explanation for this ring structure is given by the schematic of Fig. 33e. Assuming a conversion site for a shrinkage and growth of the

(c)

(4

FIG. 32: Time-resolved SEAM micrographs of Cu-Zn-A1 for square wave electron beam modulation (with 14 kHz) and for various time delays. W,, = 30 keV: (a) Secondary electron micrograph; (h) 30 ys delay; (c) 35 ps delay; (d) 40 ps delay.

mortensite platelet with conversion site lshrinkoge due to heotingl

0

rings of equal traveling distance of heat pulse towords conversion site for 301s time delay for LOus time delov

(4 FIG.33: Time-resolved SEAM micrographs at the surrounding of a martensite platelet in Cu-Zn-A1 with pulsed excitation for various delays, W , = 30 keV: (a) 30 ps delay; (b) 35 ps delay; (c) 40 ps delay; (d) 45 ps delay; (e) Schematic to interpret the arising SEAM contrast of Figs. a-d.

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LUDWIG JOSEF BALK

martensite indicated by a cross, the rings are contours of equal traveling time of a thermal wave starting from the actual electron beam entry point towards this conversion site. In this manner, the propagation properties of the thermal wave determine the shape of these rings. From the images one can measure an approximate velocity of the thermal waves of 1 meter per second, which is in excellent agreement with the theoretical value obtained for the experimental conditions chosen. The oscillatory black and white contrast within the rings is not yet explained but can be due to the non-perfect single pulse situation or a ringing of the thermal wave pulse. In the nonlinear SEAM magnitude image of Fig. 31, oval structures could be seen at the martensite locations. These are nothing else than superpositions of this thermal wave traveling effect onto the regular contrast. As the velocity of thermal waves is by three orders of magnitude smaller than the sound velocity, it may be utilized to image scatterer sites of direct heat to sound conversion with high spatial resolution. Such a possible application is indicated in Fig. 34, in which two inclusions in Cu-Zn-Al-alloy are visible, marked by letters A and B.

FIG.34: Time-resolved SEAM micrograph with 3 ps time delay after beam cut-off at inclusions in Cu-Zn-A1 alloy, W , = 30 keV (A,B: inclusion sites).

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Between these, there is a curved line visible which correlates to locations of equal travelling time towards such a conversion site. For other time delays shown here, this line both moves and changes its shape. The resolution achievable by this is better than 1 pm; the interpretation of the image itself is as a complicated, not simple structure, as is given in the example of Fig. 33. 2. Si-Fe Transformer Steel

This material shows in many respects similar results to the metal alloy discussed in the previous subsection. Additionally, two further applications of SEAM can be discussed here. One is the imaging through surface layers, the other one the imaging of magnetic domains by means of direct magnetic coupling. a. Linear SEAM In Fig. 29 one could see that the grain boundary contrast varies its attitude when changing the modulation frequency. This result, obtained there for Cu-Zn-Al, can be visualized in Fig. 35 for Si-Fe

(4 (b) FIG.35: Linear SEAM micrographs of uncoated Si-Fe transformer steel sheets, W , = 30 keV: (a) magnitude image at f = 400 kHz; (b) A sin 4 image at f = 1.9 MHz.

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sheets. Whereas the picture taken at f = 400 kHz (Fig. 35a) exhibits a grain contrast and by this a step-function-like behaviour at the boundary itself, in the 1.9 MHz-micrograph only a grain boundary contrast appears with no contrast between the grains, which denotes a peak response of the SEAM signal at the boundary. Such contrast modifications occur in a reproducible manner. However, no certain interpretation of this effect has been made. In order to reduce magnetization losses when using this material in electrical transformers, the magnetic domain configuration is modified by adding an oxide layer of about 2 p m thickness onto the sheet surfaces. This oxide shrinks during deposition and puts a definite strain onto the sheet parallel to the surface. Due to this, a narrower spacing of the magnetic domains can be achieved. It could be demonstrated that the grain and grain boundary contrast can be achieved by linear SEAM without etching away the oxide (Balk and Kultscher, 1983a; Balk et al., 1984~).In Fig. 36a, the surface of such a sheet is shown in the SE-micrograph. Part of the oxide

(a) (b) FIG.36: Influence of residual oxide coating on the Si-Fe surface, W,, = 30 keV: (a) Secondary electron micrograph; (b) Linear magnitude SEAM micrograph at f = 100 kHz.

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has remained, as two visible bright islands, whereas the other steel surface is uncovered. As to be seen by the SEAM magnitude image of Fig. 36b of the identical specimen area, one can see that the remainders of the oxide are not visible. On the other hand, a diffuse black shade arises, which certainly has a correlation to the two remaining oxide patches. This dark area is due to a higher material stiffness as a consequence of the action of the oxide onto the sheet, as all other factors for SEAM signal generation are unchanged. The reasons for the ability to image through a layer is given by the generation volume for the sound signal, which is strongly determined by the electron energy dissipation function (compare section 1I.A). For the energy of 30 keV, as chosen here, most of the electron’s energy is dissipated into the steel rather than within the thin oxide.

b. Nonlinear SEAM Whereas in the linear SEAM mode, no magnetic domains can be imaged, if a proper square wave chopping of the primary electron beam is achieved-not even for high signal offsets, the magnetic domain structure is clearly visible in the nonlinear mode at the second harmonic without any need for enhanced signal processing. The contrast is a domain contrast with a superposed bright domain wall contrast (Balk et al., 1984b). Figure 37a shows the domain configuration within various grains. In the middle grain the dark domains are much larger than the white ones, which means that this grain is close to the single domain situation. In Fig. 37b, a broadening of the bright domains towards the grain boundary is to be seen being most likey due to the existence of closure domains. In Figs. 38a and 38b, it can be seen that for perfect orientation of the grain, parallel magnetic domains can be imaged, the bright wall contrast separating the domains of different orientation. As soon as a defect or inclusion, as visible in the SE micrograph, is introduced into the surface, the magnetic domains are significantly disturbed, as seen by an additional domain of different direction at the inclusion site (at the right part of image). Figures 38c and 38d demonstrate how complex structures may arise. Both images are taken with a magnetic field applied to the sample by the arrangement shown in Fig. 25. Compared to Fig. 38b, in which a net magnetization of zero is given by the equal widths of bright and black domains, in Fig. 38c (though at a different specimen location), only some remaining black domains are visible, and in Fig. 38d, for the same location but a different direction of the magnetic field, they are just vanished. It should be mentioned that the magnetic contrast can be seen through an oxide layer as well (Balk et al. 1984c), although all figures shown here are recorded for uncovered surfaces.

(b) FIG.37: Imaging of magnetic domains in Si-Fe by nonlinear SEAM magnitude micrographs, W" = 30 keV; (a) Configuration of domains and grains, f = 77 kHz; (b) Closure domains at the grain boundary, f = 70 kHz.

(4

(4

FIG.38: On the contrasts obtained for magnetic domains in Si-Fe obtained by nonlinear SEAM magnitude images, W , = 30 keV: (a) Secondary electron micrograph of same section as in Fig. b; (b) Approximate zero net magnetization and intrusion of domain configuration by defects, f = 19 kHz; (c) Domain configuration at a specimen location with poor orientation of the grain relative to the surface, applied magnetic field orientation: horizontal from left to right-complex structures arise; f = 76 kHz; (d) Same section as in Fig. c but with antiparallel direction of magnetic field.

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B. Semiconductors Though all the different possible signal generation and contrast mechanisms are not yet quantitatively known for semiconductors, one main emphasis of SEAM applications is given by its use within semiconductor technology as a tool for nondestructive process control. As already discussed in Part 11, SEAM can be used to image all relevant features within a semiconductor, such as doped areas, pn-junctions, dislocations, etc. The advantage of SEAM over other techniques of SEM is that it can be used for any semiconductor without any restriction, opposite to cathodoluminescence which is not entirely feasible for direct band gap material; and without the need for a special specimen preparation, opposite to EBIC which necessitates the existence of a space charge within the volume for non-vanishing excess carrier concentration. Thus, quite often Schottky contacts have to be applied to a sample to measure EBIC, and furthermore, electrical contacts have to be brought to areas of interest. These needs are not present in the use of SEAM. Applications of SEAM are already covering a large variety of materials. Silicon wafer material (Rosencwaig, 1984) and silicon transistors (Takenoshita et a / . , 1985) have been investigated. By variation of the primary electron energy, a nondestructive depth profiling of such transistors can be gained (Takenoshita and Kawamura, 1986). In GaAs wafers, even slightest material variations are visible by SEAM, such as striations (Davies, 1985), and the influence of defects on GaAs devices may be imaged (Kirkendall and Remmel, 1984). Ternary systems have been examined, too, like GaAsP (Ikoma et al., 1984) and more complex systems such as CuInSez (Takenoshita, 1986). In the following, two examples will be introduced which allow discussion of many important contrasts in SEAM. InP is chosen as a material with high a priori piezoelectricity, polycrystalline silicon as a material with very low thermal expansion and a considerable amount of nonlinear contributions to the SEAM signal.

1. Indium Phosphide InP has been investigated first by Balk and Kultscher (1983b), and it could be shown that SEAM images have to be interpreted by means of three signal generation mechanisms: thermal, piezoelectric and excess carrier coupling. Imaged features may have contrasts of different physical origin than the main source for signal generation. An example for this may be the bright dislocation contrast within a highly doped region. The region contrast is due to electronic properties, whereas the bright dislocation contrast is due to a higher heating as a consequence of a high nonradiative

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carrier recombination. The contrasts gained in linear and nonlinear SEAM are quite similar at first sight, though one can see that the nonlinear second harmonic images show much more detailed information. To demonstrate this, a Zn-diffused surface is imaged by nonlinear SEAM in Fig. 39. Besides scratches and dislocations emerging into the surface (visible by white dots with a black centre), black and white lines can be seen which radially extend from a centre point at the upper left part of the image. These are centrifugal stripes originating from the liquid phase process. As the thickness of They correspond to a dopant variation of below the Zn-diffused layer is about 0.5 pm, this example shows the sensitivity of this technique. The larger dark dots are due to mistakes during the process and correlate to major dopant changes. The diffuse contrast, especially the dark regions at the wafer rim are due to mechanically stressed material regions. The black circular area at the upper right part of the picture still is part of the wafer, but there the diffused layer is etched away. The undoped crystal region shows much less signal than the layer with about lo1' cmP3 doping concentration.

W,

FIG.39: Nonlinear SEAM magnitude micrograph at 2f of a Zn-diffused InP wafer I0 keV. f = 100 kHz.

=

58

LUDWIG JOSEF BALK hatched area Zn diffused regions unhatched InP substrate

FIG. 40: Schematic of FET design of samples displayed in Figs. 41 and 42.

In Fig. 40, a FET design is sketched which appears in the following examples. All three areas-source, gate and drain-are doped at the same level, which again is a Zn doping of about lo'* cmP3. Figure 41 shows the comparison of SE micrographs to linear and nonlinear SEAM. The SE images only reveal contrast after a considerable signal offset, mainly because of topographic features such as an additional surface roughness due to technological processing. The structures revealed by the SE image, however, correlate without falsification to the doped areas. Figure 41b is a linear SEAM micrograph, Fig. 41d a nonlinear SEAM image of the same sample, although of a different area and with a higher magnification. The linear image shows that the doped areas give an overall bright contrast. The nonlinear image shows this contrast, too, but additionally it exhibits line structures corresponding to dislocations. A very important feature is to be seen in both of the SEAM images, though more clearly in the higher magnification. The structure widths, easily visible at the gate, are not correctly corresponding to the SE micrograph. One can see a mismatch of about 8 pm, which is twice the approximate value of the minority carrier diffusion length for this material. This mismatch clearly reveals the existence of the electric field at the dopant border, similar to a pn-junction field. It must be pointed out here that this is an inherent contrast within SEAM. The apparent spatial resolution at pn-junctions or similar electrical barriers will minimize the SEAM magnitude. This can be proven by comparison with simultaneously detected EBIC. To do this, a set-up as introduced in Fig. 24 can be used, if the prober needles are located to contact such a barrier on both sides. The width and the location of the region of detectable EBIC correlates perfectly with the mismatch visible in Figs. 41c and 41d (Balk et al., 1985). Following the theoretical discussion

(c) (4 FIG. 41: Investigation of FET device on InP by SEAM, W , = 30 keV: (a) Secondary electron micrograph of same section as in Fig b; (b) Linear SEAM magnitude micrograph at f = 100 kHz; (c) Secondary electron micrograph of same section as in Fig. d; (d) Nonlinear SEAM micrograph (A sin 4) at f = 5.6 MHz.

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LUDWIG JOSEF BALK

of Part 11, this image attitude should be similar for SEAM described up to now and for direct detection of the voltage change at the lower sample surface due to the piezoelectric properties of InP. The only difference will be a phase change of 180". Again this could be proven by comparing the measurements using an earthed electrode at the transducer interface for one condition, and measuring the signals at both transducer electrodes with the interfacing electrode being unearthed. If both sample surfaces are earthed, the signal is strongly attenuated (Davies, 1985), as then the periodical field associated with the sound wave is quenched leading to a subsequent quenching of the sound magnitude itself. If one increases the modulation frequency up into the high MHz regime, instead of the former mismatch of structures a pronounced resonance occurs giving rise to black and white zones around the dopant borders (Fig. 42a). The image is a mixed information of A sin 4, the contrast inversion due to a phase change, whereas the magnitude is maximum for both cases. The width and location of these zones are

(4 f =

(b)

FIG.42: High frequency SEAM micrographs of device structures on InP, Wo = 5 keV, 10 MHz: (a) Linear A sin 4 image; (b) Nonlinear A sin 4 image at 2f.

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identical to the former mismatch. In the linear SEAM image, both black and white areas can be seen which are not due to any instrumental artefact. This, for instance, can be estimated by the scan lines visible within the image. Mechanical rotation of the sample does not change the image at all. In the nonlinear SEAM micrograph (Fig. 42b)-within the accuracy of this relatively difficult experiment-only dark contrasts, but of same local extension, are to be seen. Kultscher and Balk (1986) explained this effect by the apriori existence of a DC electric field at the dopant boundary. This field correlates in its direction to the change from doped to undoped region. The sound wave as excited by the electron beam, however, is associated with an electrical A C field which correlates directionally to the crystal lattice. Due to this, the contrast inversion is determined by the relation between crystalline orientation and the direction of the DC barrier field. It is assumed that the high frequent field causes sort of a confinement and by this an effective increase of excess carriers at the barrier site. As the nonlinear SEAM signal is proportional to E2 according to theory, this contrast has to be unidirectional, the dark contrast due to the partition of sin to the signal. 2. Polycrystalline Silicon

Polycrystalline silicon has been chosen for this discussion, as it should show both semiconductor properties and grain or grain boundary contrasts like already treated in the first section of this Part. Furthermore, it is not piezoelectric and has a very low thermal expansion coefficient. Therefore, a participation of electrostrictive coupling to the overall signal should be relatively high. Actually it could be proven experimentally that for this material nonlinear signals at the second harmonic can be about 10% of the linear magnitude. The nonlinearity in this case is obviously independent of the excitation level, as nonlinear SEAM could be recorded for low primary energies and low beam currents (Balk and Kultscher, 1984). Additionally, it must be mentioned that the results obtained in nonlinear SEAM are explainable in terms of relevant parameters of this material. Therefore a detailed discussion of the linear SEAM experiments will be omitted in this subsection. However, time-resolved experiments and scan modulation SEAM, which mainly deliver the linear signal contribution, will be discussed.

a. Nonlinear SEAM Analysis of linear and nonlinear SEAM magnitude micrographs of this material did not reveal any grain contrast like those measured for metals. In the linear mode, only a slight and diffuse

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grain boundary contrast has been visible. The linear and nonlinear SEAM phase images, however, show extremely strong contrast with a sharp step function response at the boundary (Balk and Kultscher, 1983a). With this contrasts, a localization of the boundary position can be done with a spatial resolution of the order of 0.1 p m . Furthermore, the frequency behaviour of spatial resolution is far less pronounced than for metals (in the nonlinear mode, independent of frequency within the accuracy of the experiment), and all these results indicate that both in linear and nonlinear SEAM, the contribution of excess carriers to the signal is strongest. Figure 43 shows a nonlinear SEAM magnitude micrograph in comparison to the SE image. As can be notified immediately, good SEAM contrast can be obtained in spite of a very corrugated surface. The intrusion of topographical contrast into the SEAM image is neglectible. The black line within the bright diffuse zone is the actual position of the grain boundary. The contrast is due to an internally existing EBIC signal at the boundary that minimizes the SEAM magnitude. The internal EBIC is due to the

(4

(b)

FIG.43: Imaging of grain boundary and denuded zones in polycrystalline silicon by nonlinear SEAM, W, = 30 keVf = 100 kHz: (a) Secondary electron micrograph; (b) SEAM magnitude image of second harmonic (at 2f).

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existence of a space charge region at the boundary, as the grains are strongly differing in their doping level resulting in electrical barriers of up to 0.5 volts. As could be shown for the investigation of diodes, barriers of 0.1 volt are sufficient enough to attain a full EBIC magnitude (Balk et al., 1980). The width of the black line in the SEAM image is directly corresponding with the effective EBIC width as proven by simultaneous recording of SEAM and EBIC (Balk et al., 1985). The diffuse white region surrounding the boundary is caused by a lower oxygen and carbon concentration compared to the grain interior. This concentration change does not vary the electronic properties of silicon too much, which means that the parameters for excess carrier generation should remain unchanged to a first approximation. The stiffness of the material, however, is significantly weakened by a decreased oxygen concentration (Yonenaga and Sumino, 1984). Consequently, a larger SEAM magnitude has to be measured within the region of low oxygen content. These so-called denuded zones can be determined by preferential etching, too. As already mentioned, the SEAM phase angle changes rapidly at the boundary. This gross change likely correlates to the changed equilibrium carrier density. Additionally, a slight change of the phase can be measured within the denuded zone. To enhance this effect and to quantify it, a special SEAM phase technique has been used, which is demonstrated in Fig. 44 (Balk, 1986b). The lock-in amplifier used shows a discontinuity of the phase output when passing an adjustable internal phase angle. This discontinuity causes the image contrast to change from white to black when passing over this reference angle. This arbitrary contrast cannot be falsified by photographic processing; the border line between white and black area precisely defines all locations at which the internally adjusted phase angle occurs within the signal. Figure 44a is a nonlinear SEAM magnitude micrograph of another grain boundary showing the same contrasts like in Fig. 43b. Adjusting the internal reference angle of the lock-in amplifier to meet the signal response at the left side of the denuded zone at the vertical boundary gives a set of various SEAM phase images. The internal phase angle varies in an equidistant manner within this series. One can see that the white-todark border line moves from the grain interior towards the boundary until it nearly vanishes. These phase angle contours reveal the graduate oxygen segregation. As already discussed for the temporal SEAM behaviour at martensities within Cu-Zn-A1 alloys, a higher stiffness causes a faster action of the material to the electron excitation leading to a low phase delay in case of harmonic beam modulation. Thus the measured phase change within the denuded zone indicates a decrease of the stiffness from the grain interior towards the boundary, the white-to-black border lines being contours of constant stiffness.

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FIG. 44: Nonlinear SEAM phase imaging of denuded zone for various alignments of lock-in internal reference angle, W , = 30 keV, f = 10 kHz: (a) Nonlinear SEAM magnitude micrograph at 2f; (b) Phase image with reference angle aligned to 55"; (c) 60"; (d) 65"; ( e ) 70".

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b. Time Resolved SEAM In time-resolved experiments, thermal coupling contributes strongest to the overall signal. The signal can be due to direct heating of the sample by the primary electron beam and to nonradiative recombination of excess carriers generated by the electron beam (compare II.A.2.a). Without trying to explain the contrast, a timeresolved image is shown in the upper part of Fig. 45 for the same specimen location as in Fig. 44. Again the vertical boundary can be seen clearly. Additionally, two other structures are visible, one very vaguely which ends at the centre of the horizontal axis (drawn into the micrograph). The phase delay for this image was fixed to 3.4 ps. When varying the time delay, the relative contrast of the three lines changes strongly. For instance at 2.6 ps delay, all three show about equal contrast (Balk, 1986b). To analyse this effect, one could think of producing a set of time-resolved micrographs of different delay times. A quantitative comparison of these, however, would be very complicated, even if system instabilities could be avoided. Instead of this, the experimental arrangement of Fig. 22 has been used to analyse the transient SEAM behaviour. The result is shown in the lower part of Fig. 45, as indicated by the t-axis, the time span ranging from 1.6 ps delay to 4.8 ps. The outer structures extend about equally far in this time-delay

FIG. 45: Time-resolved SEAM experiments applied to polycrystalline silicon, W,, = 30 keV. Duration of primary electron beam pulse: 200 ns; pulse repetition rate: 20 kHz; resolution of boxcar integrator: 100 ps; upper part of image: SEAM micrograph; lower part of image: time delay versus linescan image.

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LUDWIG JOSEF BALK

versus linescan image, and they show a contrast which is similar to the one achieved for depth profiling experiments in photoacoustic experiments. Thus one can assume that the temporal response relates to a depth profile, although a quantitative model is not available for this correlation at present. The temporal behaviour seems to be determined by the excess carrier lifetime for this material; the vanishing of the structure after 4.8 /.LS is certainly caused by the fact that all excess carriers are recombined there. Therefore one can deduce that the two outer structures extend far into the bulk and that they are grain boundaries. The middle structure, however, is only visible within a small time span and must therefore be assumed to be a surface defect, probably a scratch. It should be emphasized here that an interpretation of the result in terms of time-of-flight of the sound wave is not feasible, as too long delay times are involved. Such timeof-flight experiments yield reasonable results in metals and can be interpreted by the propagation of sound, as shown for phase resolved linear SEAM images of crossing aluminum conduction lines on silicon (Balk and Kultscher, 1983a). Thus the result of Fig. 45 indicates strongly that a simple thermal wave model does not hold for semiconducting material. c. Scan Modulation SEAM According to Fig. 23, scan modulation SEAM experiments can be carried out. Results achieved for polycrystalline silicon show that the information gained is similar to the derivative of the linear SEAM signal with respect to the modulation coordinate. The scan modulation SEAM signal itself is considerably smaller than signals of other SEAM operation modes, as only a small change of energy deposition is attained when modulating the position of the beam entry point (Balk, 1986b). Although new applications could not be gained with this technique until now, it seems worthwhile give it more attention, as it delivers signal changes only which may result in an easier interpretation of micrographs obtained for regular specimen structures like in integrated circuits.

C . Ceramics

The investigation of ceramics by SEAM still is only in a very preliminary stage. In principle, all the discussed signal generation and contrast mechanisms should occur. But opposite to material of low disturbance of its elastic properties, like in a single crystal, in ceramics a significant attenuation of the acoustic wave occurs. This effect leads to much lower SEAM signal levels as compared to a crystal out of the same material as the corresponding ceramic. Accordingly one has to be aware of the fact that a contribution of sound propagation properties to the SEAM contrast may

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be important. For barium titanate, Kultscher and Balk (1986) could show that the results obtained for a ceramic are worse than these for a barium titanate single crystal. Whereas for the latter, good signal level and clear ferroelectric domain contrast has been observed, the signal level for a similar ceramic material has been low and the contrast showed to be quite complicated. This problem is demonstrated in Fig. 46. In the SE micrograph in Fig. 46a, one clearly can see the different grains and the ferroelectric domain structure within the grains. This domain contrast is due to a qualitative voltage contrast of the secondary electrons. Further, one can see holes (dark and surrounded by white lines due to topographic contrast) and intermediate (black) phases between the grains. The correlating linear SEAM magnitude micrograph of Fig. 46b, however, shows only very vaguely similar details. One can see the holes by white contrast, and further, one can imagine the grain structure. Only two grains, one in the centre of the micrograph and one at the right exhibit domain contrast. The reason for this poor result is mainly due to the apparently insufficient signal to noise ratio. However, it is astonishing that the grain exhibiting clear SEAM domain contrast has only a minimum SE domain contrast. By this example, one can deduce that investigation of ceramics by

(4

(b)

FIG.46: Investigation of barium titanate ceramic, W , = 30 keV: (a) Secondary electron micrograph; (b) Linear SEAM magnitude image at f = 95 kHz.

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LUDWIG JOSEF BALK

SEAM has to incorporate even more efficient detection techniques than available at present.

D. Polymers Similar to ceramics, only some first applications of SEAM to polymeric material are published. At present the signal generation mechanism is solely discussed in terms of thermal wave coupling, although there is evidence, for instance, for polyvinylidendifluoride as a sample, that piezoelectric coupling may occur, too. In this manner, it has been possible to image ferroelectric domains in this material (Balk, Kultscher, and Coufal; unpublished). Begnoche and Holstein (1984) have put their attention to the detection of cracks and delaminations in polymers. In polyimide resin, they could image subsurface delaminations, as is demonstrated in Fig. 47. In the S E micrograph, one can see the onset of the delamination at the surface, and the SEAM image shows its extension below the surface. The contrast achieved is mainly due to a phase change, which in this case dominates the SEAM image as recorded in the A sin 4 mode. The contrast origin is attributed by the authors to a change of the distance the acoustic wave has to travel towards the transducer, as sketched in Fig. 48. One important problem when examining polymers by SEAM is that necessarily a conductive coating has to be brought onto the specimen surface. If this is not done in a perfect manner and without

FIG.47: Surface crack (delamination) in polyimide resin, W,, = 10 keV: (a) Backscattered electron image; (b) Linear A sin 6 SEAM micrograph; (Courtesy of B. C. Begnoche and W. L. Holstein, du Pont de Nemours Central R & D Department, Wilmington, DE)

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electron beam

I

path of acoustic wave

FIG.48: On the contrast attained in Fig. 47 (after Begnoche and Holstein, 1984)

avoiding any specimen heating and by this specimen damage, many features as measured by SEAM may become artefacts, because SEAM may reveal elastic or thermal features as being solely due to the specimen preparation process. V. CONCLUSIONS Scanning electron acoustic microscopy has been shown to reveal many important material properties, quite often in an unexpected and exciting manner. It can be applied to the investigation of most materials without the need of an extensive specimen preparation, and it is able to deliver information on the sample even from locations below the surface. Many of the features detected by SEAM are difficult to be analyzed by other means; some of them have not been measured by other techniques at all. The spatial resolutions attained for modern SEAM instrumentation has reached a sufficient standard for many problems, being in the low micrometer regime for metals and in the submicron range for semiconductors. Depending on the SEAM operation mode being of most interest to the user, only moderate instrumentation costs are associated with the SEAM technique, certainly representing an advantage of SEAM over other acoustic microscopes. On the other hand, however, the interpretation of SEAM results is at present not unequivocal in many cases. This disadvantage, especially if compared to conventional scanning acoustic microscopy, has to be overcome in future by more detailed theories assisted by corresponding crucial experiments. Such experiments can both include test series with calibration samples and lead to a further improvement of SEAM signal processing.

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LUDWIG JOSEF BALK

Comparison of SEAM results to those obtained with other techniques, especially with other SEM modes will be of importance. Furthermore, comparison to other microscopes utilizing acoustic signals, such as conventional scanning acoustic microscopy, photo or ion acoustic microscopy, might allow separation of various signal generation and contrast mechanisms. The more quantitative the SEAM results can be understood, the further the increase of SEAM application to microcharacterization of materials and devices will extend.

ACKNOWLEDGEMENTS The author is indebted to many people who participated in this work. His main thanks have to be brought to those persons, however, who took part in the development of the SEAM techniques as established at Duisburg University. First of all, he would to thank Prof. Dr.-Ing. E. Kubalek who not only participated in many important discussions but who enabled the enforcement of this research during the last five years within his department for materials for electrical engineering. Dr. D. G. Davies from the University of Cambridge, U.K., and N. Kultscher from the author’s group have put forward the technique by experiments and theoretical treatments. B. Jager, N. Nothen, and G. Richard explored various applications within their master’s rsp. bachelor’s thesis. Dr. G. Koschek kindly assisted with experiments and took part in the discussion on SEAM applications for ceramics. The specimens shown in Part IV from the author’s work were supplied by various persons and organizations: the Cu-Zn-A1 alloy samples by D. G. Davies, University of Cambridge; the Si-Fe transformer sheets by Dr. Hastenrath from Thyssen-Stahl-AG, Duisburg,; the indium phosphide material and devices by Prof. Dr. Heime from the department for solid state electronics from Duisburg University; the polycrystalline silicon by Dr. Wagner from Heliotronic, Burghausen, F. R. G.; the barium titanate ceramic by Dr. Schmelz from Siemens AG, Miinchen, F. R. G . Parts of this work were financially supported by the ministry for science and research of the state Northrhine-Westfalia and by the Deutsche Forschungsgemeinschaft within several research projects.

LISTOF SYMBOLS

SEAM magnitude specific heat elastic stiffness constant primary electron dissipation function diffusion corrected dissipation function specimen thickness thermal diffusion length electric field

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elastic modulus piezoelectric stress constant modulation frequency; w = 2 ~ f primary electron beam current thermal conductivity minority carrier diffusion length excess carrier density distance to beam entry point at the surface local strain absolute temperature time acceleration voltage for primary electrons acoustic signal z-component of particle displacement longitudinal sound velocity primary electron energy energy penetration depth location of maximum of depth dose function linear thermal expansion coefficient stress dependent permittivity permittivity of vacuum phase angel of SEAM relative to electron beam waveform thermal wavelength acoustic wavelength material density excess carrier lifetime The international SI System of units is used throughout this paper.

REFERENCES Alpern, P., Menzel, A., and Tilgner. R. (1987). IEEE Trans. Ultrasonics Ferroelectrics, and Frequency Control, in press. Atherton, D. L., and Szpunar, J. A. (1986). IEEE Trans. Magn. MAG-22, 514. Averkiev, N . S., Ilisavskiy, Y. V., Sternin, V. M. (1984). Solid State Cornrnun. 52, 17. Balk, L. J. (1986b). Can. J. Phys. 64, 1238. Balk, L. J. (1976) PhD Thesis, RWTH Aachen, F.R.G. Balk, L. J. (1986a). Surface and Inferface AnalysB 9 , 47. Balk, L. J., Davies, D. G., and Kultscher, N. (1984b). IEEE Trans. Magn. MAG-20, 1466. Balk, L. J., Davies, D. G., and Kultscher, N . (1984~).J. Scanning Elecfron Microscopy, Part IV, 1601.

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Balk, L. J., Davies, D. G . , and Kultscher, N. (1984a). Phys. Star. Sol. ( a ) 82, 23. Balk, L. J . , and Kubalek, E. (1973). Beitr. elektronenmikroskop. Direktabb. Obe@. BEDO6, 551. (Verlag Remy, Munster, F.R.G.). Balk. L. J., and Kultscher, N. (1983a). Beitr. elektronenmikroskop. Direktabb. Oberf. BEDO-16, 107. (Verlag Remy, Munster, F.R.G.). Balk. L. J., and Kultscher, N. (1983b). Inst. Phys. Conf. Ser. 67, 387. Balk, L. J., and Kultscher, N. (1984). J . de Physique Colloque C2, 869. Balk, L. J., Menzel, E . , and Kubalek, E. (1975). IITRI Proc. Scanning Electron Microscopy, Part I, 447. Balk. L. J., Menzel, E., and Kubalek, E. (1980). Proc. Znt. Congr. X-ray Optics and Microanalysis, 8th, 1977, 613. Balk, L. J . , Richard, G . , and Kultscher, N. (1985). Inst. Phys. Conf. Ser. 76, 343. Begnoche, B. C., and Holstein, W. L. (1984). Proc. EMSA Meeting 42, 390. Baumann, T., Dacol, F., and Melcher, R. L. (1983). Appl. Phys. Lett. 43, 71. Brandis, E . , and Rosencwaig, A. (1980). Appl. Phys. Lett. 37, 98. Cargill 111, G . S. (1981). Proc. Ann. EMSA Meeting 39, 390. Cargill 111, G . S. (1980). In “Scanned Image Microscopy” (E. A. Ash, ed.), p. 319. Academic Press, New York. Cazaux, J. (1986). J . Appl. Phys. 59, 1418. Coufal, H. (1984). Appl. Phys. Lett. 44, 59. Dacol. F. H., Ermert, H., and Melcher, R. L. (1985). J . Scanning Electron Microscopy, Part 11, 627. Davies, D . G . (1983). J . Scanning Electron Microscopy, Part 111, 1163. Davies, D . G . (1985). PhD Thesis, University of Cambridge, U. K. Eberharter, G . , and Feuerbaum, H . P. (1980). Appl. Phys. Lett. 37, 698. Favro, L. D . , Kuo, P. K., Lin, M. J., Inglehart, L. J., and Thomas, R . L. (1984). Proc. I E E E Ultrasonics Symposium, 629. Favro, L. D . , Kuo, P. K., Shepard, S. M., and Thomas, R. L. (1987). Proc. IEEE Ulrrasonics Symposium 1986, in press. Ferrieu, F., and Auvert, G. (1983). J . Appl. Phys. 54, 2646. Fournier, D . , Boccara, C . , Skumanich, A , , and Amer, N. M. (1986) J . Appl. Phys. 59, 787. Hildebrand, J. A. (1986). J . Acoust SOC.A m . 79, 1457. Holstein, W. L. (1985). J . Appl. Phys. 58, 2008. Huebener, R. P., and Metzger, W. (1985). J . Scanning Electron Microscopy, Part 11, 617. Ikoma, T., Murayama, M., and Morizuka, K. (1984). Japan. J . Appl. Phys. 23, Suppl. 23-1, 194. Kirkendall, T. D., and Remmel, T. P. (1984). J . de Physique Colloque C2, 877. Koirakh, L .A., and Preobrazhncskii, V. L. (1984). Sov. Phys. Acoust. 30, 134. Kultscher, N., and Balk, L. J. (1986). J . Scanning Electron Microscopy, Part I, 33. Menzel, E., and Kubalek, E. (1979). J . Scanning Electron Microscopy, Part I, 305. Morizuka, K., Adachi, Y . , and Ikoma, T. (1982). Japan. J . Appl. Phys. 21, Suppl. 21-1,449. Murphy, J. C., Maclachlan, J . W., and Aamodt, L. C. (1987). IEEE Trans. Ultrasonics Ferroelectrics, and Frequency Control, in press. Opsal, J . , and Rosencwaig, A. (1982). J . Appl. Phys. 52, 4240. Proctor, T . M. Jr. (1982). J . Acomt. SOC. A m . 71, 1163. Reimer, L. (1979). J . Scanning Electron Microscopy, Part 11, 111. Ringermacher, H. I., and Jackman, L. (1986). In ”Review of progress in quantitative nondestructive evaluation” (D. 0. Thompson and D. E. Chimenti, eds.), 5, p. 567. Plenum Press, New York.

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Rosencwaig, A. (1984). J Scanning Electron Microscopy, Part IV, 1611. Rosencwaig, A . , and Gersho, A. (1976). J . Appl. Phys. 47, 64. Sablikov, V. A., and Sandomirskii, V. B. (1983). Sov. Phys. Semicond. 17, 50. Sasaki, M., Negishi, H., and Inoue, M. (1986). J . Appl. Phys. 59, 796. Shimizu, R., Ikuta, T . , Everhart, T. E., and DeVore, W. J . (1975). J . Appl. Phys. 46, 1581. Sieger, G. E., and Lefevre, H. W. (1985). Phys. Rev. A 31, 3929. Stearns, R. G., and Kino, G. S. (1985). Appl. Phys. Lett. 47, 1048. Takenoshita, H. (1986). Solar Cells 16, 65. Takenoshita, H., and Kawamura, T. (1986). Proc. Int. Congr. Electron Microscopy, 1 lth, 1986, 387. Takenoshita, H . , Managaki, M., and Mizuno, K. (1985). Japan. J . Appl. Phys. 24, Suppl. 24-1, 93. Tam, A. C. (1986). Review of Modern Physics 58, 381. Tronconi, A. L., Amato, M. A , , Morais, P. C., and Skeff Neto, K. (1984). J . Appl. Phys. 56, 1462. Veith, G. 11982). Appl. Phys. Lett. 41, 1045. Yamanouchi, K., Kudo, S . , and Wagatsuma, Y . (1984). Japan. J. Appl. Phys. 23, Suppl. 23-1, 191. Yamada, M., Nambu, K., and Yamamoto, K. (1985). J . Appl. Phys. 57, 965. Yonenaga, I . , and Sumino. K. (1984). J . Appl. Phys. 56, 2346.

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS . VOL . 71

Recent Progress In Particle Accelerators F . T . COLE and F . E . MILLS Fermi National Accelerator Laboratory. Batavia. Illinois

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Inventions and Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Beamcooling ................................... B . Radiofrequency Quadrupole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . PermanentMagnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Linear Induction Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . Use of Computers in Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Free Electron Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Beam Environment . . . . . . . . .................................. A . Effects of Environment on ........................... ....... B . Environmental Control . . . . . . . . . . . . . . . . . . . . . . . . . . IV . Statistical Methods and Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . SuperconductingTechnology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Radiofrequency Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI . New Kinds of Accelerators . . . ... A . Pulsed-Power Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Laser and Beat-Wave Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Wake-Field Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Two-Beam Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . Modified Betatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F . Linear Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII . Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75 79 79 80 81 84 84 86 87 87 90 90 92 92 96 98 98 99 102 103 104 104 105 105

I. INTRODUCTION It has been sixteen years since progress in particle accelerators was reviewed in these pages (Blewett. 1970). In these years. there has been dramatic progress in the design. technology. and understanding of every kind of accelerator . For example:

(i) Accelerators now reach energies an order of magnitude above those available in 1970. In addition. colliding-beam devices have reached a 75 Copyright 0 1988 by Academic Press. Inc . All rights of reproduction in any form reserved . ISBN 0-12-014671-1

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highly developed state and are understood by all to be the clear road to higher energy. (ii) Straight sections of almost arbitrary length are available in synchrotrons for beam injection, acceleration, and extraction. These stem from their invention by Collins (1961). Beam position throughout the acceleration cycle can be measured and controlled to within fractions of a millimeter or better. As a result of this control and the development of new septum devices, beam extraction has become remarkably efficient and uniform. (iii) Particle intensities are more than an order of magnitude larger than those available in 1970, largely because of the greatly increased understanding of collective instabilities in accelerators and of the means by which they can be ameliorated. So to speak, the environment of the beam is much better understood and controlled. The high intensity and advanced development of high-energy synchrotrons and storage rings have been crucial in providing experimental data in particle physics that are the basic for an enormous increase in our understanding of the nature of matter. Strong focusing (Christophilos, 1950; Courant, Livingston, and Snyder, 1952) has thus come to full maturity. (iv) Superconducting cyclotrons, linear accelerators, and synchrotrons have been built and are proving to be reliable and economical in operation. With new accelerators, nuclear physics has entered a new era of extension and refinement of experiments, particularly because of farsmaller energy spread of the primary beam, that are creating linkages between nuclear and particle physics. (v) The problems of injection into drift-tube linear accelerators have been conquered by the invention of the radiofrequency quadrupole (RFQ) system. (vi) New techniques of reducing the phase-space volume occupied by a particle beam, beam cooling, have been invented, extensively developed, and applied to improve the usefulness of accelerators for physics experiments. These techniques have verified the theories that give us a deeper understanding of weak interactions. (vii) The replacement of charging belts by chains or ladders in electrostatic generators has been almost complete and has led to a new life for these accelerators, which have found application in ion implantation and other industrial processes. (viii) There are new applications of other accelerators, such as the electron rings generating synchrotron radiation for research in atomic and condensed-matter science and for delicate industrial fabrication. Many new accelerators have been built in these sixteen years. The Fermilab proton synchrotron, originally planned to operate at 200 GeV,

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operated for many years at 400 GeV as the basis for a vigorous international program. It was joined later by the CERN Super Proton Synchrotron (SPS), which was then developed into a proton-antiproton storage ring utilizing beam cooling and used for important work in particle physics. The Fermilab accelerator now operates at 150 GeV as the injector to a superconducting synchrotron, the Tevatron, which was completed in 1983. The Fermilab accelerators are shown in Fig. 1. The Tevatron has accelerated protons to over 900 GeV and is scheduled to reach 1000 GeV (1 TeV) in the near future. Like the SPS, it will also be used as a proton-antiproton storage ring. Other operating superconducting accelerators are the National Superconducting Cyclotron at Michigan State University and the ATLAS linear accelerator at Argonne National Laboratory. Superconducting rf systems have been developed for a number of storage rings. Work on electron-positron storage rings began in the 1960’s and led to the highly successful 3-GeV SPEAR ring at the Stanford Linear Accelerator Center. It has been followed by the 10-GeV ring CESAR at Cornell University and the 20-GeV rings PETRA at the DESY Laboratory in

FIG.1: The Fermilab accelerators. The conventional Main Ring is above. The superconducting Tevatron is below. To give the scale of distances, there is approximately 60 cm vertical distance between the two beam centerlines. (Photo courtesy of Fermilab.)

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Hamburg, FRG, and PEP at Stanford. TRISTAN at KEK in Japan, a 30-GeV ring, has just begun operation. The ultimate electron-positron ring is now being built, LEP at CERN. It will reach 50 GeV in its initial configuration and will later increase to as much as 100 GeV with superconducting rf cavities. The energy that can be reached by electron-positron rings is limited by the rapid increase of rf power with beam energy ( E 4 )and it almost unfeasible to build a ring for energies larger than 100 GeV. In addition, an electron-proton colliding-beam system HE R A is being built at DESY and a new synchrotron UNK is being built at Serpukhov in the Soviet Union. It will later be made into a proton-antiproton colliding-beam system. Plans are well advanced for a 20-TeV proton-proton colliding-beam storage-ring system, SSC, the Superconducting Super Collider, in the United States. A different direction toward colliding beams is followed at Stanford, where SLC, the SLAC Linear Collider, is being built. This device is not a storage ring with continuously circulating beams, but two semicircular arcs to bring accelerated beams of electrons and positrons together for a single collision pass. The beam size must be extremely small, of the order of a few hundred Angstroms, to give particle densities large enough to reach a usable interaction rate. At lower energy, AVF (Azimuthally Varying Field) cyclotrons have been built in many laboratories, following the invention of the spiral-sector fixed-field alternating-gradient ring by Kerst (1956). These cyclotrons have been used to investigate nuclear structure in great detail. Electron cooling rings to store ion beams and to reduce their energy spread in order to reach much higher energy resolution are now being built at Indiana University and laboratories in Western Europe and Japan. TANTALUS, a small electron ring for synchrotron-radiation research was built at the University of Wisconsin in the 1960’s. Its success stimulated the adaptation of a number of rings built for other purposes, including SPEAR and CESAR among others. Two storage rings for 800-MeV electrons are now in operation, BESSY in West Berlin and ALADDIN at Wisconsin, and rings for higher energy are planned. Synchrotron radiation has important applications in the fabrication of intergrated electronic circuits and many more are expected to be built for this work. The precision of alignment and beam position needed for this industrial work are in themselves leading to new accelerator techniques and advances. Many accelerators have also been built for medical radiography and therapy. Electron accelerators for this application are available commercially, using the electrons directly or bremsstrahlung photons. Neutrons produced by accelerator beams have also been used for therapy with considerable success, and several proton accelerators built for physics research have been adapted for direct therapy with protons. The first proton accelerator specifically for therapy is now being built.

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Separate from what might be called “conventional” accelerator technology, an entirely new field utilizing very highly pulsed power has been developed, and beams of short pulses of thousands or millions of amperes peak current in the MeV energy range are now available. These beams have important applications in high-energy particle acceleration, controlled fusion, industrial treatment of materials, and possibly in food preservation. All the accelerators listed above make use of external fields for acceleration. There is also vigorous research into new methods of acceleration, in many schemes making use of the intense accelerating fields, generated by laser beams or by plasma states of matter. This research has not as yet made traditional kinds of accelerators outmoded, but many workers hope that early in the next century there will be practical new acceleration methods making use of these very high fields. These developments will be discussed in more detail in the following pages.

11. INVENTIONSAND DEVELOPMENTS

A . Beam Cooling It is traditional to think of accelerator beams as completely governed by Liouville’s theorem, so that the density of a beam of N particles in 6-dimensional phase space is constant. In fact, Liouville’s theorem is a statement about the density of system points in a 6N-dimensional phase space, and it can be rigorously reduced to a 6-dimensional space only if there are no interactions among the particles and no external systems interacting with the particle beam. The radiation field is such an external system, and the synchrotron radiation emitted by beam particles affects the phase-space volume of the beam. It was shown by Robinson (1958) that the transverse and longitudinal motions of a beam can be damped or antidamped, depending on the particular orbit properties of the structure. Separated-function synchrotrons and storage rings, in which the functions of bending and focusing the beam are carried out by separate dipole and quadrupole magnets rather than by combined-function gradient magnets, have the property that all three motions are damped and separatedfunction lattices have been used in all electron and positron rings. This has been a key factor in the success of colliding-beam electron-positron storage rings. Protons are heavy enough that synchrotron radiation has barely been observed in the highest-energy rings and has not been a factor in improving

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phase-space density. But there have been inventions of other systems with which proton beams can interact to reduce phase volume. The first of these is electron cooling (Budker, 1967) in which the proton beam scatters from a beam of comoving electrons. If we consider the motion in the center of mass system, in which both beams are at rest, we see that on the average the hotter proton beam transfers energy to the cooler electron beam. Thus the phase-space volume of the proton beam is reduced and it is cooled. TO do electron cooling, the electron beam is bent into a straight section of a proton storage ring and moves with the proton beam through the straight section. It is bent out at the end and most of the considerable energy of the electron beam is recovered by a deceleration system. Because of the relativistic increase of mass and the Lorentz transformation of fields, the cooling rate of electron cooling decreases as y 5 , and electron cooling becomes very slow at higher energy. The experiments that have demonstrated electron cooling have all been carried out at lower energies. But it is also possible to d o electron cooling with an electron beam in a separate tangent storage ring, utilizing synchrotron radiation to recool the electrons, and cool a stacked proton beam, even though slowly. Another type of cooling for heavier beams, stochastic cooling (van der Meer, 1972), makes use of the finite number of particles in a beam. The beam interacts with an external electrode-amplifier system that reduces its coherent oscillations. Because it is not a continuous fluid, but an ensemble of particles, the external system also reduces the incoherent oscillations of the beam and cools it. Stochastic cooling does not explicitly depend on the beam energy, but it does depend on the number of particles and it becomes more difficult to cool as a circulating beam is stacked. Stochastic cooling has been used with great success in the CERN proton-antiproton storage ring system. Beam cooling and the experimental evidence for it were reviewed by Cole and Mills (1981).

B. Radiofrequency Quadrupole Since the invention of strong focusing, proton linear accelerators have employed magnetic quadrupoles, usually located inside drift tubes, to focus the beam transversely, thereby removing the need for focusing grids or other obstructions in the beam region. At low energies, the drift tubes are very short and the focusing is very weak, just where space charge is relatively most important. The compromise made has always been to inject at the highest energy feasible from an electrostatic accelerator. Considerations of accessibility and maintenance dictate that the electrostatic

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accelerator operate in an unpressurized environment, limiting the injection energy to 750 keV or less. It was speculated in the 1960’s that it might be possible to modify the drift-tube ends to achieve an rf quadrupole field that could be alternated from cell to cell. The first practical realization of such an arrangement was at ITEP in Moscow (Kapchinski and Teplyakov, 1970). In their proposal, they discarded the drift tubes completely and replaced them with a fourvaned structure, as in Fig. 2, that provides a resonant structure with an rf quadrupole field on the axis. In order to obtain acceleration, the dimensions of the vanes are varied axially. This provides axial fields that accelerate the particles. The wavelength of the variations is programmed to correspond to an increasing particle velocity, corresponding to an acceleration program. Very strong focusing can be achieved at low energy by this means. Injection energies can be as low as 50 keV. A further benefit easily realized in an RFQ is adiabatic capture of the beam, leading to high capture efficiency and low axial phase-space dilution of the injected beam. The beam is tightly focused transversally as soon as it enters the RFQ and it can therefore drift axially while the vane perturbations, and hence the axial field strength, are “turned on” slowly. The rate of turn-on can be adjusted to obtain optimum adiabaticity. The magnitude of the vane perturbations is limited by considerations of aperture and peak field strength and the axial accelerating field therefore decreases as the particles are accelerated and the wavelength of the vane perturbations increases. This imposes a limit on the maximum energy to which particles can be accelerated in an RFQ. Proton RFQ’s are usually limited to energies below 2 MeV. Since the early work at ITEP, intensive study of RFQ’s has been undertaken at many laboratories in Europe and America. RFQ’s have been built at several frequencies, 80 MHz, 100 MHz, 201.25 MHz, 400 MHz, 425 MHz and 440 MHz, to be operated CW for high-intensity linacs, and as new injectors for existing linacs, or as injectors for new proposed linacs, as well as for other exotic purposes. There is a comprehensive discussion of these projects and their status in the review paper of Schriber (1985). C. Permanent Magnets

There are a number of accelerator applications in which conventional electromagnets can be somewhat awkward because of limited space available or high power consumption. Examples are the focusing quadrupoles inside the drift tubes of ion linear accelerators and the wiggler and

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FIG.2: A four-vaned RFQ structure. (Photo courtesy of Lawrence Berkeley Laboratory.)

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(a) (b) FIG.3: Permanent magnet quadrupoles. (a) A 16-segment REC Quadrupole (after S . Herb, 1985). (b) A variable-strength REC Quadrupole (after Halbach, 1983b).

undulator magnets of synchrotron light sources and free-electron lasers. In many of these applications, it is now possible to utilize permanent magnets. These are not garden-variety dime store permanent magnets with fields of a few Gauss, but magnets constructed of rare earth-cobalt (REC) alloys or some other charge-sheet equivalent material (CSEM) that are capable of reaching fields of 1 to 1.5 Tesla. Their use was first proposed by Halbach (1979, 1980) and has been pioneered by him and his collaborators. Halbach has also proposed and built permanent magnets with adjustable field strength (Halbach, 1983a and b). The field of R E C magnets is ROW active enough that a number of international workshops have been held to discuss and ritualize their design and use. In a REC permanent magnet, the desired field shape is produced by arrangement of segments of CSEM material with their fields in different orientations, as can be seen in the conceptual sketch in the first part of Fig. 3. Adjustable field strength can be achieved by making a hybrid of CSEM material and ferromagnetic steel, as shown in the conceptual sketch of the second part of Fig. 3. Tuning is accomplished by physically moving CSEM segments relative to one another. Halbach (1983b) has pointed out that the field strength and current density scale with cross-section dimensions and that there is a minimum size below which a permanent magnet must necessarily have better performance or be more economical or both. This reference gives general considerations concerning the design of permanent magnets. A recent paper by Herb (1985) discusses design of a

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tunable quadrupole in detail. Undesired higher multipoles can be minimized by orientation and relative motion of the CSEM segments. Materials for R E C magnets are available commercially and complete magnets can now be manufactured in private industry.

D . Linear Induction Accelerator The linear induction accelerator is a conceptual outgrowth of the circular induction accelerator, the betatron, and can be thought of as a betatron of infinite radius. It was apparently first proposed as early as 1923 by Bouwers and later (1939) discussed by him in a book. The real development began when Christophilos built the first one as an injector for a controlled fusion device, the Astron. There have been many others built since in the US and the USSR. Linear induction accelerators have unmatched capability for accelerating nanosecond-length pulses of kiloampere currents of electrons to energies of up to approximately 50 MeV. Like betatrons, they are limited by economics, not by physical laws. They have the additional feature that the driving magnetic-field pulse can be shaped by shaping the primary voltage to compress the beam pulse in time and thus to amplify the instantaneous current. One of the potential applications for which induction accelerators have advantages is heavy-ion fusion, where a deuteriumtritium pellet is imploded by a beam of accelerated ions (usually of several GeV energy). The pulse compression is important in this application to achieve as high a pellet temperature as possible. Further, multiple beams can be accelerated in a single linear induction accelerator, then combined to increase the instantaneous current even more. Recent reviews of this work have been given by Keefe (1986) and Wangler (1986). The large currents in these induction accelerators generate fields in the chamber that in turn act back on the beam in the way discussed below in Sec. 1V.B. Transverse fields can break up the beam (Panofsky and Bander, 1968). These phenomena must be dealt with by care in design of the system or by electronic feedback systems. Theoretical aspects of beam breakup are treated in detail by Gluckstern et al. (1985).

E . Use of Computers in Accelerators Digital computers have made revolutionary changes in almost every aspect of modern life; particle accelerators are no exception. We shall discuss separately the realtime control use and the computational use of computers.

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1. Computer Control Modern large accelerators have large numbers (of order lo5 or more) of monitor and control points; it would in principle be possible, but in practice very difficult, to keep track of this number of parameters. A computer can monitor status or parameter values indefinitely, can be given limits of variation, and can give alarms as desired. Slow feedback loops can include computers. For example, the quench-protection units of the Tevatron are monitored by local microprocessors that energize the heater coils when a voltage is detected. Too long a time would be required to carry out this function through a central control computer. In fact, this is an example of the strong recent tendency to carry out as many functions as possible through local intelligence. The central computer is then used to monitor local intelligence, to correlate information and present it to the operator, and to keep detailed records of parameter settings and failure modes. Attempts have been made to carry out orbit corrections in synchrotrons in real time, but they have not been marked with great success. Besides, they are not needed. Low-powered dc correction magnets can correct orbits at low field levels, and the accelerator can be realigned to correct orbits at high fields. The hoped-for aperture savings of real-time orbit control were not real because aperture is needed for other reasons, such as beam manipulation in injection and extraction. What has worked well is the application of linear-programming methods to compute magnet-realignment prescriptions from measured orbit deviations. With a decent program, it is possible to reduce undesired orbit deviations to a millimeter or so in a few passes. A computer can also be used to gang several parameters together, as, for example, a series of correction devices to produce a localized, adjustable orbit bump that is useful in exploring the aperture. 2. Design Computation Particle-accelerator designers began to make use of digital computation in the early 1950’s, in the infancy of computing. There have been two general directions. The first is the computation of orbits, either by transformations or by direct intergration of the differential equations of motion. For investigation of orbits of stored beams, which go through very large numbers of revolutions, it has been found that it is important to preserve the Hamiltonian nature of the equations, and techniques have been developed to integrate canonically to arbitrary order (Ruth, 1983). The second is the solution of Maxwell’s equations, either in the static

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form, Poisson’s equation, for the design of bending and focusing magnets, or in the dynamic form, the Helmholtz equation, for the design of radiofrequency cavities. These programs come in either of two forms, ones that solve the relevant Maxwell equations by relaxation (pioneered by R. S. Christian) and ones that solve by matrix inversion (pioneered by K. Halbach). It has been extremely difficult to compute fields in the full three dimensions; the usual stratagem is to make use of whatever symmetry the problem possesses and then to piece together enough twodimensional runs to give some idea of the third dimension. At this time, there is still ample scope in the design process for the building and measuring of physical models. All these kinds of accelerator computations have become highly developed art forms in themselves, occupying the attention of many specialists. There are now even specialized meetings devoted to computation methods in accelerator problems.

F. Free Electron Laser In the early days of particle accelerators, synchrotron radiation was at best a nuisance, requiring additional accelerating power to overcome its energy loss. With all that power going to waste, it was natural to try to think of some way to put it to use as a source of rf radiation. But some way to impose coherence is needed, because natural synchrotron radiation has a broad spectrum and the history of practical electromagnetic radiation shows clearly the advantages of small dispersion. Coherent transverse motion of an electron beam in a periodic transverse magnetic field can produce such coherence of the radiation, and this motion is the basis of the free electron laser (Madey, 1971). The principle of the free electron laser was proven experimentally by Madey and his colleagues (Elias et al., 1976). A precursor of the free electron laser was the Ubitron, of Phillips (1960), which utilized a longitudinal rather than transverse periodic field to induce transverse oscillations. The coherence of the electron motion enhances particular radiation frequencies and generates coherent radiation, in a manner a little analogous to a conventional bound-electron laser. The radiation wavelength A, is related to the period A, of the magnetic field by

where y is the relativistic energy of the electron beam in units of me2 and a, = eB,/k,rnc2 is the reduced vector potential of the constant field ( k , = 277/A). The two factors of y arise from the relativistic increase of mass and from the Lorentz contraction. Together, they give the free

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electron laser utility as an amplifier or oscillator at short wavelengths with feasible magnet period lengths. The intensity of the radiation emitted is obviously proportional to the electron-beam intensity, and an intense relativistic beam is therefore a natural basis for a free electron laser. But there are many variations possible on the basic geometry of a free electron laser (see Colson and Sessler, 1985 for a thorough discussion). The geometry can be linear, and it is of interest in this case to recover the residual energy of the electron beam, since at best 20 to 30% of the beam energy goes into radiation. It is possible to recirculate the electron beam, as in a storage ring. All geometries need a periodic transverse magnetic field to induce coherent oscillations of the electrons. If z is the direction of propagation of the electron beam and y is the direction of the periodic field (which varies sinusoidally in the z-direction), then the electron beam oscillates in the x-direction. This field can be generated by conventional or superconducting electromagnets. One of the interesting applications of the rare earthcobalt magnets discussed in Sec. IIC above is for the periodic fields of a free electron laser (Halbach, 1982). In the early days of free electron lasers, the perturbation fields were called wigglers or undufutors. More recently, the term undulators is used to mean a special case of wigglers with many periods of variation and resulting high brilliance and high degree of coherence of the radiation. The efficiency of a free electron laser, like that of a travelling wave tube, is limited by the loss of energy of the electron beam, which loses the coherence. It is possible to increase the efficiency considerably by tapering the wiggler period to keep constant over a larger range of energy. The free electron laser is becoming an important method of producing tunable high-power radiation of small dispersion, particularly in the millimeter wavelength region that is useful for a number of applications in science and industry. There have been a number of reviews of the theory and experiment; see, for example, Morton (1983) for the theory and Colson and Sessler (1985) for a recent comprehensive review. 111. BEAMENVIRONMENT A . Effects of Environment on Beam

1. Space charge The effects of self-fields on a particle beam is an accelerator were seen very early by Kerst (1941), who observed a saturation of accelerated intensity as injected intensity was increased. Kerst attributed this saturation to

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diminution of transverse focusing by the repulsive self force of the beam and showed that the effect is reduced by the magnetic attraction of the parallel currents of the beam. This explanation is still valid today, with some additions. First, the focusing force (and therefore the transverse oscillation frequency) is not decreased all the way to zero in a strongfocusing accelerator, but only until the beam encounters a transverse resonance. Second, there are effects of the environment outside the particle beam. For one thing, the beam can ionize residual gas in the vacuum chamber and will attract ions of charge opposite to the beam. The beam space charge is then neutralized, which counteracts the lowering of the betatronoscillation frequency. There are many more positive than negative ions, of course, and ionization electrons tend to have enough energy to escape, so neutralization is a much more important effect in electron rings than in proton or positron rings. It is a major limiting factor on beam intensity in electron and antiproton rings at lower energy. Neutralization is also used purposely in low-energy beam-transport systems as an aid in focusing. Another effect of importance is the boundary conditions imposed by the presence of the vacuum chamber and nearby ferromagnetic surfaces. The beam produces images in these boundaries and these images act back on the beam (Laslett, 1963). The effects of images become more important as the particle energies become relativistic, but space-charge effects are already smaller because of the cancellation between electric and magnetic forces and the effects of images are not particularly important for static space-charge effects. They are important for the dynamic instabilities we shall discuss next. 2. Instabilities Space charge can modify the existing focusing forces to move the motion to an existing resonance. But there are also new dynamic phenomena that arise from the interactions between particles in a beam. Collective motions like those of plasmas can be generated and can in many cases be unstable. The relation between plasma theory and accelerator theory has been explored in great detail by Lawson, and the interested reader should consult his book (Lawson, 1977). The beam current I interacts with its environment, including conducting and ferromagnetic surfaces, to generate electromagnetic potentials V and V = ZZ, where Z is an impedance that describes the environment, including the self-forces of the beam itself. It is important to note that Z can be complex; the imaginary part corresponds to inductive or capacitive environments.

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For example, the self forces of a particle bunch above the phase transition correspond to an inductive impedance and give rise to coherent longitudinal instability of the beam, the negative-mass instability first discussed by Nielsen et al. (1959). In physical terms, a particle at the head of the bunch gains energy from the repulsive force of the particles behind it. But because the motion is above transition, a particle of higher energy has a lower revolution frequency and therefore moves back into the bunch, further increasing the repulsive force. This is of course an ideal recipe for instability. We also see in this example that the self-field and the potential lead the beam current in phase and that the environment therefore represents an inductive impedance. There are many other physical causes for out-of-phase components of the potential, that is, for imaginary parts of the impedance, and these can lead to beam instability. The finite resistivity of the chamber walls can cause both longitudinal and transverse instabilities (Laslett, Neil, and Sessler, 1965). Different bunches can interact with one another through the coupling provided by the conducting walls of the chamber (Courant and Sessler, 1966). These instabilities are collective in the sense that the beam motion is coherent; all particles experience the same rate of growth. The growth rate of any of these instabilities depends on the beam current. But there is a damping mechanism arising from the momentum spread of the beam, Landau damping, and there is therefore a beam-current threshold below which the instability does not grow. As is also true in the betterknown plasma instabilities, nonlinear effects also limit the total amount of growth. But if no ameliorative measures are taken, these instabilities can cause severe disruptions of the beam and limits on attainable intensity that are well below those desired for reaching the objectives for which the accelerator was built. There are also collective instabilities in linear accelerators and they arise from the same physical causes. The beam induces fields in the environment and in turn these fields affect the beam. The result is a little different from what happens in circular accelerators. Transverse fields can be induced in the accelerating cavity and can deflect later portions of the beam, causing beam loss. This beam breakup was a concern in the 2-mile SLAC linear accelerator until understood (Panofsky and Bander, 1968). Beam breakup is seen and cured in linear induction accelerators. There are also diffusion effects in accelerators, such as the scattering of beam particles by the residual gas, the scattering of particles out of an accelerating bucket by Coulomb interactions with other particles in the bunch (the Touschek effect) and the growth of beam amplitudes from the same intrubeam scattering (Piwinski, 1974).

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B. Environmental Control Collective instabilities have been observed in many accelerators and it behooves the designer of a system whose objectives require reasonably high beam intensities to take measures to combat them. The theory is well worked out and predicts limits for the transverse and longitudinal impedances of a system. These limits depend on p , y , the momentum spread, the dispersion, which determines the frequency spread corresponding to a given momentum spread, and on the beam current. Keil and Schnell (1969) have given a simple derivation of a criterion for stability

where Z is the impedance, n is the mode number, F is a form factor of order unity, p is the momentum, p is the speed in units of c , e is the magnitude of the electron charge, Z, is the unperturbed beam current, 77 is the dispersion of the lattice, and A p / p is the relative momentum spread. Attention must then be paid in the design phase to the impedance presented by various structures in the beam pipe. Vacuum-chamber bellows, acceleration systems, pickup electrodes and similar devices all increase the impedance of the system. The structure must therefore be made as smooth as possible to keep the impedance down. It is possible with care to keep the impedance seen by the beam in a large ring down to acceptable values. The intensity can be raised further by use of feedback systems that sense coherent oscillations of the beam from pickup electrodes and damp the oscillations through fields applied to kicker electrodes. This is the same kind of electronic system as that used in stochastic cooling (in fact, stochastic cooling was conceived by van der Meer in terms of existing damping systems on the Intersecting Storage Ring at CERN). A feedback system is always limited by bandwidth and the instabilities that trouble modern accelerators are frequently in the microwave region, more difficult to reach electronically.

IV. STATISTICAL METHODSAND

QUALITY

CONTROL

Accelerator builders have always employed quality-control methods to improve the performance of their product. The Cosmotron magnet in the 1940’s and most subsequent accelerator magnets have been made of “shuffled” steel. That is, the variations of steel lamination dimensions and

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permeability are averaged out in any given magnet by stacking the magnet core from “random” selections of laminations produced at different stages of lamination production. The variation in field quality of the magnets is greatly reduced by this method. In addition, laminations can be alternated in direction to remove variations in permeability due to rolling and asymmetries in shape. As the size of the accelerator increases, this becomes awkward from the point of view of scheduling and warehousing. In the Proton Synchrotron at CERN, the magnets were assembled from many “blocks”, each of which was measured magnetically. The blocks for each magnet were chosen to give the magnet a standard magnetic strength, thus gaining a reduction in the variation of strength among the whole set of magnets. This substantially reduced the closed-orbit errors and variation in beam-envelope size in the completed accelerator. As the size of the accelerator becomes even larger, this technique also becomes unwieldly, but fortunately the number of magnets also increases, so that the choice of magnet location around the accelerator can be used to similar purpose. Advances in understanding of the effects of field imperfections, especially nonlinearities, coupled with improvements in fieldmeasurement techniques, have presented the builder with improved opportunities for improved performance. Most deleterious effects on the single-particle performance of an accelerator can be described in terms either of resonances or of global properties of the magnet system such as chromaticity, the relative variation of transverse oscillation frequency with momentum. Resonances can be described in terms of Fourier-Floquet harmonics of particular field imperfections (multipoles) in the accelerator, while the global properties are similarly Floquet averages of these multipoles around the accelerator. In a large group of magnets these can be described by linear combinations of the multipole strengths of the magnets. Global properties are controlled by systematic control of the production process or systematic corrections added to the accelerator. Resonances are controlled by noting that there is a phase associated with each Fourier-Floquet transform, and small groups of magnets can be put at locations in which their contribution to the transform cancels. For example, two magnets of equal strength located n-in phase from each other at corresponding lattice points make no contribution to the transform. Other schemes can involve three or more magnets and include lattice parameters as well. In a large accelerator such as the Tevatron, resonances through sixth order were controlled in the selection process. The result of that is that the Tevatron is a very “ h e a r ” accelerator, in spite of the well-known difficulties in achieving precision in magnets whose fields are completely determined by conductor placement. Quality control can be enhanced by careful measurements of component

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properties (as was shown and utilized by Henry Ford the Elder). In response to a serious problem of meeting tolerances on a tight schedule, the Fermilab Antiproton Source dipole magnets were assembled by selecting laminations of reduced tolerance on the basis of measurements made by inspectors at the stamping factory, with a satisfactory outcome. In the future, this process can be computerized and should lead to easier tolerances and better performance.

V. SUPERCONDUCTING TECHNOLOGY

A . Magnets The physical phenomenon of superconductivity had been known for more than a half-century before there was any sustained effort to make use of it in magnets for bending particle beams in physical research. It was not until the discovery of Type I1 superconductors, which have much higher critical fields, that fields large enough to be useful could be obtained. Whereas pure metals have critical field of a few milli-Tesla, several superconducting alloys have critical fields of approximately 10 Tesla in short samples. Niobium-titanium does not have the largest critical field, but it has the advantage of good malleability, which makes it easier to form the conductor bends needed for a practical coil; it has therefore found extensive use in the superconducting coils built to date. Superconducting coils in contemporary magnets can reach fields of 5 to 6 T on an everyday basis. Development of niobium-tin superconductor for coils, now in progress, promises even higher fields. Practical magnets with peak fields of 10 T or more are expected to be built within the next decade. There are two arguments for superconducting magnets in physicalresearch devices such as detectors, accelerators, and storage rings. These are first, the achievement of high fields to give higher accelerator performance and second, savings in operating cost. It should be noted that, even if a superconducting magnet costs more to build per unit length than a conventional magnet, it is still likely that the total construction cost will be lower with the superconducting option, because the higher field makes it possible to achieve the same energy in an accelerator enclosure that is shorter in length and therefore less costly. The first application of superconductivity was to bubble-chamber magnets. The Argonne 12-foot chamber, the first to have a superconducting field, began operation in 1966. A number of bubble chambers were built with superconducting magnets and the technology has since been

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utilized in other kinds of detectors, up to and including present-day very large colliding-beam electronic detectors. Detector magnets are in essence simple solenoids. The superconducting coil material used is cryogenically stable. That is, there is enough copper to carry all the current normally and still cool the conductor down by liquid helium if the superconductor quenches. The coil is wound on a support structure, which is then installed as a unit in a liquid-helium dewar. It is important to maintain sufficient tension during winding to ensure that the coil remains in place as the system shrinks during cooling to liquid-helium temperature. The static heat loss in operation can be made very small by careful design and the magnet can be brought to full field slowly enough that eddy-current and hysteresis losses are negligibly small. The requirements on the refrigeration system are therefore quite reasonable. Commercial helium refrigerators can be used in these applications. Fields of 4 to 5 Tesla are achieved in many superconducting detector magnets. Superconducting cyclotron magnets are similar in design (Blosser, 1979). It is less easy to achieve cryogenic stability in synchrotron and storage-ring magnets, because precise field shaping is needed and the coils must therefore be close to the field region. Thus space is at a premium. The development of conductor for these applications began in the 1960’s at Rutherford Laboratory in Great Britain. With only minor variations, the cable developed in that pioneering work is still used in magnets in many different laboratories. Many other kinds of cable have been tried and discarded. The Tevatron cable, shown in Fig. 4, is somewhat typical of the genre. In cross section, it is a keystoned rectangle approximately 6 mm by 1 mm. It contains 23 strands of circular cross section, each 0.75-mm in diameter. Each strand is drawn from a copper-superconductor assembly and contains more than 2000 niobium-titanium filaments. The cable is covered with an insulating layer. A superconducting synchrotron magnet, shown in cross section in Fig. 5, is quite unlike a conventional magnet. In the conventional magnet, the field is shaped by the ferromagnetic pole faces and the conductor position is of secondary importance. But the high fields desired in a superconducting magnet must be generated directly by the energizing coils, which are necessarily inside the ferromagnetic surfaces because of saturation. (In fact, the ferromagnetic materials plays only a minor role in a true superconducting magnet; it is entirely possible to build a magnet without iron, but the stray fields can be bothersome.) The field shape is thus determined completely by coil geometry, and coil location must be achieved and maintained very precisely. The coil geometry is such as to approximate, by the use of several layers, in some designs a cos 8 distribution, where 8 is the polar angle about the magnet centerline.

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FIG. 4: Superconducting cable as used at Fermilab. The 23 wires in this cable are splayed out to the right. Each wire contains more than 2000 niobium-titanium strands, as can be seen in the splayed-out one at the bottom. The wrapping is ground insulation. (Photo courtesy of Fermilab.)

Another kind of hybrid superconducting magnet has as its objective only the second goal above, the saving of operating cost. It may be argued that the higher fields of a true superconducting magnet are not necessarily more economical to build than somewhat lower fields, even when costs of the accelerator enclosure are included. A superferric magnet, a magnet with conventional ferromagnetic pole faces, but energized by superconducting coils, has been proposed and successfully modelled. Most people would not agree that there is a net saving by use of superferric magnets. The designer of a superconducting magnet faces a basic choice as to whether the ferromagnetic envelope is to be included in the cryogenic system and cooled to helium temperature or whether the cryostat is inside this envelope. “Room-temperature iron,” as in the Tevatron magnets, has the advantage that the time required to cool the system down is far smaller, since the thermal mass is so much smaller. On the other hand, just because the thermal mass is small, local heating, induced, for example, by stray beam striking the vacuum-chamber walls, can quench the superconducting property much more easily than in a “cold-iron’’ system. Although the only major experimental experience is with a warm-iron system that has been

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FIG.5: A Fermilab superconductingdipole. The spring-loaded“smart” bolts on top hold the cryostat in place without introducing torsional moments as the system shrinks during cooling. For scale, the assembly is approximately 0.5 m across. (Photo courtesy of Fermilab.)

reasonably successful with beam-induced quenches, the tendency in new designs for HERA at DESY and for SSC is toward cold iron. The short-sample critical field cannot be attained in a real magnet; the magnet always quenches at lower field because of the interaction between the various currents. It is possible in a practical magnet to reach 90% of the short-sample field. But when a magnet is first energized, it quenches at significantly smaller field. Through some number of pulses, the magnet quenches at higher and higher field until it reaches a stable value. This training requires a few pulses in a well-designed magnet, but many more in other designs. It was found empirically in the early development of superconducting accelerator magnets that it is crucial that the support structure holds the coils tightly in place. Microscopic local motions of coil elements apparently give enough local heating to quench the magnet. Coils held in place in a relatively soft structure like epoxy required many pulses to train and often never reach full field. A design like the Tevatron, in which the coils are clamped firmly in place by stainless-steel collars, require only one or two training pulses to reach full field.

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Even well-trained magnets will have occasional quenches, from voltage glitches or from beam-induced heating, for example. The stored energy in a superconducting magnet is of the order of megajoules and is sufficient to damage the coil severely if it is dissipated in a small region. To avoid this damage, a quench-protection system is installed. The resistive voltage across a string of magnets is monitored continuously (there is also an inductive voltage when the magnet is ramped). When a voltage is detected, a local microcomputer actuates a heating element in the magnets to quench the entire string (perhaps four magnets) within a time of the order of milliseconds and thus spread the stored energy over the entire magnet. Quench-protection systems are obviously vital to the health of superconducting coils that are not cryogenically stable. Peak fields in superconducting accelerators and storage rings have reached the level of 5 T as a result of the development work of the 1970s. The energy crisis of those years gave a further strong impetus to the development of superconducting magnets, as the cost of electric energy per year to a large laboratory reached more than $1 x 10’. Intensive development has continued through the 1980s. Peak fields of more than 6 T have been reached in prototype magnets and it is expected that fields of 10 T will be reached in the 1990s. Palmer and Tollestrup (1984) have recently given a review of the state of the field. It is too early to assess the consequences of the new developments of 1987 in warm superconductors. B. Radiofrequency Cavities

As in the case of superconducting magnets, there are two motivations for developing superconducting rf systems, but their importance is reversed. Here the first is economic; a large fraction of the average rf power pumped into a conventional rf cavity is lost to the structure rather than going into the particle beam. This is particularly important for electron or positron storage rings, in which the need for rf power to make up synchroton-radiation losses dominates the design. The second reason is to achieve higher accelerating fields, which will possibly lead to better accelerators. The development paths taken for electron and ion accelerators have been somewhat different and we shall discuss them separately. 1. Electron Accelerators

Here the objective has been to make superconducting rf cavities for use in linacs or storage rings. The first cavities were constructed directly from

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niobium sheets. Lately there has been some work to utilize niobium sputtered onto copper or alloys such as Nb,Sn. All of these have been successful. Many trials have shown that smooth, rounded surfaces are important, because sharp edges are points of high electric field. Multiplecavity structures have now developed to a repeating dumbbell shape that gives a periodic structure without sharp corners. The development has shown that fields are sharply limited by any microscopic surface defects and careful surface treatment during manufacture is a great aid in reaching maximum field strength. Similarly, surface dust severely limits the field attainable and the most successful cavities have been constructed in cleanroom environments. Higher-order modes are prevalent in superconducting cavities and must be carefully managed in order that they do not sap the rf power capabilities of the system. Quality factors of 2 x lo9 and accelerating fields of 5 MV/m have been achieved in the work at Cornell, DESY, CERN and Wuppertal. Superconducting rf cavities are being installed as part of an enhancement program at the Cornell ring CESAR. It is planned that Stage I1 of the LEP (Large Electron-Positron) ring now being built at CERN will utilize superconducting cavities in order that the beam energy can be doubled. The TRISTAN ring at KEK in Japan, which has just begun operation, will also make use of superconducting rf in a later stage, as will the electron-proton ring H E R A at DESY. Furthermore, the significant progress of the last few years in this field have led to a complete change of design for the Continuous Electron Beam Facility (CEBAF) now being designed. It was to be a conventional linear accelerator with a beam-stretching ring to provide the continuous beam, but has now been changed to a superconducting rf microtron operating in a continuous mode. There are recent reviews (Piel, 1985 Sundelin, 1985) of the state of the field that contain a wealth of valuable information. 2. Ion Accelerators The effort in ion accelerators has been in the direction of linear accelerators (since making up synchrotron-radiation loss in ion rings has not been a problem as yet). The major effort has been the ATLAS project at Argonne National Laboratory (Bollinger, 1983). This linear accelerator is an “afterburner” that is used to increase the energy of a beam accelerated by a tandem electrostatic generator from 10 to 40 MeV. The entire drift-tube and support structure are made of niobium plated onto copper. Recently it has been proposed to replace the electrostatic generator with a superconducting low-energy linear accelerator (Shepard, 1985). A comprehensive review has just been published (Bollinger, 1986).

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VI. NEW KINDSOF ACCELERATORS There has been a small effort for many year (beginning in the early 1950’s) to study new ways of accelerating particles. These efforts have usually begun with the hope of finding a much more economical particle accelerator in order to reach much higher energies, but many of the devices developed in this research have proven to be of much greater utility for other applications, such as for high-current accelerators at lower energy. We shall give brief sketches of a number of concepts and devices that have progressed from the paper to the laboratory stage. A . Pulsed-Power Technology The field of pulsed-power technology was founded by J.C. Martin in 1962 with his combination of the Marx generator, the Blumlein transmission line, and the high-power diode. As individual elements, these were not new. Marx generators had been widely used for testing electrical equipment in high-voltage transmission lines and had also been used in an early accelerator (Brasch and Lange, 1930). Blumlein (1948) had demonstrated his transmission line some years before Martin, but Martin put all these elements together to make the basis of an entirely new field of accelerators. Pulsed power is utilized in collective-acceleration devices and in wave accelerators, both of which have intense relativistic electron beams (IREB) as their basis and in induction linacs. In intense relativistic electron beams, it is possible to produce nanosecond-length beam pulses of MeV energy and thousands (or in some cases millions) of amperes peak current. There is an excellent review of pulsed-power technology by Nation (1979). 1. Collective Acceleration

When an IREB strikes a neutral gas, it is observed that some ions are accelerated to energies greater than the energy of the electron beam, so that a collective mechanism is present. The effect was first observed by Graybill and Uglum (1970). Large electric fields at the head of the beam column are generated by the self-fields of the beam. These negative fields create a virtual cathode at the beam head. The fields, which can reach 100 MV/m, ionize gas molecules and accelerate them. Unfortunately, the acceleration is not naturally in synchronism because the electric field moves with the head of the column and therefore has phase velocity much larger than the nonrelativistic ions. Continuous acceleration is therefore not easily achieved. Many ways have been suggested and attempted to overcome this difficulty. The most successful is the Ionization Front

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Accelerator of Olson (1979). In it, a staged pulsed laser beam is used at intervals along the column to ionize gas and therefore to neutralize the virtual cathode at the beam head. The major applications of collective accelerators appear to be in providing very high currents at lower energies. Interest at higher energy appears at this time to have passed on to other accelerators geometries. They are still of interest conceptually because they are an example of the large fields that can be generated and supported in a plasma.

2 . Wave Accelerators Plasmas also support a variety of electric and magnetic field waves with differing propagation characteristics. These waves can be used to generate electromagnetic fields that accelerate particles. Fainberg (1956) was the first to propose the use of these fields for particle acceleration. An IREB is usually used as the plasma medium. In such a medium, there are fast and slow plasma oscillations, fast and slow hybrid (cyclotron) waves, and electromagnetic waves. Proposals have been made to utilize all these waves for acceleration. These proposals necessarily include a mechanism for varying the phase velocity of the wave to keep it and particle bunches in synchronism during acceleration. In the Converging Guide Accelerator (Sprangle et al. (1976), the phase velocity ve of a plasma wave is increased along a guide whose radius decreases with distance. Nation and his colleagues have studied the Converging Guide Accelerator experimentally for some time and have achieved significant variation of v e . Sloan and Drummond (1974) have proposed to utilize a cyclotron wave and to vary ve by variation of the magnetic field along the guide. This work is now proceeding at a much slower pace because other geometries have stolen the thunder of the devices.

B. Laser and Beat- Wave Accelerators Because of the high power and high electric fields in a pulsed, focused laser beam, it is natural to consider lasers as a potential means of accelerating particles. Unfortunately, the electric field in a laser beam is perpendicular to the direction of propagation, so that it is difficult to obtain any sustained acceleration with a laser alone. On the other hand, the magnetic field of the laser beam is such as to bend the particle in the direction of propagation of the laser beam. If the particle interacts with the laser until its velocity is in the same direction as the laser beam, then it will have been accelerated to some energy which is determined by the laser power. If the process continues, the particle’s direction becomes opposite to the electric field of the laser beam, and the particle is decelerated to rest.

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The process continues as long as the particle continues to interact with the laser. For laser powers in the range of 1013 W, the maximum energy received by an electron can be in the GeV region. This mechanism was first proposed by McMillan (19SOa) as a possible cosmic acceleration mechanism to explain the source of high-energy cosmic radiation. Apparently most researchers are discouraged by the inherent limitations of this method, for there is no reported experiment demonstrating it. Instead, researchers have turned to three methods to gain sustained acceleration. The first is called, for historical reasons, near-field acceleration, in which the electromagnetic field is distorted by the presence of some medium or boundaries. The second is calledfur-field acceleration, in which the orbits of the particles are modified to obtain sustained energy interchange with an unmodified free electromagnetic wave. The third is plasma acceleration, in which a plasma medium is used to obtain longitudinal accelerating fields with phase velocity less than c. All intermediate combinations are also possible, including two laser beams crossing at small angles with or without external fields or plasmas. Near-field accelerators, exemplified by the grating-accelerator concept (Palmer, 1982), are in principle no different from ordinary linear accelerators except that their power source is a laser, and they are envisioned to be open structures illuminated by a laser beam. That is, they are not closed resonant structures, but rather open radiating structures like a diffraction grating that establishes a local periodic field which can be chosen to have a phase velocity less than c. Damage to the grating by the laser beam has posed a severe constraint on the accelerating field, and has led researchers to consider disposable gratings, for example, an array of small drops like those ejected by an inkdrop printer. This allows considerable liberty to the imagination of the researcher to choose the form of the structure. The far-field accelerator is exemplified by the inverse free electron laser (IFEL), in which the electron orbits are modified so as to be able to exchange energy with a free laser beam. The electrons are shaken transversely with a periodic magnetic field, creating a transverse current in the beam. This current can exchange energy with the laser electric field, accelerating or decelerating the electrons depending on the relative phase of the laser field and the transverse current. If w / c is the spatial wave number of the alternating magnetic field, there is a transverse electric field in the rest frame of the electrons of frequency 'yo, the frequency at which the electrons oscillate and can receive or give up energy to the laser field. In the laboratory system, this frequency is y 2 0 , which is the resonant frequency of interaction between the beam and the laser. The dynamics of the motion is the same as the phase motion in a linac or circular accelerator (Symon and Sessler, 19S6), exhibiting rotation, trapping, and phase

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displacement. Tapered wigglers have been extremely successful at extracting energy from IREB's. IFEL's have been studied for linear colliders up to 300 GeV (Pellegrini, 1982). They avoid the staging problem if laser losses can be made very small. At higher energies, large magnetic fields are required to obtain sufficient wave-particle interaction, and these fields cause unacceptable amounts of synchrotron radiation. The most prominent plasma accelerator concept is the laser beat-wave accelerator (Tajima and Dawson, 1974). In this accelerator, two collinear coherent (from the same laser) beams of different frequency penetrate a dense plasma. The beats between the two beams, visualized in Fig. 6, create alternating regions of high and low electric field. The ponderomotive force (electric pressure) expels the plasma electrons from regions of high rms electric field into regions of low rms electric field. This creates a longitudinal density modulation leading to a longitudinal electric field in the right direction to accelerate particles. The beat wave so formed travels at a velocity less than c, the difference being determined by the plasma density. The peak field achievable, the wave-breaking limit, occurs when the plasma density in the troughs approaches zero. The system is highly constrained by these conflicting requirements, and leads to velocities appreciably less than c only in short accelerating regions. The growth of the beat wave, called Raman Forward Scattering, may be viewed as an instability, and is the fastest instability in the system. Other instabilities, such as Raman Backward Scattering or ion-sound instabilities, limit the useful acceleration time to some tens or hundreds of picoseconds. At least at the present state of thinking, this is not in itself a severe constraint on the use of the system for e + - e- linear colliders. The problems of staging

FIG.6 : Beat wave formed by the combination of two coherent laser beams. The two sine waves have 10% frequency difference.

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enough of these accelerating regions and reusing laser power to gain efficiency have not yet been seriously addressed. Experiments have been performed to measure the strength of the beat-wave from the 9 and 10 km lines of a C 0 2 laser at UCLA (Clayton et ul., 1985). Perpendicular ruby laser light was Thomson-scattered from the moving density waves. The strength and size of the diffraction pattern observed was that due to a wave with field amplitude of 300-500 MeV/m. No electron injector was available, so acceleration was not observed. In subsequent experiments at NRC in Canada, electrons were accelerated. A companion scheme to the beat wave, the surfutron (Katsouleas and Dawson, 1983), incorporates a magnetic field perpendicular to the electric field and propagation directions. The gyro motion of the electrons allows them to maintain coherence with the beat wave over a longer distance, but at the expense of higher laser power, a strong magnetic field, and radiation losses when the electrons are relativistic. C . Wake Field Accelerators

As charged particles or beam bunches move through media or structures, they leave energy in the form of wake fields behind. Eventually, this energy is dissipated by resistive effects and ends up as heat. The goal of a wake field accelerator is to enhance this energy deposition, and to use it to provide a longitudinal field to accelerate particles. The first wake-field concept (Voss and Weiland, 1981), which is now being tested at DESY, makes use of a ring electron beam passing along the periphery of a stack of metallic discs with holes at their centers. The intense ring beam excites electromagnetic fields in the region between the discs (radial transmission lines). The field energy propagates to the center of the discs where an accelerating field is established on the axis. This field is used to accelerate a charged-particle bunch moving along the axis. In this way, an intense beam at low energy can accelerate a less intense beam of higher energy. It is not necessary to have the beams radially separated. An intense bunch travelling along the axis will leave wake fields which can accelerate a trailing bunch. In some versions of this concept, for example, the Waketron (Ruggiero, 1985), it is proposed to use protons for the driving beam, since it is more economical to accelerate protons to high energy than electrons (although narrow bunches of electrons are easier to create). Instead of radial transmission lines or discs, the beam can be passed through a plasma. The driving beam deposits energy in the form of plasma oscillations. Behind the driving beam, these oscillations appear to be a wave of

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longitudinal electric field with wavenumber o p / v , where wp is the plasma frequency and v is the velocity of the driving beam. The trailing bunch can be located at such position as to be accelerated, and in fact to take all the electrostatic energy from the plasma oscillation (by exciting a plasma oscillation that exactly cancels that due to the driving beam). There is a constraint on any wakefield accelerator implied by the previous sentence which limits the amount of energy that can be transferred from one narrow bunch to another. It can be shown from the Lorentz reciprocity relation that the energy lost per unit length by a particle or narrow bunch is related to the accelerating field induced by the bunch, and in fact is just one half the charge of the bunch times the induced accelerating field. This result is the Wake Field Theorem. (Ruth et a/., 1985). There have also been recent discussions of the transverse defocusing fields that accompany accelerating fields. This is a resurrection of McMillan’s Theorem (1950b) on the impossiblity of simultaneously achieving transverse and longitudinal focusing in an electromagnetic wave, which is just Earnshaw’s Theorem of electrostatics in a moving reference frame.

D . Two-Beam Accelerator In a primordial sense, all accelerators are two-beam accelerators. The energy in one beam of charged particles (perhaps inside a conductor) is transformed into a second beam, where the individual particle energy is much larger. There are intermediate steps of electric, magnetic or electromagnetic fields. The two-beam accelerator (Sessler, 1982) is a large extension of this transformation to a geometry in which the first beam is an intense relativistic electron beam, of some MeV energy and several kiloamps instantaneous beam current, produced by a linear induction accelerator. It is used as the driving beam in a free electron laser and energy is transferred to the second (accelerated) beam in the form of a radiofrequency field. The electron beam is reaccelerated periodically by linear induction as it loses energy to the laser wave. The second beam is accelerated in a linear-accelerator geometry parallel to the linear induction accelerator. Note that the acceleration of the second beam does not depend at all on a collective mechanism, but is entirely conventional. It is true that it is advantageous to utilize shorter wavelengths than are now used to push the onset of sparking to higher fields. This advantage is obtained in any linear accelerator. Wavelengths of the order of a millimeter are used, and the technology of waveguide fabrication has been an exercise in engineering ingenuity.

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Test of the proposed system using the ATA linear induction accelerator at Livermore have progressed to the production of rf waves. RF pulses of instantaneous power in the range of gigawatts have been observed.

E. Modified Betatron The addition of a toroidal (longitudinal) magnetic field to a conventional betatron increases greatly the momentum spread that can be contained in the field and thus the intensity that can be accelerated. This modified betatron idea appears to have occurred to Kerst and to others, but was not implemented experimentally until much later (see Roberson et al., 1985, for discussion of the history and references). Self-fields are extremely important in the modified betatron, but its basic physical principles depend completely on external fields, and it is in this sense a conventional accelerator. Several groups are now experimenting with modified betatrons and large accelerated currents have been achieved.

F. Linear Colliders The technical and economic limit on the size of electron synchrotrons and storage rings has led workers to suggest single-pass collisions of particles brought to high energy in linear accelerators. Leptons have advantages for this application. They can be accelerated in waveguide systems that are less expensive per unit energy than the standing-wave systems required for nonrelativistic baryons. They are also useful at lower energy than baryons; i.e. a 5-TeV lepton-lepton collision is equivalent for particle production to a 20-TeV baryon-baryon collision. On the other hand, higher luminosities are needed with leptons because the electromagnetic-production cross sections are smaller. There is also a stronger urge toward linear colliders for leptons because of the steep increase as a function of energy in the energy lost to synchrotron radiation, which leads to the economic limit for electron rings cited at the beginning of this paragraph. The physics basis of this suggestion is that the collision rate in colliding beams depends on the densities of the two beams at the crossing. If the two beams are shrunk to small enough dimensions, an acceptable collision rate can be achieved. The dimensions required are of the order of hundreds of Angstroms or less transversely and millimeters or less longitudinally. With these dimensions, it is theoretically possible to achieve luminosities of cm-2 sec-' or better, enough for physics experiments (see Richter, 1985 for a discussion of the physics to be achieved.)

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Assume that the acceleration has been carried out in a more or less conventional linear accelerator system. The cancellation between electric and magnetic forces reduces space-charge effects to very unimportant magnitudes for the acceleration and transport to the crossing point. The final focus can be accomplished by a quadrupole lens system (called a “low-beta’’ section and familiar from storage rings). Beam behavior at the crossing point is then dominated by the electromagnetic interaction of the two beams at the crossing point. The magnitude of the effects is described by the disruption parameter D , which is the ratio of the transverse beam size to the focal length of the focusing caused by the interaction (positive for beams of opposite sign). The luminosity is enhanced by the interaction for beams of opposite sign and the enhancement can be as large as a factor 5 or 6. There is thus a great advantage in the use of electrons and positrons, even though positrons need to be produced by an energetic beam, then accelerated themselves. Because of the acceleration of the disruption, synchrotron radiation is emitted. This beamstrahlung can be discussed classically or quantum-mechanically, with somewhat different results at very high energy. The first experimental test of linear colliders is being made in the SLAC Linear Collider (SLC), which is nearing completion at the time of writing.

VII. EPILOGUE

The reader who has labored this far will have seen that there has been a great deal of activity in particle accelerators. The great developments and expansion stemming from the invention of strong focusing have given us many new devices and, more important, a far surer grasp of the physical principles underlying accelerators and of the experimental verification of these principles. Accelerator art has given way to accelerator science. Further, considerable work is being done to investigate new methods of accelerating particles. The next sixteen years will undoubtedly be as interesting as the sixteen reviewed here.

REFERENCES Blewett, J . P. (1970). A d v . In Electronics and Elec. Physics 29, 233 Blosser, H. (1979). IEEE Trans. Nucl. Sci. NS-26, 3653. Blurnlein, A. D. (1948). US Parent 2, 465,840. Bollinger., L. M. (1983). IEEE Trans. Nucl Sci. NS-30,2065.

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Bollinger, L. M. (1986). Superconducting Heavy-Ion Linear Accelerators for Heavy Ions, Ann. Revs. Nucl. and Part. Sci. 36, 475. Bouwers, A. (1939). Elektrische Hochspannung, Springer, Berlin. Brasch, A. and Lange, F. (1930). Naturwiss. 18, 769; Z. Physik 70, 1011931). Budker, G. I. (1967). Proc. 1966 Symp. on Electron and Positron Storage Rings, Saclay. Atomnaya Energiya 22, 346. Christophilos, N. C. (1950). Unpublished letter. Clayton, C. E., Joshi, C., Darrow, C., Umstadter, D., Chen, F. F., IEEE Trans. Nucl. Sci. NS-32, 3551. Cole, F. T . and Mills, F. E. (1981). Increasing the Phase-Space Density of High-Energy Particle Beams, Ann. Rev. Nucl. and Part. Sci. 31, 295. Collins, T . L. (1961). Cambridge Electron Accelerator Report CEA-86, (unpublished). Colson, W. B. and Sessler, A. M. (1985). Free Electron Lasers, Ann. Revs. Nucl. and Part. Sci. 35, 25. Courant, E . D., Livingston, M. S., and Snyder, M. S . (1952). Phys. Rev. 88, 1190. Courant, E. D. and Sessler, A. M. (1966). Rev. Sci. Instr. 37, 1579. Elias, L. R., Fairbank, W . M., Madey, J. M. J., Schwettman, H. A , , and Smith, T. I. (1976). Phys. Rev. Ltrs. 36, 717. Fainberg, Y . B. (1956). Proc. 1956 Conf. on High-Energy Accelerators, CERN, 1956, p. 84. Gluckstern, R. L., Cooper, R . K., and Channell, P. J. (1985). Part. Accel. 16, 125 Graybill, S. E. and Uglum, J. R . (1970). J. Appl. Phys. 41, 236. Halbach, K. (1979). IEEE Trans. Nucl. Sci. NS-26, 3882. Halbach, K. (1980). Nucl. Instr & Meth. 169, 1. Halbach, K. (1982). Nucl. Instr & Meth. 198, 213. Halbach, K. (1983a). Nucl. Instr & Meth. 206, 353. Halbach, K. (198313). IEEE Trans. Nucl. Sci. NS-30, 3323. Herb, S. (1985). IEEE Trans. Nucl. Sci. NS-32, 3578. Kapchinski, I. M. and Teplyakov, V. A. (1970). Pribory i Teknika Eksp. 2, 19. Katsouleas, T. and Dawson, J. M. (1983). Phys. Rev. Lett. 51, 392. Keefe, D. (1986). Experiments and Prospects for Induction Linac Drivers, Proc. Int Symp. on Heavy-Ion Fusion, Washington, D. C. Keil, E . and Scnell, W. (1969). CERN Report ISR-TH-RF/69-48 (unpublished). Kerst, D. W. (1941). Phys. Rev. 60, 47. Kerst, D. W., Cole, F. T., Crane, H. R., Jones, L. W., Laslett, L. J., Ohkawa, T., Sessler, A. M., Symon, K. R., Terwilliger, K . M., and Vogt-Nilsen, N., (1956). Phys. Rev. 102, 590. Laslett, L. J. Neil, V. K., and Sessler, A . M. (1965). Rev. Sci. Instr. 36, 426; Rev. S C I .Instr. 36, 436. Laslett, L. J. (1963). Proc. 1963 Summer Study on Storage rings, Accelerators, and Experimentation at Super-High Energies, Brookhaven National Laboratory, Upton, New York, p. 324. Lawson, J. D. (1977). The Physics of Charged-Particle Beams, Clarendon Press Oxford. Madey, J. M. J. (1971). J. Appl. Phys. 42, 1906. Morton, P . L. (1983). Proc. o f t h e 12rh Int Con$. on High-Energy Acc., Fermilab, p. 477. McMillan, E. M. (1950a). Phys. Rev. 79, 498. McMillan, E . M. (1950b). Phys. Rev. 80, 493. Nation, J . A. (1979). Part. Accel. 10, 1. Nielsen, C. E., Sessler, A. M. and Symon, A. M. and Symon, K. R. (1959). Proceedings of the 1959 International Conference on High-Energy Accelerators, CERN, Geneva, p. 239.

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Olson, C. L. (1979). Collective Ion Acceleration, Springer-Verlag, Berlin and New York. Palmer, R. B . (1982). In “Laser Acceleration of Particles,” A I P Conf. Proc. 91, A I P , New York, p. 179. Palmer, R. and Tollestrup, A . V. (1984). Superconducting Magnet Technology for Accelerators, Ann. Revs. Nucl. and Part. Sci. 34, 247. Panofsky, W. K . H. and Bander, M. (1968). Rev. Sci. Instr. 39, 206. Pellegrini, C. (1982). In “Laser Acceleration of Particles,” A I P Conf. Proc. 91, AIP, New York, p. 138. Phillips, R. N. (1960). I R E Trans. Electron Devices ED-7, 231. Piel, H. (1985). I E E E Trans. Nucl. Sci. NS-32, 3565. Piwinski, A (1974). Proc. 9th Int. Conf. on High Energy Accelerators, Stanford, Cal, p. 347. Richter, B. (1985). In “Laser Acceleration of Particles”, A I P Conference Proc. 130, AIP, New York, p. 8. Roberson, C. W., Mondelli, A , , and Chernin, C. (1985). Part. Accel. 17, 79. Robinson, K. W. (1958). Phys. Rev. 111, 373. Ruggiero, A. G. (1985). In “Laser Acceleration of Particles,” A I P Conference Proc. 130, AIP, New York, p. 458. Ruth, R. D. (1983). I E E E Trans. Nucl. Sci. NS-30, 2269. Ruth, R. D., Chao, A . W., Morton, P. L., and Wilson, P. B. (1985). Part. Accel. 17, 171. Schriber, S. 0. (1985). I E E E Trans. Nucl. Sci. NS-32, 3134. Sessler, A. M. (1982). In “Laser Acceleration of Particles,” A I P Con5 Proc. 91, AIP, New York, p. 154. Shepard, K. W. (1985). IEEE Trans. Nucl. Sci. 32, 3574. Sloan, M. and Drummond, W. (1973). Phys. Rev. Ltrs. 31, 1234. Sprangle, P., Drobot, A , , and Manheimer, W. (1976). Phys. Rev. Ltrs. 36, 272. Sundelin, R. M. (1985). IEEE Trans. Nucl. Sci. NS-32, 3570. Symon, K. R. and Sessler, A. M. (1956). Proc. 1956 lnternationl Conference on High-Energy Accelerators, CERN, Geneva, p. 44. Tajima, T. and Dawson J. M. (1974). Phys. Rev. Ltrs. 43, 267. van der Meer, S. (1972). Stochastic Damping of Betatron Oscillations in the ISR. CERN/ ISRP0/72-31 (unpublished). Voss, G.-A,, and Weiland, T. (1982). Particle Acceleration by Wake Fieldr, DESY Report M-82-10 (unpublished). Wangler, T. P. (1986). High Current, High Brightness, and High Duty Factor Ion Injectors, AIP Conference Proc. 139, AIP, NY, p. 173.

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS. VOL 71

FOUNDATIONS OF ENVIRONMENTAL SCANNING ELECTRON MICROSCOPY G . D . DANILATOS ESEM Research Laboratory North Bondi (Sydney). Australia

I . Introduction . . . . . . . . . . . . . . . . . . . . .................................. A . Definition of ESEM . . . . . . . . . . .................................. B . Outline of ESEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...............................

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D . Purpose of Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . State of Gas in the ESEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Basic Concepts and Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Analysis of Gas Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Calculation of Conductance . . . . . . . . . ........ E . Experimental Assessment of Gas Flow ....................... Outline of General Interactions in the ESE ....................... A . Beam-Gas Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Beam-Specimen Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Specimen-Signal Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Signal-Gas Interactions . . . . . . . .................................. E . Gas-Specimen Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Beam-Signal Interactions . .................................. Electron Beam Profiles . . . . . . .................................. A . Formulation of Problem . . . . . . . . . . . . . . . . . . ....................... B . Scattering Cross Sections . . . . . . . . . . . . . . . . . ....................... C . Profiles of Infinitely Narrow Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Electron Skirt Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . Profiles of Finite Width Beam . . . . . . . . . . . . . . . . . . . . . . F. Experimental Measurements of Spot Diameter . . . . . . . . . . . . . . . . . . . . . . . . The Electron Beam and Gas System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Beam Transfer in Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Beam Interaction Volume in Gas . . . . . . . . . . . . . ................... C . Types of Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Ionization of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . Ion Concentration in the ESEM . . . . . . . . . . . . . . . . . . . . . F . Electrostatic Pinch Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

110 110 111 113 114 115 115 116 119 122 129 134 135 136 136 136 137 137 138 138 142 150 157 162 171 178 178 179 185 186 189 192

109 Copyright 0 1988 by Academic Press. Inc . All rights of reproduction in any form reserved . ISBN 0-12-014671-1

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VI. Detection . . , . . . . . . , , . . . , . . , . . . , , . , , _ .. . _ . . . . . . . . . . . _ . .. . . . . . . . . . . . . . A. Backscattered Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Secondary Electrons . . . , . . . , . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Cathodoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Auger Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Multipurpose Gaseous Detector Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Contrast and Resolution . . . . . . . . . , , . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Resolving Power . . . . . , . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Signal-to-Noise-Ratio (SNR) . . . . . . . . . , . . . . . . . . . , . . . . , . . . . . . . . . . . . . . . . VIII. Beam Radiation Effects . . . . . . . . . , . . . . , . . , . , . . . . , . . . . , . . . . , . . . . , , . . . . , . . A. Necessity of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Charging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

193 194 197 200 205 206 206 217 217 218 219 223 223 224 228 ................................................. 232 ons . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . , . . . . . . . , . . . . . . 238 A. Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 B. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 C. Conclusion . . , . . . . . . , . . . , . . . . , , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . 247 Acknowledgements . . . . . , . , . . . . . , , , . . . , . . , . . . . , , . . . , , , . . . . . , . , , , , . . . . , 248 References . . . . . , , . . . . . . . . . . . , , . . . . , , , . . . . , . , , . , , , . . . . . . . . , . . . . . . , , , . . 248 ,

,

,

I. IINTRODUCTION A . Definition of ESEM The environmental scanning electron microscope or microscopy (ESEM) has not been defined adequately yet. Initially, any scanning electron microscope (SEM) which allows the examination of specimens inside a gaseous environment could be defined as such. However, this definition is insufficient because all SEMs have some gas inside their specimen chamber even at the highest vacua attainable. Therefore, a pressure level must be specified that the ESEM can reach or exceed and that is clearly above the vacuum pressure in the SEM. It is rather difficult to find a meaningful pressure to characterize the ESEM, and for this reason it will be chosen arbitrarily. It might appear appropriate to define the ESEM as being capable of operating above the maximum possible pressure allowable by the operation of the electron gun in a SEM. However, this definition is poor, because this pressure depends on the type of gun and there is little advantage for the ESEM if it were only capable of operating at pressures not much greater than the pressure at the gun. It is, perhaps, more logical to upgrade this pressure level to a more tangible value that would also be consistent with the historical aim of the

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111

environmental microscope to observe liquid and hydrated specimens. In this case, to maintain water in its liquid phase, a minimum water vapour pressure of 609 Pa (6.09 mbar or 4.579 Torr) is required at 0°C and this pressure can be taken arbitrarily for the definition sought. The ESEM is therefore a SEM which can operate at the low pressure of a usual SEM through to, at least, the pressure required to observe liquid distilled water. In the above note, it has been tacitly assumed that the reader is familiar with a SEM. The SEM produces a finely focused electron beam which is scanned over a specimen, and the emerging signals from the beamspecimen interaction can be monitored in the form of images, graphs, digital recordings, etc. In the specific case where the detected signals are X-Rays, the instrument has been referred to as an electron probe microanalyzer, but the term SEM has prevailed generally in most cases or in conjunction with some modifier word.

B . Outline of ESEM Having defined the ESEM on the basis of what it can do, it is instructive to give a brief and general description of the instrument, so that the purpose of various aspects examined in this survey will become clear and each topic will be understood relative to the instrument. As with all types of electron microscopes, the ESEM must have a vacuum region for the generation and focusing of the electron beam (usually with pressure less than Pa) and in addition, by virtue of its definition, a region of high pressure (more than 609 Pa). These two regions must be separated by suitable means, usually achievable either by electron transparent window films, or by small apertures restricting the flow of gas. Both methods have been used in practicing environmental transmission electron microscopy. However, only the aperture method is suitable in ESEM because of the much lower accelerating voltages normally used with SEM than with transmission microscopy. This system using small apertures is described in Fig. 1 and shows the simplest practical working system for our purposes. At least two apertures are needed to limit effectively the pressure build up in the electron optics column. The gas flowing through the first pressure limiting aperture (PLAl) is pumped out via a system of tubes and pumps, and only a small fraction of the gas leaks through the second pressure limiting aperture (PLA2) in the column that can be maintained at the required vacuum by the usual pumping means. The remaining pump and valves shown are used to maintain the desired pressure in the specimen chamber and to facilitate the transfer of specimens in and out of the system. It should be noted that the PLA2 may or

112

G. D . DANILATOS

PPolepiece

Specimen

FIG.1: Diagrammatic representation of a two-stage differential pumping system for an ESEM. PLAl = first pressure limiting aperture, PLA2 = second pressure limiting aperture, RP = rotary pump, DP = diffusion pump, TMP = turbomolecular pump, LN2 = liquid nitrogen trap (cryopump), N = airlock (specimen exchange chamber), V , , V 2 ,G valves.

may not coincide with the objective lens aperture, depending on the electron optics design. If the parameters shown in the above system are chosen correctly, the electron beam can travel through the column and the two apertures with a minimum hindrance, but after it enters the specimen chamber, it undergoes collisions with the gas molecules and spreads; the originally focused spot eventually disappears. However, it can be shown that a useful beam spot survives for some distance inside the gas and, if a specimen is brought within this distance, it can be examined. This presupposes that suitable detectors have been designed and positioned correctly for the detection of the emerging signals. A schematic diagram showing the arrangement of one detection system is given in Fig. 2. The distance of specimen from the PLAl determines the relative fraction of signal detected below or above the aperture in certain modes of detection such as with backscattered electrons and X-rays. The ESEM retains generally the basic specifications of SEM such as resolution, depth of focus, variety of signals and signal manipulation. In addition, it does not require rendering the specimens conductive by various treatments regardless of accelerating voltage. The ESEM allows the use of specimen manipulators such as a liquid microinjector system, for which sufficient room must be left to introduce a capillary needle between the specimen and the aperture (see Fig. 2).

FOUNDATIONS OF ESEM

113

ELECTRON BEAM

-

B -PLA2

TO PUMP

i

C -PLAl

FIG.2: Example of detection configuration and specimen examination in the ESEM. Water droplets by suitable means can wet a sample for experiments in siru.

Dynamic observations of gas-liquid-solid systems are possible. In all, the ESEM can operate both in the presence and absence of gas and therefore it can be considered as a universal form of SEM.

C. History Much work has been published on environmental electron microscopy, mostly in connection with environmental cells for transmission microscopy and to a lesser extent recently, in connection with SEM. As some comprehensive reviews on this topic have appeared from time to time, it is sufficient for the purposes of the present survey to cite these with the addition of some minor remarks. Attempts to allow gas in the electron microscope were made very early by Ardenne and Beisher (1940). The first observation of hydrated specimens was reported by Abrams and McBain (1944), who used windowed cells. Parsons et al. (1974) used the aperture method and reviewed the field very comprehensively. A more recent extended review can be found in a book by Butler and Hale (1981). All of the above works relate to transmission electron microscopy and although much has been learnt from it, the SEM has its own peculiarities, Much new experimental and theoretical work had to take place for the

114

G . D. DANILATOS

evolution of the ESEM. As the SEM is a relatively new form of electron microscope, the ESEM is a more recent development. A review concentrating on it has been published by the present author (Danilatos and Postle, 1982b). Special mention is owed to B. W. Schumacher and his co-workers who developed and refined the electron beam transfer systems for firing an electron beam in air. He used these systems for construction of various instruments such as electron beam welders and pressure gauges but not for electron microscopes. Many of his experimental observations and theoretical calculations are applicable and very useful in the design and construction of the ESEM. Unfortunately, most of his work has remained unknown in the form of internal reports or in not easily accessible journals. His works span more than three decades and most of them were only recently acquired by the present author. A list of his main writings is given in the references. D. Purpose of Survey

From the outline of the ESEM, it might at first appear to be a logical, simple and straightforward technique to practice. However, this concept does not explain the absence of such a useful technique from the electron microscopy scene for so long, except for isolated efforts on a relatively limited scale. Also, some scepticism has inferred the opposite of feasibility of the ESEM. The truth, though, lies in the middle because this technique is neither easy nor impossible as experience has shown. With time, this technique seems now to become easy to understand and simple to operate but only after long painstaking work to sort out, both in theory and practice, fundamental problems, engineering considerations and practical questions. This survey deals with the main aspects of ESEM and aims at forming a new unity in a way not previously published. Most of the work published to date is experimental with the testing of new ideas and designs. The results of past work have established a minimum realizable domain upon which much theoretical research can be made and which in turn can prescribe new experimental directions. The main emphasis here is the understanding and development of the theory of the ESEM. To do this requires not only knowledge within the electron microscopy field in its present form, but also from other disciplines such as fluid mechanics, ionization of gases and plasma physics. Understanding the reaction of an electron beam with all states of matter is now necessary. It is important to know the fate of the electrons in an electron beam

FOUNDATIONS OF ESEM

115

while traversing short and long distances in a given gas at a particular pressure. The spatial distribution of electrons at each penetration depth is needed as it relates to contrast and resolution. The overall penetration and dissipation of energy of all electrons in the gas relates to various detection systems, to the conduction of charge and to radiation effects. The detection systems known must be modified to suit the conditions and restrictions of the ESEM. Furthermore, new detection concepts have become possible by the existence of the gas itself. The implications of these new systems may be of far reaching importance, and their mechanism of operation requires further study. The user of SEM need not be particularly concerned about vacuum technology questions especially with modern instruments which automatically evacuate or vent themselves. However, with the ESEM the state of the gas in the specimen chamber and the gas flow through the microscope must be monitored, and various parameters should be varied at will to control the environment and its effects on the specimen under examination. Elements and formulae from gas dynamics and the physics of gases have been compiled in a form for direct application to the requirements of ESEM operation. In conclusion, the main purposes of this survey are (a) to present new theoretical derivations and computations, (b) to explain and review experimental findings, (c) to survey existing literature and collect data and information relevant to ESEM and (d) to create the foundations for further use and development of ESEM. As the development of ESEM is relatively new and only limited resources have been devoted to it, there are still incomplete theories and much more experimental work required. It is hoped that the present work will help make the tasks ahead more clearly defined so that more researchers from different fields will be attracted to make new contributions. 11. STATEOF GAS IN

THE

ESEM

A . Requirements Both the designer and the user of ESEM will find it necessary to resort frequently and repetitively to the literature for data and fundamental information on the state of gas in the instrument. This information is widely spread and is sometimes difficult to find; more often the mathematical formulae are expressed in different units and require some degree of manipulation to describe the system. Therefore, it would be very helpful

116

G. D. DANILATOS

and time saving to compile a minimum of information for the immediate needs of the ESEM. Furthermore, much of this information is used in subsequent sections of this survey to analyze the electron beam penetration of gases and the overall performance of the instrument. Mathematical derivations for the stationary gas in the specimen chamber and the gas flowing through apertures, tubes and pumps are given here. Theoretical calcultions can be made for some cases, whilst for others the predictions may be poor and the employment of experimental methods more practical. The ways, problems and limitations of separating the electron optics column from the specimen chamber will become clear in this section.

B. Basic Concepts and Relations The information presented below can be found in textbooks on gas theory or vacuum technology but it has been selected and adapted to suit the needs and SI units which have been adopted throughout this survey. If other units are used in some specific cases, it will be stated accordingly. The pressure of a gas is still measured in so many different units in various textbooks, manuals and countries that a conversion table is always useful to have. The SI unit for pressure is the Pascal (Pa) = 1 N/m2 but the millibar (mbar) has widespread use and is in the simple relation 1 mbar = 100 Pa. Table I provides the relationships amongst the most frequently encountered units. Frequent use is made of the molecule or atom concentration (particles per unit volume) n of a gas at pressure p and temperature T and is given by n

=

7.243 x

T

The corresponding gas density p (mass per unit volume) is given by p = 1.203

X

M T

p_

since the molecule mass M , is

M,

M

= -=

(3)

1.66 x 10-27 M

NA where M is the molecular (or atomic) weight and NA (moIecules/kmole) is Avogadro’s number.

=

6.025 x

117

FOUNDATIONS OF ESEM ~

~~~

TABLE I RELATIONS AMONGUNITSOF PRESSURE FREQUENTLY ENCOUNTERED

1 1 1 1

Pa = mbar = Torr = atm =

(1 Pascal (Pa)

Pa

mbar

Torr

1 100 133.3 1.013 x lo5

.01 1 1.333 1013

,0075

9.87 x

0.75 1

9.87 x 10-4 1.316 x lo-’

760

1

=

N/m3, 1 bar

=

lo6 dynes/cm2, 1 Torr

atm

=

1 mm Hg)

It will also be useful to recall the ideal gas law in the forms:

PV=NRT=-

WRT M

(4)

where V is the volume occupied by the gas of N kmoles or W kg mass and R = 8314.6 J/K-kmole is the universal gas constant. The gas molecules move randomly in all directions with an average velocity u 1/2

u=

145..51(;)

The velocity of sound u is

where y = C,,/C, the ratio of specific heat capacities. It can be checked that the two velocities u and u are of the same order of magnitude: u

-= U

u

-= U

1.236

for monatomic and

1.349

for diatomic gases

The number of molecules f of a gas at rest striking unit area per unit time is nu 4

f=-=

2.636 x lOZ4p (M T )1/2

(7)

118

G. D. DANILATOS

and the corresponding incident mass g =

U

M rn f =

p - = 4.377 x 1oP3p

4

while the corresponding volume v

Another useful quantity is the mean free path which is the average distance traversed by all molecules between successive collisions. The mean free path L, is given as 1/2 77 L, = 114..5($) P where for the viscosity 7,various formulae have been developed. The Sutherland equation gives

The constants c1 and c2 are given in Table I1 for some common gases together with their molecular weight and ratio y. For illustrative purposes values of L, and 77 are also given at 100 Pa and 293 K. The molecular diameter 6 associated with intermolecular collisions is given by 62 =

2.714

(MT)’/’

X

(12)

77 ~P

~

TABLE I1

VALUES OF USEFUL CONSTANTS FOR SOMEGASES

Air A H? He H2O N2 0 2

M

Y

28.98 39.95 2.016 4.003 18.016 28.02 32.00

1.4034 1.667 1.408 1.67 1.30 1.405 1.396

14.64 19 6.48 15.13 18.31 13.85 16.49

*SI units at 100 Pa and 293 K (1 SI unit of

1) =

c2

105q

105~,*

114 133 70.6 91.6 659 102 110

1.803 2.237 0.894 1.943 0.965 1.759 2.052

6.564 6.936 12.34 19.03 4.455 6.511 7.110

10 Poise).

FOUNDATIONS OF ESEM

119

The above formulae can be found in alternative forms or units in the book by Dushman and Lafferty (1962). In the ESEM, the main independent variable is the pressure and the above formulae provide the magnitude of other quantities depending on the pressure. From these we can also get a feeling of what “high” or “low” pressure means because its significance depends on the particular aspect we consider. Thus from Eq. (1) we find that in ordinary microscope vacuum ( p = lop3Pa), there are still more than 10’’ particles per cubic meter, a number extremely high in absolute terms, or in everyday experience. However, this number is associated with a rare frequency of collisions between beam electrons and gas molecules. Its significance is different from the point of view of contamination and etching. The time scale to form a monolayer of nitrogen atoms is 3.13 x lOP4/pseconds, which gives 3 x lop9seconds at one atmosphere, 0.3 seconds at lop3Pa and 8.7 hours at Pa, as can be found from (7) and (12) by assuming that each atom sticks on impact. Therefore, the gas-specimen interaction is better understood by quantitatively considering this interaction. A further description of the static gas is gained by the average distance between closest ( T / p ) ” 3 which is much smaller than neighbours s = n-lI3 = 2.399 x the mean free path. For example, s = 3.4 X lo-* m at 100 Pa and 293 K, which is about 3 orders of magnitude less than L,. Also, the nature of flow of gas depends on the pressure level as will be seen later.

C, Analysis of Gas Flow It has been mentioned that the window method (e.g use of collodium film) to maintain two opposing pressure regions in the ESEM is not suitable because of the additional electron scattering created by the film. The amount of scattering is very large for the low accelerating voltages preferred in ESEM, as the film can have a mass thickness comparable to the minimum mass thickness of the gas, In addition, films can easily break either by beam damage, especially in the low keV range, or by mechanical puncture during operation. Furthermore, considerably larger apertures are required for the ESEM than the closely spaced mesh grids used for the environmental cells in transmission microscopy; it is unlikely that the films will sustain large pressure differences because of inadequate mechanical support. The aperture method seems to offer the best possibilities. These apertures have the property of restricting the flow of gas and creating a pressure difference between the two sides of the aperture in the same way as a voltage difference appears across a resistance when electrical current

120

G. D. DANILATOS

flows through it. This concept is well-known, and the earliest record of its use in electron physics appears to be in the work by Pauli (1920) who succeeded in passing cathode rays in the atmosphere. It has also been applied to studies of electron impact phenomena in gases (see, for example, Massey and Burhop, 1969), and a significant study and development of the method has also been done by Schumacher et al. (1953) and Schumacher (1962). The present author (Danilatos, 1981b, 1985; Danilatos and Postle, 1983) has also presented some studies and data on this topic for the actual conditions and materials used in the ESEM. The simplest system used satisfactorily for our purposes consists of a two stage pressure reduction as shown in Fig. 3a. With certain precautions, this can be analyzed in the same way as an electronic circuit where pressure corresponds to voltage, gas flow to electric current and apertures and pipes to resistors. The gas flow is usually called leak rate and is measured as mass per unit time or equivalently as volume per unit time at a given pressure, i.e. in Pam3/s. The impedance of pipes and apertures is usually replaced by its inverse, i.e. the conductance. The pumps are also characterized by an internal conductance which is referred to as speed of the pump. The equivalent circuit for the two stage system is shown in Fig. 3b. The needle valve V is associated with the variable conductance F, which regulates the

a

b

FIG.3: (a) Simplified schematic representation of components in Fig. 1 with pumps as (11,22), pipes as (12,21), PLAl as ( l ) , PLA2 as (2), specimen chamber pressurep, first stage pressure p , and second stage pr. (b) Corresponding circuit of conductances (PE= room pressure).

121

FOUNDATIONS OF ESEM

leak rate Q from an external gas source at pressure p E to establish a constant pressure p in the specimen chamber. Each component in Fig. 3a has a corresponding conductance in Fig. 3b. Thus by employing elementary circuit equations the pressures p1 and p 2 at the first and second stage can be predicted. It will be seen that the conductance is not a constant with variation of pressure in some cases, so that Ohm’s law cannot be applied, but the circuit analysis approach is still valid. We only need to know the particular values of conductance in the steady state situation. To simplify derivations, the speed of each pump can be lumped with the conductance of the attached pipes:

1 - 1 1 _ -- + -

FOl

F11

F12

1

1 -- -+

and

F02

F22

1 -

F21

where Fol replaces F I 1 and F I 2 , while FO2replaces FZ2 and FZ1.It can now be easily shown that

and

For small conductances Fl and F2 of the pressure limiting apertures, as they must be in comparison with the other conductances, the above equations reduce to P1 =

PFl FOl

and

P1F2 p2=-=Fo2

PFlF2 FOlF02

From the above equations, it is seen that the best pressure reduction is achieved with small apertures and large pipes and pumps. As the apertures cannot become indefinitely small because of electron optics limitations and restriction of the field of view by PLAl, it is best to maximize Foland FO2. From (13), it is seen that by increasing the speed of the pumps only, the conductance Fol or Fo2 will become limited by the pipes alone and there is no need to attach an arbitrarily big pump, or vice versa. In practice, the system becomes pipe limited when attempting to modify existing models of

122

G. D. DANILATOS

SEM. Examples of such modifications have been published previously (Danilatos, 1981b, 1985). However, the pumping efficiency can be optimized by properly redesigning the electron optics column such that the pipes are eliminated and the most efficient pumping means is incorporated. It is believed that this goal can be achieved by integrating the electron optics column with cryopumping, which can be extremely fast, vibration free and clean (Venuti, 1983). The main engineering problems for this are to be able to regenerate the pump easily and avoid condensation on critical parts of the electron optics column. A third pressure limiting stage may be required if the first two cannot achieve satisfactorily high vacuum for the operation of a LaB6 or field emission electron gun. However, two stages with usual medium speed rotary and oil diffusion pumps have achieved pressures less than Pa in the gun area which allows a tungsten filament to operate through its expected life. The simple analysis presented above becomes in practice very complex because of the difficulty in calculating the various conductances. It will be seen in the following section that no theoretical derivation has been found yet, that can satisfactorily predict certain conductances. Furthermore, the flow of gas through P L A l presents some special features, such as the gas jet forming downstream (above it), or the streaming and depletion effects taking place upstream (below it). These features must be considered carefully for an efficient design, construction and operation of an ESEM. D. Calculation of Conductance Only under certain well-defined conditions can the conductance of apertures and pipes be predicted accurately, whilst in many practical cases a calculation of the conductance becomes quite complex and unreliable. Otherwise, the experimental measurement can be quite simple and reliable, and this approach has been adopted to a large extent by the present author (Danilatos, 1981b). However, to do this, the most basic concepts of gas flow must be understood and a concise presentation is given below. The conductance of a given element depends on the type of flow through it. The mathematical expressions and data used have been adapted from Dushman and Lafferty (1962), Schumacher et al. (1953) and Schumacher (1962). 1. Free Molecular Flow

For pressures below a characteristic level whereby the mean free path of the molecules is greater than the size of the element, the flow is termed free molecular and the conductance is independent of pressure. This

FOUNDATIONS OF ESEM

123

condition is formally expressed by the Knudsen number being greater than unity: L,/d > 1 where d is a dimension (e.g. diameter of pipe). A small aperture of area A in an infinitely thin wall has conductance F L given by

(MT)'/2

FII, = 36.378A -

and measures the volume per unit time (m3/s) passing through the aperture at any pressure in the free molecular flow region. In this region, by increasing the pressure isothermally, the concentration of molecules increases in proportion, while their corresponding specific volume decreases in the same proportion, and as a result, the volume of gas arriving at the area A per unit time remains constant. The corresponding mass increases in proportion with the pressure, and expressed as mass per unit time per unit pressure, is given by

G:

= 4.375 x 1 0 - 3 ~ ($1'2

according to Eq. (8) for the area A . By use of Eq. (4), the conversion factor r between (18) and (19) is found to be M M r = - = 1.203 X lop4RT T

so that G:

= rFL

(21)

The leak rate Q$ under these conditions is calculated by

Q;

=

FO,(P - PI)

(22)

QoG

- G" m (P - PI)

(23)

in Pam3/s and in kg/s. It is important to note that the leak rate is proportional to the factor (T/M)'l2 when the leak rate involves volume, and inversely to the same factor when it involves mass. Thus, less mass flows through the orifice at a higher temperature which corresponds to a higher volume for a given gas, and what appears as a contradiction between Eqs. (19) and (18) is resolved by realizing that both yield exactly the same quantity of gas. It is perhaps more tangible to use Eq. (23) when calculating quantities of gas flowing through the pumps system of the ESEM in a given period of time.

124

G . D. DANILATOS

The conductance F L of a long tube is given by

4v

FL

=

1

where u is the average molecular speed (see ( 5 ) ) , H is the perimeter and A the cross sectional area at a given point along the length I of the tube. The formula (24) is reduced to Eq. (25) for cylindrical tubes of radius a and length not less than about 100 radii:

For short cylindrical tubes the conductance can be found from the corresponding conductance of an orifice of the same diameter as the tube multiplied by the so-called Clausing factor K .

F A = KF; (26) The factor K is given in Table I11 for cylindrical tubes. For long tubes this factor takes on a limiting value (8a/3I) by which the relation (26) is reduced to Eq. (25). The Clausing factor is different for different shapes of cross section. Apart from the simple case of an orifice or a tube, there are more complicated cases for combinations of orifices and tubes of different geometries and configurations (see for example Davis, 1960), but the above formulae should give at least the order of magnitude which is all that is needed on many occasions. The gas flow patterns at the entrance and exit of cylindrical tubes have been studied in detail by Dayton (1956) for molecular flow, but they are not of any immediate importance for ESEM. 2. Viscous Flow

a. Laminar Flow. As the pressure is increased in a given vessel, the Knudsen number becomes less than 0.01, which means that collisions among molecules are more frequent than collisions between molecules and walls of the tube. In this range of pressures and provided that some further conditions are fulfilled, the flow can be treated as that of a viscous fluid, which can be described quantitatively in certain simple cases. The classical Poiseuille equation for viscous fluids

125

FOUNDATIONS OF ESEM

gives the volume per unit time multiplied by pressure (Pam3/s) passing through a pipe of length 1, at the ends of which the pressures are p and p l . This is applicable under the following conditions: (i) The gas is incompressible, which generally is not satisfied but its effects can be neglected when the average flow velocity across a plane in the tube is approximately less than of the velocity of sound at that particular level. This condition is embodied in the relation Q

lru2up

< -= 95.488~’p 3

where p is the pressure at this cross section. (ii) The flow does not become turbulent, which is satisfied for smooth tubes and entrances when the Reynolds number is less than about 2000, a condition expressed by

Q<

2.612 x lo7 7uT M

TABLE I11 VALUES OF CLAUSING’S FACTORSK FOR CORRESPONDING VALUES OF l / a (FROM AND LAFFERTY, 1962) DUSHMAN

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.o 1.1 1.2 1.3 1.4 1.5 1.6

1 0.9524 0.9092 0.8699 0.8341 0.8013 0.7711 0.7434 0.7177 0.6940 0.6720 0.6514 0.6320 0.6139 0.5970 0.5810 0.5659

1.7 1.8 1.9 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 5 6 7

0.5518 0.5384 0.5256 0.5136 0.4914 0.4711 0.4527 0.4359 0.4205 0.4062 0.3931 0.3809 0.3695 0.3589 0.3146 0.2807 0.2537

8 9 10 12 14 16 18 20 30 40 50 60 70 80 90 100 lo00

0.2316 0.2131 0.1973 0.1719 0.1523 0.1367 0.1240 0.1135 0.0797 0.0613 0.0499 0.0420 0.0363 0.0319 0.0285 0.0258 0.00266 W(30

126

G . D. DANILATOS

(iii) The tube is sufficiently long, otherwise Eq. (27) must be modified by a factor

which depends on the leak rate itself. This correction takes into account the entrance effects, because the flow becomes fully developed only beyond an initial length downstream. The flow is said to be fully developed when the velocity profile becomes constant along the length and this occurs for lengths 1:

Provided Eqs. (28), (29) and (31) are satisfied and taking into account the correction (30), the conductance for laminar flow FJcan be derived from: Fj

=

9.165 x lo4 $T M(P

-

PI)

1

+ 4.285

1

+

X

lo-‘

Ma4(p2 - p?)]”’} T~TI2

For air, at 293 K, we get 16.711 F‘, = ___ 1-1 P - PI

+

[

1303.74

l2

Equivalent to Eq. (32) are the relations 7 4 P

FI’

=

16$(1

-

p;

=

+ 5.455 x

P1) loP6 MQ/qTl)

+

(34)

and p2

[+

16771Q 1 ra

5.455 x lop6 -

(35)

Therefore, the conductance and the pressure difference depend on the level of leak rate through the tube. (iv) The fluid velocity at the tube walls should be zero, otherwise “slipping” rarefied flow of the gas over the wall takes place and another correction should be introduced. This occurs in the transition range of pressure between molecular and viscous flow for which the formula below has been proposed to predict the conductance within 5% (cylindrical

127

FOUNDATIONS OF ESEM

tubes):

FLv

=

F'[

1.288 x

up,

77

(y2 + z]

(36)

where

1+

77

z= 1+

up,

2.193 x

2.709 x lop2 up, 77

and p a = ( p l + p)/2 the average pressure. Taking into account Eq. (25), we get from Eq. (36) the leak rate:

(4 (4

304.8 u3p T

a4p2 + Q = 0.197 771

1

1+

3.342 a4p2

+

771

(37)

0.014 ap M ' I 2 77

when p 1 << p . Unfortunately, not all of the conditions are met in practice and only approximate values can be obtained from the above derivations. The situation is complicated not only because the conductance depends on the pressure but also because it depends on abrupt changes in the tube diameter and even the nature of gas (Dushman and Lafferty, 1962).

b. Turbulent Flow. When the Reynolds number Re given by R,

2apU

=--

77

2MQ - 7.657 .rrqRTu

X

MQ lops 77Ta

exceeds a critical value, the flow is said to be turbulent ( V is the speed of the fluid). For cylindrical tubes, this value is taken to be in the range 2000 to 4000, and it depends on such parameters as roughness of the walls and shape of tube or its entrance. The conductance F: for turbulent flow in a tube is approximately estimated by (when p 1 e~p ) :

128

G . D. DANILATOS

where A is the hydraulic (here pneumatic) friction coefficient (Schumacher et al., 1953). For example, A = .05 for R e= 2000 and for smooth tubes. The conductance here is not dependent on pressure.

c. Viscous Effusion Flow (or Enthalpy Limited Flow). This type of flow is the most relevant flow particularly through PL A l and for the pressures mostly encountered in ESEM. It has been studied extensively by Frossel(1936), Schumacher et al. (1953) and the present author (Danilatos and Postle, 1983). This flow has some special characteristics which can dramatically influence the performance of the microscope. As the pressure difference between the two regions on either side of the aperture increases, the speed of the flow can exceed the speed of sound in the downstream region (above PLA1). This is a consequence of the free expansion of gas as it passes from the high density region to the low density one. The speed of sound in the low pressure region is less than the speed of sound in the high pressure region. The flow can reach speeds up to the sonic speed at the aperture, so that a jet of gas forms at supersonic speed in the downstream region. This jet is characterized by a shock front and some special shapes. This can become visible by scanning a beam of electrons at right angles to the flow and photographing the fluorescence of the gas at different positions of the beam (Schumacher, 1968). The method of electron shadowgraphs, or by firing an electron beam just behind the aperture and observing the afterglow excitation has also been used to visualize the jet (Boersch, 1937; Schumacher 1953; Grun et al., 1953; Schrufer, 1957). Thus it has been found that the jet shows a "hollow" or low density region along the axis some distance from the aperture, surrounded by a high density at the periphery. The conductance of apertures for this type of flow is given by (Shapiro, 1953):

The conductance in this case is also independent of pressure, as it applies to the case where maximum mass flow has been reached. This occurs when the low pressure on one side is below a critical value for a given high pressure on the other side. If the pressure is lowered below the critical value, only the shape of the gas jet changes dramatically. The conductance for tubes can be derived from the conductance of an aperture of the same diameter multiplied by a factor K,.

F:

=

K,F,"

Values for the factor Ke for a series of values of l / a are given in Table IV.

FOUNDATIONS OF ESEM

129

TABLE IV VALUES O F FACTOR K,

FOR A

OF

0 50 100 150 200 250 300

SERIESOF VALUES

l/a

400 500

1 0.87 0.79 0.73 0.68 0.65 0.62

0.57 0.52 0.48 0.45 0.42 0.40 0.37

600 700 800 900 1000

TABLE V VALUESOF THE CONSTANT OF PROPORTIONALITY FOR CONDUCTANCE OF VARIOUS GASES (Fz"= CadZ,F," = CmdZ)

air A

H2 He

HZO NZ 0 2

156 141 592 445 193 159 148

91 77 344 244 115 92 86

They have been taken from a graphical presentation attributed to Frossel by Schumacher (1982). The most reliable derivations, which are used in the design and operation of ESEM, are those for an aperture in the viscous effusion flow and the free molecular flow. In these cases, the conductance is simply proportional to the square of the diameter of the aperture times a constant of proportionality ( C , for molecular and C , for viscous effusion) which is given in Table V for some gases at 293 K.

E. Experimental Assessment of Gas Flow From the previous presentation it becomes clear that theory alone cannot provide answers to all the problems, some of which are decisive.

130

G . D . DANILATOS

FIG.4: Image of the rim of a 57 p m diameter aperture in a thin copper grid during gas flow from the atmosphere below; 15 keV, 100 PA.

There is no comprehensive discussion in textbooks on systems such as the one used for ESEM. However, it is imperative to understand the implications of the theoretical discussion in practice. Such discussion may lead to a design bypassing the pitfalls of calculations and to a design with optimum efficiency. The experimental work of previous workers on related systems such as electron beam welders and pressure gauges are very helpful, but again their conclusions cannot be transferred to ESEM without further research. Parameters in the microscope such as contrast and resolution, noise and aberrations may be adversely affected. The particular nozzles used in electron beam welders have to be replaced with apertures on thin walls (say 30 pm), the distance between apertures must be consistent with the electron optics design and so on. Therefore, much of the work on gas flow had to be repeated and complemented in the actual conditions of ESEM. The results of such work have been presented in several publications by the present author. One of the first tasks was to measure the conductances of the apertures used. Figure 4 shows an image of such an aperture, actually during gas flow from the atmosphere below (Danilatos, 1981b). It was not known how the conductance would behave for these apertures. There are two simple experimental methods for such measurements: (a) to collect and measure the quantity of gas flowing through the aperture at constant pressure for a given length of time and (b) to plot the decay of pressure vs. time as a known volume V is exhausted into vacuum through the aperture (Dush-

FOUNDATIONS OF ESEM

131

man and Lafferty, 1962). From these plots the conductance can be calculated from the equation

The second method was used to find the conductance for a set of apertures (Danilatos, 1981b). From these results, the average constant of proportionality C, was determined to be 149.6 m/s for the pressure range 1 to 100 kPa for air (Danilatos, 1985). This value is only 4% below that predicted in Table V. If, instead of the average, the constant C, is derived for each pressure separately, it is found that C, = 152 m/s at 100 kPa and C, = 141 m/s at 5 kPa and, therefore, Eq. (40) can be relied upon for practical purposes. This is important, because by knowing the leak rate through PLA1, we only need to measure the pressure at strategic points of the system in order to find the various conductances. These conductances can then be compared with the speed of pumps to determine whether the system is pump, or pipe limited, and proceed to implement the appropriate improvements. An example from a real situation is reproduced in Fig. 5 (see also Danilatos, 1985). The conductance or speed of a pump is given by the manufacturer, or can be measured by monitoring the pressure at their inlets for various known leak rates. The characteristic speed of a turbomolecular pump (i.e. the FI1)is shown with dashed lines. The abscissa for only this curve corresponds to the pressure at its inlet. By measuring the pressure p1 (see Fig. 3), the total conductance F,, can be found from the leak rate which can be taken to be practically equal to that flowing through the P L A l (Q = p F 1 ) .Then, Eq. (13) can be used to find the conductance of the pipes F12.The corresponding speed of the pump for the fixed leak rate is found by the intersection of the speed curve for the pump with the straight line representing the leak rate. At the point where the same straight line intersects the curve €or the total conductance ( F O l ) ,the abscissa is the pressure p , , and the pump speed F 1 , must be translated horizontally at the same abscissa (point Fil). By repeating this procedure for different leak rates, a curve with similar points as F ; , (pump on line) is constructed for comparison with the curve for pipes. The above analysis is not valid when the gas jet mentioned earlier strikes the aperture PLA2. In that case, larger amounts of gas can leak straight into the electron optics column. As the characteristics of this jet are a function of the geometry of the apertures and their positioning, experiments had to be performed again for the real situation of the ESEM

132

G . D. DANILATOS

n 0 -

E

LAO,

J 0

a u

-

-2-

0

U 3

73 C 0

V

-3 Constant leak r a t e 0

-I.

-2

-1

0

1

2

Pressure Logp,. Pa

FIG.5: The conductance of pipes, of pump on line and of the total system vs. pressure p , measured between PLAl and PLA2. The dashed line shows the speed of the turbomolecular pump vs. pressure at its inlet. The straight line is the locus of constant leak rate.

(Danilatos and Postle, 1983). A different experimental approach from that of previous workers was used. The PLAl could be tilted at various angles for different fixed distances from PLA2. Various sizes of apertures and pressures were used. For each set of these parameters, the pressure in the electron optics column was monitored. From a large number of data, isobaric contours were mapped for many different cases. Figure 6 shows one such example. In this, a “hollow” region is observed as by past workers. The general characteristics of the jet were confirmed with this method and, in addition, the correct position of the apertures PLAl and PLA2 relative to each other could be determined. Schumacher (1962) positioned the nozzle corresponding to our PLA2 in the hollow region to minimize the gas leak in the column. Such an arrangement was used with instruments (as a welder), where the PLAl was relatively far from the object below it, but in ESEM there are cases where an object is placed immediately below this aperture and it is not known how the gas flow will be affected. Experiments are still required to determine whether different

133

FOUNDATIONS OF ESEM

5 CNSTANCE ALONG

0

5

mm

APERTURE PLANE

FIG.6: Isobaric pressures p z of stage 2 (above PLA2) as measured when the PLA2 is positioned at a distance 1 and angle 4 relative to the PLA1. (Case with p = 100 kPa).

shapes of object in front of the aperture would affect the leak in the column adversely. Up to now, the distance between the apertures was chosen greater than the length of the jet (Danilatos and Postle, 1983). Schrufer (1957) has reported several minima and maxima of pressure with decreasing intensity along the axis of the jet, especially for higher pressures. However, these maxima and minima are insignificant in the hypobaric pressures used in the ESEM, but some complementary measurements are still to be taken for work near atmospheric pressure. Schumacher (1982, unpublished manuscript) has observed that when the gas jet is stopped by a wall with or without aperture, the flow turns subsonic via a shock-front (Mach disk) some distance in front of the wall. Between the wall and the shock-front a high stagnation pressure develops. This stagnation pressure becomes minimal when a nozzle is conically shaped and placed inside the hollow region of the jet. However, our measurements did not show much dependence of the leak rate into the column on the particular shapes of PLA2 tested. This is not necessarily in contradiction with Schumacher but perhaps the result of tilting the jet relative to the plane of PLA2, something that could influence the formation of a shock-front differently. Tilting PLAl may prove a new alternative method to remedy the stagnation pressure problem. The amount of tilting

134

G. D . DANILATOS

needed can be only 5” and should not affect the performance of the system. An equivalent approach would be to slightly deform the rim of PL Al in order to redirect the jet away from PLA2. Another solution to the stagnation pressure problem suggested by Schumacher is to deflect the jet by a second cross-jet, but this requires additional pumping which is unattractive for ESEM. Finally, the use of baffle-plates with a central hole for the beam as suggested by Schumacher has also been tested by the present author, who, in addition, experimented with other configurations for the ESEM with positive results (Danilatos and Postle, 1983). An important aspect of the gas flow in the ESEM is the state of gas immediately below the P L A l . A depletion zone with corresponding pressure gradients must extend down to some finite distance from the aperture, but definite data are not yet available. As the gas flows due to the pressure gradients, streaming should extend for a much larger distance but its effects may not be a problem. A lower pressure in the depletion zone than in the specimen chamber pressure can have a drying effect in wet specimen examination, but streaming alone may be unimportant. Parsons (1974) has reasoned that the specimen surface at 0.5 mm below a 100 pm aperture will not have an appreciable probability of drying. Our experience has shown that liquid water is maintained in equilibrium at 1 mm beneath a 400 p m aperture. Schumacher (1982) has suggested that when the leak rate through apertures is affected by the presence of the gas jet, it is more appropriate to refer to the system as a “beam transfer system” by “dynamic pressure stages” and not as “differential pumping”. In this respect, the immediate needs of ESEM for wet specimen examination at pressures up to 3 kPa have been served by differential pumping (by placing the apertures sufficiently apart). If Schumacher’s explanation is correct, dynamic pumping could be exploited for work near atmospheric pressure by placing the nozzle in the hollow region. In conclusion, whatever system is used, it should be compatible with the requirements of electron probe forming, detection, resolution, contrast, noise etc., as will be examined in the following sections.

III. OUTLINE OF GENERAL INTERACTIONS IN

THE

ESEM

As the electron beam strikes a specimen, there is a host of reactions or interactions between the primary electron beam and the specimen, and their study has constituted a fundamental topic of electron microscopy. Thus a primary electron may undergo elastic or inelastic collisions in the

FOUNDATIONS OF ESEM

135

specimen resulting in the generation of secondary (SE), or backscattered electrons (BSE), X-rays etc., and in specimen changes by molecular scission or cross-linking, atom dislocation, -etc. However, all of these different interactions are characterized by the fact that they occur between two entities: the beam and the specimen. By allowing gas around the specimen, the number and type of reactions are multiplied and it is helpful if these reactions are classified and studied in a logical manner according to some natural distinction. We can distinguish four main entities which interact with each other: beam, gas, specimen and signals. Therefore, the large number of reactions occurring in the ESEM can be lumped into six general types of interactions as will be discussed below. These general types of interactions are not independent from each other and they may influence one another. Furthermore, they do not only occur inside the specimen chamber, but some may also take place throughout the electron optics column. In addition, some special cases such as the generation of ions at the electron gun and their dependence on the gas pressure in the gun chamber (Brocker and Reimer, 1978; Wells, 1978) have to be considered as well for an overall understanding of the design and operation of the ESEM. In this section, the general reactions will be outlined in the broadest terms, and some of these will be analyzed further in later sections. A . Beam-Gas Interactions

The electron beam and the gas interact with each other and the result is (a) scattering of the beam, (b) generation of signals such as SE, BSE, X-rays, cathodoluminescence (CL) and others, and (c) modification of the gas by creating positive or negative ions, dissociation products, excited molecules and atoms etc. The beam scattering will constitute the subject of a detailed analysis, since it is decisive for the overall performance of the ESEM. This determines the limits of contrast and resolution, as these are now affected by the presence of gas. The generation of signals in the gas by the primary beam should be examined in conjunction with the signals generated by the beam-specimen interactions which are affected and are ultimately of interest to us. The signals generated by the primary beam in the gas add a constant level of noise to the corresponding useful signals from the specimen. The degree of alteration of the neutral gas should also be understood as this change might affect the role of the gas as an environmental conditioning medium. The initial purpose for introducing gas into the specimen

136

G . D . DANILATOS

chamber is to maintain a certain level of pressure which is necessary in order to maintain certain properties of the specimen (e.g. to maintain a liqbid phase or allow a particular reaction). It is of paramount importance to know how closely the gas fulfills its role as an environmental agent.

B. Beam-Specimen Interactions The electron beam when interacting with the specimen results again in (a) beam scattering which determines the interaction volume, (b) generation of signals and (c) modification of the nature of the specimen (beam irradiation effects). The beam-specimen interactions have constituted the primary objective of study in electron microscopy. This also remains a fundamental topic of study for the ESEM. The practice and theory developed and used for the interpretation of results (images, spectrographs etc) can also be applied to the specimens in the ESEM but these theories and practices have to be enriched or modified by the addition of a liquid and gaseous phase in the microscope chamber. Of course, the gas itself (alone) can be the specimen for study, and some electronic and ionic impact phenomena can be examined in a new and precise way in the ESEM. C. Specimen-Signal Interactions

This type of general interaction results primarily in signal modification and to a minor extent in specimen modification. Some signals are modified by the specimen such as the SE by a charged surface or the BSE by gross topographic undulations (by obstructing the BSE). These interactions are usually known as trajectory contrast (e.g. voltage and magnetic contrast). Much less attention has been given to the effect the signals could have on the specimen. This is because the signals escaping from the interaction volume have a lesser chance of striking back at the specimen and only under specific conditions might they affect the specimen such as the BSE directly striking protrusions of the specimen or indirectly returning at the specimen after multiple backscattering from various surfaces. Of greater importance might be the action of X-rays penetrating the specimen at much longer distances than the size of the interaction volume. D. Signal-Gas Interactions

The result of signal-gas interaction is a mutual modification both of the signal and the gas. This type of interaction is of extreme significance in the ESEM and is a new area of investigation for electron microscopists. As all

FOUNDATIONS OF ESEM

137

the microscopes in general operate under vacuum conditions, no studies under this category had taken place previously. Related studies in other fields have been done for purposes other than those of ESEM. The signal-gas interactions are various forms of particle (including photon) collisions and have been studied quite extensively in the respective fields of particle physics and radiation chemistry (plasma physics, electronic and ionic impact phenomena, ionization of gases, nuclear physics and so on). The effects of the gas on a particular signal and vice versa can be looked on as a first step in the chain of signal detection. This concept, namely, to use the gas as a detection medium as well as using the gas as environmental conditioning medium was first introduced by the present author (Danilatos, 1983a, 1983b). The gas modifies the different signals to varying degrees and it is possible that the conventional detectors (e.g. Everhart-Thornly detector) cannot operate in the traditional form or have to be modified; or new ones must be designed. The gas modification by the signals is similar to that caused by the primary beam except that it occurs over a much larger area. Furthermore, the spatial distribution of the products of signal-gas interaction is different from that of the beam-gas interaction, and this fact helps in separating the two effects. In a similar way, signals of different energy and spatial distributions may be separated from one another.

E. Gas-Specimen Interactions The gas-specimen interactions are as expected from the general physico-chemical reactions in studies outside electron microscopy. However, the products from the beam-gas and the signal-gas interaction may modify these reactions, or even initiate new reactions which could play a significant role in the overall performance of the ESEM. The gas-specimen interactions are part of a broader range of applications of the ESEM and their understanding will facilitate the proper use of this technique. Two examples of applications may be cited: (a) studies of oxide formation on metals, especially copper and iron which may be covered with oxide films of varying thickness (0.01 - 1 pm), and (b) embrittlement of metals (e.g. copper) in an environment where hydrogen can diffuse faster than water vapour, resulting in microcracks and holes at the grain boundaries (Wyman, loc. cit. in Dushman and Lafferty, 1962).

F. Beam-Signal Interactions The last combination of the four entities suggested in the opening of this section is that of beam-signal interaction. As no practical significance

138

G . D. DANILATOS

can be seen at present, the (direct) beam-signal interaction will not be considered in this study. However, the beam can affect the signals indirectly through its interaction with the gas (background noise). It is unknown if and under what conditions the specimen signals could indirectly modify the beam through their interaction with the gas (e.g. by strong ionization as in electrostatic pinch effect).

BEAMPROFILES IV. ELECTRON A . Formulation of Problem The electron distribution of a beam focused at a distance L below the PLA1, in vacuum, is modified when gas is introduced into the specimen chamber. It is of fundamental importance to know the details of the new electron distribution resulting from the collisions of electrons with gas molecules or atoms. A collision occurs when the electron passes within a characteristic area around the particle known as the total cross section aT. With each collision, the electron may loose some energy AE and become scattered through an angle 8 away from the initial direction. The average scattering angle and energy loss relative to the beam direction and energy (being in the keV range) are very small, and if the average number of collisions per electron m is not large, then the resultant average displacement from the original line of propagation is very small compared with the total distance travelled. Therefore, we can equate the distance travelled to the thickness of the gas layer through which the beam passes. Under these conditions, it can be easily shown that

m = u,nL (43) where n is the concentration of gas particles (see (1)). The mean free path of the electron L a , which is the average distance between successive collisions, is given by 1 L, = - = uTn

L - --

1.38 x

10-23

T

(44)

m uTP It is well known that the probability P ( x ) that the electron undergoes x number of collisions ( x = 0, 1, 2 . . .) is given by the Poisson distribution

In the case where the gas is sufficiently dilute, or the distance travelled very

FOUNDATIONS OF ESEM

139

small, so that the electron (almost) never suffers more than one collison, i.e. if

m << 1

(46)

then Eq. (45) reduces, for x = 1, to

P(1) = m ( l - m)

=I

rn

(47)

In other words, if we have either a single collision or none, then the probability that an electron collides is equal to the average number of collisions. The cross section is sometimes identified with the probability, but strictly speaking it is only an area which can be almost equal to the probability through Eqs. (43), (46) and (47). It is fortuitous that wT is generally a very small number so that by putting n = 1 atom/m3 and L = 1 rn, the condition (46) is satisfied and we can identify the cross section with probability: P(1) = a,. However, if we used units of the order of magnitude of a nucleus, then ffT > 1 and therefore ffTwould not be a probability. We need to calculate the probability distribution V l ( r ) , so that V,(r)27~r6r gives the probability that an electron, initially travelling on the axis of the circle with radius r , is scattered within the annulus 2nr 6r of a plane at distance L from the PLAl (see Fig. 7). The simplest case to consider first, is when the electron is unlikely to suffer more than one

1 d r J FIG.7: An electron travelling along the axis of PLAl undergoes a collision at a distance between z and z + dz through an angle between 8 and 68 and strikes a plane at a distance L from the aperture in an annulus between r and Sr.

140

G. D. DANILATOS

collision. In this case, the electron will fall within the annulus shown when two independent events happen in succession: (a) the electron travels a distance z without collision, an event with probability PI

PI

=

exp(-u,nz)

(48)

and (b) the electron undergoes a collision between z and z soiid angle 6R 6R = 2n- sin 0 SO

+ dz within the (49)

which is subtended by the annulus considered. The probability for this second event P2 is dU P --dflndz - dR where d a / d O is the differential cross section, which may be measured experimentally or predicted theoretically. Equation (50) is similar in meaning to (43) and denotes the average number of collisions. This also satisfies (46), because 652 can be taken arbitrarily small and thus (50) is a probability. The total probability that the electron strikes the annulus from anywhere along z is found by summing up the products P I P 2 :

V l ( r ) 2 mSr

=

loL

exp(-P,nz)

du

- SR n dz dfl

from which V l ( r ) = n exp(-u-,nL)

d u cos 0

d0

(52)

by use of Eq. (49) and expressing the integrand as a function of 0 from the geometry relations of Fig. 7. The only requirement for the integration of (52) is to know the differential cross section as a function of scattering angle. However, the assumption that an electron undergoes no more than one collision is only true for very low pressures, while for the most common pressures of ESEM we have m = 1 and even m = 2 or 3 as experiment has shown. In the most common case of m = 1 and according to ( 4 9 , we have about 37% of electrons suffering no collision, 37% suffering a single collision, 18% two collisions, 6% three collisions, 1.5% four collisions etc., and therefore we cannot be certain about how realistic the predictions are from (52). A derivation of probability distribution V ( r ) for plural scattering of electrons has been published by Jost and Kessler (1963) who based it on earlier theory for the angular distribution of electrons scattered through a

141

FOUNDATIONS OF ESEM

medium (Bothe, 1921; Molikre, 1948). With an average number of electron collisions m,this probability distribution is

zi, [Jo(rt){exp[-m(1

V(r) = where

h(t)

=

-?? UTL 0

{I

L

- h(t))]-exp(-m)}t

dt

(53)

du dz }Jo(rt)r dr d o L - z ( L - Z)*

-

and Jo( ) is the Bessel function of zero order. The above derivation is valid only if small scattering angles 13 = r / ( L - z ) are considered, a condition which is fulfilled in the ESEM as most of the electrons fall within a cone with semi-apex angle or lo-’ rad. However, there are two major difficulties with Eq. (53). First, we need to know the differential cross section for various gases in the energy range, 5-50 keV. These are not readily available for the most common gases such as NZ, 0, and H20 either experimentally or theoretically. The second difficulty is to carry out the triple integration for Eq. (53), because the integrands are oscillating functions of varying frequency and amplitude, and the numerical integration requires a long computer time. This difficulty may be aggravated by the complexity of the expression for the differential cross section, which is unavoidable for molecular gases. A further difficulty is added by the fact that Eq. (53) gives the distribution of electrons initially travelling within an infinitely narrow electron beam, but in the real situation the incident beam has a finite distribution of electrons which must be convoluted with (53). Hence, additional integrations are required to answer completely the question of beam distribution in the gas. Monte-Carlo computations have been extensively used for solid targets, but much less so for gases. These computations may also require a long time for the beam profile in the immediate vicinity of the original spot, because only a small fraction of electrons fall within this region. Furthermore, this method involves some averages or other drastic assumptions which may only hide the uncertainties. In the remainder of this section, we follow the analytical method of Eq. (53) and we survey the problems in the determination of differential cross sections, followed by the beam profiles for an infinitely narrow beam and then by a Gaussian distribution incident beam. Finally, these conclusions are compared with experimental measurements. The aim here is to formalize the problem for the ESEM in a rigorous way, so that more precise solutions can be worked out or retrieved from the literature during later work.

142

G . D. DANILATOS

B. Scattering Cross Sections Both differential and total cross sections are needed for our problem. A cross section is associated not only with electron scattering through a given angle but also with other types of reaction such as ionization, excitation, dissociation, molecular rotation, vibration, etc. Each interaction j is characterized by a cross section uj,the sum of which is the total cross section

so that the probability Pi,that the j reaction occurs, is

The various types of cross sections are frequently classified either as elastic, when only negligible electron energy transfer to the nucleus of the atom takes place, in the electron energy range used in the SEM, or inelastic in all other cases. We examine these two types first for monatomic and then for molecular gases. There seems to be considerable difficulty in establishing a universal theory of cross sections for all gases that can be confirmed by experiment (see Kessler, 1964a, 1964b); to attempt to review or resolve questions on electron scattering theory here would be a deviation from the initial purposes of this survey. However, some representative works are quoted to help the reader towards a more comprehensive study on the subject. Early work was done by Moliere (1948), Leisegang (1952) and Lenz (1954), and later by Burge and Smith (1962), Tavard (1969) and Bonham (1978). More thorough treatments and data can be found in the theory on atomic collisions by Mott and Massey (1965) and the books on electronic and ionic phenomena by Massey (1969) and Massey and Burhop (1969). 1. Monatomic Gases Geiger (1963,1964a) has published theoretical and experimental results for differential cross sections on the noble gases N, A, Kr and Xe, for electron energies between 37-100 keV and 5-65 mrad angle, and for He at 25 keV between 2.3 x lop4and 4 x lo-* rad. Similar work on A, Kr and Xe has been reported also by Fink and Kessler (1966). Wellenstein et al. (1973) have obtained differential cross sections on He for some angles at 25 keV. Ketkar and Bonham (1985) reported small angle absolute elastic

143

FOUNDATIONS OF ESEM

cross sections for 25 keV for He and found that their results agreed only partially with earlier reports. The experimental data available on cross sections are definitely inadequate to be used for integration of Eq. (53) and some of the theoretical derivations are not easy to apply in this case. So it was decided to adopt the same theoretical formulae used by Jost and Kessler (1963) for du/df2. This decision was aided by the fact that Jost and Kessler presented an analytical solution for two out of the three integrations in (53), thus leaving only one to be executed by numerical methods as will be seen later. These formulae based on the expressions originally given by Lenz (1954) are

due

--

dR dai

--

dR

A2

-

16[sin2($

-

(elastic)

+ sin2(2)y

o2 + (82

+

0; + 20; 8’,)(02 + 82, + 8;)’

(inelastic)

(57)

where 80 = A/2rR

J - 4E

8 --

and

A =

47T4uL

with A the electron wavelength given by A = 1.226 X lop9 [V(1 4- 0.9778

V)]-”*

(61) and V the accelerating voltage in Volts, k the atom radius, J the ionization energy, E the electron beam energy (in eV) and Eo = 511000 eV, the rest m (Bohr radius). electron energy, uH = 5.29 x The expressions (56) and (57) give good predictions for certain elements (Lenz, 1954) but they deviate outside a limited angular range for most elements (Kessler, 1964a, 1964b). A difficulty appears to be in determining the atom radius R.This is an effective distance over which the nucleus of an atom is active, since it is screened by the orbiting electrons. This enters in the Wentzel (1927) atom model for the potential: e2Z U ( r ) = -4m O r X

144

G. D. DANILATOS

Various derivations for R have been proposed, e.g. Williams (1939) and Leisegang (1952), and a discussion on this question can be found also in the paper by Burge and Smith (1962). From this last reference we adopted the expression:

which yields values compatible with the measured scattering amplitudes for electrons h(0)published by Ibers and Vainshtein (1962). Another difficulty is the choice of the correct ionization energy J . One possibility is to choose the first ionization potential of the atom. Reimer in his book (1985) quotes J as the mean ionization potential estimated by an expression proposed by Sternheimer (1966) for the mean excitation potential: J = 9.762 + 58.8Z-0,'9 (J in eV) (64) Massey (1952) has tabled differing values for the energy loss of inelastically scattered electrons from previous workers. He notes that the calculation of J cannot be carried out with any accuracy except for atomic hydrogen and suggests that J be determined experimentally once and for all for a particular substance at a given beam energy. In this work, J is taken equal to the first ionization potential but it should be adjusted in future work in accordance with prevailing theories and experimental data. The values used are given in Table VI together with the values for scattering amplitudes h(0)from Ibers and Vainshtein (1962). The expression (57) for the inelastic differential cross section is valid for

TABLE VI VALUES OF ATOMIC NUMBER Z , IONIZATION ENERGY J A N D SCATTERING AMPLITUDES &(O) FOR VARIOUS ATOMS

A H He N Ne 0

Z

. !(eV)

18 1 2 7 10 8

15.75 13.59 24.48 14.53 21.56 13.61

fa@)

x 10"' (m)

4.71 0.529 0.445 2.2 1.66 2.01

FOUNDATIONS OF ESEM

145 Z=18

O C UIO

E = 10000 J = 15 75 -18

31 0

-19 C

2 5

-20

L n

-21

2

-P

-22

c

-23

c U

-24

f

-25

\

1 ,

-5 -4 -3 -2 -1 0 1 Scattering angle Log 0, rad FIG.8: The differential cross section (elastic, inelastic and total) vs. scattering angle for argon with E and I as shown. -6

angles less than 0.17 rad (lo"), while Eq. (56) for the elastic differential cross section is valid for all angles. These are plotted for argon with the given parameters shown in Fig. 8. It is observed that the inelastic component prevails below 0.01 rad whilst the elastic prevails above 0.1 rad, so that the inelastic term is not needed in the region in which Eq. (57) is not valid. Both the elastic and inelastic components level off below some characteristic angle corresponding to those given by Eqs. (58) and (59). The quantum mechanical significance of this is that it is unlikely to observe an electron scattered below these angles. The effect of varying the beam energy can be seen in Fig. 9, where the total differential cross section for argon has been plotted at different energies. A useful quantity, the meaning of which is more obvious, is the cross section resulting in electron scattering at an angle greater than 8:

This has been plotted in Fig. 10, again for argon, with different electron beam energies. An important observation is that u(>77/2) is about one thousand times smaller than the total cross section, and therefore the

146

G. D . DANILATOS

z = 18

J = 15.75

0

E= 5000

J

-26

10000

\\' I

-6

-5

I

I

I

I

-L

-3

-2

-1

\\

20000 50000

'

100000

I

t

0

1

Scattering angle Loge. tad FIG.9: The total differential cross section vs. scattering angle at different beam energies shown, for argon.

Z=18 J = 15.75

-5

-L

-3 -2 -1 0 Scattering angle Loge. md

1

FIG.10: The cross-section for scattering into angles greater than 0 vs. 0, at different beam energies and fixed J (solid curves), for argon. By changing only J at 5000 eV, the result is shown by dashed curve.

147

FOUNDATIONS OF ESEM

backscattered electrons from the gas should represent a negligible fraction of electrons, especially because m does not exceed a few units in the case of the ESEM. This is of significance when considering the signal-to-noise ratio as will be seen later. The effect of choosing a different value for J results in a major change of the cross section at small scattering angles. This is shown by the dashed line computed for J = 209.6 eV as determined by Eq. (64). Changes at small scattering angles are important in the determination of beam profiles. For example, a beam spot of 10 nm, one mm from the PLA1, subtends a semiangle of 5 x lop6 rad. The total cross sections are frequently referred to in work on ESEM, and they are plotted in Fig. 11 for some monatomic gases versus electron beam energy. The curve for atomic oxygen is very close and slightly below that of neon, and the curve for atomic hydrogen is just above that of helium but they are not drawn for clarity. They all have been obtained by rad) up to v numerical integration of Eq. (65) from very small angles ( and found to coincide with an analytical expression derived by Jost and

Atoms

0

5

10 15 20 25 30 35 Accelerating voltage. keV

60

L5

FIG.11: The total cross section of atomic gases vs. beam accelerating voltage.

148

G. D. DANILATOS

Kessler (1963), an alternative form of which is:

where The numerical integration of Eq. (65) to find aT is not needed for monatomic gases in view of (66), but it was carried out as a test of the correctness of our previous calculations and of a computational program for the total molecular cross sections to follow. 2.

Molecular Gases

The total scattering cross section for a molecule is not simply the sum of elastic and inelastic cross sections. Additional effects are present due to binding of atoms in molecules, because the outer region is primarily responsible for scattering at the smallest angles. There is a severe lack of information especially for the most common gases such as H 2 0 , O2 and N2, and for the electron energies used in the ESEM. The scarce information available is not in a form able to provide a ready answer to our problem of electron beam profiles as they occur in the ESEM. Geiger (1964b) has published experimental and theoretical data for differential scattering sections of molecular hydrogen in the angular range 7 x lop4 < 6 < 4.3 x at 25 keV. Fink and Kessler (1967) have presented similar data for differential cross sections of N, and O2 at 35 and 60 keV in the < 0 < 70 x Further work has been reangular range 5 x ported by Liu (1973) and Ulsh et al. (1974) on the binding effects for H2 obtained by electron scattering at 25 keV. An attempt is made below to calculate molecular cross sections according to the theory found in the book by Mott and Massey (1965). First we consider the elastic cross section of the molecule. For many scattering centres, as the atoms in a molecule, let the minimum distance between centres be do and the maximum range of interaction of the incident electron be r , . In the case of coherent scattering and if

2 ndo

-> >1

A

and do

r,,

(69)

FOUNDATIONS OF ESEM

149

2.rrdo/h

r, x 1o'Om

H2 N2 0 2

H2O

rzl x 10"m

5 keV

25 keV

5 keV

25 keV

0.7461 1.0975 1.208 0.9584 0.9584 1.5151

0.039 0.211 0.216

0.018 0.098 0.099

27 40 44

61 90 99

35

78

we can apply the following derivation for the elastic differential cross section of the molecule:

where s = 4~ sin (8/2)/A and rni is the distance between atoms n and J. The function fn(f3) is the scattering amplitude from which we get

da, = Ifn(13)12 dR

(for the nth atom)

and thus we have an expression for f(13) from Eq. (56). Next we proceed to examine whether conditions ( 6 8 ) and (69) are satisfied. The do values have been taken from a Handbook on Physics and Chemistry Constants (CRC Press, Inc., 1977) and are presented in Table VII. As the maximum range of interaction can be taken to be the radius of the total elastic cross section of the atom rm = (u~.,-/T)'/~, of which values have been calculated for 5 and 25 keV in Table VII. In the same table are shown the values of 2 r d o / h . From these results, it is seen that condition (68) is satisfied adequately, while (69) is not very satisfactory. This condition becomes better at higher beam energies (shorter electron wavelengths). It is within the limitations of this approximation that Eq. (70) is integrated later in calculating the total molecular cross sections. The case of inelastic cross sections can be considered under incoherent scattering and should suffice for this work to take the sum of the individual atom cross sections as a first approximation: duii -dwi _ - (over all J atoms) dR ; df2

C

G. D. DANILATOS

150

zO1 20

18

--

16

-

I

NE TI.-

-.

.-d

e

$12

2

-

Molecules

10-

u) 0

:8 z

-

G 6-

e

L-

2-

0

I

0

5

1

I

I

LO

L5

I

10 15 20 25 30 35 Accelerating voltage, keV

FIG.12: The total cross section of some molecular gases vs. beam accelerating voltage.

By numerical integration of the sum of Eqs. (71) and (72), the total molecular cross sections of some gases have been calculated and plotted versus beam energy in Fig. 12. The curve for O2 lies just below that of N2 and is not shown for clarity. C . Profiles of Infinitely Narrow Beam

Having discussed some of the problems in finding the differential cross sections we proceed to integrate Eq. (53) which yields the profile of those electrons which have undergone collisions with the gas. This equation will be applied to monatomic gases for which the differential cross sections (56) and (57) allow two out of the three integrals to be evaluated analytically leaving only one for numerical computation. Some important conclusions will be drawn and similar conclusions should be applicable to molecular gases. The total differential cross section du/dR is found by the sum of (56) and (57):

151

FOUNDATIONS OF ESEM

in which it has been assumed that

og << 0;

(74) and only small angles are considered so that sin(O/2) = 0/2. Jost and Kessler made no mention of condition (74) and it must have been tacitly assumed. However, it is important to stress its existence because it may not always be satisfied. It is valid for high accelerating voltages and low ionization energy. We can check that for the ranges considered here, this condition is satisfied. For E = 5 keV and J = 15.75 eV, Oo = 0.104 and eE = 7.8 x while for J = 209 eV, 00 = 0.104 and OE = 1.05 x so that o', < 0;. Eventually, after integration, as has beeen shown in the Jost and Kessler paper, the probability distribution for the scattered electrons is given by

where the radial distance r has been replaced with the reduced radial distance p:

By doing this substitution, the beam profiles plotted against p do not depend on the actual dimensions rand L separately but on r / L and there is one to one correspondence between p and r , if all other parameters are fixed. Equivalently, p is the number of units ro in r with ro = 0,L. The remainder of the quantities in Eq. (75) are as follows:

=

z

-($ [ - 1- 4 -k

T )JI(T)PO(.)I In p ( Z - W J O ( ~ ) H I (-

4[Jo(@)Hi(P'd - Ji(p7)Ho(P7)1 +

(:)[Jo(T)

-

L,(pT)l}

152

G. D. DANILATOS

the second kind of order v , H , the Struve’s function of order v , and KOthe modified Bessel function of the second kind of zero order. These transcendental functions are series of infinite terms and they can be approximated by a simple expression for large enough values of the independent variable. For the numerical integration of Eq. (75), a minimum number of terms and expressions were established for a corresponding domain of the independent variable. It must be stressed that V ( p ) is a true probability distribution for which

a relation to be referred to in the interpretation of our results. Jost and Kessler have presented results of integration in a range p > 0.03 for argon and krypton, but we are clearly interested also in values of at least three orders of magnitude less than that, since for a beam spot of r = 5 nm, distance L = 1 mm and E = 5 keV, we need p = 5 x lo-’ or less. This low range of p presented particular problems during numerical integration on a VAX system. The integrand is a fast oscillating function composed of several oscillating factors with different frequencies and varying amplitude of oscillation, the nature of which depends strongly on the particular set of parameters chosen. The practical upper limit of integration shifts to higher values in inverse proportion to p. The amplitude of oscillations as well as the total value of the integrand also increase with a decrease of p. A consequence of this was that the “Simpson” (used also by Jost and Kessler) and “Romberg” method for numerical integration used from the International Maths Science Library (IMSL) took unacceptably long times, because the integrand was evaluated a large number of times within each oscillation. However, the “Gaussian” method using a preset number of evaluations of the integrand at random points proved much more efficient. It was possible to perform seventy integrations in an average time of 10 minutes, and this gave sufficient points for V ( p ) to.be plotted in the range lo-’ < p < lo2. The first result tried was for argon with identical parameters to those used in the Jost and Kessler paper, namely, E = 50000 eV, R = 1.76 x lo-” m and m = 6.8. As there is no mention or discussion of the value used for J , or the possible effect it might have on the curve fitting for their experimental results, different values were tried here. Values for J between 10-25 eV produced almost identical curves in their range lo-’ < p < 10. So it was decided to use the first ionization potential J = 15.75 eV for argon, and V ( p ) is shown in Fig. 13 in the range lo-’ < p < l o 2 . Additional results for V ( p ) are also shown in this figure and the next (Fig. 14)

153

FOUNDATIONS OF ESEM

Z=18. E=50000, J

E

15 75

1

!

I

I

-5

-L

-3

-12

I

1

1

1

-2 -1 0 Reduced radial distance Logp

1

FIG. 13: The probability distribution vs. reduced radial distance for different average number of collisions m.

6L-

>

2?

2-

-

0-

A

.-‘0

-r

f

x

-z

-

-2-

-L-

-

E -? : -8-

-10-

-12-5

I

I

I

-4

-3

-2

1

I

-1 0 Reduced radial distance Logp

1

2

FIG.14: The probability distribution vs. reduced radial distance for different average number of collisions m .

154

G . D . DANILATOS

Z~l8.E=50000. J~15.75

I O

10.8W

-5

-4

-3 -2 -1 0 Reduced radial distance Logp

1

2

FIG, 15: The cumulative probability vs. reduced radial distance for different average number of collisions rn.

for different values of rn. We then consider the cumulative probability C ( p )

W)=

i:’

V(P’)2TP’ d p ‘ ,

which gives the probability that an electron is scattered within a circle of radius p. The latter curve reaches the value of 1, as it should, according to Eq. (77). This result together with the ability to reproduce several of the Jost and Kessler curves created confidence in the present computations. This is stated because the condition (77) could not be reproduced when values of rn lower than about four or five were tried as shown in Figs. 15 and 16. This came as a surprise at first, but it was soon realized that such a result should be expected. That C ( p ) does not reach unity implies that some electrons are unaccounted for and should be found outside the range of p considered and in particular somewhere below lo-’. The missing electrons could not be found in the region below this point and should not be anywhere for which p > 0 (positive). Therefore, they must be on the axis of the (infinitely thin) beam and they constitute a purely unscattered fraction of electrons. This is confirmed by the fact that the missing fraction of electrons 1 - C, is exactly equal to the transmitted fraction given by the exponential exp (-m)for each case shown in Figs. 15 and 16 (2, is the asymptotic value of C ( p ) at high values of p ) . Hence the profile of the beam

FOUNDATIONS OF ESEM

155

2-10.E. 5OOOO. J.15.75

Reduced radial distance Logp

FIG.16: The cumulative probability vs. reduced radial distance for different average number of collisions m.

P ( p ) can be written formally: P(p)

=

%) e P m+ V(p) =P

where 6 ( p ) is the delta function and

The distinction between low and high m is not considered by Jost and Kessler. This can lead to incorrect calculations when the experimental data are normalized to satisfy (77), instead of the area under the experimental curves being set equal to 1 - exp(-rn) according to (78'). We now examine the effect of other parameters. Fig. 17 shows two sets of curves corresponding to E = 50000 eV and 5000 eV. A difference appears only towards low values of p. A variation of J by the same factor would have the same effect in the opposite direction through Eq. (67). With m = 1, a variation of R from 1.76 x lo-" m to 2.6 x lo-" m has no visible effect above p = 10-1 and negligible below this point (not shown in the figure here). Therefore, it is not clear why Jost and Kessler varied only R to fit their experimental data (especially when this has a small effect in the region worked by them) and not other parameters as well (e.g. J ) .

156

G. D. DANILATOS

-5

-L

-3 -2 -1 0 Reduced radial distance Log p

1

2

FIG. 17: The probability distribution and the cumulative probability vs. reduced radial distance for two different beam energies.

-5

-L

-3 -2 -1 0 Reduced radial distance Logp

1

2

FIG. 18: The probability distribution and the cumulative probability vs. reduced radial distance for two different gases (helium and argon).

FOUNDATIONS OF ESEM

157

Perhaps, it is because they did not consider Eq. (78), and the undue normalization of their experimental data (at the low values of m) produced an erroneous base for fitting the theory. Finally in Fig. 18, we examine the effect of atomic number for 2 = 18 and Z = 2 when m = 1. Here we note a change occurring towards high values of p. At high values of p we see the effects of elastic scattering and the difference should be attributed to the different number of elastic scattering me events corresponding to (concurrent with) m = 1 (total average number of collisions including inelastic ones). Kessler (1964b) pointed out that by considering different gases with m , = constant, the curves V ( p ) lie very close to each other despite the fact that m is very different. However, different values for m result in different V(p) for low values of p, a region in which we are interested for this work, whilst Kessler considered the region p > 0.03. Hence we should consider all collisions, both elastic and inelastic, because all deflections can have an important effect on the beam profiles from the electron microscopy point of view. It is true that for m, (elastic) sufficiently high, the electron distribution in a gas depends practically on the elastic cross sections, but we are not interested only in this regime.

D . Electron Skirt Width In the flow visualization and local gas density measurements in rarefied gases by means of electron beam probes, Schumacher (1968) reported that the central beam does not just broaden, but it rather acquires a “skirt” of scattered electrons around it, and he referred to this phenomenon as “skirting”. This visual observation is in agreement with the conclusions of the previous analysis and the phenomenon has far-reaching consequences for ESEM. It means that it is possible to use the unscattered fraction of the original incident beam without broadening, provided the original spot is much smaller that the width of the electron skirt acquired and contains sufficient current for contrast. Therefore, it is necessary to study the behaviour of the electron skirt in the special pressure range in which it occurs. This range may be described as any pressure which by (an arbitrary) definition allows more than 5% of the original electrons to pass unscattered, and it corresponds to a maximum m = 3 . The important conclusion is that the ESEM is characterized by a scattering regime which is not necessarily single scattering. A single scattering regime should be one in which, say, 95% of the electrons suffer either zero or one scattering event. This single scattering condition corresponds to m < 0.355 as can be found from Eq. (45). The ESEM range cannot be referred to as plural

158

G. D . DANILATOS

scattering either, because this means that the average number of elastic collisions is between 1 and 25, for electron beam energies 10-30 keV according to Cosslett and Thomas (1964). In the region of plural scattering, the profiles of scattered electrons are not Gaussian but they become so in the next region (me > 25) called multiple scattering. Since frequent reference will be made to the characteristic case where m is no more than about 3 or 4, it is helpful to introduce a term describing this new situation. It is suggested we use the modifier olzgo (Greek adjective oligos = few, little) for the term oligo-scattering, in the same way as single, plural and multiple scattering. It will be shown below, that the oligo-scattering region can be distinguished from the remainder of plural scattering by a different law for the electron skirt width broadening. Customarily, the half-width of a beam is defined as that which contains half of the total current. However, no distinction has been made between the unscattered and the scattered (skirt) fraction. One of the reasons could be that most work was done for solid targets in which the skirt width is of the same order of magnitude as the original spot width and the two fractions of electrons overlap. In the small amount of work found on beam broadening measurements in gases, no distinction of the oligo-scattering region is made, either, from what is generally known as plural scattering. The reason might be that no special interest existed for this particular region as happens with the ESEM. We will now review some beam broadening derivations from past work following some observations based on the previous analysis. Let us define the half width radius r1/2, or reduced radius p 1 / 2 ,as that which contains half of the skirt electrons. The unscattered fraction belonging to the infinitely thin beam is first subtracted from the total current, and it is the remainder that is characterized by a broadening measured with the half width. Referring to Figs. 15 and 16, the half width was measured versus m from each corresponding curve and the results are shown in Fig. 19. There are extra points in the figure corresponding to curves not shown in Figs. 15 and 16. The points seem to fall on an “S”-like curve which levels off for m + 0 without passing through p1,2 = 0. This is a reasonable finding which means that the electron skirt width is finite for m 0 but the corresponding probability V ( p ) + 0. In other words, at extremely low gas pressures there are unlikely to be electron collisions, but whenever they occur, they will result in a finite width shown in Fig. 19. The part of the sigmoidal curve in the oligo-scattering region may be closely fitted with the curve: ---f

plI2 = 0.08

+ 0.0848 m1.38

(79) Between m = 3 and m = 7, there is practically a straight line relationship and beyond that the curve is concave downwards. Thus, the

FOUNDATIONS OF ESEM

159

2 = 18 E =5OM)O I I

I /

/ /

P , , ~ =0 08. 0 085 m”e

I

Computed /

0 ’

OR0

-4 0

1

2

3 L 5 6 7 8 A v e r o g e number of collisions rn

9

10

FIG.19: The reduced skirt radius vs. average number of collisions from computed results as in Fig. 15 (points and solid curve). The points with rn < 3 are fitted with the dashed curve.

straight line corresponds to the transition from oligo-scattering into the total plural scattering region where practically all the electrons have suffered at least one collision. It is interesting that similar shapes have been reported by Gentsch et al. (1974) for large objective diaphragms of the transmission scanning electron microscope following Monte-Carlo computations. Also, the present results are compatible with those obtained by Reimer et al. (1970) who used the Jost and Kessler theory and MonteCarlo calculations for carbon with m > 5. However, these results were seen approximately as linear, and on this assumption it was found that r1/2

- L2

(80)

However, if we use Eq. (79) and write

m

=

22 uT

7.243 x 10 - p L T

(by combining Eqs. (43) and (l)),we finally obtain in terms of real radius r I l 2

rl12 = 0.0039 L provided

+ 0.00155 L ( P L ) ’ . ~ ~

m < 3 or, equivalently, p L < 6

(82)

(83)

G . D. DANILATOS

160 50

E

I

lrnm

50000

-

L =05mrn 0

500

1000

1500

2000

Pressure p . Pa

FIG.20: The skirt radius vs. chamber pressure at different specimen distances.

From Eq. (82) it is seen that there is no equivalence between distance L and pressure p as far as the electron skirt is concerned. Such an equivalence, though, is valid for the unscattered fraction of the total beam, i.e. an increase of pressure is equivalent to an increase of distance. The two different effects of varying either the pressure at fixed specimen distance or the specimen distance at fixed chamber pressure is shown in Figs. 20 and 21, respectively. In Fig. 21 all curves at pressures less than 1 Pa coincide with the curve at p = 1 Pa, and the electron skirt broadening is independent of pressure and depends only on distance. Next, we examine the effect of varying the accelerating voltage. From the present computations, Figure 22 shows that the reduced width decreases little with accelerating voltage but when plI2 is replaced by r (see Eqs. (76) and (61)), the variation is in fact significant. Relations like (82) have been derived for argon and helium at 10 keV and T = 293 K as follows: Argon:

r1/2 = 0.0096 L

+ 0.0169 L(PL)'.'~

(84)

Helium:

r1/2 = 0.0027 L

+ 0.00014 L ( P L ) ' . * ~

(85)

161

FOUNDATIONS OF ESEM 100 -

90 80

-

70

-

Z = 18 E = 10000 1000 Pa

5 60 N \

50

-

v)

.-3

40K

30 20 10

-

4 5 6 7 8 9 10 Distance L, rnm FIG.21: The skirt radius vs. specimen distance at different chamber pressures. 0

1

2

3

0 6-

--

rw

m :1 2 :18

0 5-

a

*2 0 L -

U

0

c

3-

0 0

*-*

2 0 2(L

0 0

10

20 30 Accelerating voltage, keV

FIG.22: The reduced skirt radius vs. accelerating voltage.

LO

50

162

G . D. DANILATOS

Various derivations for beam broadening have been proposed in past work but they differ from the ones derived above, presumably for the reason that the others are applicable in the total plural scattering regime. One such derivation is given by Eq. (80). An alternative derivation is r1/2 =

which has been adapted from Reimer (1985) to include pressure and to be in SI units (E in eV). Goldstein et a1 (1977) had previously derived the same formula except with a numerical factor 5.95 times larger. Smith and Schumacher (1974) have also produced a formula for the half width broadening given by

which has also been adapted for our purposes. A comparison between the various derivations is made by a numerical example: for m = 3 up to which the present derivation is valid, the corresponding pressure for helium is about 30 kPa, for L = 0.001 m, and we obtain by Eq. (85), r l I 2 = 13 p m ; by (86), we obtain r112 = 23 pm, by (87), rl12 = 57.8 pm and by Goldstein et al., 136.8 p m . Therefore, there is still no universal formula to express the “beam broadening” without qualifications. The present analysis may help for more precise calculations in the future and should be correct in distinguishing the two regions of plural scattering, but the numerical values depend on the correctness of the formulae for the differential cross-sections (Lenz’s theory). Previous derivations may represent the region where the plural scattering has been fully developed but there is still no agreement amongst those derivations.

E. Profiles of Finite Width Beam The preceding analysis helps to understand the behaviour of very thin electron beams, but in reality every beam has a finite width and we must express quantitatively what effect the width has on the previous conclusions and what new conclusions can be drawn for the real situation.

163

FOUNDATIONS OF ESEM

The distribution of electrons in the incident beam prior to its entry in the gas can be expressed by the Gaussian function

5 which gives the probability that an electron is located in the annulus 2 ~ d5 by Go(5)27r5d5 so that

J-:

Go(5PT5 d5

=

(89)

1

The constant E is the standard deviation and can be used as a measure of the beam width. For a parallel beam, we can initially assume that the number of electrons left unscattered in the beam diminishes exponentially and uniformly as the beam propagates through the gas. At a given distance from PLAl and pressure, the average number of collisions per electron is M ,so that the distribution probability G(5) to find an electron without any collision at this distance is given by

At the plane normal to the beam axis, at the distance considered above (i.e. at the specimen distance corresponding to m collisions), two types of electron will be arriving: those unscattered electrons described by Eq. (90) and those which have suffered any number of collisions. The density of scattered electrons at point A (see Fig. 23) on this plane is composed by the superposition of the densities of all electron skirts belonging to all the thin beams arriving at any point B of the plane at distance (from the axis of the incident beam. Each of these thin beams has an infinitesimal area p' dw dp' and is located a distance p' from the point A . The initial (incident) current probability of each point B is Go(5)p' dw d p ' , which, when multiplied by V ( p ' ) , yields the contribution of this elementary thin beam to the scattered electrons at A . The integration over the whole plane is the probability S ( p ) to find a scattered electron in the neighbourhood of A: S(P) =

J-- J- *=

The various lengths 5, p, p' and as before.

F

V(P')G"(S)P' dw

4'

(91)

are measured in reduced units of length

164

G . D. DANILATOS

FIG.23: The initial number of electrons contained in an element p’dwdp’ around a point B at a distance 6 from the axis of the Gaussian distribution (of the incident beam) makes a contribution of scattered electrons at point A located p units from the axis and p’ from B on the plane shown (at the specimen level).

Because t2= p2 + pI2 + 2pp’ cos w , we can separate variables and integrate with respect to w as follows:

where I,( ) is the modified Bessel function of the first kind of zero order. Therefore, the convolution of the two distributions (75) and (88) requires a second numerical integration for the answer sought in our initial problem. It must be stressed again that Eq. (92) is the probability for a scattered electron to be found in the vicinity of a point A at distance p from the beam axis. The cumulative probability J0pS(p’)27rpf dp’ is less than one, if there are some electrons which have not undergone any collision, but if we add those electrons given by Eq. (90), we obtain the total electron profile P ( p ) : f Y P ) = G ( P ) + S(P)

for which we always get

(93)

165

FOUNDATIONS OF ESEM

The total cumulative probability C ( p ) is now defined by C(p) =

lop

P ( p ” ) 2 4 ’ dp”

(95)

A numerical integration of Eq. (92) was performed. The integrand of (92) is a narrow, bell-shaped function, the width of which depends on E and the peak of which moves with p. A special iteration subroutine was written for the numerical evaluation which was repeated 70 times to obtain an equal number of points on a logarithmic scale in the range lop5 < p < 10’. To feel the magnitudes in this range, it is helpful to convert the reduced variable to real length: for the particular case when L = 1 mm and E = 10 keV, we find that p = lop5 corresponds to 0.1 nm, p = 1 corresponds to 110 p m and p = 100 corresponds to 11 rnm. Further, for L = 10 pm, all corresponding radii become 100 times smaller, a case which is significant for near atmospheric pressure. We thus cover a very wide range of radial distance within which practically all of the electrons fall under conditions of oligo-scattering. A typical set of results is presented below to describe some important effects. Initially, we consider a fine electron beam with E = being a value commonly found in SEM. In Fig. 24, the functions G&), S(p), P(p)

10

00

-3

0 1 2 Reduced radial distance LOgp FIG.24: The probability distribution of incident Go, scattered only S and total profile of electrons P, together with the cumulative probability vs. reduced radial distance, for the fixed parameters given on top.

-5

-L

-2

-1

166

G. D. DANILATOS

-5

-L

-3 -2 -1 0 Reduced radial distance Logp

1

2

FIG.25: The cumulative probability vs. reduced radial distance with different values of m.

and Z ( p ) are shown simultaneously. The first check is to observe that C ( p ) eventually approaches unity, which satisfies Eq. (94), and we are sure that practically all electrons are accounted for in the range chosen. Both C ( p ) and P ( p ) show two transition regions corresponding to the unscattered and scattered electrons, respectively. The beam profile is practically identical to the profile of unscattered electrons for short radial distance and also almost identical with V ( p )at large radial distance. V ( p )and S(p) differ only towards low values of p. The effect which a variation of rn causes can be seen in Fig. 25 where E = A better perspective is gained by using a linear scale to plot the same results in the neighborhood of the initial spot (see Fig. 26). The abrupt change of Z ( p ) between 0 and some limiting value over a short distance indicates that the spot can be used as a probe having a diameter the same as this transition distance. The corresponding beam profiles on linear axes are shown in Fig. 27. The profiles remain essentially Gaussian with constant E but of a lower intensity. The same conclusion applies for beams with E up to 0.01 which is much smaller than the width of the electron skirt. The beam diameter customarily obtained from pIl2 (i.e. the circle containing half of the total current-see Jost and Kessler) has no useful meaning here. This can be seen by drawing a horizontal line at C ( p ) = 0.5 and noticing the points of intersection with the curves (e.g. in Fig. 25). The

,

l,o

167

FOUNDATIONS OF ESEM Z~18.E~10000~J~15~75,~s0.0~1

m-0.5

1

2

0

2 c 6 8 Reduced radial distance p x l O ’

10

FIG.26: The cumulative probability vs. linear reduced radial distance with different values of m .

0

i

2

3

L

Reduced radial distance p x 1 0 3

FIG.27: The probability distribution of incident and total profile of electrons corresponding to Fig. 26 vs. linear reduced distance.

168

G . D. DANILATOS

point of intersection may be anywhere on two very distinct beams: the unscattered primary and the electron skirt, which play a different role in contrast and resolution. The p I l 2 remains a meaningful quantity for electron beam welders where power is the important quantity, and also in transmission microscopy where the much denser (than gas) specimens correspond to very short travel thickness (i.e. L is short) and where G(p) and S(p) are indistinguishable. Next we examine the profiles as E approaches the radius of the skirt which can be obtained from Fig. 19. For E = 0.1, Z(p) is plotted on linear axes for different values of m (see Fig. 28). It is observed that the initial beam profile becomes less well defined as rn increases. The corresponding P(p) are shown in Fig. 29 which at first sight indicate well-defined beams without appreciable change of diameter. However, this can be deceptive, if it is not noted that for higher m the tail signal level is comparable to the peak value, and the relative signal strength is low (high background level). For E = 1 and beyond, the original beam merges with the electron skirt and scattering becomes less important as can be seen in Fig. 30. The case for E = 10 is not shown because the curves are not easily distinguishable from the original Co(p). In the latter case, the original beam diameter is much larger than the electron skirt, and scattering becomes unimportant. It should be noted that the absolute values of the probability distribution

0

0L 06 08 Reduced radial distance p

02

10

FIG.28: The cumulative probability vs. linear reduced radial distance with different values of m , and F one order of magnitude less than the size of electron skirt.

169

FOUNDATIONS OF ESEM

3

Reduced radial distance D

FIG.29: The probability distribution of incident and total profile of electrons corresponding to Fig. 28 vs. linear reduced distance.

,-,

Z ~18,E=10000.J:15.75.E:1

0

1

0-16

C

2

0 lo-.

e

OOL-

a

0 02-

2 3 L Reduced radial distance p

5

FIG.30: The probability distribution of incident and total profile of electrons vs. linear reduced distance, when the size of the incident beam is the same order of magnitude as the size of the electron skirt ( E = 1).

170

G . D . DANILATOS

decrease proportionally to the square of E and this should be distinguised from the actual current distribution level which is obtained by multiplying the probability by the total beam current. An important observation is that as e increases, the useful spot current is above the exponential decay of the unscattered electron beam. This can be seen in Fig. 31, where the exponential function exp(-rn) is compared with the total beam current contained in the useful spot. The latter can be measured by the (almost) constant level reached by Z(p) in Fig. 26. This has been done for e = 0.001 and E = 0.01, for which this constant level is more well-defined than for larger beams. The additional component originates from the scattered electrons falling within the original beam or less. This finding diameter, but this effect is insignificant for E = should be compared with experimental observations presented later. A similar conclusion that the original beam diameter is maintained constant while the scattered electrons form a broad background signal level can be arrived at by considering single scattering only (Moncrief et al., 1979). However it was shown earlier that a single scattering regime occurs only if m < 0.355, but in reality, m can be much larger and the conclusions from single scattering should not be transferred to oligo-scattering without rigorous proof. It is interesting that experimental measurements by

2 .18 E .1oooo J ~15.75

0 07 0

1

r

I

I

,

1

1

2

3

4

5

6

7

Average number of collisions m FIG. 31: The normalized current contained inside the original spot size vs. the average number of collisions lies significantly above the exponential decay of current when E is sufficiently large.

FOUNDATIONS OF ESEM

171

Moncrief et al., deviated from their theoretical predictions (for single scattering) towards the small angle region which was limited to the far tail of the beam profile, i.e. to the outer region of the electron skirt. In addition, they measured the current collected by a Faraday cup with different apertures, the smallest of which was 8 pm. There is also a brief mention that the electron beam was scanned across a sharp edge with the following result: a 50 nm beam, after a 20 mm flight path, changes little up to a pressure of =10 Pa. The increase in beam diameter, up to 100 nm at 133 Pa, above this pressure is indicative of the changing shape of the beam current distribution. This statement implies that for pressure below 10 Pa, i.e. below m= 0.1, the diameter is unchanged, but the diameter doubles by the time we get to m = 1.6. This experimental observation contradicts our conclusion here that the diameter of the original spot remains constant for a very fine electron beam, which should also include the beam of 50 nm after a flight of 20 mm. However, new experimental evidence will be presented below showing the correctness of the present analysis. The beam broadening observed by Moncrief et al. was probably due to contamination or some other source of error.

F. Experimental Measurements of Spot Diameter

1. Methods f o r Diameter Measurements An apparently simple method for beam diameter measurement is to image a suitable edge at high magnification and, from the micrograph, to measure the variation of density in a direction normal to the edge by means of a microdensitometer. This method has been used frequently as, for example, in the measurement of the top-bottom effect in scanning transmission electron microscopy of thick amorphous specimens (Gentsch et al., 1974). An equivalent method is to scan the electron beam itself against the edge and monitor a suitable signal during the scan (Joy, 1974). The main problem with this method is the rapid build up of a contamination finger which renders the edge unsuitable. These methods have been improved by Reimer et al. (1979), Rishton et al. (1984) and Vaugham (1976). A more recent approach is to store two images of the same specimen area. These images are then shifted and superimposed digitally, and by Fourier analysis, the diffractogram is computed. By assuming a Gaussian distribution and applying the convolution-deconvolution theory, it is possible to deduce the beam diameter. This method has been used to correct astigmatism and determine the resolving power in the SEM (Smith, 1985).

172

G . D. DANILATOS

The measurement of beam diameter, particularly of small beams used in modern microscopes is not easy. All the above methods require either sophisticated equipment, or with the simplest ones, it may be difficult to acquire suitable materials and obtain reproducible results. The present aim is to obtain confirmation of some of the previous theoretical conclusions, and in particular, to demonstrate that the profile of the unscatttered fraction of electrons in a thin electron beam remains clear of the surrounding skirt. If this is confirmed, it will be of importance in the discussion of contrast and resolution in a later section.

2. Experimental Technique For the purposes of this investigation, the main idea in Vaugham’s (1976) technique was followed, this being the most easily accessible in terms of resources and time. The idea is to use a heated wire as a knife edge to scan the electron beam across, as heating can prevent the contamination build up. Without heating, the measurements were not reproducible as the same edge had to be scanned (focused and imaged) several times at different gas pressures, in order to establish whether the original beam broadens with increase of pressure. A platinum wire of 25 p m diameter was chosen, and by passing current through the wire, its temperature could be increased to just below the glow temperature. When the wire started glowing, the light could be detected by the photomultiplier system as a d-c level signal, and the current was lowered slightly. This wire was chosen amongst others because it had a straight edge when viewed at the highest magnification (90000X). An inherent limitation with this method is that the edge has an effective width of its own so that even if an infinitesimally narrow beam were scanned across, it would produce a finite profile width between the on and off positions on either side of the edge. There are two main causes of this effect: (a) the edge is not 100% opague over some finite distance from the edge, and (b) the signal collected may originate over a finite surface area from the edge. As the electron beam is scanned only a few beam diameters across the edge, we have the case of glancing incidence, where the beam is almost parallel to the surface. A detailed analysis of this case falls outside the limits of this work but a crude estimation of the effective edge width is attempted below. The first cause mentioned can be quantified by considering the range R, of electron penetration. This has been studied extensively and various formulae have been derived (see Reimer, 1985). Thus we can take

R, = 9E’.5 (96) where R, is in pg/cm2 and E is in keV. In the experiment below,

173

FOUNDATIONS OF ESEM

I PLAl: LOO@ pm

' I

Electran beam-'

I

2100 pm

I

i_ - _I---

W i r e cross section--. (250 pm)

1

I

12.50~1~1,

370um 3 0 pm

I'

--v-

-tu 5 0 0 pm

Insulator Insulator--

Fa ro d a y cage

1

EGth

to electrometer

FIG.32: Experimental arrangement for recording the beam profiles in the ESEM.

E = 15 keV and thus, R = 522.8 pg/cm2. For platinum, density = 21.45 g/cm3, so that the penetration depth is 244 nm. This depth defines a distance x, from the edge of the cylindrical wire over which the wire transmits electrons, and this is easily found to be x , = 0.6 nm, which is much smaller than the diameter of the electron beam used. The second cause mentioned can be diminished by collecting the electrons with the arrangement shown in Fig. 32. A Faraday cup is positioned 370 p m below the wire, so that the wire's edge lies approximately on the axis of the top aperture of the cup (12.5 p m diameter). This arrangement diminishes the amount of scattered electrons collected from the top surface of the wire near the edge. It is these electrons which make the edge appear to have a finite width which can be estimated as follows. With reference to Fig. 33, the circle represents a cross section of the wire, the scanned edge C of which is placed on the axis HD of the Faraday top aperture with radius DE. The positioning and sizes are out of

174

G. D . DANILATOS

AC = r. Wire radius

DE = R . Aperture radius B C = x,.Edge

width

D E FIG.33: Definition of the edge width x, due to scattered electrons from the arc FC into the collecting aperture with radius DE. The circle is the cross section of the wire scanned across its edge C as shown in Fig. 32.

proportion in this diagram, to be able to show clearly the arc FC over which the electrons are scattered into the aperture. The arc FC defines the effective edge width x, (=BC) which can be calculated by elementary geometry considerations:

{

xs=r 1-

Y ( R+ r )

+ / [ ( R+ r)2 - r 2 + /2]1’2] ( R + r)2 + l 2

(97)

where r = AC, R = D E , I = CD. By substituting the actual values shown in Fig. 32, we obtain x, = 3.6 nm. In this derivation it was assumed that the scattered electrons come only from the surface of the wire, while in fact they originate from a certain depth. This depth is of the same order of magnitude as xt near the edge which is many orders of magnitude less that the thickness FG corresponding to x,. (FG = 0.6 pm). Furthermore, the range R, is much smaller than the radius of the wire and the distance 1, so that the geometrical consideration of Fig. 33 should still be applicable. Therefore, the effective edge width should be close to the sum xt + x, . In conclusion, for electron beams much larger than the effective edge of the wire, the profiles recorded may be taken as a good approximation and represent the actual beam profiles.

FOUNDATIONS OF ESEM

175

The principles of the above experimental technique have been employed previously (Joy, 1974; Vaugham, 1976) to measure beam diameters in vacuum but their suitability had to be ascertained for measurements inside a gas. The main uncertainty is caused by the distance CD (Fig. 33), in the course of which the electron beam may lose electrons, due to collisions, outside the collecting aperture. This distance should be as short as possible, and the diameter of the aperture as large as possible, but these requirements are in opposition to achieving the shortest possible x, (see Eq. (97)). For the particular values shown in Fig. 32, it has been shown that the effective edge width is small enough with beams of 50 nm diameter, so we proceed to examine the effect of gas. As the beam travels the distance between the PLAl and the wire edge, it is expected to produce an electron skirt surrounding an ever weakening electron beam of unchanged diameter. We wish to test and find the current profile in the vicinity of the original diameter. The radius r1/2 of the electron skirt for L = 0.0021 m and pressure p = 2000 Pa is found from Eq. (84) to be rIl2 = 477 pm, which is much wider than the diameter of the collecting aperture. However, the expected probe arriving at the edge of the wire and (presumably) having a size close to the original probe will acquire an electron skirt of its own during its subsequent travel distance of 370 pm. This latter electron skirt has a radius according to Eq. (84) rl12= 7 p m which is close to the radius of the collecting aperture. In the experiment below, water vapour is used which has a much lower atomic number than argon, with 15 keV instead of 10 keV, and therefore r , / 2 is smaller than the aperture. It is believed that this experimental arrangement should reveal any gross variations of the probe diameter contradicting our theoretical predictions. Throughout this section, only parallel beams have been considered but in reality, the beam converges to the focused spot, with a particular semiangle a. In the present arrangement a = rad (200 pm objective aperture, 8 mm between P L A l and PLA2, 2.1 mm between PLAl and edge), and the general conclusions about beam profiles at the focused spot should not be affected by this convergence. However, it may affect the collection efficiency of the Faraday cage. We can check that the collecting aperture subtends a semiangle at the edge of the wire equal to 6.4 x lo-* rad which is larger than the beam semiangle, and therefore almost all the electrons falling in the neighborhood of the original spot are collected. A smaller collecting aperture, if used, would simply be equivalent to using a smaller objective aperture, or in other words, we would be studying effectively a corresponding smaller initial spot. At any rate, the conclusion is that this experimental technique should indicate any significant deviations from theory.

176

G. D. DANILATOS

3. Measurements The experimental technique described above enabled to obtain traces of the collected current as shown in Figs. 34 and 35. From these, it is possible to deduce the beam diameters defined to contain an arbitrary current level. We can define the diameter as the horizontal distance of the points corresponding to 25 and 75% signal level (Vaugham, 1976). In Fig. 36, the results of diameter measurements are given over a complete cycle of increasing and decreasing pressure. Good reproducibility ensures that contamination should not be present or affect our measurements. The

FIG.34: Trace of the intensity of current collected with the system of Fig. 32 as the beam was scanned across the wire edge at low pressure of water vapour (30 Pa); horizontal field width: hfw = 1100 nm.

FIG.35: Same as Fig. 34 at 1460 Pa.

177

FOUNDATIONS OF ESEM Average number of collisions m 1 2

0

2

~1.0

Water vapor u =2-62~10‘*’m~ E = 15000 eV

ZI

-0.8

3 a

-‘ L

-0.6

0 Q

-0-c

* U a, N

-02 ;

20G i n 0

:

i

2

t

r

i

1

6

i

I

8

I

t

10

1

12

00

I

I

1L

16

z”

18

Pressure px10-~,Pa

FIG.36: The measured beam diameter (spot width) together with the total spot current intensity (normalized over the initial beam current) vs. chamber pressure. The expected exponential current decay is also plotted for comparison. The top axis gives the expected average number of collisions corresponding to pressure for the constants shown.

points seem to fall about an average line drawn horizontally to the pressure axis, and therefore, this experiment confirms the basic conclusion of the theory. The beam current is also plotted in Fig. 36, where the spot current in vacuum has been taken as the unit of current. The current measurement is taken as the difference of the signal levels on either side of the transition region. In the same figure, the top axis shows the corresponding average number of collisions and the exponential exp( -m) is drawn for comparison. It is observed that the experimental curve lies clearly above the exponential decay. Initially, this could be thought of as being the same effect as shown in Fig. 31 where the current is higher due to the scattered electrons inside the original beam spot. Alternatively, it could be due to an overestimation of the total cross section used for H 2 0 in the conversion of pressure to m through Eq. (81). To check the first possibility, we can approximately estimate the diameter of the beam in reduced units to find out its order of magnitude. As we do not have precise data for the value of R for water, let us assume a conservative crude value of twice that for atomic hydrogen plus that for oxygen (see Eq. (63)) giving R = 0.1 nm, also a conservative estimate of beam diameter r = 50 nm which contains practically all of the current. For these values, through Eq. (76) we find p = 1.5 x lop3which corresponds to a difference from the exponential (see Fig. 31) smaller than the difference found experimentally in Fig. 36. Therefore, the alternative

178

G . D. DANILATOS

possibility is more likely, and the value of the cross section for water could be adjusted to make the experimental points fall close to the exponential function. There is a possibility that the differential cross section formula used underestimates the electrons scattered in the very low angle region. Already, Halliday and Quinn (1960) have made a similar suggestion based on their experimental observations. They measured experimentally the contrast in the transmission electron microscope and found it smaller than predicted by the Lenz theory. They suggested that theory gave an underestimation of the scattering into angles smaller than lop3 rad. Fortunately,such an effect should produce improved contrast in SEM contrary to transmission microscopy. Correction of Lenz’s theory has been proposed also by other’s (e.g. Kessler, 1964a; 1964b) and undoubtedly new theories should be taken into account for the calculation of beam profiles in gases. The above suggestion may raise some further questions. If the electrons are scattered at so small angles that they fall in the immediate vicinity of the original spot, an effective beam broadening could result, unless the scattering angles are so small that the electrons remain inside the beam region. A strong enhancement of the electron scattering cross sections for the rare gas atoms at small angles has been reported by Geiger and Moron-Leon (1979), but this was criticized later by Ketkar and Bonham (1985). Perhaps, an alternative explanation could be the “pinch-effect”, i.e. a self focusing phenomenon for electron beams in gases under certain conditions. This effect will be discussed in the following section. It is anticipated that with further experimentation, the ESEM can in turn help in the better theoretical understanding of electron scattering by gases and in answering outstanding questions. For example, experiments along the lines of those by Fink and Kessler (1966, 1967)-i.e. by scanning an electron beam across a target gaseous beam-but with a more powerful instrument, can now be performed. V. THEELECTRON BEAMANDGASSYSTEM A . Beam Transfer in Gas

The ESEM requires at least two pumping stages with three pressure regions. In the current prototype instrument, the average pressure in the electron optics column is about Pa, the pressure between PLAl and PLA2 is approximately 10 Pa, and the pressure in the specimen chamber

FOUNDATIONS OF ESEM

179

can vary between vacuum and 100 kPa (one atmosphere). From the previous section, we can readily find the average number of collisions for each region, and from this, the transmitted unscattered beam current. The electron optics column has a length L = 0.55 m, and from Eq. (81) and exp(-m), we find that 99.9% of the beam remains unscattered. This was calculated for nitrogen with 10 keV beam. The distance between the apertures is 8 mm, and we find accordingly that 89.3% of the beam is transmitted. Therefore, a significant loss of electrons takes place in this region, and there is scope for further improvement. Currently, there are physical restrictions with the model of SEM at hand, but a newly designed electron optics column should produce considerable improvement. This region is critical for the successful operation of the ESEM. A pressure increase of up to 50 Pa, which can easily happen either through spurious leaks, deficient pumping, or large PLA1, might be thought of as minor at first, but upon calculation, we find that only 57% of the beam remains unscattered. There is yet more investigation to be made on the effects of the gas jet forming above PLAl. If the jet represents a 20% increase of density (Schumacher, 1968) over the average static level measured by a gauge, then further improvement may be possible as was suggested in Section I1 (e.g. by tilting of the aperture). The depletion zone below the PLAl would reduce the amount of scattering to a value below the level calculated from the average specimen chamber pressure. However, little is known on the extent of this zone and relevant studies are necessary both for the design and operation of the instrument. The aim of this section is to study the electron physics of the beam-gas system in relation to the most elementary and immediate needs of ESEM. Little experimental work has been done with the ESEM in this direction and we must rely, at present, on collecting all valuable information from related fields. In the subsequent part, we consider an electron beam transferred from a vacuum region abruptly to a uniform high pressure region.

B. Beam Interaction Volume in Gas The electron beam is usually allowed to travel no more than a few mean free paths through the gas before it strikes the specimen. However, it is important to know the behaviour of the beam when it is allowed to travel unobstructed in the gas. During imaging, the beam may be scanned across edges or other vertical topographic variations where the beam travels over many mean free paths and, maybe, over the maximum possible travel

180

a

G. D . DANILATOS

b

C FIG.37: A 60 keV electron beam fired in a gas causes fluorescence over a region seen in (a) with argon and (b) with air. Prints for (c) and (d) were made from the same slide as (b) by decreasing the exposure time, at a higher enlargement. Diameter of beam exit aperture is 200 pm. (Original colour slides supplied courtesy of Professor Reimer; see also Reimer, 1985).

distance determined by the pressure and the accelerating voltage for a given gas. Certain phenomena caused by the beam need to be studied, as their effects can relate to contrast and resolution, and can influence the design of particular detector systems. These phenomena can also modify the gas itself, which in turn can influence the specimen. Initially, we should know the total interaction volume between beam and gas, namely the shape and size of it. Early observations and measurements of the properties of the interaction volume in gases have been

FOUNDATIONS OF ESEM

181

reported by Schumacher (1953): he observed that the air emits blue-violet light where the electrons can excite the gas. The boundary of the light in air is very sharp and coincides with the boundary shown on a fluorescent screen placed in the path of the beam. The isophotic lines can be drawn as the boundaries of light when different exposure times are used to produce prints from the same negative on which the luminous volume was photographed (Schumacher, 1953). Two typical shapes photographed when an electron beam is fired in nitrogen and argon have been published by Reimer (1985). Reimer has kindly supplied two colour slides from which the negative images shown in Fig. 37 have been produced. The first picture (a) is that of a 60 keV beam fired in argon at atmospheric pressure. The shape is round like an apple, but when the same beam is fired in air, having much lower atomic number, the shape is more like a pear (quoting Reimer). The names of similarly shaped objects have been used such as “tear-drop”, “plum”, or “bulb” by various authors. By reducing the exposure time as Schumacher suggested, the pictures in Figs. 37c and 37d were obtained at a higher enlargement However, these should be interpreted with caution, especially in the region of the image where overexposure (saturation) of the film has occurred. In solids, similar shapes have been found by indirect means, as by dissolving the irradiated part of a photo-resist to expose isodensity surfaces of energy deposition (Hatzakis, 1971). Also, the glow produced in a number of phosphors can be photographed and studied (Ehrenberg, 1963). The spatial distribution of the energy loss and ionization in the gas should be known for ESEM work. Grun (1957) has measured the total light intensity ZL between two planes at .z and z + dz perpendicular to the beam axis versus distance along the axis, and a typical result is shown in Fig. 38. The aperture through which the beam was fired was conically shaped and protruding into the air, so that light could be seen to come also from negative values of z (beam exit is at z = 0). This is due to backscattered electrons from other parts of the interaction volume. There is no clearly defined total depth but a practical range R can be defined by extrapolating the linear part of the curve as shown in Fig. 38. Grun found the following expression for R: R = 4.57 X (98) with R in mg/cm2 and E in keV. The actual travel distance LR corresponding to R is found through (2) as

with LR in m and E in keV.

182

G. D. DANILATOS

2

Y

.-

In C

C .-

L

0, .-

J

--

0 -

+-

R

I

Moss thickness

-+-

FIG.38: Light intensity coming from the fluorescent volume between planes at z and z + dz normal to the beam axis vs. mass thickness (equivalently z). The extrapolation by dashed line defines the practical range .

It is worthwhile to consider a numerical example relevant to the ESEM conditions: for E = 10 keV, p = 2 kPa, T = 293 K, M = 28.9 (air), we have LR = 108 mm and at one atmosphere ( p = 100 kPa), we have L R = 2.16 mm. If LR is used as measuring unit and the light intensity Z(z/L,) is normalized so that

then Z(z/L,) depends little on the beam energy in the range 5-54 keV in which Grun worked. The range can depend on the intensity of the beam current, the energy dissipation of which in the form of heat can create local variations of density. This phenomenon is observed with electron beam welders where high intensity beams are used, but heating is negligible if currents less than lo-’ A are used (Schumacher, 1953). Griin’s work has been confirmed, and further developed by Cohn and Caledonia (1970), who experimented with nitrogen in the energy range 2-5 keV. Their results have also been consistent with Spencer’s theory (1955, 1962). They measured in particular the N l ( l - ) (0, 0) radiation due to the transition of the N l B 2 2; (0) excited state to the NZX 2,. (0) ground state of the N2+ ion emitting at the 391.4 nm wavelength band. They reasoned that the fluorescence distribution should be closely proportional to both the ionization deposition and the energy loss distribution. This was based on the fact that the ratio of the total ionization cross section to the one at the 391.4 nm band is approximately constant over a wide

183

FOUNDATIONS OF ESEM

energy range examined (between 50 eV and 20 keV). Therefore, by measuring the fluorescence intensities emitted we should be able to deduce the ionization density at a particular point in the gas. This can be achieved by measuring the profile intensity of the “plum” versus distance from the axis on different fixed planes normal to the axis. By a subsequent mathematical transformation (Abel inversion), it is possible to deduce the point intensity anywhere inside the fluorescence region. The normalized point intensity GN has been worked out by Cohn and Caledonia, and their results have been redrawn in Figs. 39 and 40. The usefulness of these curves lies in the fact that we can derive the ionization density n+ by multiplying GN by a factor as in (Cohn and Caledonia):

where E is in keV, Z, the incident beam current and f is the efficiency for producing the 391.4 nm band which can be taken as 0.36 for N, (Hartman, 1968). The function G N has the highest vahes at r / L R = 0, but these values have also the highest uncertainty for z approaching zero. Using the maximum value GN = 85, at 2 kPa, Zo = 200 pA and E = 10 keV, we find n+ = 3.4 X ions/m3.

-0.2

0

0.2

0.L

0.6

0.0

1.0

1.2

Normalized axial distance zIL, FIGS.39 and 40: Normalized point intensity (of light) distribution vs. normalized axial distance for different values of normalized radial distance (redrawn from Cohn and Caledonia, 1970).

184

G. D. DANILATOS

-02

0

02

O L

06

08

10

12

Normalbzed axial distance ztCR

FIG. 40.

The validity of the above theories should be discussed in view of other possible considerations. For example, James (1955) has observed that fluorescence can be caused also by X-rays or UV, but Schumacher and Gadamer (1958) noted that this would be much weaker than the one excited by secondary electrons. A t the higher densities of air, as in Grun’s experiments, the fluorescence is mainly produced from the N2(2+) (0, 0) band of 337.1 nm wavelength, and it comes from the N2 molecules in the C3n, state which has been excited by secondary electrons (Cohn and Caledonia). A secondary electron produces fluorescence over its own range of travel, and the ionization producing this particular electron should be located somewhere in the vicinity of this range, which is short and close to the ionization point at high pressures. Furthermore, the lifetime of an excited state should be an important consideration. Long-lived excited states may be involved which can distort the spatial distribution of ionization deduced from light detection. A long-lived excited molecule may shift about considerably due to thermal movement or streaming. For example, Griin et al. (1954) found by means of spectrochronograms that the N: bands and A+ lines are emitted within less than 1 ks. This should correspond to a spread of 0.4 mm for a thermal velocity of 400 m/s but this could not be observed experimentally by them. In summary, it is possible to find the ionization distribution and energy

185

FOUNDATIONS OF ESEM

deposition, if certain precautions are observed, from the spatial distribution of the NT(l-) (0, 0) radiation by proper scaling. An alternative method with which the electron flux can be measured has been reported by Linnemann and Reimer (1981). They used a small semiconductor detector sensitive to electrons with energy above 8 keV and found an indication of how the electrons stream inside the diffusion cloud. More specifically, they measured the cumulative electron energy flux above the detector threshold at points inside the cloud but not the local ionization distribution as discussed previously.

C. Types of Reactions The different types of possible collisions between electrons and gas molecules can be described quantitatively by the corresponding cross sections plotted versus electron energy. This information can be found in the literature on electron impact phenomena (ionization of gases, plasma physics, and so on). These phenomena have been explored more in the low energy range below 1000 eV and especially for energies less than 100 eV. This region is of interest for ESEM from the point of view of detection of electrons emerging from the beam-specimen interaction volume. However, as mentioned in the previous section, the information for energies in the range of the primary beam is incomplete. Some typical cross sections have been reproduced in Fig. 41 from the -19

-4

E b

,"-20 J

C

0 U a,

m

-22

I

,

1

1

2

5 1 0

1

1 1

I

102 Electron b e a m energy E . e V

I

103

FIG.41: Comparative presentation of various electron scattering cross sections of hydrogen vs. beam energy (from v. Engel, 1983).

186

G . D. DANILATOS

-

book of v. Engel (1983). Electron-gas molecule collisions leading to 2 and various types of molecular rotation corresponding to transitions 0 1 -+ 3 (wrot0-2, wrrot1-3) of the quantum number J are described in the range of several eV. The vibrations of the atoms in the molecule are described by mvjb, the dissociation of a molecule by cdiss and the dissociaThe sum total of the lossy collisions tive ionization by uiiondiss. subtracted from the total cross section yields the elastic cross section which is dominant at low energies, but at higher energy, it is the ionization cross section wi,, which dominates. There are also other important reactions such as excitation, deexcitation (superelastic collisions), electron attachment, a subdivision of ionization cross sections, and so on. The relative strength of various cross sections depends on the nature of the gas and in Fig. 42 (v. Engel, 1983), we see an example of the dependence of the dissociative ionization for various gases.

D. Ionization of Gases Some elements, ideas and concepts from work on ionized gases are considered below as they are relevant and helpful in the design and operation of the ESEM. For an electron with energy above 1 keV, almost half of it goes into ionization of the gas and most of the remainder into excitation and kinetic energy of secondary electrons in the gas. According to Whyte (1963), the electron ion-pair formation requires an average of 34.6 eV for N2 indepenN

5.10 N

-

0 0u

6

6-

0 c

.o c

L

-

U Q,

ul ul 0

5

201 0

. . 10

20 3 0 L 0 5 0

lo2

10’

Electron b e a m energy E . eV

FIG.42: Dissociative ionization cross section of various gases vs. electron beam energy (from v. Engel, 1983).

187

FOUNDATIONS O F ESEM

dent of the electron energy down to 6 keV, and Cohn and Caledonia (1970) suggest that this energy may rise by only 5% down to 2 keV. The average energy required to ionize various gases ranges between 30-45 eV, and a single 10 keV electron in nitrogen produces about 300 ion pairs over its passage. This energy per pair formation is the ratio of the total electron beam divided by the number of pairs and should not be confused with the avaage ionization energy given by Eq. (64) or the ionization potentials of atoms and molecules. It is interesting to see that the values per pair quoted here are much less than the average ionization energies predicted by (64), and a little more than double the first ionization potential (15.5 eV for N2), which is consistent with the previous remark that approximately half of the beam energy goes into ionization. This argument favours the choice of the first ionization potential for J in the formula (59) used for the inelastic cross section earlier. The ionization potential for corresponding atoms and molecules differs little: N(14.5) vs. N2(15.5), O(13.6) vs. 02(12.1),H(13.6) vs. H2(15.4), (see v. Engel, 1983). Information on the ionization efficiency for some commonly used gases is shown in Fig. 43. For example, a 10 keV electron travelling through 1 mm of N2 at 1333 Pa ( = l o Torr) will produce 0.3 ion pairs on the average, whilst at its maximum efficiency, i.e. at about 100 eV, it will

“i 3

20

a E

:

05-

-0

0 30 2-

10-

In

a

c)

1-

0 05-

0 03I

10

I

1

20 30 50

I

lo2

I

103

I

10‘

Electron beam energy E . e V

FIG.43: Number of ion pairs per unit distance per unit pressure produced in different gases vs. electron beam energy (from v. Engel, 1965).

188

G. D. DANILATOS

produce about 10 ions over the same distance and pressure. This property is useful in the detection of signals as will be seen later. In SEM work, the secondary electrons have by definition an energy less than 50 eV. The ionization efficiency of secondaries is high towards the upper end of the region but negligible or non-existent below 15 eV. O n the formation of negative ions by electron attachment we know (v. Engel, 1983) that their formation is possible with electronegative gases. It is possible to form 0-, OF, 07, 0; with decreasing stability. Oxygen generally favours electron attachment. Negative excited nitrogen (N;)forms temporarily. With hydrogen we get H2 + e -+ H

+ H-

or H2 + e + H

+ (H*)-

In helium the negative excited ion (He*)- can form, but it is weak and temporary. No doubly charged negative ions have been observed up to now, nor H2 ions. The electron attachment cross sections are generally low, and therefore. we should find predominantly positive ions and free electrons in an ionized gas. The ions in a sufficiently weak electric field % acquire a moderate energy which is dissipated after each collision, so they move with constant drift velocity v i = p+8 where p+ is the ion mobility. Some typical values of p+ in m2/sV are He+ (0.79), H,f(1.6), Ne+(0.33), N2+(0.2), H + ( l . l ) , (air)+(.14), (air)-(O.l9), 0;(0.1), 0,(0.14), (v. Engel, 1983). However, in our work it is preferable to consider the velocity of ions and electrons as a function of % / p , as for example in Figs. 44 and 45(v. Engel, 1983). The

:201 r"' E +.

o;/o,

0

1

2

3

EIp. VImPa FIG.44: Ion drift velocity in various gases vs. electric field per unit pressure (from v.

Engel, 1983).

189

FOUNDATIONS OF ESEM cn

E

2

w

0

1

2 EJp, V/mPo

3

FIG. 45: Electron drift velocity in helium and nitrogen vs. electric field per unit pressure (from v. Engel, 1983).

ion and electron velocities are useful in the design of a gaseous detector device to be described in a later section.

E. Ion Concentration in the ESEM We have already seen how to calculate ion density through Eq. (101) but only in a well-defined case. In the actual conditions of ESEM, the electron beam usually travels only a few mean free paths and the “plum” does not develop. We could perhaps assume that the effect of backscattered electrons by the gas inside the “plum” is small, as Linnemann and Reimer (1981) have observed, but the very specimen under examination produces a very large number of backscattered electrons, secondary electrons and other ionizing signals inside the small gaseous region between the specimen and PLAl. Therefore, Eq. (101) will not yield the ion concentration in this case. Furthermore, we are interested in a region from the immediate vicinity of a very fine beam, up to distances corresponding to the minimum magnification of the microscope (maximum field of view) and beyond, inside the whole specimen chamber (e.g. for purposes of the gaseous detection device). The experimental apparatus of Cohn and Caledonia involved an electron beam with 2 mm diameter forming a plum with a range of about 20 cm. Measurements below the point of beam exit within a radius z / L R = 0.05 are either lacking, or they are not reproducible. This region is very large ( = l o mm) from the point of view of microscopy. When using a much finer beam (e.g. 10 nm), the measurements in Figs. 39 and 40 are still valid but they refer to relatively

190

G. D. DANILATOS

great distances in the microscope. The highest average value recorded in Fig. 39 (z/LR < 0.05 and r/LR = 0.0) should not be taken to represent the situation in the confined region between specimen and PLAl. A solution to the problem of finding the ion density in the conditions used in ESEM is not known. The problem seems rather complex and the discussion below is more of a description of the difficulties than its solution. The aim is to define the tasks for further work by researchers in the relevant fields. Let us consider a uniform density parallel beam of electrons with current density J and energy E. It can be easily shown that the density of electrons n , in the beam is n, =

i

-[' 31 1

- (1

I/Z

+

and a typical value for E= 10 keV, Z,, = lo-'' A and beam diameter d = 28 nm, is n, = 1.7 X 10l6 electrons/m3. If the mean free path between two ionizing collisions is Lion,then each electron produces one ion per mean free path and the rate of ion production Y per unit volume is

or equivalently through Eq. (44)

r=

jp 4.522 x 1041 uiOn T

(104)

From r we can find the frequency at which a molecule is struck by electrons: r n

-=-

uj e

where the type of u chosen determines the nature of collisions per unit time. The rate of deionization r' due to recombination, or because the ion leaves the region of concern, or strikes a wall, is

where T is the effective lifetime of the ions in the region concerned. At the

FOUNDATIONS OF ESEM

steady state we have r

=

191

r' and therefore we get

n+ =

4.522 x 1041 uiOn Tjp T

The fraction n+/n is then found as aim

Ti

n+/n = e A difficulty lies in measuring the effective lifetime T . The total lifetime of ions in an extended region can be measured, e.g. by spectrochronograms (Grun et al., 1954), and formula (106) would be applicable with this T if the corresponding ion generating beam was broad engugh extending also over the region in which the ions spend their lives. However, this is not likely to be the case in the ESEM using very fine electron beams. Their lifetime inside the beam can be extremely short, spending most of the time outside this region. A useful quantity from plasma physics relevant to our problem is the Debye length D given by (see, e.g. v. Engel, 1983):

This parameter is a characteristic distance, beyond which the electric field of a given charge has no or little effect on other charges. The absolute temperature T' refers to the temperature of the ions which can be taken tentatively equal to 1 eV. A better picture of the situation and the meaning of the above quantities is gained by considering a numerical example, the results of which are shown in Table VIII. Three cases are considered: one corresponding to a current density from a tungsten filament gun, one from a LaB6 and one from a field emission gun. In this example, we consider arbitrarily that T = s. The resulting Debye length is between 2 pm and 0.12 pm, but it becomes smaller by a factor of 0.16, if the ion temperature is taken equal to the gas temperature (293 K); these figures should be correct when the width of the electron beam is larger than these values. Under the same condition the concentration of ions in all three cases is approximately one thousandth or less than that of the gas. If T = s, the ion concentration would be one hundred times greater and it would become comparable with the original molecular concentration (63%) with the field emission gun. Such ion concentration is very high and could have important effects on the propagation of the electron beam. In this case, the Debye length would be 10 times smaller. However, in all three cases, the effective lifetime inside the beam is unknown, and the ion

192

G. D. DANILATOS

TABLE VIII NUMERICAL EXAMPLE OF USEFUL QUANTITIES ON ELECTRON COLLISIONS I N THE CONDITIONS OF ESEM FOR NITROGEN WITH T = 293 K , p = 2000 Pa, n = 4. 9 x 10’’ mol./m3, s = 12.6 nm, uion= 2.3 X lo-’’ m2, T = lo-’, E = 20 keV Quantity

Tungsten 10-If’ 28 1.6 x lo5 1.2 x 1016 1.1 x 102’ 2.3 x 10’ 1.1 x 10” 2.3 x 2.0 x

LaB,

Field emission

10-lfJ 10 1.3 x lo6 9.75 x 10’6 9.0 x lo2’ 1.8 x lo4 9.0 x 10” 1.8 x 10-4 7.3 x 10-7

1.7 4.4 x 3.4 x 3.1 x 4.4 x 3.1 x 6.3 x 1.2 x

10’ 10IR lo2’ lo5 lo2’ lo-’

(s is the mean distance between closest neighbours, see 11).

concentration both inside and outside the beam cannot be predicted by the above formulae. A rigorous formulation would, at any rate, become complicated by the generated signals from the specimen which are generally variable. It is anticipated that further work using appropriate experimental configurations in the ESEM can resolve these questions. Schumacher (1968) has already suggested that some of the beam-gas interactions could yield useful information such as measurement of temperature in diatomic gases from the translational and rotational band spectrum, or by use of the fluorescence yield with known density. Similarly, there is the possibility for measurement of the molecular and ion concentrations separately from the different atomic, molecular and ionic spectra. More experimental arrangements are possible because of the existence of a very fine probe coupled with appropriate detectors in the new conditions of ESEM. F. Electrostatic Pinch Effect

According to Halsted and Dunn (1966), a beam of several keV will ionize the gas and a plasma can form in the vicinity of the beam that has a density comparable to the beam density at Pa and hundreds of times the beam density at 1 Pa. An electrostatic potential results with an inward force on the beam, a phenomenon known as “gas focusing” or “ion focusing”.

FOUNDATIONS OF ESEM

193

The ionization products of a beam travelling through a gas are slowed down beam electrons, plasma electrons with 10-15 eV and ions with a few tens of eV. The plasma has a temperature of a few electron volts. At a pressure near 0.1 Pa, the density of the plasma electrons is several times the beam density, while the ion density is slightly in excess of the sum of plasma and beam electron density. The positive ions have negligible random energy and are freely falling to the walls. Beams with 100 to 10,000 eV have been focused both in the case where the beam is surrounded by a metal mesh or dielectric tube, and in the absence of any walls in the immediate vicinity of the beam. The electrostatic “pinch effect” takes place when the plasma ions and electrons move radially and there is no axial drainage. T o the extent that there is an axial flow, the beam will not be focused. However, an axial flow is allowed at the end of the beam. To help and enhance the radial flow, a negative potential more than -50 V should be applied to a surrounding electrode. The gas focused beams are self-centering and self-focusing. The strong sheath field near the wall is responsible for this. The focus point may be adjusted by small changes in the gas pressure or the beam parameters. There are generally several focus points occurring along the beam axis, and this effect tends to prevent the beam from broadening. No deliberate effort has been made to explore the possibility of gas focusing in the ESEM yet. It has been speculated that this effect may already have been observed (Danilatos and Robinson, 1979) during early experiments with various detectors in the ESEM. In one of these designs, the detection of backscattered electrons took place inside a cylindrical hole of a plastic scintillator detector. It is possible that the surface in the hole charged up to several tens of volts, even in the presence of gas, and the primary beam travelling through the same hole could become self-focused. Undoubtedly, if self-focusing could be effected in a practical way, it would revolutionize the whole approach of ESEM.

VI. DETECTION Here, consideration will be given to those aspects of detection which are imposed by the special requirements, restrictions and advantages of the ESEM. The same signals that occur in microscopes operating in vacuum are encountered in the ESEM, such as backscattered electrons (BSE), secondary electrons (SE), absorbed specimen current (Ia), cathodoluminescence (CL), X-rays, and others. However, the corresponding detectors require special modification and design, which are imposed either by

194

G. D. DANILATOS

the existence of gas or by geometrical restrictions due to the short specimen distance from the PLA1. A general review of the current situation is given below. A . Backscattered Electrons

Although the first wet images in an SEM were not taken with a BSE detector, it appeared for a relatively long time that BSE were the answer for an environmental SEM. In early work, a wide angle scintillator BSE detector was exclusively employed (Robinson, 1975), and in most of the subsequent work (Danilatos, 1980a; 1981b; 1985), use was made of many different geometries of BSE scintillator detectors. A review of the early use of BSE detectors has been published by Danilatos and Postle (1982b). As the BSE possess a relatively high energy, they can travel over several mm through a gas without losing much energy, so that they can be detected by a detector in the same way as in vacuum. The fraction of BSE scattered far away from the initial direction of emission from the specimen is negligible, if the travel distance between specimen and detector is not too large. Therefore, the BSE detectors must be designed to meet the geometry requirements of the ESEM. The gas per se does not seem to limit the operation of the BSE detection principle. On the contrary, the gas provides the benefit of suppressing charging, and therefore, uncoated detectors can be employed when the coating was meant to serve only as charge conductor. However, metal coating (e.g. aluminization) may still be used in the case of plastic scintillators to stop extraneous light (e.g. from cathodoluminescence) from interfering with the BSE signal, and to reflect some of the scintillation light towards the photomultiplier. The restricted space available in existing microscopes creates additional difficulties in positioning the detectors close to the specimen and to the PLAl without decreasing the efficiency of the detectors. Most of these problems can be solved effectively by redesigning the electron optics column to allow the fitting of suitable detectors together with an efficient differential pumping system. Within the limitations of an early model JEOL JSM-2 SEM, an efficient system of two symmetrical BSE detectors has been designed and used as shown in Fig. 46. The shapes and sizes were calculated to allow near optimum light transmission, good collection angle and detection of BSE at pressures required to examine wet specimens at room temperature. The two detectors allow addition and subtraction of signals to produce topographic or atomic number contrast in the usual way as in other SEMs. They have been used in the production of colour images in various combinations as reported elsewhere (Danilatos, 1986a, 1986b).

FOUNDATIONS OF ESEM

195

BEAM

C

0 = PLAZ

zPLA1

FIG.46: Relative positioning of apertures and a pair of plastic scintillator BSE detectors in the ESEM. The sample is placed close to the PLAl and signal detection is restricted over a small area around the aperture.

The efficiency of detection is crucial in an ESEM for two basic reasons: a) The primary beam quickly loses electrons out of the original spot, and b) the lowest possible beam current and accelerating voltage should be used for most untreated exposed or wet surfaces, especially for biological specimens. Several hidden factors which might at first sight seem trivial can be of paramount importance. For example, the specimen has to be placed at about 1 mm from the PLAl and precision better than 0.1 mm in the machining and fitting of the detectors is required, if most of the BSE are to be collected. Also, as a general rule, every photon that can be saved should be saved and detected by proper shaping and finishing of the detector. For operation at still higher pressures the specimen must be placed closer to the P L A l , but then the solid angle subtended by this aperture becomes significant, since a large fraction of the BSE escape through it. To maintain the useful number of electrons in the spot constant, the product p D should be kept approximately constant (a condition correct for a very fine beam). This product has been referred to previously as the scattering index (Danilatos, 1981b), and it is equal to

pD

=

1.38 x

mT/v

(110)

By substituting typical values of T = 293 K, v = 2.6 x lop2' m2 for water vapour at 15 keV, and for average number of collisions m = 1, we get p D = 1.56 Pam, which is consistent with the experimental finding of having obtained clear images with p D = 2 Pam. As the pressure is increased, the P L A l must be decreased accordingly in order to keep the leak rate Q below the maximum value tolerated by the system. This aperture is characterized by a conductance parameter C , (see

196

G. D. DANILATOS

Table V), and it can be shown that the subtended angle CI is given by (Danilatos, 1985)

27T

1 + 1.31 x

1045 ___

C,m2T2 a2Qp

where expression (110) has been taken into account. This angle increases monotonically with pressure, and above a particular pressure the detectors should be placed above the PLA1. This approach has made possible the imaging of specimens at pressures up to one atmosphere. The first image, which was of poor quality, was taken by Danilatos (1980b) but much improvement has been achieved ever since (Danilatos, 1985). In these considerations, the BSE are treated as travelling in straight lines, since the gas only marginally affects their direction in the short distances found in the ESEM. However, inside this short and confined region, multiple backscattering between the surrounding walls can become important in the detection design (Danilatos and Postle, 1982b). The placement of detectors above the PLAl has been referred to as an atmospheric scanning electron microscope, but since a combination of detection both above and below the aperture has been practiced, and not only with BSE but with other signals as well, there seems to be no justification for distinction between the various detection configurations by different names. The term environmental scanning electron microscope seems sufficient and appropriate, and incorporates all cases of detection (Danilatos, 1986~). The detection of BSE need not be restricted only to the scintillator type of detectors. Solid state detectors can also be used in the presence of gas. However, no systematic work has been reported with such detectors to establish the problems and advantages in the ESEM. In recent years, novel detection means for BSE have been created because of the very existence of a gaseous environment. It has been shown that the gas, apart from being a conditioning medium, can also act as a detection medium at the same time (Danilatos, 1983a, 1983b). The BSE ionize the gas, and the positive and negative charges created can be used to form images. An example is given in Fig. 47 obtained by collecting electrons with a positively biased electrode made by a wire in the form of a loop and placed 0.5 mm above the specimen and 0.8 mm below the PLAl. This figure compares closely with the BSE image (Fig. 48) obtained with the scintillator BSE detectors. They both show the atomic number contrast between the iron-rich and aluminum-rich regions of the mineral specimen. The differences are partly due to different contrast and signal level settings on the microscope during image recording, and also due to the high scattering index producing some noise in Fig. 47. This detection system is examined in more detail later. (The frame scanning time for photogra-

FOUNDATIONS OF ESEM

197

FIG.47: A mineral containing iron-rich inclusions in aluminum-silicon-rich medium imaged by collecting negative current with an electrode at +10 Volts in vapour pressure at 1680 Pa; incident beam at 10 keV, 230 PA, hfw = 90 p m .

Fic,. 48: Same specimen as in Fig. 47 imaged by summing the outputs of the BSE detectors of Fig. 46. Same conditions except p = 480 Pa.

phing the images throughout this work was 50 seconds unless otherwise indicated).

B. Secondary Electrons The first images of wet specimens in the SEM were obtained by use of an Everhart-Thornley secondary electron detector (Lane, 1970). This was achieved by injecting a jet of water vapour on the specimen surface with

198

G . D. DANILATOS

simultaneous pumping away of the diffusing vapour cloud in the specimen chamber. With this method, a steady state gas density is maintained immediately above the surface of the specimen, but the pressure quickly decays with distance. This method presents several disadvantages. One disadvantage is that the thin cloud can only be maintained over a restricted specimen area, and large specimens would require impractically large amounts of vapour to be injected upon them. The control of a desired environment using such a technique would be very difficult and complex to achieve and the maximum pressure not very high. Although the above system did not show much promise, Lane made some interesting observations in the context of our present experience. He observed that the collected signal increased in the presence of gas above the level observed in normal SEM vacuum. This multiplication was attributed to more secondaries being created by the original secondaries, due to their collisions with the gas. However, it is uncertain whether the SE or the BSE were responsible and to what extent each was responsible for the signal being amplified. The gaseous cloud surrounding the specimen had an unknown pressure variation which is important in determining the relative contribution of signals as is shown below. With our present form of the ESEM, it is easy to control and change the environmental conditions in the chamber, and much has been learned about the role that the gas can play in the detection system. We can now readily observe how the image changes from a BSE to a SE one. In Fig. 49, the same mineral specimen is imaged at 210 Pa with a slight positive bias on the electrode. New features have appeared while some of the old ones have disappeared. This image is formed mainly by SE as can be seen

FIG.49: Same as in Fig. 47 with electrode bias

=

+ 3 mV and p = 210 Pa

FOUNDATIONS OF ESEM

199

FIG.50: Same specimen as in Fig. 47 with a SE detector in the vacuum of a conventional SEM using 15 keV.

by its close resemblance with the image obtained in another microscope equipped with a SE detector (see Fig. 50). The pressure region over which the transition from Fig. 47 to Fig. 49 takes place depends on the gas, electrode bias and electrode-specimen configuration. The behaviour of SE in the ESEM is not fully explored yet. The majority of SE have an energy less than 10 eV, with most having energy of only a few eV, and therefore their ionization efficiency is negligible (mainly possible with excited species). They are capable, nevertheless, of forming negative ions, especially with electronegative gases. These negative ions would be about a thousand times slower than free electrons in an accelerating field but they could contribute to the SE signal. The elimination of free electrons by attachment has been worked out by electron swarm theory: the current I1 at position x, ,will decrease to 1, at position x2 so that (Massey, 1969) 12

- = exp[-a(xz - x l ) ]

I1

where a is the attachment coefficient given by a = -n Q a u r ve with Q, the attachment cross section, n the gas concentration, Ur the random electron velocity and v, the electron drift velocity. By assuming values for Q, = m2, U , = 1.3 x lo6 m/s (at 5 eV), v, = 2 x lo4 m/s (for % / p = 3 V/mPa, see Fig. 45), n =' 2.5 x lo2' atoms/m3

200

G. D. DANILATOS

(for p = 100 Pa) and x2 - x1 = 0.005 m, we find a transmission factor (unattached electrons) of 0.44, while at p = 1000 Pa this factor becomes extremely small. The attachment coefficient can be varied enormously by simply varying the pressure and the applied field. Some further aspects of the SE detection are considered in conjunction with the gaseous detector device mentioned below.

C. Cathodoluminescence Cathodoluminescence (CL) detection is possible and has been practiced in the ESEM (Danilatos, 19860. The detectors shown in Fig. 46 can perform as CL detectors by removing the plastic scintillator coating so that the clear acrylic plastic can collect and transmit the CL from the specimen. Although this configuration may not be as efficient as with specially designed detectors (Bond et al., 1974; Rasul and Davidson, 1977; Horl, 1972), it has been sufficient to obtain images of wet surfaces for the first time. This new possibility is demonstrated below by a sequence of micrographs showing the wetting and recrystalization of sodium chloride crystals placed on a carbon surface. The first image (Fig. 51) was taken at a pressure below the wetting relative humidity (76% at 18" C recorded) by means of a biased electrode at +10 V, which collects negative current. Under these conditions, the image corresponds to the BSE signal. The next image (Fig. 52) shows the same specimen by use of CL detection. Subsequently, the vapour pressure was raised until the crystals dissolved into

FIG.51: Sodium chloride crystals on carbon surface imaged with the biased electrode at +10 V and 1420 Pa of vapour; 10 keV, 230 PA, hfw = 290 I m .

FOUNDATIONS OF ESEM

20 1

FIG.52: Same as in Fig. 51 by use of the CL detectors.

FIG.53: Same as in Fig. 51 except at p crystals into solution droplets.

=

1650 Pa which resulted in dissolving the

salt solution droplets which were imaged with the biased electrode as in Fig. 53. However, nothing could be seen of the same specimen by use of the CL detectors (Fig. 54). When the pressure is lowered slightly, salt crystals appear in equilibrium with their solution (Fig. 5 5 ) when imaged with the biased electrode, but only the crystals can be seen by CL detection in Fig. 56. Upon decreasing the pressure further, new crystals are formed (Fig. 57 and 58). The availability of two independent detectors allows the examination of directionality of the emitted CL. By subtracting the two signals the result is shown in Fig. 59 for the same specimen. Finally, vapour

FIG.54: Same field of view as in Fig. 53 imaged with the CL detectors.

FIG.55: Same field of view as in Fig. 53 imaged with the biased electrode as before but at slightly less pressure p = 1640 Pa.

FIG.56: Same as in Fig. 55 imaged with the CL detectors.

FIG.57: New crystals formed in same field of view at p = 860 Pa and imaged with bias electrode as before.

F I G . 58: Same as in Fig. 57 imaged with one only CL detector in the direction of arrow

FIG.59: Same field of view as Fig. 58 imaged by subtracting the outputs of the two CL detectors: + 2 - 1.

204

G. D. DANILATOS

FIG.60: Same field of view as previous at p from CL and electrode detectors.

=

1280 Pa imaged by summing the outputs

FIG.61: Same as Fig. 60 with CL detectors only.

was readmitted, and it was observed that the crystals dissolved at 1280 Pa (Figs. 60 and 61) which is distinctly below the previous wetting pressure. Furthermore, it was surprising to notice that 60 seconds later, no large droplet of solution or any remnants of it could be seen in the image (Fig. 62). The original purpose of the above demonstration was to show the new potential of using CL detection with wet specimens and to follow up the dynamic changes as seen with this mode of detection. It was coincidental that other interesting phenomena were observed at the same time, an

FOUNDATIONS OF ESEM

205

FIG.62: Image with electrode detector 60 seconds after Fig. 61 with all macroscopic conditions same. The large solution droplet has disappeared.

indication of the possibilities open to researchers using the ESEM. No definite explanation can be offered for the above observations on the salt-solution system except some general remarks. The wetting of the crystals in Fig. 60 took place at a vapour pressure corresponding to 62% relative humidity (recorded), but the local relative humidity could be higher due to a local temperature decrease during the previous evaporation. Otherwise, the phenomenon could be attributed to a chemical change producing a more hygroscopic compound. The disappearance of the droplet in Fig. 62 is a rare phenomenon considering the number of observations made by the author and is as yet inexplicable. D . X-Rays

Scanning electron microprobe analysis of liquids has been achieved by use of window cells (Lewis and McKenzie, 1985). The liquid under examination was placed in a small cavity machined on top of a specimen stub and covered by an electron transparent film. X-ray analysis was thus possible by use of a PGT-4 energy dispersive system. Liquid Hg, CaC1, in aqueous solution and blood were analyzed with this system. No report is known on the examination of specimens with X-rays in an ESEM. Makita et al., (1982) have claimed to have examined wet fixed and unfixed biological tissues but curiously under a vapour pressure not higher than 66 Pa at room temperature. These specimens must have been as wet as possible at this low pressure and therefore not near or fully wet.

206

G . D. DANILATOS

There should be no reason to prevent the use of X-ray detectors in an ESEM, provided that the microscope design allows room for the positioning of such detectors. The main concern is with regard to the electron skirt generated by the gas. X-rays produced over a much wider region than the original spot will be detected resulting in loss of resolution. This aspect will be examined in the section on contrast and resolution. Work should be done in future to determine the limitations of this extremely useful mode of detection in the ESEM. Also, an investigation is required to determine the possibility of using the gas itself in the detection of X-rays.

E. Auger Electrons Auger electron microscopy requires ultra-high vacuum, and therefore, the presence of gas in the ESEM is not compatible with this mode. The use of the gas itself for their detection, or any other suggestion would be pure speculation at this stage. Much should be learned about the contamination process in the presence of gas before a definite verdict is expressed on this mode.

F. Multipurpose Gaseous Detector Device Throughout this section, mention was made of the fact that the gas itself can be used as a detection medium for various signals. As this approach is not unique for only one particular signal, it appears justified to examine it as a generalized, o r multipurpose gaseous detector device. Its study comes under the category of signal-gas interactions. Initially, the ionization produced by certain signals has been used for detection of these signals (Danilatos, 1983a, 1983b). Later, the excitation of gas produced by signals was also used for detection (Danilatos, 1986f). That is, various signals such as SE and BSE can excite the gas molecules which subsequently emit flourescence, which in turn can be detected in a similar way as the scintillation produced on a SE or BSE detector. Based on the above experience, it has been suggested that other reactions between signals and gas should be able to be used in the detection chain (Danilatos, 1966f). This would require the transfer or adaptation of the methods and devices used in other fields to the field of ESEM. These are the methods and techniques used to study particle impact phenomena in plasma physics, radiation physics and chemistry, and ionization of gases. More specifically, it should be possible to monitor, for example, electrongas dissociative interactions, various types of excitation and ionization,

FOUNDATIONS OF ESEM

207

electron collisions leading to vibration or rotation and so on. The different signals can presumably be differentiated by suitable hardware tuned to the corresponding different signal-gas reactions. These ideas will be illustrated below with some concrete observations made to date. 1. Zonization

Two different regimes of ionization can be distinguished. The first is when the electrode's electric field '% per unit pressure ( % / p ) is low, but able to collect the majority of ionization (saturation) current created by energetic signals. The second is when the field is strong enough to impart additional (external) energy to the positive or negative carriers created initially by the signals (high % / p ) . In the second case, the imparted energy can result in ionization during collisions along the path of the carrier leading to amplification of current. No work has been reported yet for this regime in the ESEM. For practical reasons, the early work was done at low values of % / p ,and this work will be reviewed below. This regime also helps to understand some fundamental properties of the gaseous detector device. The early observations on the ionization regime in the ESEM was described by measurements of the type shown in Fig. 63 (see also Danilatos, 1983b). The cup A shown in the figure acted both as a specimen and as collection electrode. It was made by a 4 mm diameter carbon rod, the top of which was covered by a single hole (100 pm) copper grid and placed 1.2 mm below the PLA1. The cavity underneath this hole acted as an efficient trap for the beam directed through it. The ring shaped electrode B had an inside diameter of 6 mm and was made from metal wire of 0.5 mm diameter; it was placed 0.8 mm above the cup A. The beam current (in vacuum) varied a little around 200 PA, and to make the comparison of measurements meaningful, the absolute incident beam current IZol was used as unit. One of the electrodes was earthed when the other was used for measurements. The beam was scanned across the aperture, and the difference in the current collected between the position of the beam inside the hole (1) or outside and on top of the cup (2) created the contrast during imaging. Current measurements were carried out with the beam at positions (1) and (2), and the result is plotted versus pressure (Fig. 63). The recorded current increases (absolutely) with pressure, but it increases faster with the beam in position (2). This is because, when the beam is directed inside the hole, ionization is caused only by the incoming beam, while, when directed in position (2),additional ionization is caused by the BSE and SE electrons (and all ionizing signals). The contrast (signal difference) on either side of the resulting cross-over point between curves A1 and A2 is inverted.

208

G . D. DANILATOS Pressure m1O-*.Pa

0

-1

-

-

c ( 0

-

\ I+

-2

2 3

u

0

p -3 0 0,

0:

-4

-5

FIG.63: Recorded current with electrode A (cup), or electrode B (wire loop) vs. pressure, when the beam is directed inside the hole of the cup ( A l , B1) or outside it (A2, B2).

There is no cross-over point if the collector electrode (B) is separate from the specimen, because in this case the recorded current in position (2) is always above that in position (1). The whole situation is reversed when the electrodes are negatively biased so that the positive ions collected can overcome the negative electrons. In vacuum, the electrode collects some negative current even when it is biased with a negative voltage because of the energetic electrons which can overcome the negative barrier. When the pressure is increased, the positive current is much higher in position (2) than in position (1) and a cross-over point is observed for electrode B but not for electrode A. When electrode A is negatively biased, more negative current is deposited in the hole than on the surface of the cup, and this difference is increased by the extra positive ion collection in position ( 2 ) . A systematic study for several gases in the pressure range 0-2000 Pa and electrode bias between -10 and +10 Volts has been carried out to establish the general trends of ionization, to help understand the fundamentals of imaging by the gaseous detector device and to improve its efficiency and performance in future designs. Some representative results are presented below. Because in this work we deal with both positive and negative currents, these are measured on the corresponding positive and

209

FOUNDATIONS OF ESEM

I/II~I

.' 3

Argon

.' 2

E = 10 keV

p = 500 Pa

I

-10

-8

-6

-4

-2

I

tt -'

02

-2

FIG.64: Recorded current with electrode B vs. electrode bias at beam positions (1) and (2) at the constant pressure shown.

negative axis. Thus, Fig. 64 shows the variation of recorded current with electrode B for the two beam positions versus bias for argon at a fixed pressure. In vacuum, the curve B1 coincides practically with the abscissa, and B2 is wholly negative approaching asymptotically the negative abscissa and reaching a near saturation value at some positive bias. This saturation corresponds to the point where most of the SE have been collected. As gas is allowed in the chamber, the pattern in this figure appears with a cross-over point between B1 and B2 moving towards less negative values. If the difference between B1 and B2 is taken as a measure of contrast, then this contrast increases with increase of pressure. An example of a higher pressure and a different gas (H20) is given in Fig. 65. By keeping the same conditions as in Fig. 65 and using the specimen A as collector, the recorded currents are shown in Fig. 66. The general trend is a shift towards negative values of current with the cross-over point on the positive abscissa. The nature of gas determines the relative strengths of positive and negative current and the level of the total recorded current. Thus when using helium, the total current is always negative in the range of bias shown in Fig. 67. The trends shown above must be born in mind in the design of a

t'

Water vapor p = 2 kPa

E = 10 keV

-----____ -10

-8

-6

-L

-2

82

i' 1-5

FIG.65: Same measurements as in Fig. 64 but with water vapour at p = 2000 Pa. 5

I/II,I L

3

Water vapor p:ZkPa

E =10 keV

2

Bias , V

1 0

2

L

6

0

10 I

-1

-.

-1

FIG.66: Same conditions as in Fig. 65 but by use of cup A as collecting electrode

211 - 5

I/IL,I

.. L

-10

-8

-6

-1

-2

.. 3

Helium p.2kPa

.. 2

E :lo keV

.. 1

Bias . V

0

2

L

6

0

10 4

L

A2 ..-3 ..-L

FIG.67: Same measurements as in Fig. 65 but with helium.

gaseous detector device and in the interpretation of contrast. The statement that going from positive to negative bias inverts contrast is approximately correct. More precisely, it should be stated that contrast is inverted when we pass the cross-over point. Experiments of this type can help understand the ionization state of the gas in the conditions used in the ESEM and also measure the amplification of signal. These first experiments lack the precision of properly designed Langmuir probes, but it is possible to obtain first order approximations. There is a relationship between saturation current Z, and ion density n+ for plasmas (v. Engel, 1983)

where A is the electrode area, and u+ the perpendicular velocity of the ion at the sheath edge (Bohm velocity) which is usually 103-104 m/s. A rough estimate of the surface area of the electrode along the total unshielded length of wire is A = 3 x lop5 m2, and taking Z, = 3 x 10-lo A (since Z, = 190 PA) from B1 in Fig. 65, we find n+ -- 6 x 10” ions/m’, which is

212

G. D. DANILATOS

three orders of magnitude lower than the maximum concentration estimated by Eq. (101) for nitrogen from the maximum value of GNpublished by Grun (see numerical example after Eq. (101)). With such a low ion concentration, the Debye length is 0.03 m (for T + = 1 eV), which is generally less than the dimensions of the specimen chamber but more than the specimen-PLA1 distance. Therefore, the gas may or may not behave as a plasma, depending on the actual electrode configuration and the true values of It+ and T + in the region concerned. When the beam is directed inside the hole, the BSE and SE from the specimen are effectively suppressed and ionization occurs by the primary beam only, provided the electron skirt is smaller than the hole. This can be checked by the saturation values of B1 in Fig. 64 and the ionization efficiency from Fig. 43. With an ionization efficiency of 0.37 ion pairs/mPa, the expected value for the saturation current is 0.23, while we read 0.35 in Fig. 64. The difference can be attributed to electrons in the skirt striking the aperture grid outside the hole. From relationship (84) we = 20 pm, which means that half of the scattered electrons are find within 40 p m diameter. As the electron beam was scanned a little off-centre across the hole, the tail of the skirt should strike the top surface, and the generated signal should create the additional ionization current. Indeed, the difference between measured and expected values becomes less both in absolute and relative values when the pressure is decreased and vice versa. There are two competing effects: one tends to decrease contrast by scattering electrons out of a probe, and another tends to increase contrast by ionization. Therefore, in measurements of profiles of ionization currents, these two competing effects must be taken into account for the calculation of signal gain. In the present measurements, the difference B2-Bl can be used directly as a measure of signal amplification, provided that both the scattered and unscattered beam electrons fall inside the hole in position (1) and outside the hole in position (2). Otherwise, this difference will represent an underestimation of amplification gain. It must be remembered in these considerations of gain that the beam current in vacuum has been used as a measuring unit, but this unit must be replaced by the BSE or SE current in vacuum when the amplification of these signals is sought correspondingly. It is fortunate that the primary beam produces a gain around unity, or generally less (it depends on gas, pressure, accelerating voltage and travel distance), while the physical upper limit of gain for BSE with an average energy, say, 10 keV is about 300. However, this limit cannot be reached in practice, because the BSE are not allowed to dissipate all their energy into the gas and not all the ion pairs are collected. This is a case for future experimentation and studies to design an efficient device to maximize the

FOUNDATIONS OF ESEM

213

collected current. There are several possibilities or effects known in the field of ionization of gases that can be exploited. For example, the “Penning effect” can increase the ionization efficiency considerably. The SE are not expected to create any substantial amplification as the majority of them have an energy less than 10 eV. Those SE with higher energy can produce an ionization current. A system of shielding electrodes with appropriate bias and gas pressure can be used to separate currents corresponding to electrons with different energy. The signal separation can then be followed by a signal amplification in the high % / p regime. 2. Imaging

Some of the above ideas on the gaseous detector device can be illustrated by simple means through imaging. Following the same specimen as in Figs. 47 through to 50, we can see new variations on the image by changes of various parameters. By applying a negative bias -10 V, the contrast should be inverted according to Fig. 65. Indeed, this is shown generally to be the case in Fig. 68 compared with Fig. 49. This proves that positive ions can be used for imaging. It is interesting to note that this corresponds nearly to the SE image, and therefore, the high energy SE together with low energy BSE (perhaps around 100 eV) should be responsible for the characteristic features appearing on this image (the low energy SE do not ionize the gas). By raising the pressure only, the positive ions produce an image close to the BSE as shown in Fig. 69, in which the output from the electrode has been

FIG.68: Same specimen as in Fig. 49, now imaged with a negatively biased electrode at -10 V, at 200 Pa.

214

G . D. DANILATOS

FIG.69: Same conditions as in Fig. 68 except at 700 Pa. The image has been electronically inverted.

inverted electronically to make its comparison with Fig. 48(and Fig. 47) easier. The positioning of the collecting electrode also determines the type of image produced. By moving the loop electrode (B) around the side of the stub below the level of the specimen (7 mm lateral and 5 mm vertical displacement), we obtain Fig. 70. In this, the characteristic features of the SE image are absent (at the same pressure), but the atomic number contrast is also suppressed. It shows mainly topographic contrast, and it

FIG.70: Same specimen as before with electrode moved around the side and biased with +5 V in nitrogen at p = 200 Pa.

215

FOUNDATIONS OF ESEM

FIG.71: All conditions same as in Fig. 70 except at p

=

880 Pa

can be attributed to the low take-off angle BSE. The electrons can ionize the gas at a relatively long distance, where the electrode can collect the resulting current. With all parameters constant except by raising the pressure, we obtain Fig. 71, in which the familiar Z-contrast is recovered. In this case, the high take-off angle BSE should be responsible for the contrast, since they can produce enough ionization before they lose their energy by absorption on the top walls. It is the relative intensity of the various contributions from signals which determines the total image. It is instructive to include also two images of the same specimen obtained with the CL detectors. Figure 72 shows the CL image at 220 Pa

FIG.72: Image of the same specimen obtained with the CL detectors at 220 Pa

216

G. D . DANILATOS

FIG.73: All same as previous figure except at 840 Pa.

pressure of N2, and it looks practically the same as the SE image. By raising the pressure to 840 Pa, the characteristic SE feature seen in the middle-right is preserved contrary to Fig. 71, where it has disappeared. The image is only more noisy due to the weakened beam at higher pressure. This can be explained by the different relative strength of signals under different detection modes. In Fig. 71, the BSE produce ionization current which overshadows the current due to SE coming from the feature. In Fig. 73, the BSE do not play such a role, as they are not detected. It is further interesting to note that the bright features on the lower left region are only present at low pressure and they are suppressed at higher pressure when we use both the SE and CL mode. This may infer that this effect is due to charging at low pressure and to suppression of charging at high pressure. Charging in the ESEM will be discussed in a later section. 3. Excitation While experimenting with CL detection, it was found that the fluorescence of the gas could be used as a scintillator detector. When the gas produced fluorescence within the spectral response of the light pipe and photomultiplier used, new information could be recorded on the image, distinctly different from the ionization detector device, and different from the CL of the specimen. The reader is referred to a recent report (Danilatos, 1986f) for specific illustrations. Some gases like O2 and H 2 0 did not produce any detectable scintillation while others, such as He and N2, produced strong scintillation. The scintillating gases differ from the plastic scintillator detectors in that they can be excited by low energy

FOUNDATIONS OF ESEM

217

electrons such as SE and low energy BSE, as the specimen is in intimate contact with and surrounded by the gas (detector) so these signals can easily excite it. Obviously, the CL signal of the specimen is superimposed with that generated by the gaseous scintillation detector device. To separate the specimen CL, a non-scintillating gas must be used, or equivalently appropriate wavelength filters should be introduced. The light output can be increased by the use of a suitable gas or mixture of gases such as Ar/N2 which scintillates stronger than air. The time response of scintillation is important for imaging at high scanning rates. Again, a suitable spectral response can be chosen by appropriate filters. In the case of air, most of the afterglow of N2 is quenched by O2 with a simultaneous gross light output reduction of about 20% (Schumacher and Gadamer, 1958). We have already seen that electrons with different energies excite different spectral responses, and therefore, this would be a way to separate the different types of electron signals. This can be generalized to include other signals. In conclusion, the gas can be used as a multipurpose detector device for any signal-gas interaction which can be monitored in the ESEM.

VII. CONTRAST AND RESOLUTION

A . Objective Contrast and resolution have been studied, discussed and debated extensively throughout the history of electron microscopy. Here, we wish to know how they are affected in the conditions of ESEM. Contrast and resolution generally depend on the primary beam, the specimen and the detection system. The effect of the nature of the specimen is the same as in SEM except that we may now deal more frequently with specimens of low atomic number and density. The effect of the detection systems is again the same as in SEM only when the same detection systems are compatible with the new conditions (e.g. aluminized scintillator detectors). However, the detectors for ESEM can be different, for example, uncoated scintillators, or completely new ones, as the multipurpose gaseous detector device. A thorough undertaking of the effect of various detectors is beyond the aim of this survey, because much more research is needed to better understand this domain. However, the effect of the primary beam on contrast and resolution can be discussed in this section on the basis of the preceding presentation. Our knowledge was mainly empirical in the past, but the following analysis can become a basis for future investigations.

218

G. D. DANILATOS

B. Resolving Power If all other factors are favourable, the limit of resolution, or resolving power, of an SEM is about equal to the beam diameter. We have seen that under conditions of oligo-scattering, the original beam does not broaden but it weakens and acquires an electron skirt. Therefore, the limit of resolution should be the same in ESEM as in SEM. This statement is correct with two qualifications: (a) the other conditions still remain favour'able and (b) the gas pressure is not excessively high. The other conditions are: 1) the detection mode used is associated with a beam-specimen interaction volume not larger than the beam diameter, 2) there is always sufficient contrast and 3) the beam irradiation effects are not problematic. Some of these conditions will be examined later. First, we consider the effects of pressure. We have seen in Section IV that with regard to electron skirt, pressure and specimen distance are not equivalent. By doubling the pressure we have to halve the specimen distance in order to remain in the oligo-scattering regime, but the diameter of the electron skirt becomes smaller (i.e it is not constant). The relation between pressure, distance and skirt diameter can be found by equations like (82), (84) and (85). For example, by maintainingpL = constant, or p L = 0.49 Pam corresponding to m = 1 (see Eq. 81), the skirt width is proportional to L :

r,/2 = 0.014 L for argon at 10 keV. For helium, we obtain correspondingly p L

=

10.1 Pam and

r l I 2= 0.0053 L

Although for low Z gases the r l I 2is less than for high 2 gases at a given L , the reverse is true at a distance equal to the mean free path: at one atmosphere, we have L, (argon) = 4.9 p m and L, (helium) = 101 pm, SO that r 1 / 2(argon) = 69 nm while r , / 2 (helium) = 540 nm. As long as the original spot is one order of magnitude less than the skirt width, the resolving power remains constant, provided that the exponential decay of the useful spot intensity allows a satisfactory signal-to-noise ratio. When the original spot is the same magnitude or greater than the skirt width, both the width and the intensity remain practically constant for low values of m. For intermediate values of spot size, calculations as in Sec. IV can determine the precise beam profile but again, for m not more than about unity, the useful spot size is practically unaffected. It is interesting to note that at very high pressures the skirt width becomes such a small size at corresponding short distances and that the

FOUNDATIONS OF ESEM

219

skirt itself can be used as a probe in certain modes of detection. For example, in X-ray microanalysis, the resolution is determined by the size of the beam specimen interaction volume which is much larger than the spot size and may be larger even than the skirt width. In this case, the total of scattered and unscattered beam can be used for microanalysis, and it happens that the higher the pressure the better. For low pressures and long distances, the elemental analysis would correspond to the total area spanned by spot and skirt which can be quite large. It is not clear at this stage whether the information orginating from the spot can be separated out from the total signal. In conclusion for this mode, if the pressure and the specimen distance could be adjusted so that the electron skirt coincides with the beam-specimen interaction volume, the original resolution would be restored in the ESEM. It should be very profitable to test the above ideas with modern instruments employing very fine electron beams. The available prototype ESEM, being a modified old model SEM, is limited by the original manufacturer’s specifications.

C . Signal-to-Noise Ratio (SNR) As was pointed out above, resolution should be considered in conjunction with the contrast of a particular feature under examination. In particular, the signal-to-noise ratio (SNR) should be estimated to determine whether the feature is visible at all in the first place. In this survey, we examine the effects that the introduction of gas has on the SNR measured in vacuum. We can start with the theory found in Wells’ book (1974) on SNR, which we then modify to suit the conditions of ESEM. Under vacuum conditions, a given electron beam current Zb scanned over a raster produces, at the noise bottleneck, a useful signal (feature) S,l,, which is superimposed on a background level given by &Ib. In the case of an efficient detection system, the noise bottleneck is usually at the signal emerging from the specimen, so 6, + SB is the fraction of the original beam producing the total signal, whilst the remainder fraction 1 - S, - SB is lost in the form of uncollected electrons. The useful signal is usually allocated a number of M gray levels. If the gray levels are allocated in such a way that the SNR is constant from the darkest to the brightest parts of the image (constant reliability condition), then the beam current is related to K , the SNR, as follows:

where

T

is the dwell time per pixel element.

220

G. D. DANILATOS

For fixed K , M and 7, the required current cannot be less than a minimum value I,,, corresponding to the ideal condition of SB = 0 (no background noise) and aA = 1 (100% conversion of the beam to useful signal) :

K2M2e

I,,,= 47

In the ESEM, the original beam splits into a fraction of electrons q remaining in the original spot size and a fraction 1 - q going into the electron skirt. The fraction of electrons scattered outside the skirt is should be negligible in the oligo-scattering regime. The factors 8, and replaced by new ones Sb, and Sg . In order to maintain the same I,,,, (e.g. constant SNR), the beam current should be adjusted accordingly to I;, +

=

A

1

Therefore, the problem in ESEM is to calculate the new Sb, and 6b. The S i is decreased in the same proportion as the original beam

sb, = 46,

(120)

The 6; is not as simple to derive because it depends on the actual conditions prevailing. This factor is composed of the sum of three terms in the most general case. One term is 468 and is due to the weakened beam spot. Another term is due to the electron skirt and depends on the particular specimen and the magnification used. For low magnifications corresponding to a raster larger than the skirt, this term can be found by the scattered electron fraction 1 - q multiplied by a conversion factor between 8, and ,6 + as, depending on the nature of region around the point scanned. For high magnifications producing a raster smaller than the skirt, this term depends on the conversion factor of the electrons falling outside the field of view as well. A conservative estimate for the low magnifications is to take the maximum conversion factor 6, + 6 B , which may also be assumed for the high magnifications. The third term can come from the action of the beam before it strikes the specimen, such as the ionization current of the beam in the case of the gaseous detector device and is denoted by ab. Thus, the total factor sought is 6;

q6B

+ (1 - q)(6, + )6, + 6b

Therefore, by Eqs. (120) and (121), Eq. (119) becomes

(121)

FOUNDATIONS OF ESEM

221

The above equation is the general case which leads to important conclusions under specific conditions as is shown below. (i) If 6 B + 8 b -=cSA, Eq. (122) becomes

When the beam traverses one mean free path, q = exp(-l), so that

23.8 I & = I , -. 6,

In other words, the current must be increased by 23.8 times to maintain the same SNR (compare Eq. (124) with (117) under the present condition). (ii) If SA + 6 h -=c aB, we get

which means that the required current increases by 1/q2. This is a slower rate than in case (i), but the current is already high in view of the background noise. For the case of one mean free path

I;,

=

46h

I, q26:,.

Examples

The most favourable conditions are in case (i). For M = 10, K = 5 and 50 ps (i.e. for 1000 lines in 50 seconds), we have I , = 2 PA. By

T =

FIG.74: Aluminum oxide spheres imaged with the BSE detectors (sum) of Fig. 46 at 500 Pa of water vapour; 5 keV, 15 PA, hfw = 60 pm.

FIG.75: Same as in Fig. 74 except at p

FIG.76: Same as Fig. 74 except at p

=

=

1100 Pa.

2060 Pa.

FOUNDATIONS OF ESEM

223

= 0.1, the actual current necessary calculated by Eq. (124) is assuming 16 = 476 PA. If we accept M = 4 and k = 3, the required current is only 27.5 pA as compared with 1.15 pA in vacuum. In the case where aB = 6b = 0.1 and 6, = 0.02 for the same 1, = 2 PA, the beam current required is 32 nA for a specimen distance of one mean free path. If the detector does not collect the 6b, as in the case of an aluminized scintillator detector where 8 b can be practically zero, the required current would be 17 nA, as opposed to 2 nA in vacuum. Examples of the amount of noise seen in an image of a carbon specimen at 5 keV and 2 pA can be found elsewhere (Danilatos, 1985). Here, some additional examples are given in Figs. 74, 75, and 76. These images were taken with the BSE detector configuration shown in Fig. 46 and show aluminum oxide spheres. The specimen was placed approximately 0.5 mm below the PLAl, and a beam of 5 keV and 15 pA was used. The total scattering cross section of H20 according to Fig. 11 is a, = 7 X m2 at 5 keV (or less according to experimental measurements in Fig. 36). The corresponding mean free paths calculated are 1.16 mm at 500 Pa, 0.52 mm at 1100 Pa and 0.28 mm at 2060 Pa. A subjective evaluation of these images indicates that the loss of resolution with increase of pressure is due to loss of visibility on account of noise. This is consistent with the theoretical predictions in this survey. Also, it can be observed in each image that the local variation in depth corresponds to different SNR. This demonstrates that when the mean free path is a fraction of a mm, an accuracy of some tens of microns is required in placing the specimen below the PLAl. As a general conclusion, contrast and resolution can be maintained in ESEM, provided the beam current is increased by a certain amount. More precisely, the resolution will be governed by the spot size corresponding to the increased current. This increase, however, may cause undesirable beam irradiation effects, some of which can effect contrast and resolution as will be seen in the next section.

EFFECTS VIII. BEAMRADIATION A . Necessity of Study

The deterioration of SNR together with beam radiation effects constitute the most serious difficulty in the ESEM. The SNR should not be a serious problem on its own, that is, for specimens not affected by beam radiation, because the noise can be compensated for by an appropriate increase in beam current as we saw in the preceding section. This increase,

224

G. D. DANILATOS

of course, will affect the ultimate resolving power of the instrument because a larger current corresponds to a larger beam diameter. However, this loss of resolving power may be superseded by irradiation effects, in which case they will be the limiting factor. Therefore, every effort should be made to use the lowest possible current and accelerating voltage by proper design of the electron optics, pumping and detection systems. By beam effects, it is meant all effects whether damaging or not. These are known as charging, heating, contamination and damage which can be in the form of atom dislocation, loss of crystallinity, cross-linking, molecular scission, mass loss, etching, or general chemical reactions. These effects occur in all types of microscopes. However, the presence of gas may modify these effects or even create new ones. There is extensive literature on this topic and as yet, many cases are still only partially understood. An understanding of radiation effects, or a knowledge of, at least, when and to what extent a particular effect occurs, is of utmost importance for the ESEM. This is because, one of the basic objectives is to observe totally unmodified surfaces, or study a particular chemical reaction. This complex question cannot be dealt with in this survey, and it should be taken up during individual research applications in the future. A limited selection from a large stock of observations is presented below in order to warn the reader about this problem and prevent unnecessary misinterpretations in future uses of ESEM. B. Charging It is fortunate that charging is not a problem in the ESEM, in which uncoated and untreated insulator specimens can be examined, as opposed to conventional SEM. Charging can be suppressed in the vacuum of SEM by use of low accelerating voltage, but in the ESEM, suppression occurs in its full accelerating voltage range. This occurs naturally through the good electrical conductance of the ionized gas. The question arising is at what pressure an effective charge suppression takes place. Charging appears in different forms. Sometimes, it becomes directly visible as flickering or edge brightness. Image distortion may or may not be directly visible. These gross forms of charging are generally eliminated with a few tens of Pa pressure. The precise pressure level of elimination depends on the ion concentration, specimen and incident beam parameters. It is more appropriate to refer to this question as charge suppression rather than elimination, as some charge can in most cases be present in the steady state condition. We should then decide whether this charge suppression is satisfactory for a particular application. For example, the measurement of a wool fibre swelling in water vapour is affected when the

FOUNDATIONS OF ESEM

225

FIG.77: BSE image of a gold coated and earthed polystyrene (optical) diffraction grating with an out-of-focus uncoated wool fibre placed 1.5 mm above the grating in nitrogen at 30 Pa; 15 keV, 850 pA, grating spacing = 10 p n , scan time = 50 s .

vapour (or total) pressure in the chamber is below 100 Pa, an artifact which becomes noticeable only with accurate fibre diameter measurements. Measurements of electrical potential and charge densities on cylindrical metal wires and polymer fibres can be made with a technique used by Weitzenkamp (1969). According to this technique, a fibre is placed some distance above an earthed grating and by focusing on the grating, we can observe the amount of distortion and beam deflection, which is a measure of charge on the fibre. This effect can be seen in Fig. 77, where the dark zone is an out-of-focus wool fibre placed above a gold coated polystyrene diffraction grating with 10 ,urn spacing. The PLAl-grating distance was 3 mm, and the fibre was positioned halfway between these. The amount and form of distortion of the grating lines depend on the scanning speed as can be seen in the next image (Fig. 78) by use of 5 seconds per frame as opposed to 50 seconds in the previous one. The direction of scanning lines relative to the specimen is responsible for the unsymmetrical distortion observed. The fibre responsible for these images is shown in focus in Fig. 79. A lower accelerating voltage (10 kV) at a little higher pressure, still shows pronounced distortion as in Fig. 80. The use of lower kV may correspond to less charging, but at the same time, the deflection is more pronounced. Thus, a little distortion still appears at 200 Pa when using 5 kV as in Fig. 81, but no distortion is observed in Fig. 82 at 100 Pa and 15 kV. No calibration was attempted to determine the absolute level of electric potential on the fibre, but this method gave a good indication of charging artifacts that can be present at low pressure in this particular

FIG.78: Same field of view as in Fig. 77 at p = 40 Pa and scan time = 5 s.

FIG.79: Same wool fibre of previous image in focus.

227

FOUNDATIONS OF ESEM

FIG.81: The wool fibre-grating system in a different direction at p 350 PA, scan time = 50 s.

FIG.82: The wool-fibre-grating system in a different direction at p 850 PA, scan time = 50 s.

=

=

100 Pa; 5 keV,

100 Pa; 15 keV,

application. T o take measurements of dry fibre diameters, dry helium was used at about 500 Pa, instead of vacuum. The above, or related methods, can be used to determine the level of surface charging and its suppression in the ESEM during applications. The suppression of charging artifacts by gas was known to early microscope designers (Cosslett, 1951) and was later used by other workers (Pfefferkorn et al., 1972; Parsons et al., 1974; Moncrieff et al., 1978). Moncrief et al. (1978) have proposed that charge neutralization is not

228

G . D. DANILATOS

sensitive to gas pressure, provided only that there is sufficient gas to produce a compensating ion current. They observed that a gas pressure of 10 Pa eliminated charging artifacts in observations on sodium chloride, as judged by image sharpness. Hence, they concluded, it is often sufficient to rely merely on a residual poor vacuum without the deliberate introduction of gas. However, the experience of the present author and the above sited examples do not agree with such a general conclusion.

C. Contamination Contamination is almost always found in electron microscopy, and only with very clear systems and ultrahigh vacuum can it be effectively controlled. The latter applies to the type of contamination arriving from residual hydrocarbon gases in the specimen chamber. Contamination can also appear on specimens not properly prepared, on which surface hydrocarbons are already absorbed and which show high surface mobility (see e.g. review by Reimer, 1985). Contamination may or may not occur in the ESEM. Lane (1970) and Parsons et al. (1974) have reported the beneficial (cleaning) effects that a gaseous environment can have. The present experience is that contamination has not been a problem with most applications undertaken. This may have resulted by the continued effort to use the lowest possible accelerating voltage and current with not very high magnifications. However, as it was mentioned earlier, contamination was observed when attempting to measure the profile of a beam scanned across an unheated wire. Heide (1960) has reported the possibility of contamination and etching occurring simultaneously inside an environmental cell of a transmission electron microscope. H e actually measured the rate of build-up of contamination which can be positive, zero or negative, depending on the nature and pressure of gas. A brief attempt to observe the same effects in the ESEM was without success. The cause is believed to be the different accelerating voltage, different specimen and environmental conditions and the different characteristics of the SEM as opposed to a conventional transmission electron microscope (e.g. scanning mode, scanning rate, bulk specimen). The possibility of etching and contamination counteracting each other would be of importance in the ESEM, and a systematic search should be undertaken in future work. It is important to establish how contamination affects the surface properties of uncoated, untreated specimens and in particular that of liquids. Occasionally, a thin crust is observed to form on the surface of water, and it is not known whether this is caused by deposition from the

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~

FIG.83: Nickel. :hromium wire in contact with water held at the tip of a glass (:apillary needle, at 1800 Pa of water vapour; 10 keV, 200 PA, wire diameter = 44 im.

gaseous phase or whether it is the product of a chemical process triggered by the action of the beam on contaminants in the liquid phase. A large amount of “strange” phenomena have been recorded during the operation of the ESEM. As most of these observations were unexpected, no proper controls were introduced, and their study fell outside the specified tasks of the work. It is with such an understanding that the following excerpt is presented. During studies on contact angles, made by observing the “advancing” and “receding” miniscus of liquids on fibres, metal wires were also tested. A nickel-chromium wire can be seen in contact with water (Fig. 83) held at the tip of a capillary needle of the microinjector system (Danilatos and Brancik, 1986e). The wire could be moved relative to the water, and the contact line was monitored. The water was not distilled and there was a possibility that it was contaminated with some organic matter from previous use of the needle on wool fibres. Initially, the water surface looked smooth with continuously varying contrast. However, after several minutes of observation under the beam, some distinct dark patches appeared on the surface. The wire was moved a short distance in one or the other direction along its axis and, omitting the intermediate patterns, the configuration of the water surface is seen in Fig. 84. The surface shows discontinuous contrast and “bumps”, a variation of which can be seen in the subsequent image (Fig. 85). By pulling the wire away from the water, the result is shown in Fig. 86. By a further small movement along its axis, a crust structure is clearly revealed on the surface of the liquid (Fig. 87). By separating the “water” from the wire, it acquired a solid-like and stable

FIG.84: Same system as in Fig. 83 showing irradiation effects.

FIG. 85: Same system as in previous figure after additional exposure to radiation.

FIG.86: Same system as in previous figure with wire displaced some distance away from needle.

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FIG.87: Same system as in previous figure with wire displaced some distance along its axis.

FIG.88: Same system as in previous figure with wire separated from “water”

appearance (Fig. 88), but by bringing the wire and “water” back in contact, the liquid-like behaviour returned and it readily wetted the wire as in Fig. 89. By yet a further detachment, the solid-like form returned (Fig. 90) and the same phenomenon was repeated several times. These observations were not furthered to determine the role of the nickelchromium in these reactions during which the dark patches seemed to associate with it. The crust extended much further over the liquid system, and it is not clear whether it represented a contamination effect, or whether the phenomenon should be studied under some other heading.

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FIG.89: Same system as in previous figure with wire re-attached to “water”

FIG.90: Same system as in previous figure with wire again separated from “water”

D. Damage

Several examples of beam damage will be given below as it appeared in to very high levels, or as it occurred in the normal course of investigations. This presentation is kept to a minimum as some data has already been reported (Danilatos and Brooks, 1985; Danilatos, 1986d), and a future report is intended to include the main study. The aim here is to caution the prospective user of ESEM from the possible misuse of the instrument and to stress the need for employing the lowest possible beam dose. This is also aimed at the designer of an ESEM who should employ the most updated

ESEM by either deliberately increasing the radiation dose

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FIG. 91: Typical radiation effects on wool fibre surface under different exposures (times and magnifications) and pressures in nitrogen; BSE (sum of detector outputs) image with 10 keV. 200 PA, hfw = 50 pm.

FIG.92: Normal appearance of wool fibre surface under low radiation exposure; BSE image with 5 keV, 150 PA, hfw = 50 p m .

and efficient beam focusing, detection and specimen handling techniques. A typical appearance of damage on wool fibres is shown in Fig. 91. This specimen was observed at various magnifications up to 1 0 0 0 0 ~by use of a 10 keV and 1650 pA beam current. It was exposed under the beam continuously for 10 minutes in an atmosphere of nitrogen between 300 and 1000 Pa. Different types of damage took place: cutting, etching, pitting, creasing and bubbling. None of these visible effects took place when using 5 keV and 150 pA under repeated imaging as in Fig. 92. However, the

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FIG.93: Same fibre as in Fig. 92 following irradiation with 20 keV, 320 PA, in helium at 100 Pa for 10 mins; BSE image with 5 keV, 150 PA, hfw = 50 p m .

FIG.94: Wool fibre irradiated with 10 keV, 200 PA, in water vapour at 400 Pa for 10 mins; BSE image with 10 keV, 200 PA, hfw = 50 prn.

same fibre suffered severe mass loss from within, and bubbles appeared on the surface following exposure of the fibre for 10 minutes at 20 keV in 100 Pa of helium (Fig 93). The magnification at which the exposure took place, in this and the following cases, can be inferred from the distinct damage raster seen on the fibre. The bubbling becomes more intense when using water vapour (Fig 94). The observed features are not craters of burst bubbles as the low accelerating voltage used for imaging the same specimen reveals (Fig 95). Cluster-bubbles like flowers and severe mass

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FIG.95: BSE image of same specimen immediately after previous image with 5 keV, 150 pA.

FIG.96: Wool fibre irradiated with 20 keV, 1350 PA, in argon at 400 Pa for 10 mins; BSE image with 20 keV, 130 PA, hfw = 50 pm.

loss is shown in Fig. 96 following irradiation for 10 minutes in argon. A fibre irradiated under the conditions of Fig. 97 was imaged with the gaseous detector device by use of the floating graphite rod, around which the fibre was wrapped, as current collector. Note that the dark region on the surface of the same fibre does not appear in a subsequent image taken with a BSE detector (Fig. 98). The difference can be explained by assuming that a thin carbonized layer has formed on the heavily irradiated area and that SE are the main contributors to the contrast in Fig. 97. This explanation is compatible with the knowledge that a carbon layer has low

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FIG.97: Wool fibre irradiated with 10 keV, 3800 PA, in water vapour at 740 Pa for approximately 30 mins. Imaged by collecting the ionization current with the fibre mounting rod (floating, no bias) and the same beam parameters; hfw = 60 pm.

FIG.98: Same fibre imaged with a BSE detector (200 PA) after previous image

SE yield (see e.g. Reimer, 1985). The BSE collected could not “see” the thin layer because their information depth far exceeded the thickness of the layer. Observations of beam damage (lethal effect) have been made on whole live Leptospermum fluvescens seedlings. The examination of live and fresh biological specimens has been reported previously (Danilatos, 1981a; Danilatos and Postle, 1982b). Live seedlings were imaged along their entire body inside the ESEM under saturation water vapour pressure at room temperature using 7 keV beam. Following this examination, they were returned to a wet petridish where they continued to grow during

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FIG.99: Cell collapse appearing on the stem of live Leptospermumflavescens some time after its examination in the ESEM under saturation water vapour pressure with 7 keV and about 1500pA beam (BSE).

FIG.100: Bacillus apiarius spores with loss of edge definition during prolonged imaging; 10 keV, 200 PA, hfw = 13 p m (BSE).

several days monitoring. However, if the same seedling was examined again on the following day, the previously imaged cells appeared collapsed (Fig. 99), an event that took place between the examinations. Such collapse did not take place when using lower beam current and monitoring the image on a video recorder for brief exposures. Beam radiation effects can also affect contrast and resolution adversely. For example, the poor definition of Bacillus apiarius shown in Fig. 100 is not due to a resolution limit imposed by the instrument or the original specimen. It is due to beam damage on the specimen as can be seen in the

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FIG. 101: Image of spores at three times less magnification than previous image.

next image (Fig. 101) by lowering the magnification and noting the raster corresponding to the higher magnification. Much improved images of the same specimen are shown in the next section.

IX. OPERATION ANDAPPLICATIONS A summary, discussion and conclusion is presented in this final section through a description of normal operation and applications of ESEM. To avoid a long speculative discussion on all possible developments of the system and its applications, only a small number of examples is given here from the available data and results obtained with the prototype machine. It can be said, though, that the full potential has not yet been realized as evidenced from the results to date. The present survey has demonstrated that the ESEM is a viable and functional tool with two reservations; (a) the instrument must be correctly designed and (b) it must be properly operated. There is not much room for compromise. Most of the work over recent years concentrated on defining and fulfilling these reservations. The applications undertaken were limited not by physical considerations of the technique but by insufficient resources being available to allow further developement and use of ESEM. A . Operation

A concise description of basic requirements and useful tips for the operation of ESEM are given below. The instrument can be started with a

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vacuum as any other SEM. The specimen chamber should be connected through regulating valves to a water reservoir or to containers with other gases. The relative humidity in the specimen chamber cannot become 100% if the specimen chamber and the water reservoir are at the same temperature because of the finite value of conductance of the intermediate tubes and valves. Saturation vapour pressure conditions can be ensured by incorporating an (additional) water container in the vicinity of the specimen or by raising the temperature of the external reservoir. In experiments that entailed consecutive wetting and drying of a specimen, the second method was found more practical. The leak of vapour through PLAl is continuously replenished from the liquid phase in the water reservoirs and the specimen. This should lead to lowering of the effective temperature of the system. However, this lowering of temperature can be minimized by choosing a relatively large water reservoir with large exposed surface. Several grams of water in a small aluminum reservoir on the specimen stub has resulted in only a couple of degrees lower temperature. Good heat conductivity of the reservoir also contributes to stability. A microinjector system, as mentioned in the beginning (Fig 2), can also be used for local wetting of specimens. For atmospheres other than water vapour, different gases can be transferred from compressed cylinders with an inflatable balloon. There is a tendency not to incorporate a specimen exchange chamber (airlock) in most SEMs. While the absence of this feature can be justified for operation in vacuum, its presence can be very helpful in the ESEM design and operation for various reasons. To maintain a specimen fully hydrated in the time of transfer from atmospheric pressure to saturated water vapour pressure, the pressure around the specimen must be decreased monotonically to the equilibrium value. This requires a water reservoir to replenish the pumped out vapour during the process. If this reservoir is separated from the specimen via valves and tubes, there is a danger that the pressure around the specimen will decrease below the saturation level during pumping down. Thus the water reservoir must be placed as close to the specimen as possible. This reservoir should not be placed inside the specimen chamber because of the danger of splashing water on critical parts (e.g. PLA1, detectors) during outgassing. Therefore, it should be connected to the main chamber via a large bore valve. In addition, there should be a parallel connection with a needle valve to regulate the pressure for levels less than saturation. An airlock (specimen exchange chamber) incoporating a water reservoir can have the following advantages: (a) The pump down time is shortened. (b) The amount of water vapour being pumped out is less, and this eliminates the need to introduce vapour traps for protection of the associated pump.

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(c) Perhaps most importantly by virtue of the airlock, air will not leak in and out of the electron optics column and in particular through the PL Al and PLA2, which increases the risk of blockage and contamination, each time a specimen is taken in or out of the system. The introduction of additional valves to stop air flow through P L Al and PLA2 may be difficult to design and incorporate in the already restricted space in their vicinity. (d) In cases where the specimen must remain in contact with liquid water, the critical parts in the specimen chamber will remain protected form splashing. It must be emphasized that the role of airlocks in the ESEM goes beyond that of microscopes operating in vacuum. Their extra role will be to precondition and condition both the specimen and the specimen chamber and ensure smooth operation of the instrument. The ESEM airlocks require new and special consideration in their design. Another important part of an ESEM which must comply with the requirements arrived at in the preceding survey is the specimen stage. This should be equipped with electronic controls to place and move the specimen at a short distance below the P L Al without touching critical parts of the instrument or destroying the specimen. These controls should produce an accuracy of at least l p m . The accurate positioning at the optimum distance allows the use of the minimum beam current with best imaging. The computerization of modern electron optics in microscopes should be extended to control the airlock and its environment, the specimen chamber environment, the specimen stage and the various pumping stages, all under a unifying logical scheme. An important factor in the operation of ESEM is the specimen preparation. It is sometimes said that ESEM “abolishes” preparation. This is not generally correct, as the amount and type of preparation depends on the specimen. The most elementary requirement is mounting the specimen correctly. As the usual adhesives may be incompatible with many wet specimens, other means to support and fix the specimens should be improvised and established. Aluminum foils, clips, pins or small cavities have been used. On many occasions, the surface tension of liquids is sufficient support. However, a thin film of liquid over the examined area produces very poor contrast, especially on biological tissue. Hence, special preparation techniques or controls should be found to improve contrast. Many of the existing fixing and staining techniques can still be used in the wet state. Perhaps, these could be adapted or new ones developed for the ESEM. After all, quite often the purpose of treatments is to reveal some hidden substructure or feature, and it is a challenge to achieve a similar result for hydrated specimens.

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B. Applications This author has been involved mainly with applications in the field of wool fibre research, while activities in other fields were restricted to plain imaging, observations and demonstrations of the capabilities of ESEM. This instrument proved very useful and effective in determining the shape of Bacillus upiurius between dry and wet states (Danilatos et al., 1984) shown in Figs. 102 and 103. The incident beam current was not increased

FIG.102: BSE image of Bacillus apiarius spores dispersed on carbon surface, in vapour pressure corresponding to 12% relative humidity at room temperature, under minimum beam exposure; 10 keV, 200 PA, hfw = 7 pm.

FIG.103: Same specimen as in previous figure at 99% relative humidity.

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FIG. 104: Bacillus apiarius spores on sticking tape without dispersing, at 240 Pa of water vapour, with same beam conditions as previously.

FIG.105: The root of a fully hydrated live Leptospermum fluvexens at room temperature; 15 keV, 210 PA, hfw = 250 pm (BSE).

in the wet state, so the image appears noisy, but the resolution is practically the same. This example shows the best resolution with unstained biological specimens to date. Good contrast has been achieved by dispersing the spores on a polished carbon surface with water. This way of mounting the specimen minimized the factor Sb and hence required less beam current. These images should be compared with Figs. 100 and 101 which demonstrate the effect of beam damage on resolution. They should also be compared with Fig. 104 in which the spores were not dispersed, and

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FIG.106: Part of stem near the leaf of same specimen under same conditions as previous image.

FIG. 107: Leaves of previous specimen.

contrast and resolution are again poor in the regions where the spores are lumped together. Therefore, with a little care in preparation and specimen handling, imaging can be improved significantly. The examination of living specimens has already been established (Danilatos, 1981a; Danilatos and Postle, 1982b). For example, the images in Figs. 105, 106 and 107 show the root, stem and leaves of a live Leptospermum pavescence in the fully hydrated state just after germination. This type of specimen could be imaged at various stages of growth. Figure 108 shows the middle layer of its seed coat as it splits open during

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FIG.108: Seed coat of Leptospermum Javescens during germination imaged under same conditions as before.

FIG.109: BSE image of suint and dirt particles on wool fibres in the dry state (100 Pa) following extraction in petroleum spirit; 10 keV, 130 pA, hfw = 90 p m .

germination. The crystals observed in the image have not been dissolved away by applying the preparative techniques of conventional SEM. Some examples from the applications to wool fibre research are given below. For wool scouring, it is important to know the type and distribution of various components of matter on the fibre surface after shearing. The light microscope has its limitations in these studies, and the ESEM has offered valuable complementary information. For example, untreated raw wool fibres can be imaged at various relative humidities between the dry

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FIG. 110: Same specimen as before at 95% relative humidity.

and wet state. This discriminates the hygroscopic from the non hygroscopic components as well as their abundance and distribution. The point of relative humidity at which a particular component dissolves is a useful clue in identifying the component. The fibres can be partially cleaned with suitable surfactants to preferentially remove certain components and then study the remainder material on the fibre surface. The cleaning can be done outside the microscope as a pretreatment, or in situ with the microinjector device. Figure 109 shows suint and dirt particles left behind after extracting greasy wool fibres in petroleum spirit. By introducing water vapour in the chamber, the same fibres are seen in Fig. 110, where the suint has gone into solution as opposed to some dirt particles which appear unchanged. To identify the corresponding points between the dry and wet states, account should be taken of the fibre twist which invariably takes place during changes of relative humidity. A further example is shown in Fig. 111 of a totally untreated fibre where the various contaminants form a continuous layer swollen in the wet state but much thinner and partially transparent to the electron beam in the dry state (Fig. 112). For further examples on wool fibre work, the reader is referred elsewhere (Danilatos and Brooks, 1985). A11 applications of ESEM have been done in an environment not exceeding the saturation water vapour pressure at room temperature; only the possibility of imaging at or near atmospheric pressures has been demonstrated, in several reports, by the present author. The main difficulty at these high pressures has been the placing of the specimen at the correct distance from the PLA1. N o attempt was made to construct a special specimen stage, and the available one provided an extremely crude

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FIG.111: Totally untreated greasy wool fibre at 95% relative humidity with other conditions same as before.

FIG.112: Previous fibre in the dry state.

movement. Only by trial and error could the specimen be moved and imaged. These difficulties must be overcome before routine applications are attempted at one atmosphere. However, imaging has been practised, and the quality of images has improved significantly by comparing the first images (Danilatos, 1980a, 1980b) with later ones (Danilatos and Postle, 1982a; Danilatos, 1985). An example (not the best) is given in Fig. 113 showing a stoma and surrounding cells on a fresh leaf at ambient conditions (1 atm, 20" C and about 60% relative humidity). It should be pointed out that all images presented in this work were

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FIG.113: BSE image of a freshly cut leaf ot Leptospermum jlavescens at atmospheric pressure; 15 keV, 850 PA, hfw = 62 p m .

obtained without any signal processing apart from plain signal mixing. Electronic methods such as noise averaging to improve image quality are yet to be employed and, therefore, significant further advancements in this respect are feasible. C. Conclusion

In this survey, an effort has been made to present the fundamentals of theory and practice of environmental scanning electron microscopy. On the one hand, the overemphasis of the advantages and speculation of the potential of ESEM, which is yet to be realized, has been deliberately avoided. On the other hand, the problems and difficulties as experienced and perceived by this author have been outlined and highlighted. The most basic requirements for the design, construction, operation and applications have been analyzed and discussed. The ESEM should be seen as a natural progression and development of SEM. The former incorporates or extends the latter. Its uses include those in vacuum and also those in a gaseous environment ultimately up to a pressure of one atmosphere. The gaseous environment and the introduction of the multipurpose gaseous detector device can yield novel information. Biology should be a field to benefit from it, but, generally, many applications can be found in other fields of research. Both inorganic and organic physical sciences stand to benefit from it, in academic and industrial research. It is hoped that this survey has furnished the evidence and assurance for continued research on a wider scale in the future.

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ACKNOWLEDGMENTS Electro-Scan Corporation is gratefully acknowledged for the financial support during the preparation of the manuscript. I also wish to thank D.H. Tester for reading and commenting on the manuscript, A.L. Tester for her prompt and efficient typing and T.M. Novak for the presentation of quality drawings.

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Moliere, G. (1948). Zeits. Naturf. 3a, 78. Moncrieff, D. A . , Robinson, V. N. E., and Harris L. B., (1978). J . Phys. D: Appl. Phys. 11, 2315. Moncrief, D. A., Barker, P. R., and Robinson, V. N. E. (1979). J . Phys. D: Appl. Phys. 12, 481. Mott, N. F., and Massey, H. S. W. (1965). “The Theory of Atomic Collisions”, Oxford Clarendon Press. Parsons, D. F.,Matricardi, V. R., Moretz, R. C., and Turner, J. N. (1974). Adv. Biol. Med. Phys. 15, 161. Pauli, W. E., (1920). Zeifs. Phys. 21, 11. Pfefferkorn, G . E., Gruter, H., and Pfautsch, M., (1972). Scanning Electron Miscrosc. 147. Rasul, A., and Davidson, S. M. (1977). Scanning Electron Microsc. I, 233. Reimer, L., Gilde, H., and Somrner, K. H. (1970). Optik 30, 590. Reirner, L., Volbert, B . , and Bracker, P. (1979). Scanning 2, 96. Reirner, L. (1985). “Scanning Electron Microscopy”, Springer-Verlag, Berlin. Rishton, S. A., Beaumont, S. P., and Wilkinson, C. D. W. (1984). 1.Phys. E: Sci. Instrum. 17, 296. Robinson, V. N. E. (1975). Scanning Electron Microsc. I, 51. Schriifer, E. (1957). Zeits. angew. Phys. 9, 88. Schurnacher, B. (1953). Annalen der Physik 13, 404. Schumacher, B . , Stuttgart, und Hechingen (1953). Optik 10, 116. Schumacher, B. W., and Gadarner, E. 0. (1958). Can. J . Phys. 36, 659. Schurnacher, B. W. (1962). Ontario Research Foundation Physics Research Report No. 5806. Schumacher, B. W. (1968). Ontario Research Foundation Physics Research Report No. 6604. Schumacher, B. W. (1982). Upublished manuscript. Smith, K. C. A. (1985). J . Microsc. 139, 177. Shapiro, A. H. (1953). ”The Dynamics and Thermodynamics of Compressible Fluid Flow”, The Ronald Press Company, New York. Smith, R. C., and Schumacher, B. W. (1974). Nucl. Inst. and Methods 118, 73. Spencer, L. V. (1955). Phys. Rev. 98, 1597. Spencer, L. V., and Coyne, J . (1962). Phys. Rev. 128, 2230. Sternheimer, R. M. (1966). Phys. Rev. 145, 247. Tavard, C. (1969). C. R. Acad. Sc. Paris 268, 773. Ulsh, R. C., Wellenstein, H. F., and Bonham, R. A. (1974). J . Chem. Phys. 60, 103. Vaughan, W. H. (1976). Scanning Electron Microsc. 1, 745. Venuti. G. S. (1983). Scanning Electron Microsc. IV, 1555. Weitzenkamp. L. A , , (1969). J . Phys. E: Sci. Instrum. 2, 561. Wellenstein, H. F., Bonham, R. A., and Ulsh, R. C. (1973). Phys. Rev. A 8, 304. Wells, 0. C. (1974). “Scanning Electron Microscopy”, McGraw-Hill Book Company. Wells, 0. C. (1978). Scanning 1, 182. Wentzel, G. (1927). Zeits. Phys. 40, 590. Whyte, G . N. (1963). Radiation Res. 18, 255. Williams, E. (1939). Proc. Roy. SOC. A 169, 531. Wyman, L. L. (1933). Trans. A.I.M. E . 104, 141. Wyman, L. L. (1934). Gen. Elec. Rev. 37, 120. Wyman, L. L. (1934). Trans. A.I.M.E. 111, 305. Wyman, L. L. (1937). Trans. A . I . M. E. 137, 291.

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOL. 71

Optical and Acoustic Device Applications of Ferroelastic Crystals STEVEN W. MEEKS IBM Research Alrnaden Research Center San Jose, California

B. A. AULD Edward L. Ginzton Laboratory Stanford University Stanford, California

I. Introduction .................................................... 11. Periodic Domain Walls and Ferroelastic Bubbles in NPP . . . . . . . . . . . . . . . . . . . . . .................................. A. Periodic Domain Wall Arrays B. Free Energy Theory of NPP Pe omain Gratings . . . . . . . . . . . . . . . . . . . 111. Interaction of Optical and Acoustic Waves with Ferroelastic Domain Walls A. Acoustic Reflection from NPP Domain Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Optical Reflection from an a-type Ferroelastic Domain Wall in NPP . . . . . . . IV. Optical and Acoustic Devices Using NPP Periodic Domain Wall Gratings . . . . . . A. Tunable Active Optical Grating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Tunable Active Grating Laser .................................. C. Tunable Acoustic Filter .................................. V. Conclusions and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Future Directions . . . . . . . . . . . . . . . . . . . . . . . . ................ References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 1 256 257 281 292 293 304 327 327 336 339 350 350 352 354

I. INTRODUCTION Ferroic (hysteretic) materials, such as ferromagnetics and ferroelectrics, have long been of interest to physicists and engineers because of their switchable configurational states with distinct macroscopic material properties. In physics, this interest has led to the development of an extensive body of knowledge concerning ordering in solids, phase transitions, 25 1 Copyright 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved ISBN 0-12-014671-1

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domain wall formation, and so on. Engineers have focused on the possibilities for technological exploitation and have realized a variety of applications in the areas of electronic memories (for example, magnetic bubbles, light valves, and displays of various types) and transduction materials (for example, polarized ferroelectric ceramics). Ferroelastics, another class of ferroic materials, are also of great interest because the abrupt change in physical properties at a ferroelastic domain wall constitutes an interface that reflects optical and acoustic waves (Meeks et al., 1983; Meeks and Auld, 1983; Meeks and Auld, 1985; Tsukamoto et al., 1982, Meeks et a l . , 1985a; Meeks et a l . , 1985b; Meeks and Auld, 1986). The position of ferroelastic domain walls can also be tuned by addressing the material with a stress field. This chapter will discuss tunable arrays of ferroelastic domain walls that have been used to create several demonstration devices. The potential applications of these domain arrays are numerous and exciting. They include: tunable active gratings for lasers, tunable diffraction gratings, tunable Bragg reflection gratings, tunable acoustic filters, optical modulators, and optical domain wall memories. A ferroelastic material is one in which there exist at least two states of spontaneous strain, which may be switched via an applied stress. Ferroelasticity is the mechanical analogue to ferromagnetism or ferroelectricity. Figure 1 shows a comparison. Ferromagnetism shows a hysteresis between magnetic field and magnetic flux density, ferroelectricity hysteresis between electric field and polarization, and ferroelasticity hysteresis between stress and strain. For this reason, it is the mechanical analogue to ferromagnetism and ferroelectricity. Ferroelasticity was discovered by Aizu (1969) and is the most recent addition to the family of ferroic or hysteretic materials. A more detailed description of ferroelastic hysteresis is shown in Fig. 2. The shape of the ferroelastic single crystal is shown at four positions on the hysteresis loop. If one begins at the top of the loop (at the point of positive spontaneous strain) and proceeds around the loop in a counterclockwise manner, one can see the shape (strain) of the crystal at various points on the loop. This loop is for a ferroelastic which exhibits two states of spontaneous shear strain at zero stress as indicated by the shear distortion from a rectangle at zero stress. As a negative stress is applied, a ferroelastic domain wall will nucleate at the left (or right) side of the crystal and will rapidly move to the right (or left). At the point of zero overall strain, the domain wall will be in the center of the crystal, so that equal amounts of positive and negative strain are present. If the negative shear stress is continued, the wall will move completely to the opposite side of the crystal. so that the crystal is entirely in the negative strain state. A positive shear

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t

253

MAGNETIC FLUX DENSITY

-

MAGNETIC FIELD

FERROMAGNET

t

ELECTRIC POLARIZATION

* ELECTRIC FIELD FERROELECTRIC

t

STRAIN

STRESS FERROEL ASTI C

FIG.1: Hysteresis loops of three ferroic materials.

stress applied at this point will nucleate a domain wall from the right (or left) side of the crystal which will move to the left (or right) leaving the crystal in the original positive strain state. The strains involved in ferroelastic crystals can be quite large, for example, neodymium pentaphosphate (a pure ferroelastic abbreviated NPP) has a strain of 8.7 x lop3 when switching between its two domain states. Such strains can be produced by the small stress of 14 kN/m2 (2 psi) in the case of NPP. Strains of this size would normally break or permanently deform ordinary materials.

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FIG. 2: A ferroelastic hysteresis loop showing the shape of the crystal at various points in the loop.

During the first decade after the formulation of the ferroelastic concept and the discovery of the first ferroelastic-ferroelectric gadolinium molybdate (GMO) (Aizu et af., 1969), a high optical quality material, applications to electrically-operated optical shutters, moving fine line source, read only memories, and electronically variable bulk and surface acoustic wave delay lines were investigated in a number of laboratories (Kumada, 1972; Barkley et af., 1972; Coldren et al., 1977; Lemons and Coldren, 1978; Lemons et af., 1978). A unique property of ferroelastics, by contrast with ferromagnets and ferroelectrics, is that planar domain walls with certain orientations are metastable at arbitrary positions in the crystal. Because of this fact, there exist exciting prospects for using this feature to create electronically programmable periodic grating arrays of ferroelastic domain walls for optical and acoustic device applications. The particular ferroelastic to be discussed in this work is the pure ferroelastic neodymium pentaphosphate (NPP) of stoichiometry NdP,OI,. This ferroelastic was discovered by Danielmeyer and Weber (1972) and was originally intended for use as a high neodymium concentration laser material. A pure ferroelastic is one in which the strain is not coupled to the magnetization or the electric polarization. NPP is a monoclinic crystal of point symmetry 2/m with a second order ferroelastic phase transition at 145°C. Above its phase transition it is an orthorhombic crystal of point symmetry mmm. The ferroelastic species as described by Aizu (1969) is mmmF2/m. This notation simply describes the point symmetry change at

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the phase transition. The space group of NPP is P2,/c. There are two types of domain walls or elastic twins which can exist in NPP. The first type is called an a-type domain wall (Weber et al., 1975) and it is the lowest energy and most frequently occurring wall. This wall is associated with a change in the c crystal axis, as shown in Fig. 3 . To go from one domain state to the other, one rotates the crystal axes by 7~ about the a crystal axis. The angle 2 6 between the adjacent crystal surfaces is approximately 1”.Figure 3 also shows the second type of wall which is denoted a b-type wall. The b-type walls are associated with a change in the a crystal axis. In this case, the opposite domain state is obtained by rotating the crystal axes by 7~ about the c axis as shown in Fig. 3 . The angle 6 is a function of temperature and will go to zero at the phase transition temperature of 145°C (Budin et al., 1975). As one can see from Fig. 3, crystals of NPP have a structural “kink” between two twin states, which can be moved by the application of small shear stresses (2 psi). Part I1 of this chapter presents techniques for injecting pairs of these domain walls into ferroelastic crystals. Also discussed in Part I1 is the discovery of the analogue to a ferromagnetic

0

so’

t

- TYPE DOMAIN WALL a

lo

DOMAIN WALL

0’

FIG.3: The two types of domain walls in NPP; a-type (top) and b-type (bottom)

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bubble, the ferroelastic bubble. An additional discovery of a means of injecting uniformly periodic arrays of ferroelastic domain walls into NPP is presented. A method of tuning the period of these ferroelastic arrays is also described. Part I11 discusses the physics of optical and acoustic wave interaction with ferroelastic domain walls. In the fourth section of this chapter, we present several demonstration devices which use periodic arrays of ferroelastic domain walls. These devices include a tunable diffraction grating, a tunable active optical grating, a tunable acoustic bulk wave filter, and a tunable active grating laser. The concluding section discusses the future directions of this research and gives a summary of the chapter.

11. PERIODICDOMAINWALLSAND FERROELASTIC BUBBLESI N NPP

This section presents some experimental and theoretical results concerning periodic domain walls and ferroelastic bubbles in NPP. A review of previous work in creating periodic structures in ferroic and non-ferroic materials is given at the beginning of this section. Two techniques of creating periodic and aperiodic structures are the lateral domain wall injection technique and the optical injection procedure. The optical technique is particularly exciting, since it offers the promise of optically writing an optical interference pattern onto a crystal of NPP. Another domain wall injection technique is used to create uniformly periodic domain walls in NPP, and is known as the quasi-static nucleation of zig-zag or periodic domain walls. This technique is used to create periodic domain structures with a period of 100 to 0.5 microns. The short range periodicity is excellent and is uniform to within a fraction of an optical wavelength. The long range periodicity is uniform to within 5 2 % of the period. The nucleation process of these periodic structures is described in terms of a newly-discovered domain structure, namely the ferroelastic bubble. The ferroelastic bubble is the elastic analogue to the well-known ferromagnetic bubble. Four different techniques of tuning the period of the arrays are described. The arrays may be tuned relatively rapidly. One of the tuning techniques has tuned the period of a 100 micron array to about 3 microns in 100 ms. The maximum rate of tuning is not yet known. A section has been included which explains the optical diffraction from arrays of NPP domain walls. The best Bragg efficiency is obtained from a crystal with a 58 micron period array and is 77%. Efficiencies of greater than 90% should be obtained from crystals which are anti-reflection coated. The final section of this chapter presents a phenomenological theory which constructs the free

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energy of these periodic structures as the sum of the wall, strain, and interaction energies. The theory gives an excellent fit to experimental data. This theory also predicts the collapse of certain types of these periodic structures at about a 3 micron period. The collapse is due to the combination of the rapidly increasing wall and interaction energies. It is predicted that the upper limit on the period of these zig-zag structures will be limited by the crystal size and not any of the energy terms. It is also predicted that these periodic structures will exist in the rare-earth analogues to NPP: LaPP, PrPP, TbPP. A . Periodic Domain Wall Arrays This section begins with a review of previous work in producing periodic domain structures in ferroic and non-ferroic materials. Other topics are: a brief discussion of early attempts to create periodic structures in ferroelastics, optical injection of ferroelastic domain walls, ferroelastic bubbles and the nucleation process of NPP periodic arrays, the tuning process of NPP periodic arrays, and optical diffraction from these domain gratings. 1. Previous Work on Periodic Domain Structures

It is clear that any technique permitting realization of programmable gratings for the diffraction and reflection of optical and acoustic waves will have important technological implications. The literature contains work on the use of rotationally twinned ZnSe (Dewey and Hocker, 1975) and “stack of plates” of GaAs (Thompson et al., 1976) to produce enhanced non-linear optical effects. Both of these materials are non-ferroic and have fixed period arrays. Zig-zag arrays of ferromagnetic domains have been produced in NiCoP and CoTi amorphous films and are being investigated for use in memory devices (Hamzaoui et al., 1984; Sanders et a / . , 1977). Kim and Khvan (1983) have studied the interaction of acoustic waves and periodic ferromagnetic domain structures in FeBO, and YFeO, wafers. They were able to tune the period of the array from 200 to 600 microns by using an ac field to demagnetize the sample. Two dimensional arrays of magnetic bubbles have been produced in thin garnet films (Slonczewski and Malozemoff, 1978; Garel and Doniach, 1982). These bubble arrays are envisioned for use in memory devices. Ferroelectric and ferroelectric-ferroelastic materials have been used to produce periodic structures via a variety of techniques. Takeuchi and Yamashita (1982) have created a surface acoustic wave reflector by poling

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in a periodic structure in a modified lead titanate ceramic. Belov and Serdobol’skaya (1984) have created a high frequency transducer by periodically poling ferroelectric lead germanate. Newnham, Miller, Cross and Cline (1975) have created a two-dimensional array in the same ferroelectric by using a two-dimensional poling mask. Enhancement of secondharmonic generation in LiNbO, has been produced by an array of laminar ferroelectric domains (Feng et al., 1980). These arrays were produced by periodically varying temperature fluctuations during the growth of the crystal. Periodic stored electric fields have been produced in LiNbO, by photoinduced charge migration (Gottschalk et al., 1983). The stored electric field interacts with an acoustic wave via the electroacoustic effect wherein the stored electric field causes a change in the acoustic velocity. This effect has been used to create bulk acoustic wave filters in LiNb0, (Oates et al., 1985). The period of the array is fixed. To create a different period array the crystal must be reilluminated with interfering light beams. Quasi-periodic domain arrays have been produced in the ferroelasticferroelectric gadolinium molybdate (GMO) by bending and torsion (Krainyuk et al., 1984; Fousek er al., 1976). Some degree of tuning was obtained by increasing the magnitude of the stress. Quasi-periodic structures evidently are produced spontaneously in the ferroelectrics, ferroelastics and ferroelastic-ferroelectrics GMO, tanane, triglycine sulfate, and lead phosphate upon cooling through the Curie point (Bhalla and Cross, 1981; Bornarel and Legrand, 1981; Dolino et al., 1970; Torres et al., 1982a). The first discovery of nearly periodic zig-zag walls in a ferroelastic was made by Flippen and Haas (1973) in GMO and lead phosphate. These zig-zag walls were created by clamping two ends of the crystal and applying shear forces to the free faces. In this case, in contrast with our experiments on NPP (to be discussed in this section), the periodicity direction of the wall is perpendicular to the force direction. Two other, more recent papers (Otko et al., 1983; Dudnik er al., 1983) mention zig-zag walls in KFe(MoO,), , KIII(WO,)~, and Pb3(As0J2 (lead orthoarsenate) but say nothing about their nucleation process, optical or acoustic properties. Another recent Soviet paper (Alekseev, 1983) presents a bulk-to-surface acoustic wave conversion device using a regular array (presumably a zig-zag array) of ferroelastic domains in lead orthophosphate-lead orthovanadate. The authors give no details on how such an array was produced.

2. Early Attempts at Stanford This section will present some early research conducted at Stanford University on producing periodic structures via a “lateral blade domain

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injection procedure” summarized in Fig. 4 (Meeks et al., 1983). The process shown in Fig. 4 is also called nucleation of stripe domains. The ferroelastic crystal is placed in three point bending as shown, and a shear stress of opposite sign to the crystal’s current state is applied to the transverse surfaces via two plastic knife edges. This process causes blade-shaped domains to nucleate underneath the knife edges and move toward the opposite surface. When the stress reaches a critical value, the inner pair of walls of the blade domains collide to form the “stripe” shown at the bottom of Fig. 4.This behavior is typical of GMO, and by repeating the process at shifted positions along the crystal, a periodic grating of domain walls can be created. Figure 5 shows a quasi-periodic grating in GMO which was created via the lateral blade domain injection procedure at shifted positions along the crystal. The period is approximately 1 mm. The contrast between domain states is due to the birefringence of GMO. The domain walls can be positioned by sliding the line forces (the knife edges) along the transverse surfaces. The lateral domain injection procedure described above has been found to have its roots in some rather obscure Soviet research of the nineteen-thirties and forties on mechanical

ATIVE SHEAR FORCE BLADE DOMAINS GROW FROM SURFACE SUPPORT

AS STRESS I S INCREASED BLADE DOMAINS APPROACH OPPOSITE SURFACE

F I N A L STATE A PAIR OF b - T Y P E WALLS, CALLED A “STRIPE” DOMAIN

FIG.4: Nucleation process for a stripe domain

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STEVEN W. MEEKS AND B. A. AULD

FIG.5: A quasi-periodic array of stripe domains in GMO with a period of approximately 1 mm. This array was injected using the lateral domain wall injection process illustrated in Fig. 4.

twinning in metals and certain minerals (Cahn, 1953). These Soviet experiments were performed on calcite crystals by applying a line force to the crystal surface with a knife edge. This generated blade domains, then called elastic twins. It was reported that when sufficient force was applied to extend the domain approximately half way across the crystal, it suddenly extended across the thickness of the sample, creating a thin lamellar domain across the sample. Increasing the load beyond this point increased the thickness of the lamella. The double line force geometry of Fig. 4 was apparently not tried. The application of a double line force to GMO always produced the blade-to-stripe domain sequence shown in Fig. 4. When this same set of forces was applied to NPP, a sequence (to be described in this section) of bubble-to-zigzag domains was almost always followed, with blade domains being produced only occasionally. The exact reasons for the difference between the behavior of GMO and NPP are unclear. The reason that NPP occasionally nucleates blade domains is suspected to be related to

APPLICATIONS OF FERROELASTIC CRYSTALS

26 1

the sharpness of the knife edge, with a sharp edge producing a blade and a duller edge a bubble. The Soviets have found a similar criterion for the production of blade domains in calcite. They found that a concentrated load was required to produce a blade domain. A distributed load produced no blade domain at all (Cahn, 1953). Confirmation of this theory in NPP must await further investigation. 3 . Optical Injection

The domain patterns previously discussed were created by applying quasi-static mechanical shear stresses to a GMO or NPP crystal. Domain patterns can also be created optically in NPP using laser beams (Meeks et al., 1985b). This process is illustrated in Fig. 6. Anisotropic thermal stresses are set up by localized heating of a focused laser beam. The anisotropic thermal stresses are a result of the low 2/m symmetry of the NPP crystal. The anisotropic thermal expansion produces shear stresses which cause blade domains to nucleate and grow as the surrounding area restrains thermal expansion. The threshold intensity of this process is about 20 kW/cm2 for a 1 mm-thick crystal. Near the heated portion of the crystal, the strains are very large, but the energy required to nucleate domains inside a ferroelastic crystal is so large that twinning (domain production) generally begins near the edge of the crystal where the nucleation energy is much lower. The thermal stresses near the crystal edge are tangential (hoop) in orientation. These hoop stresses place the outer

c &lI A

A

,boil /

Y

MONODOMAIN INITIAL STATE

NUCLEATIONS OF BLADE DOMAINS

PLANAR WALLS FORM FROM BLADES (A-TY PE WALLS)

LASER~FT MOVING WALLS

-> BY TRANSLATING

BEAM

LASER BEAM

‘TRANSLATE

BEAM

FIG.6: Laser beam domain wall nucleation in NPP.

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STEVEN W. MEEKS AND B. A . AULD

portions of the crystal in tension, leading to twin nucleation in the upper right and lower left quadrants of the b plate of NPP in Fig. 6. Hoop stresses in the [loll direction favor twinning, but those in the [ f O l ] do not. Blade-like twins begin at the edges and grow into the crystal parallel to [loo] (the a direction), eventually coalescing into a pair of planar a-type walls. Curved twin boundaries straighten out to lower the elastic wall energy. Minimum wall energy occurs for (001) wall orientation (an a-type wall) where structures of the two twin states are well-matched (Weber et al., 1975). Once formed, the domain wall pair can be translated along the crystal by slowly shifting the position of the laser beam. This same translation can be obtained by slowly moving the laterally applied line forces used to inject the domain pattern in Fig. 4. A rough estimate (Kingery et al., 1976) of the thermal stresses obtained in laser injection can be obtained from the expression E a A T , where E is Young’s modulus, a is the linear thermal expansion coefficient, and AT is the temperature rise of the heated zone. For oxides, E is about 10l1 N/m2 and a is about lOP5K-l. If a temperature rise of 1°K due to laser heating is assumed, then the resulting thermal stress is 1 MN/mZ, comparable to the coercive stress in most ferroelastic crystals. Laser-induced twinning has been observed previously in ferroelasticferroelectric GMO and ferrobielastic quartz. However, the twins were much more difficult to induce in these materials, and even more difficult to control. The coercive stress wc required to induce mechanical twinning in NPP is much smaller than in quartz or GMO. Measurements (Weber et al., 1975) on NPP crystals at room temperature gave a, = 14 5 3 kN/m2 to induce a-type domain wall motion. For GMO (Keve et al., 1970) the coercive stress is about 1 MN/m2, and for quartz (Aizu, 1973), it is 500 MN/m2. Laser induced twinning in quartz is possible only at high temperatures where a, decreases to less than 10 MN/m2. In GMO, laser twinning was observed (Novak et al., 1977) at room temperature, but only for certain restricted geometries. When a c plate of GMO was exposed through a slit oriented parallel to [loo], numerous spike-like twins parallel to (110) and (TlO) were produced. It is much easier to generate twins in NPP because of its low coercive stress. A second advantage of NPP is the well-defined wall orientation. NPP belongs to the low symmetry ferroic species mmmF2/rn in which one-wall orientation is highly preferred. As pointed by Weber and associates (1975), the a-type twin-wall orientation is by far the easiest to nucleate and control. The situation is quite different for GMO and quartz. GMO is a ferroelastic, as NPP is, but its symmetry is higher. On cooling through its Curie temperature, GMO transforms from tetragonal to orthorhombic,

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corresponding to species 4/mmmFmmm. There are two symmetryequivalent wall orientations in ferroelastic GMO that cause problems during the laser experiments because they nucleate with equal ease. Very complex twin patterns with intersecting twin walls are observed when the crystals are irradiated (Novak et al., 1977). Even more complex phenomena occur in quartz. (Anderson et al., 1976). Quartz is a secondary ferroic belonging to ferrobielastic species 622F32. A ferrobielastic crystal differs from a ferroelastic crystal in that there is no spontaneous strain; the domain states of a ferrobielastic are identical in strain orientation until a stress is applied, but differences in elastic constants cause the domains to strain differently. For this type of ferroic, there is no unique wall orientation. Domain configurations of many interesting shapes have been induced by laser illumination (Anderson et al., 1976). In some cases the shape of the ferrobielastic twin resembled the shape of the irradiated spot, but in others it did not. In any case, the interpretation of the quartz results is a good deal more complex. The laser-induced twinning in NPP apears to be far more useful than in quartz or GMO for three reasons: (1) only low beam intensities are required because the coercive stress is much lower, (2) one domain wall orientation (a-type) is highly preferred, so that only a single family of stripes is produced, and ( 3 ) the domains can be moved about because of their high mobility. The majority of the descriptions in this chapter will be concentrated on strictly periodic gratings, but the lateral domain wall injection procedure, as well as the optical injection technique described above, are also capable of generating a chirp grating structure, or any other desired pattern, for signal processing or optical spatial filtering. The optical injection of domain walls is particularly exciting because it opens the possibility of optically writing an optical interference pattern onto a crystal of NPP. The energy required to write a domain pattern could be greatly reduced by using a thin plate of NPP (50 microns or so) and writing with a laser tuned to one of the absorption lines of NPP, where the absorption is extremely strong. The pattern may be erased by mechanically stressing the crystal, or by rotating the crystal by 180" about the a crystal axis and then reapplying the same optical pattern. The rotation about the a axis will reverse the direction of the stresses, and hence erase the pattern. 4. Quasi-static Stress Nucleation Figure 7 shows a single crystal of NPP with four periodic ferroelastic arrays simultaneously present. This is a b plate of NPP; that is, the b

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f40pm i

C FIG.7: Four periodic arrays in a single crystal of NPP. The horizontal walls are a-type walls and the vertical walls are 6-type walls. The longest period present is 20 microns (at the far left) and the shortest is 6 microns (second from the right).

direction is out of the page, the c direction is vertical, and the a direction is horizontal. Typical dimensions of the b plates used in these experiments are 1 mm (b-dimension) x 5 mm (c-dimension) x10 mm. Arrays have also been produced in samples with proportions significantly different from the above dimensions, namely, 2.2 mm (b-dimension) x l . 1 mm (c-dimension) x6.9 mm (a-dimension). The crystal is being viewed between a pair of polarizers. The domains are visible because of the birefringence of NPP as discussed in Part 111. The vertical lines in Fig. 7 are planar domain walls perpendicular to the domain walls in the periodic array. The horizontal walls are a-type walls, and the vertical walls are 6-type walls (Weber et al., 1975). These periodic gratings are stable in the absence of any external force. Arrays of approximately 25 micron period have been seen to be stable up to the Curie temperature of 145°C. It is of particular interest to note that these arrays are uniformly periodic and tunable (as will be shown in this section). The short range uniformity of these periodic arrays is on the order of a tenth of an optical wavelength. In the best arrays, the long range array period varies by +2% over an array length (the c-dimension) of 5 mm. This is much better than the long range

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variation of zig-zag arrays in GMO which appears to be about k 100% over the same array length (Flippen and Haas, 1973). The better long range uniformity in NPP is likely related to the better NPP crystal quality and the much lower coercive force (compared to the interaction force) of NPP. The advantage of GMO arrays over NPP is that it is likely that GMO arrays may be tuned directly with an electric field (since GMO is also ferroelectric), while NPP arrays can be tuned only indirectly with an electric field. It was found that the long range uniformity of NPP arrays could be improved by a low temperature anneal of 2 hours at 300°C. Presumably, this annealed-out small internal strains which have some effect on the long term periodicity. In general, the uniformity of the arrays was good enough that no anneal was required. The longest period array (at the far left) in Fig. 7 has a period of 20 microns, and the shortest has a period of 6 microns. Figure 8 shows a more detailed photograph of a periodic zig-zag array in NPP with a period of about 10 microns. The vertical line at the left of the photograph is a b-type wall and is not the edge of the crystal. This figure clearly shows that these arrays form delta functions (points) at each end of the grating. The walls are not parallel but are curved with a slight s-shape. The ratio of plus or minus domain state width to the total array period is a function of the lateral position in the array. This ratio varies from less than 1% at the array tips to 50% at the center of the array. Figure 9 shows a comparison of three arrays. The array at the far left has a period of 37 microns and the two arrays on the right have periods of approximately 4 microns. Only a small portion of the width of the

FIG.8: An array of about 10 micron period in NPP. This photograph clearly shows the delta function tips at either end of the array and the slight s-shape of the a-type walls. The vertical line at the left of the figure is not the edge of the crystal but is a b-type wall.

266

STEVEN W. MEEKS AND B. A . AULD

40pm

FIG.9: Three periodic arrays in NPP. The array at the left has a period of 37 microns and the arrays at the right have periods of about 4 microns. This photograph gives an idea of the range of tunability of these periodic structures.

37 micron period array is shown. This photograph gives an idea of the range of tunability of these arrays. The nucleation process of these periodic structures in NPP is shown in schematic form in Fig. 10. At the top of the figure the initial state of the NPP crystal is such that there are two domains present separated by a trapped or unmoveable b-type wall. The crystal is then subjected to three-point bending via a support and a negative shear couple. This stress configuration causes lenticular shaped or ferroelastic bubble domains to appear beneath the stress points. These bubble domains repel one another and move toward the center of the crystal as the stress is increased and fill the region between the stress points. As soon as the bubbles have filled the crystal they quickly coalesce into a pair of zig-zag or periodic domain walls. The walls will have different periods because they are subjected to different stresses in the three-point bending. Once the stresses are released the right-hand array will remain, and the amplitude of the left-hand wall will decrease to zero leaving a periodic array between two b-type walls as shown at the bottom of Fig. 10. The amplitude of the left-hand periodic wall decreases to zero because its very short period makes it nearly unstable; thus any small stress will cause it to change to a planar b-type wall. As mentioned in Section 2, NPP occasionally nucleates via blade domains into a pair of b-type walls. The reason for this is suspected to be

APPLICATIONS OF FERROELASTIC CRYSTALS

267

C

a b B t a

[TRAPPED

b-TYPE WALL

INITIAL STATE

1NEGATIVE SHEAR FORCE

r+

INJECTION OF LENTICULAR (BUBBLE 1 DOMAINS +

SUPPORT

I

SUPPORT

LENTICULAR (BUBBLE) DOMAINS FILL THE CRYSTAL BETWEEN THE STRESS POINTS

SUPPORT

LENTICULAR (BUBBLE) DOMAINS COALESCE INTO A PAIR OF ZIG -ZAG DOMAINS

FINAL STATE A SINGLE ZIG-ZAG WALL REMAINS WHEN STRESS I S REDUCED TO ZERO

FIG. 10: The nucleation process of a periodic or zig-zag array via a quasi-static shear stress.

related to the sharpness of the stress points. Zig-zag walls in GMO have been created by clamping two ends of the crystal and applying shear forces to the free faces (Flippen and Haas, 1973). In this case, by contrast with our experiments on NPP, the periodicity direction of the domain walls is perpendicular to the force direction. The periodic array trapped between the two b-type walls at the bottom of Fig. 10 is stable in the absence of any external force. Additional periodic structures may be injected into the same NPP crystal by translating the shear couple laterally along the crystal and repeating the process indicated in Fig. 10. This process has been used to inject at least 6 different periodic structures into the same NPP crystal

268

STEVEN W. MEEKS AND B. A. AULD

(see Fig. 7, which shows 4 such structures). The trapped b-type wall at the right of Fig. 10 is not necessary. Simply placing a trap, consisting of a glass cover slide on the right surface of the crystal will prevent the zig-zag structure from moving out of the crystal after it is nucleated by the quasi-static stress. The lenticular domains or ferroelastic bubbles shown in schematic form in Fig. 10 are analogous to the well-known ferromagnetic bubbles in magnetic garnets (Slonczewski and Malozemoff, 1978; Garel and Doniach, 1982). This is the first report of the observation of ferroelastic bubbles. In Section 2 a brief mention was made of some early Soviet experiments concerning twinning in metals and minerals. These are described in detail by Cahn (1953), where an account is given of radial lenticular domains generated in zinc crystals by pressing or impacting a small sphere on the cleavage surface. In the Soviet experiment the plane of the lenticular lamella is normal to the surface of the specimen, by contrast with the parallel orientation observed in the experiments here. No other experimental evidence was cited for the existence of such twins, and there was no account of lenticular twins being created by a line force on the surface and subsequently breaking away from the surface, as shown in Fig. 10. Torres (1981) shows lenticular domains in lead phosphate, which he refers to as needle domains. These were apparently created spontaneously at the Curie point and are trapped in the crystal by internal stresses. Torres (1981) gives no information on how they may be nucleated or if they are mobile under an applied stress. Figure 11 shows an aperiodic array of ferroelastic bubbles in NPP (Meeks et a l . , 1985b). In Fig. 10 the forces are applied so as to create a couple tending to switch the strain state of the entire crystal. In Fig. 11 the positions of the shear couple forces are shifted in a way that they will not switch the strain state of the crystal. In the terminology of Fig. 10, the applied stress in Fig. 11 is a positive stress. The left side of the crystal in Fig. 11 is fixed to the support to prevent the crystal from rotating. The applied stress produces lenticular shaped ferroelastic bubbles which appear underneath the transverse line forces and move inward, repelling one another, eventually filling the region between the stress points. These same forces, when applied to a crystal of GMO, will not produce lenticular bubbles. Ferroelastic bubbles share certain properties with ferromagnetic bubbles. They have a lenticular cross section of uniform strain, corresponding to one of the strain states, which extends through the thickness (the b direction) of the crystal. The bubbles are lenticular because the energies of the allowed wall directions are very anisotropic. Thus the bubbles form with a maximum of the low energy wall (a-type) and a

APPLICATIONS OF FERROELASTIC CRYSTALS

269

c 11: An aperiodic array of ferroelastic bubbles in NPP. The bubbles are lenticular in cross section. Fiti.

minimum of the high energy wall (b-type). They are a closed region of one (strain) polarization state which extends through the thickness of the crystal; bubbles of the same polarization state repel one another; they exist only in the presence of an external (stress) field; and they may be moved by application of an external (stress) field. However, they can be trapped in a crystal with no external stress if a stress pattern is built,into the crystal; for example, by inducing microcracks into the crystal, or by coating the crystal surface in such a way as to induce a shear stress in certain regions of the crystal. The lenticular bubbles in Fig. 11 vary in spacing and lateral width because of the variation in stress throughout the crystal. Lateral dimensions of these elastic bubbles range from an estimated 500 microns to 100 microns. The thin dimension of the bubbles ranges from about 10 microns to 1 micron. If the bottom stress point in Fig. 11 is shifted to

270

STEVEN W. MEEKS AND B. A . AULD

Q-jJ b-TYPE WALLS

(a)

PAIR OF b-TYPE WALLS

I

NEGATIVE SHEAR FORCE INJECTION OF LENTICULAR (BUBBLE) DOMAINS

A ZIG-ZAG WALL TRAPPED BETWEEN A PAIR OF b-TYPE WALLS

A ZIG-ZAG WALL SEPARATED FROM A SINGLE b-TYPE WALL

(f)

MULTIPLE ZIG -ZAG WALLS OF DIFFERENT PERIODS TRAPPED BETWEEN PAIRS OF b-TYPE WALLS

FIG. 12: A catalogue of the various domain patterns which can be produced in NPP.

APPLICATIONS OF FERROELASTIC CRYSTALS

27 1

the right so as to reverse the direction of the shear force, then the sequence of Fig. 10 will be initiated. Many different domain patterns can be obtained in NPP. Figure 12 shows a catalogue of the various domain states which have been obtained in NPP. Figure 12(a) shows the stripe domain pattern, Fig. 12(b) shows the ferroelastic bubbles, Fig. 12(c) shows a zig-zag wall plus a single b-type wall. In Fig. 12(d), the pattern is a zig-zag wall trapped between a pair of b-type walls, Fig. 12(e) is a zig-zag array separated from a single b-type wall, and Fig. 12(f) is a pattern consisting of multiple zig-zag arrays (see Fig. 7).

5. Tuning Ferroelastic Arrays Not only are we capable of nucleating these highly periodic arrays, but we are also able to tune their period in a controllable manner, as illustrated in schematic form in Fig. 13. The tuning process begins by starting with the crystal in the final state of Fig. 10. A negative shear force is applied near the left b-type wall and the bottom stress point is moved to the right while maintaining the shear stress. This process causes domain walls to nucleate from the side of the crystal and move inward. The domain walls repel one another, thus they form the very regular array shown in the figure. Continued motion of the bottom stress point will reduce the period to about 3 microns. At about a 3 micron period the structure collapses into a planar b-type wall. The reasons for this collapse will be explained in the next section. This technique has been used to tune from a domain wall period of 100 microns to 3 microns. Once the stress is released, the period remains at the value it had immediately before stress release, as shown in Fig. 13. Periods down to 0.5 microns have been obtained with a periodic array trapped between two b-type walls as in Fig. 12(d). The exact reasons why this structure is more stable than the one in Fig. 12(c) are unknown, but it suspected that the additional b-type wall may “short-out’’ some of the interaction and strain energy in the wall tips, thus making the structure stable at shorter periods. The maximum period obtainable with these structures appears to be limited by the physical width, W , (see Fig. 12(c)) of the crystal. The largest crystals available have widths of about 25 or 30 mm, and this implies that periods of 250 or 300 microns should be obtainable. A slightly different tuning technique may be accomplished by applying a quasi-static shear stress without moving the bottom stress point as was done in Fig. 13. This can be visualized by considering the second drawing from the top in Fig. 13. The bottom stress point is placed very near the

272

STEVEN W. MEEKS AND B. A. AULD I N I T I A L STATE

b -TYPE WALL

t TRAPPED b-TYPE WALL

N EGAT I V E I S H E A R FORCE

SUPPORT >

TUNING ARRAY BY SLIDING BOTTOM STRESS POINT TO T H E RIGHT

F I N A L STATE W I T H ZERO A P P L I E D STRESS. P E R I O D OF ARRAY I S M U C H SHORTER

FIG.13: One technique for tuning the period of a zig-zag array.

right-hand trapped b-type wall. The upper stress point is left at the position shown in Fig. 13. When the stress is increased, this causes domain walls to nucleate from the edges of the crystal and move inward, just as when the bottom stress point was moved to the right. The crystal is simply lowering its energy by making more of the negative strain state present in the crystal. These periodic arrays can be tuned rapidly by using this technique. The speed of tuning is controlled by the magnitude and speed with which the stress is applied. This technique has been used to tune the period of an NPP array from 100 microns to about 3 microns in about 100 ms. The maximum rate of tuning achievable in this way is not yet known.

APPLICATIONS OF FERROELASTIC CRYSTALS

273

A third method of tuning has recently been discovered in collaboration with Eric Szarmes of the Ginzton Laboratory. This technique consists of using miniature piezoelectric transducers to generate a static thermal stress via the localized heating of the lossy PZT-5A transducer. The technique is very simple and consists of bonding the c face of a NPP crystal containing an array with a cover slide trap attached to one end, to the miniature transducer. The acoustic power at 5 MHz is then raised to its maximum level of approximately 125 mW. The static thermal stress generated by localized heating of the PZT-5A causes the array to move against the trap and to reduce its period. The most recent results have shown tuning from 20 down to about 10 microns. A greater degree of tuning can be obtained by using a greater acoustic power, and hence a larger thermal stress. It is believed that the stress required to tune the array is a function of the period of the grating, with smaller periods requiring a larger stress. A more efficient way of generating the thermal stress would be to use a miniature resistive heating element. This tuning technique is the most exciting of the three mentioned since it allows electrical tuning with a miniature heating element. However, the tuning speed is slow. None of the techniques mentioned have been able to retune (increase the period) the arrays. The reason is unclear and is a topic for future research. A fourth method of tuning these arrays may possibly be found in optically-generated thermal shear stresses (see Section 3 ) . Although this technique has not been used to tune arrays, there is no reason why optically generated thermal shear stresses should not act in the same manner as the quasi-static mechanical, acoustic thermal or resistive thermal stresses discussed in the preceding paragraphs.

6 . Optical DifSraction from Periodic Domain Arrays

Figure 14 shows the diffraction pattern for a 58 micron period NPP grating which has been angle-tuned so that there is a Bragg enhancement at a fifth order transmitted Bragg spot. The term transmitted Bragg spot can be understood by considering Fig. 15(a) which shows the slowness section curves (the inverse of the optical velocity) for a NPP ferroelastic domain wall. The transmitted and reflected waves are obtained by phase matching along the domain wall. Figure 15(a) shows two transmitted waves, ki2)/w and kt(l)/w.The undeflected wave, k { ' ) / w ,is approximately polarized in the three direction of Fig. 20, and the deflected transmitted wave, k$*)/w,is approximately 1-polarized. When the deflection angle of the ki2)/wbeam corresponds to a Bragg angle of the array, the transmitted spot (k$')/w)will

274

STEVEN W. MEEKS AND B. A . AULD

FIG. 14: Diffraction pattern of a 58 micron array in NPP which has been angle-tuned so that Bragg enhancement occurs at fifth order. The Bragg spot is at left of the photograph and the undeflected spot is roughly in the center of the photograph.

have a greatly enhanced intensity. This is what is meant by a transmitted Brugg spot. Notice that the polarization of the transmitted Bragg spot is orthogonal to the incident polarization. The reflected waves from the domain walls will be weak because they do not satisfy the Bragg condition. Another novel feature of these arrays is that the Bragg spot may be switched from fifth order on the left to fifth order on the right by switching the polarization of the incident light. This is due to the nature of the transmission of light through the domain walls. An illustration of what happens to the transmitted waves when the incident polarization is switched by 90" is shown in Fig. 15(b). This novel feature will allow one to make a switchable beam splitter. The power in the Bragg spot may be switched from the left-hand fifth order (or any other order selected for Bragg enhancement) to the right-hand fifth order as rapidly as one can switch the polarization of the incident light (that is, from Mode 1 to Mode 2), without changing the incidence angle of the incoming light.

APPLICATIONS OF FERROELASTIC CRYSTALS 1

Y , b.

275

kb w

t

DOMAIN WALL I N a - b P L A N E

(4 v'. b.

kb -

TED

t

DOMAIN WALL IN 0 - b P L A N E

(b) FIG.15: Slowness section curves showing (a) transmitted and reflected waves when mode 1 is incident at an angle less than the critical angle for mode 2, and (b) when both modes are incident at an angle less than the critical angle.

276

STEVEN W. MEEKS AND B. A. AULD

The experimental setup used to generate the diffraction pattern of Fig. 14 is very similar to those of Figs. 39 and 43. The differences are that the NPP crystal now has an array present and the 5 cm focal length lens has been replaced by a telescope, for shrinking or expanding the beam diameter. The transmitted Bragg spot efficiency is a function of the diffraction order chosen to satisfy the Bragg condition. Figure 16 is a plot of the diffraction efficiency (defined as the ratio of the power in the Bragg spot (PI*) to the power incident on the crystal) of the transmitted Bragg spot versus diffraction order. The array period in Fig. 16 is 58 microns within a 610 micron thick crystal. The incident beam is 1 mm in diameter and is incident near the tips (delta functions) of the array. It was found that the diffraction efficiency was greatest near the delta function tips, which agrees with the findings of the delta function acoustic grating (see Part IV). As Fig. 16 shows, the diffraction efficiency is greatest at the fifth order. The reason for the peak at fifth order is related to the angular variation of the power transmission coefficients of the domain walls. When the beam diameter was about 1 mm, the long term variation in the array period became noticeable as diffraction ghosts in the diffraction pattern. It was discovered that shrinking the laser beam diameter to between 500 and 200 microns would improve the diffraction efficiency and reduce the diffraction ghosts. The maximum diffraction efficiency was 77%, which

40

1 0

1

2

3

4

5

6

7

DIFFRACTION ORDER

FIG.16: Transmitted Bragg spot efficiency as a function of the diffraction order. The array has a period of 58 microns and the diameter of the incident beam is approximately 1 mm. Somewhat better results may be obtained by using a smaller diameter beam.

APPLICATIONS OF FERROELASTIC CRYSTALS

277

occurred for beam diameters between 200 and 500 microns. This is the case shown in Fig. 14 which is using a beam diameter of 200 microns, directed at the tips of a 58 micron array in a 610 micron thick NPP crystal. A maximum occurs in the diffraction efficiency because of the improving long term variation as the diameter of the beam is decreased, combined with the decrease in efficiency as fewer domain walls are intercepted. If the crystal had been anti-reflection coated the diffraction efficiency would be expected to be greater than 90%. The optical diffraction shown in Fig. 14 is in the transition region between Raman-Nath and Bragg diffraction. If the diffraction is well into the Bragg regime (a thick grating), then no transmitted Bragg spots will be observed. In the case o f a thick grating, the only diffracted spots are the well-known reflected Bragg spots. This is because the thick grating extensively interacts with the beam, and only large angle reflected Bragg spots are observed. Figure 17 shows the diffraction pattern of the same array in which light of mode 1 polarization is incident at an angle corresponding to the critical angle of mode 2 (81.5' internal to the crystal). The beam diameter is

FIG. 17: The diffraction pattern of a 58 micron array which has been angle-tuned for the reflected Bragg spots P,, and P I , . Mode one polarization is incident on the array. The diameter of the incident beam is about 200 microns. The efficiency of the P I , reflected Bragg spot is about 16%.

278

STEVEN W. MEEKS AND B. A. AULD

200 microns in this case. The angle 81.5" is chosen because this corresponds to the peak reflectivity of mode 1 polarization, which was measured to be 2.2% per domain well (see Fig. 44, Part 111). The diffraction pattern is very clear, with well-formed spots, and does not have diffraction ghosts. This is an indication of the excellent short range periodicity of NPP arrays. The spot on the left of the photograph is the undeflected spot from the laser. The bright region extending over a number of spots in the center of the photograph is due to the reflected PZ1 Bragg spots. The reason the bright region extends over a number of spots is due to the leaky mode which appears at the critical angle for mode 2 (see Fig. 40, Part 111). The reflected Bragg spot for mode 1 (PI1) is at the far right of Fig. 17. The efficiency of this Bragg spot is about 16%. The efficiency is poor because only about 7 domain walls are intercepted by the 200 micron diameter laser beam. A greater number of domain walls could be intercepted by using a larger diameter beam, but when a large fraction of the array width is intercepted the diffracted spots are distorted due to lensing effects of the curved domain walls. In summary, the most efficient and best-quality diffraction spots were obtained by using transmitted Bragg spots with the incident beam directed at the tips of the NPP grating. Figure 18 shows the diffraction pattern of the same array as in Fig. 17 with mode 2 polarization incident nearly normally to the crystal surface (at near grazing incidence to the domain walls). This pattern is typical of a phase transmission diffraction grating, with the exception of two bright spots at about twentieth order on the far left and far right of the figure. The origin of these spots can be explained by reference to Fig. 19. When a mode 2 polarization wave is incident at near grazing it will phase match to a transmitted mode 2 wave travelling along the domain wall (k;')/w) and a reflected ( k ! l ) / w ) and transmitted (k{')/w) mode 1 wave traveling at an angle of 81.5" to the normal to the domain wall (see Fig. 41(a), Part 111). This is what is happening in Fig. 18. The incident mode 2 wave phase matches into two mode 1waves propagating at 81.5", which happens to be a Bragg angle of the 58 micron array at about twentieth order. In Part I11 it will be explained that the optical slowness surfaces of NPP are mirror symmetric about an a-type domain wall. This implies that the indices of refraction are also mirror-symmetric. This raises the question: "HOWcan a domain wall grating which has equal indices in the contiguous domain states act as a phase grating?" This puzzling question may be answered by considering Fig. 20. This figure shows the index or slowness surface principal axes (1,3 and 1',3') of two contiguous domain states (states I and 11) when one is looking down the b or y' crystal axis. If light propagating in the b direction, (into the page) with an arbitrarily oriented linear polarization, is incident on the crystal, then the electric field components along the principal axes will adjust their amplitudes so that the

FIG. 18: The diffraction pattern of a 58 micron array with mode two polarization normally incident in a 200 micron diameter beam. The undeflected spot is in the center of the photograph and the bright spots at about twentieth order are grazing incidence Bragg spots.

DOMAIN WALL IN a-b PLANE

f

FIG. 19: Optical slowness curves showing a mode 2 polarization wave which phase matches into a transmitted mode 2 wave and two grazing incidence Bragg spots which appear at about twentieth order in Fig. 18.

280

STEVEN W. MEEKS AND B. A. AULD X'

, '

, 3'

Lf'

I

STATE

I

DOMAIN WALL I N O - b PLANE

STATEII

J

FIG.20: Optical index surface axes for two adjacent a-type domains. Light propagating along the b or y' axis of an arbitrarily oriented linear polarization is normally incident on the crystal. The linear polarization decomposes into the four waves shown when it enters the crystal.

boundary conditions are satisfied. For an arbitrary polarization the components along each principal axis will, in general, be different. Figure 20 indicates this by showing Fl, F1., S,, S3, (the fast component along the 1 axis, the fast component along the 1' axis, etc.) as being scalars of different lengths. The angle 8 is the tilt angle of the index or slowness surface with respect to the a crystal axis, and is 9.5" at 1.05 microns and room temperature (see Fig. 33, Part 111). Decomposing these components into z' and x ' components and adding the resulting waves gives the result ETOTAL = {(Fl - Fl,) sin 8 eikl'r+ (S, - S,,) cos 8 eik3-r }2'

+ { ( F ~+, F

~ cos )

e eikl*r- (s, + s,,) sin e eik3.r}i'

(1) where kl and k3 are the propagation wavevectors for the 1 and 3 polarizations, respectively, in both domain states (since the indices are equal). The intensity of the resulting wave is given by

APPLICATIONS OF FERROELASTIC CRYSTALS

28 1

where the first five terms are due to the vector addition of the waves in the two domain states, and the last term is a spatial interference term. The result of Eq. (3) is that a grating of domain walls will exhibit a spatial intensity variation whose modulation amplitude is proportional to sin(28). The reason for the interference is the fact that the 1' and 3' axes are not coincident with the 1 and 3 axes. This allows the phase interference of a portion of the 1' component (which has wavevector k,) with a portion of the 3 component (which has wavevector k3). The same statement can be made about the 1 and 3' components. Thus the domain wall grating is still acting as a phase grating even though the indices of contiguous domain states are mirror-symmetric!

B. Free Energy Theory of NPP Periodic Domain Gratings This section will present a phenomenological free-energy theory for the stability of NPP periodic domain gratings. The free energy of these periodic domain gratings is constructed from three energy forms: the wall energy, the strain energy, and the interaction energy. Expressions for each of these energy terms is derived. The total energy is minimized with respect to the width, W , of the array to arrive at curves for the period, A, of the array versus the width of the array. Individual energy terms are then examined to see which terms cause the collapse of the structure. Figure 21 shows a simplified model of a periodic domain wall grating. The grating is modeled as a saw-tooth array composed of straight sections of domain walls. In reality, the straight sections are curved as shown in Fig. 8. The period of the array is A, the width W, and the length L . One half of the

FIG.21: Model of a zig-zag array using straight, rather than curved wall segments

282

STEVEN W. MEEKS AND B. A. AULD

vertex angle is 8 and the length of one straight section is I , as shown in Fig. 21. The total energy of these domain arrays is composed of three terms: the wall energy, the strain energy, and the interaction energy. The wall energy is the energy due to a simple tilt boundary and is proportional to the area of the domain wall

EWALL = Plt (4) where P is the energy per unit area of the domain wall, and t is the thickness of the crystal. The length of one straight section is

where the small-angle approximation, tan(8) = 8, and the binomial expansion have been used. The coefficient of the wall energy P must be a function of angle since tilting the domain wall from the plane where lattice matching occurs (the (001) plane) will create large strains (dislocations) which quickly raise the energy. The dependence of P on angle can be determined by considering that tilting the domain wall by a + 8 must be the same as tilting a wall by a - 8, by symmetry. Thus the wall energy can only contain even powers of 8. An additional constraint is that the wall energy must approach the energy of an untilted a-type wall for 8 = 0. These arguments lead to the following form for P

P

=

P o + P102

(6)

where only the lowest even power of 8 is considered. The resulting expression for the wall energy of N domain walls tilted at an angle 8 is

The strain energy is the energy which is trapped in the dislocations at the tips of the grating (see the tips in Fig. 8). This energy is also known as the energy of a wedge disclination (Torres et af., 1982b). The total energy of an array of wedge disclinations may be calculated by considering the electrostatic analogy of a linear array of electric dipoles separated by the grating period, A, and located at the grating tips (Torres et al., 1982b). Laplace’s equation requires that a potential which is periodically varying in one dimension must be exponentially decaying in the other dimension. This means that the strain energy is exponentially decaying from the tips in the direction of the width of the array (the a crystal direction). The depth of penetration is roughly one array period, A. Thus, the total volume which

APPLICATIONS OF FERROELASTIC CRYSTALS

283

VSTRAIN AtL

(8)

is strained is but A = 2L/N, where N is the total number of domain wall. Thus the strain energy is 6(8)L2t

ESTRAIN = ___ N

(9)

where 6 is the energy per unit volume of strained crystal, and the factor of two has been absorbed into the constant 6. The angular dependence of 6 can be determined by considering that the amount of strain trapped in the tips is directly proportional to the vertex angle. Since the elastic strain energy is proportional to the square of the strain, then the constant 6 must be proportional to 02. Torres and associates (1982b) obtained an identical angular relationship in their angular variation of the energy of a wedge disclination. Since the strain energy must go to zero at 8 = 0" (when 8 = 0" there are no tips) then 6 must have no constant term attached to it. Hence the expression for the strain energy is &TRAIN

60e2L2t N

= ___

2 where, in the last expression, use has been made of the relationship A = 2L/N. The final (and most complex) energy term is the interaction energy between domains. This derivation is similar to that given by Torres and associates (1982b). Most of the interaction forces produced between the domains are due to the disclinations localized at the domain extremities (Torres et al., 1982b). The interaction energy between a pair of domain tips is (Torres et al., 1982b)

where the interaction energy has been normalized so that it is zero at a domain wall separation of A = L , the width of the crystal, and y is the energy per unit thickness of the crystal. Notice that the interaction energy is not explicitly dependent on the width of the array since the interaction forces are localized at the domain tips. The angular dependence of y can be gleaned from Torres and associates (1982b) which shows the coefficient of

284

STEVEN W. MEEKS AND B. A . AULD

the interaction energy to be proportional to the square of the density of edge dislocations. Since the density of edge dislocations is directly proportional to the vertex angle, then this implies that y must be proportional to the square of the vertex angle, (213)~.The total interaction energy is obtained by summing the energies of all the interacting pairs in the array. This calculation will assume a very long array in which end effects are negligible. In the array in Fig. 21 there are N - 1tips separated by A, N - 2 separated by 2A, N - 3 separated by 3A, etc. Thus the total energy is

=

[2 i= 1

^I

( N - i) In i -

L

yoe2t

The sum can be separated into two terms, identified as Sum 1 and Sum 2, with Sum 1 a simple arithmetic sum. This decomposition gives

N

Sum 1 =

A C ( N - i) In i= L 1

-

N ( N - 1) A In 2 L

=

2 N I n i - C i In i i=

N

N

Sum 2

1

i= 1

N

= ~ ~ n ~ ! - x i I n i I=

1

= N ( N In N - N ) =

N 2 In N - N 2

-

-

P

N2 -In 2

x In x dx

N

N2 1 +-4 4

where Sterling's formula and an integral approximation have been used in Eq. (16). For large N the 1/4 term in Eq. (16) can be ignored and the

285

APPLICATIONS OF FERROELASTIC CRYSTALS

result is Sum 2

=

N2 2

- In N

3

- - N2

4

Thus for large N Sum.1 + Sum 2

=

N ( N - 1) A N2 3 In - + - In N - - N 2 2 L 2 4

(18)

Hence the total interaction energy is

The one remaining unknown in Eqs. (7), (lo), and (19) (other than P o , y o ) is the variation of the vertex angle with the width of the array. This has been determined experimentally and is shown in Fig. 22. The angle shown in Fig. 22 is one-half of the vertex angle (the angle 6 shown in Fig. 21) and is an average angle determined from the geometric relationship Al(2W). Figure 22 shows the angular variation for two

P , , a0, and

8

=

0 . 8 0 5 mm t h i c k c r y s t a l

* =

5

-

X

0.40-

1 . 5 2 mm

thick c r y s t a l

Y

* "

>

. . .

XY y

0.20-

0'04 '

.>

*

114

211

'

WIDTH

2 ! 8 ' 3 1 5 ' 412 ' 4f9 O F R R R A Y I N mm

'

516

'

613

'

FIG.22: Measured vertex angle versus width for two different thickness NPP crystals. The solid line is a linear least squares power fit to the 1.52 mm-thick crystal data.

286

STEVEN W. MEEKS AND B . A. AULD

different crystal thickness. The 1.52 mm thick crystal data has been fit to a power law @(in radians)

=

9.3057 x lop4 w-0.3530174 (20)

Equation (20) is displayed (in degrees) as the solid line in Fig. 22. The maximum vertex angle is about 3.4". At angles greater than this the structure collapses to a 6-type wall. It should be noted that the experimental data in Fig. 22 is for a zig-zag structure plus one 6-type wall, as in Fig. 12(c). The maximum vertex angle for the structure in Fig. 12(d) will be different, since this structure has been seen to exist down to smaller periods (0.5 microns). The total energy of a NPP array is therefore

ETOTAL = EWALL + &TRAIN

+ yoe2t

+ EINTERACTION

In

+In N L 2

- - N2 4

Dividing Eq. (21) by the thickness t , and using the relation N = 2L/(A) yields

Equation (22) is an expression for the energy of an NPP periodic array as a function of the width of the array. It has been experimentally observed that, upon release of the stress required to nucleate the periodic structure, the width of the array will increase so as to minimize the energy of the structure (see Fig. 10 and the discussion following). This same behavior is observed when tuning an array. It has also been observed that the width of the array may be increased or decreased a certain amount about its equilibrium value via an external stress without altering the period of the array. The point of this discussion is that the width W of the array is the free parameter which adjusts itself to minimize the energy. This approach is quite different from that of Torres and associates (1982b) who minimize the energy with respect to the number of domain walls. In the present calculation the number of domain walls is assumed constant over a small range of the width near the energy minimum. The equilibrium width is

287

APPLICATIONS OF FERROELASTIC CRYSTALS

obtained by differentiating Eq. (22) with respect to W (recalling that 8 is a function of W, Eq. (20)), and setting the resulting equation equal to zero. At this point experimental data on the array period, A, versus width, W , is used to determine the unknown parameters Po, PI , and 'yo. There are only 3 parameters since S, is divided into both sides of the derivative equation and is set equal to one. Setting So equal to one is equivalent to normalizing Eq. (22) to a particular system of units. The unknown parameters are determined via a three parameter linear least squares fit. The experimental data used in the least squares fit was taken from a 1.52 mm thick NPP crystal with a single periodic structure and one 6-type wall present as in Fig. 12(c). The resulting constants are

Po = 3.0881 x p1 = 1.6642 x

lo-''

-5.56391 x

'yo =

so = 1.0 When the above constants are used in Eq. (22), they yield the free energy versus width curves shown in Figs. 23 and 24. The parameter shown

1.281 0

'

I

1.5

'

I

3

'

'

4.5

'

I

6

.

I

7.5

'

I

9

*

'

18.5

'

I

12

'

'

13.5

'

15

WIDTH OF PERIODIC ARRAY I N m m FIG.23: Total free energy of a NPP array versus width of the array. The variable parameter is the period of the array.

288

7

3

STEVEN W. MEEKS AND B. A . AULD

7.60

/-

WIDTH OF PERIODIC A R R A Y IN m m FIG.24: Total free energy of a NPP array versus width for periods between 10 and 2 microns.

in these figures is the period, A, of the array. Figure 23 shows a distinct energy minima for periods between 100 and 10 microns. The value of the energy at the minima gradually increases as the period decreases. Figure 24 shows that this process continues as the period decreases below 10 microns. However, the increase of the energy at the minima is now very rapid (notice the scale change between Figs. 23 and 24). Notice that there is a particularly large increase between 4 and 2 microns. Experimentally, it has been observed that these periodic structures collapse at about 3 microns into a planar b-type wall. This is what is indicated in Fig. 24. The energy of the periodic structure at the energy minima increases rapidly for periods below 10 microns until it exceeds the energy of a b-type wall at about 3 microns, whereupon the structure lowers its energy by collapsing into a 6-type wall. One can thus predict that the energy of a single b-type wall lies between the 4 and 2 micron curves on the scale of Fig. 24. A shorter period would be obtained if a crystal could be found which has a larger b-type wall energy. The reason these structures can exist down to such short periods is due to the large anisotropy between the a- and 6-type walls. The large anisotropy is due to the low symmetry of the 2/m crystal which leacj to the a-type walls being highly preferred. As has been mentioned earlier, the structure shown in Fig. 12(d) has been seen to exist

APPLICATIONS OF FERROELASTIC CRYSTALS

289

FIG.25: Strain energy of a NPP array versus width for periods between 100 and 10 microns.

down to 0.5 microns, possibly due to some of the strain or interaction energy being “shorted out” by the additional b-type wall. The upper limit of the array period is limited only by the length of the crystal. The rest of this section will be devoted to examining the individual energy terms of Eq. (22) to see which terms cause the collapse of the structure. Figure 25 shows the strain energy versus width for periods between 100 and 10 microns. The energy decreases with increasing width and decreasing period. Figure 26 shows the wall energy versus width for periods between 100 and 10 microns. The important point to notice in this figure is that the wall energy increases very rapidly with width for periods less than or equal to 10 microns. Figure 27 shows the strain (dotted line) and interaction energy (solid line) versus width for periods between 10 and 2 microns. The nature of the interaction energy can be gleaned from Fig. 27. If the width is fixed and additional domain walls are added to the structure by decreasing the period, then Fig. 27 shows that the interaction energy increases, hence the interaction energy is a repulsive force. It is this interaction energy which produces such uniformly periodic arrays in NPP. The interaction energy increases with decreasing period whereas the strain energy decreases. The interaction energy exceeds the strain energy at about a 4 micron period, as can be seen from Fig. 27. The reason for the

290

STEVEN W. MEEKS AND B. A. AULD

4.50-

5

WIDTH O F P E R I O D I C RRRRY IN

rnrn

FIG.26: Wall energy of a NPP array versus width for periods between 100 and 10 microns.

solid line = interaction energy dotted line= strain energy

WIDTH O F P E R I O D I C R R R A Y IN

mm

FIG.27: Interaction and strain energies versus width for periods between 10 and 2 microns.

APPLICATIONS OF FERROELASTIC CRYSTALS

29 1

collapse of the structure can now be attributed to a combination of the rapidly increasing wall energy (see Fig. 26) with the rapidly increasing interaction energy. It is this combination which causes a very rapid increase in the energy minima value for periods below 4 microns and the subsequent collapse of the structure to a b-type wall. Figure 28 shows a summary of the results of this section. This figure shows the experimental data of period versus width of an NPP periodic array plus one b-type wall (see Fig. 12(c)). Data are shown for two different thickness crystals. The data for the 1.52 mm thick crystal have a solid line drawn through them, taken from the phenomenological theory shown in Figs. 23 and 24. Notice that the theory gives an excellent fit to the experimental data. The data for the 0.805 mm thick crystal have a straight line interpolation between data points. The longest period arrays obtained in this work were 100 microns in period. They were of the type shown in Fig. 12(d), and are not displayed in Fig. 28. Contrary to the predictions of the theory, there is some crystal thickness variation of period versus width, particularly for widths above 2 mm. The origin of this thickness variation may be due to some type of edge effects which were ignored in this

3

WIDTH OF ARRRY I N

rnrn

FIG.28: Period of a NPP array versus width for two different thickness crystals. The solid line drawn through the 1.52 mm-thick data is from the phenomenological model discussed in the text. The line drawn through the 0.805 mm data is a straight line interpolation between data points.

292

STEVEN W. MEEKS AND B. A . AULD

This section has presented some experimental and theoretical results concerning periodic domain walls and ferroelastic bubbles in NPP. A review of previous work in creating periodic structures in ferroic and non-ferroic materials was given at the beginning of this section. Two techniques of creating periodic and aperiodic structures were the lateral domain wall injection technique and the optical injection procedure. The optical technique is particularly exciting since it offers the promise of optically writing an optical interference pattern onto a crystal of NPP. Another domain wall injection technique was used to create uniformly periodic domain walls in NPP, and is known as the quasi-static nucleation of zig-zag or periodic domain walls. This technique has been used to create periodic domain structures with a period of 100 to 0.5 microns. The short range periodicity is excellent and is uniform on the order of a tenth of an optical wavelength. The long range periodicity is uniform to within 2 2 % of the period. The nucleation process of these periodic structures is described in terms of a newly-discovered domain structure, namely the ferroelastic bubble. The ferroelastic bubble is the eIastic analogue to the well-known ferromagnetic bubble. Four different techniques of tuning the period of the arrays are described. The arrays may be tuned relatively rapidly. One of the tuning techniques has tuned the period of a 100 micron array to about 3 microns in 100 ms. The maximum rate of tuning is not yet known. A section has been included which explains the optical diffraction from arrays of NPP domain walls. The best Bragg efficiency was obtained from a crystal with a 58 micron period array and was 77%. Efficiencies of greater than 90% should be obtained from crystals which are anti-reflection coated. The final part of this section presents a phenomenological theory which constructs the free energy of these periodic structures as the sum of the wall, strain, and interaction energies. The theory gives an excellent fit to experimental data. This theory also predicts the collapse of the periodic structure at about 3 microns. The collapse is due to the combination of the rapidly increasing wall and interaction energies. It is predicted that the upper limit on the period of these zig-zag structures will be limited by the crystal size and not any of the energy terms. It is also predicted that these periodic structures will exist in the rare-earth analogues to NPP: LaPP, PrPP, TbPP (Weber et al., 1975). 111. INTERACTION OF OPTICALAND ACOUSTIC WAVES WITH FERROELASTIC DOMAINWALLS

The abrupt change in physical properties at a ferroelastic domain wall constitutes an interface that reflects optical and acoustic waves. This section will discuss the physics of these reflections and is divided into two

APPLICATIONS OF FERROELASTIC CRYSTALS

293

parts. The first subsection discusses the general topic of acoustic wave interaction with ferroelastic domain walls. The second subsection describes how optical waves reflect from NPP ferroelastic domain walls. In Section A we use the Christoffel equation to calculate the normal incidence acoustic reflection coefficients of a- and b-type domain walls of NPP and LaPP. The reflection of acoustic waves, in this case, is due to a change in the polarization of the wave and not a change in acoustic impedance at the domain wall. The reflection coefficients of NPP are much larger than other ferroelastic-ferroelectrics such as GMO. Certain of the reflection coefficients exhibited anomalously large values. The large values are likely due to the vibration of the domain wall. Two devices which use reflections off single domain walls, are presented. The devices are a tunable comb filter and a 0 to 4.5 microsecond tunable delay line. A practical delay line will probably operate at 50 to 100 MHz instead of the 5 MHz used in this work. NPP has a low enough acoustic attenuation to allow operation at these frequencies.

A . Acoustic Reflection from NPP Domain Walls This section presents a theory of acoustic reflection from a- and b-type NPP domain walls at normal incidence. The performance of devices such as delay lines, comb filters, and acoustic grating filters is dependent upon the value of the domain wall reflection coefficients. The delay line and the comb filter are two devices which rely upon reflections from a single domain wall. These two devices will be described in this section, and an acoustic grating filter will be discussed in Part IV. 1. Acoustic Reflection Coeficients The acoustic propagation directions considered here are in the a-c plane of NPP (Fig. 3). This plane of NPP is normal to the b-axis, a two-fold symmetry axis. Because of this symmetry, acoustic propagation in any direction in this plane comprises a b- (or y - ) polarized pure shear wave, plus a quasi-longitudinal (QL) wave and a quasi-shear (QS) wave polarized in the a-c plane. The pure shear wave does not suffer an impedance or polarization discontinuity at a domain wall hence it does not reflect and will not be considered further. The first step in solving this boundary condition problem is to solve the Christoffel equation (Auld, 1973) for propagation in the a-c plane of a 2/m crystal. The general form of the Christoffel equation is

k2Tiiv, = pw2v, where k is the wavevector, Tii is the Christoffel matrix, vj are the particle

294

STEVEN W. MEEKS AND B. A. AULD

velocity components, p the density, and w the angular frequency. The dispersion relation is obtained by setting the characteristic determinant of Eq. (23) equal to zero

I k2r,(l,, ly , 1,)

- pw26i,I

=0

(24)

where I,, ly, and 1, are the direction cosines of the propagation direction. Equation 24 can be solved for the eigenvalues of Eq. (23), which are the inverse of phase velocity (or slowness) as a function of propagation direction. For propagation in the a-c (I, = 0) plane of a monoclinic 2/m crystal, Eq. (24) reduces to

k 2 a - pw 2 0 k2E

0 k2/3 - pw2 0

k2& 0

k2y

=o

(25)

- Pw2

where a = c,,lf

+ c5J5 + 2c151,1,

p

= C551f

+ C441: + C331: + 2C351zIx

(28)

= C1&

+ C351:

(29)

E

= C & :

-k (C13

(26) (27)

C55)1,1x

In obtaining these coefficients it is assumed that c46 is negligible, as shown by experiment (Errandonea, 1980). Equation 25 separates into a linear (the b polarized pure shear wave which will not be considered) and a quadratic factor given below

k

+

+

+

+

- = (2p)1/2{cll cos2 4 c33 sin2 4 c55 (cI5 c35)sin 2 4 w ?[[cl1 cos2 C$ - c33sin2 4 - c55 cos 2 4 ( ~ 1 5- c34 sin 2412

+

(30)

+ 4[C15 cos2 4 + c35 sin2 4 + ( ( ~ 1 3 + C55)/2) sin 2 ~ $ ] ~ ] ~ / ~ } - ~ ’ ~ where I, = cos(4) and ly = sin(+) have been used after substituting Eq. (26) through Eq. (29) into Eq. (25). 4 is the angle between the x or a axis and the propagation direction given by k. The positive sign in Eq. (30) refers to the QL wave and the negative to the QS wave. The corresponding waves in the alternate domain state are obtained by rotating the stiffness matrix by T about the a or c axis, respectively (see Fig. 3), depending upon whether one is considering an a- or b-type domain wall. The result of these manipulations is a stiffness matrix in which certain elements change sign.

295

APPLICATIONS OF FERROELASTIC CRYSTALS

The elements are all positive in one domain state and certain off-diagonal elements become negative in the opposite state as shown below.

stiffness matrix

=

c23

c33

0

5 C35

0

0

c44

0

0 C4h

Thus the slowness curves of the opposite domain state can be obtained by simply changing the sign of c15 and c35 in Eq. (30). A plot of the two slowness curves for the two possible domain states is shown in Fig. 29. The stiffness elements of LaPP (Errandonea, 1980) have been used in calculating the curves of Fig. 29 since the elements of NPP are not available. LaPP is the rare-earth analog to NPP and is also a ferroelastic of the same 2/m point group. It is expected that the stiffness values for NPP will be similar to those of LaPP. Notice, that to go from one domain state to the other, one simply rotates the slowness curves by n-about the z or c axis. The same procedure is followed for an a-type wall, with the rotation about the a or x axis. Notice that whether the rotation is about the a or c axis the resultant pair of curves always has the same relationship. Consider a non-normally incident wave at an arbitrary angle, @,as

STATE

II

PZ/W

FIG.29: Change in the NPP slowness surfaces for a b-type wall

296

STEVEN W. MEEKS AND B . A. AULD

shown in Fig. 29. Snell's law, shown below, requires a transmitted QL wave at a different angle, Or, with a greater velocity given by the inverse of the length of k J w .

ki sin 6, = k, sin 6, A reflected QL wave of wavevector k, is also required in the incident medium. Thus the reflection of non-normally incident acoustic waves is due to a discontinuity in phase velocity. There is also a refraction of the acoustic wave at the boundary, since 0, does not equal 0,. A normally incident QL or QS wave has no velocity discontinuity. However, there is a discontinuity in particle velocity polarization which leads to a reflected wave required by the continuity of particle velocity boundary condition. The particle velocity is given by Eq. (23) after substituting for the eigenvalues given by Eq. (30). These manipulations give

I:[

1

1 =

y -

* J(a - y ) + 2

Q

2E

4E2

I

"x

(31)

where the plus, minus signs refer to the QL, QS polarizations, respectively. The acoustic boundary conditions are that there be continuity of particle displacement velocity v and traction force T A across the interface (Auld, 1973). Mathematically these boundary conditions are expressed as

-

v = v'

(32)

T.A=T'.A

(33)

and

at the boundary. The particle displacement velocity polarizations are obtained from Eq. (31) and the traction forces normal to the wavevector (the traction forces normal to the domain wall if normal incidence is considered) are given by 9=?p.Vp.v

(34)

where p is the density, Vp is the phase velocity given by the inverse of the slowness in Eq. (30), and the minus (plus) refers to a positive (negative) traveling wave. For the particular case of normal incidence on an a-type wall the phase velocity and polarization are

APPLICATIONS OF FERROELASTIC CRYSTALS

297

where

and Q , (Q2) refers to a Q L (QS) wave, with the plus/minus signs referring to Q, , Q 2 , respectively; and c33

vP=

[

+ c55 * J(C,,

- c33)2

+ 445

2P

I

1/2

(37)

where the plus/minus signs refer to QL, QS polarizations, respectively. For the case of normal incidence on a b-type wall the phase velocity and polarization are

where

with Q3 (Q4) referring to a QL (QS) wave, and

[

c11

vP=

+ c55 2 J(c,, 2P

- css)2

+ 4c,:

1

with the plus/minus signs analogous to Eqs. (36) and (37). The phase velocities (which are unchanged for normal incidence) and particle velocity polarizations of the opposite domain state are obtained by substituting in 5 c3s, as indicated by the stiffness matrix the oppositely signed value of ~ 1 or above. This implies that the sign of Q, , Q2, Q3, and Q4 will change in the opposite domain state. The model of a b-type domain wall used in this calculation is shown in Fig. 30. This figure shows the change in crystal axes as one crosses a b-type domain wall in NPP (or any (RE)PP where R E = La - Tb) (Weber et al., 1975). The lower half of Fig. 30 shows the simplified model which neglects the 1" angle between the faces in the two domains and assumes c46 = 0. There are five waves to be matched at the boundary (the domain wall) as shown at the bottom of Fig. 30. The incident wave can be either a QL or QS (depending upon which reflection coefficient is desired), with a QL and QS reflected, and a QL and QS transmitted. The model of an a-type wall is very similar to Fig. 30, except that the axis which changes is the c axis (see the a-type wall in Fig. 3). The calculation of the reflection coefficients for

298

STEVEN W. MEEKS AND B. A. AULD

either an a-type or b-type wall is identical in form. The differences occur in the values of V p , and the particle displacement velocities, as shown in Eqs. (35-40). Thus the calculation to be carried out below is correct for both an a- and b-type wall when the acoustic wave is normally incident. Suppose a QL wave is incident, then the velocity and traction force fields of the incident and reflected waves are

=

I X ' [

vz QL,

where i

=

1 or 3, and A'

[

B' B' * Qi

]

A =

B

J T T p B'

["XI

vz QS,

=

(44)

[

c'

C'

=

. Qj

4

]

sos, = PVpq,C'2 + pVp,,C'Qj2 where j = 2 or 4, and C' = C / ( 1 + QT)'/*,and an exponential spatial and time variation is understood. For the transmitted waves

where the subscripts i, j , have the same meaning as before, and D' = D / ( 1 Q:)'/* and E' = E/(1 + Q;)'/*. Notice that for the transmitted waves the sign of the z component of the particle displacement velocity has changed from plus to minus. This is a result of the rotation of the slowness

+

299

APPLICATIONS OF FERROELASTIC CRYSTALS

MODEL IGNORES I" ANGLE AND ASSUMES C 4 6 " O

0

ZZ

INCIDENT

a

a REFLECTED

FIG.30: Model of a b-type domain wall of NPP or LaPP.

surfaces about the a or c axis, which results in a change in sign in certain terms of the stiffness matrix, that leads to a change in sign of the z component of v, as can be seen from Eqs. (3.9, (36), (38), and (39). The change in the particle velocity polarization at a domain wall is 24.8" for an a-type wall and 23.3" for a b-type wall. The result of matching boundary conditions (Eqs. (32) and (33)) is the following inhomogeneous set of four equations and four unknowns: 1

-1

-1

Ql

Q,

Qi

VPQL VPQS VPQL 'PQS VPQLQ~ VPOSQ, - VPQLQ~ - VPQSQ,

B' C'

D' E'

(53)

300

STEVEN W. MEEKS AND B. A . AULD

The ratio of the reflected longitudinal amplitude to the incident longitudinal amplitude is given by R,:

This ratio is determined from Eq. (53) by using Cramer's rule and the result is

RII

vk?L

=

G Q L

+

-

V$QS

(55)

GQS+ V P Q S V P Q ~ Q+? Q,')

The shear reflected amplitude with a longitudinal wave incident is given by

The shear reflected amplitude with a shear wave incident is

where A is the amplitude of the incident shear wave in Eq. (57),and i = 1 or 3 and j = 2 or 4 in Eqs. (53) through (57). Substituting in the elastic constants of LaPP gives the numerical values for the amplitude reflection coefficients for an a- and 6-type domain wall at normal incidence, summarized in Table I. It is expected that the reflection coefficients for NPP will be very similar to those of LaPP. All of the above reflection coefficients are large enough to be useful in practical devices. These coefficients are about 15 dB larger than the corresponding reflection coefficients of GMO (Lemons and Coldren, 1978). It is particularly noteworthy to observe the very large values of RsI. The slightly larger values of reflection coefficients for the a-type wall are due to the 1.5" larger polarization change for an a-type wall over a b-type TABLE I AMPLITUDE REFLECTION COEFFICIENTS FROM A SINGLE a- OR b-TYpE INCIDENCE. DOMAIN WALLOF NPP OR LaPP AT NORMAL b-type

a-type

R// Rd RSS

Linear

dB

Linear

dB

0.0606 0.1728 -0.0606

-24.3 -15.2 -24.3

0.0486 0.1454 -0.0486

-26.3 -16.7 -26.3

301

APPLICATIONS OF FERROELASTIC CRYSTALS

wall. An experimental determination of R,, for a b-type wall was made at 6.4 MHz for a guided mode in a mini-plate of NPP. The measured value was R,, = -13.7 dB. The anomalously large value of R,, is likely due to the vibration of the domain wall under the applied dynamic acoustic field (Lemons and Coldren, 1978; Laikhtman and Tagantsev, 1975). Lemons and Coldren (1978) also attributed the anomalously large R,, of GMO to a vibration of the domain wall. In their case, the other reflection coefficients were unaffected since an incident longitudinal wave does not have the proper stress components to switch the configurational state and the wall therefore does not vibrate. It is believed that this will also be the case in NPP. Consequently, experimental values of Rll and RSlshould show good agreement with theory, as in GMO (Lemons and Coldren, 1978).

2. A Tunable N P P Delay Line and Comb Filter This subsection will discuss two demonstration devices which use acoustic reflections from a single domain wall. The first device to be discussed is a tunable comb filter. A comb filter is a device which has a frequency spectrum which allows only certain equally spaced frequencies to pass through it. Its frequency spectrum looks like a comb, hence the name. The tunable NPP comb filter is shown in Fig. 31. A schematic of the comb filter is shown in the upper part of Fig. 31. It consists of a b plate of NPP with an attached c-polarized a-propagating shear wave transducer. A b-type domain wall has been introduced into the plate, and on the left side

IZI

300R

P Z T TRANSDUCER P O L A R IZ AT ION

200R

IOOR

5

I

I

5.5

6.5

FREOUENCY ( M H z )

7.

I

I

I

I

5.5

6.5

7.5

FREQUENCY ( M H z )

FIG.31: A NPP tunable comb filter

302

STEVEN W. MEEKS AND B. A. AULD

of Fig. 31 the wall is near the transducer. When a cw signal is applied to the transducer and the impedance measured, the resulting curve at the bottom left of Fig. 31 is obtained. This impedance spectrum consists of a series of low Q widely spaced peaks. These peaks are due to an acoustic resonance set up between the transducer and the strongly reflecting domain wall. The spacing of the peaks is related to the length of the acoustic cavity between the transducer and the domain wall. The wall can be moved to the opposite end of the NPP plate by means of a non-linear acoustic field or by mechanically stroking the crystal with a toothpick. The resulting impedance spectrum with the wall at the opposite end of the crystal is shown on the right side of the figure. In this case, the spectrum consists of a series of high Q closely spaced peaks. The closer spaced peaks are a result of the longer cavity length, since the spacing is given by c/2L, where c is the speed of sound and L is the spacing between the wall and the transducer. A higher Q results in the second case because the losses (which are principally due to the transmission of the wall) remain the same and the stored energy goes up because of the greater number of wavelengths in the longer cavity. Similar results would be obtained with an a-type wall. In this case an a-polarized c-propagating shear wave is required. The tunable NPP delay line is obtained by using a tone-burst instead of a cw wave in the transducer-NPP composite shown at the top of Fig. 31. The result is shown in Fig. 32. The top of the figure shows the applied electrical wave and the resulting reflected acoustic wave when the wall is near the transducer. The bottom of the figure shows the same two pulses with the domain wall at the far end of the crystal, as indicated at the upper right of Fig. 31. The transducer-NPP composite is obviously acting as a delay line with a mechanically- or electrically-variable (0 to 4.5 microseconds) delay. The delay may be altered by moving the domain wall via a mechanical stress or an electrically generated thermal stress. If the polarization of the transducer is changed to the b direction, the NPP plate will propagate a b-polarized pure shear wave, as indicated by the theory of this subsection. The preceding theory also indicated that no reflections would be observed for this polarization. This experiment was tried on the above delay line and, indeed, no reflections were observed for a bpolarized wave, thus verifying the reflection theory. This subsection has presented a discussion of how acoustic waves interact with ferroelastics. We presented a reflection theory which was used to calculate the normal incidence reflection coefficients of a and b-type domain walls of NPP and LaPP. The reflection coefficients are much larger than for other ferroelastic-ferroelectrics such as GMO. Certain of the reflection coefficients exhibited anomalously large values. The large values are likely due to the vibration of the domain walls. Finally, two

APPLICATIONS OF FERROELASTIC CRYSTALS

ELECTRICAL REFLECTION

303

ACOUSTIC REFLECTION

FIG.32: Reflected shear pulses from a tunable b-type NPP domain wall. The top photo is with the wall near the transducer and the bottom photo is with the wall at the opposite end of the crystal.

devices which use reflections from single domain walls, were presented. The devices were a tunable comb filter and a 0 to 4.5 microsecond variable delay line. A practical delay line would probably operate at 50 to 100 MHz instead of the 5 MHz used in this work. NPP has a low enough acoustic attenuation to allow operation at these frequencies.

304

STEVEN W. MEEKS AND B. A. AULD

B. Optical Reflection from an a- Type Ferroelastic Domain Wall in NPP This section presents the solutions of the general electromagnetic wave equation in an anisotropic medium. These solutions are used to compute the optical power reflection coefficients of an a-type NPP domain wall. We compare the theoretical and experimentally measured power reflection coefficients from an a-type domain wall. Included in this section is an explanation of how the two polarizations of light scatter from NPP domain walls. Optical reflection coefficients are discussed here only for an a-type wall. The reason for this choice is that Part I1 presented a method for creating arrays of a-type walls, and the theory to be discussed here explains the reflection and transmission behavior of these arrays. Analysis for a b-type wall is entirely analogous. The theory described in this subsection will show that a wave crossing an a-type domain wall experiences no change in index, hence it does not refract. The reflections from an a-type domain wall are most unusual. The reflection is due to a change in the polarization of the wave, not a change in index. The theory discussed in subsections 1 and 2 will explain how an optical wave can reflect from an interface without a refraction of the transmitted wave. The final portion of this section explains the origin of the contrast between adjacent domain states when viewed with polarized light. The contrast is due to the tilt of the index surface axes of contiguous domain states. 1. Derivation of the General Biaxial Slowness Surface

This subsection will present the theory of optical reflections from a ferroelastic domain wall. Of particular interest is the power reflection coefficient as a function of incidence angle. The calculation begins with computation of the optical slowness surfaces (or index surfaces) of light in a biaxial crystal of NPP. These are obtained by solving for the eigenvalues of the general wave equation in a biaxial crystal, starting from Maxwell’s curl equations. dH V X E = -pOdt

Take the curl of Eq. (58) and the time derivative of Eq. (59) V

X

(V

X

E)

= -/.LO

d - (V X H) dt

APPLICATIONS OF FERROELASTIC CRYSTALS

d2E at2

d

-(VXH)=&O-+-+-

dt

d2P

dJ

at2

dt

Substitute Eq. (61) into Eq. (60)

For nonconducting media ( d J / d t )

V

(V X E)

X

0. Thus the wave equation becomes 1 d2E d2P

=

+- - -Po? c; dt2

For linear optics the polarization is related to the electric field by P

=

(64)

E~XE

where x is the tensor susceptibility. Substituting Eq. (64) into Eq. (63) yields the general wave equation for the propagation of light in an anisotropic medium

v

X

(v x

1 d2E E) + -- = c;

dt2

1 d2E __ c; Xdt2

-

-

Equation (65) is the electromagnetic analog of the Christoffel equation in acoustics (Eq. (23)) and can be solved in exactly the same way. If a wave of the form exp {i (k r - w t ) } is assumed, then V ik and d / d t -iw. Thus the wave equation becomes

-

k

X

(k x E)

k

X

+ (EYE

-(El

2

=

XE

or

(k

E)

X

=

(3

- - (1 + x)E

It is assumed in what follows that the coordinate axes are taken to be principal axes for the susceptibility x. In these coordinates x is diagonal, with three different diagonal elements in the general biaxial case. Equation (67) implies that k is not in general orthogonal to E. However, since ~ o ( l+ x)E = D

Eq. (67) can be rewritten as

showing that D is always perpendicular to k.

306

STEVEN W. MEEKS AND B. A . AULD

The general wave equation (Eq. (67)) can be put in a matrix form by explicitly writing out in component form the indicated cross products on the left hand side. This gives

k x (k x E)

=

S(k,k,E, - k$,

-

Exkl + kxk,E,)

- Exkykx- k,k,Ez + Eyk2) + IZ(E,k,k, - k;E, - k;E, + kyk,Ey) - j^(k;E,

(69)

The tensor product on the right of Eq. (67) becomes

where xll, x22,and x33are the principal susceptibility elements. Now put the results of Eqs. (69) and (70) into Eq. (67), move Eq. (70) to the left-hand side, divide by k2, and use n: = 1 + xi;and 1, = k x / k ,1, = k y / k , 1, = k z / k . The result is

where I,, 1, , 1, are the direction cosines of k . The eigenvalues k j = nio/co (where i = 1 , 2 , 3 and nj are the principal indices of refraction) of Eq. (71) are obtained by setting the determinant of the three by three matrix in Eq. (71) equal to zero. This yields the equation for the general biaxial slowness, or index, surface shown in Fig. 33. The resulting surface consists of two sheets, since there are two allowed indices for each direction of propagation. The two sheets touch at the optic axes, which lie in the 2-3 plane of the surface. In NPP the principal axes of the slowness surface do not lie along the crystal axes (Huber et al., 1975) because of the low symmetry 2/m monoclinic crystal. Axes labeled 1, 2, 3 in the figure are the principal axes of the index or slowness surface, while a , 6, c are the monoclinic crystal axes. An angle of 9" exists between the 3 axis and the c monoclinic axis at room temperature and a wavelength of 1.05 microns (Huber et al., 1975). In the figure, the z' axis shown is a laboratory

APPLICATIONS OF FERROELASTIC CRYSTALS

.

2

2

2

2

b

b

b

307

FIG.33: Index or slowness surface of NPP at room temperature and a wavelength of 1.05 microns.

reference axis chosen to lie perpendicular to the a-b plane of the a-type domain wall. The tensor susceptibility y, is referred to the 1, 2, 3 triad of axes (the principal axes). The 1, 2 , 3 and x', y ' , z' axes are mutually perpendicular triads. Axes a , b, c are the monoclinic crystal axes with b perpendicular to a and c but the angle between a and c is 90.5" for NPP at room temperature (Huber et al., 1975). Figure 33 also shows a number of cross sectional cuts through the slowness surface. The first cut is in the 2-3 plane where the eigenvalues consist of a circle and an ellipse which touch at the optic axis. In the 2-2' plane the curves are more complicated ovaloids which nearly touch. The index curves in the 2-z" plane also form complicated ovaloids with a larger gap between the curves. In the 2-1 and 1-3 planes the index curves consist of a non-intersecting ellipse within a circle and a circle within an ellipse, respectively. 2. Optical Scattering in the 2'-b

Plane

Although Eq. (71) was referred to the principal axes of the susceptibility tensor x, the general wave equation (Eq. (67)) is not restricted to any particular coordinate system. It is necessary only that the propagation direction, 1 (defined by I,, ly , lz), and the susceptibility matrix be referred to the same coordinate system. Some problems are considerably simplified

308

STEVEN W. MEEKS AND B. A. AULD

by choosing coordinate axes that differ from the principal axes of the susceptibility tensor. For example, suppose the incident light wave is confined to the 2'-b plane, perpendicular to the plane containing the a-type domain wall (the a-b plane) of Fig. 33. The properties of optical wave propagation in this plane are described by a section of the slowness surface in the same plane. The easiest way to derive an equation describing this section is to rotate the coordinate system of the susceptibility tensor by 9.5" about the b axis and then set I,, = 0. This coordinate system rotation is performed by the transformation

[x'l = [a1 [XI [GI 0

sin q

0

0

cos

x33

-sin

0 cos 71 (72)

where 7 = 9.5". The resulting susceptibility matrix in the new coordinate system (the x ' , y', z' system) is then (73) where

xil = xll cos2 r] + x33sin2 71 sin 277 xi3 =

(XI1

-

x33)

and

xi3 = ,yI1sin2 77 + x33cos2 Substitution of Eq. (73) into the general wave equation (Eq. (67)) yields a homogeneous set of equations similar to Eq. (71), except that now the equations are referred to the rotated set of coordinates ( x ' , y ' , 2 ' ) . The final step in obtaining the equation for the slowness surface section in the 2'-b plane is to set 1,. = 0. This yields

309

APPLICATIONS OF FERROELASTIC CRYSTALS

where

E

=

/yflzf

Setting the determinant of the 3 x 3 matrix in Eq. (74) equal to zero and solving for k / w yields a bi-quadratic equation describing the desired section of the slowness surface. It consists of two branches, described by the two solutions k l / w and k 2 / w of Eq. ( 7 3 , given below in Eq. (76).

+

(:L2

i3: -

=

c$E cos2 8 - A ( C cos2 0

+ n$ sin2 0) - B ] + A B - D

=

0

[ B + cos2 8(AC - E ) + An; sin2 01 2cg(nz sin2 e + c cos2 e) *{[cos2 8(E - A C ) - An$ sin2 8 - BIZ - 4(nz sin2 8 + c cos2 B ) ( A B 2c2,(4 sin2 e + c cos2 0)

where the positive (negative) sign defines solution one (two), and A = 1+

B

=

nfi(1 +

xi3)

c = 1 + xi3 D

= n;(X;3)2

E

= ( X a 2

co = 3 x 108 m/s = speed of light

(76)

310

STEVEN W. MEEKS AND B. A. AULD

5

w

s v)

-

LL

-

0

OPTICAL SLOWNESS CURVES FOR 9S0 ROTATION

X W

n

z

1.57

I I I I I I I I I I I I I I I I 1 1 I I I I I 1 1 1 1 1 1 I I I I I I

These solutions are shown in Fig. 34 as a function of 8, the angle between k and the Z' axis. The principal indices of refraction at the 1.05 micron wavelength used in this calculation were taken from Huber and associates (1975). The slowness section curves derived above, and shown in Fig. 34, are for one of the possible domain states of the crystal. Slowness curves for the opposite domain state are obtained by rotating the susceptibility tensor by 7~ about the a crystal axis. The result of this rotation is to change z' to -2' and y' to - y ' . This results in a change in the sign of x i 3 . This produces a change in the sign of 6 in Eq. (74). However, there is no change in the slowness section curves since 6 (in particular xi3) appears only as a squared term in Eq. (76). Hence, the slowness section curves are mirror symmetric about the a-b plane (the plane of the a-type domain wall), as shown schematically and to a greatly exaggerated scale in Fig. 35(a), which is just an angular plot of Fig. 34. The a--6 plane of the domain wall is perpendicular to the plane of Fig. 35(a). The two domain states are indicated by the different shading in Fig. 35(a), and the intersection of the shading lines is the position of the domain wall (which is, of course, perpendicular to the page). The curves representing mode 1 (the slow wave) and mode 2 (the fast wave) are not simple circles or ellipses but are the more complicated ovaloids given by Eq. (76). The implications of this mirror symmetry are very interesting. First of all, it means that a wave crossing an a-type domain wall experiences no change in index, hence it does not refract or bend as indicated by ki2)/o

APPLICATIONS OF FERROELASTIC CRYSTALS

311

kb y! b, w

MODE

MODE

DOMAIN STATE

= I ILaII

1

t

DOMAIN WALL IN a - b PLANE

(4

MODE

MODE

t

DOMAIN WALL IN a - b PLANE

(b)

FIG.35: Optical slowness curves on a polar plot (greatly exaggerated) for an a-type domain wall showing (a) mirror symmetry of the slowness section curves, (b) scattering of a mode 2 incident wave.

312

STEVEN W. MEEKS AND B. A. AULD

and kj2)/W in Fig. 35(b). The obvious question at this point is: “Does an optical wave reflect at all if there is no index discontinuity?” First of all, one must realize that in an anisotropic crystal the electric field is required to lie along certain directions given by the polarization eigenvectors of Eq. (71) or (74). Eigenvectors for one domain state differ from those of the other by a rotation of 7~ radians about the a axis. Figure 36 shows this relation for the electric fields (in the rotated system of coordinates) of incident and transmitted waves traveling at an angle @fromthe z’ axis. This shows that the y’ (or tangential) components of the incident and transmitted electric fields are not continuous at the plane of the domain wall. It is this discontinuity which requires the presence of a reflected wave to satisfy the boundary conditions demanding continuity of tangential E and tangential H. Notice that at normal incidence the Eypcomponent is zero. Thus there is no optical reflection at normal incidence. This is in contrast to the acoustic case (Eqs. (32) and (33)) where the 3-D vector boundary conditions demanding continuity of the vector velocity field v does require a reflected wave, because the sign of the normal component of v changes sign when a normally incident wave passes from one domain state to another. The fundamental reason for the difference between the acoustic and optical behavior at normal incidence is that the acoustic boundary conditions are 3-D vector in nature, while optical boundary conditions are 2-D vector in nature. In summary, the reflections from an a-type domain wall are most unusual. The reflection is due to a change in the polarization of the wave, not a change in index. Thus, one has the unusual situation of having a reflection without a refraction!

7 .tyn -E ‘ Y

r/

FIG.36: The change in the electric field of an optical wave upon crossing an a-type domain wall at angle 0.

APPLICATIONS OF FERROELASTIC CRYSTALS

313

Figure 35(b) also shows that an incident wave of polarization belonging to the inner mode (mode 2) will phase match into four waves: two transmitted and two reflected. Figure 37(a) shows that an incident wave of

t DOMAIN WALL I N a

-b

PLANE

(4

t

DOMAIN WALL I N a - b P L A N E

(b) FIG.37: Slowness section curves showing (a) transmitted and reflected waves when mode 1 is incident at an angle less than the critical angle for mode 2, and (b) when both modes are incident at an angle less than the critical angle.

314

STEVEN W. MEEKS AND B. A . AULD

the outer mode polarization (mode 1) will also phase match into four waves. If both polarizations are simultaneously incident then it is possible for eight waves to be produced, as shown in Fig. 37(b). If the two incident polarizations are contained in the same beam then two of the transmitted and two of the reflected waves will very nearly coincide, as shown in Fig. 37(b), because the angular separation is small, owing to the small change in index. For a thin crystal the separation of the beams will be a small fraction of the total beam diameter. The result is that one sees a total of six waves (or spots) instead of eight. The presence of two pairs of overlapping waves, as indicated by Fig. 37(b), can be detected by the use of a polarizer to separate the orthogonally polarized spots. Figure 37(a) also shows that there will be a critical angle when the projection of the k vector of the incident mode 1 on the domain wall just touches the inner slowness curve. Mathematically, the critical angle for mode 2 is the angle 0, given by the solution of

When the angle of incidence is less than O,, then a mode 2 polarization wave will be produced by a wave of mode 1 polarization. When the angle of incidence is greater than 0,, mode 1 will not produce a propagating mode 2 wave. Thus, for incidence angles of mode 1 greater than O,, only two waves will be produced (one transmitted and one reflected), both of mode 1 polarization. Experimental observation of these phenomena will be described in the next section. 3. Power Reflection Coeficients As seen above (Figs. 35(b) and 37(a)) each incident polarization has in general two reflected waves and two transmitted waves. This implies that five waves must be matched at the boundary. The polarization of the waves is obtained from the first two lines of Eq. (74), once the eigenvalues k l / w and k 2 / w are known.

p p

=

(77)

APPLICATIONS OF FERROELASTIC CRYSTALS

315

where a , p, 6 , and E are defined after Eq. (74) and have different values for modes 1 and 2. The subscripts I and I1 on the above polarizations refer to the two possible domain states. The polarization is a function of the angle of incidence as can be seen from the definitions of a , p, 6, and E . When mode 1 is the incident wave then the five waves to be matched at the boundary are (see the waves which phase match a mode 1 incident wave in Fig. 37(a)):

Here, SQ is the amplitude of the mode 1 incident wave, 93 the amplitude of the mode 1 reflected wave, (e the amplitude of the mode 2 reflected wave, %' the amplitude of the mode 2 transmitted wave and 52' the amplitude of the mode 1 transmitted wave and an exponential time variation is understood. The magnetic fields corresponding to Eq. (79) are computed from 1 H=-kXE PW

For the directions of the reflected and transmitted wave vectors, use is made of Snell's law

k!') sin( oi

=

k!') sin( or2)

Wa>

316

STEVEN W. MEEKS AND B. A. AULD

and the geometrical relations:

et2= 180" - Sr2 St,

=

61

e,,

=

180" -

e,,

In Eq. (81b) Si, is the angle of incidence of mode 1, Or, is the angle of reflection of mode 1, Or, is the reflection angle of mode 2, S,, is the transmission angle of mode 1, and /It2 is the transmission angle of mode 2. All angles are measured with respect to the z' axis. Equations defining the wave amplitudes d,93,V,93' , (e ' in Eq. (79) are obtained from the field continuity boundary conditions af the domain wall

This is an inhomogeneous set of four equations and four unknowns. It can only be solved numerically, and a microcomputer was programmed to calculate the amplitude ratios (namely %/d and %/d)for the various scattered waves. T o calculate the power reflection coefficients, the ratio of the reflected to the incident power must be calculated. This is done by calculating the ratio of the reflected energy leaving a unit area of the domain wall per second to the incident energy striking a unit area of the domain wall per second. This is equivalent to calculating the ratio of the z' component of the Poynting vector of the reflected wave to the z' component of the Poynting vector of the incident wave. Hence, the power reflection coefficients are defined as (E H)Fode 1 reflected R1, = (E H)FOde 1 incident (83) (E R21 = (E

H)=n;lode 2 reflected

H ) y d e 1 incident

(84)

When the angle of incidence of mode 1 becomes greater than the critical angle for mode 2, Ral goes to zero since a propagating wave can no longer phase match into the mode 2 polarization. This means that Or2 becomes complex and Or, is replaced with ei2 + ia'. The real part of the complex angle is Oi2 = 90" and the imaginary part is given by substituting

317

APPLICATIONS OF FERROELASTIC CRYSTALS

the complex angle into Snell's law, with the result

(85) sin(Oil) = k!*)(90")cosh(a') Substitution of a' from Eq. (85) and the complex angle for 6,, into the calculations required in Eq. (83) gives Rll at incidence angles greater than the critical angle for mode 2. Calculation of the reflection coefficients for mode 2 incident is completely analogous to the above case, except that there is no critical angle for mode 2 incidence. In Fig. 35(b), because the mode 2 curve lies inside the mode 1 curve, even a mode 2 wave traveling parallel to the domain wall phase matches into a mode 1 wave propagating at a real angle. The power reflection coefficients for mode 2 incidence are found to be (E H ) y d e 2 reflected R22 = (E H ) y o d e 2 incident (86) R12 =

(E (E

H ) y o d e 1 reflected

(87)

H ) y o d e 2 incidence

Numerical evaluation of Eqs. (83), (84), (86), and (87) at 1.05 micron wavelength and different angles of incidence generated the curves in Fig. 38. The angle of incidence shown in the figure is the angle between the

I

I

I

I

I

I

I

I

I

t-

z

1.05 MICRON WAVELENGTH

w

u

LL LL

w

8 2

0 t-

u

W

1

LL

w

(r

CK

W

z

a

do 0

90

ANGLE OF INCIDENCE OF MODE I OR MODE 2 FIG.38: Theoretical optical power reflection coefficients from a single a-type domain

wall at 1.05 microns.

318

STEVEN W. MEEKS AND B. A. AULD

normal to the wall and the direction of propagation of the incident wave. That is, 90" is grazing and 0" is normal incidence. The reflection coefficients at angles greater than 75" are much greater than the 1 x reflection coefficients of the domain wall of another ferroelastic, Rochelle salt (Tsukamoto et al., 1982). Figure 38 shows that RI1 has a peak in its reflection coefficient at 81.5". The apparent peak value shown is about 21%, (note that the ordinate of Fig. 38 is a logarithmic scale) but the actual value is 100%.The difference is due to the sharpness of the peak and a slight undersampling in the numerical computation. The peak is due to the critical angle of RZ1,which appears at 81.5" (if one is rotating from grazing to normal). A t an angle of about 30", R12 and Rzl go to zero, meaning that there is no mode (polarization) switching upon reflection at this angle. This behavior is a kind of Brewster's angle for a domain wall. It is also important to note that all the reflection coefficients go to zero at normal incidence (zero degrees), as predicted from the behavior of the polarization of the waves upon crossing the domain wall (see Fig. 36). This last fact has important consequences for device applications of arrays of these domain walls, as will be discussed in Part IV.

4. Comparison of Theory and Experiment The following paragraphs will present the experimental techniques used to obtain the scattering patterns and the power reflection coefficients of light at NPP a-type domain walls. A comparison of theoretical and experimental scattering patterns and reflection coefficients will be made. (i) Scattering Patterns Figure 39 shows a schematic of the experimental setup used to obtain the scattering patterns of light from NPP

,(

ROTATOR

DOMAIN A - TWALL YPE?

NPP

CRYSTAL

.

LASER QUARTER WAVE PLATE

1 -TRANSMITTED SPOTS

~

LINEAR POI ARIZFR .~-

FOCAL LENGTH

A - TYPE DOMAIN WALL

NPP CRYSTAL SHOWING ORIENTATION OF CRYSTAL AXES

-REFLECTED SPOTS I

SCREEN

FIG.39: Schematic of the experiment used to observe the scattering patterns of light from an a-type domain wall.

APPLICATIONS OF FERROELASTIC CRYSTALS

319

a-type domain walls. The linearly polarized HeNe laser light is converted to circularly polarized light via a quarter wave plate, and the desired component of linear polarization is selected by rotating a linear polarizer to the desired angle. The light is then focused onto the domain wall with a 5 cm focal length lens. The NPP crystal is placed on a rotator so that the scattering patterns may be observed as a function of the angle of incidence of the 0.6328 micron HeNe light. The scattering patterns are observed on a screen which is placed about 1 meter from the NPP crystal. The combination of the quarter wave plate and the linear polarizer allow the selection of mode 1or 2 polarization for the incident wave. When the linear polarizer is adjusted so that the incident polarization excites only mode 1in the crystal, the scattering pattern should be that predicted by Fig. 37(a). Figures 40(a) through (c) show the experimental scattering patterns for various incidence angles, when mode 1 is the incident polarization. Figure 40(a) shows the scattering pattern for an incidence angle of 90" (grazing incidence). In this case, mode 1polarization excites only a single mode 1 transmitted wave. In Fig. 40(b) the angle has been changed so that the angle of incidence is less than 90" but greater than the critical angle for mode 2. As predicted from Fig. 37(a) there are only two spots: the left spot is the transmitted mode 1 and the right spot is the reflected mode 1. When the angle of incidence is less than the critical angle for mode 2, then mode 1 will excite mode 2 waves as indicated by Fig. 37(a). The experimental results are shown in Fig. 40(c). The second and third spots from the left are the transmitted and reflected mode 2 waves, respectively, which were excited at the critical angle. The smearing of the second and third spots from the left is not due to Poynting vector walkoff since the slowness surfaces of mode 2 are very nearly circular for angles near 90", as can be seen from Fig. 34. It is probably due to some type of leaky mode which occurs near the critical angle. The leaky mode travels along the domain wall, radiating as it travels, resulting in the smeared spots (TZ1and RZ1)of Fig. 40. The spot furthest to the left in Fig. 40(c) is the transmitted mode 1wave and the spot furthest to the right is the reflected mode 1 wave, R l l . Figures 41(a) through (c) show the scattering patterns of light, for various incidence angles, from an a-type domain wall when both mode 1 and 2 polarizations are incident on the wall. This is the case which is schematically illustrated in Fig. 37(b). Figure 41(a) is at the grazing angle of 90". This photograph shows that the mode 2 polarization will phase match into mode 1 polarization (the spots on the far left and far right) even at a grazing angle. This is suggested by the schematics in Figs. 19 and 35(b). The central spot in Fig. 41(a) is a combination of mode 1 and 2 transmitted spots. The spots shown in Fig. 41(b) are for an angle which is between the critical angle and 90". Comparison with Fig. 40(b) shows that two additional spots are present, namely the far left and far right spots. These spots are

320

UNOEFLECTEO SPOT TII

TI I

TI I

RI I

T2I

R2I

Rll

FIG.40: Photographs showing the scattering of light from an a-type domain wall when mode 1 polarization is incident at: (a) grazing (90"), (b) an angle less than grazing and greater than the critical angle, (c) an angle less than the critical angle.

the transmitted and reflected mode 1 polarizations, TI2and RI2 respectively, which are produced by the mode 2 incident wave. The second spot from the left in Fig. 41(b) is a transmitted spot consisting of both mode 1 and 2 polarizations. The third spot from the left is a reflected spot which consists of both mode 1 and 2 polarizations. In Fig. 41(c) the angle has been decreased to where it is now less than the critical angle for mode 2. As

APPLICATIONS OF FERROELASTIC CRYSTALS

321

R22,

TI 2

T I I,

TI 2

T22

R22, T2I R 2 I R l l

FIG.41: Photographs showing the scattering of light from an a-type domain wall when modes 1 and 2 are simultaneously incident at: (a) grazing (90°),(b) an angle less than grazing and greater than the critical angle, (c) an angle less than the critical angle.

322

STEVEN W. MEEKS AND B. A. AULD

TI 2

T22

R22 4 2

FIG.42: Photograph showing the scattering of light from an a-type domain wall when mode 2 is incident at an angle of approximately 78".

Fig. 37(b) indicates there will be eight spots present when both polarizations are incident. However, only six are visible because two pairs of spots overlap, as explained previously. The three spots visible on the left of Fig. 41(c) are the transmitted spots and the second spot from the left consists of two overlapping spots of orthogonal polarization, as can be checked with a polarizer. The three spots on the right of Fig. 41(c) are reflected spots with the fifth spot from the left consisting of two overlapping spots of orthogonal polarization. The smearing is again probably due to some type of leaky mode which occurs near the critical angle. Notice that three images of the incident laser beam (3 transmitted and 3 reflected) are produced. This is an apparent trirefringence. However, there are only two polarizations present as indicated by Fig. 37(b). Figure 42 shows the scattering pattern for mode 2 incident at an angle of approximately 78" This experimental observation should be compared with Fig. 35(b). The far left spot is the transmitted spot of mode 1 polarization, and the spot second from the left is the undeflected transmitted spot of mode 2 polarization. The third spot from the left is the reflected spot of mode 2 polarization and the fourth from the left is the reflected spot of mode 1 polarization. The case of mode 2 incidence does not show a critical angle behavior as does the case of mode 1 incidence.

(ii) Measurement of Power Reflection Coeficients An experimental verification of this theory was performed by measuring the reflection coefficients from a single domain wall at 0.6328 microns and comparing these values to the theory calculated at the same wavelength. The only change which must be made in the theory is to replace the 1.05 micron value of 9" of the tilt angle 6 in Fig. 33 with the 0.6328 micron value. The experimental setup used to make the tilt angle and the reflection coefficient measurements is shown in.Fig. 43. This setup is very similar to that used to

APPLICATIONS OF FERROELASTIC CRYSTALS

323

ROTATOR

HeNe LASER QUARTER WAVE PLATE

LINEAR POLARIZER

LENGTH METER

NPP CRYSTAL SHOWING ORIENTATION OF CRYSTAL AXES

FIG.43: Schematic of the experiment used to measure the power reflection coefficients of a single a-type domain wall.

observe the scattering patterns (Fig. 39). The difference is that a power meter sensitive to HeNe light is placed at the position of the desired reflected spot and the power of the reflected spot is measured as a function of angle of incidence of the selected mode upon the domain wall. The tilt angle 6 was measured by rotating the crystal so that the light was incident at grazing upon the domain wall. Then the linear polarizer was adjusted so that only mode 2 light was incident. This results in a scattering pattern which looks like Fig. 41(a). The spots to the far left and far right of Fig. 41(a) are linearly polarized in the 3 and 3' directions, respectively, with an angle of 26 + 1 degrees between their polarizations (see Figs. 19 and 46). The angle between the polarizations is 19" at 1.05 microns and room temperature which implies that delta is 9". However, the angle 6 is a function of temperature, and wavelength, and the purpose of this experiment is to measure delta at 0.6328 microns and at room temperature (23°C). A polarizer was placed at the output side of the crystal and the extinction angle between the far left and far right spots of Fig. 41(a) was measured to be 17.8" at room temperature and 0.6328 microns. This implies that 6 = 8.4 0.2 degrees. The reflection coefficients were measured as shown in Fig. 43. The desired reflection coefficient was chosen by adjusting the input linear polarizer so that only the desired mode was incident, and then the HeNe power meter was placed at the position of one or the other reflected spots. The presence of the correct mode is detected by observing the scattering patterns. For example, the input polarization can be adjusted so that mode 2 never appears at the critical angle for

*

324

STEVEN W. MEEKS AND B. A. AULD

mode 2. This means that the incident light is exciting only mode 2 polarization in the crystal (see Fig. 35(b), and Fig. 37(a) and (b)). The resulting comparison of theory and experiment at 0.6328 microns for mode 1 incidence angles between 70" and 90" is shown in Fig. 44. The experimental values have been corrected for the reflections from the surfaces of the NPP sample used to obtain the experimental data. The agreement between theory and experiment is good over the angle range shown. The good agreement is particularly satisfying since the theory used is a zero parameter fit theory. The largest discrepancy is in RI1 at the critical angle of 81.5". This is caused by angular averaging in the experimental data, where an incident beam 1.5" in angular width was used. The comparison between theory and experiment for mode 2 incident is shown in Fig. 45. Again good agreement between theory and experiment is seen. The careful reader will note that at grazing incidence in Fig. 45, energy is not conserved since RI2 is shown as being nonzero and R22 is equal to 1.0 at 90". The answer to this apparent discrepancy is that the value of RI2 actually goes to zero at 90", but it approaches zero with such a large slope that it is impossible to show on the scale of Fig. 45. Experimentally one always sees a finite value of RI2 at grazing, since the incident beam always has some small angular spread.

-10

10

I

- THEORY AT 0.6328 MICRONS

---

EXPERIMENT AT 0.6328 MICRONS

i

EXPERIMENTAL AND THEORETICAL POWER REFLECTION COEFFICIENTS FROM A SINGLE A - T Y P E NPP DOMAIN WALL

I 1

1

1

1

I

1

1

1

1

l

1

1

1

1

1

1

1

I

325

APPLICATIONS OF FERROELASTIC CRYSTALS I

1

k THEORY AT 0.6328 MICRONS EXPERIMENT AT 0.6328 MICRONS

lo-'o

I I70

I

EXPERIMENTAL AND THEORETICAL POWER REFLECTION COEFFICIENTS FROM A SINGLE A - T Y P E NPP DOMAIN WALL 1

1

I

I

I

I

1

I

I

I

I

I

I

1

1

I

I

I

1 I

90 ANGLE OF INCIDENCE OF MODE 2

FIG.45: A comparison of theoretical and experimental power reflection coefficients from a single a-type wall at 0.6328 microns for mode 2 incident.

5 . Explanation of Contrast Between Domain States under Polarized Light Part 1I.A showed photographs of a pair of domains viewed between crossed polarizers. This section will explain why there is a contrast between adjacent opposite domain states. Figure 46 shows the principal index surface axes for a pair of adjacent a-type domain states when viewed along the b crystal axis (see Fig. 33). When the orientation of the crystal is rotated so that linearly polarized light from the first polarizer lies along the 1 or 3 axis, the resultant light passing through the crystal will remain linearly polarized at the same angle as the incident linear polarization. The result is that the output polarizer (which is oriented orthogonal to the input polarizer) will block the light polarized along 1 or 3. Hence the unprimed domain state will appear dark under the above conditions. However, light polarized along 1 or 3 will have components along both 1' and 3'. Hence, light from the primed domain state will be elliptically polarized and a component of this light will be transmitted through the orthogonally oriented output polarizer. Thus, the primed domain state will appear bright when viewed under these conditions. Rotating the crystal by 19" (the angle between 1 and 1' or 3 and 3 ' ) will reverse the contrast. That is, the primed state will now be dark and the unprimed state will be bright. If the crystal is rotated through 360" there will be four complete periods of the brightdark, dark-bright sequence. If the crystal is oriented so that the input

326

STEVEN W. MEEKS AND B. A . AULD XI

I

DOMAIN WALL I N a - b PLANE FIG.46: The index surface axes for an adjacent pair of a-type domains when viewed along the b or y ’ axis.

linear polarization is along the a or a’ axis, then each of the domain states will produce identical elliptical polarizations whose major axes are rotated by 19” with respect to the other. Since the output polarizer is oriented perpendicular to the a axis (i.e., along z’), it will pass equal components of the light from each domain state. The result is that each domain state appears equally bright and there is no contrast between the states. All of the phenomena discussed above have been verified experimentally. The discussion given above has been for a pair of a-type domains, the situation for b-type domains is entirely analogous. This subsection has presented an optical reflection theory of a NPP ferroelastic a-type domain wall. The reflection was found to be due to a change in the polarization of the wave, and not to a change in the index, as the wave crosses the domain wall. This leads to a wave which can be reflected without a refraction in the transmitted wave. The theoretical power reflection coefficients for the two incident polarizations have been computed and compared with experiment at 0.6328 microns. The magnitude of the power reflection coefficients for a single wall is greater than for angles greater than or equal to 75”. In particular, the 1x theoretical value at the critical angle (81 So)is unity! Unfortunately, the reflection coefficients go to zero at normal incidence. However, an array of domain walls operated at the critical angle of the walls should show a large reflection. The final section of this chapter explained the reasons why there is a contrast between a pair of adjacent domain states. The contrast is due to the tilt of the index surface axes of the contiguous domain states.

APPLICATIONS OF FERROELASTIC CRYSTALS

327

Iv. OPrICAL AND

ACOusTtc DEVICESUSING NPP PERIODICDOMAINWALLGRATINGS

This section presents two demonstration devices which use the periodic domain walls in NPP; a tunable active grating (TAG) and a tunable acoustic filter (TAF). The T A G discussed in the following section shows quasi-cw gains of about 1.14 db (30%) at the first- and fourth-order Bragg spots. Nearly all of the gain of an NPP monocrystal is found to appear as gain in the Bragg spots of the ferroelastic grating. The discrepancy between the predicted and measured optical gain in NPP is attributed to up conversion in the NPP crystal. This problem can be circumvented by using a pulsed pump or substituting La+3 or Y+3 for some of the Nd+3 in the crystal lattice. A third device, a tunable active grating laser (TAG laser), has not yet been demonstrated, but its design and potential advantages are described in Section B of this part. The TAG laser is predicted to have the ability to tune between the various lasing lines of Nd+3without a tuning element that is external to the lasing medium. This laser may also have the ability to tune between the various longitudinal modes of an NPP laser. Although it is not emphasized in this section, these domain arrays have the obvious application as tunable optical diffraction gratings. The TAF discussed in Section C shows good agreement between theory and experiment. The theory is used to predict the acoustic stopbands of an NPP array. Two acoustic grating filters are constructed, which have passbands at 34 and 68 MHz, and 43 and 86 MHz. The frequency response of NPP arrays is unusual because there is no impedance change upon crossing a domain wall. This leads to frequency responses which have missing passbands as compared to an ordinary alternating impedance grating. It is predicted that these domain arrays will make excellent stopband transmission filters for shear waves. Such grating filters should also be useful in tunable SAW filters or resonators. A . Tunable Active Optical Grating

This subsection describes an optical ferroelastic grating which is pumped with green light (5145 angstroms) so that it has optical gain at the lasing transitions of Nd+3. Neodymium in NPP has significant gain at wavelengths near 0.9, 1.05, 1.32, and 1.9 microns (Blatte et al., 1973). In this case the tunable active optical grating uses optical gain at 1.05 microns.

328

STEVEN W. MEEKS AND B. A. AULD

1. General Experimental Arrangement The optical arrangement for this experiment is given in Fig. 47. It consists of a 0.5145 micron argon-ion laser which is used to pump both a 1.05 micron NPP probe laser and a NPP crystal (1.5 mm thick) containing a ferroelastic grating. The probe or signal beam from the NPP laser is combined with the 0.5145 micron pump beam at a dichroic mirror. The combined beams are then focused onto the NPP crystal which contains a grating. The residual 0.5145 micron beam is filtered out via a long pass filter and the amplified 1.05 micron beam is detected with a photodiode. The resulting signal is displayed on an oscilloscope. The grating gain was measured by computing the ratio of the 1.05 micron signal with the pump present to the signal with the pump beam blocked. The probe laser shown in Fig. 47 is a design which uses a near-spherical cavity with a 1.5 mm thick piece of NPP (without a grating) as the active element. The mirrors have a 5 cm radius of curvature and are coated for 100% reflectance at the input and 97% reflectance at the output at 1.05 microns. The mirrors transmit about 90% of the 0.5145 micron pump beam. Since the cavity is nearly spherical the separation between the mirrors is approximately 10 cm. The laser quality focusing lens at the input to the NPP probe laser is a 5 cm focal length lens which focuses the 1 mm radius pump beam to a 8 micron waist in the NPP crystal. At the output of the NPP laser is a long pass filter which filters out any remaining green (0.5145 micron) light. The absorption length of NPP at 0.5145 microns is approximately 750 microns, hence in a 1.5 mm thick NPP crystal about

EAMSPLITTER

PLUS ARRAY

LENS

NPP PROBE LASER

FIG.47: Experimental setup for measuring the gain of a NPP tunable active grating.

APPLICATIONS OF FERROELASTIC CRYSTALS

329

SLOPE 14

0 0

20

40 60 80 ABSORBED POWER (mW 1

FIG.48: Slope efficiency of a NPP probe laser.

80% of the pump light is absorbed. The slope efficiency (the output power versus input absorbed power) of this probe laser was measured and is displayed in Fig. 48. Output power is measured on a calibrated photodiode while the input pump power is increased. The result is the linear increase in output power at a slope of 32% as shown in Fig. 48. This slope efficiency compares favorably with a theoretical value of approximately 37%. Slope efficiency is limited by the ratio of the pump wavelength to the lasing wavelength. This ratio, which is 0.49 in this case, is the maximum possible value of the slope efficiency. Threshold for lasing was measured to be 22 mW of absorbed pump power, the lowest repeatable threshold obtained for this laser design (using 6 plates of NPP). 2. Optical Gain Measurements in a Monodomain Crystal A preliminary experiment was performed in a monodomain crystal, as a baseline for the tunable active grating experiment. The experimental setup is nearly identical to that shown in Fig. 47, except that the 1.5 mmthick NPP crystal at the left side of Fig. 47 does not contain an array and the pump and signal lasers strike the crystal at normal incidence. This classical laser amplifier experiment gave the results shown in Figs. 49 and 50.

330

STEVEN W. MEEKS AND B. A . AULD

I .35 --a-

P

Wo = 5.0pm

lo’ t = 1.20 3!=

a

3

a

1. 1-05 1.00

0

0.2

0.4

0.6

PUMP POWER

0.8

1.0

1.2

(watts)

FIG.49: NPP gain without a grating versus pump power with

WX

as a parameter.

Figure 49 shows the gain (the ratio of the output signal power with the pump present to the signal power with the pump beam blocked) versus input pump power. The intensity of the signal beam was kept well below the 1.05 micron saturation intensity and the ratio of the waist of the signal beam to the waist of the pump beam (w,”/wOp)was kept constant at a value of 1. In this way a constant longitudinal overlap of the two beams was maintained. The three curves in the figure correspond to three values of the pump and signal waists. A maximum gain of 30% occurred for a pump value of about 0.8 watts of green light. The curves showed a steady decrease in slope as the pump and signal beams were focused to smaller waists. This effect is due to the saturation of the pump beam. If the intensity of the pump beam were far from saturation then the gain would increase exponentially with pump power. As the pump intensity approaches the saturation intensity the curve bends over and eventually approach a flat line at an intensity much greater than the saturation intensity. The decreasing slope of Fig. 49 with decreasing pump waist and, therefore, increasing intensity is an example of this saturation effect.

33 1

APPLICATIONS OF FERROELASTIC CRYSTALS

% 5 2

0

1.25

a!-

=c :

=

3 t

P

1.20

?

a

h

1

0

i

0.2

1

1

1

0.4

l

0.6

1

l

0.0

1

1

1.0

1

/

1.2

PUMP POWER ( w a t t s )

FIG.50: NPP gain without a grating versus pump power with w:’/tv,’ as a parameter.

Figure 50 shows the gain of monodomain NPP versus pump power with wG/wOp as a parameter. The purpose of this experiment is to determine the optimum value of this ratio. As Fig. 50 shows, the best gain is obtained with a w,”/wX ratio of 1.0. This is somewhat different from the value predicted via a small signal analysis which is 1.43. The difference is probably due to the large pump intensities used in Fig. 50, which means the small signal analysis is no longer valid. The saturation intensity of the 0.5145 micron pump transition is 960 kW/cm2. This intensity corresponds to an intensity of the pump beam at the beam waist (at a maximum pump power of 0.77 W), for the three cases illustrated in Fig. 49, of approximately

230 kW/cm2 for wg

400 kW/cm2 for w:

=

=

7 . 2 microns

5.5 microns

475 kW/cm2 for wX = 5.0 microns Thus the greatest intensity is about one-half the saturation intensity. A

332

STEVEN W. MEEKS AND B. A . AULD

rough evaluation of the gain at such an intensity is obtained by calculating the population inversion due to pumping at that level. This population inversion is

where AN is the saturated population difference between the pump level and the ground state, ANo is the small signal population difference (the ground state population of Nd+3 ions), I is the pump intensity, and ZSat is the saturation intensity. When Z is one-half of Z,,, ,then AN is two-thirds of ANo in this simple four-level laser material model. This result means that about one-third of the ground state population is excited into the upper laser state, yielding a gain per unit length

G

= euANz

or GdB - - 4.34

(TAN

Z

=

9.3 dB1100 microns

Here GdBis the power gain in dB, u the fluorescence cross section is equal cm’, AN = (1/3) ANo = (4/3) x loz1atoms/cm3, and z is to 1.6 X the longitudinal overlap distance. If the 5.5 micron signal and pump beam waists are overlapped for one Rayleigh range (150 microns) then the expected gain would be 14 dB or a factor of 25 in the power! Obviously, a glance at Figs. 49 and 50 shows that nothing near these gains is obtained. The reason for this enormous discrepancy is that NPP is not behaving like the simple four-level laser material used in estimating the gain. A significant amount of gain quenching is occurring. Gain quenching in laser materials is due to at least four mechanisms. They are cross relaxation, excited state absorption, up conversion, and impurity quenching. All of these mechanisms play some role, but the dominant mechanism at the high cw excitation levels used here is up conversion (Blatte et al., 1973). The process of up conversion is illustrated in Fig. 51. When two Nd+3 nearest neighbors are both in an excited state then it is possible for one of the excited states to undergo a non-radiative transition to the lower laser level, at the same time exciting the neighboring Nd+3 ions to a higher level (labeled “pump state” here). The decay from the lower laser level and the pump state is rapid (indicated by the wavy arrow). Thus the two initial

APPLICATIONS OF FERROELASTIC CRYSTALS

333

PUMP STATE

LOWER LASER LEVEL GROUND STATENd+3

Nd+3

FIG.51: Illustration of up conversion in NPP.

excited states have been reduced to a single excited state by a radiationless process. This is the mechanism by which up conversion reduces the gain of a laser material like NPP. This process is particularly relevant to NPP because of its high Nd+3 concentration and consequent close spacing of Nd+3 ions ( 5 angstroms). The closer the spacing of the two ions the more likely they are to interact via the up conversion process. A solution to the up conversion problem is to reduce the Nd+3 concentration so that the ion spacing is increased. The efficiency of the up conversion process varies rapidly with the ion spacing, so that a relatively small decrease in concentration can result in a rapid decrease in up conversion. This solution in NPP is implemented by substituting La ions for Nd ions, to create the ferroelastic NdLaPP. The concentration of La can be varied continuously from 0 to 100% while still obtaining a ferroelastic compound, since pure LaPP is a ferroelastic of the same species as NPP (Plattner et al., 1980). The up conversion process illustrated in Fig. 51 requires a finite time to occur. It has been estimated that the lifetime of this process is about 100 microseconds in Nd: YAG (Danielmeyer and Blatte, 1973) and it has also been shown that nearly pure NPP (1% substitution of yttrium) has a gain of 26 dB/cm when pumped with a 1 microsecond pulse from a flash-lamp pumped dye laser. This corresponds to a population inversion of 25% of the ground state ions (Kruhler et al., 1973). The reason for such a large inversion in this case is that the 1 microsecond pump pulse is much shorter than the time required for the up conversion process to occur. Thus one can estimate that the lifetime of the up conversion process in NPP is somewhere between the 100 microsec for ND: YAG and 1 microsec. The data of Figs. 49 and 50 were obtained with a quasi-cw pump. Quasi-cw means that the pump beam was chopped as shown in Fig. 47. Two different pump pulse lengths of 3.5 ms and 400 microsec were used. Each case yielded the same results, as one would expect from the estimation of the

334

STEVEN W. MEEKS AND B. A. AULD

lifetime of the up conversion process. The conclusion is that up conversion imposes a serious limitation on the available gain in cw NPP laser amplifiers. This problem can possibly be eliminated or greatly reduced by substituting La for some of the Nd in the lattice. U p conversion is not a problem, even in pure NPP, if pulsed (1 microsec) lasers are desired.

3 . Optical Gain Measurements in a 4.9 Micron Domain Wall Grating Figure 52 shows the gain in the fourth-order Bragg spot of a 4.9 micron period array in NPP at a w:/wg ratio of 1.25. The two curves correspond to two different values of w:, but with the same ratio of wi/wg. The NPP grating is in a 1.52 mm-thick crystal, hence A2/A = 23 p m << thickness, where A is the grating period, and A is the optical wavelength. This corresponds to a “thick” grating and is well into the Bragg regime of

DETECTOR 4 t h ORDER

1.30 -

GRATl NG LONG PASS FILTER

c

a

4 3a 0+ I 2 a

3c-

a

1.25

-

1.20

-

3

a

5

1.15 -

a

-

(3

1.10

1.05

-

-

LOOI

0

1

1

0.2

1

1

0.4

1

1

0.6

PUMP POWER

1

w,”

IOpm

wo”

I1.4pm

1

0.0

I

1

1.0

1

1

1.2

(watts)

FIG.52: NPP gain in the fourth-order Bragg spot of a 4.9 micron array with w ~ / w = ~ 1.25.

APPLICATIONS OF FERROELASTIC CRYSTALS

335

diffraction. At the waist of the beam (its narrowest diameter, which is in the center of the crystal) these beams intercept about 8 or 9 domain walls. At the edge of the crystal they intercept about 15 domain walls. The resulting efficiency of the grating is a rather poor 13% and 14% for the 10 and 11.4 micron waists, respectively. An additional problem is that the beams intercept about 36% of the 100 micron width of the 4.9 micron period array. As was shown in Part 11, the a-type domain walls which make up these arrays are slightly curved. When a large fraction of the array is intercepted by an optical beam, the curvature of the domain walls becomes important. Thus in Fig. 52 the lensing effects of the curved domain walls is significant. This results in a distorted Bragg spot. A smaller beam could have been used but the efficiency would then decrease, because fewer domain walls would be intercepted. However, despite these restrictions, some gain is still observed. The curve for the 10 micron waist beam at the fourth-order Bragg reflection shows the same gain and slope as the gain curve without a grating (wG/wOp = 1.25 of Fig. 50). The ratio of the output power in the fourth-order Bragg reflection beam to the power in the input signal beam remains below unity because of the poor efficiency of the grating. The 11.4 micron waist beam at the fourth-order Bragg reflection shows a slightly larger efficiency but a somewhat lower gain. Figure 53 compares the gain in the first-order Bragg reflection to the gain in the same crystal without a grating. The efficiency in this case is considerably larger (34%) because the walls are more reflective at the smaller angle required for the first-order Bragg reflection. The net output power, however, is less than the input power, even at the maximum pump power, due to the poor efficiency of the grating. A comparison with the monodomain curve shows that most of the available gain appears in the first-order Bragg reflection. A summary of the results of the grating with gain experiments are that most or all of the available gain of the NPP crystal can be obtained at the Bragg spots of the array. Unfortunately, these arrays are inefficient because of the small number of domain walls that are intercepted. The Bragg spots of the arrays are distorted because a substantial portion of the width of the array is intercepted by the optical beam, which results in lensing effects from the domain walls. Better results might be obtained by using a longer period array, together with a larger diameter spot so that the lensing effects could be reduced. The problem in this case will be to obtain sufficient gain with the large spot size. However, a large gain could be obtained by using a pulsed pump source, as discussed earlier. A large cw gain can be obtained by using Nd,Lal-,P501, as gain medium. The dilution of the Nd+3 with Lat3 will greatly reduce the up conversion problem discussed earlier. The one problem with

336

STEVEN W. MEEKS AND B. A . AULD DETECTOR I s 1 ORDER

1.35

-

1.30

-

a I 1.25

-

r p

STRAIGHT

1.05 BEAM

‘NPP WITH GRATl NG LONG PASS FILTER

5 2 PI-

8 2

t

8

-

I t a 3 a

5

1.20

-

1.15 -

Q W

1.10

MONODOMA IN

1.05 -

-~:=11.4prn

WITH GRATING

1.00

0

0.2

0.4

0.6

0.8

1.0

1.2

PUMP POWER ( w a t t s )

FIG.53: NPP gain in the first-order Bragg spot of a 4.9 micron array with wi/w,” = 1.25.

Nd,Lal-,P5OI4 is that for increasing~La+3content up to x = 0.5, the crystais show an increasing number of cracks parallel to (010) (Plattner et al., 1980). However, many crystals show large sections free of such cracks and these have been used to produce laser rods of composition Ndo.5Lao.5P5014(Plattner et al., 1980). The cracking is presumably due to a mismatch in lattice parameters. If the cracking proves to be a problem one can use Nd0.25L+.75P5014(which has less cracking), or NdyY1-,,P5OI4 which crystallizes in the region 0.15 < y 5 1 in the monoclinic P2,/c structure (the same as NPP) and is ferroelastic with fewer cracking problems (Plattner et al., 1980).

B. Tunable Active Grating Laser This section will describe the principle of a laser device which uses the periodic structure in these NPP crystals as a filtering mechanism. When

APPLICATIONS OF FERROELASTIC CRYSTALS

337

these periodic arrays were originally discovered it was hoped to use them to construct a tunable distributed feedback laser, with light reflecting at normal incidence to the domain walls. However, as was discussed in Part IILB, these domain walls do not reflect optical waves at normal incidence, thus it is not possible to construct a distributed feedback laser. However, it is still possible to use non-normal incidence Bragg reflections from the array to create a tunable active grating laser (TAG laser). The T A G laser has not yet been demonstrated but a discussion is included here to point out the potential benefits of a periodic structure internal to an optical gain medium. A schematic of the TAG laser is shown in Fig. 54. NPP is both a ferroelastic as well as a high gain and high Nd+3 concentration laser material (Blatt et al., 1973; Plattner et al., 1980; Kruhler et al., 1973; Danielmeyer and Weber, 1972; Huber et al., 1975; Damen et al., 1973; Weber et al., 1973; Singh et al., 1975; Danielmeyer et al., 1973; Tofield et al., 1975). The combination of a tunable grating with a good infrared laser material is unique and lends itself to novel laser schemes. The NPP crystal at the center of Fig. 54 contains a domain array which is angle-tuned to a transmitted Bragg spot of the grating. The term transmitted Bragg spot was explained in Part II.A.6. The optical mode on the left half of the laser cavity is polarized in the 3 direction of Fig. 33 and in the 1 direction on the right half of the laser. Both the 1 and the 3 polarizations have sufficient gain to lase in NPP (Huber et al., 1975). When the deflection angle of the kj2)/wwave corresponds to a Bragg angle of the array, the transmitted wave (ki2’/w, see Fig. 15(a)) will have a greatly enhanced intensity. The transmitted Bragg spot is reflected back by

OUTPUT BEAM/

MIRROR AGG

L\ MIRROR

NPP CRYSTAL WITH INTERNAL GF2ATING TUNED FOR TRANSMITTED BRAGG ANGLE

FIG.54: NPP tunable active grating laser (TAG laser).

338

STEVEN W. MEEKS AND B. A . AULD

a mirror at the right side of the laser cavity and is converted back into its original polarization by the domain array. Thus there is no net polarization change after one round trip in the laser cavity. The reflected waves from the domain walls will be weak because they do not satisfy the Bragg condition. This type of diffraction has been used to produce a grating with an efficiency of 77%, obtained using 0.6328 micron light with an uncoated NPP crystal 610 microns-thick with a 58 micron period array. The optical diffraction in this case is in the transition region between Raman-Nath and Bragg diffraction. A photograph of the resulting diffraction pattern was shown in Part II.A.6., Fig. 14. If the crystal were anti-reflection coated then the diffraction efficiency would be expected to be greater than 90%. When this same 58 micron array is used in reflection (so that reflected Bragg spots are produced) then its efficiency is only 16%, for the same conditions that produce the 77% efficiency of the transmitted Bragg spot. Optical interaction with arrays of NPP domain walls was more fully discussed in Part II.A.6. The grating in Fig. 54 will serve as a wavelength selective filter of the radiation in the laser cavity. The particular use of this grating will depend upon the degree of wavelength selectability the NPP grating can provide. If the wavelength selectivity is very sharp, the grating can be used to select between the numerous longitudinal modes of the laser cavity. If the selectivity is somewhat less, the grating may be used to tune between the different lasing lines of NPP (0.9,1.05, 1.32, and 1.9 microns). The distinct advantages of this type of laser are that it has a gain medium and a tunable filter in a monolithic structure. This may lead to a laser which can be tuned between the lasing lines of NPP or a laser which can select between the longitudinal modes of a laser cavity. The tuning may be accomplished without any external cavity element since the tuning element is internal to the gain medium. An estimate of the threshold pump power of the laser illustrated in Fig. 54 is obtained from the expression for the lasing threshold pump power required for an end pumped, laser pumped laser (Kubodera et al., 1979).

where L, is the round trip power loss, h is Planck’s constant, fp is the frequency of the pump, w Iis the waist of the lasing mode, wp is the waist of the pump laser, u is the emission cross section, T~ is the fluorescence lifetime, and q, is the absorption efficiency of the pump light. If the

APPLICATIONS OF FERROELASTIC CRYSTALS

339

parameters of the above equation are chosen to be

L, = 0.5 A, = 5800

A

u = 1.6 x SO-19 cm2 Tf =

120 ps

q,= 0.90 wl = 90 pm

w, = 45 pm then the calculated threshold is 0.78 watts of 5800 A light. This would require mirrors with a radius of curvature of 5 cm, separated by 5 cm. This pump power could be greatly reduced by increasing the efficiency of the grating through use of an antireflection coating on the NPP crystal. The 0.78 W pump power required can be obtained from many cw laser sources (for example, an Ar-ion laser); however, cw operation will not be possible with pure NPP (if 50% round trip losses are assumed) because of the up conversion problem. On the other hand, it will be possible to operate this laser (even with pure NPP) by using a pulsed pump. In this case the threshold should be the 0.78 W quoted above, which is easily obtainable with a flash lamp pumped dye laser. Continuous wave operation could be obtained by using Nd La PP in place of NPP so as to circumvent the up conversion problem. This type of operation is needed when it is desired to modulate the beam, as for instance in optical communication. C. Tunable Acoustic Filter

This subsection presents a tunable acoustic filter which uses the periodic domain arrays to filter a normally incident acoustic wave. A theory is presented for computing the passbands of an NPP array. The experimentally-measured passbands of a 74.8 and 95.1 micron period arrays are presented and compared with theory. 1. Experimental Arrangement

Figure 55 shows the setup of Mr. Larry Clarke of Stanford University which was used for measuring the reflection coefficient of arrays of NPP domain walls. The NPP crystal with an array present was placed in a water

340

STEVEN W. MEEKS AND B. A. AULD

I m m DIAMETE PIEZOELECTR

WATER BATH

NPP CRYSTAL W I T H PERIODIC ARRAY (1.5mm

RECEIVEDSIGNAL

-t FREQUENCY

N

FREQUENCY

( b) FIG.55: (a) Experimental setup for measuring the reflection passband of NPP arrays, (b) reflected signal from the surface of sample (signal 1) plus array ringing (signal 2) and schematic spectra of signals.

bath and the domain walls were oriented as shown in Fig. %(a). The dimensions of the crystal are 10 mm in the a dimension by 5 mm in the c direction by 1.5 mm in the b (thickness) dimension. A broadband 1 mm diameter PZT piezoelectric transducer, with 3 dB bandwidth from 20 to 76 MHz, produces an acoustic pulse which travels through the water and into the crystal containing the array, It is positioned near the tips of the

APPLICATIONS OF FERROELASTIC CRYSTALS

341

array, as shown in Fig. 55(a), to take advantage of the more efficient reflection of a delta function array (as will be shown in the next subsection). A portion of the broadband acoustic pulse reflects from the crystal surface and returns to the transducer (signal 1 in Fig. 55(b)). This reflected pulse is followed by the narrowband ringing of the ferroelastic grating (signal 2 in Fig. 55(b)). Schematics of the frequency spectra of the broadband pulse and narrowband ringing are shown at the bottom of Fig. 55(b) (obtained in the experiment, to be described, by FTTprocessing the time domain signals on a microcomputer). The frequency spikes in the Fourier transformation of the ringing signal occur at the stopband frequencies of the grating. 2 . Theoretical Prediction of the Reflection Filter Passbands of NPP Gratings

The theory used to calculate the reflection filter passbands of these NPP periodic structures is a modified type of the chain matrix method (Sittig and Coquin, 1968; Yeh et al., 1977). The theory assumes that a finite number of array elements is present and that each end of the array is terminated in a matched impedance. A graphical description of the theory is shown in Fig. 56. Since the last section of the array is terminated by a matched impedance, there will be no reflected wave once the wave leaves the array. Thus, the single transmitted wave will have amplitude toAo, there to is the amplitude transmission coefficient of the final reflecting surface. The reflected amplitude is Bo = poAo,where po is the amplitude reflection coefficient of the final reflecting surface. The amplitudes A l and B1 are related to A . by simply adding up the waves at the second reflecting surface from the right Altl

=

AOelP1"+ plBoe-'P1'i

B1 = A l p l

+ Botle-JB1'l OUTPUT

An JVm&

A2 JuvlA

...... Bn 4u-UwL

B2 cs\hn

I-4

-

FIG.56: Illustration of the waves used in the theoretical computation of the reflection passbands of NPP arrays.

342

STEVEN W. MEEKS AND B . A. AULD

Using Eq. (88) in Eq. (89) yields

B1

=

A 0P1eiPdl + BOe-iPIli fl

= Y1Ao and

where a. = 1, -yo = po, and p l , tl are the amplitude reflection and transmission coefficients, respectively, of the second reflecting surface from the right. In a similar manner it can be shown that A 2 and B2 are related to A l and B , by aleiP212

A,=[ a2Ao

+ p2y1 - i P z h f2

IA0

and

where p2 and t2 have meanings analogous to pI and t , The general recursion relations for a, and yn are

Hence, the n-th right propagating and left propagating waves are related to

APPLICATIONS OF FERROELASTIC CRYSTALS

343

A0 by

A,

=

Bn

=

(Y,AO

(96)

Y~AO (97) The overall transmission coefficient is obtained by setting the amplitude of the n-th incoming wave to unity. Thus

or the transmitted power is

Similarly, the reflected power is obtained from

The recursion relations (Eqs. (94) and (95)) were programmed on a microcomputer and used to compute the power reflection coefficient of two different period NPP arrays. Part 1I.A showed that this type of array in NPP has slightly curved walls, which form points (delta functions) at the edges of the array. The photographs of the periodic structures in NPP show that the ratio of plus or minus domain state width to the total array period is a function of the lateral position in the array. This ratio (called the array fraction) varies from less than 1% at the array tips to 50% at the center of the array. The value of the array fraction has a pronounced effect on the position and magnitude of the reflection coefficients (Sittig and Coquin, 1968). Figure 57 shows the computed power reflection coefficient of 54 periods (corresponding to an array length of 5 mm) of a 95.1 micron period NPP a-type array with an array fraction of 1% (a delta function array). The RN reflection coefficient of a single a-type domain wall was used in this calculation for the values of p , (see Table I). The array shows strong reflections at the frequencies given by

where A is the array period and A, is the acoustic wavelength. The peak

344

STEVEN W. MEEKS AND B. A. AULD

0.00

a

40 60 ea FREQUENCY I N MHZ

20

1

a

FIG.57: Theoretical reflection passband of a 95.1 micron period NPP delta function array (fraction = 1%) consisting of 54 periods.

reflectivity is about 99% at the passbands of the array. The passband frequencies are located at 34 and 68 MHz. The FWHM bandwidths are about 3 MHz. Figure 58 shows the computed reflection from the same 95.1 micron array, but with an array fraction of 0.25. This array will have reflection passbands (or stopbands, if used in transmission) at the frequencies given by Eq. (101). Notice that there is no reflection passband at 68 MHz in Fig. 58. This is because there is not an alternating sign in the single wall reflection coefficients of NPP domain walls. The absence of an alternating reflection coefficient suppresses the 68 MHz reflection passband. This array is not quite as efficient a reflector of acoustic waves as the delta function array of Fig. 57. The peak reflectivity is about 97% at the 33 MHz passband. The FWHM bandwidth is 2.5 MHz which is less than that of the delta function array. In Fig. 59 the reflection coefficient versus frequency is plotted for a 95.1 micron period array with an array fraction of 0.5. This array shows passbands at the frequencies given by Eq. (102). In this case, the bandwidth and reflectivity at the 68 MHz passband are the same as those of Fig. 57. Also, the 34 MHz passband is missing for the same reason discussed above for the 68 MHz passband. Arrays of NPP have an unusual frequency behavior because of the lack of an impedance change between adjacent domains when the acoustic wave is incident normal to the domain wall (see Part 1II.A). The absence of an impedance change means that the sign of the reflection

APPLICATIONS OF FERROELASTIC CRYSTALS

345

FIG. 58: Theoretical reflection passband of a 95.1 micron period NPP 0.25 fraction array consisting of 54 periods.

w

w

0.00 0

20

40

60

80

100

F R E Q U E N C Y I N MHZ FIG.59: Theoretical reflection passband of a 95.1 micron period NPP 0.5 fraction array consisting of 54 periods.

346

STEVEN W. MEEKS AND B. A. AULD

coefficient is unchanged when passing through an array of alternating domain states. The result of this behavior is to shift the position of the stopbands and passbands. Suppose, for example, that the center of an NPP array is chosen as the region of the array to interact with the acoustic waves. In the center of these arrays the ratio of plus or minus domain state widths to the total array period is 0.5. A hypothetical array, in which there is an impedance change at the boundaries, would have passbands (or stopbands, if used in transmission), for an array fraction of 0.5 at the frequencies given by Eq. (101). However, an NPP array, because of its lack of an impedance change and hence absence of alternating sign in the single wall reflection coefficients, will have passbands (or stopbands, if used in transmission), for an array fraction of 0.5 (i.e., in the center of the array) at the frequencies given by Eq. (102). An analogous relationship exists for the array fraction of 0.25 case. A 0.25 fraction array with an impedance change will reflect at the frequencies given by Eq. (102), while an NPP array of the same fraction will reflect at the frequencies given by Eq. (101).

3. Comparison of Theoretical and Experimental Refection Filter Passbands of NPP Arrays Figure 60 shows a comparison of the experimental and theoretical power reflection coefficients versus frequency for a NPP grating with a period of 95.1 microns (Meeks et al., 1985a). The theoretical curve shown in Fig. 60(a) is the same as that of Fig. 57 (array fraction = 1%).It shows strong reflections at 33 and 68 MHz, as predicted by the theory. The bandwidths of the reflection passbands in Fig. 60(b) cannot be compared directly with the theoretical results in Fig. 60(a) since the experimental data is from a FFT on a 200 ns sample of the array ringing as shown in Fig. 55(b), while the theoretical results are for a cw signal. Weak spikes in the experimental results surrounding the dominate spikes (at 33 and 68 MHz) are due to some residual ringing of the transducer. Figure 61 shows a comparison of the theoretical and experimental frequency response of a NPP delta function (fraction = 1%) 74.8 micron period grating. This grating has been tuned via the technique discussed in Part 1I.A. The theoretical curve in Fig. 61(a) shows reflection passbands at 43 and 86 MHz, with FWHM bandwidths of 4 MHz. This increase in bandwidth compared with Fig. 60(a) is due to the greater number of periods (69) in the array. The reflection coefficient at the reflection passbands is 100% and the sidebands are larger than those of Fig. 60(a), again due to the larger number of array periods (Sittig and Coquin, 1968). The experimental results are given in Fig. 61(b), showing passbands at 41.5

APPLICATIONS OF FERROELASTIC CRYSTALS

347

I .OO

+ z

W

0.80

H

V H

LL

L W 0

0.60

$ +

0.4'2

u H

u W

2W 0 . 2 e lY

0.0e

20 40 60 80 FREQUENCY. IN MHZ

100

(4 1.00 0)

.c

c 3

r;

-

0.80

0

c

2 0.60 2 LL LL

8

0.40

V

z

8 'u

0.20

w _I

LL

ki

0.00 0

20 40 60 80 FREQUENCY I N MHz

100

(b) FIG.60: Comparison of (a) theoretical reflection passband of a 95.1 micron period NPP delta function array consisting of 54 periods, (b) experimental reflection passband of a 95.1 micron period NPP delta function array containing 54 periods.

348

STEVEN W. MEEKS AND B. A. AULD

0

20

40

FREQUENCY

60

IN

80

100

MHz

(b)

FIG.61: Comparison of (a) theoretical reflection passband of a 74.8 micron period NPP delta function array consisting of 69 periods, (b) experimental reflection passband of a 74.8 micron period NPP delta function array containing 69 periods.

APPLICATIONS OF FERROELASTIC CRYSTALS

349

and 83 MHz. The small spikes surrounding the main peaks in Fig. 61(b) are again due to the ringing of the piezoelectric transducer. Both Figs. 60 and 61 show experimental reflection passbands which are shifted to slightly lower frequencies than the theoretically-predicted values. The possible reasons for this shift are that the grating period is slightly longer than the measured value or the elastic constants of NPP are slightly different from those of LaPP, which were used to compute the speed of sound in NPP. Table 1 indicates that lower frequency passbands, with similar characteristics, may be obtained by using a shear wave (and hence, Rss) to interact with the array. As discussed in Part III.A, the value of R,, for a b-type domain wall is much larger than the predicted value in Table 1. This was attributed to the vibration of the domain wall under the dynamic stress of the incident shear wave. It is expected that R,, for an a-type domain wall will show the same behavior. The requirement for a stopband transmission filter with excellent sidelobe suppression is that the single wall reflection coefficient approach unity (Sittig and Coquin, 1968). Thus, since R,, is expected to be large (greater than or equal to -13.7 db) then it is expected that a stopband transmission filter with excellent sidelobe suppression may be constructed by using a shear wave as the incideht wave. The attenuation of a longitudinal wave, used in these experiments was measured to be 2 dB/cm at 24 MHz. The relatively large attenuation in NPP will limit the high frequency use to about 100 MHz. This section has presented two demonstration devices which use periodic domain walls in NPP; a tunable active grating (TAG) and a tunable acoustic filter (TAF). The T A G discussed in Part 1V.A showed quasi-cw gains of about 1.14 dB (30%) at the first- and fourthorder Bragg spots. Nearly all of the gain of an NPP monocrystal was found to appear as gain in the Bragg spots of the ferroelastic grating. The discrepancy between the predicted and measured optical gain of NPP was attributed to up conversion in the crystal. This problem can be circumvented by using a pulsed pump or by substituting Lat3 or Y+3 for some of the Nd+3 in the crystal lattice. A third device, a tunable active grating laser (TAG laser), has not yet been demonstrated, but its design and potential were described in Part 1V.B of this chapter. The T A G laser is predicted to have the ability to tune between the various lasing lines of Nd+3without a tuning element that is external to the lasing medium. This laser may also have the ability to tune between the various longitudinal modes of an NPP laser. Although it was not emphasized in this section, these domain arrays have the obvious application as tunable optical diffraction gratings. The TAF discussed in Part 1V.C shows good agreement between theory and experiment. The theory is used to predict the acoustic

350

STEVEN W. MEEKS AND B. A. AULD

stop-bands of an NPP array. Two acoustic grating filters were constructed with passbands at 34 and 68 MHz and 43 and 86 MHz. The frequency response of NPP arrays is unusual because there is no impedance change upon crossing a domain wall. This leads to frequency responses which have missing passbands, as compared to an ordinary alternating impedance grating. It is predicted that these domain arrays will make excellent stopband transmission filters for shear waves. Such grating filters should also be useful in tunable SAW filters or resonators. V. CONCLUSIONS AND FUTURE DIRECTIONS A . Summary

This chapter has presented the discovery of a means of creating uniformly periodic domain structures in a ferroelastic crystal, neodymium pentaphosphate (NPP). Ferroelastics are a type of ferroic material that has at least two states of spontaneous strain, which may be switched by application of a stress. The transition zone between two strain states, a ferroelastic domain wall, is a planar interface which can reflect optical and acoustic waves. Thus, the uniform and non-uniform domain structures which can be created in NPP have potential applications as tunable active gratings for lasers, tunable diffraction gratings, tunable Bragg reflection gratings, tunable acoustic filters, optical modulators, and optical domain wall memories. Part I1 presents periodic domain walls and ferroelastic bubbles in NPP. At the beginning of this section a review of previous work in creating periodic structures in ferroic and non-ferroic materials is discussed. Two techniques for creating periodic and aperiodic structures in NPP and GMO are the lateral domain wall injection technique and the optical injection procedure. The optical technique is particularly exciting since it offers the promise of optically writing an optical interference pattern onto a crystal of NPP. Another domain wall injection technique was used to create uniformly periodic domain walls in NPP and is known as the quasi-static nucleation of zig-zag or periodic domain walls. This technique has been used to create periodic domain structures with periods between 100 and 0.5 microns. The short range periodicity is excellent and is uniform on the order of a tenth of an optical wavelength. The long range periodicity is uniform to within *2% of the period. The nucleation process of these periodic structures is described in terms of a newly-discovered domain structure, namely the ferroelastic bubble. The ferroelastic bubble is the elastic analogue to the well-known ferromagnetic bubble. Four different

APPLICATIONS OF FERROELASTIC CRYSTALS

35 1

techniques of tuning the period of the arrays are described. These techniques are two types of quasi-static mechanical stress tuning and two thermal stress generation techniques, one acoustical and one optical. The arrays may be tuned relatively rapidly. One of the tuning techniques has tuned the period of a 100 micron array to about 3 microns in 100 ms. The maximum rate of tuning is not yet known. A section has been included explaining the optical diffraction from arrays of NPP domain walls. NPP gratings form an unusual type of phase grating. Phase difference between contiguous domain states is due to the tilt of the index surface axes, and not to a difference in index of refraction. The best Bragg efficiency of an NPP grating was obtained from a crystal with a 58 micron period array and was 77%. Efficiencies greater than 90% should be obtained from crystals which are anti-reflection coated. The final subsection presents a phenomenological theory which constructs the free energy of these periodic structures as the sum of the wall, strain, and interaction energies. This theory gives an excellent fit to experimental data. It also predicts the collapse of the periodic structure at about 3 microns. The collapse is due to the combination of the rapidly increasing wall and interaction energies. An upper limit on the period of these zig-zag structures is predicted to be limited by the crystal size and not any of the energy terms. It is also predicted that these periodic structures will exist in the rare earth analogues to NPP: LaPP, PrPP, and TbPP. Part I11 considered the interaction of optical and acoustic waves with ferroelastic domain walls. This section is divided into two parts. The first part of the section derives the acoustic reflection coefficients, at normal incidence, of the a- and b-type domain walls of NPP and LaPP. The reflection coefficients are much larger than in other ferroelasticferroelectrics such as GMO. Certain of the reflection coefficients exhibit anomalously large values. The large values are likely due to the vibration of the domain wall. Two devices are discussed, using reflections off a single moveable domain wall. The devices are a tunable comb filter and a 0 to 4.5 microsecond tunable delay line. A practical delay line would have to operate at 50 to 100 MHz instead of the 5 MHz used in this work. Fortunately, NPP has a low enough acoustic attenuation (2 dB/cm at 24 MHz) to allow operation at these frequencies. The second half of Part 111 discusses the interaction of optical waves and ferroelastic domain walls. In particular, an optical reflection theory of an NPP ferroelastic a-type domain wall is presented. The reflection is found to be due to a change in the polarization of the wave, and not a change in the index, as the wave crosses the domain wall. This leads to a wave which can be reflected without a refraction in the transmitted beam. The theoretical power reflection coefficients for the two

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STEVEN W. MEEKS AND B. A . AULD

incident polarizations have been computed and compared with experiment at 0.6328 microns and the agreement is good. The magnitude of the power reflection coefficients for a single wall is greater than 1 x 10 -3 for angles greater than or equal to 75". In particular, the theoretical value at the critical angle of 81.5" is unity. The experimentally measured value is 2.2% per domain wall at 81.5". The experimental value is less than unity because the experimental number is measured with an incident beam which contains a range of angles. Hence, the experimental value is an angular average over a very sharp peak. Unfortunately, the reflection coefficients go to zero at normal incidence. This last fact means that a true distributed feedback laser cannot be constructed using these periodic gratings. However, an array of domain walls operated at the critical angle of the walls should show a large reflection. Subsection III.B.5 explains why there is a contrast between a pair of adjacent domain states. The contrast is due to the tilt of the index surface axes of contiguous domain states. Part IV presents two demonstration devices using periodic domain walls in NPP; a tunable active grating (TAG) and a tunable acoustic filter (TAF). The T A G showed quasi-cw gains of about 1.14 dB (30%) at the first- and fourth-order Bragg spots. Nearly all the gain of an NPP monocrystal was found to appear as gain in the Bragg spots of the ferroelastic grating. The discrepancy between the predicted and measured optical gain of NPP was attributed to up conversion in the crystal. This problem can be circumvented by using a pulsed pump or by substituting La+3or Y+3 for some of the Nd+3 in the crystal lattice. Both NdLaPP and NdYPP crystallize into the same space group as NPP and, hence, should also show periodic structures. The TAF showed good agreement between theory and experiment. Two different passband filters were constructed, having passbands at 34 and 68 MHz and at 43 and 86 MHz. It is predicted that these domain arrays will make excellent stopband transmission filters for shear waves. Such grating filters should also be useful in tunable SAW filters and resonators. A tunable active grating laser (TAG laser) was described in this section. The TAG laser is predicted to have the ability to tune between the various lasing lines of Nd+3without a tuning element that is external to the lasing medium. This laser may also have the ability to tune between the several longitudinal modes of an NPP laser. An additional rather obvious application of these gratings is their use as tunable optical diffraction gratings.

B. Future Directions This work has pointed out the potential and advantages of the creation of periodic and aperiodic arrays in ferroelastic materials such as NPP. However, the surface has only been scratched. Numerous device applica-

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353

tions remain to be investigated and significant basic scientific questions remain unanswered. The most promising devices are yet untested. Among these devices are a tunable active grating laser (TAG laser) which uses periodic domain walls in NdLaPP or NdYPP. This laser should circumvent the up conversion problem which limited the gain in the optical device described in Part IV. The optical domain wall injection technique is particularly exciting since it may be used to create a type of optical memory. The memory pattern may be a programmable optical Fresnel lens, a programmable acoustic chirp grating or a special type of grating for optical or acoustic signal processing. Another untested and promising device is a tunable surface acoustic wave filter. There also exists the untested possibility of using an acoustic wave to modulate the period of an NPP grating so as to create a new type of optical modulator. One of the best advantages of the uniform ferroelastic gratings in NPP is the large range of tunability of the period. This work has shown a number of ways to tune the period. One tuning technique, the optically generated thermal stresses, remains untested. Another possible tuning technique is to use the large strains available from an electrostrictive material like lead magnesium niobate (PMN) to tune the grating period. This technique is likely to be much faster than the optical, acoustic, or resistive thermal tuning techniques. In the realm of basic physics there are numerous unanswered and intriguing questions. For example, what is the nucleation process of zig-zag arrays in GMO, and why is the periodicity of GMO so poor compared to NPP? The absence of bubble nucleation in GMO, the mechanism for the nucleation and breakaway of ferroelastic bubbles in NPP under the applied line force? Why can NPP arrays be tuned over a very large range in the direction of decreasing period but cannot, as yet, be untuned? Is it possible to improve the long term periodicity of NPP? Another question of important pragmatic interest is the upper limit of the domain wall velocity in NPP and how quickly does the velocity approach this limit with increasing stress? The potential of NPP as a memory material needs to be investigated. For example, can individual ferroelastic bubbles be written onto a crystal of NPP using the thermal stresses generated by an optical beam? If so, can these bubbles be “channeled” in a manner similar to magnetic bubbles? Another very important basic question is: Are there other ferroelastic-ferroelectrics which exhibit zig-zag walls with the excellent periodicity of NPP and the additional feature of allowing direct electric tunability through the piezoelectric effect as with GMO? It is quite possible that this research may someday lead to a new class of programmable optical and acoustic devices. The key to realizing this new class of devices lies in achieving an improved experimental and theoretical understanding of ferroelastics and ferroelastic-ferroelectrics through the

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STEVEN W. MEEKS AND B. A. AULD

above suggested research. It is hoped that this work will stimulate sufficient interest so that research will continue toward making ferroelastics a viable and important device technology.

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Krainyuk, G. G., Otko, A. I., and Nosenko, A. E. (1984). Sov. Phys. Solid State 26, 1582. Kruhler, W. W., Jeser, J. P.. and Danielmeyer, H. G. (1973). Appl. Phys. 2, 329. Kubodera, K. Otsuka, K., and Miyazawa, S. (1979). Appl. Opt. 18, 884. Kumada, A. (1972). Ferroelectrics 3, 115. Laikhtman, B., and Tagantsev, A. (1975). Sov. Phys. Solid State 17, 1127. Lemons, R., and Coldren, L. (1978). Proc. o f t h e IEEE Ultrasonics Symp., 188. Lemons, R., Geary, J., Coldren, L., and Mattes, H. (1978). Appl. Phys. Lett. 33, 373. Meeks, S. W., Auld, B., Maccagno, P., and Miller, A. (1983). Ferroelectrics 50, 245. Meeks, S. W., and Auld, B. (1983). Proc. of the IEEE Ultrasonics S y m p . , 535. Meeks, S. W . , and Auld, B . (1985). Appl. Phys. Lett. 47, 102. Meeks, S. W . , Clarke, L., and Auld, B. A. (1985a). Proc. of the IEEE Ultrasonics Syrnp., 325. Meeks. S. W., Auld, B. A. and Newnham, R. E . (1985b). Jpn. J . Appl. Phys. 24, Supplement 24-2, 568. Meeks, S W., and Auld, B. A. (1986). Proc. Infer. Symp. on Applications of Ferroelecrrics (Lehigh University). Newnham, R. E., Miller, C. S. Cross, L. E., and Cline, T. W. (1975). Phys. Stat. Sol. (a) 32, 69 Novak, R. F., Anderson, T. L., and Newnham, R. E. (1977). J. Appl. Cryst. 10, 349. Oates, D. E., Gottschalk, P., and Wright, P. V. (1985). Appl. Phys. Lett. 46, 1125. Otko, A., Nesterenko, N., Krainyuk, G., and Nosenko, A. (1983). Ferroelectrics 48, 143. Plattner, R. D., Kruhler, W. W . , Zwicker, W. K . , Kovats, T., and Chinn, S. R. (1980). J . Cryst. Growth 49, 274. Sanders, I. L., Jones, R. M., and Collins, A. J . (1977). J . Phys. D: Appl Phys. 10, 2503. Singh, S., Miller, D . C., Potopowicz, J. R., Shick, L. K. (1975). J . Appl. Phys. 46, 1191. Sittig, E., and Coquin, G . (1968). IEEE Trans. on Sonics and Ultrasonics SU-15, 111. Slonczewski, J. C., and Malozemoff, A. P. (1978). In “Proc. Int. School of Physics ‘Enrico Fermi,’ Course LXX” (A. Paoletti, ed.) p. 134. North-Holland. Takeuchi, H., and Yamashita, K. (1982). J . Appl. Phys. 53, 3024. Thompson, D. E., McMullen, J. D., and Anderson, D. B. (1976). Appl. Phys. Lett. 29, 113. Tofield, B. C., Weber, H. P., Damen, T. C., and Liao, P. F. (1975). J . Solid State Chern. 12, 207. Torres. J . (1981). Ph.D. Thesis, “Etude de la transition de phase ferroelastique du phosphate de plomb.” University of Paris VI. Torres. J. Roucau, C . , and Ayroles, R. (1982a). Phys. Stat. Sol. (a) 70, 659. Torres, J . Roucau, C . , and Ayroles, R . (1982b). Phys. Stat. Sol. (a) 71, 193. Tsukamoto, T., Hatano, J., and Futama, H . (1982). J . Phys. SOC. Japan 51, 3948. Weber. H. P., Damen, T. C., Danielmeyer, H. G., andTofield, B. C. (1973). Appl. Phys. Lett. 22, 534. Weber, H. P., Tofield, B. C., and Liao, P. F. (1975). Phys. Rev. B11, 1152. Yeh. P.. Yariv, A., and Hong, C. (1977). J . Opt. SOC. A m . 67, 423.

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOL. 71

Applications of Scanning Electron Microscopy in Archaeology SANDRA L. OLSEN Department of Cell Biology and Anatomy The Johns Hopkins School of Medicine Baltimore, Maryland

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Preparation Methods for Archaeological Specimens . . . . . . . . . . . . . . . . . . . . . . . . . 111. Applications of SEM to Archaeological Materials ........................... A. Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Animal Materials ................................. C. Lithic Materials . . . . . . . . . . . . . . . . . . . . . . .................. D. Glass, Ceramics, Metalwork, etc. . . . . . . .................. IV. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . ....................... ...............

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I. INTRODUCTION Archaeologists are in the dubious position of having to span several disciplines, including anthropology, history, and the natural sciences. Because our data are chiefly material objects, that is remnants of past cultures, their environs, and their creators, we often find ourselves borrowing methods, techniques, and principles from other fields such as biology, physics, chemistry, and material science. As early as 1969, Brothwell advocated the use of scanning electron microscopy (SEM) in the analysis of archaeological samples. Pointing out the advantages of SEM over light microscopes, he demonstrated how it could be used to study ancient bone, dentition, textile fibers, hair, plant remains, and stone tools (Brothwell, 1969: pp. 564-566). As illustrated by the increasing number of articles published in the past decade which include SEM as a part of their methodology, it is clear that the scanning electron microscope has taken on an important role in the analysis of archaeological data. The growing popularity of sessions on archaeology and art history at the SEM Conferences and the participation of scholars from nine nations in the 1986 SEM 357 Copyright 0 1988 by Academlc Press, Inc All rights of reproduction In any form reserved ISBN 0-12-014671-1

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in Archaeology Conference in London (Olsen 1988a) also bespeak the expanding awareness of the potential applications of SEM in our field. The SEM has been shown to have numerous specific applications on a wide variety of materials, but because of time, expense, and difficulties involved with specimen preparation, it is rarely used in exclusion of other analytical instruments. In fact, one of the great strengths of SEM is its complementarity with optical microscopes. Whereas the optical microscope provides a simple and inexpensive means of analyzing bulk samples, the SEM achieves a higher standard of analysis on a greatly reduced population of objects. The well-known advantages of the secondary electron emission mode over optical microscopy apply to the study of archaeological specimens as well as other objects. The vast and nearly continuous range of magnifications greatly exceeding the optical limit of around 1000 times, the increased depth of field (which is about 300 times greater than for an optical microscope), and the high resolution (practically speaking around 200 A in the SEM) are all important factors in the choice of SEM for archaeological analysis of microscopic surfaces. Even at low magnifications the high quality of scanning electron micrographs and stereo-pairs enables the researcher to demonstrate his or her findings clearly in published form. At present, most studies using SEM rely on the secondary electron image (SEI) and are concerned primarily with the observation of surface topography. Much of the work involves low magnifications between 10 and 1,000 times, although specific problems may occasionally require higher magnifications. A wide range of archaeological materials including metals, glass, faience, pottery, stone, soil particles, pigments, bone, teeth, fingernails, skin, hair, eggshell, mollusks, insects and parasites, plant remains, wood, pollen, fibers, and so on, have been examined with secondary electron imaging. The second most common use of the SEM is for determining composition, generally using energy dispersive x-ray analysis (EDAX). The advantages of using x-ray microanalysis with a SEM are numerous. It provides a relatively quick and nondestructive means of obtaining qualitative information on the constituents of a material without much specimen preparation. At this level the sample may only need to be coated with carbon, unless it is sufficiently conductive without coating. For more quantitative studies the sample may need to be sectioned and polished, but this still allows the specimen to be used for other forms of analysis. An x-ray microprobe is sometimes preferred because of its superior quantitative results, but since these instruments are generally more expensive and less common, access may be less convenient than for a SEM-EDAX. X-ray microanalysis has been used by researchers on metals, ceramics, glass,

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faience, bone, and other archaeological materials. Elemental mapping has been extremely enlightening in the study of metal alloys and for identifying inclusions in pottery. Backscattered electron imaging (BEI) has seen more limited application, but has the advantage of supplying both topographic and compositional information simultaneously. It also eliminates the problem of the edge bright-up effect due to charging, which is so common with archaeological specimens that are poorly conductive. This is especially important if the edge of the object is the chief area of study as in wear analysis of stone, bone, or metal tools. Cathodoluminescence (CL) has received little attention by archaeologists, but it has been shown to have value in the examination of quartz grains by soil analysts (Krinsley and Hyde, 1971) and for determining the likely sources of thermoluminescence signals in prehistoric ceramics (Singhui and Zimmerman, 1979). Auger electron emission is one of the least commonly employed SEM modes in archaeology. This may be due to a combination of limited accessibility to microscopes with Auger detectors and a lack of common knowledge among archaeologists about the principles and applications of this mode. In one case, however, Auger electron spectroscopy was used to analyze the constituents of Greek bronze arrow tips (Polak et al., 1983).

11. PREPARATION METHODSFOR ARCHAEOLOGICAL SPECIMENS

Working with archaeological materials may pose problems when samples are prepared for examination with a scanning electron microscope. Sometimes archaeological specimens are replaceable or available in vast quantities, as with soil samples, pollen, and certain kinds of stone, bone, or pottery collections. In these cases, it is easy enough to justify the sectioning, metal-coating, or other destructive alterations necessary for optimal observation in the SEM. Very often this is not the case, however, as when the samples are unique or very rare, and conservation becomes a primary concern for the researcher. In these situations, alternative methods of specimen preparation must be found, such as the avoidance of coatings and adhesives, the selection of fragments of material small enough to fit into the chamber without sectioning, or the use of replicas. Thought must be given to the kinds of analysis to be performed on the sample before any preparation is carried out. For example, if microanalysis is to be conducted, obviously the specimen should be coated with carbon rather than a metal alloy, such as gold-palladium.

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In some cases, further analytical techniques may need to be performed after SEM observation, requiring careful planning during preparation. On rare occasions, the sample may be later radiocarbon dated, in which case contamination by coatings and adhesives should be avoided. Whenever possible, the use of coatings and adhesives should be restricted to samples that are considered expendable or replaceable; if several kinds of analysis are to be performed on a given sample, then the most destructive tests or preparation techniques should be done last. It is not unusual for specimens to be housed and curated in a museum which does not have a loan policy for individuals or foreigners or will not allow modifications to be performed on the objects. In these situations, the researcher may find it necessary to replicate the specimen in order to study it at other facilities or to avoid destructive treatment of the original. In addition to problems pertaining to the conservation measures associated with the care and handling of rare archaeological samples, many of the difficulties encountered in preparation are specifically related to the nature of the material examined. The size, conductivity, porosity, and state of preservation of archaeological samples are the chief sources of problems with preparation. With increasingly larger SEM specimen chambers, archaeologists now have more freedom to study whole artifacts without the need to replicate or section them. The option of viewing small fragments rather than complete objects is very often feasible, since so many archaeological materials are fragmentary when recovered. Even with a large vacuum chamber, size limitations may still be a serious problem if the material is very porous. Bone and antler, for example, are problematical since it may be difficult to evaluate the chamber if large samples are used. Placement of specimens in a desiccating chamber for two to three days prior to observation in the SEM can facilitate outgassing. If a Charge Free Anticontamination System (CFAS) is incorporated in the SEM, then large, porous specimens can be studied. The CFAS maintains a significant vacuum differential between the column and the chamber, so that objects can be viewed in a poor vacuum. The results are significant for archaeologists, since not only can large samples be studied, but also nonconductive samples can be viewed without coating (Claugher, 1988). If a CFAS is not available, then the conductivity of the archaeological material is important. As mentioned above, metal coating may not always be a viable procedure with rare or valuable objects or those that will be displayed in museum exhibits. There are several alternatives to metal coating, however, which minimize the problem of charging consider-

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ably. Many archaeological materials are sufficiently conductive without coating if certain precautions are observed and if only low magnifications are to be used. Transparent anti-static coatings can be applied just prior to viewing to reduce charging with no serious deleterious effects. Increasing the working distance, slowing the scanning speed, reducing the accelerator voltage, and minimizing the viewing time prior to photographing a particular area will all help avoid charging effects. Wrapping a metal wire around the object and twisting its ends around the specimen mount will help drain off charging, as well. It has been found that stone, bone, shell, pottery, and metals can usually be studied at magnifications under 1000 times if the above recommendations are followed. Whenever possible, such as when samples are expendable, or when experimental imitations are to be examined, it is clearly preferable to coat the object with gold-palladium for normal imaging or carbon for microanalysis and to attach the specimen firmly to a stub with a conductive adhesive such as silver or carbon dag. In many cases, the best solution for SEM analysis of archaeological samples is to replicate the area to be studied. The most common procedure is to make a silicon rubber mould of the surface of the object. The negative replica can then be covered with a conductive metallic coating and viewed directly in the SEM, or it can be used to produce a positive resin replica for study. Considerable information has been published on replicating techniques with useful comparisons between different commercial products (Pfefferkorn and Boyde, 1974; Pameijer, 1979; Larsen, 1979; d’Errico et al., 1982; Rose, 1983; Bromage, 1985).

OF SEM TO ARCHAEOLOGICAL MATERIALS 111. APPLICATIONS

What follows is a review of the kinds of applications to which SEM has been put in archaeological analysis. For convenience, this has been organized according to the kinds of material studied, though in many cases artifacts are composed of more than one type of material. A . Plants The study of plant remains such as pollen, phytoliths, seeds, and wood, has benefitted greatly from SEM. Palynologists can use SEM to identify pollen grains because the high resolution and great depth of field at large magnifications allow identification of minute anatomical features. Because

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pollen studies rely on relatively large samples, however, the optical microscope is generally used for processing the bulk of the pollen. Some studies have attempted to locate plant opals (phytoliths) on the surfaces of prehistoric harvesting tools (Anderson, 1980), but a more reliable line of evidence might be derived from the collection of soil from storage pits and food preparation areas. Piperno (1984) has compared phytoliths of maize with those of wild grasses derived from precolumbian deposits in Panama. Though not an archaeological study, a recent publication on phytoliths (Brandenburg et al., 1985) demonstrates how secondary electron imaging reveals only superficial plant silica, while backscattered electron imaging can bring out the subsuperficial opaline silica bodies with sufficient resolution to make identifications. The SEM-ED AX was also used for elemental mapping to locate and show the distribution of silica in dried leaves. This study illustrates the value of using nondestructive observation with SEM over a normal optical microscope and incorporates three of the SEM modes in the analysis. In addition to taxonomic identification of plant remains with an aim toward reconstructing the palaeoenvironment and human diet (Y arnell, 1976), morphological alterations in seeds indicative of domestication are clearly recorded in scanning electron micrographs. For example, Smith (1984, 1985a, b) has noted changes in Chenopodiurn fruit from sites in the Southeastern U.S. that suggest domestication. The SEM has also been employed to uncover certain limitations of archaeological evidence. Colledge (1988) has shown that the pericarp layers on seeds of cereals like wheat and rye do not provide conclusive proof of domestication. The difficulties of identifying fragmentary and much altered archaeological seeds and, therefore, the need for studying large samples with the SEM to insure proper identification are highlighted by Butler (1988). Most prehistoric seeds have been preserved by carbonization, usually from charring. Although this facilitates SEM observation, often eliminating the need for metallic coating, it may lead to serious distortion of important morphological characteristics. To understand the kinds of changes that occur during heating, including warping and shrinkage, palaeoethnobotanists experimentally char modern specimens for comparison (Ockenden and Lott, 1983; Rossen and Olson, 1985). Through microanalysis, it is possible to distinguish between macrobotanical remains that are carbonized from those that are merely blackened from the absorption of manganese dioxide in the soil. Electron spin resonance has also been used to recognize the radical carbon signal in prehistoric grain to confirm whether a seed has been heated (Hillman et af., 1983). Inclusions due to decay and permineralization in plant remains have

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been identified through x-ray microanalysis of beans from northeastern North America (Ockenden and Lott, 1983: p. 1484). Wood charcoals, which are important sources of dates through radiocarbon dating and dendrochronology , also yield information on the palaeoenvironment and human utilization of plant products. Comparisons between scanning electron micrographs of modern charred wood (Fig. 1) and archaeological samples are important for taxonomic identification (Rossen and Olson, 1985; Prior, 1983, 1987). As Prior (1987) has pointed out, a light microscope may fail to provide sufficient resolution to allow identification of charcoals below the generic level, whereas SEM is much more successful.

B. Animal Materials A variety of animal materials which are rarely preserved in archaeological sites, such as insects, eggshell, hair, finger-nails, and blood have been examined with the SEM. Insect carapaces and delicate body parts collected from soil deposits can be identified with the aid of the secondary electron mode (Kenward, 1978: P1.I-IV). The structure of ostrich eggshell

FIG.1: Transverse section of modern charcoal of Sugar Maple (Acer sp.). 130 x . (photo kindly donated by D. Blakeslee, Dept. of Anthropology, Wichita State University).

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from prehistoric sites in Cape Province, South Africa, was illustrated in a scanning electron micrograph in a study which used 13C/’*C ratios in the shell as an indicator of vegetation and palaeoclimate (von Schirnding et al., 1982). Occasionally, unusual circumstances result in the preservation of ancient hair from humans or other mammals. The SEM is a valuable tool in the identification of the species from which hair was derived (Sato et al., 1982). As an example, the SEM has been used to observe the external surfaces of hairs from mummified Egyptian cats (Armitage and CluttonBrock, 1980). By comparing the cut ends of hairs belonging to the Lindow Man, the recently discovered British bog burial, with modern hairs trimmed with scissors and a razor it was possible to speculate about the means used in the Iron Age to cut hair (Brothwell and Dobney, 1986). The SEM photographs showed that the ends of the prehistoric hairs were stepped like those experimentally cut with scissors, despite the fact that no scissors are known from the Iron Age. The Lindow Man’s nails were also studied using SEM in an attempt to make inferences about his occupation (op. cit. 1986). The smoothness of the bog man’s nail contrasts sharply with the broken, scratched nail of a modern farmer, suggesting that the Iron Age man may not have been a common laborer. Blood-typing from tissue taken from the Twentieth Egyptian Dynasty ruler, Nakht, was made possible by the fact that blood cells, photographed with the SEM, were found to be intact (Hart et af., 1980). Mollusks from archaeological sites provide important information about the palaeoenvironment, the human diet, and the use of shell for tools and ornaments, as well as being a source for radiocarbon dates. Because of the possibility of postdepositional diagenetic changes in terrestrial or freshwater mollusks, radiocarbon dating of shell has been considered relatively unreliable. Examination of shell surfaces with the SEM, combined with x-ray diffraction, however, can lead to identification of post depositional contamination which might introduce errors in dating by the addition of calcite through recrystallization of the shell’s surface (VitaFinzi, 1981). The surfaces of archaeological bone record and preserve their history, from formation in the living animal to retrieval by the archaeologist. Beyond the histology of the bone itself, archaeologists can learn much about its cultural treatment and the natural processes affecting its preservation and the site’s formation. Cultural processes which leave traces on the bone surface include such things as butchering, marrow extraction, burning, and artifact manufacture. Natural actions alterring bone after the animal has died are produced by a vast range of agents including wind, water, soil, ultraviolet light, roots, and other animals. The field of

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taphonomy which examines these processes, relies heavily on both macroscopic and microscopic alterations in the surface topography of bone to reveal the causes for bone accumulations and factors that destroy bone. The SEM is becoming an important tool in the analysis of bone and tooth surfaces for archaeologists and palaeontologists alike. It has been used with success in the study of dental wear of extinct and extant species of primates (Wyckoff, 1973; Walker, 1980, Peters, 1982) in order to correlate abrasion patterns with diet. The relationship between fluoride content and wear rates in Australopithecine teeth has also benefitted from the application of SEM (Puech et al., 1988). Nutritional intake of minerals is recorded in human teeth and bones from archaeological sites and can be detected with SEM-EDAX (Schneider, 1986, Lambert et al., 1983). Many studies have looked at enamel prisms and tooth surfaces with the scanning electron microscope in order to identify species of mammals found in a site and as an aid in determining age of animals by dentition (Hillson, 1988; Gantt and Cring, 1981). Bacterial and food particle inclusions in dental calculus have been carefully examined to learn about the potentials for demonstrating the presence of diseases in populations and dietary intake (Dobney and Brothwell, 1986). Cultural modifications of human teeth during life have been recorded from various parts of the world and analyzed with SEM. Examples include drilling of Maya incisors so they could be inlaid with jade and hematite (Gwinnett and Gorelick, 1979), interproximal grooves formed either from grit in the diet or the use of some kind of toothpick in prehistoric Irish populations (Power and 0’ Sullivan 1988), and striations on the buccal surface of incisors from Spain created when a stone knife scratched against the teeth while cutting off pieces of meat (Fernandez-Jalvo and Bermudez de Castro, 1988). Natural damage, including polish, abrasion, and impact fractures, inflicted on antlers during the life of the deer have been studied with the SEM and contrasted with use wear on antler tools (Olsen, 1984) (Figs. 2 and 3). Evidence for butchering at early hominid sites, important to our understanding of the roles of hunting and scavenging in the cultural development of humankind, has been distinguished from natural grooves and scratches on bone from Olduvai Gorge, Tanzania, and other sites with the aid of SEM (Potts and Shipman, 1981; Shipman and Rose, 1983a and b). Studies using experimental replication have demonstrated how butcher marks are formed with stone tools (Bromage and Boyde, 1984) by comparing microscopic features in the grooves on prehistoric bones with those made on fresh bone by the experimenter. Identification of different

FIG.2: Natural polish and abrasion striations on tip of deer antler tine; 100 x .

FIG.3: Use damage in the form of pitting at the tip of experimental antler tine flaker used to knap flint; 13.5 X .

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types of butcher marks, such as chopping, scraping, and slicing, with stone vs. metal tools, has aided in interpreting the techniques employed in

butchering. Burning of bone and teeth causes microscopic, as well as macroscopic, changes in surface morphology which are dependent on the maximum temperature reached. Using magnifications of 1000 to lO,OOOX, microstructural alterations have been observed which help reveal the thermal histories of archaeological remains (Shipman et al., 1984). Bone artifacts record the various methods employed in their manufacture in remarkable detail, allowing archaeologists to accurately reconstruct the stages of manufacture and, to some extent, the kinds of tools used to modify the bone. It is possible, for example, in most cases to distinguish between the use of a flint tool for scraping a bone and a granular stone abrader for grinding the bone surface away (d’Errico et al., 1982-83). In well-preserved specimens it is also often possible to state whether a stone or a metal tool has been used in the manufacturing process (Olsen, 1988b; Figs. 4 and 5). Additionally, it is relatively easy to recreate the manufacturing steps involved, especially when microscopic evidence is supported with examples of unfinished pieces and debitage.

FIG.4: Bone scraped experimentally with flint flake; 14.5 x

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FIG. 5: Bone scraped experimentally with steel carpenter’s scraper; 22

X.

As tools are used, they acquire microscopic traces of use in the form of pitting, striations, abrasion, polish, and fractures. These are indicative of how the tool was held, its relative life span, and sometimes, within gross categories, the materials upon which it was used (Olsen, 1984; Fig. 3 ) . An interesting example in which SEM helped to support a researcher’s hypothesis for the function of bone artifacts was a case in which wear patterns on the bottoms of prehistoric European skates were explained by MacGregor (1975). Experimental replication of impact fractures, rounding, and crushing at the tips of bone and antler projectile points that struck parts of the prey’s skeleton helped confirm the function of various forms of prehistoric points when examined with the SEM (Arndt and Newcomer, 1986). Natural processes which alter bones after the animal dies are the subject of the subfield of palaeontology known as taphonomy. Work with the SEM in identifying the morphological differences between traces created by various agents has been extensive in the past decade. Pitting and striations made by carnivore gnawing, grooves formed by rodent gnawing, erosion of surfaces of bones digested by predatory birds and carnivores, dendritic patterns of root etching, weathering cracks, and trampling striae are only a few examples of taphonomic phenomena observed on bone with the SEM (Shipman, 1981; Olsen, 1984; Cook, 1986). Relating the patterns

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of surface traces to the site context and other macroscopic information is important for distinguishing between natural alterations, like trampling, and cultural processes, such as butchering (Andrews and Cook, 1985; Behrensmeyer et al., 1986).

C. Lithic Materials SEM has been used only to a limited extent on artifacts made of stone. For the study of microscopic wear traces on flint tools, optical microscopy has generally been preferred, but a few researchers have shown how valuable SEM can be for this type of material. In the examination of surfaces and cross-sections of sickle blades with a highly developed sheen, it was learned that this reflective polish was due to fine abrasion (Meeks et al., 1982) rather than an accumulation of plant silica (Anderson, 1980) or the formation of a vitreous layer due to friction. Interpretation of secondary electron images must be done with care, however, since different workers can interpret similar images in very different ways. Unger-Hamilton (1984) demonstrated that oval or oblong objects embedded in the surface of flint tools were not phytoliths derived from the use of the implements in harvesting (Anderson, 1980), but were natural inclusions found to be present in unused flint. Heat-treating of flint, done to improve its knapping qualities, changes the color, luster, and texture of the stone. Comparisons between unheated and heated experimental pieces showed a change from a rough texture in the raw state to much smoother after heating (Johnson, 1985). Although useful as a supplementary line of evidence for heat-treating, the secondary electron images are somewhat subjective. Electron spin resonance (Robins et al., 1981) and thermoluminescense analysis (Pavlish and Sheppard, 1983) provide more quantitative and objective evidence for heat-treating, since the texture of flint can be extremely variable. When dealing with a translucent material like quartz, the study of wear striations, pitting, and chipping can be improved by using a SEM rather than a light microscope (Knutsson, 1988). Acid etching helps enhance the wear striations to facilitate their study. When actual stone artifacts should not be coated with carbon or gold-palladium, or sectioned to fit into the SEM chamber, replicas may be substituted. D’Errico (1988) has reviewed various silicon rubbers for moulding and describes the use of positive replicas of stone tools made from resin. All of the research mentioned above dealt with chipped stone, but other types of stone, which are carved, drilled, or ground into shape, have

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also been studied with the SEM. By comparing silicone impressions of the holes drilled in seals from the Near East and beads from Sri-Lanka with those in experimentally drilled stone it was possible to reconstruct the kinds of drills used (Gorelick and Gwinnett, 1979, Gwinnett and Gorelick, 1986). Some preliminary work has been done on the analysis of sediments from archaeological sites using SEM, but little has been published to date. Considerably more has been accomplished by geologists, however. One such study (Krinsley and Hyde, 1971) on quartz grains employed the cathodoluminescence mode to reveal features below the layer of precipitated silica which were not visible with an optical microscope or in the secondary electron mode. Mineral pigments found either as raw material or actually on finished artifacts can be observed with the secondary electron mode (Fig. 6) and identified with x-ray microanalysis.

D. Glass, Ceramics, Metalwork, etc.

A variety of manufactured materials such as glass, faience, ceramics, terra cotta, and metalwork have been examined with SEM. It has been found that x-ray microanalysis of ancient glass can help determine its approximate age and location of manufacture (based on similarities with other datable glass of similar origin). It can also aid in choosing the optimal methods of conservation and restoration and can prove authenticity of artifacts (Hreglich and Verita, 1986). By observing sectioned and polished surfaces of Egyptian faience paste with the secondary electron imaging mode, methods of manufacture have been reconstructed (Vandiver, 1982; Tite et al. ,1983). Using an electron microprobe, the effects of weathering on faience glazes were identified (Tite et al., 1983). Baked clay, terra cotta, and ceramics have all been studied with the aid of SEM, using chiefly the secondary electron mode and x-ray microanalysis, but backscattered electron imaging and cathodoluminescence have also had a role in their analysis. Many examples of research have employed some combination of optical microscopy (usually petrographic), SEM, electron microprobe analysis, x-ray fluorescence, x-ray diffraction, Mossbauer spectroscopy, neutron activation analysis, and thermal analysis (Edwards and Segnit, 1984; Stimmell et al., 1982; Tite et al., 1982). The primary interests are in determining the types of mineral and organic constituents in a particular pottery clay or glaze, how the piece was made, its firing temperature, and its physical qualities. Impressions of organic material may be clearly recorded in clay, such

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FIG.6: Crushed specular hematite pigment collected from the archaeological site of Kinishba Pueblo, Arizona; 125 x .

as the replicas of rice grains in pottery from Ban Chiang, Thailand (McGovern and Vernon, 1983). The outer surfaces of pottery have been analyzed with SEI and x-ray microanalysis in order to learn more about differences between glazes (Bower et al., 1986, Gillies and Urch, 1983). Back-scattered electron imaging of polished sections shows the clay matrix, mineral inclusions, and voids, while providing information about the composition of the material (Freestone et al., 1985). Polished sections of sherds can show the microstructure of ceramic pastes and the interface between glazes or slips and the body under SEI. Important information about the elemental composition of the glaze or paste can be learned through x-ray micro-analysis of sections (Tite et al., 1982; Maggetti et al., 1981). Polished sections are also needed to establish the degree of vitrification, a key to the firing temperature, durability, and hardness of the ceramic ware (Tite and Maniatis, 1975; Stimmell et al., 1982). Refiring until vitrification increases noticeably allows the original firing temperature to be estimated within 50 to 100°C if it is below the range of temperature where stability is reached (Tite er af., 1982).

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Erosional changes in ceramics, detectable with secondary electron imaging of a polished surface, are important considerations for determination of environmental stability of different types of clay (Franklin and Vitali, 1985) and for the conservation of ancient pottery. Several studies concerned with understanding variability in thermoluminescence dates from baked clays and pottery have benefitted from SEM. Secondary electron imaging has been employed to examine the surfaces of quartz grains in baked clay etched with HF acid during pretreatment (Bell and Zimmerman, 1978) to find out how differential loss of material reduces the alpha dose to varying degrees. Grain transparency in quartz can affect beta and gamma sources, so inspection of the surface texture of archaeological samples with the SEM can help establish ratios of frosted vs. transparent grains (Bell and Mejdahl, 1981). Cathodoluminescence can locate the grains in pottery which are most likely contributors for thermoluminescence dating. By focusing an electron microprobe on the luminescent grains from prehistoric ceramic samples, it was learned that quartz and feldspar were the most significant minerals, with apatite and zircon contributing small amounts (Singhvi and Zimmerman, 1979). As with ceramics, archaeological metalwork has been studied using a combination of analytical methods. The major topics of research in archaeometallurgy fall within the categories of composition and manufacturing processes. The secondary electron mode is used primarily to examine metal surfaces for evidence of manufacturing techniques. Because the samples are conductive, coating is not necessary, although if corrosion is severe, a thin layer of gold-palladium will usually improve the image. Because metal objects are often too large to be placed in the SEM chamber and too valuable to be sectioned, silicone rubber moulds of the surfaces are frequently made. In most cases, the mould is viewed directly rather than producing a positive cast since it is easier to examine grooves and pits if they are raised (Lowery et al., 1971). The precision of replication with silicone rubber is so great that microcrystalline changes along grain boundaries are even reproduced (Goodburn-Brown, 1987). It has been possible to see changes in surface textures from “as-cast” areas to annealed areas on replicas of bronze artifacts, as well (op. cit. 1987). By looking at silicone rubber moulds of tool impressions in ornate metalwork archaeometallurgists have been able to reconstruct ancient tool kits containing punches, tracers, gravers, scribers, etc. Because of distinguishing features in some tool marks, it has even been demonstrated that an individual tool was used to make several different pieces and to see how the tool was modified through time as it became worn or broken (Larsen, 1984).

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FIG. 7: Disintegrated plant material, which, mixed with clay, formed the core for a gold/copper/silver bead made with the lostwax process. The necklace bead is from the Tairona area of Colombia, dated to ca. 10th century A.D. The patterning of the vestured pits could be used to identify the taxon of hardwood used to produce the charcoal. (Photo and information kindly donated by D. Scott, Department of Conservation, Institute of Archaeology, University of London.)

Occasionally, organic materials are preserved within metallic artifacts, such as when lost-wax casting cores are still present inside the object. Scott (Fig. 7) has found plant debris inside a clay core of a Tumbaga necklace bead from the Tairona area of Northern Colombia dating to around the Tenth Century A.D. The charcoal from inside the gold/copper/silver alloy bead retained enough anatomical features to allow close taxonomic identification of the hardwoods used. Similarly, corrosion products found on iron artifacts in a Saxon cemetery in Mucking, Essex, England, replaced the cells of wood lying in direct contact with the metal objects, replicating the anatomical features in some detail (Keepax, 1975). Both an electron microprobe and a SEM-EDAX system may be used to study the composition of metal alloys. Elemental mapping displays the distribution of different metals across the surface or section of an artifact (Scott, 1983). Back-scattered electron images of an area provide both topographic and compositional information, so that using BE1 and the elemental map of the same area together helps in the interpretation of how metal alloys and coatings were fabricated (Scott, 1986; Fig. 8).

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(d)

Au

FIG.8: Elemental maps for (a) silver, (c) copper, and (d) gold from a section of the bead described in Figure 7. The backscattered electron image shown in (b), over a 20 p scan, shows some darker regions in the alloy as black spots which correspond to interdendritic porosity in the alloy casting. Superimposed in the BE1 scan are lighter grey zones which are due to corrosion. The elemental maps can be used to investigate the distribution of the alloying constituents which would not be expected here to give rise to phase precipitation: the composition suggests a homogeneous matrix, apart from coring which may be present as a result of dendritic segregation. The features shown here, in fact, appear to have little direct relation to casting segregation, but are due to the effects of severe corrosion of the necklace after burial. The areas rich in copper and low in gold seen as medium grey in (b) and as the bright areas in (c) are the only uncorroded regions on the bead, and can therefore be used to obtain reasonable analytical data by spot analyses under SEM/EDAX or with a microprobe. The enhancement in the apparent gold concentration evident in the elemental maps is due entirely to copper loss by corrosion. (Photos and information kindly donated by D. Scott, Department of Conservation, Institute of Archaeology, University of London.) Image is 110 p across.

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Using an electron microprobe, Notis (1982) showed that non-metallic inclusions in metal artifacts and slag can produce information about metallurgical processes, forging temperatures, the extent of oxidizing or reducing conditions in the furnace, and the origins of ore sources (Notis, 1982: p. 246). Auger electron spectroscopy (AES) appears to have potential use for archaeometallurgists concerned with the surface composition of metal artifacts. In analyzing a Greek bronze arrowhead with a scanning auger microprobe (SAM), Polak et al. (1983) were able to detect the presence of magnesium oxide, an unusual constituent of bronze for that date (Sixth Century B.C.E.). Although largely semi-quantitative, AES has several advantages: 1) it conveys information only from the surface of the material with very little subsurface penetration, 2) it has spatial resolution superior to that of x-ray beams, 3) it can detect elements of light atomic weight (above helium), and 4) it can recognize chemical states so that corrosion products can be separated from the original metal (Polak et al. 1983). As with other electron beam instruments, information can be obtained from spots, line scans, or imaging so that data can be derived from pinpointed locations or built up over larger areas for elemental mapping.

CONCLUSIONS

It is evident from these examples of research that SEM is becoming an important analytical tool which has many applications in archaeology. As scanning electron microscopes become more readily available in academic institutions around the world we shall be seeing even more use of SEM to solve a variety of problems concerning ancient materials. Archaeologists, themselves, are becoming increasingly more aware of the potential uses of SEM to supplement optical microscopy, perform elemental analysis, and yield information in various frontiers of analytical exploration. We continue, however, to enhance our knowledge through the work of scientists in other fields and our greatest achievements are frequently derived from cooperative research between archaeologists and members of other scientific disciplines. REFERENCES Anderson, P. (1980). A Testimony of Prehistoric Tasks: Diagnostic Residues on Stone Tool Working Edges. World Archaeology 12(2), 181-194. Andrews, P. and Cook, J. (1985). Natural Modifications to Bones in a Temperate Setting. In Man 20. 675-691.

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Array(s) aperiodic, 257, 268, 350 fraction, 343-344 periodic, 256, 271 zigzag, 267, 272, 281, 353 See also Domain structure Auger electron, 2 detection, 206 energy dissipation and, 6 Auger electron microscopy, 375

A

Accelerators, particle. See Particle accelerators Acoustic microscope, 5 Acoustic wave, 2, 4 attenuation, 303 contrasts and, 24-26 coupling mechanism, 16 detection systems, 27-31 device applications for ferroelastic crystals, 251-256, 292-327 disturbance of, 22, 25 free electron laser, 87 linear, 40 lock-in, 34-35 nonlinear signal, 21 phase shift, 17 propagation properties, 5 , 24-26, 293-301 reflection coefficients, 293-304 Air. firing of electron beam in, 114 Aluminum applications, 40 Amplification techniques, 3 and harmonic modulation, 19 photomultiplier, 29 video, 10 Amplitude ratios. 314-318 reflection coefficient, 300, 341-344 scattering, 144, 174 Analog scan generators, 33 Anisotropy, 20 contrast mechanisms and, 23 and cubic material, 22 thermal stress, 261-262 Anticontamination system, charge free, 360 Antiferromagnets, 19 Aperiodic domain walls, 257, 268, 350 Archeology, SEM applications for, 357-359 animals as, 363-369 glass. ceramics, metalwork, 370-375 lithic materials, 369-370 plants as, 361-363 and specimen preparations, 359-361 Argon applications, 160, 218

B Backscattering electrons, 181-183, 189 coefficient, 23 detection, 193- 195 imaging, 359 See also Scattering Beam blanking system. See Chopping SYStem, electron beam Beam cooling, 79-80 Beat-wave accelerators, 99-102 Betatron of infinite radius, 84 modified, 104 Blood- typing applications, 364 Bolometers, 26 Boxcar integration temporal analysis using, 35-37, 40 time-delayed, 46-51, 65-66 Bragg efficiency. 251-252 Bragg spot, 274-281 fourth order, 334-336 BSE. See Backscattering electrons Bubble, ferroelastic Properties O f , 268-271 Bubble-chamber magnets, 92-93 C

Capacitive detectors, 31 Carbonization, 362 Cathodoluminescence detection system, 31, 56, 193, 200-205 generation, 13.5 and thermoluminescence signals, 359

381

382

INDEX

Ceramics applications, 3, 14,28,66-68,370375 Charge carriers excess, 3, 9, 17-18 free, 23, 360 Charging artifacts, radiation, 224-228 Chopping system(s), electron beam, 2, 4, 9, 35, 37 as a function of frequency, 14, 29, 40 Circular induction accelerator, 84 Clausing’s factors, 125 Coated material, 18, 359 See also Uncoated material Collective acceleration, 98-99 Colliding-beam electron-positron storage rings, 79 Collodium film, 119 Computers, in particle accelerators, 84-86 Conductance, variable, 120-122 calculation of, 122-129, 130-134 constant of proportionality for, 129 Conductivity, thermal, 12 contrast mechanisms and, 22 Constants, 17 beam width, 163 free energy, 287 gas, 118 piezoelectric stress, 16 of proportionality for conductance, 129 Contamination, electron beam radiation, 228-232 Contrast mechanisms, 4-5, 21-22 between domain states and polarized light, 325-326 and resolution, 217-223 and signal generation, 22-23 Cooling, electron/stochastic, 80 Coupling mechanisms, 8-19 excess carrier or electrostrictive, 17-18, 21, 23 magnetic, 18-20 piezoelectric, 14-17, 23 thermal wave, 8, 10-14 Cross section, scattering, 139, 143 amplitudes, 144, 174, 178 flourescence, 332 and gas ionization, 186-192 for Gaussian beam energies, 152, 162-171 for narrow beam energies, 150-162

Crystal ferroelastic, 251-256, 263-292 formation, 200-205 quasi-static stress nucleation of, 263-271 single, 26, 29 Crystallographic contrast, 22. 61 Cubic material, 21, 22 crystal orientation in, 22 Current, electron beam, 4-5 densities, 16 low, 21 measuring, 176-178 modulation, 32-34 and thermal wave coupling, 12 Cu-Zn-Al-Alloy applications linear, 40-45 nonlinear, 45-51 D

Damage, electron beam radiation, 232-238 Defect tomography, three-dimensional, 26 Deflection, laser beam, 27 Deformation dependence, 17 Density excess carrier, 17-18, 21 high beam versus total beam, 16 Depletion zone, 179 Depth dependence, 7 of electron penetration, 5-8 Depth dose function, 8 Detection system(s), 187-188 Auger electron, 206 of backscattered electrons, 194-197 cathodoluminescence, 31, 56, 193, 200205 contacting, 27-28 contrast and resolution, 217-223 electrical, 31-32 flourescence scintillator, 216-217 gas medium, 206-217 interaction product, 2-3, 26, 27 magnet, 93 materials, 26, 29, 30 noncontacting, 30-31 optical, 31 and piezoelectric transducers, 28-30 and pyroelectric transducers, 30 of secondary electrons, 197-200

INDEX Dielectric materials, 3, 9, 17 contrast mechanisms in, 23 and elastic wave generation, 15 nonlinearities and, 21 Diffraction efficiency, 276-278 Diffusion length, 7 equation, 20 Dimensions, three calculating, 20 cubic material and contrast mechanisms. 22, 24, 26 defect tomography, 26 for quasi-static stress nucleation, 263-265 Direct band gap material, 56 Dissipation volume, electron energy, 4 acoustic wave coupling, 16 in a gas, 182-186, 188 in a solid, 5-8 thermal wave coupling, 10-14 Distribution factors, 16 Domain structure free energy theory, 281-292 mechanical strain and, 19, 261-262 needle, 268 stripe, 259-260 walls in ferroelastic crystals, 2.52-292 Donor. fixed charge, 16 Doping concentrations, 3 Drift tubes. 80 E

Effusion flow, viscous, 128-129 Elastic wave properties, 16 and contrast mechanisms, 23 conversion of thermal waves to, 12 and differential cross sections, 142-145 generation of, 15 Electrical detectors, 31-32 Electric field, 16 contrast mechanisms and, 23 electrostriction proportionality to, 21 ions in a weak, 188-192 Electric square field gradient, 17 Electron accelerator, 96-97 Electron beam, 2-3, 138-142, 150-162 chopping system(s), 2, 4, 9, 35, 37, 40 cooling, 80 cross section, 139, 142-150, 143, 162, 174, 178

383

diameter, 20-21. 150, 157, 162-178, 189 effects of environment on, 87-90 and gas interaction, 135-136, 142-150, 160-162, 178-186 modulation of, 2, 4, 9, 10-14, 21, 25, 37, 66 pulsed, 4 radiation effects, 223-238 scattering, 5 , 6, 21, 135-136, 139-142, 152- 162 See also Environmental scanning electron microscopy; Specimen, parameters and properties; Scanning electron acoustic microscopy Electron beam induced current (EBIC) contrasts, 24, 56 within laser diodes, 37 Electron column, 2, 33-34, 111 Electron energy dissipation, primary. See Dissipation volume, electron energy Electron gun, 2-3, 191 Electron microprobe, 2, 5-8, 111 experiments, 38 of metal alloys, 373-374 skirt width, 1.57 X-ray detection by, 205-206 Electron-solid interaction, 2-3, 5-8 and energy dissipation, 5-8, 16 Electrostatic pinch effect. See Pinch effect, electron beam Electrostriction, 2, 4, 9, 17-18 properties, 21 See also Excess carrier coupling Enthalpy limited flow. See Effusion flow. viscous Entry point, electron beam, 4, 6 contrast mechanisms in, 23 current modulation at, 33-34 density, 21 electrostriction and, 21 infrared intensity of, 31 pure square law and, 21 Environmental scanning electron microscopy beam-signal-gas-specimen interactions, 134- 137, 178- 192 contrast and resolution, 217-219 defined, 110 detection systems, 193-206 electron beam profiles and effects, 138171, 223-232

384

INDEX

Environmental scanning electron microscopy (Continued) gas flow and conductance in, 115-129. 130- 134 history of, 113 operations and applications, 238-248 See also Scanning electron microscopy: Scanning electron acoustic microsCOPY Equation(s) amplitude, 314-318, 341-344 angle of incidence, 314-318 backscattering, 181-183, 195 Christoffel, 293-301 conductance, 121, 122-129 differential cross section, 150-152 electron beam spot diameter, 172-178 electron skirt width, 158-160, 162 free energy, 282-288 gas/pressure theory, 116-118, 121 ion density, 190-192 Maxwell’s curl, 304-307 motion of energy dissipation, 11, 16, 17, 22, 86 nonlinear heat diffusion, 20 Poiseville, 124 probability distribution, 139-142, 152 signal-to-noise ratio, 219-223 thermal wave, 12 ESEM. See Environmental scanning electron microscopy Excess carrier coupling, 9 and thermal wave magnitude, 13, 14 F Faraday cages, 9 Far-field acceleration, 100 Ferroelastic crystals, 251-304 acoustic device applications for, 292, 293304, 339-350 optical and acoustic wave interactions, 292-293 optical device applications for, 292. 304327, 330-336 tuning, 269, 271-273 Ferroelectric domains, 3, 251-256, 353 Ferromagnetic domains, 3, 18, 251-256 bubble, 269, 292, 304 Fixed charge donors, 16 Flourescence, gas, 180-182

measuring, 183-186 as scintillator detector, 216-217 Fourier transformation, 341 Free charge carriers, 23 Free energy theory, 281-292 Free molecular flow, 122-124 Frequency collision, 190-192 electron beam modulation, 2, 17, 19, 21, 25, 40 sound wave, 2, 28-30 of tunable comb filter, 301 See also Harmonic modulation G

Gallium arsenide, 6, 7 Gas cell, 27 Gas dynamics, ESEM, 115-129 and conductance calculations, 122-129 as detection system, 206-217 experimental assessment, 129-134 flow analysis, 119-122, 129-134 and ionization, 186-192 molecular, 145-150 monatomic, 142- 145 pressure calculations, 116-118 and signal-beam-specimen interactions, 135- 138, 142- 150, 178- 186 Generation volume contrast origination in, 23-24 and propagation of acoustic wave, 24-26 Glass applications, 370-375 Grain boundary, 41, 44-45, 52, 61 See also Contrast mechanisms Gratings, tunable applications, 252, 329, 334, 336, 339 free energy theory, 281-292 H

Harmonic modulation, 4, 9 acoustic wave propagation and, 24-26 excess carrier, 17 magnetic coupling, 18-19 nonlinear signal generation and, 21, 40 piezoelectric coupling, 17 thermal wave coupling, 10-14 Heat energy dissipation, 6, 7, 8, 13, 20 thermal wave coupling, 13, 20 Heating, target specimen, 2, 4

INDEX Helium applications, 160, 188, 218 Helmholtz equation, 86 Hysteretic behavior, 21 Hysteretic materials, 251

385

compared to nonlinear, 20-21 defined, 40 Liouville’s theorem, 79 Liquid microinjection system, 112 Lithic materials, 369-370

I Imaging, contrast, 213-216 Indium phosphide applications, 56-61 Impedance of gas pipes, 120 space charge, 89-90 Imperfections, subsurface, 25, 68 Infrared emission, 31 Infrared spectrometer, 31 Interaction mechanisms, 2-3 acoustic and optical wave, 292-326 beam-gas, 135-136, 142-150, 160-162, 178-186 beam-signal, 137 beam-specimen, 2-3, 5-8, 136 free energy equations, 282-287 gas-specimen, 137 signal-gas, 136- 137, 206-2 17 Interdigital transducers, 29 International Math Sciences Library (IMSL), 1.52 Ion accelerator, 97 Ion concentrations, in ESEM, 189-192 Ionization and beam/gas scattering. 144-145, 1.52, 181-182, 184-185, 186-192, 207-213 energy dissipation and, 6 sound. 5 Isobaric pressure, 133 Isotropic heat production, 22-23 L Laminar flow, 124-127 Laser(s) accelerators, 99-102 excitation, of sound, 5, 18, 31 free electron, 86-87 tunable active grating, 252 Leak rate, 120, 123 and conductance, 126 presence of gas jet and, 134 Linear colliders, 104-105 Linear induction accelerator, 84 Linear signal effects, 16, 17

M Magnetic coupling, 9, 18-20 Magnetic field, 2, 19-20 contrasts and, 24 free electron laser, 86-87 magnetostriction correlation to, 21 surfatron, 102 variable, 39 Magnetic materials, 2 ferror-, 18 SEAM arrangement for, 38-39 Magnetohydrodynamic waves, 19 Magnetostriction, 9, 20 Magnetostrictive coupling, 2, 4, 19 and pure square law, 21 Magnets, permanent, 83-84 Magnets, superconducting, 86, 92-96 Magnitude variation contrast mechanisms and, 22, 24 wave form, 16, 18 Martensite(s), 21, 23 applications, 4 1-44, 46-5 1 Materials, SEAM, 18, 25, 38 applications, 39-44, 45-51, 56-66. 66-70 See also individual types Matrix inversion, 86 Mean free path, 118, 122-124, 138, 190 Mechanical strain, 19 periodic, 18 Metal applications, 3, 13, 40-55 Metalwork applications, 370-375 Micrographs, SEAM contrast mechanisms. 21-22 interpreting, 2, 3 nonlinearities and, 20, 21 Microprobe, electron. 2 Microscope acoustic, 5 optical, 358 scanning auger, 2 Minority carrier diffusion length of, 7, 15-16 lifetime, 14 Mirage effect, 27

386

INDEX

Mode conversions excess carrier and thermal wave, 18 and mechanical stress, 19 thermal to elastic wave, 11, 12-13, 21 Modulation, electron beam, 2 reduction of, and magnetic contrasts, 24 scan, 37, 66 See also Harmonic modulation Momentum transfer, 9 Monodomain crystal experiments, 329-334 Monte Carlo calcutations for energy dissipation in a solid, 5 for scattering probability distribution, 141

N Near-field acceleration, 100 Needle domains, 268 Nitrogen applications, 192 Nonlinear signal generation, 20-21 defined, 40 materials, 45-51 NPP (Neodymium pentaphosphate). See Ferroelastic crystal Nucleation process, 260 0 Optical detectors, 31 Optical diffraction, 273-281 Optical gain measurements in a microdomain wall grating, 334-336 in a monodomain crystal, 329-334 Optical injection, 261-264 Optical reflections, 304-314 Orientation, domain wall, 261-264 Oscillation factors, 152 P Paleontological applications, 368-369 Particle acceleration and superconducting technology, 92-96 beam environment, 87-90 current assessments of, 75-79 inventions and developments, 79-87, 98105

radiofrequency cavities, 96-97 statistical methods and quality control, 90-92

Penetration properties, 5-8 Periodic domain walls and ferromagnetic bubbles, 256-292 tuning, 271-273 Permittivity tensor deformation dependency, 17 stress dependency, 17 Phase shift acoustic wave, 17 causes of, 9 signal inversions and, 18 Photoacoustic signal compared to electron acoustic images, 18 nonlinear, 21 sensing techniques, 27 Photomultiplier, 29 Photons, excitation by, 18 Piezoelectric effects, 2, 4, 8, 10 contrast mechanisms and, 23 of coupling, 14-17, 23 stress constant for, 16 Piezoelectric transducers, 28-30 Pinch effect, electron beam, 178, 192193 Plastics applications, 15 pn-junctions, 3, 16 contrast mechanisms and, 23-24, 56 Poiseuille’s equation, 124 Poisson’s equation, 86 Polarity inversion, 17 Polarization wave, 314 Polarized light, and contrast, 325-326 Polycrystalline silicon, 61-66 Polymer applications, 3, 68 Ponderomotive force, 101 Power reflection coefficients, 314-318 measurement of, 322-325 Pressure, ESEM gas and beam transfer, 178-186 calculations, 116-118 and pumping, efficiency, 119-122, 178179 Primary dissipation function, 16 Probability distribution, 139-142, 152-157, 169-171 Proton-antiproton storage ring, 77 Pulsed electron beam, 4, 98 time-delayed, 46-51 Pure square law, 19-20, 21 Pyroelectric transducers, 30

INDEX

Q Quartz applications, 369-370 Quasi-static stress nucleation, 263-271 Quench protection system, 96 R Radiation effects, electron beam, 223-224 contamination, 228-232 damage, 232-238 Radiofrequency cavities, 96-97 quadrupole, 80-81 Recombination process, 3 Reflection. ferroelastic wall, 252-256 coefficients, 300-304, 314-318, 322-325 optical, 304-314 with n o refraction, 312 Resolution, 41, 44-45 contrast and, 217-223 limit of. 218-219 Reynold's number, 127

s Scan coil, 10 Scanning auger microscope, 2 Scanning electron acoustic microscopy contrast mechanisms in, 21-26 electron-solid interaction, 2-3, 5-8, 16 micrographs, 2, 3, 20 misinterpretations, 5 operation set-ups and applications, 2, 20, 34-53, 56-70 pulsed excitation of, 4 signal detection mechanisms, 27-31 and signal generation, 2-3, 4, 5-8, 9, 16, 20-21 Scanning electron microscope archeological applications, 357-370 chopping unit, 32 history, 113-114 interaction products of, 2-3, 9 modification, 26-27 See also Environmental scanning electron microscopy; Scanning electron acoustic microscopy Scattering amplitude, 144, 318 cross section, 139, 143, 145-150, 162, 174, 178

387

optical, 307-314 patterns, 318-322 piezoelectric coupling and, 16 probability distribution, 139-142, 152157, 169 site, 5 , 6, 21, 159, 164-165 skirt width, 157-162, 168 See also Backscattering SEAM. See Scanning electron acoustic microscopy SEM. See Scanning electron microscope Semiconductors applications, 3, 14, 56-66 and contrast mechanisms, 23, 56 primary beam generation within, 3, 6, 18, 21, 23, 56 properties of, 3, 30 Shock front, 128 Signal generation processes and energy dissipation in a solid, 5-8 contrast mechanisms and, 22-23 inversion of, 18 nonlinear, 20-21 types, 2-3, 4-5, 10, 20 See also Detection systems Signals-to-noise ratio, 147, 219-223 Silicon dependence of strain, 18 ferromagnetic domain contrasts, 18-20 -iron applications, 38-39, 40, 51-55 n-doped, 15, 18 polycrystalline, 56, 61-66 transistors, 56 Sine wave, 19 Sinusoidal electron beam variation, 4 Skirt width, electron, 157-162, 168 and limit of resolution, 218-219 Snell's law, 315-317 Sound wave, 2, 21 detection system, 28-30 length of, 24 See also Ultrasound wave Space charge region, 24, 87-89 Spatial distribution, 14, 16, 17, 44 Specimen, target chamber, 27-31, 119-121 contrast mechanisms and, 23 detectors, 27-31 in electrostrictive coupling, 17 manipulators of, 112

388

INDEX

Specimen, target (Continued) nonlinearities and, 21 parameters and properties, 2 and signal interaction, 136 See also Environmental scanning electron microscopy; Scanning electron acoustic microscopy Square wave, 4, 9, 19 synthesized, 33 Steel sheets, transformer, 18-19 Stiffness, local, 23 Stochastic cooling, 80 Storage rings, 77, 79, 80 Superconducting technology, 92-96 Surfatron scheme, 102 Sutherland equation, 118 Synchroton radiation, 79, 86

T Temperature gas, in ESEM, 116-118 variation, in SEAM, 11, 18, 21 Tensor permittivity, 17 susceptibility, 305-307 Tensor susceptibility, 305-307 Thermal expansion coefficient, nonv'anishing, 2 Thermal heating, 7, 8, 21 Thermal stress, 261-263 Thermal wave properties, 3, 4, 8, 9 coupling, 10-14 detection system, 30 and silicon-dependent strain, 18 Three dimensional theory, 22, 24 See also Dimensions, three Time delays, 22 Time-resolved images, 40 See also Boxcar integration Trajectory contrast, 136 Transducers interdigital, 29 piezoelectric, 28-30 pyroelectric, 30 tunable comb filter, 301-302 Transistors, silicon, 56 Tunable devices acoustic filter, 339-341 active grating laser, 336-339 active optical grating, 327-329 comb filter, 301-304

reflection filter pass bands, 341-350 Turbulent flow, 127-128 Twinning, laser-induced, 261 Two-beam accelerator, 103-104

U Ultrasound wave, 2 V

Vacuum chamber, 360 equipment, 27 permittivity, 17 ultra-high, 206 Vane perturbations, 81 Velocity, thermal wave, 11 Vibrational mode patterns, 24 Video amplification, 10 Viscosity, 118 effusion flow, 128-129 laminar flow, 124-127 turbulent flow, 127-128 Voltage(s) detection systems, 30 and electron scattering skirt width, 160162 pinch effect, 192-193 recording of, by ESEM, 111 recording of, by SEAM, 21 W Wake field accelerators, 102-103 Wall, domain. See Domain structure Wave accelerators, 99 Wave-breaking limit, 101 Wave form magnitude, 16, 18 types, 2, 4, 10-14, 16, 19 See also Individual types Wavelength acoustic, 11, 343 optical, 292 thermal, 11,12

X X-ray(s) detection of, 2, 111, 205-206 generation, 6, 135, 184 microanalysis, 358-359, 362