Principles of Electron Optics Vols 1, 2, 3

1843 Pages·1998·70.18 MB·English

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The last attempt to cover systematically the whole of electron optics was
made by the late Walter Glaser, whose negaldnurG der kitponenortkelE
appeared in 1952; although a revised abridgement was published in the
hcubdnaH der Physik four years later, we cannot but recognise that those
volumes are closer to the birth of the subject, if we place this around 1930,
than to the present day.
Furthermore, electron optics has been altered dramatically during these
intervening decades by the proliferation of large fast computers. Analytic
expressions for the aberration coefficients of superimposed deflection and
round magnetic lens fields, for example, have been derived only recently,
partly because the latest generation of microlithography devices required
them but also because they could only be evaluated by numerical methods:
the earlier practice of seeking models permitting hand calculation could
never have served here. Again, computer calculations have shed consid-
erable light on electron gun behaviour, as the length of Part IX testifies
convincingly; in 1952, Glaser was able to condense his account of gun theory
into four pages!
The growth of electron optics is not, however, solely due to the com-
puter. Many systems that had not been thoroughly explored have now
been analysed in detail and, in many cases, we have had to renounce the
attempt to reproduce in detail new results, however interesting, to keep the
number of pages within reasonable limits. This work should therefore be
regarded as both a textbook and a source-book: the fundamentals of the
subject are set out in detail, and there the student should find everything
needed to master the basic ideas or to begin the analysis of some class
of systems not yet explored; the principal electron optical components are
likewise dealt with in great detail. Where optical elements that are not
quite so common are concerned, however, we have felt at liberty to direct
the reader to original articles and reviews, or specialist texts, to leave space
for topics of wider interest.
The following chapters are, moreover, limited to geometric optics:
wave optics is to be covered in a companion volume. With the SchrSdinger
equation as starting point, we shall there examine the propagation of elec-
tron waves in electrostatic and magnetic fields and study image formation
and resolution in the principal electron optical instruments. This demands
some discussion of electron-specimen interactions. A chapter will be de-
voted to the four broad themes of image processing: discretization and
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coding; enhancement; restoration; and analysis, description and pattern
recognition. In another, we shall give an account of the steadily grow-
ing field of electron holography. Finally, we shall return to the optics of
electron sources in order to understand the concept of coherence and we
shall show how the notions of brightness, partial coherence and various
associated spectral functions are inter-connected.
Students of electron optics have been fortunate in that many excellent
textbooks on the subject have appeared over the years, the first when the
subject was still young (Briiche and Scherzer, 1934; Myers, 1939; Klem-
perer, 1939; Picht, 1939); these were followed in the 1940s by the en-
cyclopaedic Zworykin et al. (1945), Cosslett (1946) and Gabor (1945).
Many books on the subject appeared in the 1950s, of which the texts by
Glaser already mentioned, Sturrock (1955) Grivet et al. (1955, 1958) and
Kel'man and Yavor (1959) are the most important for our present purposes.
Subsequently, however, the flow has shrunk to a trickle, new editions and
short introductory texts dominating, with the exception of the multi-author
volumes edited by Septier (1967, 1980, 1983); conversely, monographs on
limited topics have become more common. Although certainly 'standing
on the shoulders of giants', the present volumes do differ considerably from
their many predecessors in that the developments of the past twenty years
are accorded ample space.
For whom is this work intended? A knowledge of physics and math-
ematics to first degree level is assumed, though many reminders and brief
recapitulations are included. It would be a suitable background text for a
post-graduate or final year course in electron optics, and much of the ma-
terial has indeed been taught for some years in the University of Tiibingen;
a course in the University of Cambridge likewise covered many of the prin-
ciples. Its real purpose is, however, to provide a self-contained, detailed
and above all modern account of electron optics for anyone involved with
particle beams of modest current density in the energy range up to a few
mega-electronvolts. Such a reader will find all the basic equations with
their derivations, recent ideas concerning aberration studies, extensive dis-
cussion of the numerical methods needed to calculate the properties of
specific systems and guidance to the literature of all the topics covered.
Composition of volumes such as these puts us in debt to a host of col-
leagues: many have permitted us to reproduce their results; the librarians
of our institutes and the Librarian and Staff of the Cambridge Scientific
Periodicals Library have been unflagging in their pursuit of recondite and
elusive early papers; Mrs. StrSer has uncomplainingly word-processed hun-
dreds of pages of mathematical and technical prose; Mrs. Maczkiewicz and
Mr. Inial have taken great pains with the artwork as have Mrs. Bret and
her colleagues with the references; Academic Press and Professor Dr K.-H.
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Herrmann, Director of the Institut fiir Angewandte Physik der Universit£t
Tiibingen, have generously supported this work; the Zentrum f(ir Daten-
verarbeitung has provided the text-editing facilities needed for _FT ~. To all
of these we are extremely grateful. We also thank the many authors and
publishers who have been good enough to allow us to reproduce published
drawings. The details are as follows.
REGNIRPS VERLAG: Figs 17.4-5, 36.6-7, 36.11 and 42.1-7 from Grund-
lagen der Elektronenoptik by W. Glaser; Fig. 43.2 from the article by
D. Kamke in Handbuch der Physik 33; and Figs 36.3-4, 36.13, 36.17 and
36.36-37 from the chapters by F. Lenz, W.D. Riecke and T. Mulvey in
Magnetic Electron Lenses.
EHCILTFAHCSNESSIW :TFAHCSLLESEGSGALREV Figs 35.5, 36.8-9, 36.15,
36.18-26, 36.27-33, 36.35, 41.3-4, 41.7, 41.11, 42.15, 49.3 and 50.6-8 from
Optik.
ETUTITSNI FO PHYSICS: Figs 35.10, 36.38-40 and 36.43 from J. Phys. E:
Sci. Instrum.; Fig. 36.16 from Repts Prog. Phys.; and Fig. 35.3 from
the Proceedings of the Fifth European Congress on Electron Microscopy
(Manchester).
ESENAPAJ SOCIETY FO ELECTRON :YPOCSORCIM Figs 36.12, 36.34 and
41.5-6 from .Y Electron Microsc.
DNALLOH-HTRON GNIHSILBUP Co.: Figs 36.41-42 from Ultramicroscopy;
and Fig. 42.17 from Nucl. Instrum. Meth.
ESENAPAJ LANRUOJ FO APPLIED :SCISYHP Figs 35.13-14 and 36.44-45.
VEB REHCSTUED VERLAG RED :NETFAHCSNESSIW Fig. 36.14 from Ezp.
Tech. Phys.
IEEE: Figs 40.24-25 from IEEE Trans Electron Devices.
CIMEDACA PRESS: Figs. 45.8-9 and 48.7-8 from Adv. Opt. Electron
Microsc.; Figs 40.14-19 from Microcircuit Engineering .38
"Now, soldiers, march away; And how thou pleasest, God, dispose the day/"
Henry V, on the eve of the battle of Agincourt...
ecaferP
The last attempt to cover systematically the whole of electron optics was
made by the late Walter Glaser, whose negaldnurG der kitponenortkelE
appeared in 1952; although a revised abridgement was published in the
hcubdnaH der Physik four years later, we cannot but recognize that those
volumes are closer to the birth of the subject, if we place this around 1930,
than to the present day.
The difference between Glaser's work and our own is much greater
in the present volume than in the two volumes on geometrical optics, for
whole branches of the subject have come into being since 1956. The rep-
resentation of the image-forming process by transfer functions has yielded
a much deeper understanding of the notion of resolution. The develop-
ment of highly coherent light and electron sources has made holography
possible and the invention of the electron biprism has rendered it practi-
cal. The widespread availability of large fast computers and the gradual
introduction of microscope-computer links, as well as the peculiarities of
the electron image-forming process, have generated considerable interest in
digital image processing. Lastly, a theoretical advance in optical coherence
theory clarifies some obscure points in the related electron optical theory.
Only a very small fraction of the present text finds a counterpart in
Glaser's work, therefore, and Parts XII-XVI are entirely new. Part XI, on
the basic wave-mechanical formalism, follows the original work of Walter
Glaser and Peter Schiske quite closely, however, for there is little new to
report there apart from the investigations based on the Dirac equation.
Like Volumes 1 and ,2 this work is intended to be both a textbook
and a source-book. The fundamentals of the topics covered are presented
in detail but the reader who wishes to go more deeply into a particular
subject will need to examine the original articles, review articles and more
specialized textbooks. This is particularly true of themes that are closer to
electron microscopy than to electron optics and of image processing. For
the former, we have included two chapters on beam-specimen interactions
but these are intended merely to initiate the reader into the beginnings
of this vast subject. For the latter, and despite the length of Part XV,
we have had to be selective and refer frequently to other texts in this field.
Furthermore, image processing is a field in rapid growth and the reader will
need to complement our account of the fundamentals with the contents of
conference proceedings and the journals that specialize in these themes.
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The earlier work on wave optics is all brought together in Glaser's
two great texts of 1952 and 1956. Of the other earlier works on electron
optics, only those of Picht (1939, 1957, 1963) and de Broglie (1950) devote
much space to the subject. The subjects of Parts XII-XVI are all more
recent and no single volume attempts to cover them all. Specialized texts
do of course deal with their particular topics in much more detail than we
can and we refer to--and lean on--these in the relevant chapters. Only
Part XIV has generated a classic textbook, Electron Microscopy of Thin
Crystals by Hirsch et .la (1965), the record of courses given at a summer-
school in 1963. Once again, therefore, we can say that, although "standing
on the shoulders of giants", the present volume differs from other books on
the themes discussed here in that developments of the past thirty years are
set out in detail and in a uniform presentation.
For whom is this work intended? A knowledge of physics and math-
ematics to first degree level is assumed, though many reminders and brief
recapitulations are included. It would be a suitable background text for a
post-graduate or final year course in electron optics or electron image for-
mation or electron image processing and some of the material has indeed
been taught for some years in the Universities of Tiibingen and Toulouse.
Its real purpose, however, is to provide a self-contained, detailed and above
all modern account of wave-mechanical electron optics, with image forma-
tion, interference, holography and coherence as the principal examples of
application. This is complemented by a survey of the ways in which dig-
ital image processing can be made to participate in image interpretation
and microscope control. The basic equations are given, the applications are
discussed at length and ample guidance to the related literature is provided.
Composition of a volume such as this puts us in debt to a host of
colleagues: many have permitted us to reproduce their work and have of-
ten provided illustrations; the librarians of our institutes and the Librarian
and Staff of the Cambridge Scientific Periodicals Library have been unflag-
ging in their pursuit of recondite and elusive early papers; Mrs Str5er has
uncomplainingly word-processed hundreds of pages of mathematical and
technical prose, aided by Mrs Lannes and Mrs Davoust; most of the art-
work has also been produced by Mrs Str5er, using computer software rather
than the drawing pen; the remainder has been prepared by Miss Quessette
and Mr Caminade; the references have been typed by Mrs Bret and her
assistants; Mr Aussoleil and Mrs Altibelli have provided computer exper-
tise; Academic Press has generously supported the production costs. To all
of these we are extremely grateful. We also thank the many authors and
publishers who have been good enough to allow us to reproduce published
drawings. The details are as follows.
ECAFERP
EIMEDAKA VERLAG: Fig. 63.9 (T. Leuthner et al.) from Physica Status
Solidi.
NACIREMA PHYSICAL SOCIETY: Fig. 72.2 (J.-i. Matsuda st al.) from
Review of Scientific Instruments.
ELSEVIER, DNALLOH-HTRON GNIHSILBUP Co.: Figs 63.6 (D. Joy et al.)
and 66.15 (K. Ishizuka) from Ultramicroscopy.
ESENAPAJ LANRUOJ FO APPLIED PHYSICS: Fig. 54.3 (H. Tomita et al.).
ESENAPAJ SOCIETY FO ELECTRON MICROSCOPY: Fig. 63.7 (A. Tono-
mura) from Journal of Electron Microscopy.
LACISYHP YTEICOS FO JAPAN: Fig. 54.1 (A. Tonomura and .H Watanabe)
from Nihon Butsuri Gakkai-shi; Figs 62.11, 63.1 and 63.8 (A. Tonomura
et al.) from Proceedings of the Second International Symposium on the
Foundations of Quantum Mechanics in the Light of New Technology.
PRENTICE-HALL: Fig. 76.10 from Syntactic Pattern Recognition by K.S.
Fu.
LAYOR LACIPOCSORCIM :YTEICOS Figs 71.6 (R.E. Burge et al.) and 77.3
(W.O. Saxton et al.) from Journal of Microscopy.
GNINNACS YPOCSORCIM :LANOITANRETNI Fig. 75.6 (W.O. Saxton) from
Supplement 6 to Scanning Microscopy; Fig. 76.4 (C.E. Fiori et al.) from
Scanning Electron Microscopy.
~IT~ICOS FRAN~AISE ED MICROSCOPIE :EUQINORTCELE Fig. 62.5 (G.
MSllenstedt) from Journal ed Microscopie.
SPRINGER-VERLAG: Fig. 54.2 (G. MSllenstedt and .H Wahl) from Die
Naturwissenschaflen; Figs 60.4 (F. Lenz), 60.9 (F. Lenz and E. Krimmel),
61.5 (G. MSllenstedt and H. Diiker) and 62.9 (W. Bayh) from Zeitschrifl
fiir Physik.
ROLYAT & FRANCIS: Fig. 66.11 (W.B. Krakow et al.) from Philosophical
Magazine; Figs. 78.4-7 (J.T. Foley and E. Wolf) from Journal of Modern
Optics.
WILEY-LIeS: Fig. 75.8 (F. Zemlin et al.) from Journal of Electron Micro-
scopy Techniques.
EHCILTFAHCSNESSIW :TFAHCSLLESEGSGALREV Fig. 77.2 (W.O. Saxton)
from Optik.
For while the tired waves, vainly breaking,
Seem here no painful inch to gain,
Far back through creeks and inlets making
Comes, silent, flooding in, the main.
Introduction
1.1 Organization of the subject
The properties of beams of free electrons, released from a material source
and propagating through a vacuum region in some device, are of interest in
many diverse fields of instrumentation and technology. The study of such
electron beams forms the subject of electron optics, which divides naturally
into geometrical optics, when the wavelength is negligible, and wave optics,
in which effects due to the finite wavelength are considered. This first vol-
ume is concerned with geometrical optics, a knowledge of which is needed
to analyse an extremely wide range of instruments: cathode-ray tubes;
the family of electron microscopes, which now includes the fixed-beam and
scanning transmission instruments, the scanning electron microscope and
the emission microscope; electron spectrometers and mass spectrographs if
we include charged particles other than electrons; image converters; elec-
tron interferometers and diffraction devices; electron welding machines; and
electron-beam lithography devices. We could indeed include electron accel-
erators, such as betatrons and electron synchrotrons, but a rather different
approach is often more useful in those machines. This list is by no means
complete but it already demonstrates the great diversity of the possible
applications of electron optics.
Over the years, a vast amount of knowledge about the many branches
of electron optics has been accumulated and we have therefore had to be
selective. The main emphasis is on the principles of electron optics, and
technical details are only included to bridge the gap to the practical appli-
cation of these principles. This seems justified, for the principles remain
unaffected by the passage of time whereas instrumental development is so
rapid that surveys and review articles are the best means of charting its
progress.
The physical properties of electrons in a free beam may be classified
as follows:
(a) corpuscular properties;
(b) wave properties;
4 .1 NOITCUDORTNI
(c) macroscopic interactions;
(d) microscopic or atomic interactions;
(e) radiative properties.
A similar classification is given by Sturrock (1955).
The corpuscular properties are described by classical (relativistic) me-
chanics, the electron being regarded as a charged particle acted on by
electromagnetic forces. For almost all electron optical devices, extensive
studies must be made on the assumption that these corpuscular properties
alone are important and the present volume is almost wholly confined to
the corresponding geometrical optics. Geometrical particle optics is very
similar for all charged particles, ions in particular, and Parts I and X are
written in such a way that many of the relations derived are valid for ions
and electrons, or can be converted straightforwardly.
The rest-mass of the electron is extremely small, a characteristic that
has important consequences for the technology associated with electron
beams. Only quite modest voltages are needed to accelerate electrons to
a very high velocity, and the time of flight between the departure of an
electron from the cathode and its arrival at its destination in a typical
device is so small that it can almost invariably be ignored completely. It
is therefore quite sufficient to study the purely geometrical shape of the
electron motion within the beam, although a time-like curve parameter
may prove to be advantageous in numerical calculations.
A further consequence of the extremely small inertia of the beam elec-
trons is that deflection by suitably placed magnetic or electrostatic fields
occurs virtually instantaneously, in synchronism with the applied voltages
or currents, unless the frequency involved is very high indeed. The perfor-
mance of many devices relies upon this property. We shall consider electron
motion only in static, that is, time-independent fields. This is justified even
when studying the deflector in a scanning device, the time of flight being
so short that the applied field is quasistatic; the time dependence is then
merely a common amplitude factor.
A knowledge of the wave properties of the electron is essential to
understand the concept of resolution in electron microscopes, to ana-
lyse the interactions between electron beams and targets of all kinds, and
to analyse the behaviour of electron interferometers and diffraction devices
and of course to comprehend electron holography. These topics will occupy
much of Volume 3.
The macroscopic interactions in an electron beam are a consequence
of the fact that the latter may be regarded as a cloud of negative charges,
which creates an electric field; this is superimposed on the external applied
field and can thus alter the focusing properties of the device. In principle, of
course, this occurs for every electron beam, but in reality such space charge
1.1 NOITAZINAGRO FO THE SUBJECT
effects are of importance only when the local beam intensity is very high.
The space charge density can be treated as a macroscopic observable and
the associated field calculation remains within the framework of classical
electrostatics; we therefore call these interactions macroscopic. Such effects
occur mainly in electron guns where the beam intensity can be high, and
are therefore dealt with in Part IX, devoted to guns. Such effects are also
extremely important in accelerators, but these are not within the scope of
this book.
The microscopic or atomic interactions are the various scattering pro-
cesses that occur within the beam on the atomic scale. Such processes
arise when an electron beam encounters a specimen or target and electron-
electron collisions may also occur within the beam. The latter give rise
to the Boersch effect, an anomalous broadening of the electron spectrum
at beam waists, which are themselves enlarged. Classical collision theory
is capable of providing an approximate explanation of this effect, which is
examined briefly in Chapter 49. Collisions between beam electrons and the
atoms in a target can only be properly understood in terms of quantum
mechanics; some space is devoted to this topic in Volume 3.
Finally, we come to the radiative properties of the electron, essentially
the emission of bremsstrahlung when the acceleration is very high. This
occurs mainly in high-voltage electron microscopes where particles with an
energy of 1 MeV or more collide with the specimen placed in the path of the
beam. Although the staff around the microscope must be protected from
this radiation, the damage to the specimen is negligible in comparison with
that inflicted by the mechanical bombardment. The bremsstrahlung caused
by the acceleration of the electrons in vacuo only becomes important at the
energies encountered in high-energy physics, which are beyond the scope
of these volumes; we therefore ignore bremsstrahlung throughout.
Our theme is thus the study of the motion of electrons, regarded as
classical charged particles of negligible extent, through static electric or
magnetic fields. We begin with the derivation of the conservation laws for
the electron motion and cast these into a form particularly well suited to
electron optics. Various forms of the trajectory equations are established
but these are not at all satisfactory for our purpose, which is the study
not of single trajectories but of whole families of electron paths: not bal-
listics but optics. It is Hamiltonian theory that enables us to make the
transition. As early as 1827, Hamilton drew his famous analogy between
geometrical optics and classical mechanics; this tells us that, just as in
optics, there must exist a mechanical characteristic function, or eikonal,
with the property that the trajectories are always locally orthogonal to the
surfaces of constant value of this function. This is true only in the absence
of magnetic vector potentials; in the general case, when magnetic fields