Table Of ContentP. GRIVET
Professor at the University of Paris
With the Collaboration of
M.-Y. BERNARD, F. BERTEIN, R. CASTAING,
M. GAUZIT AND A. SEPTIER
ELECTRON OPTICS
SECOND ENGLISH EDITION
IN TWO PARTS
Translated by P. W. HAWKES
Revised afresh for this Edition by A. SEPTIER
Part 1 OPTICS
PERGAMON PRESS
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Copyright© 1972 Pergamon Press Ltd.
All Rights Reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
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wise, without the prior permission of Pergamon Press Ltd.
First English edition 1965
Second (revised) English edition 1972
Library of Congress Catalog Card No. 72-132964
This book is a translation, with much revision and
addition, of Optique Electronique, originally
published in French by Bordas Editeur, Paris
Printed in Great Britain by A. Wheaton & Co., Exeter
08 016226 6
PREFACE TO THE SECOND ENGLISH
EDITION
WE HAVE tried to improve this new edition of Electron Optics for the
benefit of two categories of reader. First of all, we have endeavoured
to make it more useful to the graduating student. With this in mind we
have, for example, added some introductory sections describing selected
but nevertheless classical methods of calculating electric and magnetic
fields; these indications are intended as a guide for the beginner who
sometimes feels lost in the abundant specialized literature.
On the other hand, we thought it essential to keep the research worker
(even the beginner) informed of the important recent progress in the
field: this seems to us an essential prerequisite for a book which aims
at helping scientists to form their scientific taste and choose their own
path in research.
This proved to be a fascinating but difficult task because activity in
the field of electron optics has been both important and successful
during recent years. The familiar magnetic objective has been sig
nificantly perfected, mainly by its discoverer, Professor Ruska, while
the practical introduction of superconducting lenses gives some realistic
hopes of a breakthrough in the domains of high resolution and high
energy: today, several careful measurements prove that a resolving power
of 4 A is already achieved and that one can distinguish lines spaced
1 or 2 A apart: the traces of Bragg planes are clearly distinguishable and
these results give good reason to hope that in a not too distant future the
individual atoms of most solids will be made visible by high-voltage
electron optics.
On the theoretical side, the phenomenon of interference between two
electron beams has gained in interest, as it may be usefully compared to
the superconducting interferometer, a more mysterious but also more
practical instrument making use of the stability of Cooper electron pairs
and producing beats in the time domain instead of fringes in space. For
this reason, greater care has been taken to bridge the gap between re
fractive index theory and the theory of the phase shift for electron waves.
The new appearance of this second edition is again mainly due to the
efforts of Dr. Septier and the new text was also very ably translated into
English by the English specialist of electron optics, Dr. Hawkes. I am
glad to thank them for their renewed efforts on behalf of this book,
in the name of all our team. The success of the first edition induces me
xi
Xii PREFACE TO THE SECOND ENGLISH EDITION
to express our gratitude to the founder of this team during the hard times
of the forties, Academician Dr. Ponte. We hope that the qualities of
this book reflect in no negligible part the precious lessons of his two
teachers during the twenties, Professor L. de Broglie and Sir John (J. J.)
Thomson: their creative enthusiasm still had a beneficial impact on us
40 years later.
PIERRE GRIVET
PREFACE TO THE FIRST ENGLISH
EDITION
WITH the appearance of this new edition in English it is a pleasure to look
back at the original French version of the book; the latter is not so very
old, and yet how important have been the advances which have been made
since its publication, in 1955 and 1958. The most fundamental sphere of
application of electron optics, electron lenses, seemed at that time to have
been fully explored, but nevertheless, the subject has a fresh appeal to young
research workers. The methods of calculation have developed beyond
recognition, for nowadays no-one hesitates to invoke the aid of an electro
nic computer, so that the atmosphere of slightly timorous respect in which
the differential equations to be solved used to be enveloped has practically
disappeared. The importance of these electronic computers has been shown
by the major discoveries which have resulted from their use, the behaviour
of the quadrupole lens, for example. The need to consider this new type
of lens was imposed by the requirements of nuclear physicists; none of the
ordinary methods was suitable for studying these lenses, but even so, their
properties and their surprising qualities are now well known after less
than five years' study—ordinary lenses, with their much simpler structure,
had to wait almost two decades before being thoroughly understood.
Other pleasant surprises await us in the instrumental field. To begin with,
the electron microscope is the most perfected instrument, having bettered
the performance which the theoreticians were reasonably hoping for around
1949. In their caution, these latter were doubtless too severe in their
estimates of the limiting resolving power which could be attained, for all
over the world today, industrial instruments of various nationalities—
English, German, Japanese, French and Russian—are in current use and reach
and even slightly exceed the most optimistic of the estimates of the theo
reticians of ten years ago.
Still more astonishing are the results which have been obtained with this
microscope. Ten years ago, it was still thought that the electron microscope
was capable of giving only a rather frozen view of reality, unnaturally
stiff like the view which we are given of the life of prehistoric organisms
by paleontology. But at Toulouse, Professor Dupouy has already begun to
study living biological cells with the aid of very high voltages; and even in
more ordinary laboratories, we have no longer to be satisfied with an ex
amination of a replica or desiccated skeleton of reality. Proper sections can
now be cut which show the real structure of the dead cell. The success is
still more striking where solids are concerned; with an electron microscope
xiii
Xiv PREFACE TO THE FIRST ENGLISH EDITION
we can fasten on to the very life of a metal, by filming, for example, the
evolution of the dislocations when the metal is heated; this can be
performed directly on a very thin layer cut from a block of the metal
being studied.
Metallurgy provides us with yet another example of a great success. The
metallurgists have now whole-heartedly adopted the electron probe; with
its aid, they are able to perform extremely detailed and accurate metallurgical
analyses.
This analyser was invented in France in 1949, and since 1954 Castaing
has made a highly perfected form available to the metallurgists. It has taken
six years for metallurgists all over the world to become convinced of
the excellence of this method, and 1960 marks the beginnings of world
wide employment of this micro-analyser. This example demonstrates how
useful it always is to struggle for the propagation of scientific ideas and
methods, even when they have received the most brilliant experimental
confirmation in the laboratory.
In these present times it is always necessary to make a very great effort
towards the diffusion of scientific thought and the renewal of experimental
methods and to disseminate them among a wide public, as, in the last
resort, it is this public which reaps all the benefit. It is for this reason that
the senior author of the French edition feels justified in his delight at seeing
that this book is going to present the ideas of the French school of electron
optics to an English-speaking public, to a public whose language is that
of the country in which the "electron" was born.
It is a pleasure to thank the many colleagues, both at home and abroad,
who have graciously contributed to this work by helping us to clarify some
difficult points, or by providing us with illustrations taken from their own
personal work. From among them, we should like to single out Professors
Castaing, Dupouy, Fert, Lallemand, Mollenstedt, Muller, Nozieres and
Pernoux, and Doctors Duchesne, Haine, Mulvey, Stohr and Wlerick.
We are also grateful to various industrial firms who furnished us with
certain documents, and in particular to C.S.F. and O.P.L. (Paris) and
Zeiss (Oberkochen).
This book, in its present form, owes much to the painstaking work of
Dr. Septier, who brought it up to date. Dr. Hawkes has been more than
a translator, and his profound knowledge of Electron Optics is present, if
not apparent, in many parts of this book. Last, but not least, I should like
to express my personal gratitude, and that of most of my colleagues in this
enterprise, to Professor Marton; without his continual encouragement
during the past fifteen years, much of the research and teaching included
within these pages would perhaps never have been performed.
PIERRE GRIVET
CHAPTER 1
FUNDAMENTAL FEATURES AND BASIC
TECHNIQUES
1.1 THE HISTORICAL BACKGROUND
Towards the end of the nineteenth century, physicists directed a large
proportion of their efforts towards elucidating the properties of cathode
rays which, by virtue of their rectilinear propagation, exhibited a close
affinity with light rays. An example is furnished by the celebrated experiment
in which Crookes introduced a metal cross into the path of the rays and
threw its shadow onto a fluorescent screen. That there was, however, a
fundamental difference between light rays and these cathode rays composed
of electrons in motion, was demonstrated by Pluecker and Goldstein who
showed that the latter are deflected by magnets and by charged bodies.
Later, with the revolutionary new ideas which followed the discovery
of the wave nature of the electron by L. de Broglie, it became apparent that
this deviation could be regarded as an optical property; further, the explora
tion of the vast new sphere of phenomena, now classed generically as "elec
tron diffraction", could begin.
The creation of this "physical optics" of electrons led to a more profound
examination of particle mechanics, and the analogy between the dynamics
of a material point and geometrical optics, which had been formulated
in theory by Hamilton in 1827, soon provided the foundations for the new
subject of "electron optics". This "corpuscular" optics—valid for charged
particles other than electrons: ions for example—consists in studying the
laws which govern the behaviour of electrons from their source, through the
"object", to the image which they trace out upon either a fluorescent
screen or a photographic plate.
After the first lenses had been built, by H. Busch (1927) and by Davisson
and Calbick (1931), the new optics developed rapidly, considerably aided
as it was by the important advances in "radio valve" techniques which were
taking place.
In fact, many of the difficulties were becoming less important: in part
icular, to obtain a vacuum within a capacious envelope containing large
metal surfaces had become a straightforward procedure and fluorescent
powders were now standard industrial products. Technology, too, provided
fascinating scientific problems to be solved, and from the beginning, electron
3
4 ELECTRON OPTICS
optics has been used successfully both to unravel the mysteries of oxide-
coated cathodes and secondary emission, and to satisfy the requirements
of television engineers.
To-day, electron optics is a branch of science which has achieved maturity,
a branch represented by a rich diversity of instruments—cathode ray tubes,
electron microscopes and electronic image converters for example. Through
out the whole of this vast field of applied electron optics, however, it remains
true that there are two alternative ways of controlling a beam of cathode
rays. The beam passes through the aperture either of an "electrostatic
lens", in which the rays are deviated by the electric field produced by a
system of annular electrodes, or of a "magnetic lens ", where annular magnets
or current-carrying coils surround the beam.
Two quite different methods of exploring the theory of electrons in electric
and magnetic fields are possible.
If, from the beginning, we examine the analogy between the trajectory
of an electron and the track of a light ray, it is possible to define a refractive
index, a function of position n(r, z), in such a way that the path of the
particle is identical with that which a light ray, obeying the usual rules of
refraction, would trace out in a medium with refractive index n. Once
n has been established, it becomes a simple matter to tabulate the pro
perties of electron lenses by a direct transposition from those of their
optical models; this is not, however, physically particularly meaningful in
the case of the magnetic lens. In his book Optique Electronique et Cor-
pusculaire (1950), de Broglie has displayed both the power of this method,
and the symmetry which can be established between optics and electro
magnetic theory.
Alternatively, the elementary classical formalism of the laws of mechanics
and electromagnetism can be used, but this involves rejection of the power
ful range of optical methods. However, although the investigation is made
less concise, it does relate the optical properties more directly to the con
crete features of the electrical experiment. Even if we deliberately restrict
the extent of our vision, we do nevertheless avoid the abstract mathematical
reasoning which is necessary to relate elementary geometrical optics to
Hamilton's theory. For this reason, we shall—to begin with—employ the
trajectory method.
1.2 OUTLINE OF A DEMONSTRATION IN
ELECTRON OPTICS
The formation of an image by an electron lens can be demonstrated with
the apparatus shown schematically in Fig. 1. An electron gun, which com
prises an oxide-coated cathode and an accelerating grid C held at a poten-
x
FUNDAMENTAL FEATURES AND BASIC TECHNIQUES 5
tial 0 is placed within an evacuated envelope. The cathode is held at a
l9
temperature of about 800°C by an incandescent heating element and elec
trons, in consequence of their thermal motion, are ejected with a small
velocity which corresponds for the majority to an energy of less than 0-1 eV.
Cathode
Image Object
1r.
<S>--0
$2 *i ^2^1
Lens Gun
FIG. l. Diagram of the basic demonstration.
The velocity t\ at which they pass through the grid is given by the con
servation of energy relation
\mv\ = e0 .
x
The initial velocity is negligible in comparison with the velocity produced
by 0 which is usually of the order of thousands of volts. The beam then
l9
illuminates the object, which is a grating cut in the diaphragm D passes
l9
through the lens L, and finally forms an image on the plate D , which is
2
coated with some fluorescent substance. The potential of the lens L is
negative with respect to the potentials of D and Z> , which are held at the
x 2
same potential as the outer electrodes H and H\ the purpose of which is to
localize the effect of the lens. The extent of the lens field is of the order of
magnitude of the diameter of the holes in the grids; outside (between the
object and the grid H and between the grid H' and the screen), the field is
zero and the potential has the constant value 0 .
1
1.3 THE OBJECT
Electronic devices have been adapted to enable a great variety of objects
to be examined; however, despite outward appearances, the optical pro
perties of these instruments can always be traced back to those of the appara
tus shown in Fig. 1, an electron gun in conjunction with a grating, the
properties of which we shall now examine in more detail.
6 ELECTRON OPTICS
1.3.1 Opaque Object
A grating is a characteristic example of an object which is genuinely
opaque to fast electrons; the bars of a grid are at least some dozens of
microns thick, and even though they be made of some light metal, aluminium
or beryllium for example, the electrons will be stopped and their energy
FIG. 2. The electron image of an opaque object (zinc oxide); magnification 20,000.
FIG. 3. The image of an opaque object (zinc oxide) "illuminated" by Li+ ions
(Gauzit, 1951).
