Advances in Electronics and Electron Physics, Volume 81

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 81

EDITOR-IN-CHIEF

PETER W. HAWKES 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 CEMESILaboratoire d'Optique Electronique du Centre National de la Recherche ScientiJique Toulouse, France

VOLUME 81

ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego New York London Sydney Tokyo Toronto

This book is printed on acid-free paper.

@

0

COPYRIGHT 1991 BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATlON STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.

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United Kingdom Edition published by ACADEMIC PRESS LIMITED 24-28 Oval Road, London NWI 7DX

LIBRARY OF CONGRESS CATALOG CARD

NUMBER:49-7504

ISSN 0065-2539 ISBN 0- 12-014681-9 PRINTED IN THE UNITED STATES OF AMERICA

91 92 93 94

9 8 1 6 5 4 3 2 1

CONTENTS CONTRIBUTORS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . PREFACE.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii ix

Applications of the Integral Equation Method to the Analysis of Electrostatic Potentials and Electron Trajectories G. MARTINEZ AND M. SANCHO I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Integral Equations for Conductors and Dielectrics.

........

111. Numerical Technique. . . . . . . . . . . . . . . . . . . . . . . . . . IV. Examples.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Conclusions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2 6 15 40 40

Energy-FilteringTransmission Electron Microscopy L. REIMER

I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Physics of Elastic and Inelastic Electron Scattering

111. IV. V. VI.

........

Instrumentation and Modes of Operation. . . . . . . . . . . . . . Electron Spectroscopic Imaging. . . . . . . . . . . . . . . . . . . . Electron Spectroscopic Diffraction . . . . . . . . . . . . . . . . . . Summary and Prospects . . . . . . . . . . . . . . . . . . . . . . . .

Bod0 von Borries: Pioneer of Electron Microscopy HEDWIGVON BORRIES

I. 11. 111.

IV. V.

43 44

62 75 105 1 18

127

Design Principles of an Optimized Focused Ion Beam System Y. L. WANGAND ZHIFENG SHAO Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Beam Profile and Beam Radius. . . . . . . . . . . . . . . . . . . . 180 Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

vi

CONTENTS

Electron Microscopy in Berlin 1928-1945 C . WOLPERS

21 1

Canonical Theory in Electron Optics JIVE XIMEN I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Conventional Aberration Theory in Lagrangian

Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Canonical Aberration Theory in Hamiltonian Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Applications of Canonical Aberration Theory . . . . . . . . . . . V . Canonical Electron Beam Optics . . . . . . . . . . . . . . . . . . . VI . Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SUBJECTINDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CUMULATIVE AUTHORINDEX. . . . . . . . . . . . . . . . . . . . . . CUMULATIVE SUBJECT INDEX. . . . . . . . . . . . . . . . . . . . . .

231 236 239 245 255 264 268 275 279 285 311

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

G. MARTINEZ(l), Departamento de Fisica Aplicada 111, Fac. de Fisicas, Universidad Complutense, Madrid, Spain L. REIMER (43), Physikalisches Institut, Universitat Munster, D-4400 Munster, Germany M. SANCHO(l), Departamento de Fisica Aplicada 111, Fac. de Fisicas, Universidad Complutense, Madrid, Spain ZHIFENCSHAO(177), Department of Physiology, University of Virginia, Box 449, Charlottesville, Virginia 22908 HEDWIGVON BORRIES (127), Clara-Viebig-Strasse 11, D-4000 Diisseldorf 1, Germany Y. L. WANC(177), Institute of Atomic and Molecular Sciences, Academia Sinica, P. 0. Box 23-166, Taipei, Taiwan, 10764

C. WOLPERS (21 l), Gartengang 3, D-2400 Liibeck, Germany JIVEXIMEN(23 I), Department of Radio-Electronics, Peking University, Beijing, 100871, China

vii

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PREFACE All the articles in this volume are centered around the general theme of charged particle optics. This field continues to develop vigorously, sometimes in unexpected directions, and the present reviews reflect some recent trends. Not all the chapters deal with the present and near future, however. In Supplement 16, The Beginnings of Electron Microscopy, I invited further contributions on this theme, and two such historical essays are included here. The first, by Frau von Borries, widow of the late Bod0 von Borries, charts in detail the work of one of the main collaborators of Ernst Ruska in the early years of electron microscope development. Frau von Borries paints a vivid picture of both the public and private life of one of the pioneers of the subject. The other historical paper, by Dr. C. Wolpers, began as a survey of the work of Helmut Ruska, brother of Ernst, but has been broadened to evoke Berlin in the pre-war and wartime years as seen by an electron microscopist. This is a valuable reminder of early medical work with this new instrument and includes a list of the destinations and fates of the first batches of Siemens microscopes. The other four chapters are more traditional. G. Martinez and M. Sancho present some recent developments in methods of calculating the properties of electrostatic focusing systems. L. Reimer describes the new subject of energyfiltering transmission electron microscopy. This can indeed be called a new activity since, although energy filters have been used for many years, energyfiltered imaging has only recently become widespread. This review, in which both scattering theory and imaging modes are discussed, will, we hope, be of great value to the growing number of users of these techniques. The fourth chapter, by Y.L. Wang and 2. Shao, takes us into the realm of ion-beam system design for microlithography. The principles underlying the design of these systems are presented and examined critically, and guidelines are deduced from them. The final chapter is by Ximen Jiye, who has already contributed a Supplement on particle optics to these Advances. Here, he brings together and harmonizes his recent work on an approach to the Hamiltonian theory that he has been developing for the past few years. I am most grateful to all these authors for the time and effort that they have devoted to their reviews for this volume. I also wish to add a word of special appreciation to those at Academic Press, Boston, who helped to produce the cumulative index to the first 81 volumes, included in this volume: Robert Kaplan, Senior Editor; Jody Morrow, Editorial Assistant; Natasha Sabath, ix

PREFACE

X

Managing Editor; and Cynthia Weber, indexer. I have no doubt that all users of the series will echo my thanks for this index, which renders this great body of research surveys, begun 43 years ago by L. Marton, much more accessible. As usual, a list of forthcoming articles is given below. FORTHCOMING ARTICLES

Image Processing with Signal-Dependent Noise Parallel Detection Magnetic Reconnection Vacuum Microelectronic Devices Sampling Theory Nanometer-scale Electron Beam Lithography The Artificial Visual System Concept Speech Coding Corrected Lenses for Charged Particles The Development of Electron Microscopy in Italy The Study of Dynamic Phenomena in Solids Using Field Emission Pattern Invariance and Lie Representations Amorphous Semiconductors Median Filters Bayesian Image Analysis Applications of Speech Recognition Technology Spin-Polarized SEM The Rectangular Patch Microstrip Radiator Electronic Tools in Parapsychology Image Formation in STEM Low Voltage SEM Z-Contrast in Materials Science Languages for Vector Computers Electron Scattering and Nuclear Structure Electrostatic Lenses CAD in Electromagnetics

H. H. Arsenault P. E. Batson A. Bratenahl and P. J. Baum I. Brodie and C. A. Spindt J. L. Brown Z. W. Chen J. M. Coggins V. Cuperman R. L. Dalglish G. Donelli M. Drechsler M. Ferraro W. Fuhs N. C . Gallagher and E. Coyle S . and D. Geman H. R. Kirby K. Koike H. Matzner and E. Levine R. L. Morris C. Mory and C. Colliex J. Pawley S . J. Pennycook R. H. Perrot G. A. Peterson F. H. Read and I. W. Drummond K. R. Richter and 0.Biro

xi

PREFACE

Scientific Work of Reinhold Rudenberg Metaplectic Methods and Image Processing X-Ray Microscopy Accelerator Mass Spectroscopy Applications of Mathematical Morphology Developments in Ion Implantation Equipment Focus-Deflection Systems and Their Applications The Suprenum Project Electron Gun Optics Cathode-Ray Tube Projection TV Systems Thin-Film Cathodoluminescent Phosphors Parallel Imaging Processing Methodologies Diode-Controlled Liquid-Crystal Display Panels

H. G. Rudenberg W. Schempp G. Schmahl J. P. F. Sellschop J. Serra M. Setvak T. Soma 0.Trottenberg Y. Uchikawa L. Vriens, T. G. Spanjer, and R. Raue A. M. Wittenberg S . Yalamanchili Z. Yaniv

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ADVANCES I N ELECTRONICS A N D ELECTRON PHYSICS. VOL 81

Application of the Integral Equation Method to the Analysis of Electrostatic Potentials and Electron Trajectories G. MARTINEZ AND M. SANCHO Departamento de Fisica Aplicada 111 Fac. de Fisicas, Uniuersidad Complutense Madrid, Spain

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 11. Integral Equations for Conductors and Dielectrics . . . . . . . . . . . .

111. Numerical Technique . . . . . . . . . . . . A. Method of Moments . . . . . . . . . . . B. Evaluation of the Coefficients . . . . . . . IV. Examples. . . . . . . . . . . . . . . . . A. Electrostatic Model for Ion Channels . . . . . B. Four-Aperture Electrostatic Lens . . . . . . C. Space-Charge Effects in Lenses . . . . . . . V. Conclusions, . . . . . . . . . . . . . . . References,. . . . . . . . . . . . . . .

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

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

1 2 . . . 6 . . . 6 . . . . 8 . . . 15 . . . . 16 . . . . 22 . . . . 36 . . . 40 . . . 40

I. INTRODUCTION The numerical methods for the analysis of electric and magnetic fields have been an area of continuous interest in the last decades. With the advent of high speed computers, a variety of efficient techniques have been developed that allow us to obtain the solution of almost any desired electromagnetic field configuration. For the electrostatic case, the problem is reduced to getting the solution of the Poisson equation V2q5 = - p / E over a region R, subject to boundary conditions, usually of Dirichlet type. General approaches to the numerical solution of this equation are finite difference schemes, with or without variational formulations and integral equation methods. Any of these approximate methods can convert the differential equation into a linear algebraic

* Portions of this article and Figs. 14, 15, and 16 appear in a previous article by the authors (Reference 28), published and copyrighted by Elsevier Science Publishers (Physical Sciences & Engineering Div.), and are reproduced with their permission. I Copynght Q1991 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0- 12-014681-9

2

G . MARTINEZ AND M. SANCHO

system. Relaxation techniques and random walk simulations have frequently been used to solve the algebraic equations, but nowadays the easy access to efficient matrix inversion algorithms incorporated in subroutine libraries makes direct methods preferable. Relative merits of the different approaches have been the subject of extensive discussion (Steele, 1987). In general, the election of the most convenient method for solving a potential problem is very much dependent on the following factors: i) Facilities of computing memory size and time available. Difference methods, which use a mesh defined over the volume, are much more memory and time consuming than integral equations, which set node points only over the domain surface. ii) The shape and symmetry of the region of interest. Curved contours do not fit well to mesh points defined in finite difference schemes. If the problem has rotational or translational symmetry, a two-dimensional formulation is possible and requires a simpler treatment. Another aspect to consider is if the field problem domain extends in all directions to infinity, i.e., if we have an exterior problem. In that case an integral formulation that considers only points around the boundary is better suited. iii) Medium linearity and uniformity. Difference formulae can be used even when nonlinear and nonuniform media are present. Integral equations are only valid for linear media but can be applied to the frequent case of boundaries over which the permittivity varies discontinuously. The integral formulation gives directly charge densities induced on the conductor surfaces or the potential and electric field at any desired point. Therefore, it has been frequently used for the calculation of capacitance coefficients of a set of conductors or the computation of trajectories in the electrostatic focusing of ion beams, with or without space charge effects (Renau et al., 1982; Martinez and Sancho, 1983a; Munro, 1987). 11.

INTEGRAL EQUATIONSFOR CONDUCTORS AND

DIELECTRICS

In order to derive the integral equations for electrostatic problems, it is convenient to start with an analysis of the discontinuities occurring in the integrals associated with the potentials produced by single or double layers of charge. These integrals are of the form dS‘

APPLICATION OF THE INTEGRAL EQUATION METHOD

3

The integral I(r) is a continuous function, but its normal derivative approaches different limits from each side of the surface. These limits are (Kellogg, 1967)

where n is the outwardly directed normal at r, ( d I / d n ) + ,( d ! / d n ) - are the limits of the integral from the outer and inner side, and ( d I / d n ) , is the integral at the surface (taken as its Cauchy's principal value). Similarly, the potential produced by a double layer J(r) is discontinuous, the limits from either side being related to the value Jo at the surface by the equations

+ 2nt(r)

(5)

J- = Jo - 2nr(r).

(61

J+ = Jo

Now, we will deduce an integral equation for the electrostatic potential in a geometry including conducting and dielectric media. First of all, if we have a set of charged conductors, the potential that they produce is

where a(r') is the charge density and S, represents the surface of all the conductors. When Eq. (7) particularizes to points lying on the surface of any conductor where the potential is constant and known, it constitutes a Fredholm integral equation of first class. Its solution gives a(r') and then the potential at any point, using Eq. (7) again. We consider now a system of conducting and homogeneous dielectric bodies, as shown in Fig. 1. We will treat the dielectric interfaces as transitions from one dielectric body with permittivity ci to the vacuum and then to another dielectric with c j or to a conductor and assume that the transition layer is vanishingly thin. The potential at any point inside a dielectric volume is produced by all sources present in the space. In our case these are basically surface charges on the conductors with density a(r') and dipole distributions over the polarized dielectrics, described by the polarization vector P(r'). In addition, other

4

G. MARTINEZ A N D M. SANCHO

FIG.1. Schematic drawing of a set of conducting and dielectric bodies.

possible sources, such as space charges with volume density p(r’), can be considered. Then we have

(8) where R = Ir - r’l, V, represents the volume of the dielectric J, V is the total volume, and S, is the surface of all conductors. If we express P(r’) = e0(k - 1) E(r’), Eq. (8) becomes

Using partial integration and replacing the integrals of the divergence by surface integrals, we obtain

APPLICATION OF THE INTEGRAL EQUATION METHOD

With the substitution V2(1 / R ) = -4nh(r to the dielectric volume V,, Eq. (10) becomes

-

5

r’), and if the point r belongs

To obtain an integral equation we apply this expression to a point very close to the surface S,, an interface between the dielectrics I and L . Because of the continuity of the potential, and using Eqs. (5) and ( 6 ) to write the terms corresponding to this interface as integrals from the surface, we get

for the field point on a dielectric interface; k, and kL are the relative permittivities of the media I and L, which are in contact along the interface. For points on an interface dielectric-conductor, 4(r) is constant and the corresponding integral vanishes, so there is no discontinuity and an equation similar to Eq. (11) is obtained,

where k, is the electric permittivity of the medium in contact with the conducting surface at r. Potentials at the conductors are known, so Eqs. (12) and ( 1 3) are a system of integral equations for the potential along the dielectric interfaces and the charge densities on the conductors. Once these unknowns have been obtained, Eq. (1 1) gives the potential at any desired point. An expression for the electric field at r E V, is also readily obtained from the potential given by Eq. (1 I), ds’

6

G. MARTINEZ A N D M. SANCHO

111. NUMERICAL TECHNIQUE

We are interested in solving the set of integral equations by a method that must have two main characteristics: power and flexibility. These criteria will enable the study of a wide variety of problems with the highest efficiency. In what follows, we describe the numerical technique that we have developed to attain this goal. A . Method of Moments Harrington (1968) has provided a unified treatment for the numerical solution of linear operator problems. His approach, the method of moments, involves the expansion of the unknown solutions in a series of basis functions and the use of a set of weighting functions to obtain a linear algebraic system. The approach we will follow, closer to the physical picture, is to divide the contours into a set of subsections of nonuniform size chosen in accordance with the expected nonuniformity of the potential and charge density. Thus in the vicinity of metallic corners, the charge density varies approximately as r-", r being the distance to the corner and n an exponent that depends on the corner angle (Jackson, 1980).A similar reasoning can be applied to the variation of 4 along a dielectric interface. Thereafter, we divide the surfaces into progressively smaller subareas close to the vertex, so that a constant value of a or 4 can be assumed on each of them. Mathematically it is equivalent to the use of pulse functions defined over the corresponding subsection as basis functions in the moment method, but the election of nonuniform subareas has proved to have an accuracy comparable to that of much more complicated versions. A second choice, which further simplifies the computation of the matrix elements, is the use of Dirac delta functions as weighting functions. On the other hand, we also approximate the space charge distribution by a set of discrete volume elements in such a way that p can be considered of uniform magnitude inside each of them; this will facilitate the calculation of the constant vector of our system. According to the previous considerations, let the index j go from 1 to k to account for conducting subareas, from k + 1 to rn for dielectrics ones, and from rn 1 to n for volume elements. The resulting algebraic system, obtained from Eqs. (12) and (13), is then of the form

+

m

k

6 i

=

1

Aijaj

j= 1

Cbi = const. =

+ j =1 k+l

Bij6j

k

rn

i= 1

i=k+l

1 D,aj + 1

+

Cijpj, j=m+ 1

Eij4j +

(i = k

+ 1 ... m)

n

1 ejpj,

i=m+ 1

(i = 1 ... k),

(15)

APPLICATION OF THE INTEGRAL EQUATION METHOD

7

corresponding to points on the dielectric and on the conductor surfaces, respectively. The expressions for the coefficients are

with R, = Ir, - r;l. Details on analytical evaluations of these coefficients, based on their physical interpretation, are given below. The resultant matrix equation has no special characteristics, such as sparsity or definiteness, but can be solved by standard techniques. We have used the Crout reduction method (Gerald, 1984). After the determination of a(r) on conducting surfaces and &r) at dielectric .interfaces, the potential and field at any point of the space can be calculated from the discrete forms of Eqs. (1 1) and (14), i.e., k

&ri)

+

Aijaj

+ 1

j= 1 k

E(r,) =

j= 1

rn

D;aj

=

j=k+l rn

j=k+l

n

E ; j 4 j + j = m + l Fijpj, Bij+j +

ri E V,

(23)

ri E &.

(24)

n

1

Cijpj,

j=m+ 1

Dij, Eij and Fij have the same mathematical expressions as D,, Eij and Ej, and

6, R i

1 A!. = 'I 4nkic0

B V! , =

where Rij = ri - rJ.

k4nki j-1

Rij ds' -

j

sJ jan' L ( " . )R; dsi

(25) (26)

8

G. MARTINEZ A N D M. SANCHO

B. Evaluation of the CoefJicients In calculating these coefficients it is helpful to consider their physical meanings. Thus, those containing the form jsj l/Rijds’ or j, l/Rijdv’are proportional to the potential created at point ri by a uniform charge of unit amplitude over the subarea Sj or in the volume Vj. Similarly, coefficients with an integral of the form jsJ d/dn’(l/Rij)ds’are proportional to the flux of the electric field created by a unit charge at ri, across the subarea Sj. On the other hand, fS,Rij/R;ds’ or f v Rij/R:du‘ represent the field produced at ri by a unit charge uniformly histributed over Sj or inside Vj, and f , d/dn’(Rij/R;)ds’ is minus the gradient of the flux of the electric field produced by a charge at ri across Sj. In problems with rotational symmetry there are two basic types of subareas into which we can divide any surface: annular and cylindrical. Moreover, for problems including space-charge effects it is convenient to consider cylindrical volume elements. For some configurations, truncated conical subsections would also be adequate, but the calculation of the associated coefficients involve, in general, numerical integrations and these will not be treated in the following. In all cases considered, analytical closed expressions can be deduced for the coefficients. This is an important characteristic of our version of the method of moments because it allows the utilization of a minimum size for the matrix equation in the solution of electrostatic problems. In what follows, we will give the formulae used in the obtainment of these quantities; they will be classified according to the type of subareas and volume elements previously mentioned. Most of the expressions can be found in advanced electromagnetism textbooks and particularly in Durand (1964),but we have preferred to list them for the sake of completeness.

1. Coeflcients Containing the Form

1

a. Circular Annular Subareas The starting point is the potential at the point (ri,zi) due to a disk of radius R, located at an axial distance zj and uniformly charged with r ~ , n -&(1 - E‘)-z 2

R2 -r2 + ___ ’ K(k) rl

APPLICATION OF THE INTEGRAL EQUATION METHOD

9

where

and K ,E and TI represent the complete elliptic integrals of the first, second and third kind, respectively. The parameters E and E' compensate for the discontinuity in Eq. (28) due to the charge layer and have the values

&=I

-1, z < o 0, z = o 1, z > o

/=(

-1, Ti < Rd 0, ri = R , 1, Ti > Rd.

(294

There are several particular cases in which Eq. (28) reduces to simpler equations,

(Rd

1

+ ri)E(k)+ (Rd - ri)K(k) .

The coefficients we are searching for may now be calculated by superposition of the potential due to a disk of radius equal to the external radius of the annulus, charged with a = + 1, and that of a disk of radius equal to the internal radius, charged with a = - 1.

b. Cylindrical Subareas In this geometry the potential created by a semiinfinite cylindrical layer is used. That quantity is expanded in a series of Legendre polynomials and has different expressions depending on the region in which the field point is located (see Fig. 2). For a point (ri,zi) in region I, the potential produced by a cylinder of radius R,, with its origin at zj and charged with a is In(d + z ) - -

-

10

G . MARTINEZ A N D M. SANCHO

FIG.2. Different regions for the calculation of the potential due to a semi-infinitecylindrical layer.

For region 11, we have

2 In Rc - ln(d - z) 1 --

f

2n c"_/2

P2n-1(COSQ)

2n=l

Finally, for points in region I11 the potential is In&

1

.

(34)

(

+ n1= 0cy1/2 2 n+ 1 R, ~yn+1P2n+l(cosQ)],

(35)

where Pn(cos9) are the Legendre polynomials,

c?,,2= (-1y

1 x 3 x ... x (2n - l), , 2 x 4 x ... x 2n

c01/2 =

1,

(36)

and d = [r: + (zi- z ~ ) ' ] ~ / ~ . The coefficient associated with a strip of width zjl - zjz is obtained by superposing the potentials created by two semi-infinite cylinders of radius R,, charged with densities + 1 and - 1, shifted along the axis and with their origins at zjl and z j 2 .

2. Coeficients Containing the Form

lVj 1

Gdv'

For this type of coefficient we only have characterized the one corresponding to a finite cylinder uniformly charged with volume density p, because any space charge distribution can be approximated by a set of such cylinders. Hence, we start with the determination of the potential created at the point (ri,zi)by a semi-infinite cylinder of radius R,, charged with p (see Fig. 3). This value can be obtained by integration, through the radial distance, of the

APPLICATION OF THE INTEGRAL EQUATION METHOD

11

(r, .z,l

FIG.3. Different regions for the calculation of the potential created by a semi-infinite cylinder.

potential due to a semi-infinite layer uniformly charged (Eqs. 33 to 35). Depending on the region to which the field point belongs, different expressions are obtained. Thus, for region I we have

For points in region I1 the integration gives d(ri9 zi)

-z[(k)2[ln(d

-

-

(1

-

(;)2)ln(d

+ z ) - 2Iny + 13 + 21nR, - 1 -

z) -

c 2n(n + 1) (5)2nP2n-l(c~~9) . d c11’2

a,

When 9 tends to r, the potential converges to the value

For region I11 we obtain 4(ri,zi) -

-”’[(’) 4tO

+

f n=O

2

Cln(d+z)-2Iny+

2cy 112 1 -4nZ

(-[;)2n-1

[(3’ -

-

11-

11 1 1 ln(d - z)

2(n

+ In d - 0.5

+ l)(n + 2)

1

(38)

12

G. MARTINEZ A N D M. SANCHO

For 9 = n, this expression gives

$(o, zi) = pdZ -

4%

[

( % r ( l n R,

-

0.5) - In 2 - 0.5

2(n

+ l)(n + 2))]. (41) cn_:'2

Finally, for region IV, (In R , - 0.5) - In d

+ 0.5

(42) In these formulae y = d sin 9, P,(cos 9) are the Legendre polynomials, and coefficients C! l i 2 are given in Eq. (36). The potential due to a finite cylinder is obtained by superposing the potentials created by two semi-infinite cylinders of radius R,, charged with densities + 1 and - 1 shifted along the axis for a distance equal to the length of the cylinder. Finally, the potential due to a hollow cylinder is given by the appropriate superposition of two cylinders of radii R , and R, equal to the internal and external radii of the annulus, respectively.

3. Coescients Containing the Form

s,2)(d,)

- -

In this case we are dealing with the calculation of the flux of the electric field of a charge q, at ( r i ,zi), through the area S j . a. Circular Annular Subareas We first write the flux of a charge q through a disk of radius R,; in this equation we take as positive the flux toward the negative z direction,

1

22 F(Sj) = - ~ ( 1 ~ ' )+n -[e'(l - rn2)'i211(k,m)- K ( k ) , rl where 2, k, r l , m and E, E' are given in Eqs. (29a to 29e). For some particular cases we have

(43)

Z

for ri = (O,z,),

(44)

13

APPLICATION OF THE INTEGRAL EQUATION METHOD

F(Sj) = 0,

for ri = (ri,O).

(46)

The value we want may be obtained by appropriate superposition of the flux across two disks. b. Cylindrical Surfaces The flux through a semi-infinite cylindrical layer is related to that of the disk. For example, it is easy to see in Fig. 4 that for a charge q in the region z = zi - zj > 0, the field lines that enter the circular area of radius R, are the same as those that give the net outward flux through the cylindrical surface. Let F, be the value obtained in Eq. (44) and F, the flux we look for; depending on the relative position of q, F, is given by

F,=F,,

for z > O

or z < O

for z < O

F,=F,+41rq,

and r i > R,,

and r i < R,.

There are also some particular expressions; thus in the plane z flux is

and for ri = R,

F,

=

i".

(47) (48) =0

the

z>o

& + Irq, z < 0.

As in the previous calculations, the flux across the cylindrical layer is computed by superposing the contributions of two semi-infinite cylinders conveniently shifted along the axis.

FIG.4. Diagram for the calculation of the flux through a semi-infinite cylindrical layer.

14

G . MARTINEZ AND M. SANCHO

4. Coeficients Containing the form

js,;

ds’.

a. Circular Annular Subareas The components of the field at ( r i ,zi),due to a disk of radius Rd charged with (r at z j , are

[(

E,(ri,zi) = -I’ 1 - g ) K ( k ) - E ( k ) ]

2 n ~ ,ri

I1

,

~‘(1 - rn2)”211(k,rn) - K ( k )

E z ( r i , z i )= -

(52)

where the variables and parameters have the same meaning as in Eqs. (28) to (30). Particular simple cases are

OR; z EZ(O,Zi) = --

1

(54)

The expressions for circular annular subareas are obtained by adequate superposition. b. Cylindrical Subareas the expressions

We have now for a semi-infinite cylindrical layer

1

- m2)’/211(k,rn)+ K ( k ) ]

(55)

with the customary meaning for the symbols used. The field for a finite cylindrical surface is obtained by superposition of two contributions of this type, adequately shifted.

5. CoefJicients Containing the Form

s,

$01

We restrict our attention to cylindrical volume elements. To obtain the components of the field due to a cylinder, we have performed an approach similar to that used for the coefficientsFij. Thus, for the axial component E, a t the point ( r i ,zi),the elemental contributions of semi-infinite cylindrical

APPLICATION OF THE INTEGRAL EQUATION METHOD

15

surfaces, uniformly charged, are integrated. We have

As there is no closed analytical expression for Eq. (57),we have developed K ( k ) in a power series and performed the integration term by term (Byrd and Friedman, 1971).We then write

where c , are the coefficients of the expansion for K ( k ) .The integrals appearing in Eq. (58) are reducible to a summation (Gradshteyn and Ryzhik, 1980). For the radial component, it is easier to use flat disks, uniformly charged, as differential elements and extend the integration between the limits z 1 and z2 of the cylinder, that is

:j :(( c)

Er(rj,zi)= __ 2,Y&,

-

2 K ( k ) - E ( k ) ) dz'.

(59)

We also expand E ( k ) in series. Then after some algebraic manipulations, Eq. (59) becomes

2 2 ( " - 1 ) r ~ - 1 R ~-( cd,,

-0

. 5 ~ , , - ~1 ) ~ ~ ~ d z ' ) . (60)

where d , are the coefficients of the series development for E(k). Again, the integrals in Eq. (60) are calculable by means of the appropriate reduction formulae. Furthermore, it is possible to generate each term using calculations previously stored, which allows for a very efficient algorithm.

6. Coeficients Containing the Form

js,

-

(RRi)dst -

In this case the components can be obtained by derivation of the corresponding electric flux given by Eqs. (43) to (50). We will not include the rather complex expressions, some of which can be consulted in Algora del Valle et a!. (1987). IV. EXAMPLES The integral equation formulation described in Section I1 can be applied to the study of a great variety of problems in which the potential distribution, for a given set of boundary conditions, is needed. In this section we intend to

16

G . MARTINEZ AND M. SANCHO

illustrate with three representative examples, the way that must be followed for the obtainment of the parameters characterizing the system under analysis. The first one is a bioelectrical problem dealing with transport through ion channels in membranes; its simulation requires the use of two dielectric media as well as polarizing conductors. The second and third examples are related to the Electron Optics area: given a distribution of polarized conductors, their imaging properties are investigated. The last example also shows how spacecharge effects can be incorporated into the equations. The particular version of the numerical technique developed here limits the applicability to problems with rotational symmetry; however, this is not a serious restriction as many practical systems can be represented by this type of geometry. A. Electrostatic Model for Ion Channels

Biological cells are surrounded by a membrane that protects their components from the environment. In most cases, the membrane consists of a lipid bilayer forming a dielectric shield that prevents penetration by ions. It can be shown that the lipid represents a large electrostatic energy barrier (Parsegian, 1969). Of course, metabolites must traverse membranes, and several transport mechanisms have been proposed (Fromter, 1983). One of the most relevant is the transport mediated by fixed channels, where the particle crosses the membrane through a performed permeation path. During the last years considerable experimental, as well as theoretical, work has been done in order to get a deeper insight into that mechanism (Andersen, 1983; Jordan 1986; Jordan et al., 1989). It is generally agreed that long-range electrostatic forces significantly influence ionic transport through membrane spanning channels. An adequate integral formulation of the problem will allow us the analysis in detail of this type of interaction. A different integral approach has been formulated previously by Jordan (1982), but it was inadequate for the incorporation of exact boundary conditions. 1. Image Potential

Figure 5 shows a schematic drawing of a cylindrical channel piercing a membrane of electric permittivity E ~ The . pore and the water are supposed to be characterized by the same permittivity el. An ion of charge q is located at z, and induces surface charges along the phase boundaries. Certainly, real channels will not have exact rotational symmetry, but this approximation will permit the use of our numerical technique without introducing too much error.

APPLICATION OF T H E INTEGRAL EQUATION M E T H O D

17

FIG.5. Cross-sectional diagram of a cylindrical channel spanning a membrane of electric permittivity e l . The bulk water and the channel region have the same permittivity E , .

According to the formulation given in Section 11, the potential at a point lying on the membrane boundary is obtained from Eq. (12).In this case there are not any conducting surfaces and the expression reduces to

where x = and the normal n' is taken in the direction outward from the membrane. For the numerical solution of Eq. (61), we make a division of the phase boundary into n small subareas that have the form of flat circular annuli or cylindrical sections and assume that the induced potential on each of them is constant. Hence, the above expression can be approximated by the set of algebraic equations

ri being the position vector of the midpoint of S i . The matrix elements Bij are proportional to the flux of the electric field created by a unit charge at ri across Sj and can be obtained from Eqs. (43)-(50). After computing the potential distribution along the phase boundary, application of Eq. (1 1) enables us to find the potential at any point of the aqueous medium. This value is given by

18

G . MARTINEZ AND M. SANCHO loo0

-

€00

>

E

1 0

5

10

15

20

6

FIG.6. Image potential &,,, for an ion at the center of the channel as a function of the halfwidth to radius ratio, 6. The asymptotic value (broken line) for an infinite pore is 0.978 volts.

which, expressed in a discrete form and ignoring the contribution of the charge q, may be used to determine the image potential &,, i.e., the potential created by the induced charges at the ion position zo along the channel axis. Figure 6 shows this value, for a monovalent cation at zo = 0 as a function of the halfwidth to radius ratio, 6 = h/rc.We have chosen = 80 c0 and c2 = 2c0,which approximately represents a lipid-water system. The image potential is positive, as might be expected for > 1, and increases with 6. It tends to the asymptotic value 0.978 volts obtained for a pore of infinite length (Parsegian, 1975). Finally, we must point out that for a Gramicidin-like channel (6 = 5) the potential barrier for passage of a monovalent cation is 0.476 volts, a still significant value. As we will see, this barrier may be altered by the presence of other charge sources such as dipoles along the channel, charges on conductors placed near the membrane, etc.

2. Polarized Channel When a voltage is applied to the pore, Eq. (61)must be modified in order to include the effect of the charges on the electrodes; in addition, there is another expression for points lying on the conducting surfaces S,, derived from Eq. (13). We assume that the electrodes are flat circular disks, placed at both sides of the channel at a distance T h' from the center and polarized with k V,.

APPLICATION OF THE INTEGRAL EQUATION METHOD

For simplicity we also take q

= 0. Then

19

we have

r E diel. bound.

r E cond. surf. &r), being in Eq. (66), equal to f V, depending on the position of r. Applying the same numerical technique as in the previous study we obtain =

c Bijq5j + c c Eij+j + C n

m

j=1

j=n+ 1

n

m

4i = j = 1

j=n+ 1

AijOj,

Dijaj =

(i = 1 .. . n),

+ v,, zi = -h' ,

(i = n

+ 1 ... in),

(68)

where A, and D, are related to the potential that is created at point ri by a uniform charge density of unit amplitude over S j . These coefficients may be computed by means of the corresponding analytical expressions given in Eqs. (28)-(36). When the algebraic system is solved for aj and c#I~,we are able to determine the potential at any point of interest. Table I shows field at the center of the channel (in units of Vo/6)and the fractional potential drop across the channel, as functions of the ratio 6 . It must be pointed out that these quantities depend on the electrode position, the tabulated ones corresponding to a distance h' = 6h. Jordan (1982) has reported values for

TABLE I ELECTRIC FIELD AT THE CENTER OF THE CHANNEL AND FRACTIONAI OF THE RATIO 6 POTENTIAL DROPAS FUNCTIONS Field at the center

Fractional potential drop

6

W 0 / 4

v/vo

15.0

0.815 0.794 0.774 0.738 0.648 0.526

0.792 0.772 0.752 0.716 0.625 0.499

10.0

7.5 5.0 2.5 1.25

20

G . MARTINEZ AND M. SANCHO

V& of 20% greater than that shown in Table I; this is presumably due to the fact that the procedure used by Jordan to include the effect of the applied potential is strictly correct only in the limit of very long, narrow channels and overestimates the field in the pore interior (Jordan, 1989).

3. Dipolar Effects It is known that the kinetics of narrow channels, such as Gramicidin in lipid membranes, is strongly influenced by electrostatic interaction between the ion and the permanent dipoles of the polypeptide. Furthermore, several recent studies have focused on the behavior of analogues of Gramicidin A in which one or more amino acids were replaced by others with side chains of different polarity (Andersen et al., 1987; Daumas et al., 1989). To simulate this experimental situation, dipolar rings near the pore wall are superposed to the geometry given in Fig. 5. These distributions are characterized by a total moment p and can have radial and axial components and be situated at different positions along the channel lumen. For the polarized channel, the corresponding integral equations are now

231 +4s(r), x+1

+ 4s(r),

r E diel. bound.,

r E cond. surf.,

(70)

where 4sis a source term containing the contributions of both ion and dipolar rings and represents the potential of these charges in an indefinite medium of permittivity The partitioning of the boundaries into small subareas in which the unknowns-charge densities or potentials-are supposed to be constant gives the corresponding set of algebraic equations. Its solution allows us the determination of the potential along the channel axis for several different situations. After a systematic analysis of the computed data we conclude the following remarkable results: 1) Radial components of the dipole moments have very little influence on the potential profiles. This can be interpreted as produced by the cancellation of the dipole field by the “image dipole” induced in the medium E ~ In. the case of axial dipoles, both potentials add. 2) The effect of “negative” dipoles (pointing toward the channel center) is to increase the central barrier, while positive ones facilitate ion passage. 3 ) Negative dipoles at the center of the channel tend to sharpen the barrier.

APPLICATION OF THE INTEGRAL EQUATION METHOD

21

Positive dipoles tend to widen it and produce a central potential well. 4)Large positive dipoles can produce noticeable wells at the channel mouth. Figure 7 illustrates the effect of two axial dipole rings located at fh in a gramicidinlike channel; in Fig. 8 the contributions of four dipole rings, two at the ends and two at the center, are superposed.

0.4 -

0.2 -

0.0-

-02

-4

-2

2

0

4

z/h

FIG.7 . Potential profile in a channel with one dipole ring at each mouth. (Vo = 25 mV; dipole ring radius rd = 0.99 r,; I : p = - 3 Debyes: 2: p = 0; 3: p = + 3 Debyes).

- O 2 L - -

-40

L

-2 0

1

I

00

-I

L~~

20

A

i

40

z l h

FIG.8. Potential profile in a channel with four dipole rings: two at the center (kh/12.5) and one at each mouth. ( Vo = 25 mV; dipole ring radius rd = 0.99 r,; p = + 8 Debyes).

22

G. MARTINEZ AND M. SANCHO

It can be seen that axial dipoles pointing toward the pore mouths produce binding positions for the ion and produce potential profiles, such as the one depicted in Fig. 8, which have been proposed to explain the currentvoltage characteristics of Gramicidin channels (Levitt, 1986). B. Four-Aperture Electrostatic Lens

The electrostatic lenses that have been used to focus beams of charged particles have usually consisted of either two or three electrodes, each having the form of either an aperture or a cylinder. The focal properties and aberrations of such lenses have been extensively studied (Grivet, 1972; Harting and Read, 1976; Hawkes, 1987).Although multi-electrode lenses (by which we mean lenses consisting of more than three electrodes) are expected to be better for some purposes and to have properties that are more flexible than those of the simpler two and three electrode lenses, they have been studied less often. In characterizing such lenses Heddle (1971), Kurepa et al. (1974) and Chutjian (1979), have made the approximation of treating them as combinations of independent two and three element lenses, which is valid only in a restricted range of geometrical configurations and operating voltages. More recently we have applied our method to the analysis of a four-cylinder lens (Martinez and Sancho, 1983b). As in calculating the axial potential distribution, the technique deals with all the electrodes as a whole; we were able to characterize the operating conditions of practical interest without restrictions. In this paragraph, we present the study of a four-aperture lens following a similar development. 1. Calculation of Electron-Optical Properties

Figure 9 shows a cross-sectional diagram of the lens chosen for study. An external equipotential contour, added for the sake of calculation of the optical parameters, is not shown in the figure. The configuration has a horizontal axis of rotational symmetry and a plane of symmetry perpendicular to this axis (the reference plane). The diameter D of the apertures is taken as the fundamental unit of length, and all the parameters will be expressed in units of D . The spacings S between the electrodes are O S D , and their thicknesses T are 0.05D. It is assumed for convenience that the lens is to be used for focusing electron beams and that the applied voltages V , , V,, V, and V, are measured with respect to the cathode from which electrons originate. We can apply the integral formulation to a set of polarized conductors in vacuum and in absence of space charge and use Eq. (7). For the purpose of calculation, the electrodes are divided into n subareas that have the form of flat circular annuli or narrow cylindrical sections. Under the assumption that the

APPLICATION OF T H E INTEGRAL EQUATION METHOD

FS i b5 i P

23

si

5-050

FIG.9. Cross-sectional diagram of the four-aperture electrostatic lens chosen for study. The fundamental unit of length is the diameter D.The potentials V , , V2,V3 and V, are measured with respect to that of the cathode.

charge density aj is constant on each subsection of area Sj, the potential at the midpoint ri representative of the subsection i can be expressed as n

4i(ri) =

Dijoj,

( i = 1 . ..n),

j= I

with

Having evaluated coefficients Dij by means of the appropriate formulae given in Section 111, Eq. (71) can be solved to obtain the charge densities. At this stage we are able to determine the potential at any point within the lens. In particular, we can compute the axial potential, &), that will allow the characterization of its optical parameters. Since the reference plane of the lens is a plane of reflection symmetry it is possible to halve the number of subsections required by making use of symmetric and antisymmetric configurations to express 4(z) in terms of the superposition (Martinez and Sancho, 1983b)

24

G . MARTINEZ AND M. SANCHO

where +o, &,, +c are the axial potentials when the electrode potentials (Vl, V2,V,, V,) have thevalues(1, - 1,-1, l),(-1, -1,1, l ) , a n d ( - l , l , - 1 , l ) respectively. For each of these sets of electrode potentials the charge distribution is either symmetric or antisymmetric about the reference plane, and and hence only subsections on one side of the plane need be considered. The first order properties of the lens are completely characterized by the focal and midfocal lengths, which can be obtained by integration of the Picht equation (Grivet, 1972)

where R ( z )is the reduced ray path and where the derivative +’(z) is determined by numerical differentiation of +(z). The integration of Eq. (74) has been carried out by a second order Runge-Kutta method. Because the starting and final points of the trajectories are taken to be in field-free regions on either side of the lens, all the values obtained are asymptotic parameters. Calculated values of the object focal and midfocal lengths, f l and F , respectively, and image midfocal length F2 as functions of V2/V, are given in Fig. 10. The corresponding values of the image focal length f 2 can be deduced from the relationship

A comparison with the parameters of the four-cylinder lens (Martinez and Sancho, 1983b) shows a very similar behavior, although the lens studied here is, in general, stronger. Since the trajectories of the charged particles in the lenses having voltages Vl, V,, V3 and V, are the time-reversed ones of those in the retarding lenses having V ; = V,, V ; = V3, V ; = V, and Vk = V , , the calculated parameters can be used for obtaining those of the complementary retarding lenses (see Martinez and Sancho (1983b) for the conversion formulae). In this way the range of voltage ratios V4/V1 for which the focal lengths have been calculated can be extended to include retarding lenses having V4/V1 as low as 0.1. The spherical aberration can be characterized by the third-order coefficient C, defined by the relation (Grivet, 1972)

Ar

=

MC,a;,

(76)

where Ar is the radius of the disk formed in the Gaussian image plane by nonparaxial rays starting from an axial object point with a maximum half angle a. and M is the linear magnification for a given object position. Further, it can be shown that C, is a fourth-order polynomial in 1/M (Harting and Read, 1976): C,(M) = C,

+ C,,M-’ + CS2M-, + C,3M-3 + C,,M-,.

(77)

APPLICATION OF T H E INTEGRAL EQUATION M E T H O D

25

I FIG.10. The object focal length f , / D , object midfocal length F , / D and image midfocal length F , / D as functions of V J V , , Each plot corresponds to a fixed voltage ratio V4/V,.and the numbers on the curves indicate the values of VJV,. Note that the horizontal scale is logarithmic for V2/V, > I and linear for Vz:V, < I.

26

G. MARTINEZ AND M. SANCHO

D

+-

0.51 I -0.5 0

1'

1

-0

O.!

-I

0

05

1

2 VJVI

(4 FIG. 10. (Cont.)

5

10

APPLICATION OF THE INTEGRAL EQUATION METHOD ~

.

0

-

l i

. 0

l i

1

-05

0

05

2

1

V,IV>

(f )

FIG. 10. (Cont.)

A

1

5

10

27

28

G. MARTINEZ A N D M. SANCHO

0

05

1

0

05

1

I

-05

-

2

I

I

5

-

2

L

_

I

_

5

U

APPLICATION OF THE INTEGRAL EQUATION METHOD - 7I

1

TTT

L

L

10

0

<

c

1

1

-05

0

05

1

-05

0

05

1

L

2

5

x)

2

5

10

V d v,

(1)

FIG. 10. (Con[.)

29

30

G . MARTINEZ A N D M. SANCHO

u, 0

-05

-05

0

05

2

1 v2 1

v,

(1) FIG.10. (Cont.)

5

10

APPLICATION OF THE INTEGRAL EQUATION METHOD

31

Thus, the coefficients Csi are frequently used to characterize the spherical aberration. Table I1 shows the values obtained for the einzel operating mode V4/V1 = 1. 2. Energy Scanning at Constant Image Position and Magnification Triple-electrode electrostatic lenses have two variable voltage ratios, and so they can be used to focus a beam of charged particles in such a way that the image position is kept constant while the ratio of the final to initial energy of the charges is varied (Heddle and Kurepa, 1970; Harting and Read, 1976). In general, the linear and angular magnifications are not constant. If it is required to keep two parameters constant, such as both the position and magnification of an image, a third variable, voltage ratio, is necessary and the lens must consist of at least four electrodes. In a previous study (Martinez et al., 1983) we showed how a four-cylinder lens can be used to provide an image at a fixed position together with either a constant linear or angular magnification. In what follows, we extend the analysis to a four-aperture lens. The geometrical configuration of the lens chosen for study is the same as that considered in the preceding subsection, (cf. Fig. 9). For a given set of electrode polarizations, the image linear magnification M , the focal lengths fl and f z , the midfocal lengths F, and F2 and the object and image distances P and Q are related through the expressions (Harting and Read, 1976)

In choosing the most appropriate combinations of P, Q and M values, it is important to bear in mind the behavior of the system as the voltage ratios V,/Vl, V3/V1 and V4/V1 are changed. As an example we show in Fig. 1 1 the relationship that must be maintained between V2/V1 and V3/V1 to keep either Q constant (full curves) or M constant (broken curves), when P and V4/V1 have the fixed values 2 and 5 respectively. If both Q and M are required to be constant, then the necessary values of Vz/Vl and V3/V1 are given by the points at which the full and broken curves cross. For example there are two crossing points corresponding to Q = 4, M = -2, one corresponding to Q = 2, M = - 1, but none corresponding to Q = 2, M = - 2 . By plotting such curves for other values of V4/V, (while keeping P constant), we are thus able to determine the relationship that must be maintained between the electrode potentials for those combinations of P, Q and M for which crossing points exist. Not all the crossing points represent experimentally suitable modes of the lens. Thus, the crossing points for Q = 4,M = - 1 have low values of both VJV, and V3/V1 and occur in a region where the Q and M curves tend to lie close to each other, which implies that Q and M are sensitive to small changes

32

G. MARTINEZ AND M. SANCHO TABLE I1 SPHERICAL ABERRATION COEFFICIENTS FOR THE MODEV4/Vl

=

1

V3jVl = 0

-0.3 0.0 0.5 1.o 2.0 5.0 10.0

6.47 E + 1 9.00 EO 1.07 E + 2 4.90 E + 2 4.65 E + 2 2.61 E + l 4.52 EO

5.29 EO -2.67 E + 1 -4.05E+2 -1.94 E + 3 - 1.80 E + 3 -8.43 E + 1 -9.69 EO

1.75 E + 1 3.68 E + 1 5.84 E 2 2.90 E + 3 2.64 E 3 1.08 E + 2 1.02 E + 1

+ +

6.15 EO -2.67 E + l -3.81 E + 2 -1.94 E + 3 - 1.73 E + 3 -6.62 E + l -6.38 EO

1.01 E + l 9.00 EO 9.54 E + 1 4.90 E + 2 4.30 E + 2 1.65 E + l 2.39 EO

-4.98 -4.05 -1.38 -3.35 -1.69 -9.11 -7.54

E+ 1 E+2 E+4 E+5 E+4 E+ 1 EO

1.47 E + 1 1.07 E + 2 3.47 E + 3 8.38 E + 4 4.20 E + 3 2.36 E + 1 2.84 EO

-3.74 -1.79 -1.73 -3.86 -5.03 -9.08 -9.30

E+2 E+3 E+4 E+4 E+3 E+ 1 EO

9.88 E + l 4.63 E + 2 4.37 E + 3 9.65 E + 3 1.27 E + 3 2.59 E + 1 3.77 EO

-6.73 -8.33 -9.98 -1.01 -8.05 -2.67 -7.22

E+ 1 E+ 1 E+ 1 E+2 E+ 1 E+ 1 EO

2.21 E + l 2.58 E + 1 2.83 E + 1 2.70 E + I 2.10 E + I 9.34 EO 4.05 EO

VJV, = 0.5

-0.3 0.0 0.5 1.o 2.0 5.0 10.0

1.25 E + I 9.53 E + 1 3.47 E + 3 8.38 E + 4 4.39 E + 3 2.86 E + 1 3.80 EO

-4.57 E + 1 -3.81 E + 2 - 1.38 E + 4 -3.35 E + 5 - 1.73 E + 4 - 1.01 E + 2 -9.10 EO

6.90 E + 1 5.83 E + 2 2.07 E + 4 5.03 E + 5 2.57 E + 4 1.40 E + 2 1.08 E + I VJV, = 2

-0.3 0.0 0.5

1.o

2.0 5.0 10.0

8.88 E + 1 4.28 E + 2 4.19 E + 3 9.69 E + 3 1.27 E + 3 2.11 E + I 2.83 EO

-3.54 E + 2 - 1.72 E + 3 - 1.69 E + 4 -3.87 E + 4 - 5.03 E + 3 -8.11 E + l -7.39 EO

5.40 E + 2 2.63 E + 3 2.56 E + 4 5.79 E 4 7.53 E + 3 1.25 E + 2 1.10 E + 1

+

VJV1 = 5

-0.3 0.0 0.5 1.o

2.0 5.0 10.0

1.18 E + 1.64 E + 2.33 E + 2.74 E + 2.57 E + 9.34 EO 3.10 EO

1 1 1 1 1

-4.81 E + l -6.55 E + I -9.02 E + I - 1.02 E + 2 -9.02 E + l -2.67 E + 1 -4.70 EO

8.21 E + l 1.07 E + 2 1.39 E + 2 1.49 E + 2 1.24 E + 1 3.56 E + 1 7.01 EO

APPLICATION OF THE INTEGRAL EQUATION METHOD

,

m

I

I

1 I , [ /

2

Q=

02

1

33

L\

I

I

I I l l 1

1

I

1

I

I

I / / , ,

v3/v,.2

x)

FIG. 1 1 . The relationships that must be maintained between VJV, and V,/V, when P V'/V, = 5, and either Q is constant (full curves) or M is constant (broken curves).

=

2,

in VJV, or V3/V1. Furthermore, the angle of crossing is very small at these points, and so it is difficult to establish the values of the potentials accurately. This type of working point is therefore excluded from further study. The other crossing points showed are suitable, however. The two that have the highest values of V,/V, give the smallest aberration coefficients, and so we have searched for this type of working point for all the combinations of P, Q and M that we have considered. When this type does not exist or when it exists over only a small range of values of V4/Vl, we give, instead, data for the crossing points that have the lowest values of V3/Vl. For convenience, we present the data on the required voltage ratios in a parametric form for five sets of values of P, Q and M . The voltage ratios of each set are fitted by least squares polynomials giving

where x = V4/Vl. For sets 1 and 4, two series of coefficients A,, and B,, are necessary to cover the whole range of the variable x. The values of the fitted coefficients for the five sets are given in Table 111. If one of the focal parameters is known for a constant P, Q and M condition then the remaining three can be obtained from Eq. (78).We therefore show in Fig. 12 the dependence on V4/V1 of the object midfocal length F , for each of the five sets.

TABLE 111 COEFFICIENTS FOR

THE

POLYNOMIALS GIVING THE VOLTAGE hnos

Set

number

1

1

2

3

2.0 2.0 - 1.0 1.5124 E + 1 1.5588 E + 1 - 6.5774 EO 1.5366 EO - 2.0945 E- 1 1.7245 E-2 -8.4145 E-4 2.2353 E - 5 - 2.4874 E - 7 2.6139 EO 2.9010 E + I -7.3381 EO 1.3194 EO - 1.5568 E- 1 1.1747 E-2 - 5.4223 E - 4 1.3887 E-5 -1.5075 E-7 1.o - 20.0

2.0 2.0 - 1.0 8.2951 E + 2 - 1.9125 E + 2 1.9825 E + 1 - 1.1499 EO 4.1193 E-2 -9.3253 E-4 1.3037 E-5 -1.0295 E-7 3.5185 E- 10 - 2.9730 E + 2 9.1443 E + l -9.6829 EO 5.9230 E - 1 - 2.2430 E - 2 5.3707 E-4 - 7.9403 E - 6 6.6283 E - 8 -2.3945 E-10 20.0 - 52.0

3.0 3.0 - 1.0 4.0630 EO 6.3111 EO - 3.4702 EO 1.1511 EO -2.2298 E- 1 2.5890 E - 2 -1.7374 E-3 5.9895 E-5 - 7.5304 E - 7 -1.0513 EO 1.3352 E + 1 -6.1856 EO 2.1819 EO -5.3443 E-1 8.4363 E - 2 -8.1195 E-3 4.3129 E-4 - 9.6749 E - 6 1.0 - 11.2

4.0 4.0 - 1.0 1.9994 EO 4.8849 EO -2.1187 EO 5.3373 E- 1 -4.7132 E-2 - 3.2342 E - 3 6.3283 E-4 0.0 0.0 - 1.7107 EO 1.3221 E + I -9.8541 EO 4.7535 EO - 1.3519 EO 2.0143 E- 1 -1.2227 E-2 0.0 0.0 1.0 - 5.2

FOR

Set number

P

Q M A0 A, A2 A3 A4 A5 A6 A, BO

Bl B2 B3

B4 B5 B6

B, B8

EACHOF

THE

FIVESETS

4

4

5

2.0 4.0 - 2.0 1.8732 EO 1.4658 E + 1 - 4.1764 EO 8.6106 E- 1 -1.0748 E-1 7.3073 E-3 -2.0601 E-4 0.0 0.0 3.6845 E- 1 4.9228 EO 3.1312 E-1 - 1.8914 E- 1 2.9529 E-2 -2.1848 E-3 6.3684 E-5 0.0 0.0 1.0 - 9.0

2.0 4.0 - 2.0 -1.9149 E + 2 9.8953 E + 1 -1.8056 E + I 1.7640 EO -9.5286 E-2 2.6983 E-3 -3.1261 E-5 0.0 0.0 1.9772 E + 2 - 8.2800 E + 1 1.5880 E + 1 -1.5418 EO 8.1520 E-2 - 2.2372 E - 3 2.4816 E-5 0.0 0.0 9.0 - 20.6

4.0 2.0 -0.5 5.4690 EO -6.1675 E-1 8.5818 E - l - 3.5559 E - 1 9.7738 E - 2 -1.6683 E-2 1.6827 E - 3 -9.1371 E-5 2.0560 E - 6 5.2193 EO 1.2890 E + 1 -6.9861 EO 2.4832 EO - 5.7224 E - 1 8.3186 E-2 - 7.3486 E - 3 3.5920 E - 4 -7.4444 E-6 1.0 - 11.5

APPLICATION OF THE INTEGRAL EQUATION METHOD

35

V' I v. Fici. 12. Variation of F , / D with VJV, for the five sets of values F', Q and M specified in Table 111.

To characterize the aberrations of the lens we use the third order aberration coefficient C, defined by Eq. (76). The calculated values of this coefficient are shown in Fig. 13 as a function of V4/V,, for each of the sets. The data given in Table 111 and Figs. 12 and 13 refer to lenses for which V,/V, 2 1. The corresponding data for retarding lenses can be obtained by comparing the four-aperture lens having voltages V,, V 2 , V, and V4 with the time-reversed analogue having the voltages V', = V,, V ; = V,, V ; = V, and V ; = V, respectively. The polynomial expansions given by Eqs. (79) now become

v; 1 N B,(x')'-", v;

v;

-=

v;

n=O

c N

-=

An(X')l-",

n=O

where x ' = V J V ; and the object and image distances and magnification to which they relate are

p'=

Q,

Q'=

p,

M ' = M-'.

(81)

The image midfocal length F ; and the spherical aberration coefficients can also be derived from the data in Figs. 12 and 13 and the corresponding conversion formulae (Martinez et al., 1983).

36

G . MARTINEZ A N D M. SANCHO

V'/ v, FIG.13. Variation of CJD with V,/V, for the five sets of values, P, Q and M specified in Table 111.

The retarding version of the set labeled 4 has the same values of P, Q and M (namely 4, 2 and -0.5 respectively) as the accelerating version of the set labeled 5. Hence the total range of values of V4/V, for which these values of P, Q and M can be maintained extends from 1/20.6 to 11.5, thereby covering more than two decades. Similarly sets 1,2 and 3, all of which are self-reversing (in the sense that P = Q = P' = Q', M = M ' ) , have V4/V, ranges of 1/52 to 52, 1/11.2 to 11.2 and 1/52 to 5.2 respectively. These ranges are notably wider than those obtained by the authors for the four-cylinder lens (cf. Martinez et al., 1983). This characteristic together with the fact that the four-aperture lens is comparatively more compact makes it, in general, preferable. C . Space-Charge Effects in Lenses

An interesting aspect of the integral equation method is that it lends itself readily to the solution of electron-optic problems involving space charge. However, as has been noted by Kasper (1987), the direct evaluation of the integral contributions of space charge elements to the potential and the field may represent a great amount of computing time.

APPLICATION OF T H E I N T E G R A L E Q U A T I O N METHOD

37

Renau et a / . (1982) have described the general application of the formulation as well as their version of the numerical technique. These authors included space-charge effects using the approximation of linear segments of charge. Given the error cumulative characteristic of the trajectory computation and the iterative scheme used in this algorithm, it is advantageous to use analytical expressions for the elementary contributions of the space charge. We illustrate this procedure in the following study. 1. Formulation of the Problem

Figure 14 shows a cross-sectional diagram of the system under study. We are dealing with a lens proposed by Liebl (1983) for a SIMS equipment. It consists of three plane-apertured electrodes arranged coaxially on the normal of a conducting surface. For the given values of the potentials applied to the electrodes and neglecting space-charge effects,the lens focuses a primary beam of single charged positive ions into a very thin spot and, at the same time, acts as an emission lens for secondary negative ions originating from a surface point. In a previous work (Martinez er ul., 1987), we have obtained some of the trajectories for primary and secondary ions and the results agree qualitatively well with those given by Liebl. Now, we study the case in which the perveance of the primary beam, defined as P = M ” 2 / V - 3 ’ 2 for singly charged ions of mass number M , is high enough to cause space-charge effects. Consider the primary beam traveling through the lens. The integral equation for the potential at any point orl the electrodes is the same as in Eq. (7) except for a source term that takes into account the contribution of the beam; hence

-

v1

t

OLh ~

v,

~

V, h i

TARGFT

v,:o

FIG.14. Cross-sectional diagram of the assembly. Primary ions, generated in a region at potential V,. enter the lens with energy e(Vp - V 3 ) ;secondary ions leave the target with energy eFl I 2- 10 eV. The operating voltages are V, = V2 = 3.55 V, and V,, = 4.5 V,.

38

G. MARTINEZ A N D M. SANCHO

where a(r')are the charge densities on the surface S, of the conductors and p(r') is the beam charge distribution in the volume V,. For the numerical solution of Eq. (82) we make, similar to the previous cases, a division of the conductor surfaces into n subareas and the beam into m volume elements and assume that the charge densities in each of them are constant. For simplicity, we take the volume elements with the form of small cylinders, and the radius of each cylinder is taken to be equal to that of the beam envelope at zj = (zlj + zzj)/2, where z l j and z z j are the axial coordinates defining the cylinder. We then have n

q5i(ri)=

n+m

1

Dijaj +

j= 1

Kjpj,

(i

=

1 ... n),

j=n+ I

where D, is given by Eq. (72) and

Having in mind the physical interpretation of D, and &j we can compute these coefficients by means of the corresponding expressions given in Section 111 (see also Martinez and Sancho (1 988) for details). 2. Computation of the Trajectories The solution to Eq. (83), together with the trajectories in the beam, are obtained by an iterative scheme. This has been done with some approximations in order to simplify the computer program. First, the primary ion source is ignored and the integration starts at a distance h from the third aperture with zero slope; second, a uniform beam density along the radius has been assumed; third, collisions between primary and secondary ions are ignored and the beam is treated as laminar; and finally, the effect of the axial component of the beam is neglected as it is much lower than the one produced by the lens. As a first step in the iteration, the primary beam profile is determined with all the P k values equal to 0. The resulting beam is divided into small cylinders and a charge density Pk is assigned to each, according to the current density and velocity at the point (rk,zk). The surface charge densities are then recalculated by means of the expression

obtained by matrix inversion of Eq. (83). The beam profile is redetermined using the new oi and the pk. Several iterative cycles are completed until the beam profile does not change appreciably.

APPLICATION OF THE INTEGRAL EQUATION METHOD

39

In calculating each new beam profile, we need to know the electric field created by the beam itself. To obtain the radial component of the field, we use Eq. (60). Adding the contribution of the lens we have the total field at each point of the trajectory and then the integration is performed by a central difference formula. Figure 15 illustrates the results for five values of the perveance; as P increases, the lens is less effective in focusing the primary beam and the repulsion becomes more and more important. The number of required iterations also increases with P from two to five. Figure 16 shows the influence on the the secondary ions. For P = ( A V - 3 ' 2 ) the trajectory for a secondary ion, which emerges with an initial energy of 4 eV and parallel to the axis, is very similar to that obtained ignoring space charge. For higher perveances, the lens focusing action is screened and even annulated by the positive beam.

1 . , . , . , 20

10

,

. , ,

z(h)

r

,

30

l

,

40

FIG. 15. Profiles of an Ar' ion beam for five values of the perveance. The target is located at z = 0 and the electrodes at z / h = I , 2, and 3, respectively.

20.

lo-'?

L

05

lo

.

,

m

30

. - , 40

z(h)

FIG.16. Trajectories of a secondary negative ion of atomic mass 100 for three values of the perveance of the primary beam.

40

G. MARTINEZ A N D M. SANCHO

V. CONCLUSIONS The examples presented in the previous section show clearly that the integral equation method represents a quite advantageous formulation for the majority of electrostatic problems, the exception being those with permittivity varying continuously through the medium. The method has several characteristic advantages: the geometry effective dimension is reduced by one; the potential and field are obtained at any particular point independently from others; and for a given geometry, the matrix coefficients can be obtained once and then used for different conditions of polarization or source distributions. It has been argued that the integral equation method is awkward to apply because it requires numerical evaluation of complicated integrals appearing in the matrix elements due to the use of nontrivial basis functions. We have shown that these coefficients can be calculated analytically-for systems with rotational symmetry-without loss of accuracy. This can be achieved by taking constant basis functions and making a nonuniform division of the boundaries according to the expected variation of the fields along them. The accuracy of the results depends mainly on the number of subareas used to simulate the system. In all the studied cases, fulfillment of boundary conditions permits an error estimation for the potential values less than 0.5%. It is believed that this is quite tolerable for most practical purposes, since the actual physical problems will seldom coincide with the proposed models. This high precision is possible with a moderate matrix size. For instance, the matrix maximum dimension used for the ion channel model was 80 x 80, which implies an optimum behavior in the computing time and memory size required. Significant developments of the integral equation method are desirable and also expected in the near future. Analysis of systems with not exact rotational symmetry, as the gramicidin channel, could be undertaken by a perturbative technique without introducing an excessive complexity. In the Electron Optics field, the introduction of nonuniform space charge beams would be useful for many practical problems. Work is, at present, being carried out in both these directions.

REFERENCES Algora del Valle, C., Sancho, M., and Martinez, G . (1987). J . Appl. Phys. 61,4571. Andersen, 0.S. (1983).Biophys. J . 41, 119. Andersen, 0.S., Koeppe, R. E. 11, Durkin, J. T., and Mazet, J. L. (1987). In “Ion transport through membranes,” p. 295. Academic Press, New York.

APPLICATION OF T H E INTEGRAL EQUATION M E T H O D

41

Byrd, P. F.. and Friedman. M. D. (1971). “Handbook of Elliptic integrals for Engineers and Scientists.” Springer-Verlag, Berlin. Chutjian, A. (1979). Rev. Sci. Instrum. 7,981. Daumas, P., Heitz, F., Ranjalahy-Rasoloarijao, L., and Lazaro, R. (1989).Biochimie 71.77. Durand, E. (1964). “Electrostatique 1.” Masson, Paris. Fromter, E. (1983). In “Biophysics.” (W. Hoppe, W. Lohmann, H. Mark1 and H. Ziegler, eds.). p. 465. Springer-Verlag, Berlin and New York. Gerald, C. (1984).“Applied Numerical Analysis.” Addison-Wesley, Massachusetts. Gradshteyn, I. S., and Ryzhik, 1. M. (1980). “Tables of Integrals, Series and Products.” Academic Press, New York. Grivet, P. (1972). “Electron Optics.” Pergamon Press, Oxford. Harrington, R. F. (1968). “Field Computation by Moment Methods.” Macmillan, New York. Harting, E., and Read, F. H. (1976).“Electrostatic Lenses.” Elsevier, Amsterdam. Hawkes, P. W. (1987). Nud. Instrum. and Merh. A258.462. Heddle, D. W. 0.(1971).J . Phys. E 7.981. Heddle, D. W. 0..and Kurepa, M. V. (1970). J . Phys. E 3, 552. Jackson. J . D. (1980).“Electrodinamica Clasica.” p. 76. Alhambra, Madrid. Jordan, P. C. (1982). Biophys. J . 39, 157. Jordan, P. C. (1986). In “Ion Channel Reconstitution.” ( C . Miller, ed.), p. 37. Plenum Press, New York. Jordan. P. C. (1989).Private communication. Jordan, P. C., Bacquet, R. J., McCammon, J. A., and Tran, P. (1989).Biophys. J . 55, 1041. Kasper, E. K. (1987). Nucl. Instrum. and Meth. A258.466. Kellog. 0. D. (1967).“Foundations of Potential Theory,” p. 160. Springer-Verlag, Berlin. Kurepa, H. V., Tasic M. D., and Kurepa, J. M. (1974).J . Phys. E 7,940. Levitt, D. G . (1986). Ann. Rev. Biophys. Biophys. Chem. 15, 29. Liebl, H. (1983).Int. J . Mass Specrrom. Ion Phys. 46, 51 1 . Martinez. G., and Sancho, M. (1983a). Am. J . Phys. 51, 170. Martinez, G., and Sancho, M. (1983b).J . Phys. E . 16, 625. Martinez, G., and Sancho, M. (1988). Int. J . Mass Specrrom. Ion Processes 84, 221. Martinez, G., Sancho, M., and Read, F. H. (1983).J . Phys. E 16,631. Martinez, G., Sancho, M.. and Garcia-Galan, J. C. (1987). An. Fis. Ser. B 83, 225. Munro, E. (1987). Nucl. Instrum. and Mcth. A258.443. Parsegian, V. A. (1969). Nature 221,844. Parsegian, V. A. (1975). Ann. N . Y . Acad. Sci. 264, 161. Renau, A., Read, F. H., and Brunt, J. N. (1982).J . Phys. E 15,347. Steele, C. W. (1987). “Numerical Computation of Electric and Magnetic Fields.” Van Nostrand Reinhold. New York.

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ADVANCES IN ELECTRONICS A N D LLECTRON PHYSICS . VOL 81

Energy-Filtering Transmission Electron Microscopy L . REIMER

.

Physikalischrs Institut. Unitwrsitai Munster Munsfer. FRG

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . II . Physics of Elastic and Inelastic Electron Scattering . . . . . . . . . . A . Elastic Scattering . . . . . . . . . . . . . . . . . . . . . B. Inelastic Scattering . . . . . . . . . . . . . . . . . . . . C. Electron Energy-Loss Spectrum (EELS) . . . . . . . . . . . . . D . Multiple Scattering Effects in the Energy-Loss Spectrum . . . . . . . I11. Instrumentation and Modes of Operation . . . . . . . . . . . . . A. Spectrometers and Filter Lenses . . . . . . . . . . . . . . . B . Dedicated Scanning Transmission Electron Microscope . . . . . . . C . Electron Energy-Loss Spectroscopy in a Transmission Electron Microscope D . Operation Modes of an Energy-Filtering Electron Microscope . . . . . IV . Electron Spectroscopic Imaging . . . . . . . . . . . . . . . . . A . Review of Imaging Modes . . . . . . . . . . . . . . . . . B . Zero-Loss Imaging . . . . . . . . . . . . . . . . . . . . C. Plasmon-Loss Imaging . . . . . . . . . . . . . . . . . . D . High Energy-Loss Imaging . . . . . . . . . . . . . . . . . E . Elemental Mapping . . . . . . . . . . . . . . . . . . . . V . Electron Spectroscopic Diffraction . . . . . . . . . . . . . . . . A . Amorphous and Debye-Scherrer Ring Patterns . . . . . . . . . . B . Single-Crystal Diffraction Patterns . . . . . . . . . . . . . . . VI . Summary and Prospects . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

43 44 44 47 49 58 62 62 67 69 70 75 75 I6 91 96

.

. . .

.

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

. . . . . . . .

102 105 105

. .

Ill

. . . .

. . 118 . . 119 .

.

119

I . INTRODUCTION

In conventional transmission electron microscopy (CTEM). contrast and resolution are obtained by elastically scattered electrons . The contribution of inelastically scattered electrons to the image is often useless because of the delocalized interaction or the chromatic aberration of the objective lens . Though thin specimens for high resolution result in a small fraction of inelastically scattered electrons. the influence of inelastically scattered electrons and their delocalized interaction have to be taken into account for the 43

.

Copyright 1991 by Academic Press Inc All righls o l reproduction in any form reserved . '

~

8

ISBN O-l2-014681-9

44

L. REIMER

discussion of contrast in crystal-lattice imaging, for example. For thick specimens, the large fraction of inelastically scattered electrons blurs the image by chromatic aberration. In analytical electron microscopy (AEM), the analysis of emitted x-rays by means of a lithium-drifted silicon detector is an established method for the measurement of local elemental composition. Increasing use is made of electron energy-loss spectroscopy (EELS) of transmitted electrons where the energy-loss spectrum is generated by a prism spectrometer below the camera chamber. Information about crystal structure and orientation is furnished by electron diffraction. Most of the analytical electron microscopes can work with a nanometer electron probe for local analysis. In energy-filtering transmission electron microscopy (EFTEM), the zeroloss electrons or electrons passing an energy-loss window of the EELS are used for image formation. This can be achieved by using the scanning mode in a dedicated scanning transmission electron microscope (STEM) or in a TEM with a spectrometer behind the camera chamber or by using an imaging filter lens in the column of a TEM. The conventional TEM and STEM modes can be combined in this way with the mode of electron spectroscopic imaging (ESI) and electron spectroscopic diffraction (ESD), and different modes can be used to record an EELS spectrum. An EFTEM can therefore make full use of elastic and inelastic electron-specimen interactions. This review summarizes the physical background and the possibilities of EFTEM. After a review of the relevant physics of elastic and inelastic scattering in Section 11, the instrumentation of EFTEM is described in Section 111. The theoretical approaches for understanding the contrast and examples of application are presented in Section IV for electron spectroscopic imaging (ESI) and in Section V for electron spectroscopic diffraction (ESD).

11. PHYSICS OF ELASTIC AND INELASTIC ELECTRON SCATTERING

A . Elastic Scattering

Elastic scattering of electrons involves a collision with the nucleus, and the kinetic energy transferred to the nucleus can be neglected for small scattering angles 6' due to the low electron mass. Even the excitation energy of a phonon is lower than 0.1 eV. Larger energy losses can only be observed at large scattering angles. For 80 keV electrons scattered through 6' = 90" at copper atoms, the energy transferred to the nucleus is of the order of 1 eV (Boersch e f al., 1967). However, in high voltage electron microscopy with 0.2-1 MeV, the energy loss and energy transfer to the nucleus can increase to a few tens

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

45

of eV, which can cause a displacement of atoms in solids. Consequently, 50 mrad contributing to an those elastically scattered electrons with 0 I image or a diffraction pattern can practically be treated as zero-loss electrons, especially because the energy spread of thermionic and field-emission electron guns is of the order of 0.5-2 eV and 0.2-0.3 eV, respectively. For resolving the energy losses by electron-phonon interactions, a monochromatization of the primary beam to the order of 1 meV is necessary (see Section III.A.2). The differential cross-section do,,/dR of elastic scattering can be described as a Rutherford scattering at the Coulomb potential V(r) of the nucleus, which is screened by the atomic jellium, V(r)

-

e2Z e2 e2Z + z - __ exp( - r/R), 4ne0r j = ! 4ne0(r- rj) 4 7 1 ~ ~

= -~

1

(1)

where r and rj are the coordinates of the incident electron relative to the nucleus and the Z atomic electrons, respectively. In a Born approximation of the quantum-mechanical calculation of the differential elastic cross-section da,,/dR, the last term of Eq. (1) (Wentzel model of screening) can be used with an atomic radius R = U,Z-''~ (aH= 0.0569 nm = Bohr radius of hydrogen atom), resulting in

where E

= eU

+

do,,

4Z2R4(1 E / E J 2

di2

4

-- -

and E,

= moc2 =

I c1 + ( 0 / 4 ) 2 1 2 '

51 1 keV and

O,,

= ii2nR

(3)

is the characteristic screening angle of the order of 30-40 mrad for E 80 keV. The total elastic cross-section is defined by gel =

l:

(dae,/dQ)27tsin H d6, N

6:

(dael/dR)2n0do,

=

(4)

and substitution of Eq. (2) in Eq. (4)(Lenz, 1954) results in

in units of cm2, where 4, = u/c. The dash-dotted line in Fig. 1 shows this dependence of a,, on the atomic number Z. Consideration of the atomic shell structure by Hartree-Slater functions or the Thomas-Fermi model for high Z (Schafer et nl., 1971) results in the dashed line. The latter values have been

46

L. REIMER

1

1

2

3

5

10

4

. , . . . I

20 30 50

90

2-

FIG. 1. Total elastic cross-sections uC,for 100 keV electrons versus atomic number Z ; full line: Eq. (6) (Langmore et al., 1973); dash-dotted line: Eq. (5); dashed line: calculated (Schafer et a!., 1971);circles: experiments for C , Ge and Pt (Reimer and Sommer, 1968).

approximated (Langmore et al., 1973) by

which is shown by the full line in Fig. 1. These calculations of gelresult from scattering at free atoms. The dense packing of atoms in a solid can be considered in first order by an overlap of neighbouring atomic potentials (muffin-tin model) and results in lower values of dg,,/dR at small scattering angles and therefore in smaller values of gelas shown by three experimental values (0)for C , Ge and Pt (Reimer and Sommer, 1968) in Fig. 1 (see also values of the mean-free-path mass thickness x,, = l/Na,,, identical with x, of the Lenz theory, for 50-300 keV electrons in Table I). The characteristic angle 8, for elastic scattering does not agree well with the value calculated by Eq. (3) from the Lenz theory. According to Eq. (2), it should be possible to obtain 8, from the dependence of experimental differential cross-sections da,,/dR on 8. However, with the exception of electron scattering on gas targets, multiple scattering cannot be avoided, and for the later description of scattering contrast it is more useful to fit experimental values of transmission for different apertures (Section IV.B.l) by an appropriate set of xel and 8, values (Table I).

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

47

TABLE I VALUESOF THE TOTALMEAN-FKEE-PATH OF ELASTIC SCATTERING Y,, IN UNITS OF pg/Cm2 AND THE CHAKACTERISTIC ANGLE 0, OF ELASTIC SCATTERING IN mrad FOR C, Ge, Pt AND

DIFFERENT ELECTRON ENERGIES E I N keV. C

Ge

E

%I

0,

.Ye I

50 80 100 300 7 50 1200

27 39 47 114 139 168

59 33 28.8 17.8 10.2 6.5

12.3 17.5 20 42 59 62

Pt 0” 40.3 35 31.2 19.0 11.5 6.8

&I

12.1 16.5 19 31.6 51 47

00 47.4 40.5 38.6 16.2 13.2 8.0

B. Inelastic Scattering Inelastic scattering results from the interaction of incident electrons with atomic electrons. The total kinetic energy is not conserved but reduced by the energy that is needed to excite an electron from the initial (0)to the final state (n).The cross-section of such an inelastic scattering process can be calculated using the golden rule of quantum mechanics:

The wavefunctions I), and I), are multiplicatively composed of incident and scattered plane waves exp( -2nik * r) with wavevectors k, and k, and wavefunctions uo and u, of the atomic electrons, respectively. Substitution of the potential V ( r )from Eq. (1) results in

where

is the generalized oscillator strength (GOS);the unit vector u is parallel to the scattering vector q‘ = kn - k, with Iq’12 = (8’ + O ; ) / A 2 and

-

AE E,+ E 0, = AE/mv2 = - AE/2E E 2E,+ E ~

48

L. REIMER

denotes a characteristic angle of inelastic scattering with an energy loss AE. In case of an ionization, the atomic electron can be excited to a continuum of final states and a GOS per unit energy loss dfon(q’,A E ) / d ( A E )results in the double-differential cross-section

This shows that an accurate knowledge of atomic eigenfunctions and the band structure in solids is necessary to calculate inelastic cross-sections. For the discussion of contrast effects it is often sufficient to have a good estimate of the fraction of inelastically scattered electrons as a function of atomic number without knowing the detailed EELS. Inelastic cross-sections reported by Inokuti (1979) and Eusemann et al. (1982) are shown in Fig. 2 as dashed and dotted lines, respectively, and the approximate formula (Wall et al., 1974)

as a full line, where gE = J/mu2 and J N 13.52 = mean ionization potential. These calculations for single atoms have to be used with care because the

- 91 - 01

1

2 3

10

20 30

90

ZFIG.2. Total inelastic cross-sections uin for 100 keV electrons versus atomic number Z ; calculated by Eq. (12) (Wall et al., 1974) (full line), by lnokuti (1979) (dashed line), by Eusemann et a/. (1982) (dotted line) and by Ashley and Ritchie (1970) for plasmon losses (triangles); experimental values by Isaacson (1977) (circles).

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

49

wavefunctions and energy states of the outer electrons, which strongly contribute to oinrare quite different in a solid. Figure 2 contains two calculations (triangles) using a formula of Ashley and Ritchie (1970) for an electron plasma. Measurements of oin by Isaacson (1977) are plotted in Fig. 2 as circles. These values can be approximated by Eq. ( 1 2). A n important quantity for calculating the scattering contrast (Section 1V.B.I ) and estimating the fraction of inelastically and elastically scattered electrons is the ratio

of the total inelastic to elastic cross-sections. Whereas the ratio of the experimental values indicated by circles in Figs. 1 and 2 results in v = 2.8, close to the value v = 3.0, measured by Badde and Reimer ( 1 970), Egerton (1976) and Reimer and Ross-Messemer (1990), the ratio for carbon films becomes too low ( v = 1.58) when using Eqs. (12) and (6),because the corresponding values of oC,from Eq.(6) (full line in Fig. 1) result in values higher than the experiments (circles). Recent measurements of this ratio v using unfiltered and zero-loss filtered transmissions of thin films are shown as l/v vs. Z in Fig. 3 (Reimer and Ross-Messemer, 1990)together with the values of Egerton ( 1 976). They can be approximated by the dependence on reciprocal atomic number Z given in Eq. (13). The lower values for antimony are caused by a recrystallization of the evaporated films. Values of v = 4.0 have to be expected for cryosections (H 20). The differential cross-section for inelastic scattering, analoguous to Eq. (2) for elastic scattering, can be written (Koppe, 1948; Lenz, 1954; Reimer, 1989a)

Though this formula does not make use of the special shape of the EELS discussed in the next section, it can be used as an approximation to discuss scattering contrast (Section lV.B.l) for apertures o! >> 'v J / 2 E .

C . Electron Energy-Loss Spectrum ( E E L S ) 1. Contributions to the EELS

Electron energy-loss spectra can be divided into the following regions, which are demonstrated for carbon, aluminium and calcium in Figs. 4a-f.

50

L. REIMER 5.0

1.0

3.0

t

c

I

>

2D

10

0

I

I

10

20

I

30

I

1

LO

50

1

60

70

80

90

ZFIG.3. Measurements ( a ) of the ratio of the total elastic-to-inelastic cross-section l/v = uc,/uinvs. atomic number Z (Values ( x ) of Egerton (1976) for comparison).

The zero-loss peak of unscattered and elastically scattered electrons inside the collection aperture decreases exponentially with increasing thickness and is identical with the zero-loss filtered transmission Ti,(Section IV.B.l) of the selected specimen area. The plasmon-loss region from A E = 0 - 30 eV contains broad (C in Fig. 4a) and sharp (A1 in Fig. 4c) volume plasmon losses as collective oscillations of the electron plasma and multiples of these losses with increasing thickness (see Fig. 6 ) . Beyond a critical scattering angle 0, (see Eq. (19))plasmon losses are strongly damped and single electrons of the plasma are predominately excited. Surface modes of plasma oscillations result in surface plasmon losses lower than the volume losses. This region also contains interband transitions and energy losses by Cerenkov radiation. The EELS beyond 30 eV contains edges caused by the inner-shell ionizations. These edges start at A E = E, where EI is the energy difference between

€3.00. 1103

;

\

.-A +--+.--+--

+--

a) Carbon (plasmon)

-71 1

I

0.

oo-;o

I

- +--+---

w

I

t

Fic;. 4. Electron energy-loss spectra of amorphous carbon with a) plasmon loss and b) K edge, aluminium with c ) plasmon loss, d ) L,, edge and e) K edge, calcium fluoride with f ) Ca I.?, edge.

52

,-.-1.50 +lo7

c ) Al (plasmon)

+

0. Ct

1.5c

*lo'

0. 01

+.-

\

I

+---

-t-

d ) A l (L edge)

75

100 125 ENERGY LOSS [eVI

FIG.4.(Cont.)

150

175

i. 00

53

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

I

1400

1600 ENERGY LOSS CeVl

1800

yJ-lf I Co ( L edge)

1

t

h

o'odO

275

300

325 350 375 ENERGY LOSS [eVI FIG.4.(Cont.)

400

455

A0

54

L. REIMER

the binding energy of the I = K , L , M or 0 shell and the Fermi level. Excitations of atomic electrons to higher energy states result in a long tail behind the edges, which can be sharp as for the K edges of C and A1 (Figs. 4b,e) or delayed as for the L edge of Al (Fig. 4d). The edges show an Energy Loss Near Edge Structure (ELNES) influenced by the electronic structure and the valence state of the atoms and an Extended Energy Loss Fine Structure (EXELFS) depending on the type and distance of neighbouring atoms. Because these latter structures are important for the analysis of EELS but not for imaging processes, the reader is referred to the review of Egerton (1986). 2. Plusmon Loss Region A comprehensive review of plasmon losses has been published by Raether (1980). Here only the most important results, which will be important for the discussion of EFTEM, are summarized. The plasmon region between 0 and 30 eV can be described by the dielectric theory that correlates the energy-loss spectrum to optical constants in the ultraviolet and soft x-ray spectrum. A distortion of the electron plasma of the conduction and valence bands is induced by the periodic electric field E of electromagnetic waves of frequency o or by the field pulse related to the moving electron with a broad spectrum of frequencies. This results in a frequency dependent complex refractive index n + i K , where K is the absorption index or in a complex permittivity

+

~(o =)E ~ ( w ) k 2 ( w )= (n

+i ~ ) ~ .

(15)

The excitation of an oscillation with frequency o results in an energy loss A E = hw and the differential cross-section of inelastic scattering with momentum hq ( q = 8/A) is related to E by the dielectric theory (Ritchie, 1957; Geiger, 1968):

with the Bohr hydrogen radius aH,the number N, of electrons per unit volume, the characteristic angle 8, of Eq. (10) and lm[ - l/&] = E ~ / ( E+~ E : ) . The formulations of inelastic cross-sections by the GOS in Eq. ( 1 1) and by the dielectric theory in Eq. (16) are equivalent. According to Eq. (lo), a plasmon loss of A E = 16 eV results for E = 80 keV in 8, = 0.1 mrad. This shows that the angular distribution of inelastically scattered electrons is peaked at very low scattering angles. However, (02 + 8$' in Eqs. (11) and (16) has to be multiplied by 2 d d 8 to calculate the contribution to scattering between 8 and 8 + do, and a large fraction is scattered within 8, < 8 < 8, where 6, is a cutoff angle of Eq. (19).

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

55

Calculations for a free electron gas result in

with a damping constant y and a maximum at the plasmon frequency

oil = Npe2/Eom*,

(18)

where N, = density of valence electrons of effective mass m*. This means that an electron can excite collective longitudinal density oscillations of the plasma of conduction and valence electron bands with an energy loss AE,, = hw,, in the region 0-30 eV. However, the plasmon frequency can be shifted to higher or lower values when excitations of bound states exist beyond or behind the plasmon energy, respectively. Equation (18) can explain shifts of the plasmon energy when N, varies in alloys, for example. The plasmon losses AEpl and their widths show a parabolic dispersion in the sense that they increase with increasing scattering angle 13. Such a dispersion of the Al plasmon loss can be seen in the angular resolved EELS of Fig. 14b. According to Eq. (16), the plasmon-loss intensity decreases with increasing H as (e2 e$’ and is strongly damped beyond a critical cutoff angle

+

0,

‘v

(19)

AE,Jmvv,

of the order of 7-10 mrad where single electron excitations dominate ( v F = Fermi velocity). Whereas the volume plasmon losses are excited inside the whole specimen volume, surface plasmon modes can be excited as surface-charge waves with plasmon energies smaller than the volume plasmon loss (Stern and Ferrell, 1960). For thin films, the surface plasmons split into two energy-loss components with symmetric and antisymmetric charge distributions at opposite surfaces. With increasing thickness the surface plasmon loss A ESPsaturates to a value A E,, = A Epl(1

+ E)-

I”,

(20)

where E is the relative permittivity of the neighbouring medium, typically vacuum, oxide or supporting film. This means a decrease to AEsp = AE,,/& for vacuum ( E = 1) on both sides. Surface plasmon losses are predominately excited in reflection EELS experiments where the electron beam strikes the surface at oblique incidence. They can also be excited by polarization when an electron flies parallel to the surface in a vacuum at distances of the order of a few nanometers but without penetrating the material (Section IV.C.2).

56

L. REIMER

3. Ionization of Inner Shells a. Shape of Ionization Edges Ionization of an inner shell results in an energy-loss edge at AE = E,, where El is the ionization energy defined as the energy difference between the Fermi level and the energy level of the shell I = K , L, M , N or 0. Energy losses AE > Er result from transitions to free states beyond the Fermi level and to a continuum of free states. The shape of ionization edges varies with atomic number and ionized shell (Ahn and Krivanek, 1983). The K edges of Li (55 eV) to Si (1839 eV) show a “saw-tooth’’ shape with a sharp increase at AE = El and a long tail beyond (Fig. 4b,e). The L edges from Al (73 eV) (Fig. 4d) to Br (1550 eV) consist of strong narrow L2 and L3 edges ( “ L 2 3 edge” if not resolved) and a weak L , edge with differences in the shape. The edges from Mg to CI show as pure elements a delayed maximum (“sleeping whale” profile), which can change to a sharp step at EL for oxides. The edges from K to Cu show intense “white lines” (Fig. 4f) at the edge caused by the excitation of 2 p electrons to the unoccupied 3d states. When the 3d shell is occupied, edges from Zn to Rb again show the delayed edge. Md5 edges followed by weak M23 edges can be observed from Se to W. Edges of Se-J and Lu-W show a rounded edge with a strong delay of the maximum, and the elements Cs-Yb show white lines due to excitations from 3d to the unoccupied 4f shell. The N45edges of Ba-Lu show an intense edge with a resonance maximum 10-20 eV beyond the ionization energy and a changing fine structure. The O,,-edge is only important for Th and U. The decrease of EELS intensity below and beyond an edge can be approximated by a power law with an exponent s = 3-5 depending on material and aperture:

dl/d(AE) = AAE-‘.

(21)

An Energy Loss Near Edge Structure (ELNES), which depends on the band structure and the valence state of the atom in a compound or solid, is superposed on the edge profiles of pure elements. For further details the reader is referred to Egerton (1986). For example, the ELNES of C becomes the background of the Ca white line, which can result in difficulties for elemental mapping and quantitative analysis of small Ca concentrations. An Extended Energy Loss Fine Structure (EXELFS)can be observed as a small undulation of the background up to a few hundreds of eV beyond the edge and can be used to determine the arrangement of surrounding atoms in a solid. This structure has no importance for imaging techniques.

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

57

b. Inner-Shell Cross-Section The cross-section of inner-shell ionization can be calculated from the generalized oscillator strength (GOS) introduced in Eqs. (9) and (1 l), when the initial wavefunctions U ( I ) have been obtained by the Hartree-Fock-Slater method. Analytical formulae have been reported for the K-shell (Bethe, 1930; Madison and Merzbacher, 1975; see also SIGMAK program of Egerton, 1986), the L-shell (Choi et al., 1973; see also SIGMAL program of Egerton, 1986) and the M-shell ionizations (Choi, 1973). Figure 5 shows the GOS for the carbon K shell excitation as a function of energy loss A E and scattering angle d. The step function at the right corresponds to the K edge superposed on the continuously decreasing background from the valence electrons, which is found in an EELS with a small aperture. The maximum at the right side for energy losses beyond the K edge is the Bethe ridge with a maximum at the Compton angle d c :

sin2& = d,$

= (AE)fEf[l

+ (E

-

AE)/2E0]N AEfE

(22)

for an energy loss A E, e.g. 8, = 50 mrad for A E = 2 0 0 eV and E = 80 keV. This angle results from classical scattering at a quasi-free electron. The broadening of the Bethe ridge is caused by the momentum distribution on the atomic

FIG 5. Generalized oscillator strength (GOS) of carbon K shell excitation with the K edge (left)and Bethe ridge (Cornpton peak).

58

L. REIMER

orbital. Also, the free electron excitation of valence electrons shows a superposed Compton peak or Bethe ridge (Egerton, 1975; Boyce and Embling, 1980; Ritchie and Howie, 1988) (see also Section V.A.4 and Figs. 39 and 40). The GOS df,(q’,AE)/d(AE) has to be multiplied by [AE(OZ 8;)l-l to become proportional to the differential cross-section of Eq. (11). Shapes of EELS spectra established by calculating the GOS have been reported by Leapman et al. (1980) and Rez (1982) for E = 80 keV and a = 10 mrad. They show the same tendency as the edges shown in Fig. 4. The delayed maximum of L edges can be attributed to a modification of the Coulomb potential by a “centrifugal barrier.” Of special interest for quantitative EELS and elemental mapping (Section 1V.E) is a partial cross-section

+

a(ct,A)=

(i (B:+A

d2a

d(A E) dR

2n sin 6 d8 d(A E ) ,

for scattering inside an aperture a and an energy-loss window of width A between E, and E, + A beyond the edge at an energy loss E I . These partial cross-sections can be calculated by the SIGMAK and SIGMAL program of Egerton (1986) or by the numerical approach of Joy (1982). Partial crosssections measured by the ratio method of quantitative EELS relative to the cross-section of oxygen have been published by Hofer (1987a,b, 1989), Hofer et al. (1988), and Auerhammer et a!. (1989).

D. Multiple Scattering EfSects in the Energy-Loss Spectrum The influence of multiple scattering on EELS can be described by the following theoretical approaches. In case of sharp plasmon losses, the probability P, of finding multiples of plasmon losses AE = n AEp,(Fig. 6) after passing a foil of reduced thickness p = t/Ap, is a Poisson distribution

where Apl is the mean-free-path of plasmon losses. However, deviation from this distribution can be found when limiting the aperture a for recording an EELS because the angular broadening increases with the multiplicity n and only electrons with scattering angles 8 I CI are recorded. The crystal orientation also has an influence on the ratio P,/P,, of first-plasmon and zero-loss intensities. Though plasmon losses preserve the Bragg contrast (Section IV.B.2), this ratio is not independent of specimen tilt (Pyrlik, 1978a,b). The intensity of the first plasmon loss ( n = 1) in Eq. (24) should increase as pe-P, which shows a maximum for p = t/A,, = 1. The mean-free-path of

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

59

a

energy loea i n eV

t = 4 8 0 nm

200

300 400 500 600 energy loea in e V FIG.6. Comparison of calculated (a$) (without zero-loss) and recorded (b,d) EELS of 480 nm aluminium and 230 nm carbon films for apertures of 4, 10 and 30 mrad (z = r/A, A = total mean free path). -0

100

60

L. REIMER

energy lomm i n eV

t =230 nm

300

K

150

.

energy 1000 i n e V

FIG.6 . (Cont.)

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

61

inner-shell ionization at 80 keV ( e g , A, = 3 pm for carbon) is much larger than A,, = 60 nm of carbon. Therefore, the intensity of ionization edges increases as the specimen thickness and should reach a maximum at t = AK. However, multiple plasmon and inner shell scattering processes result in a convolution of the K edge or other edge profiles with the intensity distribution of the zero-loss and plasmon loss part of the EELS including elastic scattering, which broadens the angular distribution and decreases the intensity passing through the objective aperture. For a calculation of the dependence of EELS on thickness and scattering angle, it is necessary to evaluate the distribution f ( w , O , z ) of electrons as a function of energy loss w, scattering angle U and reduced thickness z = t / A , (A, = total mean-free-path for elastic and all inelastic scattering pro0). cesses) using theoretical approaches for a single scattering function O(w, Attempts to solve this problem have been made by Monte Carlo calculations (Reichelt and Engel, 1984), by a semi-analytical method (Johnson and Isaacson, 1988)and by a Fourier method (Reimer, 1989b).The latter uses the following sequence of operations applied to the single-scattering function aqw,0): f ( w , 0,z) = P -IT-' exp[z(G

-

l ) ] with

G

=

TP [O(w,O)],

(25)

where P = projection, P - ' = deprojection, T = two-dimensional Fourier transform in 0 and w, and T - = inverse Fourier transform. The sequence of a projection P on the 0,-axis and a Fourier transform in 0, reduces the necessary two-dimensional Fourier transform in the Ox, Uy plane to a one-dimensional in 0,. Comparisons of calculated and observed EELS spectra using 20, 50 and 150 pm objective diaphragms are shown for thick aluminium and carbon films in Figs. 6a-d. They contain the Poisson-like distributions of multiple plasmon losses. The L edge convolved with the plasmon-loss distribution shifts its maximum to higher energy losses (Figs. 6a,b). EELS spectra of carbon films (Figs. 6c,d) show a most probable energy loss at p A E , , because of the low cross-section of the carbon K shell. The most probable energy loss of thick films can also be estimated by the Landau (1 944) formula

with

5=

NAZ (47ccsO)2E A ze4

~

-pt

(26) and

Qmin= J 2 ( 1- p2)/4E,

confirmed, for example, at low electron energies of 20 and 40 keV (Reimer et al., 1978) and high energies within 200 keV-1 MeV (Sevely et al., 1974).

62

L. REIMER

The formulae for the exact shape and the half width of the Landau energy distribution agree less well with experiment. The most probable loss can be used for estimating the thickness of thick specimen layers. 111. INSTRUMENTATIONAND MODESOF OPERATION A . Spectrometers and Filter Lenses 1. Prism Spectrometers

Figure 7 shows the principle of a magnetic 90" prism spectrometer with magnetic induction B perpendicular to the electron beam. Electrons from a point source S follow a circular path with radius (27)

r = mv/eB

and are focused at S'. The dependence of r on the electron momentum mu results in a dispersion Ay/AE at the energy-dispersive plane. Normally, this focusing will act only on the component of momentum in the x-y plane (Fig. 7) but not on the component in the x-z plane. This results in a line-

0

-

,'

\

Energy-dispersive plane

FIG.7. Magnetic prism spectrometer with 90" deflection and curved polepieces with radii r and r2 for correction of second-order aberrations (Q = final image plane).

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

63

shaped energy-loss spectrum parallel to z. It can become difficult to adjust a narrow slit in the energy-dispersive plane exactly parallel to z, and the lines may be bent by aberrations. This can be avoided by double focusing. The perpendicular B field is not cut off sharply at the polepiece edges but shows a curved fringe field that acts as a cylindrical lens for momenta in the y-z plane. When the edges are not perpendicular to the optic acis but inclined by appropriate angles and c 2 (i.e., E = 26.6"),the foci in the x-y and x-z planes can be made to coincide. In practice, the radii of magnetic sector fields are of the order of 10-20 cm, which results in a dispersion Ay/AE of a few micrometers per electronvolt. This low dispersion needs very accurate positioning of the slit for sequential recording and a post-spectrometer optics when the spectrum has to be enlarged for parallel recording (Section 1II.D). Increasing the spectrometer entrance angle y results in aberrations, and the aberration figure in the energy-dispersive plane limits the energy-loss resolution. The most important second-order aberration can be corrected by curving the edges as shown in Fig. 7 (Egerton, 1980) or alternatively by placing sextupole lenses before and after the spectrometer. This allows a resolution of 1 eV up to y = 10 mrad to be achieved. The resolution is reduced by the finite size of the source S, and an important point when using a prism spectrometer is to keep the diameter of the source small enough. A further limitation of resolution is, of course, the energy width of the electron gun, which is of the order of 0.5-2 eV for thermionic guns and 0.2-0.3 eV for field-emission guns. For further details about prism spectrometers the reader is referred to Enge (1967) and Egerton ( 1 980, 1986). A prism spectrometer is used in combination with electron microscopes either in a dedicated scanning transmission electron microscope where S is the electron probe at the specimen (Section 1II.B) or in a conventional transmission electron microscope where S is at the focus of the last projector lens. The final image at the fluorescent screen lies at Q in Fig. 7, and there is a conjugate plane Q' behind S' where an energy-filtered image of small size can be recorded (see also Section 1II.C). 2. Wien Filter In crossed electric and magnetic fields perpendicular to the axis the two components of the Lorentz force F = -e(E + u x B) will be compensated when v = IEl/lBl.

(28)

Electrons of velocity v then move on axis through the filter, whereas electrons with an energy loss A E are deflected (Fig. 8). A slit in front of the filter

64

L. REIMER -~ Electron source

A

- - Aperture diaphragm Deceleration lens

*

,B-Field

-u -

--IF =zoov

Wien filter

‘i-Field

Acceleration lens

Spectrum

FIG.8. Wien filter with crossed electric and magnetic fields.

spreads out to form an EELS. For high dispersion Ay/AE and short filter length, the high-energy electrons have to be decelerated to a few hundreds of eV and accelerated after passing the filter (Boersch et al., 1964; Andersen, 1967; Curtis and Silcox, 1971). Such a filter has also been used in a STEM instead of a prism spectrometer (Browne, 1979; Batson, 1985). The advantage of the Wien filter is that it provides high resolution below 100 meV. This type of filter has also been applied for high-resolution EELS of energy losses by phonons and molecular vibrations by using a first Wien filter in front of the specimen to monochromatize the electron beam (Boersch et al., 1969; Schroder and Geiger, 1972).

3. Filter Lenses Boersch (1948, 1953) and Mollenstedt and Rang (1951) first tried to filter images and diffraction patterns in energy by means of retarding-field electrostatic lenses, which transmitted only the zero-loss electrons; the filtering effect was obtained either by means of a grid at the central electrode or by increasing the central potential. Aberrations in this type of lenses limited their

ENERGY-FILTERINGTRANSMISSIONELECTRON MICROSCOPY

I

FiIter lens

Filter exit plone

EELS

65

I Achromatic image plane’

-

E

E-AE

Energy-dispel- w e plane

FIG.9. Schematic action of a filter lens and its important planes.

further application. Only in the form of a cylindrical electrostatic lens has the “Mollenstedt analyzer” (1949)’beenused in many laboratories for the investigation of the plasmon-loss region of EELS. A real filter lens should be symmetric, with an filter-entrance plane that contains either an intermediate image or a diffraction pattern and a conjugate filter-exit plane with a magnification M = 1 behind the filter lens (Fig. 9). The image at the filter-exit plane is achromatic, which means that electrons with different energy losses pass through the same image point of the achromatic plane under different angles, and electrons of the same energy loss are focused in the energy-dispersive plane to form an electron energy-loss spectrum (EELS). This plane is conjugate to the focal plane of a projector lens in front of the filter, which contains either a demagnified image of the crossover (primary beam of a diffraction pattern) in the case of electron spectroscopic imaging (ESI) or a demagnified image of the diaphragm, which selects the area contributing to the selected-area electron diffraction pattern at the filterentrance plane in the case of electron spectroscopic diffraction (ESD). The size of this “source” in the focal plane, together with the energy width of the electron gun and aberrations of the filter lens, limit the diameter of the zeroloss peak in the energy-dispersive plane with which the EELS is convolved. A second projector lens behind the filter can either magnify the energy-dispersive

66

L. REIMER Specimen Objective lens Objective diaphragm

1 st Oiffraction pattern

Selector diaphragm 1 st Projectw system

1 st Intermediate image 'Crossover' plane

Filter entrance diaphragm Filter entrance plane Filter Achromatic image

2nd Projector system

Final screen Detector

plane

Final image or diffraction pattern

EELS image or diffraction mode

FIG. 10. Castaing-Henry filter lens in a ZEISS EM902 operating in the ESI mode

plane to the final screen for observing the EELS or magnify the filter-exit plane for ESD and ESI. A filter lens that fulfils these conditions was developed by Castaing and Henry (1962) and is shown schematically in Fig. 10 in the version used in the ZEISS EM902. The electrons are deflected through 90" by a magnetic prism, retarded and reflected by an electrostatic mirror more negatively biased than the cathode, and deflected again through 90" to be on axis again. Though this Castaing-Henry filter lens, modified by Henkelman and Ottensmeyer (1974), works well in the ZEISS EM902 and all the corresponding illustrations in this review have been obtained with this instrument, it has the following disadvantages. The potential at the retarding electrode, and therefore the acceleration voltage, cannot exceed 80 kV to prevent electrical breakdown. Due to a second-order aberration of the filter lens, electrons of equal energy loss from off-axis points in the filter-entrance plane are not exactly focused in the energy-dispersive plane but form a caustic pattern (see Fig. 13d). As a consequence, the selected energy window in the final image plane is not uniform but changes parabolically from the center to the periphery of the final image.

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY Point source

67

1)

so

0

Filter entronce plane

S O

1 0

Sssextupoles

Achromatic image plone

I I Energy-dispersive plane

FIG. I I . a-filter lens with correction elements due to Lanio (1986).

The limitation of electron energy to 80 keV can be overcome by using a fully magnetic deflection system consisting of four magnetic prisms (Fig. 11) with R-shaped electron trajectories. Such an R-filter has been used up to 1 MeV (Perez et al., 1975). The correction of the second-order aberration can be realized by means of a filter lens shown in Fig. 11 with sextupoles as correction elements at the center (Lanio, 1986; Lanio et al., 1986). A corrected Wien filter (Section III.A.2) can also be used as an imaging filter lens (Rose, 1987,1989) but needs a deceleration from the primary energy to about hundred electronvolts.

B. Dedicated Scanning Transmission Electron Microscope A dedicated scanning transmission electron microscope (STEM) uses a filed emission gun as the electron source (Fig. 12). The smallest cross-section of

68

L. REIMER

Field-emission tip

First anodeSecond anode-

Scanning coils

Detector for elastically scattered electrons

1in Iun no- 05s electrons FIG. 12. Dedicated scanning transmission electron microscope (STEM) with a magnetic prism spectrometer.

the electron beam called the crossover is demagnified by a lens of short focal length to form an electron probe of the order of 0.1-0.2 nm at the specimen. The probe can be scanned by an x-y scanning coil system. A prism spectrometer, as in Fig. 12, or a Wien filter (Section III.A.2)generates an EELS. For image recording, different signals can be extracted simultaneously from the cone of scattered electrons. These are, for example (Crewe et al., 1975; Colliex and Mory, 1984):

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

69

1) unscattered electrons I,,,, which pass the prism spectrometer with low collection aperture B and zero energy loss; 2) inelastically scattered electrons I,,,, with a large fraction at small scattering angles; and 3) mainly elastically scattered electrons at large scattering angles that can be recorded by an annular detector. An EELS can be recorded with a stationary electron probe. When parallelrecording the EELS intensity by a CCD, either EELS from selected specimen points can be recorded sequentially or a larger number of electron spectroscopic images (ESI) with different energy windows can be recorded simultaneously by scanning the specimen sequentially. The number of selected energy windows times the number of pixels per image will only be limited by the digital storage capability.

C . Electron Energy-Loss Spectroscopy in a Transmission Electron Microscope

Electron energy-loss spectroscopy in a conventional transmission electron microscope can be realized by placing a prism spectrometer below the camera chamber, which needs no changes in the lens column of the CTEM. The source plane S of the spectrometer should coincide with the focal plane of the last projector lens. The two modes of image coupling and diffraction coupling then can be used (see Egerton, 1986). The former works with a demagnified specimen area at the focal plane and a diffraction pattern on the final screen, and the latter works with a demagnified selected-area diffraction pattern at the focal plane and an image on the final screen. (In an EFEM with filter lens (Section 1II.D) these modes are analogue to ESD and ESI, respectively.) A diaphragm in front of the spectrometer selects an acceptance angle y (Fig. 7) and an image area Q. As in the EELS mode of a dedicated STEM, a postspectrometer lens system can magnify and adapt the EELS spectrum on a CCD for parallel recording (Egerton, 1984; Krivanek et al., 1987; Krivanek, 1989; Scott and Craven, 1989; Shuman, 1981; Zaluzec, 1989). The whole illuminated specimen area is damaged while recording the EELS from a small selected area in the final image plane when not using the STEM mode of a TEM. In this STEM mode, the prespecimen field of the objective lens of the TEM acts as an additional condenser lens to form an electron probe with diameters of z 1-5 nm on the specimen. A prism spectrometer can also be used for energy-filtered imaging because the image plane Q in front of the spectrometer can be focused at a conjugate plane Q’ behind the energy-selective plane S’ (Fig. 7) and this plane can be

70

L. REIMER

parallel-recorded by a diode array (Shuman and Somlyo, 1981, 1982; Ajika et al., 1985). However, the image at Q’ is not achromatic. The energy window selected by a slit in the plane s’has to be small, and the field of view with a diameter of a few millimeters on the viewing screen is limited by the acceptance angle fl of the spectrometer. This method can also be used in a dedicated STEM for energy filtering of convergent diffraction patterns (McMullan et al., 1990),or the diffraction pattern is scanned sequentially pixel by pixel (see Hagemann, 1981). D. Operation Modes of an Energy-Filtering Electron Microscope

Electron spectroscopic imaging (ESI), electron spectroscopic diffraction (ESD), and electron energy-loss spectroscopy (EELS) can be achieved in an energy-filtering transmission electron microscope with a filter lens functioning in the modes described below (Reimer et al., 1988). The reported numerical values are those of the Castaing filter in a ZEISS EM902. 1. Electron Spectroscopic Imaging (ESI) The filter-entrance plane (Fig. 10) contains a magnified image of the specimen. The focal plane of the first projector lens cmtains a demagnified diffraction pattern with the shadow of the objective diaphragm which acts as a “source” for the filter lens (see also discussion of the EELS mode in Section III.D.3a). The diameter of this shadow of the objective diaphragm decreases with increasing magnification. The second projector lens behind the filter lens can magnify either the achromatic filter-exit plane with a 70 x magnification or the energy-dispersive plane with a 260 x magnification and a dispersion of AylAE = 0.5 mm/eV on the fluorescent screen. This high dispersion allows direct viewing of the EELS and adjustment of the zero-loss and the energy-selecting slit on axis. Energy filtering with an energy loss AE = e AU is achieved by increasing the acceleration voltage at the cathode to U = 80 kV + AU. This shifts the EELS in the energy-dispersive plane, but the energy-selecting slit selects only on-axis electrons with an energy loss AE and a total energy eU - AE = 80 keV. Therefore, nothing changes in the electron optics between specimen and final image when the selected energy loss is increased. The shift of the acceleration voltage only changes the focusing of the electron beam by the two condenser lenses, which can be compensated by changing the excitation of the condenser lens in synchronism with AU. An unfiltered image can be observed by withdrawing the slit in the energydispersive plane. As mentioned in Section III.A.3 the only difference between the filter-exit (achromatic) image and the image at the filter-entrance plane is

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

71

that electrons with energy losses pass the same image point at another angle to the axis. The only aberration of importance will be the chromatic aberration of the second projector lens, and differences between the image and that seen in a CTEM will only be important when observing a thick specimen with a broad EELS spectrum. In contrast to a STEM with a sequential spatial scan of 512 x 512 or 1024 x 1024 pixels and simultaneous recording of the EELS by parallel recording, ESI with a filter lens can produce in sequence images with different energy losses, which can be simultaneously recorded on a 6 cm x 9 cm photographic emulsion with about lo7 number of pixels, assuming a resolution of about 20 pm. An imaging magnetic prism spectrometer (Section 1II.C) can only filter a field of view of 3-5 mm in diameter, which is then recorded by an diode array of 512 x 512 2: 2.5 x lo5 pixels.

2. Electron Spectroscopic DifSraction (ESD) The filter-entrance plane contains a selected-area electron diffraction pattern (SAED) with camera lengths within the capability of the lens system (50 cm-2.5 m). The source at the focal plane of the first projector lens is now a demagnified image of the selected-area diaphragm, which also decreases in diameter with increasing magnification (see also discussion of EELS mode in Section III.D.3.a). Whereas diffraction patterns can be recorded only sequentially, pixel per pixel, in a STEM or a TEM with a spectrometer, ESD with a filter lens can be observed on the fluorescent screen or recorded on a photographic emulsion. The post-specimen lens system of a STEM and an imaging magnetic prism spectrometer (Section 1II.C) also allows filtered convergent beam electron diffraction patterns to be recorded simultaneously by means of a diode array (McMullan et al., 1990).

3. E E L S M o d e s An EELS spectrum can be observed on the fluorescent screen or recorded simultaneously by a photographic emulsion in the spectrum mode (a), and a spectrum can be recorded sequentially by a scintillator-photomultiplier detector in the image mode (b) or the diffraction mode (c). a. EELS Spectrum Mode The second projector lens is focused on the energy-dispersive plane to observe the EELS on the fluorescent screen. The EELS is either generated with an image (ESI mode) or a diffraction pattern (ESD mode) at the filter-entrance plane. These modes make it possible to observe the spectrum directly and to control the position and the width of the energy-selecting slit.

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FIG. 13. Magnified EELS in the energy selective plane of a 40 nm Al film: a) in the ESD mode ( M = 3000) with convolution of the plasmon losses by Debye-Scherrer rings of the demagnified diffraction pattern in the “source” plane (no objective aperture, 50 pm selector diaphragm); b) as a) with a 20 pn objective diaphragm; c); in the ESI mode with convolution by the demagnified 50 pm selector diaphragm (20 pm objective diaphragm); and d) in the ESI mode with a 100 pm selector and 20 pm objective diaphragm showing the superposed caustic created by second-order aberration of the filter lens.

As discussed in Section III.D.l the “source” at the focal plane of the first projector lens is a demagnified diffraction pattern in the ESI mode. Therefore, without an objective aperture diaphragm, the EELS spectrum becomes convolved by a system of Debye-Scherrer rings when using an evaporated aluminium film (Fig. 13a),for example. This convolution can be decreased by introducing an objective aperture, which limits the “source” to scattering angles 0 < 0 < u and/or by increasing the magnification (Fig. 13b). In the ESD mode, the source is a demagnified image of the selector diaphragm for selected-area electron diffraction, and the EELS becomes convolved with the shadow of this diaphragm (Fig. 13c), which decreases with increasing magnification. This means that working with large apertures of the order of 10-20 mrad needs high magnifications of 20.000-50.000 x (Bihr et al., 1988) when the EELS resolution and the width of the selected energy window should be of the order of 1-2 eV, determined by the limiting energy width of the thermionic electron gun. Figures 13a-c were obtained with a 100pm diaphragm in the filterentrance plane, which selects a circle of 2 cm diameter on the final image plane.

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On withdrawing this diaphragm, the image on the whole fluorescent screen contributes to the EELS which now becomes convolved with the caustic figure of the second-order aberration (Section III.A.3)(Fig. 13d).This blurring of the EELS can be avoided using a corrected magnetic filter lens (Fig. 12). b. E E L S Image Mode In the ESI mode with a filtered image at the final image plane, the second projector lens is focused on the filter-exit plane. A small diaphragm of a few mm in diameter in front of a scintillatorphotomultiplier combination below the camera chamber selects a small image area with a corresponding diameter in the specimen plane, which varies inversely with the magnification, e.g., 20 nm when selecting with a 2 mm diaphragm at a magnification of 100,000 x. When the EELS is shifted by superimposing the ramp voltage A U on the accelerating voltage, ESI images with increasing energy loss A E = e AU are successively observed, and the intensity passing the selected area is modulated by the intensity of the EELS of the selected area.

c. E E L S Diffraction Mode The ESD mode is used with a filtered diffraction pattern at the final image plane. A diaphragm in front of the detector selects an aperture (solid angle) in the diffraction pattern, which can be changed by altering the diameter of the diaphragm or the camera length. Shifting the acceleration voltage now results in a sequence of ESD patterns with increasing energy loss, and the intensity passing through the diaphragm and recorded by the detector is again an EELS spectrum. By tilting the primary beam on the specimen or by deflecting the ESD pattern by means of coils behind the second projector lens, the diaphragm can select solid angles in the ESD pattern at different scattering angles and the EELS can be recorded on Bragg spots, on Kikuchi lines and bands or at large scattering angles up to 0.1 rad for recording the Compton peak (Section V.A.4).

4. Angular and Spatially Resolved E E L S The dependence of scattered intensity on scattering angle 6 and energy loss A E can be recorded by the method of angular-resolved EELS. This method has been employed by several authors, with spectrometers that allow a line across a diffraction pattern to be selected and show a perpendicular dispersion of the spectrometer (Mollenstedt analyzer: Cazaux, 1969; Leonhard, 1954; Metherell, 1971; Wien filter: Curtis and Silcox, 1971).In the ESD mode with a filter lens, this can be achieved by setting a 1-5 pm slit through the diffraction pattern at the filter entrance plane (Fig. 14a) (Reimer and Rennekamp, 1989). Because electrons of different energy loss pass the filter-exit (achromatic) plane

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L. REIMER

FIG. 14. a) Angular resolved EELS mode with a slit in the filter entrance plane and observation of a defocused achromatic image plane. b) Example of an angular resolved EELS from an evaporated 480 nm polycrystalline aluminium film.

at different angles to the axis (Fig. 9 and 14a) and are focused in the energyselecting plane, a defocused image of the filter-exit plane creates a perpendicular EELS from each point on the slit, as demonstrated for multiple plasmon losses in Fig. 14b. This diagram contains information about the angular width of single and multiple plasmon losses (AE = 15 eV), and the dispersion of volume plasmon losses can be seen as a parabolic curvature of the first plasmon loss. Further applications of angular-resolved EELS are discussed in Section V.A.4. When using the ESI mode and the slit at the filter-entrance plane to select a line through the image, we get a perpendicular EELS for each image point (spatially resolved EELS), which can be used for parallel recording of EELS from different points of the specimen (Cundy et al., 1967, 1968, 1969).

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75

SPECTROSCOPIC IMAGING IV. ELECTRON A. Review of Imaging Modes

Figure 15 shows schematically the imaging modes (1-6) that can be used for electron spectroscopic imaging (ESI) with selected energy-loss windows at different parts of the EELS: 1. Zero-loss imaging with unscattered and elastically scattered electrons eliminates the contribution of inelastically scattered electrons to the image intensity. This can increase the scattering contrast (Section 1V.B.l), phase contrast (Section IV.C.2), Bragg contrast (Section IV.B.2) of thin films, and Lorentz contrast (Section IV.B.4) and avoids the blurring by the chromatic aberration disc especially for thicker films where the fraction of inelastically scattered electrons dominates. Whereas elastic scattering processes are localized near the nuclei, high resolution is decreased by the more or less delocalized inelastic scattering processes (Isaacson et al., 1974; Kohl, 1983). 2. Plasmon-loss imaging (Section IV.C.3) will not be of interest for high resolution because of the delocalization of the order of nanometers. It can be employed for selective imaging when different phases of the specimen show differences in their EELS plasmon region.

-

L. Contrast

0

tuning

-

a1 Thin specinen

A€

250eV

I

bl Thick SDecirnen

BJ6.

Most probable Loss

FIG.15. Imaging modes of electron spectroscopic imaging (ESI) with selected energy windows at different parts of the electron energy loss spectrum.

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3. Structure-sensitive imaging at A E = 250 eV just below the carbon K edge (Section IV.D.l) generates a minimum contribution of carbon to the image intensity and the relative contrast of noncarbon atoms is strongly increased, though with different strength for different elements. 4. Contrast tuning in the energy-loss interval 0-250 eV (Section IV.D.2) can optimize contrast differences in biological sections between strongly stained (dark) and less stained (bright) regions; this is of interest for the imaging of thick sections to see and record structures in both regions simultaneously. 5. Elemental mapping (Section 1V.E) needs two or three ESI below and beyond an ionization edge of the element of interest. The former are used for digital extrapolation of the background and for subtraction of the latter from the image beyond the edge to produce an elemental map. 6. Most probable loss imaging (Section IV.D.3) is of interest when the zero-loss intensity falls below The intensity at the most probable energy loss-the maximum of the Poisson distribution in Eq. (24) of multiple plasmon losses or the maximum of a Landau distribution in Eq. (26)-can then remain large enough for focusing and recording. The resolution will be limited only by the chromatic aberration caused by the width of the selected energy window.

B. Zero-Loss Imaging 1. Scattering Contrast of Amorphous Specimens

a. Transmission Without Filtering The scattering contrast is generated by the decrease in the number of electrons (transmission) that pass through the objective aperture a and contribute to the image. In contrast to the phase contrast discussed in Section 1V.C.1, we neglect interference effects between the primary electron wave and elastically scattered waves. In order to analyze the scattering contrast from the single scattering of atoms discussed in Sections I1.A and B, we introduce a mean-free-path mass thickness xeI(ct)for scattering through angles 0 > a (in units pg/cm2), which for elastic scattering, for example, is related to da,,/dR in Eq. (2) by

where NA = Avogadro’s number, NA/A = number of atoms per gram and eel= total elastic cross-section of Eq. (5). Substitution of Eq. (14) in a for-

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77

mula analogous to Eq. (29) for inelastic scattering results in (Lenz, 1954)

1

I xnr

+ 21nCl + (8,/~r)~].

For the calculation of the unfiltered transmission we introduce the intensity I as the current density in A/cm2 of electrons passing through the aperture with 0 < 8 < a. The decrease of intensity in a mass thickness element dx = p d z becomes

with the “contrast thickness” 1 -=-+xk(a)

1

1

xel(tl)

(32)

where x e I = A/NAoelis the total elastic mean-free-path, which is identical with x, of the Lenz (1954) theory. Integration of Eq. (31) with I = I, at x = 0 results in

Knr= l / l , = exp[ - x / x k ( a ) ] . (33) This formula has the advantage of describing the dependence of transmission on aperture in terms of only two parameters xeI and 0, (Table I), which depend on electron energy and atomic number. In the In qnfvs. x plot of Fig. 16, the exponential decrease in Eq. (33) appears as a linear decrease. The exponential law of Eq. (33) resulting from single-scattering theory agrees with experiment (Lippert, 1954, 1956; Reimer, 1961; Reimer and Sommer, 1968) up to mass thicknesses of z 50 pg/cm2 (0.5 pm organic material of density p = 1 g/cm3) though the condition of single scattering is not fulfilled. For larger mass thicknesses the transmission is higher than expected from Eq. (33) because electrons scattered through angles 8 > a can be rescattered by multiple scattering to angles 0 < a (Lenz, 1954; Zeitler and Bahr, 1957; Reimer and Sommer, 1968). The angular distribution of scattered electrons becomes very broad, and as a consequence the transmission becomes proportional to the solid angle AQ = m2.

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50

100

150

200

25Owglcd300

FIG. 16. Semilogarithmic plot of transmission without energy filtering (Tunr)for 80 keV and different objective apertures a as a function of mass thickness x = p t of carbon films showing the deviation from an exponential law of transmission at large thicknesses. The lower straight lines are due to the zero-loss filtered transmission (Tii)from Fig. 18a. MPL means the intensity in most probable loss images with an aperture of 30 mrad and an energy width 6 = 10 eV.

FIG. 17. Flow of intensities I,,, Ii, and I,, of elastically, inelastically and unscattered electrons, respectively, to angles 0 smaller and larger than the objective aperture a.

b. Transmission with Zero-Loss Filtering We also use the algorithm developed for the unfiltered transmisssion Tunf for the zero-loss filtered transmission Til.The flux diagram of Fig. 17 results in the following system of coupled differential equations for the unscattered intensity I,, of the primary beam and the elastically and inelastically scattered intensities I,, and Ii, passing through the aperture tl (Reimer and Ross-Messemer, 1989, 1990):

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79

+

with l/x, = l/xel l/xin.The solution for the transmissions making use of the ratio v of Eq. ( 1 3) of the inelastic-to-elastic cross-sections becomes

T,, = exp[ -x/x,]

Ti,= I , ,

= exp[ -x(l

+ I,, = exp

[

-x

+ v)/x,,]

-

(xe:(a)

+

(35a)

k)]

Tnf= T,, + T,, + T,, = exp[-x/x,(a)].

(354

xnf

The sum of intensities in Eq. (3%) is the unfiltered transmission of Eq. (33)for a film of mass thickness x = pt without energy filtering as observed in a conventional TEM. The results for Tunf and Tfi, calculated by Eqs. (3%) and (35b), respectively, are semi-logarithmically plotted in Figs. 18a-c for three apertures c1 = 4, 10 and 20 mrad and C , Ge and Pt, respectively, using the values of Table I. Measured transmissions Tunfand T,,, confirm that the modified single scattering theory can be used up to mass thicknesses of about 40-50 pg/cm2. The transmission Ti,for c1 = 4 mrad (lowest straight lines of Figs. 18)is nearly identical with Tunin Eq. (35a). The contribution I,, of elastically scattered electrons passing through the objective diaphragm can be neglected, and such a small aperture (20 pm diaphragm in a ZEISS EM902) is sufficient to measure the exponential decrease of the primary, unscattered electrons. Figure 19 shows the dependence of the fractions T,, and T,, on film thickness calculated by Eqs. (35a-c) for c1 = 20 mrad using a linear scale. The fraction T,, of elastically scattered electrons passing through the aperture is smaller than the fraction T,,of inelastically scattered electrons for all elements and the difference between these fractions is largest for carbon due to the large value of v.

c. Contrast Enhancement in Zero-Loss Filtered Images The enhancement of contrast by zero-loss filtering will be discussed for a stained biological section. Figures 20a and b demonstrate the increase of contrast by zero-loss filtering of a 0.2 pm liver section-stained with uranyl acetate and embedded in epon-as an example where the limit of unfiltered imaging is reached and zero-loss filtering results in a strong improvement of contrast and resolution. Two extreme cases will be discussed in which the observed structure is larger and smaller than the chromatic aberration disc (Reimer and Ross-Messemer, 1989). For structures larger than the chromatic aberration disc, the section will show local mass thicknesses xc and xs of the pure resin consisting mainly

-1-

-1.5-

Germanium

0

-2’

(ci

FIG. 18. Transmission T,,, and Ti, of a) carbon, b) germanium and c) platinum films in unfiltered and zero-loss filtered images as a function of mass thickness x aperture a for 80 keV electrons. 80

= pt

and objective

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY a.20

81

rnrad

s

0

10

20

X-

30

LO * g / c r n 2 50

FIG. 19. Fractions T,, of elastically and 7;" of inelastically scattered electrons passing through an objective aperture a = 20 mrad versus the mass thickness x.

FIG.20. Micrographs of epon embedded liver sections (OsO, fixation, uranyl-acetate stained, I 2 0.2 pm) recorded with objective apertures a = 20 mrad in a) the unfiltered and b) zero-loss filtered mode.

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of carbon (C) and of the staining element (S), respectively. The unfiltered transmission of a stained area becomes

with the contrast thicknesses xk in Eq. (32) for C and S. The bright field contrast for unfiltered and zero-loss filtered images becomes Cunf

= (Tunf.C+S - q n f . C ) / T u n f , C

= exp(-xS/xk,S) -

xS/xk,S

(37)

where Tunf,cand T,il,c denote the transmissions of the pure section where the carbon contribution to the contrast dominates. The last part of Eq. (37) results from a Taylor series of the exponential for small xs, for which we get an estimate of the gain of contrast

Substituting values for S = Pt (representative for Os, Pb, W, or U), Ge and carbon, the gain Go as a function of objective aperture a is shown in Fig. 21. The measured values are obtained by oblique shadowing of polystyrene spheres on a 9 &cm2 carbon film with a platinum film and measurement of the transmissions in Eqs. (37) and (38). The high gain for carbon increases the contrast of thickness variations caused by the microtome chatter in Fig. 20.

0 0

10

a-

20 mrad

30

FIG.21. Increase of the gain Go = C,,,/C,,, in contrast by zero-loss filtering with increasing objective aperture a and thin films of C, Ge and Pt on a supporting film. Experimental points: Pt and carbon film on a carbon substrate.

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83

Though these experiments and the theoretical approach give a more quantitative background for understanding the contrast in the zero-loss mode, it will be difficult to predict the gain of contrast for particular structures in biological sections because of the variation of both the local concentration of staining elements and the mass thickness of the matrix, which will be affected differently by fixation, dehydration, embedding and loss of mass by radiation damage. As an example, we measured a gain of about 1.3 on and between myelin lamellae stained with OsO, and embedded in epon. A gain of 1.6 was found for TMV virus (Langmore and Athey, 1987). A qualitative demonstration of the increase of contrast by zero-loss filtering has also been shown for copolymers (Kunz et al., 1987). For structures smaller than the chromatic aberration disc of diameter

d,

= C,(AE/E)a,

(40)

such as ribosomes or membranes, substitution of the chromatic aberration constant C, = 1.7 mm, the width AE 2 50 eV of the EELS for a 0.2 pm section, and a = 10 mrad in Eq. (40), results in d , Y 10 nm. In practice d, increases less than linearly with increasing a as shown for the resolution of edges (Reimer and Gentsch, 1975), where a diameter d, = 7 nm has been measured for a = 10 mrad, E = 100 keV and C, = 2.2 mm after traversing 0.23 pm polystyrene. For large thicknesses and structures smaller than d,, the inelastically scattered electrons will only contribute to the blurred background, and only the elastic (zero-loss filtered) part of the transmission contributes to a sharp image. Thus zero-loss filtering increases the contrast not only due to the gain Godiscussed above but mainly by avoidance of the blurred contribution of the inelastically scattered electrons to the background. The maximum gain in the case of total blurring of the inelastic contribution to image intensity can be obtained by substituting in the nominator of Eq. (37) the elastic (zero-loss filtered) difference of transmissions Cunf =

(T,i,,c+s-

T,il.C)/Tunf.C,

(41)

which results, with Eq. (38), in the gain G,

achieved by avoiding chromatic aberration; this is plotted in Fig. 22 as a function of xc for different a. We see that G, = 3.3 for a = 10 mrad and x = 20 pg/cm2 ( t 2: 0.2 pm), for the condition of Fig. 20. This contrast gain should be independent of the elemental composition of the observed structure. The unfiltered image (Fig. 20a) shows the blurring caused by chromatic aberration and the zero-loss filtered image (Fig. 20b) shows sharper details

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and an increase in the contrast of the nucleoplasm and the endoplasmatic reticulum, for example.

d . Dark Field Imaging This mode can be realized by shifting the objective diaphragm, tilting the incident beam, or by using an annular condenser diaphragm or a series of conical beam tilts so that the unscattered primary beam is absorbed by the objective diaphragm (Reimer, 1989a). The transmission depends on the sum I,, + Ii,. Figure 19 shows that the contribution of inelastic scattering is larger than that for elastic scattering so that zero-loss filtering increases the contrast (Frosch et al., 1987). When looking at structures containing high Z elements on a carbon film or in a carbon matrix, the background due to inelastic scattering by carbon will be decreased much more strongly. Shifting the objective diaphragm is the easiest way of obtaining dark field imaging, but it has the disadvantage that the selected off-axis rays result in a chromatic error streak superposed on the on-axis chromatic aberration disc of Eq. (40). This streak can also be avoided by zero-loss filtering (Reimer et al., 1989)but for very large shifts (scattering angles) the spherical aberration of the objective lens also results in streaks in the zero-loss image. Therefore, the tilted beam method, which avoids the off-axis errors, will also be the best for zeroloss filtering. 2. Bragg Contrast of Crystalline Specimens We know from theory (Humphreys and Whelan, 1969; Howie, 1963) and experiments (Watanabe, 1964; Castaing et al., 1967; Cundy et al., 1967, 1969; Kuwubara and Uefuji, 1975; Craven et al., 1978; Bakenfelder et al.,

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

85

1990a) that the Bragg contrast is preserved in inelastic scattering processes that excite plasmons or inner-shell ionizations of low ionization energy. Figure 23 shows a typical influence of energy loss on the superposition of bend and edge contours in a wedge-shaped and bent aluminium foil. Plasmon-loss filtering with an energy window at A E = 20 eV in Fig. 23a shows approximately the same contrast as zero-loss filtering. With increasing energy loss, the pendellosung fringes are blurred as demonstrated by placing an energy selecting window at A E = 300 eV in Fig. 23b. Such blurring effects have also been shown by Stobbs and Bourdillon (1 982) and Bakenfelder et al. ( I 990a) for thickness contours recorded with the plasmon and L losses of A. This blurring can be explained by the angular distribution of inelastic scattering, which becomes equivalent to a spectrum of excitation errors and results finally in an increasing blurring of edge and bend contours with increasing energy loss (Metherell, 1967; Duval and Henry, 1977; Doniach and Sommers, 1985; Rossouw and Whelan, 1981; Bakenfelder et al., 1990a). If lg(t,w ) is the intensity of the primary (g = 0) or a Bragg reflected beam g as a function of foil thickness t and tilt parameter w = st,(<, = extinction length), resulting from the dynamical theory of electron diffraction, the inelastic image intensity with an energy loss A E = n A E p l becomes wor

AE) =

I,([, w,

1

+ w)F(w,A E ) d w

P,(t,AE).

(43)

The square bracket contains the convolution of I,(& w ) with

which is the normalized angular distribution of inelastically scattered electrons in Eq. (16). The scattering angle 0 = (Ox, 0,) is projected on the x axis

AE

FIG.23. Bend contours in an aluminium foil a) plasmon-loss filtered]AE 300 eV.

=

=

20 eV) and b) at

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L. REIMER

parallel to g, and w = &$,/d,,,. The maximum values w, and 0, in the integration limits of Eqs. (43) and (44) correspond to the minimum of the cutoff angle 13,in Eq. (19) or objective aperture a. The last factor in Eq. (43) is the Poisson distribution of Eq. (24), which represents the probability for exciting multiples of plasmon losses; The influence of the convolution with F and multiplication with P is demonstrated by a two-beam calculation in Fig. 24 for selected energy windows at AE = 0 eV and 45 eV and tilt parameters w = 0 (exact Bragg condition) and w = 1.3, respectively. Figure 24a with AE = 0 eV shows the edge contours for the reflected beam (dark field) with a period 5, and a reduced period &,eff = for w = 1.3 in Fig. 24b. The decrease in intensity with increasing thickness t/<, is caused not only by the absorption term of the dynamical two-beam theory containing the absorption lengths lb but also by the exponential decrease of the Poisson distribution of Eq. (24) for n = 0. The corresponding full curves for AE = 45 eV in Figs. 24c and d show a maximum at a higher thickness where the Poisson distribution for n = 3 has its maximum. The dashed curves in Figs. 24c and d are obtained by the convolution with F in Eq. (43). The blurring is a minimum for w = 0 because the reflected intensity is symmetric in w. This explains in principle the blurring effects observed in Fig. 23b for a high energy loss, whereas the image at AE = 20 eV in Fig. 23a is less affected by this blurring effect.

<,/dv

II

w.1.3

1

FIG.24. Edge contours calculated by the dynamical two-beam approximation for the Bragg condition a) w = 0 and b) w = 1.3. Modifications for an energy loss A E = 45 eV at c) w = 0 and d) w = 1.3 considering the Poisson distribution (full curves) and an additional blurring by the spectrum of excitation errors (dashed curves).

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

87

The convolution in Eq. (43) becomes comparable with the discussion of Bragg contrast in the STEM mode when the Poisson factor is omitted and the angular distribution of the incident electron probe is substituted for F. Experiments and calculations also showed a blurring of edge and bend contours and a preservation of part of the lattice defect contrast when using large probe apertures to get the smallest probe size (Reimer, 1973; Booker et al. 1974; Maher and Joy, 1976; Reimer and Hagemann, 1976). Decreasing the probe aperture, or decreasing the detector aperture due to the theorem of reciprocity, results in a contrast comparable to the conventional TEM (CTEM) mode. Both the STEM and the ESI zero-loss modes avoid the chromatic aberration of Eq. (40), which is superposed on the blurring effects. The observed Bragg contrast in unfiltered images is hence a superposition of the elastic and inelastic images, the latter being blurred by both the spectrum of excitation errors and the chromatic aberration. (The contribution of inelastically scattered electrons to crystal lattice fringe and crystal structure imaging is discussed in Section 1V.C.) Zero-loss filtering of crystalline specimens can separate the unblurred elastic image. Figure 25 shows an example of an evaporated aluminium film. Zero-loss filtering can be applied up to mass thicknesses of N 150 pg/cm2 at E = 80 keV, where the averaged transmission falls below and the exposure time becomes longer than 100 seconds (Reimer et al., 1989; Bakenfelder et al., 1990a).Thicker specimens can be investigated by most probable loss imaging (Section IV.D.3b) up to -300 pg/cm2. These limits can, in both cases, be increased in orientations with anomalous transmission (channeling) (Lehmpfuhl et al., 1989).The 80 k V zero-loss images are comparable with unfiltered 200 kV CTEM images, where the chromatic aberration is reduced due to the denominator E in Eq. (40) (Bakenfelder et al., 1990b). ESI can also be used to investigate the preservation of contrast for electrons scattered between the Bragg spots and the primary beam by using a shifted objective diaphragm (Bakenfelder et ul., 1990a). Electrons scattered

FIG.25. Comparison of a) unfiltered and b) zero-loss filtered images of a 420 nm polycrystalline aluminium film.

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quasi-elastically by thermal diffuse scattering at phonons show no conservation of Bragg contrast (edge and bend contours) in zero-loss filtered images as expected from theory. However, the intensity between the Bragg spots is modulated by the probability YY* of the Bloch-wave field at the nuclei and becomes proportional to j Y Y * dz (Section V.B.l). Plasmon-loss images selected by a diaphragm near the Bragg spots or near to the primary beam show the preservation of dark and bright field intensities, respectively. A diaphragm centered between Bragg spots selects the angular distributions of inelastically scattered electrons from both spots, which results in a superposed dark field image. Preservation of contrast can also be observed in imaging of lattice defects. Craven et al. (1978) reported a conservation of bright field stacking fault contrast by filtering the L-shell loss signal of silicon at A E = 100 eV. Figure 26 shows images of a stacking fault in Cu-7%AI at ,three tilts with a comparison of zero-loss images with images at A E = 300 and 100 eV, respectively (Bakenfelder et al., 1990a). The contrast should decrease at higher losses of the order of 1 keV when the scattering processes becomes more localized.

FIG. 26. Stacking faults in Cu-7XAI imaged in the zero-loss mode and with AE

=

300 and

100 eV, respectively, for three orientations a)-c) indicated by the position of Bragg spots and

Kikuchi lines on top.

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89

3. 2:Ratio Contrast The idea of Z-ratio contrast arises from the fact that the ratio gel/oinin Eq. (13) is proportional to 2. In a dedicated STEM, a large fraction of the elastically scattered electrons can be collected by an annular dark field detector in front of the spectrometer (Fig. 12). A large fraction of the inelastically scattered electrons passes through the aperture of the spectrometer and can be separated from the zero-loss electrons. Because these fractions are proportional to the corresponding cross-sections and to the mass thickness for thin specimens (single-scattering approximation), the ratio of elasticto-inelastic signals becomes proportional to the atomic number Z (Crewe et al., 1970; Carlemalm and Kellenberger, 1982; Egerton, 1982; Reichelt et a/., 1984; Carlemalm er al., 1985; Jeanguillaume and Tence, 1987; Haider, 1989). Ideal 2-ratio contrast should show only the local mean value of 2 independent of local specimen thickness (Jeanguillaume and Tence, 1987). In practice this is approximately true only when using thin specimens. Ottensmeyer and Arsenault (1983) transferred the idea of 2-ratio contrast to the ESI mode of a TEM with a filter lens. The following calculations and measurements of 2-ratio contrast shall show the limits of this mode in EFTEM (Reimer and Ross-Messemer, 1990). An “elastic” image can be observed by digital calculation of the difference image

K I ( ~ , , ~=zT) , ~ I ( ~-z )T , ~ I ( ~ I ) ,

(45)

using zero-loss images with large (a2 2 20 mrad) and low aperture (alI 5 mrad). The image contribution from inelastically scattered electrons is given by the difference image

of unfiltered and zero-loss filtered images. In the single-scattering approximation for small mass thicknesses we can a z ) K geland T,,,(az)K ginand the ratio assume that T,,(a,, R ( a , , a Z , x ) = T,1(a,,a2,x)/Tn(a2,x)

l/v

(47)

should be proportional to l/v = 2/20 in Eq. (13) and independent of aperture and mass thickness x. However, the values of the normalized ratio R,,,,

=

R(a1, a2

7

X)

x 2O/Z,

(48)

plotted versus the mass thickness in Fig. 27, show very strong deviations from the expected unity value. The decrease of R,,,, with increasing Z (curve parameter) for small x is obviously caused by too low an aperture a 2 , which does not collect all the elastically scattered electrons. The stronger decrease of the ratio with increasing x for low Z can be attributed to the

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"'7

0 0

20 pg/crn2

10

1 30

X-

FIG.27. Normalized ratio R,,,, for Z contrast from Eq. (48) vs. mass thickness x for different elements (a, = 2 mrad, a, = 20, 50 and 100 mrad).

high value of v, which increases the number of inelastically scattered electrons at the expense of the elastic fraction, though they still pass through the aperture. This demonstrates that the ratio in Eq. (47) of difference images does not fulfil the condition for a good Z-ratio contrast. Since we obtained good values of v by using the following ratio (Reimer and Ross-Messemer, 1990), we calculated a "Z-ratio contrast" by K

= In('L)/In(Til),

(49)

using Eqs. (35b,c) and plotted as K vs. 2 in Fig. 28. The bars are experimental values for a = 30 mrad. Though the Z-contrast becomes more linear for c1 = 75 mrad, this is an unreasonably large aperture for practical work. The resulting 2-ratio contrast becomes approximately independent of mass thickness because a log(T) vs. x plot of transmissions (Figs. 18a-c) shows that log(T,iI)and log(T,,,) are both proportional to x so that the ratio of these quantities is constant up to mass thicknesses x N 40 pg/cmz. 4. Lorentz Contrast The Lorentz microscopy mode is used in CTEM for the imaging of ferromagnetic domains and of the magnetization ripple in thin films of thickness t with a magnetic induction B parallel to the film plane. The Lorentz

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

91

1Omrad

08-

I

Y

o.6

040.2-

-,0

10

i0

I

40

$0

I

1

I

50 60 70 80 ZF I G . 28. Calculated “Z-contrast” K given by Eq. (49) vs. atomic number Z for different apertures CL in mrad. Bars: experimental values at a = 30 m a d . 0

force F = - e v x B results in an angular deflection

(50) An iron film of thickness t = 50 nm and a spontaneous induction B = 2.1 Tesla results in E, = 0.1 mrad for E = 100 keV. In the Fresnel mode of Lorentz microscopy, a strong defocusing of a few millimeters is used to detect magnetic domain walls either as divergent (dark) or convergent (bright) images. The intensity profile of the divergent wall image can be used for measurement of the domain wall thickness (Wade, 1962). However, the profile is modified by a convolution with the angular distribution of inelastic scattering (Reimer and Kappert, 1969).Mory and Colliex (1976) showed that zero-loss filtering avoids the inelastic contribution and increases the contrast of divergent wall images. The influence of zero-loss filtering on small-angle diffraction patterns and on laser diffractograms from ferromagnetic films is discussed in Section V.A.2. E,

=

eBt/mo.

C. Plasma-Loss Imaging

1. Scattering Contrast Caused by Plusmon Losses According to Eq. (24), the intensity of the first plasmon loss increases a p e - P ( p = [ / A p lwith ) increasing thickness t and passes through a maximum at t = A,,, (see also Ii, of all inelastically scattered electrons in Fig. 19). The sensitivity on t is demonstrated in Fig. 29c by zero-loss imaging and in Fig. 29d by plasmon-loss imaging of a carbon foil with open and partially closed holes (The other images of Fig. 29 showing increased phase contrast at over- and underfocus are discussed in the next section). The open (upper)

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b

~.

d

f

FIG.29. Carbon film with open (top) and closed holes (bottom) zero-loss filtered with A E = 0 eV ( a m ) and plasmon-loss filtering with an energy window at 25 f 5 eV (b,d,f) in under (a,b), near (c,d)and overfocus (e,f) at defocusing distances Az = - 1.5 pm, -0.5 pm and + 1.5 pm, respectively. The arrows indicate typical changes in contrast from bright to dark and reverse (Bar = 50 nm).

hole in Fig. 28c with the full intensity of the primary beam becomes of course dark in the plasmon-loss image of Fig. 28d. This can be of advantage for recording images with such areas, which are overexposed in the conventional bright field or zero-loss mode. In contrast to the conventional dark field mode, where the primary beam is absorbed by the objective diaphragm, the primary beam here is absorbed by the shift of the EELS across the energyselecting slit. The partially closed (lower) hole in Fig. 28c shows two areas of smaller thickness (higher transmission). The central area looks a little bit darker than the annular region. This is a well-known optical illusion, caused by the faint black and white phase contrast (Fresnel fringes) surrounding these areas.

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

93

Conversely, the plasmon-loss image in Fig. 28d shows increasing intensities K t for the central, annular and surrounding regions. When observing thicker specimens (polystyrene or inorganic particles) with strongly varying thickness, the maximum of intensity can be observed for t = Apl. On shifting the selected energy window to higher energy losses, the intensity maximum shifts to higher thicknesses. Often a stained biological section shows no significant difference in zeroloss and plasmon-loss images, though one would expect that the higher mass thickness of stained structures would result in a higher intensity in the plasmon-loss image. However, the higher scattering contrast due to staining is caused in both zero- and plasmon-loss imaging by scattering of electrons through angles larger than the objective aperture so that the structure appears dark in both images. Additionally, differences in the EELS in the plasmon-loss region can result in contrast differences (see also Section III.C3). A plasmon-loss image can, therefore, become a complicated overlap of these different contrast mechanisms, which have to be taken into account when discussing the contrast. 2. Phase Contrast of lnelastically Scattered Electrons In Section IV.B.1 we calculated the scattering contrast by treating the electrons as particles and establishing the fraction of electrons that passes through the objective diaphragm. At high magnifications (and with a low illumination aperture and high defocusing also at lower magnifications), the amplitudes of the primary and elastically scattered waves have to be superposed with correct phase at the final image, and we observe the intensity as the absolute square of the amplitude. Phase contrast is thus caused by interference of the scattered and the unscattered electron waves. A specimen structure of period A or spatial frequency 4 = 1/12 shows a diffraction maximum at a scattering angle 0 = A/A = 4. An aperiodic specimen shows a spectrum of spatial frequencies that can be obtained by a Fourier transform of the transmitted amplitude, which is phase-shifted by the local inner potential of the specimen. The scattered wave shows a phase shift of 90" or n/2 relative to the incident wave, and no contrast will be observed when imaging without any additional phase shift. The spherical aberration constant C, of the objective lens and a defocusing Az causes a phase shift (wave aberration) depending on the scattering angle H (Scherzer, 1949):

The phase factor exp[ -iW(q)] results in a phase contrast transfer function

94

L. REIMER

(CTF) B,,(q) = - 2 sin W(q)

(52)

for spatial frequencies q = O / l (Hanszen, 1971). Only when the incident plane wave is parallel and monochromatic is the illumination coherent. In reality, we have partial coherence due to limited spatial coherence associated with the finite value of the illumination aperture and limited temporal coherence due to the energy spread AE N 1-2 eV of the electron gun (Hanszen and Trepte, 1971; Frank, 1973) or to the width 6 E of the selected energy window. Partial coherence results in an incoherent superposition of image intensities obtained from the superposition of the amplitudes of the partial waves of single electrons. Kohl and Rose (1985) showed that elastically scattered partial waves are coherent in spite of very small recoil energies, whereas partial waves of inelastically scattered electrons are incoherent relative to the primary and elastic partial waves and also to inelastic partial waves that differ in the final object states. These are, for example, the excitation of plasmons or single electrons with different transferred momenta -hq' = -h(k, - k,) where k, and k, are the wave vectors of the incident and inelastically scattered wave, respectively. Plasmon excitation also shows a dependence of energy loss on the scattering angle (dispersion), and we assume for the further discussion that partial inelastic electron waves scattered in different directions are incoherent, though this needs a further theoretical discussion and should be taken as an approach for low energy losses and spatial frequencies only. This approximation will hence be useful only for nonlocalized inelastic scattering processes. This concept of incoherent partial inelastic waves with different k, has also been used to explain the blurring of Bragg contrast of edge and bend contours in Section IV.B.2. The phase contrast transfer function can thus be calculated, including partial spatial coherence with the angular distribution of inelastic scattering (Reimer and Ross-Messemer, 1990). These calculations are confirmed by comparison with the phase contrast images with zero-loss and plasmon-loss filtering in Figs. 29a-f, which show zero-loss and plasmon-loss filtered images (top and bottom row, respectively) of a carbon film with holes imaged in under (left), near (central) and overfocus (right column). The images with the plasmon-loss need long exposure times of N 100 s when a small illumination aperture 51 mrad is employed, because the intensity of the plasmon loss is low for thin films. We worked with an energy window of 6 E = 10 eV, which, however, should have little influence on the decrease of phase contrast in the first main transfer band of the CTF at high defocusing. Phase contrast structures with the carbon plasmon loss at lower defocusing and 6 E = 4 eV have also been observed by Martin et al. (1989) in the ESI mode and by Craven

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

95

and Colliex (1977) in a dedicated STEM. Contrast reversals from bright to dark and vice versa are indicated by arrows in Fig. 29. The plasmon-loss filtered focus series (Figs. 29d-f) shows a stronger dependence on film thickness caused by scattering contrast near open and closed holes of the carbon film because the image intensity will be proportional to the local thickness whereas the zero-loss filtered bright field images show only a small decrease of transmission. A knowledge of the contribution of inelastically scattered electrons to lattice fringe and crystal structure images is important for the discussion of unfiltered high-resolution images (e.g., Boothroyd and Stobbs, 1989), because the necessary comparison with multislice calculations gives only the contribution of the elastically scattered electrons. Lattice fringe contrast in graphitized carbon (Craven and Colliex, 1977) and crystal structure imaging of silicon (Ajika et al., 1985) has also been found with reduced contrast in the plasmon-loss image. For calculating the plasmon-filtered images of crystal lattices a modified multislice theory can be used (Wang, 1988). 3. Selective Plasmon-Loss Imaging Normally, the contrast of biological sections does not change appreciably when the plasmon loss of carbon is selected instead of the zero loss because the scattering contrast from heavy elements is caused in both cases by elastic scattering through angles larger than the objective aperture c1 (see also Section 1II.C.l). The contribution of heavy elements used for fixation and staining is normally buried in the broad carbon plasmon loss. Selective imaging by energy-loss filtering, resulting in an increase of image intensity, is therefore of more interest for phases in inorganic specimens with sharp and different plasmon losses. Henoc et al. (1970) obtained bright images of He bubbles in aluminium at AE = 11 eV, which disappeared when the 15 eV plasmon loss of aluminium was selected. Brighter images of Be precipitates in Al have been observed by Castaing (1975) at AE = 19 eV, the plasmon loss of Be. Figure 30 shows how small evaporated In and Sn crystallites on opposite sides of a carbon film (zero-loss image in Fig. 30a) can be selectively imaged by their very sharp plasmon losses at AE = 12 and 13 eV (Figs. 30b,c) respectively, when using a narrow energy window with a width of 1 eV. Selection of surface plasmon losses can result in a bright rim around particles because such losses can even be excited at distances up to a few nanometers when the electron causes a polarization but does not strike the particle directly. This has been observed in a dedicated STEM (Marks, 1982; Howie and Milne, 1984; Batson, 1986) and by EFTEM with a Castaing filter lens (Reimer et al., 1988).

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L. REIMER

FIG.30. Carbon film with evaporated In (top) and Sn (bottom) films with island structure imaged by a) zero-loss and their b) AE = 12 eV and c) 13 eV plasmon losses, respectively (Bar = 50 nm).

FIG.3 1. ESI of a liver section of 60 nm (Os0,-glutaraldehyde fixed, uranyl-acetate stained and epon embedded) a) zero-loss filtered and b) ESI at AE = 250 eV with “structure-sensitive” contrast.

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

97

D . High Energy-Loss Imaging 1. Structure-Sensitive lmuging

Imaging of a biological section 60 nm thick (Os0,-glutaraldehyde fixated, uranyl-acetate stained and epon embedded) at an energy loss A E ‘v 250 eV just below the carbon K edge at A E = 285 eV offers greater “negative contrast” (Fig. 31b) than the increase of positive contrast by zero-loss filtering in Fig. 31a (Probst and Bauer, 1987; Bauer, 1988; Reimer and Ross-Messemer, 1989). This “structure-sensitive contrast” allows an image of biological sections to be formed with a minimum contribution from carbon and a relatively strong contribution by noncarbon atoms (P, S and staining elements, for example) inside the biological structure. At medium energy losses ( A E = 50 eV) the contrast has a minimum. These contrast reversals have their parallel in intersections of the EELS spectra at a heavy metal stained part of a section (nucleus) and at the pure resin, for example (Fig. 32). The first intersection is at A E = 50-70 eV. Below the carbon K edge, the observed slower decrease of the EELS intensity with increasing A E at a stained area (nucleus, curves la and 2a for different apertures) as compared with the curves 1b and 2b at pure resin (epon) is caused either because of lower exponents s in the decrease a A E - ” of Eq. (21) and/or because of L , M or N edges of the noncarbon elements below A E = 250 eV.

0 ’

I

I

,

200

250

300

I

350

Energyloss

1

400 eV

-

FIG.32. EELS of section shown in Fig. 31 from areas at a) the nucleus and b) pure epon for two apertures a,.

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L. REIMER

These changes of contrast with varying energy loss therefore depend on the local composition of the section. The advantage of this method is that the contribution of carbon is kept to a minimum and this “structure-sensitive contrast” can show more details than a conventional dark field image. In front of the K edge, the EELS and image intensity at the nucleus are nearly twice that of pure resin when using an objective aperture of c1 = 6 mrad. Analogous effects of contrast reversals can be observed in model specimens containing the metal as an evaporated film of mass thickness x , on a carbon substrate of mass thickness x , (Reimer and Ross-Messemer, 1990). We therefore used these specimens for the quantitative investigation of structure-sensitive contrast, which can be described by the following theoretical approach. The inelastic scattering from the majority of primary and plasmon-loss electrons up to A E = 250 eV is proportional to the mass thickness and, for the number of electrons in the interval A E , A E + dE, we find N ( A E ) d E = (Nc + N,)dE = N,(c,x,

+ c,x,)dE,

(53)

where c = [ d ~ / d ( A E ) ] 2 s ox, N,/A. This number of electrons below the carbon K edge increases linearly with increasing mass thickness and reaches a maximum at about 100 ,ug/cm2. We can therefore assume that the linear approximation of Eq. (53)will be valid for x I 20 pg/cm2 and we get (Ns/Nc)2soev = C , X S / X C >

(54)

with c, = c,/c,. A plot of measured values of C = Np,/Nc versus the mass thickness ratio x p l / x cis shown in Fig. 33 for Pt films on carbon. The intensities N,, + N, and Nc are measured by a scintillator-photomultiplier combination at the carbon-metal layer and at the pure carbon layer, respectively. Values of

1212 10

2.78 Pt A E = 2 5 0 e V

-

8

I S V

2 0 XPt

“c

FIG.33. Ratio C = Np,/Nc = (Ipl+c- I,-)/I, of the number of electrons scattered at A E = 250 eV by the staining metal (platinum, NPI)and by the carbon film (N,) versus the ratio xpl/xc of their mass thicknesses.

99

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY TABLE I 1

CONSTANTS c, FOR ESI IMAGINGAT A E = 250 eV (STRUCTURE-SENSITIVE CONTRAST) FOR THREE APERTURES a A N D cd FOR ANNULAR DARKFIELDIMAGING WITH 2, = 4 mrad A N D r z = 30 mrad. c, for

ESI at AE

=

250 eV

c,

for annular dark field

z

Element

a=4

10

30 mrad

unfiltered

6 13 14 22 25 29 32 78

C Al Si Ti Mn Cu Ge Pt

1 .o 3.0 1.4 1 .o I .2 2.3 2. I 2.3

1 .o

4.0 2.0 1.3 1.5 3.2 3. I 2.3

I .o 4.7 2.8 2.0 2.0 4.2 3.1 2.3

0.8 I 0.8 I 0.84 0.86 0.88 0.89 0.65

1 .o

zero-loss filtered

I .o I .3 1.4 1.7 1.9 2.0 2.1 1.8

c, are listed in Table I1 for three different objective apertures. These results show that the contrast relative to carbon is increased at A E = 250 eV for all elements but the amount of increase shows large variations that can be attributed to the different distance of the edges below 250 eV, their different decrease with increasing A E and to the unknown contribution of the tail of single electron excitation at A E = 250 eV. For a comparison with conventional techniques, the dark field mode also shows bright stained structures in contrast to dark structures in the bright field mode. The dark field intensity also increases with increasing thickness but already reaches a maximum for 10-20 pg/cm2. Therefore, a formula analogous to Eq. (53) can be developed with the constant c d instead of c, in Eq. (54) (Reimer and Ross-Messemer, 1990). The dark field intensity is calculated as the difference of transmissions for two apertures u2 > al. The coefficients c, and cd are listed in Table I1 for comparison. It is interesting that c d in Table I1 is always less than unity in unfiltered dark field images, which means that the same increase of mass thickness by Ax results in a larger increase for carbon than for other elements. Conversely, all cd values are larger than unity in zero-loss filtered dark field images. In most cases c, is larger than c d which demonstrates the advantage of ESI at A E = 250 eV as a structure-sensitive “dark field” technique. This type of contrast is not restricted to biological sections. In doubly evaporated Ag-Au films on rocksalt, the Ag crystals appear bright just beyond the Ag Mdq5edge at A E = 440 eV and below the edge where the contribution of Ag is a minimum as it is for C below the C K edge-the Au crystals appear bright (Keusch er al., 1986).

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2. Contrast Tuning The discussion of Figs. 31 and Fig. 32 in the last section showed that the EELS intensity distribution of stained and unstained parts of a section is quite different and can show intersections. In thick sections, stained structures can become very dark and it will not be possible to record the full dynamic range of image intensities in a single micrograph. By varying the energy window in the range 0-200 eV (contrast tuning) energy losses can often be found for which the contrast of strongly and less stained and of unstained areas lies within the dynamic range of a photographic emulsion (Bauer et al., 1987;Wagner, 1990). 3. Most-Probable-Loss Imaging

a. Biological Sections The EELS of thick sections consists of a Landau distribution with a most probable energy loss at A Ep = p AE,, where p = t/A,, with the carbon plasmon loss AE,, ‘v 25 eV and a mean-free-path Ap, N 90 nm in organic material of density p = 1 g/cm3 for E = 80 keV; this gives AEp = 270 eV for a 1 pm section. The zero-loss transmission after passing a 1 pm (100 pg/cm2) layer is about (Fig. 18a).The intensity at the most probable loss is large enough to record an image either by dedicated STEM (Colliex et al., 1989) or by EFTEM with a filter lens (Bauer et al., 1987) as shown by measurements (MPL) in Fig. 16 (Reimer et al., 1991). This can increase the limit of zero-loss imaging (x I 70 pg/cm2) to x I 150 pg/cm2. The latter method decreases the very strong chromatic aberration of unfiltered images which, however, will be limited by the width of the selected energy window and the large aperture necessary to obtain sufficient intensity. STEM modes can avoid chromatic aberration because there is no imaging lens behind the specimen. However, the top-bottom effect discussed in Section IV.D.4 has to be taken into account for both modes. High voltage electron microscopy (HVEM) is another possibility for observing thick sections. The chromatic aberration decreases with increasing energy due to the electron energy E in the denominator in Eq. (40) and the width 6 E of the EELS decreases because of the increase of the mean-free-path for plasmon losses. The product C, u can be assumed to be constant. ESI images of 0.7 pm sections at 80 keV are comparable with micrographs in conventional TEM at 200 keV (Bauer et al., 1987), though there are differences in contrast-the ESI image shows more details.

-

b. Crystalline Specimens Most probable loss filtering of crystalline specimens increases the useful thickness from N 150 pg/cm2 (zero-loss filtering, Section IV.B.2) to -300 pg/cm2 (Reimer et al., 1989; Bakenfelder et al., 1990a). The largest thicknesses for zero-loss and most probable loss imaging are about a factor two larger than those mentioned before for biological

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

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sections as amorphous specimen because the mean absorption coefficient pCrysf for orientations without strongly excited low-order Bragg reflections is about half of pamOrph for amorphous specimen ( T = exp( -@); Reimer, 1967; Bakenfelder et al., 1990a). We discussed in Section IV.B.2 the influence of the angular distribution of inelastically scattered electrons on Bragg contrast, which is equivalent to a spectrum of excitation errors. The very broad angular distribution (diffraction pattern) of thick specimens shows no Bragg spots but only defect Kikuchi bands (Section V.B.2). These are formed in the lower part of the thick specimens whereas the upper (entrance) part acts more as a diffuser by multiple scattering. In thin specimens, Bragg contrast is generated by intercepting the Bragg diffracted beams at the objective aperture. In thick specimens, directions exist in the diffuse cone that are Bragg diffracted to the primary beam direction. The image intensity becomes dependent on Elg (see Eq. (66)), which cancels the pendellosung fringes of dynamical theory, and only variations in anomalous transmission (channeling) are observed (see also rocking curve of a three-beam case in Fig. 41). The intensity variation caused by this channeling contrast becomes lower than the pure Bragg contrast and a bent foil appears more uniform. However, lattice defects can still be observed, though with reduced contrast. This contrast is analogous to the “multibeam imaging” mode in HVEM (Hashimoto, 1974) where the primary and diffracted beams can pass through a large aperture diaphragm and can overlap in the final image. The same effect can be observed at 100 keV in STEM when working with the large electron probe aperture that is necessary to get a small electron probe (Reimer and Hagemann, 1976). Here the large aperture is externally generated by electron optics. Tile chromatic aberration in ESI imaging of thick foils at 80 keV is comparable with conventional TEM at 200 keV (Bakenfelder et ul., 1990b) though the latter needs much shorter exposure times and shows sharper Bragg contrasts due to the reduced angular spectrum of excitation errors. The possible advantage of ESI of crystalline specimens in HVEM are discussed by Bakenfelder et al. (1990a). 4. Top-Bottom Effect The last sections showed that chromatic aberration can be suppressed by most probable loss imaging in EFTEM and can be avoided in dedicated STEM or in the STEM mode of a TEM. However, both modes show a topbottom effect (TBE) caused by the spatial broadening due to multiple scattering. First, we discuss the TBE in the STEM mode. Structures at the top (entrance side) of a thick specimen (Fig. 34a) are scanned by the electron probe with a diameter d , limited by the diameter of the crossover, the energy spread

102

L. REIMER E l e c t r o n probe

Electron beam

tom a) l o p sharp b) Bottom diffuso STEM

c1 Bottom sharp d) l o p diffuse E S I mode of T E M

FIG.34. Top-bottom effect lor structures a) at the top (electron probe diameter d,) and b) at the bottom of a thick carbon film in the STEM mode (lateral beam broadening ds). In the ESI mode structures c) at the bottom are illuminated by an increased aperture a, and d) at the bottom can be imaged with a minimum diameter d i at an optimum defocusing.

of the electron gun, and the aberrations of the probe-forming lens. Structures at the bottom (exit side) (Fig. 34b) are scanned by the spatially broadened electron probe of diameter d,. For 100 keV electrons and 1.1 pm polystyrene this results in d, = 15 nm (Gentsch et al., 1974). We now discuss, with the aid of Figs. 34c,d, the influence of multiple scattering on the TBE in the EFTEM mode. We irradiate with an electron beam of illumination aperture mi. Structures at the bottom (Fig. 34d) are irradiated by an aperture a, increased by multiple scattering. When chromatic aberration is neglected, the objective lens can focus on this plane, and the structures at the bottom appear sharp. Electrons scattered at structures at the top are distributed over a diffuse circle at the exit side. Up to this point, the TBE in STEM and TEM modes is reciprocal. However in the case of TEM we should be able to focus structures at the top and these would appear sharp if the trajectories of scattered electrons were straight within the specimen. Multiple scattering disturbs this possibility of focusing, and we find a minimal disturbed diameter d: when focusing at a plane between top and bottom (Reimer and Gentsch, 1975). This diameter is smaller than d, observed for bottom structures in the STEM mode. Normally, this TBE cannot be observed in conventional TEM because of the superposed strong chromatic aberration disc of -20 nm in diameter for 80 keV, m = 5 mrad and 1.1 pm polystyrene, for example (Gentsch et al., 1974). When we avoid the chromatic aberration by most probable loss imaging in the ESI mode, this TBE in the EFTEM mode can be recognized and becomes 8 nm for 1.1 pm polystyrene in agreement with calculations (Reimer and Ross-Messemer, 1987).

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

103

E . Elemental Mapping Elemental mapping in transmission electron microscopy can be realized with the x-ray signal from an energy-dispersive x-ray analyzer (Somlyo, 1984) or with a series of ESI images below and beyond the ionization edge of the element of interest (Adamson-Sharpe and Ottensmeyer, 1981; Ottensmeyer, 1986; Shuman et al., 1986). In the case of x-ray elemental mapping, the specimen is scanned by an electron probe. Pulse heights within a selected x-ray energy window generated by characteristic x-ray quanta of the element are recorded as dots in a x-ray map. The density of dots is a measure of the concentration of the element. It is a disadvantage that the x-ray continuum in the selected pulse-height window also contributes to the map, which decreases the analytical sensitivity. There are not enough recorded x-ray quanta per pixel element in a reasonable time frame to be able to subtract a background signal from windows below and beyond the characteristic x-ray line unless scan times of several hours are acceptable. The subtraction of a nonspecific background signal can be better realized in the ESI mode, though the signal of the edge of interest is often much smaller than the background. One ESI image just beyond the edge and two below the edge(Fig. 15)withenergywindowsof width Aatenergy lossesAE,,AE,,AE, and intensities I , , I , and I , , respectively, have to be recorded and digitized either by scanning photometry of exposed photographic films or by direct recording with a CCD camera coupled to a fluorescent layer and a fiber plate (e.g., Roberts ef al., 1982; Zaluzec, 1989).The digital images are processed by the following two methods to get a signal proportional to the number of specific atoms.

I . Three- Window Method The signal difference AEi + A / Z

CI,(a, AE) - B,(u, AE)1 d W ) = IIb,A) - B,(a, A)

S,(%A) =

(55)

AEi -A12

for a quantitative analysis depends on the aperture u and the width A. The background below and beyond the edge is assumed to be proportional to AAE-” in Eq. (21). Therefore, a minimum of two additional windows with signals I, and I , below the edge are necessary to determine the two constants A and s, s = ln(13/lz)/ln(AE,/AE~) and

A A = (I,/AEiS + 13/AE;”)/2,

(56)

and the extrapolated background for window 1 beyond the edge becomes R , = AAAEY“.

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In the case of Ca, for example, the Ca L edge (Fig. 4f) consists of a white line spectrum superposed on the ELNES of the C K edge (Fig.4b). In this case it can be better to record ESI at, below and beyond the white line with the signals I , , I , and I , respectively, and B , = ( I , + 1 3 ) / 2(Colliex, 1986). 2. Thickness Corrected Four- Window Method The EELS at the edge is convolved with the intensity distribution of the zero-loss beam and the plasmon losses, which create a signal Io(a,A) in an energy window from A E = 0 to A E = A. This signal decreases exponentially with increasing mass thickness at the pixel position. This limits elemental mappings to films thinner than the mean-free-path A,, of plasmon losses (A,, = 90 nm for carbon at 80 keV). In quantitative EELS (Egerton, 1986) the number N of specific atoms per unit area can be calculated by

The partial cross-section o(a,A) is defined in Eq. (23). A knowledge of a(a,A) allows us to estimate N . Therefore, a fourth signal I, with the same width A should be recorded at the zero and plasmon loss and the ratio Sl/Io should be used for all elemental mapping of structures that appear darker than the background in the bright field mode (Leapman, 1986; Shuman el al., 1986). The advantage of this method is demonstrated in Fig. 35 for a 0.07 pm polystyrene sphere on a carbon film uniformly covered with an evaporated CaF, film. The three-window method with Eq. (55) results in a decrease of the Ca map below the sphere (Fig. 35a). The thickness corrected method with Eq. (56) results indeed in a more uniform Ca map (Fig. 35b), which can also be seen in the linescans over the sphere.

(a) (b) FIG.35. Elemental mapping of Ca from an evaporated, uniform film of CaF, on carbon covered with three 0.09 pm polystyrene spheres. The three-window method (a) results in a “decrease of Ca” below the polystyrene spheres, whereas this decrease by multiple scattering can be compensated by the thickness-corrected four-window method (b).

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

105

The most frequent application in biology is the elemental mapping of P, Ca and S (e.g., Arsenault and Ottensmeyer, 1983, 1984; Blottner and Wagner, 1989; Dopfner and Wiencke, 1990; Harauz and Ottensmeyer, 1984; Heinrich et al., 1990; Kortje et al., 1990; Ottensmeyer et al., 1988). Analytical sensitivities of clusters of N 150 phosphorus atoms (Ottensmeyer et al., 1988) in energy filtering microscopy and only a few uranium atoms in the STEM (Mory and Colliex, 1989) have been demonstrated under favorable conditions. However, embedding in sections increases the background and its noise, and such high sensitivity needs an incident charge density of the order of a few Couloumbs/cm2 for exposure ( 1 C/cmZ N 6 x lo4 electrons per nm2) resulting in strong radiation damage (mass loss of matrix already at N lo-’ C/cm2, delocalization of atoms by ‘v 1 nm, loss of noncarbon atoms in the range lo-’ - 10” C/cmZ). A major problem for biological material is the extraction of the element of interest during chemical fixation, dehydration, embedding and sectioning. New embedding resins like Novocryl can considerably decrease the extraction (Lehmann, 1991). The best method for preservation is cryofixation and cryosectioning and cryotransfer to the microscope. This method will become of increasing interest when sufficiently thin cryosections can be prepared routinely. The zero-loss mode can be used to increase the contrast of these unstained frozen hydrated sections (Lautenschlager et al., 1987; Probst et al., 1989). Most of the staining, cytochemical and antigen labeling methods developed for TEM use heavy metals to obtain sufficient scattering contrast. Elemental mapping also allows us to use staining and precipitation with low Z atoms showing a pronounced edge, fluorine for example (Costa et al., 1978). An important condition for elemental mapping is to use specimens with thicknesses smaller or of the order of the mean-free-path of plasmon losses, which is -200 nm for carbonaceous material, rr 120 nm for A1 at 80 kV but shorter for high 2 solids. Therefore, elemental mapping of thinned solids (e.g., Bauer er al., 1988; Zanchi et al. 1977; Ottensmeyer et al., 1988) will only be successful for very thin areas near edges. For example, precipitates need a minimum foil thickness for optimum TEM investigation, which often is too thick for elemental mapping. Clearly, an increase of the mean-free-path by using higher electron energies and pure magnetic filter lenses will become very important for the elemental mapping and EELS of inorganic specimens. V. ELECTRON SPECTROSCOPIC DIFFRACTION 4.Amorphous and Debye-Scherrer Ring Patterns 1. Amorphous Diflraction Patterns

The diffuse diffraction maxima of amorphous films (Fig. 36) can be used to determine the radial density distribution p(r) of atoms where 4nr2p(r)dris

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d.15 nm

I

I

AE=OeV

\

Scattering angle

9

-

FIG.36. Radial intensity records of the diffraction pattern of a 27 nm amorphous germanium film: unfiltered, zero-loss and plasmon-loss filtered at AE = 18 eV.

the probability of finding neighbouring atoms inside a shell between radii r and r + dr. The radial intensity distribution

’,

oscillates around the curve nlf(O)( which would be observed for independent scattering at the n atoms contributing to diffraction with a scattering amplitudef(O)(Leonhardt et al., 1961)(q = e/A = spatial frequency). Inelastic scattering causes a background dli,/dQ, which will be discussed later. Zeroloss filtering not only increases the contrast of the diffuse maxima by removing the inelastic background, but it also gives a better fit of a curve proportional to nlf(o)12 to the recorded radial intensity distribution dl,,/dR (first part in Eq. (58))in order to separate the oscillating second part in the square bracket of Eq. (58). When forming the normalized function the radial density distribution results from an inverse Fourier transform (Leonhardt et al., 1961; Graczyk, 1979; Cockayne and McKenzie, 1988; Liu et al., 1988): 4nr2p(r)= 4nr2p0

:1

+ 8nr

i(q)sin(2nqr)qdq,

where po = N / V denotes the mean number of atoms per unit volume.

(60)

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

107

Figure 36 shows three radial intensity distributions of diffraction patterns of an amorphous germanium film: unfiltered, zero-loss filtered (elastically scattered electrons only) and filtered with the plasmon loss at AE = 18 eV in the ESD model. These distributions can be recorded either by densitometry of exposed photographic emulsions or directly by scanning the diffractogram with deflection coils behind the last projector lens across a slit in front of the scintillator-photomultiplier combination, which is also used for recording an EELS. Diffuse maxima can also be found in the plasmonloss filtered record. This demonstrates that the inelastic electrons are also diffracted. However, instead of the primary beam of small illumination aperture associated with elastic scattering, the intensity distribution of inelastically scattered electrons has to be convolved with the angular distribution of Eq. (8) of inelastically scattered electron ~ ( + $;)-I. 6 ~ The characteristic angle 13, 2~ AE/2E in Eq. (10) increases with increasing energy loss AE. Though the angular distribution of this Lorentzian profile shows a strong peak in the range 0 < 6 < 8 E , it falls slowly with increasing 8, especially when multiplied with dQ = 2 d d 8 to get all inelastically scattered electrons between 8 and 8 + d8 independent of azimuth (see also Section II.C.2).Therefore, it is mainly the tail of the Lorentzian profile at larger 0 that contributes to the blurring and decreases the amplitude of the diffraction maxima and minima by generating a diffuse background. 2. Small-Angle Electron Diflraction Small-angle diffraction patterns can be recorded when the diameter of the primary beam spot is reduced by decreasing the illumination aperture ai to about rad and when the camera length is increased (Mahl and Weitsch, 1960; Ferrier, 1969; Wade and Silcox, 1967). This allows us to record periodicities d with diffraction maxima at scattering angles 6 = I / d L 2ai and to detect periodicities d I I / 2 a i N 200 nm for L = 4.2 pm ( E = 80 keV) and ai = rad in catalase and collagen (Mahl and Weitsch, 1960), for example, or to record diffuse diffraction maxima caused by the mean distance of lattice distortions and of crystals in an evaporated film with island structure (Wade and Silcox, 1967). Figure 37 shows as an example the radial intensity distribution in a small-angle diffraction pattern of a thin Ag film on a carbon substrate. Zero-loss filtering (Fig. 37a) shows the central primary beam and a halo with a maximum at 6 N I / d = 0.4 mrad, which is related to the mean distanced N 10 nm of the crystallites. Filtering at AE = 25 eV (Fig. 37b) does not show the halo, and the record consists of a convolution of the primary beam with the angular distribution of inelastically scattered electrons. This absence of any halo can be explained in terms of an excitation volume of plasmons of the order of 5 nm, which is smaller than the mean distance

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AE: 2 5 eV

FIG.37. Radial densitometer record of a small-angle diffraction pattern of an Ag film with island structure evaporated on a carbon substrate film,a) zero-loss filtered, b) plasmon-loss filtered with AE = 25 eV.

between the crystals, and the excited inelastic wave does not “see” the other neighbouring crystals. Zero-loss filtering has also been applied to platinum aggregates in an annealed Pt/C film prepared by simultaneous vacuum evaporation of the two elements (Castaing, 1969; Duval and Henry, 1973). Whereas the diffraction maxima of the halo contain information about the distribution of the distance between particles, the decrease of diffuse scattering intensity contains information about the radius of gyration as a measure of the size of particles. A future decrease of the illumination aperture by using a field emission gun in combination with zero-loss filtering will allow us to make full use of the small-angle diffraction as in small-angle x-ray diffraction (Guinier and Fournet, 1955). Periodicities A in the range 0.1-1000 nm can also be investigated qualitatively and quantitatively by light optical Fraunhofer diffraction at micrographs on developed photographic films with a magnification M , so that MA = 0.05-1 mm (Berger and Harker, 1967; Reimer et a/., 1973).This technique has also been used to determine the gaps and envelope of the contrasttransfer function by laser diffraction at the granularity of phase contrast of carbon films (Thon, 1966), or the ripple structure of ferromagnetic films (Reimer et al., 1973). In all cases, zero-loss filtering will increase the corresponding contrast and the intensity modulation in the laser diffraction pattern. 3. Debye-Scherrer Ring Patterns The Debye-Scherrer ring patterns from polycrystalline films show an increasing background of inelastically scattered electrons with increasing film

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

109

FIG.38. a) Unfiltered and b) zero-loss filtered Debye-Schemer diffraction patterns of a 410 nm evaporated A1 film.

thickness though part of the background is also caused by thermal-diffuse (electron-phonon) scattering without energy loss. Zero-loss filtering results in an increase of ring intensities relative to the background as demonstrated in Fig. 38 for an evaporated 410 nm Al film (Reimer et al., 1990). Zero-loss filtering of Debye-Schemer ring patterns is also of interest for diffraction at apatite crystals in calcified tissue sections where the resin causes a strong diffuse background (Barckhaus et a[., 1990, 1991),for example. When recording the intensities in a diffraction pattern with an energy window at higher energy losses A E , the rings, including the primary beam, are blurred (convolved) by the angular distribution of multiple inelastic scattering, which also increases as A E. Therefore, diffraction patterns without energy filtering contain the elastic diffraction rings with a width equal to the illumination aperture superposed on a broader ring consisting of rings belonging to the spectrum of energy losses. For narrow rings the latter can make it difficult to extrapolate the background below the rings. Therefore, quantitative work on ring intensities needs zero-loss filtering (Horstmann and Meyer, 1960,1965).Grigson coils (Denbigh and Grigson, 1965) can be used to record zero-loss filtered amorphous and Debye-Scherrer patterns by scanning the pattern across a diaphragm in front of an electron detector (Tompsett, 1972; Kuwabara and Cowley, 1973). 4. Compton Scattering As discussed in Section II.C.3.b scattering of primary electrons at the quasi-free electrons of the jellium results in the Bethe ridge or Compton peak (Fig. 5) with a maximum at the Compton angle O, which increases in proportion to the square root of A E due to Eq. (22).This Compton peak can be observed by ESD as a diffuse ring that increases in diameter with increasing selected energy loss A E (Fig. 39). Quantitative records through the Bethe ridge can be obtained by radial scans through the diffraction pattern at a fixed

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FIG.39. Shift of the Compton peak (Bethe ridge) to increasing scattering angles with increasing selected energy losses a) A E = 0, b) 200 eV, c) 400 eV and d) 800 eV in ESD patterns of a thin graphite film.

energy loss (Fig. 40a) or by recording an EELS at a fixed scattering angle 8 of about 5" (Fig. 40b), which also contains the C K edge (Williams and Bourdillon, 1982; Williams et al., 1984). Another possibility of observation and quantitative analysis is the method of angular resolved EELS (Section III.D.4) (Reimer and Rennekamp, 1989). This phenomenon is useful for interpreting ESD patterns, and furthermore, the intensity profile of linescans (Figs. 40a,b) through the Bethe ridge can be used for a quantitative analysis of atomic orbitals. The intensity profile of the Bethe ridge is caused by the projection of the momentum distribution of atomic electrons on the scattering direction (z):

where n( p ) is the probability density distribution of momentum. The Fourier transform

of a recorded intensity profile is the autocorrelation function of the ground

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

c

AW = 700 eV x = 6 rglcmz

la

m -r

50

Scattering angle 8

11I

\ -

100 mrod 100 mrod

C !-edge 8 1 80 mrod x I 17.2 )rg /cmZ

0

500

AE

1000

1500 eV

2000

(b)

FIG.40. a) Radial scan through an EDS pattern of amorphous carbon with a Compton ring at constant energy loss. b) EELS at 0 = 5" with the Compton peak beyond the C K edge.

state wavefunction. This method is in common use in x-ray Compton scattering (Williams, 1977; Cooper, 1985) for testing calculations of atomic orbitals in solids and has been applied to linescans by electron diffraction (Williams and Bourdillon, 1981). An advantage of this method is the shorter recording time and the possibility of analyzing areas of a few micrometers in diameter. The specimen has to be thin because the Bethe ridge is strongly influenced by multiple scattering.

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B. Single-Crystal Diffraction Patterns 1. Diffraction and Scattering Processes in Single Crystals Before discussing typical energy-filtered diffraction patterns of singlecrystal foils, we summarize the most important effects that can be observed in these patterns. Elastic scattering of electrons in crystals results in Bragg diffraction spots, pairs of excess (bright) and defect (dark) Kikuchi lines and excess and defect Kikuchi bands. Thermal-diffuse scattering can result in diffuse streaks connecting the Bragg sports (Honjo et al., 1964; Komatsu and Teramoto, 1966; Boersch and Jeschke, 1970). Additional spots and streaks can be observed in crystals with defects, which will not be discussed here. Electrons can propagate in crystals only as a Bloch-wave field because of the periodicity of the crystal lattice (Hirsch et al., 1965; Reimer, 1989a). The simultaneous excitation of n Bragg spots with reciprocal lattice points g, including the primary beam (gl = 0) results in a branching of the dispersion surface ( j = 1,. . .,n) where the n 2 wavevectors

k($

= k(j) + g,;

j = 1, ..., n

(63)

start at the excitation points on the dispersion surface and end on the origin and the excited lattice points g, of the reciprocal lattice. A plane wave of wavevector k y = kl;" + g, as part of the Bloch-wave field can be described by = dj'CI;"exp[2ni(kbj)

+ g,) .r] exp[ -2nq%],

(64)

with the excitation amplitude dj) = Cbj) of the j t h Bloch wave for normal incidence on the crystal foil, the eigenvector components Cl;" and the absorption parameters q'j' of waves starting at the j t h branch of the dispersion surface. The total Bloch-wave field

is the sum of the Bloch waves in Eq. (64) over all j and g . The amplitudes $g of the primary or Bragg diffracted beams and their intensities lgare obtained as a sum over all j and fixed g :

This superposition of waves with different wavevectors causes beating, resulting in a depth modulation with a period (extinction length) of the primary beam and the diffracted waves; the intensity oscillates between the primary and reflected beams (Fig. 24). Tilting the specimen or the primary beam results in the symmetric rocking curve with pendellosung fringes on both sides of the Bragg position at k,/g = +0.5 shown in Fig. 41a for the intensity

re

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

1 13

Cu LO nrnl 220 -band

-10

-0'5

k,Ig--

O5

1'0

- 0.5

k,Ig-

O5

10

FIG.41. Dependence of a) the primary beam intensity I, and Bragg reflected intensity I, (g = 220) (rocking curve) and El, (defect band) and b) the large-angle scattering probability cx Ug,,Y,*,, dz (excess band) as a function of the tilt parameter k,/g for the three-beam case of copper at E = 100 keV.

1

I,,o of the g = 220 reflection of Cu at E = 100 keV, for example. The rocking curve of the primary beam intensity I, is asymmetric due to anomalous absorption for k , / g < 0.5 and anomalous transmission for k , / g > 0.5. The rocking curve can be observed by using a large illumination aperture in the STEM mode of a TEM. The Bragg spots become circular and contain intensity variations due to the rocking curve of the dynamical theory of electron diffraction (convergent beam electron diffraction, CBED). Inelastic scattering processes such as plasmon excitations and ionizations with energy losses lower than about 0.5 keV show predominately intraband scattering (Howie, 1963) and preserve the Bloch-wave field though with slightly different wavevectors, which results in the preservation of Bragg contrast discussed in Section IV.B.2. In diffraction patterns, the angular distribution of inelastically scattered electrons results in a blurring of the Bragg spots analogous to the increase of width of Debye-Scherrer rings with increasing energy loss. Pairs of excess and defect Kikuchi lines are generated as intersections of the Kossel cones of semiapex 90"-0, with the observation plane when the number of diffusely scattered electrons is different on either side of the lattice planes. In thick foils, multiple elastic and inelastic scattering results in a broad angular distribution, which is equivalent to an irradiation with an incoherent cone of large illumination aperture. The same number of electrons is then

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incident on both sides of the lattice planes and the Kikuchi line contrast is canceled. Inside this cone, directions exist that contribute to the direction of observation by transmission or by Bragg scattering, and the observed intensity is equal to the sum of intensities of Bragg spots including the primary beam (direction of observation) (Thomas and Humphreys, 1970):

This overlap of B r a g reflections and the primary beam cancels the pendellosung fringes of the rocking curves. However, the anomalous absorption results in defect Kikuchi bands (upper curve in Fig. 41a) which can be observed at the center of diffraction patterns from thick foils especially when the Bragg diffraction spots have disappeared because of the absorption of the primary Bloch wavefield (Pfister, 1953; Cowley et al., 1970; Reimer et al., 1977; Reimer, 1979).These defect Kikuchi bands are also observed when the incident aperture is widened by placing an amorphous foil in front of the specimen (Nakai, 1970) or by using a convergent electron probe and forming overlapping diffraction circles in convergent beam diffraction patterns (Kossel pattern) (Cowley et al., 1970). Excess Kikuchi bands are generated when localized scattering processes, such as large-angle thermal-diffuse (electron-phonon) scattering or ionization processes of inner shells with energy losses larger than -0.5 keV, are excited at the atomic sites on the lattice planes. The probability of inner-shell ionization, for example, becomes proportional to the probability density VinY; of the primary Bloch wave field in Eq. (65) with nodes or antinodes at the nuclear positions depending on the orientation of the crystal relative to the primary beam. The inelastic Bloch wave generated by inner-shell ionization can be described as a spherical wave from a “point source” at the nucleus. The width of the “source” decreases with increasing energy loss, and localization at the nuclei on the lattice planes becomes sharp enough for energy losses larger than about 0.5 keV. A Bloch wave propagating in the direction k,,,, which can be related to a point in the electron diffraction pattern, is emitted with the probability Y,Y t,, of this Bloch wave at the nucleus. This probability can be obtained by calculating Yo,,Y~,,for a Bloch wave field with an electron wave of wavevector - k,,, (reverse direction of k,,,). The total diffracted intensity becomes proportional to YinYg Yo,,Y~,,. This can also be seen as a consequence of the theorem of reciprocity (Kainuma, 1955). The intensity distribution in the electron diffraction patterns becomes proportional to the integral ~You,Y~,,dz (Fig. 41b) because kin and Yindo not change relative to the crystal. This scattering process results in excess Kikuchi bands when the direction k,,, of observation is varied, as can be seen in diffraction patterns of thin foils due to thermal-diffuse scattering into larger angles (Pfister, 1953)

-

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

1 15

and as shown below due to localized inner-shell ionization processes. The directions of the primary wave or of partial waves in a cone of incident, diffusely scattered electrons at low angles are constant resulting in nonvarying averaged values of 'Pi,"$. Such excess bands are also observed for x-ray emitted from nuclei on the lattice planes (Howie et al., 1970) and in electron back-scattering patterns (EBSP) (Venables and Harland, 1973; Reimer, 1979; Reimer et al., 1986). In electron channeling patterns (ECP) obtained by scanning electron microscopy, the pattern of excess bands is obtained by rocking the incident beam and modulating the synchronously scanned TV tube by the back-scattered electron signal. Therefore, 'Pi,'€' $ varies. and the detector with a large solid angle averages over the variation caused by ~ O U t Y U , .

Contrast reversals of excess to defect Kikuchi bands are observed at the center of diffraction patterns with increasing thickness when the cone of diffusely scattered electrons becomes broader (Komuro et al., 1972; Reimer, 1979; Reimer et al., 1977). Such contrast reversals can also be observed in ECP and EBSP (Reimer, 1979; Reimer et ul., 1977, 1986) and the specimen tilt and the direction of observation determine which type of band dominates and whether the excess bands change to defect Kikuchi bands. We show next that energy filtering can also result in a contrast reversa! to excess bands with increasing energy loss. 2. Energy-Filtered Diflraction Patterns of Single Crystals Energy filtering of single-crystal diffraction patterns (Creuzburg and Dimigen, 1963; Castaing, 1969: Meyer-Ehmsen and Siems, 1974; Philip el al., 1974; Egerton ef al., 1975; Reimer and Fromm 1989; Reimer et al., 1988, 1990) can be used to enhance the Bragg spots, the elastic contribution to thermaldiffuse streaks and Kikuchi lines and bands by zero-loss filtering, separation of plasmon contribution to Kikuchi lines and bands and of the contribution of inner-shell ionization processes. The influence of energy filtering on the diffraction pattern will be demonstrated in a series of increasing energy loss compared with diffraction patterns without energy filtering. Figures 42a and b show unfiltered and zeroloss filtered ESD patterns of a thin Sn foil. The diffuse streaks due to scattering by transverse acoustical phonons are enhanced by zero-loss filtering and disappear in thin foils in plasmon-loss filtered images, indicating that these streaks are caused by electron-phonon scattering with a negligible energy loss. When the foil thickness is increased, the diffuse streaks are also observed in the plasmon-loss filtered image due to elastic-inelastic scattering and the streaks appear more diffuse due to the convolution with the angular distribution of the plasmon loss.

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FIG.42. a) Unfiltered and b) zero-loss filtered E S D patterns of a Sn foil with thermal diffuse streaks caused by scattering at transverse acoustical phonons.

The series of ESD patterns in Figs. 43 of a N 50 nm 111-oriented Si foil show the influence of energy filtering on Kikuchi lines and bands when the selected energy loss is increased. Increasing energy loss (Fig. 43b-d) results in an more severe blurring of the Bragg spots with the angular distribution of the inelastically scattered electrons. The intensities in the system of excess and defect Kikuchi lines also vary due to the increasing angular width of the inelastically scattered electrons with increasing A E. At higher losses (Fig. 43e,f), the Bragg spots disappear and the ESD pattern shows only excess Kikuchi bands. The discussion of electron diffraction in the last section showed that excess bands are caused by the probabilities of Y,,,Y&, at the atomic sites with a band profile shown in the example of Fig. 41b. The intensity and the contrast of the excess bands and of the defect high-order

FIG. 43. E S D patterns of a 111-oriented Si foil ( t 2 50 nm) a) unfiltered, b) AE c) 16 eV, d) 100 eV, e) 1800 eV and f ) 2000 eV.

=0

eV,

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

117

FIG.44. ESD patterns of a 1 1 I-oriented Si foil ( I = 800 nm) a) A E = 100 eV, b) 500 eV and c) 1300 eV.

Laue-zone Kikuchi lines near the center of the 1 11 pole increase when passing from A E = 1800 eV to A E = 2000 eV (Figs. 43e,f): the K ionization edge of Si is at A E = 1839 eV. These high-order Laue-zone (HOLZ) lines can also be observed in convergent-beam diffraction patterns and their position depends strongly on small variations in electron energy and/or lattice parameter (Rackham et a/., 1974). (All ESD patterns are recorded and reproduced with the same mean brightness.) The reason for this increase of quality will be discussed later. Figures 44a-c show a series in 111 orientation of a thick Si foil ( r 2 800 nm). All patterns show defect Kikuchi bands also when passing the Si K edge. We know from the discussion in the last section that the incoherent superposition of Bragg reflections results in defect (dark) Kikuchi bands with a profile given by Eq. (67) and the upper curve of Fig 41a. These typical changes in the type of Kikuchi bands are explained schematically by Fig. 45. In thin foils (Fig. 45a), the EELS at high losses is generated mainly by electrons directly scattered in one large energy loss from the region of the primary beam and the plasmon loss to high energy loss. This results in excess bands ( E ) proportional to YoU,Y&,.A small fraction of the EELS comes from the primary beam and plasmon region by multiple smaller energy losses, which superpose with their Bragg intensities to form a defect band (D) proportional to ZZg.In front of the K edge, part of the excess band contrast is canceled by a smaller part with defect bands. This explains the fainter contrast of excess bands in Fig. 43e as compared with Fig. 43f beyond the K edge. In a semi-thick section (Fig. 45b) the multiple inelastic scattering becomes more pronounced and the defect part in the EELS increases, so that the defect character dominates below but the excess part is still larger beyond the K edge. In thick foils (Fig. 45c) the excess part decreases in intensity because electrons directly scattered from the primary beam will be transferred

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n

I

, I

Plasmon-loss region

SiK-,edge region

I

a ) thln

O iOeV

AE-

1

I I

1039eV

XAJ '.-

D

0

AE

-..:.

-:-

I

-

FIG.45. Schematical EELS for a) thin, b) semithin and c) thick foils with contributions to defect (D)and excess (E) bands.

to higher electron losses by multiple inelastic scattering and the defect part dominates at all thicknesses (Figs. 44a-c). We expect that the difference of diffraction patterns beyond and below an ionization edge at high energy losses will show excess bands only for thin and semi-thin foils. Such difference patterns can be used for ALCHEMI (Atomic Localization by CHannelling Enhanced MIcroanalysis (Spence, 1980; Spence and Tafto, 1983). The intensity of the excess Kikuchi bands should show differences when filtering at ionization edges of different elements placed at different atomic sites due to the distribution of nodes and antinodes of the Bloch wavefield inside a unit cell (Weikenmeier and Kohl, 1989). When recording EELS spectra at different positions relative to a Kikuchi band, differences in the ratio of Al and Mg K edge amplitudes have been recorded in a spinel MgAI,O, (Tafto and Krivanek, 1982), for example. When using ESD, the comparison of differences of diffraction patterns beyond and below the K edges of Al and Mg should show simultaneously the differences due to channeling for all Kikuchi bands and scattering angles. These results on silicon foils demonstrate the principal differences in ESD patterns when the energy loss is varied. In practice it is important that zero-loss filtering can increase the contrast of Bragg diffraction spots and, depending on foil thickness, an optimum energy loss can be selected for imaging predominatly Kikuchi lines (Reimer et al., 1990). Superposition of both micrographs will allow the exact foil orientation to be determined over a larger range of thickness.

ENERGY-FILTERING TRANSMISSION ELECTRON MICROSCOPY

1 19

VI. SUMMARY AND PROSPECTS The foregoing discussion of contrast mechanisms and of experimental results demonstrates that energy filtering electron microscopy (EFTEM) is becoming a routine method either by using commerically available scanning transmission electron microscopes (STEM) or energy filtering lenses in a transmission electron microscope (TEM). This opens up a new dimension of analytical electron microscopy, due to the combination of electron spectroscopic imaging (ESI) and diffraction (ESD) and electron energy loss spectroscopy (EELS). ESI at 80 keV with unscattered and elastically scattered electrons (zero-loss imaging) can increase scattering and phase contrast of amorphous specimens and avoids the blurring by chromatic aberration. This allows us to investigate biological sections up to 0.7 pm and, by most probable loss imaging, even up to 1.5 pm, which becomes important for the 3D reconstruction from a series of thick sections, for example. “Structure sensitive contrast” by ESI at A E = 250 eV just below the carbon K edge can reduce the contribution of carbon to a minimum and the dark field like image intensity is generated dominantly by the increased EELS intensity of noncarbon atoms. Zero-loss imaging of crystalline specimens increases the Bragg contrast, though plasmon scattering also preserves this contrast. However, image blurring by chromatic aberration and a decrease in Bragg contrast by a spectrum of excitation errors due to the angular distribution of inelastically scattered electrons can be avoided by zero-loss filtering.This allows crystalline specimens to be investigated up to mass thicknesses of 2 150 pg/cm2 and up to N 300 pg/cm2 by most probable loss imaging; still larger thicknesses can be investigated in orientations showing anomalous transmission. The ESI using distinct plasmon losses can separate and analyze different phases in alloys when they differ in their EELS spectrum. In the mode of elemental mapping, digital difference images can be produced with an ESI beyond the ionization edge of the element of interest and an extrapolated background image obtained from two ESI below the edge. This technique can be combined with quantitative EELS analysis from selected specimen areas. The ESD offers the advantage of removing the background of inelastically scattered electrons in diffraction patterns, which increases the contrast of amorphous and Debye- Scherrer rings, of small-angle diffraction patterns and of single-crystal diffraction patterns. By filtering with energy losses of a few hundred eV, a Compton ring pattern caused by single-electron excitation can be recorded and analyzed to extract the momentum distribution of valence electrons. The diffuse streaks caused by electron-phonon scattering can be filtered by zero-loss filtering and the filtering of single-crystal diffraction

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patterns by plasmon and higher energy losses allows us to separate their contribution to Kikuchi lines and bands. Beyond ionization edges with energy losses larger than about 500 eV, the ESD intensity increases and becomes proportional to the excited Bloch-wave intensity at the atoms with the specific edge, which can be used for ALCHEMI (atomic localization by channeling enhanced microanalysis). Whereas the Castaing-Henry filter lens with a retarding field electrode cannot be used beyond 80 kV, future energy filtering microscopes with purely magnetic filter lenses and multipole correction elements will allow EFTEM to be employed in microscopes with acceleration voltages larger than 100 keV. The development of magnetic sector-field spectrometers will make it possible to record a corrected image behind the EELS at the energy dispersive plane at higher voltages. ACKNOWLEDGMENT

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOL 81

Bod0 von Borries: Pioneer of Electron Microscopy HEDWIG VON BORRIES Clara- Viebiy-Strasse 1 I 04000 Diisseldorf I Diisseldorf. Federal Republic of Germany

Prior to his death in summer 1988, Ernst Ruska was the last surviving member of the three-man team that had devoted its life’s work to electromagnetic electron microscopy and had worked together successfully for many years. As the younger sister of Ernst and Helmut Ruska and subsequently wife of Bod0 von Borries, I am now the only surviving contemporary to have witnessed the development of this science at first hand from its beginnings in 1928. Each stage remains vividly etched on my memory, from the earliest vague optimism to the difficult struggle to accomplish industrial production and subsequent worldwide acceptance. Bod0 von Borries’ unexpected death prevented him from realizing his plans to document the development’s infancy. However, with the help of his records, I have been able to verify my recollections. With the exception of the patent application of March 17, 1932, the scientific collaboration of 1931 to 1934 that culminated in the highresolution electron microscope has remained in obscurity. This record is intended to illuminate this period and to describe Bod0 von Borries’ life’s work. In January 1928,the Ruska family moved from Heidelberg to Berlin, where Father had become professor of history of the natural sciences one year before. In the difficult economic situation of the time, we children were educated largely in Berlin. My elder brother, Walter, an engineer with Askania, lived in the family home until his emigration to the USA in 1929. Following her training as a trade school teacher, my sister Elisabeth also returned to live with our parents. Ernst was studying electrical engineering in Berlin, and Helmut was in Heidelberg studying medicine. A friend of Ernst occupied Helmut’s room in Berlin on an exchange basis. I myself lived in the family home during most of my education. The children of my deceased sister, Maria, also lived with my parents for a number of years. My eldest brother Hans had died 12 years previously. Our parents kept a modest but open home. Frequently we would bring friends and colleagues back with us. In this large circle, each would tell of whatever he was involved in at the time as we sat round the dinner-table, and interesting discussions evolved. 127 Copynght C 1991 by Academic Press. Inc All nghts of reproduction in any form reserved ISBN 0-1 2.01468 1-9

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Ernst began his research work in December 1928, by then in his seventh semester, with Professor Matthias in the Knoll Group. He spoke on many occasions of the stroke of luck that allowed him to work alongside so many experienced postgraduate students preparing their doctorates. On April 1, 1929, Bod0 von Borries joined the circle of young graduate engineers working on the cathode-ray oscillograph for their doctoral theses. He quickly earned a reputation for considerable open-mindedness, especially during discussions, and a willingness to help with experiments. Ernst frequently spoke of his new colleague’s qualities at home. Von Borries had studied in Karlsruhe, Danzig and Munich and passed his final degree examination with distinction at the beginning of his ninth semester. Following a brief period of employment with the Minden-Ravensberg Elektrizitatswerke, he successfully applied to work for his doctorate under Professor Matthias. Bod0 von Borries hailed on his father’s side from a Prussian family of jurists; his mother’s family were industrialists from the Rhineland. His father was a district administrator of Herford, his grandfather a Privy Councillor in Minden. His maternal grandfather was chairman of the board of directors of the Phoenix steel works. Bod0 von Borries completed his secondary education in Herford. He had a particularly successful relationship with his parents and sister, who was four years his senior. He maintained close friendships with many of his schoolfriends throughtout his entire life. Each day during the afternoon coffee break, the six postgraduates and an equal number of undergraduates discussed the progress of their closely related research under the supervision of Dr Knoll. Bod0 von Borries settled in so quickly that three studies on the cathode-ray oscillograph were published with Dr Knoll as early as 1930. That same year, Ruska completed his diploma thesis and took his final degree examination. In this work, he acknowledges the assistance provided by Bod0 von Borries and Martin Freundlich. Faced with an unemployment rate of more than 30 percent at that time, Ernst’s initial attempts to find a paid position failed. With great reluctance, our parents allowed him to continue his studies, unpaid, with the Knoll Group. In April 1931, he submitted his first joint study with Knoll (Knoll and Ruska, 1931). On June 4,1931, Knoll gave a lecture under the auspices of the Cranz colloquium of Berlin-Charlottenburg Technical University on the current level of development work on the cathode-ray oscillograph. During his presentation, he also reported that on April 7, 1931, Ruska had “successfully made the first two-stage image and photographic recording of a mesh screen with an overall 16-fold magnification”. “die erste zweistufige Abbildung und die fotografische Aufnahme einer Netzblende bei 16facher GesamtvergroBerung gelang.”

In the preceding weeks, his work with Knoll had been Ruska’s sole preoccupation.

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Some days before this lecture, during the Whit week von Borries and Ruska for the first time spent a holiday together, a cycling trip to the Baltic Sea (Fig. 1). From this stage onwards, von Borries and Ruska worked intensively together because of their shared uneering belief in the future of electron microscopy. Since von Borries had still to complete his doctorate (Fig. 2), he and Ruska frequently worked at night or on days off, as illustrated by his diary. If Mother discovered that they were still working at two or three in the morning, she unscrewed the electric fuses and took them to bed with her. The first joint and decisive patents were applied for on March 17, 1932. Bod0 von Borries submitted his doctoral thesis on March 24, 1932. This indicates that his studies of electron microscopy had to be conducted largely alongside his normal work. This remained the case while he was employed as an assistant, as well as later when both he and Ruska worked in industry. I recall from many conversations that the relationship with Knoll deteriorated after the Cranz colloquium. The study group felt that Knoll was devoting insufficient time to its work (Fig. 3). I mention this development because it resulted in von Borries and Ruska collaborating even more closely in their calculations, drafts and experiments without Knoll’s knowledge. In November 1931, they began a joint study (von Borries and Ruska, 1932). This

FIG. 1. Bod0 von Borries and Ernst Ruska on holiday together for the first time, May 1931

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FIG.2. Cathode-ray oscillograph. Optical images using the CRO became the basis for highresolution electron microscopy.

was submitted for publication on April 22,1932, without Knoll’s involvement. However, it was also during this study that the idea of high-magnification electron microscopy was conceived. Before his departure, Knoll was devoting his efforts to his own postdoctoral thesis in March 1932 under Professor Matthias and was therefore no longer involved in developing the high-resolution electron microscope, about whose future he had certain reservations (Knoll, 1935). On March 10, 1932, von Borries and Ruska had a detailed interview with Professor Matthias. This resulted in their joint work on the electron microscope being authorized and von Borries being offered a position as a

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FIG.3. The Knoll Group (doctoral candidates and undergraduates) during a laboratory coffee break in the High-Tension Institute of Berlin-Charlottenburg Technical University, 1931. From right to left: Knoblauch, Schaudien, Freundlich, Czemper, Ruska, Andrieu, Knoll, Blume, von Borries. Other Group members included Elmer, Hochhausler and Lubszynski.

private assistant and successor to Knoll. In a letter to his parents dated March 12, 1932, he wrote: On Thursday, Ernst and I saw the professor in order to gain authority for our joint work. The interview was conducted in an extremely pleasant atmosphere. I explained to the Professor that I had planned to undertake various scientific studies which were inexpensive and promised good results, but also that, for financial reasons, I would not be able to come back after Easter. He then suggested that I should set up and combine the two cathode-ray oscillographs built according to my design, which would allow me to conduct my investigations. I would be paid the sum of 150 Reichsmarks, for approximately two months’ work. This offer is not yet quite firm, since he did not know exactly that money was available. “Donnerstag war ich mit Ernst beim Professor, um unsere gemeinsame Arbeit genehmigen zu lassen. Die Besprechung spielte sich in den angenehmsten Formen a b und in ihrem Verlauf sagte ich dem Professor, daB ich an sich noch verschiedene wissenschaftliche Untersuchungen vorhatte, von kleinem Aufwand und nettem Ergebnis, aber wegen finanziell nach Ostern nicht wiederkommen

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wurde. Da bot er mir an, daO ich die beiden nach meinem System gebauten Kathodenstrahloszillographen herstellen und zusammensetzen sollte und dabei meine Untersuchungen machen konnte. Dabei sollte ich 150,- Reichsmark verdienen, etwa fur zwei Monate. Dieses Angebot ist noch nicht ganz fest, weil er noch nicht seine Gelder genau wuI3te.”

On March 20, 1932, Professor Matthias sent the following letter of employment: Dear Mr von Borries, I am delighted that you have decided to remain in Berlin for the time being. To enable you to make arrangements, please find below the terms and conditions in writing. Your activity will initially be guaranteed for four months beginning on April 1st. I shall notify you in good time if your appointment is extended. However, it is extremely important that you begin immediately on April lst, so that work can continue without interruption. It is very probable that the entire institute, including workshops and cathode-ray oscillograph development, will be moved to Neubabelsberg.. . . In principle, I shall not then be able to reimburse travel expenses separately. To take account of this, I will then increase your monthly remuneration to 175 marks. Your appointment is being paid from private funds. I assume that, in addition to supervising production of the cathode-ray oscillograph, you will also deal with cathode-ray oscillograph questions in general and, in particular, with the installation and initial operation of the other cathode-ray oscillographs, including preparations for the transfer of the associated experimental facilities. This should still leave some time for the work planned with M r Ruska. I should be able to have some additional funds released for that project and other similar work later. I hope to have an opportunity of speaking to you and M r Ruska before your departure as regards the entire work project, and also to discuss Mr Ruska’s letter. Please confirm briefly that you are in agreement with the above proposals. Yours sincerely, Matthias. “Lieber Herr v. Borries, es freut mich, daO Sie sich entschlossen haben, vorlaufig in Berlin zu bleiben. Damit Sie disponieren konnen, gebe ich Ihnen im Nachstehenden schriftlich die Bedingungen an. Ihre Tatigkeit wird vorlaufig a b 1. April auf vier Monate sichergestellt. O b sie verlangert werden kann, werde ich Ihnen rechtzeitig sagen. GroI3en Wert lege ich aber darauf, daO Sie schon am 1. April ubernehmen, damit die Arbeiten ohne Stockung weitergehen. Es ist stark damit zu rechnen, daB sehr bald der ganze Betrieb einschlieDlich Werkstatten und KO-Entwicklung nach Neubabelsberg verlegt wird, . . .Fahrkosten kann ich dann grundsatzlich nicht besonders vergiiten. Dagegen will ich mit Riicksicht hierauf Ihre monatliche Entschadigung auf 175 Mark erhohen. Die Anstellung erfolgt aus privaten Mitteln. Ich nehme an, daO Sie auljer der Uberwachung der KO-Herstellung sich auch um die KO-Angelegenheiten im allgemeinen kummern und insbesondere um die Aufstellung und Inbetriebsetzung der sonstigen

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KO’s, auch Vorbereitung der Verlagerung der diesbezuglichen Versuchseinrichtungen. Zu der mit Herrn R. geplanten Arbeit wird Ihnen doch wohl noch Zeit bleiben. Fur solche und ahnliche Arbeiten werde ich auch wohl wieder einige Mittel freibekommen. Ich hoffe, vor Ihrer Abreise uber den ganzen Arbeitskomplex noch mit Ihnen und Herrn Ruska auch im Hinblick auf sein Schreiben sprechen zu konnen. Wenn Sie mit den vorstehenden Vorschlagen einverstanden sind, bitte ich mir kurz Ihre Zustimmung zu bestGtigen. Mit freundlichem GruD Ihr Matthias.”

The letter from Ruska to which Professor Matthias refers informed him that on March 17, 1932, von Borries and Ruska had applied for electron microscopic patents regarding the magnetic pole-piece lens and intermediate screen (von Borries and Ruska, 1932a, 1932b). On March 24, 1932, von Borries submitted his doctoral thesis. His appointment as an assistant began o n April 1, 1932. His collaboration with Ruska into the early hours of the morning also continued, as the following diary entries show: April 2, 1932-Ernst to dinner in my room. Worked late. April 3, 1932-Sunday. Went for a walk with Ernst. Coffee at the Ruskas’. Dimensioning work. Dinner. Worked late. April 4, 1932-Electron physics. Ernst in my room until late, working. April 7, 1932-Meeting with professor. April 8, 1932-Saturday. Ernst came to dinner, stayed until 3 a.m. April 9, 1932-Sunday. Ernst came over after lunch to d o calculations at my place. April 11, 1932-Meeting with professor. April 13, 1932-Dinner at the Ruskas’. Electron microscope report.

The report in question, which was discussed with Professor Matthias after careful compilation by the two men, was Ruska’s application to erect an additional apparatus for the doctorate he was about to take. The report was submitted on March 13, 1932. (See Ruska, 1979, Appendix D.) Ruska does not refer at all to the joint study in the above-named work, merely stating in Chapter 10:“B. von Borries, who had completed his thesis on March 24,1932, and then became a private assistant to A. Matthias with effect from April 1, 1932, left Berlin at the end of February 1933.. . .” Let us return to April 1932, however. On April 18th, the transfer of the Institute from Charlottenburg to Neubabelsberg commenced. Despite the loss of time caused by the move, the ordered cathode-ray oscillographs were delivered on time by the Institute for High-Tension Installations to the Siemens-Schuckert-Werke (SSW) and Berliner Elektrizitats-Werke AG (Bewag) in mid-1932. This institute had mastered the problems of highvacuum engineering, an achievement also of vital importance to electron

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microscopy. Bod0 von Borries wrote the following in a letter to his parents dated August 27, 1932: O n Friday morning, I visited SSW. They said my cathode-ray oscillograph was not properly sealed. I discovered that the pump was insufficiently heated, so that my visit was really rather unnecessary. However, D r Estorff and Dr MullerHillebrand were very nice. Dr Estorff is director of the switching substation proving ground.. . . I asked Dr Estorff about the possibility of a position. He replied that he would be happy to employ me as soon as an opportunity arose of getting anyone in, but this was out of the question at the moment. He suggested that I should keep in touch with him. I was then taken on a very enjoyable tour of the switching substation. Desolately quiet and empty.. . I a m now designing a new cathode-ray oscillograph in the laboratory. Last week I did all the calculations both for the new CO and for our study (electron microscope).” “Freitag fruh war ich bei SSW. Mein KO sollte undicht sein. Ich stellte fest, daD die Pumpe ungenugend geheizt war. So war mein Kommen deswegen ziemlich uberfliissig. Aber Dr. Estorff und Dr. Muller-Hillebrand waren sehr nett. Dr. Estorff ist Vorstand des Versuchsfeldes des Schaltwerks.. . . Mit Dr. Estorfl sprach ich ma1 wegen Stellung. Er sagte, er wolle mich gerne einstellen, sowie nur irgendeine Moglichkeit sei, einen Mann hereinzukriegen. Momentan sei jedoch diese Moglichkeit noch nicht einmal im Bereich des Erwagens. Ich solle aber laufend mit ihm in Verbindung bleiben. Ich bin dann sehr nett durch’s Schaltwerk gefuhrt worden. Trostlos still und leer.. . Im Labor konstruiere ich jetzt einen neuen KO. Vorige Woche habe ich allerhand gerechnet, was einerseits fur diesen KO, andererseits fur unsere Arbeit ist (Elektronenmikroskop).” (See Fig. 4.)

On September 17th, he wrote: During the week I have been working solidly on the Ruska study in the evenings. I am now satisfied that a very difficult chapter has been finally resolved and that it can be presented in a sufficiently elegant way. This is when work is fun. “In der Woche habe ich laufend an der Ruska-Arbeit abends gewerkt, mit der Genugtuung, da13 ein sehr sprodes Kapitel jetzt endlich in Losung geht und auch eine hinreichend elegante Darstellung erlaubt. Das macht dann SpaD.”

Since von Borries had to keep an eye on the two cathode-ray oscillographs delivered, he had regular opportunities to meet Dr Estorff and Dr MullerHillebrand. During these meetings, he received repeated confirmation that they wanted to engage him as soon as possible. The High-Tension Installation Study Society sponsoring the Institute for High-Tension Installations held six lecture evenings, with the first taking place on November 7,1932. Professor Matthias and Dr Knoll opened the series. In the following weeks, Knoblauch, von Borries, Elmer, Holzer and Ruska gave lectures on their specialized study areas. Freundlich appears to have been the

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.--

I

~

FIG.4. Manuscript of the letter from Bod0 von Borries to his parents, quoted on page 134.

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FIG.4. (Cont.)

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only postgraduate working for his doctorate under the supervision of von Borries not to have given a presentation. Bod0 von Borries went through the candidates’ lectures with them in detail, in some cases until 3 a.m. He discussed Ruska’s contribution with the author on December 7th, 8th, 9th and loth, prior to its presentation on December 12th. Afterwards, von Borries had to compile a report from all the lectures. Although fully occupied by all this during the day, von Borries still spent 97 evenings and weekends working in collaboration with Ruska on electron microscopy in 1932. Bod0 von Borries’ father planned to take early retirement on health grounds at the beginning of 1933. This made it impossible for von Borries to continue to accept a contribution towards his living costs from his parents. He was therefore glad when he found a position as graduate engineer with the Rheinisch-Westfalische Elektrizitatswerke in Essen. Although the decision to leave Berlin was not easy, he was sure that Siemens-Schuckert would keep its word and that he would soon be back in Berlin and able to continue working intensively on gaining acceptance for electron microscopy. On January 2, 1933, von Borries informed professor Matthias that he had to give up his assistant’s post beginning March 1st. On the same day, Ruska, Freundlich and von Borries drafted an agreement laying down who was to publish which scientific studies and with whom. The document, which was signed by all three, also contained very precise details of which periodicals were considered suitable (Fig. 5j. In January, before Ruska went on holiday, he and von Borries completed their study entitled “How the electron microscope shows films under ray penetration” (von Borries and Ruska, 1933). In February, von Borries met Knoll on many evenings to prepare the paper “Blackening of photographic layers by electrons and fluorescence generated by electrons” (von Borries and Knoll, 1934jfor publication. From April 12th to 18th, Ruska was invited to the home of von Borries’ parents so that both could work on another study, also involving Professor Matthias: “A new form of current measuring system on the cathode-ray oscillograph” (Matthias et al., 1933). When von Borries moved to Essen, it became impossible for him to participate directly in experiments. However, in some 170 pages of correspondence written by the end of 1933, a lively exchange of ideas went on as regards the development, construction and conducting of experiments that were to be carried out and had been jointly planned prior to von Borries’ departure. Ruska reported regularly on all experiments, asking for von Borries’ opinion when difficulties arose. He received suggestions and design diagrams in return. Letters were sent back and forth on the subject of several planned publications, and von Borries was asked for his assessment and corrections. Bod0 von Borries took charge of the patent applications in order to lessen the load on Ruska, since this was something that could be done from

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FIG.5. Manuscript of the agreement between Ruska, Freundlich, and von Borries, quoted on p. 137.

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Y

FIG.5. (Con?.)

Essen. In the course of the following 10 months, 12 letters were written in which both sides referred to the major joint apparatus study that was agreed upon on January 2, 1933. In November von Borries took a week's leave at Ruska's request, with the purpose of going-to Berlin to discuss difficulties and conduct joint experiments. On December 7, 1933, he wrote to Ruska that he had typed 28 pages relating to patents since his Berlin visit-that is, in the space of 10 days-while still doing his normal work. This included the application for the third joint patent, dated November 30, 1933.

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The sole unfinished task in von Borries’ work schedule for December 1933was to “compile the apparatus study.”On December 12th, Ruska sent the jointly agreed study entitled “On progress in the construction and performance of the magnetic electron microscope” (Ruska, 1934) to the Zeitschrgt fir Physik. He did not inform von Borries of this until December 21st, by which time the publisher had confirmed acceptance of the article. Deeply upset by this, von Borries considered writing to the publishing house and discussed this with his father over the Christmas period. However, because in recent years there had been several instances of studies lying around for too long and being preempted by publications of other scientists, the father and son resolved to let the matter lie. Since the problematic patent applications by Rudenberg had already been made at the time, and priority disputes with AEG had already commenced, von Borries did not wish his differences with Ruska to become known. He was unwilling to cause any damage to the project in which he had invested so much work since the middle of 1931. Moreover, he believed that the joint patent applications would secure his position. Ruska entered employment with Fernseh AG on December 1,1933. However, both von Borries and Ruska were determined to continue promoting the cause of electron microscopy. Work on the equipment in Neubabelsberg was later taken up by Krause and Muller, amongst others. My brother Helmut had been working as a junior medical doctor in Heidelberg since 1933. He had done most of his studies there, apart from two semesters in Innsbruck. In February 1934, my mother suffered a severe stroke that left her paralysed on one side. In March, I sat the examination to complete my professional training, after which I took charge of nursing my mother for a fairly lengthy period. My friendship with von Borries began immediately upon his return to Berlin and culminated in a very happy marriage. Bod0 von Borries had maintained his contacts with Siemens-Schuckert. On May 29, 1934, he was invited for an interview and a detailed tour of the switching substation. On the next day, having consulted his parents, he accepted the position he had been offered. On July 1, 1934, he became Dr Muller-Hillebrand’s successor as laboratory manager. During the second half of 1934,as von Borries’diary reveals, he worked on 38 days with Ruska outside working hours; in 1935 they spent some 70 evenings working together, primarily on patents, all of which were the original work of both men but were now registered by only one of them in each case. Applications were thus submitted by von Borries on the following dates: December 6,1934; April 23,1935; April 25,1935; May 10,1935. Those applied for in Ruska’s name were dated December 1,1934; December 13,1934; April 7, 1935; and April 27, 1935. They also continued to work on articles for publication. During the same period, Ruska held one, and von Borries, three

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public lectures. The most acclaimed of these was given on December 12, 1934, in the Haus der Technik in Essen (von Borries, 1935). Having presented the wide range of applications of the electron microscope, von Borries concluded as follows: No further decisive improvements can be anticipated in the field of light microscopy. However, in three years of rapid development, the electron microscope has already overtaken the light microscope in terms of resolution capacity. Although it will never replace the light microscope or render it superfluous, it will stand alongside it and, we hope, expand our knowledge in the sphere of the minute by orders of magnitude if we are successful in arousing interest and involvement in this area.

“Die Lichtmikroskopie hat entscheidende Verbesserungen nicht mehr zu erwarten. Das Elektronenmikroskop dagegen hat in dreijahriger rascher Entwicklung das Lichtmikroskop bereits heute im Auflosungsvermogen iiberholt. Wenn es auch das Lichtmikroskop niemals verdrangen oder iiberfliissig machen wird, so wird es sich doch danebenstellen und hoffentlich unsere Erkenntnis um GroBenordnungen in das Gebiet des Kleinsten hinein erweitern, wenn es gelingt, Interesse und Beteiligung an dieser Arbeit zu erwecken.”

The two men also continued their efforts to get industrial enterprises and the Kaiser-Wilhelm Society interested in the electron microscope. (For a list of these efforts, see Ruska, 1979 Appendix E.) This list is part of von Borries’ estate. After all negotiations had failed in July 1935, a year of discouragement followed. Nevertheless, this did not prevent the two men from continuing to work on electron microscopy, of whose eventual success they remained convinced, on 100 evenings and days off in 1936. Not until 14 months later, on September 2, 1936, did von Borries propose to Dr Kottgen, the chairman of the board of directors of SSW, that the company set up a position for electron optics and agree to develop the electron microscope. On September 4th, he presented Dr Kottgen with a memorandum concerning electron-optical equipment and its commercial significance. Helmut Ruska had come to Berlin to the Charite with his boss, Professor Siebeck, in the spring of 1936 and aroused his interest in electron microscopy. Profesor Siebeck met von Borries and the Ruska brothers on September 29, 1936, and, on October 2nd, wrote an expert assessment on the significance of high-resolution electron microscopy for medicine and biology. On October 5, 1936, von Borries submitted the development concepts for electron microscopes and other electron-optical equipment to Dr Kottgen, chairman of the board of directors of SSW, and Dr von Buol, chairman of the board of directors of Siemens & Halske. O n October 18th, von Borries stated his position in writing as regards the protective scope of the patent applications of Rudenberg as well as those of himself and Ruska. O n October 23rd, von

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Borries and Ruska met Dr von Buol, Dr von Siemens and Dr Luschen to discuss the scale required for the laboratory to be established for developing the electron microscope. On November 3rd, von Borries negotiated for two and a half hours with Dr von Buol and Dr Luschen. On November 27,1936, von Borries and Ruska provided Siemens & Halske with detailed plans of the tasks and organization of the development post being set up; on November 30th they discussed the contractual conditions that would apply in the event of their employment with S & H. Over the same period several meetings also took place with Dr Harting of Zeiss-Jena. Zeiss had indicated its willingness to restart the negotiations that had been broken off in June 1935. Serious talks took place concerning the company’s opportunities, so that contracts were ready for signature with both companies by Christmas 1936. Two points favoured Siemens: first, the patent situation (Rudenberg), and second, the fact that the predominant emphasis of the assignment was electrotechnical rather than optical. To this was added the opportunity of remaining in Berlin, where both men had friends and relatives. O n December 22, 1936, the employment contracts were prepared for their posts as senior engineers and laboratory directors to take effect on February 1, 1937. On January 16, 1937, a contract was prepared to regulate the sale to S & H of the three joint patents and the four patents applied for individually by each of the two men, as well as future royalties. The two inventors were granted power of attorney on January 26, 1937. All these agreements were identical for both von Borries and Ruska. Planning and procurement commenced at Siemens & Halske on February 1st. In March/April, both men were called up at the same time for military training in Potsdam. This had already been postponed several times. The two men planned to set up the laboratory during these weeks to such an extent that work could begin in earnest upon their return. They were fortunate in being able to spend some of their off-duty time in negotiations at the Patent Office, at Siemens and at the employment office. Finding suitable employees was not easy. Even months later in June, a letter I received said: “Siemens’ own workshops are so over-employed that the electron microscopy work cannot get started.” In summer 1937,both men married. From this point onwards, I was able to witness professional developments even more closely, especially since my husband maintained his habit, established with his parents, of reporting each day on his work. Together with Mrs Ruska, I drove to the laboratory in the evenings with food when our menfolk lost track of time. Often we returned home alone because experiments continued well into the night. O n December 2, 1937, the first electron microscope built at Siemens according to the design of von Borries and Ruska was switched on-that is, after six months of industrial development following the initial phase in which

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the laboratory had to be set up. On December 7th, Dr Hermann von Siemens and Professor Kiipfmiiller were the first to see the equipment demonstrated. The initial Siemens electron microscope was a new design incorporating all the theoretical conclusions of recent years. Even those involved were surprised at how well it functioned from the very outset. Work with this prototype instrument began in January 1938. The days were fully taken up with further developing the equipment. Only evenings and nights remained for Helmut Ruska’s application studies. He had been released from clinical duties in the meantime and was working full-time in the Spandau laboratory. During the whole of February 1938, his wife and small daughters scarcely saw him because he and von Borries stayed in the laboratory until one, two or even four o’clock in the morning and only made it back by foot as far as our flat. Bod0 von Borries was now interested in all the facilities that could make life easier for users. This pronounced interest in user aspects led to his working hand in hand with users and later gave him the best insight into both the equipment and its applications. Bod0 von Borries was already well-known in specialist circles as a result of his lectures on oscillographs and surge voltage protectors, delivered in universities as well as technical and scientific associations. Indeed, he received an ever-increasing number of requests to give lectures on electron microscopy. He regularly took advantage of this opportunity to arouse interest among additional groups. Depending on the event organizer, he was able to go into further detail about the instrument’s applications from 1938 onwards. At the beginning of the year, he delivered lectures in Mahrisch-Ostrau, at the Technical University of Prague, the Laue Colloquium in Berlin and at IGFarben Hoechst; on September 19th, he addressed the Physicians’ Congress in Baden-Baden, His lecture at the Technical University in Stuttgart in front of a very large audience on September 21st primarily highlighted the possible applications of electron microscopy. From then on, von Borries undertook lecture tours lasting several days every few months. During working hours he conducted negotiations with industrial enterprises, scientists and the technical offices of Siemens & Halske; in the evenings he delivered lectures. Thus, on October 31, 1938, he spoke before the Association of German Engineers (VDI) in Kassel; on November 1, 1938 he addressed 400 biologists in Frankfurt; on November 2nd he delivered a lecture in the Siemens building in Mannheim; on November 3rd he addressed the chemical, natural scientific and medical societies in Basle; and on November 4th and 5th, he delivered successive lectures to the VDI and Association of German Electrical Engineers (VDE) in Stuttgart and Koblenz. Consequently, 2000 scientists had heard his lectures in the course of a single week. On July 1, 1938, Carl Friedrich von Siemens, head of the Siemens

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company; Hermann von Siemens, Chairman of the Supervisory Board; Mr Vogler, Chairman of the Stinnes Group; Mr Thyssen, head of the Thyssen Group; Dr von Buol, Managing Director Siemens & Halske; and Dr Kottgen, Managing Director of SSW all visited the laboratory. On this occasion, von Borries and Ruska were granted substantially greater independence. In addition, a major press event was planned in order to make this top technological achievement known to a wider public. This took place on July 20, 1938. Bod0 von Borries, Ernst and Helmut Ruska had split their lectures up into specialist areas and followed them up with explanations to those interested in the microscope. Press reports appeared all over Germany and some even abroad. The year 1938 saw the method gain recognition. Members of the laboratory for electron optics penned eleven published articles, including five by von Borries and Ruska, two additional papers by von Borries, Ernst and Helmut Ruska, and one each by von Borries and Dosse, Glaser, Miiller and Helmut Ruska. In the quiet period between Christmas and the New Year, von Borries met daily with Ernst and Helmut Ruska to consider how to create an independent laboratory dedicated to application aspects. This planned institute was approved in principle by Siemens & Halske on February 16, 1939. Thanks to support from the board of directors, the laboratory for super microscopy was established quickly and generously equipped with three of the first volume-produced instruments. Attached to the laboratory for electron optics, it was managed by Helmut Ruska and Dr G. A. Kausche. In February 1939, von Borries delivered lectures in Goslar. Diisseldorf, Cologne, Hanover and Kiel, all in the space of a week. In March an electron microscope was presented at the Leipzig Trade Fair for the first time; it was the first volume-produced model. Lectures followed in Konigsberg, Osnabriick and Dortmund. Electron microscopes had previously been built exclusively for laboratory use; now an initial small series was built for sale. It was provided with a shield to protect users against overvoltages. Whereas the appearance of the microscope changed considerably, its design was already fully developed. This instrument was also initially called the “Siemens electron microscope by von Borries and Ruska”. Since Ruska was at a disadvantage from the alphabetical order, von Borries agreed that the names should be reversed in the instrument name. However, alphabetical order was to be retained for joint publications, photograph captions, etc. Twenty-seven joint works by von Borries and Ruska were published in the years 1932 to 1940. After this date, only two joint works concerning the historical development of electron microscopy were published (von Borries and Ruska, 1944a, 1944b). The fear that war could break out had been growing steadily in the

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meantime. It came as no great surprise when conscription was introduced on August 26,1939, and war was declared on September 1, 1939. A few days later, von Borries was due to be sent to the front. As things turned out, however, he was transferred to an air reconnaissance unit and remained in Berlin. Alongside his military service, he also worked full and half days at Siemens. On November 24th, von Borries delivered a lecture in the Huus der Echnik in Essen; on November 30th, he addressed a celebratory gathering in the Congress Hall of the German National Museum in Munich. The 1400 guests in attendance represented the largest audience of his entire career. At the request of Siemens & Halske, he was registered as pursuing a reserved occupation: On December 28, 1939, he was released with the rank of lance corporal, never again to be called up. Of course, we were happy and grateful thus not to be separated by the war. Ernst Ruska was never called up; Helmut was transferred several times between the front and home. The sons of my sister, Maria, were drafted on completion of their secondary schooling; the elder boy was killed. We had no more news from my emigre brother, Walter, until 1946. On April 28, 1940, the application laboratory for super microscopy was officially opened. It comprised a total surface area of more than 650 square metres, housing eight laboratories equipped according to specialty, an archive and administrative offices; its most important features were three electron microscopes. The opening ceremony lasted for five hours and guests included mainly scientists, high-ranking state officials and the press. After the welcoming address and introductory lecture by Dr Hermann von Siemens, speeches were made by the following: Professor Siebeck, head of the Charite Dr Riehm, President of the Reich Biological Institute Professor Dr Lembke, Director of the Prussian Test and Research Institute for the Dairy Economy Professor Eitel, Director of the Kaiser Wilhelm Institute (now MaxPlanck Institute) for Silicate Research Dr Schmieder, IG-Farben Physical Laboratory Dr Meldau, patent lawyer, Chairman of the Berlin VDI Dust Committee. All of the speakers had seconded employees to the laboratory for super microscopy or had worked there themselves. The lectures were published together with an essay by Helmut Ruska in a book entitled “The electron microscope as a research tool” (1941). By this stage, as many as 41 scientific publications had been produced by the laboratory for electron optics and the laboratory for super microscopy.

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Electron microscopy was publicised as a German achievement and exploited for propaganda purposes. This was good for Siemens, so the company took a favourable view of the many lectures. Wherever von Borries was speaking, he also conducted talks with the bodies that had invited him. These frequently led to sales negotiations in the following years. In addition, he briefed employees in Siemens & Halske’s technical offices, which were located in almost every major city in Germany as well as in the capital cities of Europe. In 1940, he was also able to present the method of surface microscopy that he had developed. Despite the exertion involved, he always returned from these trips full of enthusiasm: He was warmly received wherever he went and found these visits very stimulating. We tried to return the great hospitality he had experienced. When business associates were in Berlin for negotiations, we invited them to our home, for it was safer there during the war than in the city’s hotels. On June 22, 1941, war was declared with Russia. My husband returned immediately to Berlin from his holiday in order to hold onto his most important colleagues during the next wave of conscription. On July 3, 1941, all researchers who had been involved in electron microscopy at an early stage were awarded the silver Leibnitz medal of the Prussian Academy of Sciences. The roll of honour read: von Ardenne, Boersch, von Borries, Briiche, Knoll, Mahl and Ruska. Soon afterwards, Helmut Ruska and Karl-Heinz Wolpers were again drafted as army doctors. They were the earliest and most important users of electron microscopy in medical research. From the front line both of them made every effort to complete publications they had already started working on. From January 16th to 30th, 1942, I was able to accompany my husband on a longer lecture tour, thus fulfilling a wish he had often expressed. At temperatures of - 20 to - 30°C and under complete blackout conditions, we were warmly welcomed everywhere we went. Following my husband’s stay in Prague, we visited Vienna, Linz, Constance, Strasbourg, Karlsruhe, Freiburg, Heidelberg, Mannheim and Ludwigshafen together. Two days later he set off on his next lecture tour to Liibeck, Hamburg and Berlin. Bodo von Borries was invited to give a lecture tour in Sweden by Professor Sjostrand, who had carried out research into poliomyelitis very early in the Berlin laboratory for super microscopy and had obtained one of the first microscopes. This visit to a neutral country made a deep impression on him as he travelled from Malmo to Stockholm, Uppsala, Lund and Goteborg: The atmosphere there was completely different, free from militarism and propaganda, blackouts and rationing. Further foreign lecture invitations took von Borries to Amsterdam, The Hague, Delft, Paris, Brussels and Ghent.

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In 1943, he made three lecture tours abroad. The first covered Vienna and Bucharest, the second Vienna, Sofia, Belgrade and Budapest. On his third journey, he lectured in Rome, Milan, Locarno, Zurich and Bern. His foreign lectures were particularly well attended. Between 1934 and June 1, 1943, he had delivered 72 lectures on electron microscopy, including 24 abroad. During the same period, Ruska addressed 14 gatherings, including one outside Germany. The very different, but mutually complementary gifts of the two men were the basis of their joint success for many years. Foreign trips sometimes also provided an opportunity of getting to know English specialist literature that was not available in Germany. In this way, von Borries and Ruska came across an article describing the state of electron microscopy developments in the USA. A large number of scientists and technicians were working on the electron microscope in the context of medical research; they had many more instruments at their disposal than the scientists at home. In Germany, in contrast, Wolpers had been back at the front for one year and Helmut Ruska was called up for the third time. It seemed inevitable that American research would outstrip German efforts in a short time. Against this background, negotiations were conducted with civil and military agencies at the highest level until both researchers were again released. On August 1,1943, a radio announcement stated that women and children should evacuate Berlin if possible. The first severe bombings of Hamburg had taken place in the preceding days. On the next day we left for our holiday as already planned; I and the children did not return to Berlin. Ruska’s wife and family travelled with us to her parents in the Black Forest. During the following days, panic-stricken women fled Berlin in thousands with their children. The attacks on the city were becoming steadily more frequent and heavier, so that it was a great mental relief to the men to know that their families were in relative safety. November 22, 1943, saw the first blanket attack on Berlin. An employee whose flat was hit moved in with us and stayed for a long time. On November 26, 1943, von Borries was seriously injured during voluntary fire-fighting activities in the Wernerwerk plant. He was subsequently decorated with the Kriegsuerdienstkreuz mit Schwertern. Shortly afterwards, another homeless colleague moved into the flat that our children and I had evacuated. In spite of all the difficulties, the production and delivery of electron microscopes continued. On October 29, 1943, the laboratory for electron optics was even granted additional staff. The mental strain of war increased as relatives and friends were killed. Their widows and children needed comfort and help. However, right to the end, the men were allowed a short break with their families every few months. This almost certainly contributed to the stability of

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all concerned. It was thus possible for us to spend Christmas 1943 together with all the children. In February 1944, von Borries and Ruska received similarly worded letters from the state chancellery, in which each was awarded 20,000.00 Reichsmarks in recognition of their services to electron microscopy. In the meantime, two microscopes and the majority of personnel from the super microscopy laboratory had been moved to the island of Riems in the Baltic Sea. Because of the increasing number of daytime attacks, von Borries approached the commandant of the nearby Spandau citadel and requested that the laboratory staff be permitted to take refuge there when the air-raid warning sounded. The request was granted immediately. In fact, no members of staff of either laboratory were killed while at work. At the beginning of 1944, von Borries and Ruska conducted negotiations aimed at finding a new location outside Berlin for the laboratory for electron optics as well, first of all in central Germany, then in the south, and finally in Westphalia. All these attempts were in vain, however, owing to the aircraft activity and sophisticated technical requirements. In summer 1944, postwar reorganization plans were discussed in several meetings with the managing director, Dr von Buol; these included the separation of development and production. Bod0 von Borries was to take charge of a department for research and test equipment, including electron microscopes, cathode-ray oscillographs, mass spectographs, X-ray equipment for technical purposes, electrocardiographs and encephalographs. At the same time, we had to leave our accommodation in the Black Forest as it was required for evacuees from the western front. We were fortunate enough to be taken in by relatives in Westphalia. In October 1944, the three children and I moved into temporary housing. We had a floor space of 30 square metres, no electricity for months and no private water supply for years. October 6, 1944, saw the heaviest daytime attack on Spandau. Bod0 von Borries had sent the entire staff to the citadel bunker. He stayed in the laboratory building, equipped with a helmet, gas mask and protective clothing. With debris falling all around following direct hits on either side, he sustained only slight injuries as he stood in a sheltered doorway. His survival in this way was miraculous; it was an experience he often spoke of in later years. Clearing up began that same afternoon before many of the staff knew what had happened to their own homes. A detachment of one hundred soldiers was assigned to assist with the clearance work. In the application laboratory the remaining electron microscopes were buried up to shield level, but plans were soon drawn up for their recovery and repair. A large number of fire bombs had fallen on the electron optics laboratory, but the flames could be

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extinguished once the raid was over. Machine components, semifinished products and templates remained intact. This is how von Borries described the situation in his letters: October 6th, evening: “Anxious days go by while we wait for decisions to be taken. Tomorrow clearance begins with a vengeance. I will d o everything I can to organize help from outside and to see that everything is rebuilt.. . . The pump stands and glassworks are not beyond repair.. . .” October 7th: “Mr Leifer (production director) came to the laboratory today. He looked at everything and then authorized my rebuilding proposals. Now it’s a question of getting things organized.” October 9th: “Dr von Buol visited us today. He also supports the idea of continuing work on all the previous tasks in the same building. He said he would try to help obtain alternative accommodation for us.” 6.10. nachts: “Bis Entscheidungen fallen, vergehen noch sorgenvolle Tage. Morgen gehen wir mit Schwung an das Aufraumen. Ich selbst werde alles dransetzen, von aul3en Hilfe zu organisieren und den Wiederaufbau durchzusetzen.. . Die Pumpstande und die Glasblaserei sind ubrigens auch nicht irreparabel.. .” 7.10. “Heute war Direktor Leifer im Labor”. Er hat alles angesehen und dann meinen Aufbauvorschlagen zugestimmt. Nun kommt alles aufs Organisieren an”. 9.10. “Heute war Direktor Dr. von Buol da. Auch er ist dafur, wieder alle bisherigen Aufgaben im gleichen Haus zu bearbeiten. Bei der Beschaffung von Ersatzraum will er behilflich sein.”

Ruska was on holiday during these events. On his return, all the important decisions had already been agreed upon with the management. Given that experimentation was unthinkable during the next few weeks, von Borries decided to break off outstanding experiments and complete his postdoctoral thesis. At the end of November a conference on the “Status and performance capacity of electron microscopy” was held in Berlin. Despite the dangerous war situation, 150 people attended. Bod0 von Borries delivered a lecture on the “Limits of electron microscopy”. During sick leave due to furunculosis, and after our joint deliberation, he decided not to accept a lecturer’s position following his postdoctoral interview since this would have necessitated taking an official oath of allegiance to Adolf Hitler. In spite of ever-increasing obstacles (frequent air-raid warnings, prolonged working hours including Sundays, unheated premises), work continued. Proofs were still being printed on time and articles published regularly. Letters and parcels arrived reliably, albeit much delayed. Manuscripts were sent to me

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in the country for safekeeping. It was clear that the country’s collapse was imminent. It became more and more probable that Berlin would fall into Russian hands following an embittered struggle. From mid-February 1945 onwards, von Borries renewed his efforts to transfer part of the laboratory for electron optics to the West. It took weeks to obtain factory space, accommodation and all the necessary authorizations. In most cases, results could be achieved only by personally visiting the authorities. Journeys from Berlin to Westphalia could take up to 24 hours depending on the circumstances. Destroyed sections of railway line and bridges meant that large areas had to be covered on foot. Long delays were caused by air-raid warnings. Movement between the small towns of Westphalia was possible only by bicycle, however inclement the weather. Having secured new premises for a large section of the laboratory and also received assurances of accommodation for the employees, von Borries returned to Berlin for the last time on March 20th. Within two days, he succeeded in procuring two railway waggons and all the necessary authorizations. He had also arranged accommodation for the employees and equipment held on the island of Riems in the West. Because of the war, Miinster University had been moved to Bad Salzuflen. The rector was willing to provide rooms and accommodation for the equipment and eight employees. However, the instruction from Dr von Buol on March 22nd to move the production plant to the West as well could no longer be carried out. Bod0 von Borries hoped to bring everything possible into the West to enable him to rebuild quickly after the war. He was convinced that in Berlin everything would be either destroyed or dismantled. Ruska, on the other hand, preferred to continue working for as long as was feasible and to wait and see what the future would bring. The reactions of each man to this situations were absolutely typical. On the very last goods train to leave Berlin for the West, the waggons arrived at a small station in Westphalia. They contained two complete electron microscopes, the complete set of design documents and picture archive as well as accessories, tools and machine tools. With the assistance of a very helpful transport convoy and a few of his own employees, everything was placed securely under lock and key by Easter Saturday. Bod0 von Borries recorded the transfer period in great detail shortly afterwards. O n the day after Easter he attempted to reach his equipment and employees in their new location by bicycle. He was forced to turn round and hide when he saw a convoy of armoured vehicles coming towards him. He then came back home under cover of darkness. One day later, around one hundred allied military vehicles drove through our village heading eastward.

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That same evening von Borries wrote: “We have reached the end of an era. We must seek a new beginning. Bitter times lie ahead . . . . The sad thing is that Ernst and our most experienced personnel have probably not yet managed to leave Berlin with the main production plant; relocating it is now out of the question. The laboratory has probably been split up. The development tools, but only a few of the staff, are here. The production facilities and most of the people are in Berlin.. . . Perhaps my fears are unjustified and the people and equipment from our laboratory are on the move, maybe already on this side of the Elbe. We must also hope that Helmut and his team are on their way from Riems to Bad Salzuflen. If Germany can ever recover from this self-wrought devastation, then only by means of honest labour unencumbered by empty words. We must have courage and set about our task.. . . If mankind retains an objective picture of the past, horror and shame about everything that has happened will prevail. Positive achievements will pale into insignificance by comparison.” “Wir sind in der Wende der Zeiten zusammen und miissen nun den neuen Anfang suchen. Bittere Zeiten werden kommen . . . Das Betrubliche ist, da13 die Hauptfertigung mit Ernst und den erfahrensten Mitarbeitern wahrscheinlich noch nicht aus Berlin heraus ist und nun wohl auch nicht mehr verlegt werden kann. So ist das Labor getrennt worden. Hier ist alles Entwicklungsgut aber niir wenige der zugehorigen Menschen. In Berlin ist die Fabrik und die Mehrzahl der Menschen . . . Vielleicht sind meine Sorgen aber auch nicht begriindet und die fehlenden Menschen und Sachen unseres Labors sind bereits im Rollen, vielleicht schon iiber die Elbe. Auch da13 Helmut mit seinen Mitarbeitern schon auf den Weg von Riems nach Bad Salzuflen ist, kann man hoffen. Wenn Deutschland aus den Triimmern, in die sein Weg es gefiihrt hat, sich je wieder erholen kann, so fuhrt dieser Weg iiber ehrliche allen Phrasen abholde Arbeit. Die wollen wir tapfer in Angriff nehmen . . . Bliebe den Menschen, ein objektives Bild der Vergangenheit, so miiBte Entsetzen und Scham iiberwiegen, iiber alles was geschehen ist. Das Gute wurde demgegenuber verblassen.”

During the week, von Borries went off to inspect the rescued inventory. But he also had to attend to his family’s growing needs. He immediately began proof-reading as yet unpublished studies and thinking out the first broad outlines of his book. At the first available opportunity, he tried to contact the Siemens management in Munich via the Bielefeld technical office, subsequently deciding to visit them in person. On July 12th, he set off by bicycle for Munich from our temporary accomodation. He had planned the journey so that he could stop off at old associates’ homes. Since no postal communications existed at the time, he always had a large number of letters to pass on that, for many people, represented the first signs of life from relatives and friends after the war. In return, he was given a place to sleep or a bowl of hot soup.

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In the Ruska family’s home town of Heidelberg, he learned of the death of my mother in April. He also had intensive talks with Professor Siebeck. In Schramberg he visited my father, Ernst’s wife and parents-in-law, and Helmut’s first wife. His time in Munich was devoted primarily to Siemens as well as visiting other relatives. Following discussions with Ernst von Siemens and other high-ranking officials, the following written agreement was made: July 26, 1945 “For the coming months and until further notice, we task you as our employee to record the experience gained by you during the past years in the form of a complete, extensive report.. . . It is agreed herewith that the development and production of super microscopes cannot be recommenced at present. However, the company remains firmly committed to revitalizing this area as soon as the financial situation and external circumstances permit this in any way. Dr von Borries will use the interim period to write a textbook on super microscopy and work on a draft for a simple, low-cost super microscope.... In the event of further super microscopy activities being impossible, Dr von Borries shall take charge of the initial development and production of cathode-ray tubes in Erlangen.” 26.7.1945

“Fur die nachsten Monate beauftragen wir Sie, als unseren Angestellten, bis auf weiteres Ihre in den vergangenen Jahren gesammelten Erfahrungen in Form eines geschlossenen umfangreichen Berichtes niederzulegen. Ubereinstimmend wird festgestellt, daB derzeit die Entwicklung und Fertigung.. . von Ubermikroskopen nicht aufgenommen werden kann. Es besteht jedoch die feste Absicht, das Gebiet wieder aufleben zu lassen, sobald die finanzielle Lage und die auBeren Verhaltnisse dies irgend gestatten werden. Herr Dr. v. Borries wird die Wartezeit benutzen, um ein Lehrbuch iiber die Ubermikroskopie zu schreiben und sich mit dem Entwurf eines einfachen moglichst billigen Ubermikroskops beschaftigen.. . . Sollte sich in einiger Zeit herausstellen, daO die Ubermikroskopie nicht wieder aufgenommen werden kann, so sol1 Herrn Dr. v. Borries in Erlangen die dann anlaufende Entwicklung und Fertigung der Braunschen Rohren verantwortlich iibertragen werden.”

He was to continue to be responsible for the two electron microscopes, tools, etc., whose existence was to be kept strictly secret. Bod0 von Borries returned on August 4th refreshed, and full of ideas and confidence. During these weeks, my husband and I had not been in touch with each other, so that this was the first opportunity of exchanging both our good and bad news. During von Borries’ absence, Ruska had turned up at our temporary home on his way to Heidelberg and his family in the Black Forest. The entire electron optics laboratory in Berlin had been dismantled and taken to Russia, including all 40 finished and partly finished electron microscopes.

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All the production equipment had also gone. In addition, Ruska and the other scientists had been put under pressure to move to Russia as well. Ernst had spent each night at a different location during this period to avoid abduction. In the meantime I had also received news from Helmut. The transfer of the laboratory from the island of Riems to the West had already commenced when everything was interrupted by Germany’s fall. Like hundreds of thousands of German civilians, Helmut and his future second wife came to the West with the tide of soldiers returning from the eastern front. They travelled by train, as passengers in military trucks, on horse-drawn carts and on foot. Astonishingly, even the wagons with the microscopes on board also made it to the West. They were confiscated by the British and taken to England. Helmut initially remained in Plon in Schleswig-Holstein; Wolpers also got through to the same area. Immediately after his return from Munich, von Borries began work on the draft of his planned book: “Super microscopy: Introduction, examination of its limits, and outline of its results”. Basing it on previous articles, he had completed the manuscript of his book (von Borries, 1949) as early as the beginning of 1946. However, publication was delayed until 1949 when the publishing houses were again granted permission, and paper, to print. On August 21, 1945, Helmut Ruska and his wife moved to our village; Helmut stayed there for a number of years. From August 24th to 27th, the Ruska brothers met at our home, Together with von Borries, they discussed their ideas for the future. Contrary to the advice of Ernst von Siemens that all three should remain in the West, Ernst Ruska decided to return to Berlin, which had, in the meantime, been divided into sectors. Helmut Ruska wanted first of all to publish the results of his work in Riems. Work became extremely difficult during the following two years as a result of shortages of food, heating materials and clothes for the children, evening power cuts, etc. Protein and fat rations reached an all-time low directly before the currency reform, with a monthly allocation of 100 grams of meat and 50 grams of fat. Before the war von Borries, Glaser and Ernst and Helmut Ruska had concluded an agreement with the Hirzel publishing house concerning an electron microscopy handbook. Work was now started on this major task by Glaser and von Borries. But despite repeated promises to the publisher, neither Ernst nor Helmut Ruska wrote their contributions. Since the handbook never appeared, only parts of this work were published elsewhere. Siemens could not decide for a long time whether to recommence the production of electron microscopes in Berlin or Erlangen. Deliberations on this question dragged on for eighteen months. While Ruska set about the preliminary work for an improved instrument using the documents returned

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from safekeeping in West Germany, von Borries maintained contact with universities and scientists with a view to securing subsequent sales agreements. While Ruska was assembling one of the previously confiscated instruments, he was offered an opportunity to go to America for six months. Siemens agreed, provided that von Borries would then take charge of the Berlin section. The details were arranged in several meetings during March and April 1947. The labour, housing and ticket offices approved the plan, and von Borries moved back into part of our old flat. But a problem arose when he was ready to resume his former position. Ruska had told Mr Schwenn, the director, that he no longer wished to work and share responsibilities with von Borries because they had always stood in each other’s way and had differing opinions on development questions. Ruska cancelled his planned stay abroad. This unilateral breaking-off of their partnership was a great personal disappointment to von Borries, especially since both Mr Schwenn and the old team had welcomed him with great warmth during his seven-week stay in Berlin. Bod0 von Borries left Berlin and immediately began negotiating a future appointment with the agencies with which he had remained in touch over a prolonged period. These were primarily the Max Planck Society in Gottingen, the Federal Weights and Measures Office in Braunschweig and Siemens Erlangen, where plans had already been made for the period after Ruska’s return. In the long term, however, these plans would have involved a move away from electron microscopy. Further technical development of the electron microscope was planned in Braunschweig, but the position finally went to Hans Boersch. An institute was planned in Gottingen to focus predominantly on the application of electron microscopy. Helmut Ruska had already been earmarked as the candidate desired to take charge of work on medical applications. Many interviews had already taken place with Heisenberg, Hahn, Wirtz, Telschow, von Laue, Pohl, Gerlach and von Auvers. All were in favour of establishing such an institute. Plans were so advanced in Gottingen that I cleared our flat in Berlin. On my arrival in Gottingen with all our furniture, I learned that the majority of the Senate, which was not interested in electron microscopy, had rejected the idea of the new institute. The military government then (July 1947)took von Borries to Hampstead in England. During interrogation there, the German scientists were treated correctly. The victors were not hostile; interviews were courteous and geared towards specialized subjects. From July 14th onwards, von Borries worked in the National Institute of Medical Research, just five minutes from the camp. The Institute had an RCA microscope and one from Siemens originally from the island of Riems. First of all he made the Siemens microscope fully operational again, then he took recordings for the local institute and conducted

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his own experiments. From this point onwards, he continued to work there when not ordered to other places. He was also permitted to use the library as a guest, receiving reprints of papers; Zworykin gave him a copy of his book. Furthermore, he was invited to private homes, for example by Professor Cosslett, after he had restored the former Krupp electron microscope to working condition. He was deeply impressed by the freedom and tranquility of Cambridge University, as well as the excellent study facilities. At this time he wrote a report on how he thought international cooperation in electron microscopic research should be organized; this was seven years before the international society was actually founded. Within a few days the climate had improved to such an extent that Professor Cosslett proposed to von Borries that he continue to work there for some time on a contractual basis, deliver lectures at forthcoming conferences, maintain the microscope and train young scientists. Bod0 von Borries was convinced at the time that the Siemens microscope was far better than the RCA version with which he was by now well familiar. He warned Siemens of future tough competition and stressed the importance of restarting microscope production as soon as possible. Only five of the forty or so microscopes available at the end of the war in Germany remained. At the same time, two to three hundred instruments were in operation in the United States and approximately thirty in England. Bod0 von Borries’ professional future was still in the balance as 1947 ended. He concentrated on adding to his book the measurements obtained in Great Britain, and on publication of his postdoctoral thesis (von Borries, 1948); the journal “Optik” now wished to publish this work, which had not been printed in 1945. The food situation had deteriorated to such an extent by now that survival became all-important. To improve our diet we planted potatoes, vegetables and sugar beets in our small garden, as well as tobacco, which we exchanged for grain. The children grew 7 cm each year, but their weight went down. They were often ill. At the beginning of 1948, Siemens Erlangen again offered von Borries a position in charge of electron microscope part production as well as other responsibilities. His personal preference was to invest all his efforts in the science of electron microscopy, particularly since he had just started working on several original studies. Before he had made his decision, von Borries was requested to attend an advisory meeting at the Max Planck Institute for Iron Research in Diisseldorf, which wished to purchase an electron microscope. As early as his first meeting with Professor Wever of the Max Planck Institute (MPI), a plan emerged to establish a department for electron microscopy in conjunction with Siemens with von Borries at its head. Professor Wever was extremely enthusiastic at the thought of having a microscope at his disDosal

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one or two years earlier than anticipated and also one of the first specialists on hand to set up and advise on the instrument. Further discussions took place that same day, most importantly with Dr Petersen, executive chairman of the German Ironworkers’ Association. Despite uncertainty surrounding the imminent currency reform, Dr Petersen was convinced that they simply had to have the courage to take such a risk and then see how it turned out. In contrast to the difficulties experienced in Gottingen and Braunschweig, no doubt ever existed as to the willingness of those involved in Dusseldorf to work together with Siemens. Undeterred by all the disappointing events of recent years, that evening my husband was confident that a successful partnership was now possible. During subsequent meetings it was decided to found an institute independent of the MPI. To make electron microscopic studies available to as many scientists as possible, von Borries planned at an early stage to supervise external studies on the one microscope available in West Germany (the other instrument had been returned to Berlin in the meantime). Further financial sponsorship was needed if this were to be achieved. Beginning in March 1948, therefore, he entered negotiations with the Education and Trade and Industry Ministries of North Rhine-Westphalia; Professor Mochow, Bayer Leverkusen; Professor Kikuth, Dusseldorf Medical Academy; Henkel & Co. and Siemens. The diverse interests represented by these founder members of the society sponsoring the Institute were harmonized relatively quickly. On June 8, 1948, the meeting to found the “Gesellschaft fur Ubermikroskopie e.V. zu Dusseldorf” was held. Before the month was out, the microscope, design drawings, microscopic records, auxiliary assemblies and machine tools had all been transported to Dusseldorf. The currency reform fell between the founding meeting and the beginning of work. All members continued to make the same contributions in new Deutschmarks. On Siemens’ behalf, von Borries took charge of advising scientists interested in acquiring electron microscopes, giving advice to the company’s technical offices, and designing a less costly, more easily operated electron microscope that still offered sufficient power. In those days it was scarcely conceivable that the many interested parties could purchase these expensive instruments. Work began on July 1,1948, with a staff of two. The microscope was presented to the first executive committee meeting just four weeks later in very good condition. Work progressed quickly, although the employees appointed during the next few months were, without exception, absolute newcomers to the field of electron microscopy. News of the Institute’s foundation and availability of an electron micro-

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scope travelled so fast that, even in 1948, studies were produced by old and new guest scientists. The following were among the first to appear: Professor Dr Domagk, Bayer, Wuppertal (tuberculosis) Professor Dr Glemser, Dr Lutz, Dr Baumann, Aachen (tungsten studies) Professor Dr Griin, Diisseldorf (aerosols) Professor Dr Hofmann, Regensburg (inorganic chemical substances) Professor Dr Koch, Dusseldorf (steel following various heat treatments) Professor Dr Meldau, Harsewinkel (examination of industrial dust prior to producing his dust chart) 1948 saw the end of power-sharing in Berlin. Different currencies had been in circulation in the eastern and western parts of the city for months. The blockade continued. The West countered Russian pressure with the airlift and by founding the Senate and the Free University. The economic situation remained precarious, though, and the political situation was fraught with uncertainty. Ruska travelled to the West for talks lasting several days: He was seriously considering moving to the West after all. Helmut Ruska, too, had returned to Berlin in 1948. He was working at the Humboldt University in the eastern sector. With the political pressure on academics steadily increasing, he loaded his electron microscope onto a truck and drove it through the back streets into West Berlin. There he moved to the Free University. When von Borries went to Gottingen to fetch part of our furniture, which had been stored there since 1947, to equip his institute, Professor Hahn suggested that the Institute should become part of the Max Planck Society. The members of the Super Microscopy Society wished to retain the Institute's independence, however. In January 1949, the German Coal-Mining Directorate in Essen became the eighth member of the Dusseldorf Society. The official inauguration of the Institute took place on February 15,1949. All the members attended, including the Education Minister, Christine Teusch, and Dr Hermann von Siemens, as well as most of the German scientists originally involved in electron microscopy. A celebratory colloquium was held on the next day in the headquarters of the iron industry. Before the assembled experts and colleagues, von Borries proposed the establishment of a German society for electron microscopy with Ruska as its chairman. Those present were unanimous in their support. Ruska was elected in his absence, while von Borries was appointed secretary. That same evening I drove with Helmut Ruska and his wife to Father's funeral. News of his death had arrived during the inaugural ceremony. Because of his official guests, my husband was unable to accompany me on this difficult journey. Ernst Ruska and his wife did not join us from Berlin.

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On March 17, 1949, the 17th anniversary of the application for the fundamental patents, von Borries was appointed an honorary professor of the Medical Academy in Diisseldorf. Two months after its foundation, the first meeting of the German Society for Electron Microscopy took place in Mosbach. The achievements of Briiche there in the postwar years were very impressive. With a team of 12 scientists, he brought the performance of the AEG electron microscope up to a level comparable with that of the Siemens instruments. Furthermore, and more significantly, AEG was also able to deliver its own products. Foreign companies had brought out high-performance instruments by now as well. This showed that Siemens should have built up their production capacity in the West-a cause in which von Borries had invested such energy. The warning that a five-year interruption in supply would severely undermine Siemens’ position was now regrettably confirmed. Similar potential was lost in the case of small microscopes, which foreign companies also introduced to the market earlier. From the very outset in Diisseldorf, working with several users on one microscope while testing new improvements at the same time was difficult. Consequently, as during the development phase in Berlin, work continued well into the night. The North Rhine-Westphalian Institute for Super Microscopy was also designing a small magnetostatic electron microscope. The new instrument’s requirements were sufficient power for most examinations, considerably reduced manufacturing costs and simpler operation. Work on the new instrument advanced so quickly that the first pictures could be taken on October 1, 1949. Throughout von Borries’ eighteen months of employment in Diisseldorf, we had not succeeded in finding a home where the family could be together under one roof again. In the end we were compelled to build our own house. Because this involved additional work, I took sole responsibility for finding a plot of land, discussing plans with the architect and dealing with the authorities. We completed the building plans between Christmas 1949 and the New Year, working from our temporary accommodation. By now, young scientists from 25 different institutes and industrial enterprises were studying at the Institute in Diisseldorf. The Institute’s funds were so limited that the fees paid by guest scientists became vital, especially since Siemens cut its contribution. By 1956, in the space of eight years, 145 papers had been published by guest scientists. Despite his close advisory rble and many invitations, von Borries never appeared as a coauthor: he felt that a person providing a service in a paid capacity should not share in the credit for publications. As a result, von Borries devoted himself increasingly to applications, advice and organization on the one hand, and theory and teach-

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ing on the other as he enjoyed his lecturing activities at the medical academy so much. Returning to 1950, the progress that had been made on the magnetostatic electron microscope in cooperation with Leitz was such that industrial production seemed imminent. Attempts to negotiate collaboration between Siemens and Leitz in this field were initially unsuccessful. The next electron microscopy conference took place in April in Bad Soden. During this meeting, von Borries managed to interest Boersch and Mahl in working together on the handbook of electron microscopy that he had been planning for ten years. In addition, he agreed with the Hirzel publishing house to revive the Zeitschrijt fur Wissenschaftliche Mikroskopie, which had last been printed in the war years, and to supplement it with an electron microscopic section. He took on the editorial responsibility for the supplement himself. In the meantime, von Borries was also involved in the patent committee of the Protection of Industrial Rights and Copyright Association. This body comprised inventors with the common objective of having patents extended to take the war and postwar period into account. The first hearing in the federal parliament was not very encouraging, but following numerous negotiations and meetings with industrial representatives and politicians, a breakthrough was achieved in October 1952 in the Haus der Lander, Konigstein. The federal parliament subsequently passed a law extending the patents concerned by five years. The Siemens microscope newly designed by Ruska was given an excellent reception at the Hanover Trade Fair in May 1950,but it was not yet available for sale. The French conference was held in September in Paris. Foreign guests were invited, including many Germans. The week-long event was an opportunity for many scientists from the early days to meet, among them d’Ans, Bartels, Boersch, von Borries, Cosslet t, Dosse, Duhm, Glaser, Induni, van Itersen, von Laue, Martin, E. Ruska, Schulze, and Wolpers. With memories of the occupying army still fresh, the relationship between the hosts and the German participants was still rather tense. Electron microscopy was by now indispensable in medicine and a growing number of technical fields. Consequently, von Borries was invited to address the VDIs and VDEs of many cities, as well as technical universities and higher education establishments. His lectures were always very carefully tailored to suit the audience concerned. Since he welcomed such opportunities to tell more people about electron microscopy and its applications, he soon had a full lecturing schedule. As the months passed, the continual load on the Institute grew, as did the wish of members and guest scientists alike to have their own instruments. To

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improve study facilities, von Borries applied to the German Research Society for a new Siemens high-power microscope for his own institute. He succeeded in gaining the support of the Emergency Association for German Science as regards financing. He also proposed the establishment of electron microscopic community institutes at suitable universities with the aim of providing study opportunities for scientists from various fields. These plans required detailed preparation with the individual universities. By now, von Borries was also a member of the “Arbeitsgemeinschatt fur Forschung des Landes Nordrhein-Westfalen”, nowadays the Academy of Art and Science of the state of North RhineWestphalia. The new contacts thus made enabled him to convert other professors to his way of thinking. During the same months we had built the basement and ground floor of our house, which was located just five minutes from the Institute, and a temporary roof had been put on. The family moved in just before Christmas 1950. Caught up in the hectic work schedule of that year, von Borries failed to notice that, since the middle of 1950, Ruska had omitted his name from the list of authors of electron microscopic recordings and presentations in Siemens publications. When the executive chairman, Dr Petersen, brought the matter up at a meeting of members of the North Rhine-Westphalian Society for Super Microscopy on December 18, 1950, it emerged that this had been neither noticed nor approved by Siemens officials. Bod0 von Borries’ great love was designing and experimentation. This led to numerous patent applications. In addition to growing organizational duties, he continued to devote his efforts to developing the small magnetostatic microscope. The significance of this device, as he saw it, was confirmed by the fact that a similar instrument was introduced to the market by RCA. The Institute also worked on improving accessories designed to facilitate the user’s work. In view of the modest funds available, representing not even a tenth of the development resources provided by Siemens in Berlin, only affordable studies were possible. The results of the laboratory for guest scientists had shown that, if even limited resources were fully exploited, a great deal could be achieved. In May 1951, the German Society held its conference in Hamburg. Bod0 von Borries was elected executive chairman. He delivered a detailed lecture on his small magnetostatic microscope (von Borries, 1952). More lectures were presented by members of the Diisseldorf Society than by those of any other institute. During the first ten months of 1951,7,000recordings were made for guest scientists alone-on a single microscope dating back to 1939. For several days in October 1951, Siemens representatives met with the executive committee

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of the Diisseldorf Society. Although the Berlin design engineers considered the small microscope to be good, easy to operate and inexpensive to produce, Siemens was unwilling to introduce a competitor to products it already had on the market. The subsequent years of negotiating licensing agreements with Leitz spoilt the instrument’s chances of success. When all the obstacles were finally removed, von Borries died suddenly and only the few prototypes remained (Fig. 6). Some years later Ruska had a small magnetostatic microscope designed by the Max Planck Society, in which several of von Borries’ patents were used. Siemens went on to produce this instrument, which was marketed from 1967 onwards under the name Elmiskop 51. As a result of his close cooperation with the German iron industry, von Borries was invited to deliver two lectures at the conference for coal mining and iron by the mining college in Leoben in Austria. This enabled him to address meetings in Innsbruck and prepare for the next conference. Although von Borries had formally left Siemens when the Dusseldorf Society was founded in 1948, he had reserved the right to return to the company after three years. The time had now come to make a final decision on his future. Siemens stated that no suitable position could be found for von

FIG.6. Von Borries at his magnetostatic electron microscope.

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Borries in the electron microscopy sector. Instead he was offered a leading post in cathode-ray tube development. He regarded the suggestion that he should give up electron microscopy as quite unacceptable. He had devoted twenty years of his life to developing, asserting the cause of and publicizing electron microscopy. He had brought electron microscopy to Siemens. He had committed his exceptional creativity to working passionately and tirelessly for this cause. He had constantly paid due attention to economic aspects, so that development costs remained within the bounds of reason. Moreover, he had declined honorary appointments because of his perceived moral obligation to maintain personal contacts in the company’s interest. His efforts to move the laboratory at the end of the war and rescue so much material considerably facilitated the new beginning in Berlin. He was willing to accept any fair solution, but not one that involved his abandoning electron microscopy. Bod0 von Borries recorded these sentiments in a detailed memorandum composed at the request of the executive committee members of the Dusseldorf Society. After many meetings and discussions, the members accepted his reluctant withdrawal from Siemens. A different and more acceptable solution had to be found. Although his professional insecurity was a heavy burden for a responsible head of household with five children, von Borries’ appetite for work appeared to be increasing. He maintained and developed his associations with scientists, industrial enterprises and ministries. When the new foundry institute was officially opened in Dusseldorf, von Borries delivered the inaugural lecture: “Work on the electron microscope, and electron microscopy as an indispensable future research method”. A ceremony was held on June 3, 1952, to mark the appointment of Professor Max von Laue as an honorary member of the German Rontgen Museum. As a member of the board of trustees and treasurer, von Borries delivered a celebratory lecture on spectral analysis and X-ray spectroscopy. He also presented Professor von Laue with the Rontgen plaque (Fig. 7). The Dusseldorf Institute again contributed many lectures to the Tubingen conference in June 1952. It was also an occasion to meet up with old acquaintances, many of whom we now regarded as good friends. The tradition of inviting a few foreign participants to visit the Dusseldorf Institute immediately afterwards had already been established. Following long-standing cooperation with the iron industry institute in Aachen, contacts were also built up with other institutes in Aachen. The joint institute for electron microscopy, which is still in existence, was founded in 1953. The concept of institutes in Bonn and in the Medical Academy in Dusseldorf was beginning to take on a more concrete form.

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FIG.7. Von Borries presents Professor von Laue with the Rontgen plaque, June 1952.

Efforts were being made by the executive committee of the Diisseldorf Society to incorporate the Institute in a university in North Rhine-Westphalia. By Christmas 1952, the final details concerning von Borries’ appointment to the technical university in Aachen with effect from January 1: 1953, had been settled. At the time one of our children was in hospital, in danger of losing an eye. We had to take turns spending the night at his bedside. We were glad when Christmas finally came. After an unusually demanding and unsettled year, we now looked ahead to the new year with confidence and much optimism about the future. Early in 1953, the part of the Institute devoted to medical applications was inaugurated within the walls of the Diisseldorf Medical Academy. This also marked the beginning of protracted negotiations on the new building intended to house the whole Institute in the same location. Building work had also already commenced on the Bonn institute. On January 31st, von Borries was sworn in as a full professor. This event was celebrated in the Institute as well, since it gave the employees added job security.

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Bod0 von Borries began immediately with a lecture course in Aachen that was continued during the academic holidays. As the summer semester got under way, he also had to deliver lectures on precision mechanics because the chair he occupied had also to cover this subject. Although this additional responsibility involved extensive studying to become familiar with this new subject, it also led to new contacts with representatives of science and industry. Some Siemens experts were very willing to assist, so that the workload involved in this undesired lecture course remained manageable. Once the business ties with Siemens had been broken, things improved greatly on a personal level. In particular the director, Mr Bleisteiner, realized by now that the information he had been given for years had been one-sided and incomplete, and he clearly reflected this in his conduct. Due to his university activities, von Borries concentrated increasingly on his own publications, advice for users, training of young scientists and general organizational tasks. The resources of the Diisseldorf Institute remained limited. Industrial enterprises that had used the Institute now had to be encouraged to become members of the Society, and in some cases this was successful. This allowed development work on the magnetostatic microscope, to which von Borries had repeatedly returned since 1940, to continue with modest funding. Investigations were also conducted into improving the auxiliary equipment for preparation. At the major rationalization exhibition in Diisseldorf in 1953 entitled “Better living for everyone”, the North Rhine-Westphalian Institute for Super Microscopy was awarded the Grand Prix for its excellent organization. Dr Petersen, the executive chairman, died suddenly at Christmas in 1953. The Institute lost a man from whose contributions and staying power it had greatly benefited. He was succeeded by Professor Riess of Bayer Leverkusen. The beginning of 1954 brought with it an immense volume of work. Planning continued on two fronts: for the new building in Diisseldorf, and for the new large institute being set up in Aachen. At the same time, much work still had to be done on building our own home. Each step forward was a source of pleasure, however. At the time I often wondered just how long a human being could keep up this amount of work. Bod0 von Borries thrived on the sincerity in the attitude of most of his colleagues; this repeatedly gave him fresh impetus and stimulation. A conference on applied electron microscopy took place in Ghent from April 7 to April 10, 1954. On this occasion, the programme committee was extended to include Belgium, Sweden and Switzerland. The list of the many scientists present who were interested in international cooperation included Cosslett, Fert, Habraken, Kellenberger, Locquin, Mahl, Le Poole,

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Sjostrand and Vandermeersche, who had organized the conference. At the closing session, a resolution was passed to intensify international cooperation still further. That summer many foreign colleagues visited the Institute and our home, which was still under construction. In addition to working at the Institute, delivering lectures, leading seminars and supervising house building, carefully preparing his lectures for the London conference took up much time. The International Conference on Electron Microscopy took place in London from July 15 to July 21,1954. Following a day’s lecturing in Aachen, we set off by car at midnight and headed for Ostend via Liege and Brussels. After a stormy crossing we drove through Kent and Canterbury, arriving in London on the evening of July 14th. The Joint Commission met on July 15th. On the 16th, von Borries delivered the opening address on “The physical situation and the performance of high-resolving microscopy using fast corpuscles” (von Borries, 1954). During the final session on July 21st, the International Committee elected von Borries as chairman and eltecutive president almost unanimously. Professor Cosslett was nominated First Secretary. Professor Sjostrand from Sweden agreed to host the next European conference, and thus the first meeting of the International Federation of Electron Microscope Societies, in two years’ time in Stockholm. Detailed preparatory discussions then took place that same evening. The following day, we visited Professor Cosslett and his wife in Cambridge, first at the Cavendish Laboratory, then at their home. Before returning to the USA, Professor Marton and his wife visited the Dusseldorf Institute; they were followed shortly afterwards by Professor Picard and his wife. Both couples also visited us at home. Bod0 von Borries’ election in London was a mark of recognition of his tireless efforts to improve international cooperation. As well as receiving countless foreign guests in his Institute, he had also travelled to many countries. Until now, however, he had never been given the opportunity to get to know American electron microscopic research institutes. During the rebuilding phase following the war, the only way to afford such a trip was to work in the USA for a period. Bod0 von Borries now received a chance to go there: He was invited to join a group of experts visiting the USA for one month to study electronic measuring and control systems and their applications in industry and research. He successfully postponed the journey so that he could also attend the American electron microscopy convention in Chicago from October 14 to October 16, 1954. There, he delivered a lecture on the magnetostatic electron microscope and received numerous invitations to give lectures and visit institutes. He was thus able to make appointments to coincide with his group itinerary. The official visit programme of the expert party was very full. They visited sixteen companies producing electronic measuring and control

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equipment, and eight research institutes. Bod0 von Borries also gave twelve lectures and visited fourteen universities, which frequently employed electron microscopes in several institutes. The visit was extremely demanding. In the evenings he was often invited out by fellow specialists, on some occasions also with the entire party and their excellent tour guide. All the participants were delighted by the natural generosity with which they were received. During the visit to the New York Institute of Health in Albany, Helmut Ruska invited the party to spend the evening with him. He was working there at the time before coming back to Germany in 1958. Three institutes asked von Borries to spend an intermediate semester or even a full year in the USA. By the same token, many American colleagues were keen to spend a sabbatical in Dusseldorf. The wide range of applications of the electron microscope deeply impressed von Borries. At least twelve institutes were working on the micromorphology of the muscle in America; in Germany the only group working in this field was at the Dusseldorf Institute. A large number of microscopes were available in America with more and better-trained operating staff. In addition, teaching and administrative tasks placed less strain on researchers. RCA and Philips were both working very hard on further technical development. Clearly, greater efforts were needed in Germany if the country was to remain competitive in the fields of development and application. During the American electron microscopy convention in Chicago, von Borries met Professor Glaser, who now lived in the USA. Glaser explained that he had been asked by the Nobel committee to put forward proposals for the Nobel prize for physics. He intended to submit the names of von Borries and Ruska. I was instructed to send documents to the USA. Prior to his return to Germany, von Borries met Glaser again and discussed these documents with him before Glaser submitted his nomination. During the return journey by sea, the four tour participants began writing their report on the current state of electronic measuring and control instruments and their applications in laboratories and companies (von Borries, 1956). A few days after von Borries’ return from the USA, the Dusseldorf Society had its general meeting. Bod0 von Borries opened the proceedings with a short report on his experiences in America. The more important items on the agenda included the 1955 budget and, most significantly, the planned new building in the grounds of the Medical Academy. A Japanese electron microscopist was our guest that Christmas. Dr Ito had worked for an extensive period at the Institute. The noise and dirt caused by the house construction had taken its toll on everyone. Only our

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four- and five-year-old daughters had enjoyed it. They spent a lot of time with the workmen, fascinated by what was going on. We desperately needed the break until January 2nd to recover our strength. Most of the time was spent with our children. 1955 was another turbulent year. The Institute’s financial position continued to cause concern. The members were unwilling to increase their contributions to a level that would cover the growing number of employees and rising wage costs. Bod0 von Borries therefore had to set about finding new sources of money. Repeated meetings with the Max Planck Society, the German Research Association and the Founders’ Association for German Science produced only modest amounts; money was generally still in short supply. This situation led von Borries to the conviction that central institutes had to be founded: These would be equipped with only one high-performance microscope but several more application microscopes. Experience in his own Institute had proved that this could produce excellent results, provided that the instruments were well maintained and thus always operational. Invitations to speak about his experiences flooded in from all quarters after his trip to America, each time with a different point of emphasis. In January many consultants from Siemens’ technical offices gathered in Karlsruhe to hear such a lecture. Bod0 von Borries spoke for three hours on companies, universities and electron microscopy in the USA. This was followed by detailed questions and answers. Interest in the USA was considerable at the time, especially since many of those present had an opportunity to go to America for a few years, The afternoon session thus took the form of a lively discussion on the American way of life, schods, living costs, and so on. Since von Borries delivered his lectures freely using only a few notes, their composition consisted primarily of selecting and arranging slides according to a summary of the specific topic. Only strictly scientific lectures required more involved, detailed preparation. Bod0 von Borries continued to meet with the ministries in order to procure funds for the Institute’s new building. Further institutes were to be founded with the help of the German Research Association and the Research Council. All these agencies were also very interested in developments in the USA, and particularly in von Borries’ assessment of automatic recording of measured values, which had been the prime objective of his visit. The German conference for electron microscopy began in Miinster on March 28, 1955. Bod0 von Borries opened the conference and was again elected executive chairman. His report on electron microscopy in the USA was also received with great interest. The ultramicrotome developed in Diisseldorf was included in the exhibition of pictures and equipment on display.

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During the conference we learned that Ruska was leaving Siemens and moving permanently to the Max Planck Society. Here, he developed and built a high-performance microscope in later years. Immediately after the Munster conference, the French conference for electron microscopy was held in Toulouse. The standard of apparatus available in the institutes and the quality of the presentations were outstanding. Bod0 von Borries discussed plans for the 1956 conference of the international society with the chairmen of the various national societies. Once again I witnessed how the meetings resulted in many close personal conversations as well as discussions of scientific and organizational matters. We took advantage of the return journey and glorious weather just after Easter to visit some of the most splendid sights in the South of France. During the 1955 summer semester, the number of students attending lectures in electron optics increased substantially. As well as lectures and seminars, excursions also took place to various institutes specializing in applications, and frequently to Philips in Eindhoven. By the same token, scientists from other universities frequently visited the Dusseldorf Institute with groups of students. That summer we took our three adolescent sons on a five-week camping holiday by car through Austria, North Italy and Switzerland. The last week prior to our departure was extremely hectic with professional activities, and von Borries also had various official appointments to keep during our holiday. Fortunately, my husband found it easy to switch from work to family and leisure pursuits. This was our longest holiday ever, and we thoroughly enjoyed everything we did, from picking berries and mushrooms and visiting ancient cities such as Venice, Verona, Bern and Basle, to driving or walking through the countryside to lakes, glaciers and waterfalls. Bod0 von Borries was elected to the scientific council of the Study Group of the Industrial Research Association (AIF) when it was founded in 1954. In this capacity he attended conferences on gear technology in Bingen and precision mechanics in Berlin. His work on precision mechanics was intended to assist the further development of the magnetostatic microscope and ultramicrotome. During a meeting of the presiding committee of the Industrial Research Association in Bad Konigstein, von Borries spoke to the federal minister for science and the president of the German Research Association about the organization of science and research sponsorship. He felt that these areas needed improvement if Germany was to continue to match foreign competitors. His efforts in the committee for applied research of the German Research Association, of which he was president, were also aimed at convincing other agencies of the need for more generous cooperation. He had become actively involved in the German Research Association several years

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before, when he was asked to give his expert opinion on applications from his special field. In addition, he approached this body with proposals of creating training opportunities for electron microscope operators and users. Seminars on various application sectors held in Aachen, Dusseldorf and Miinster were intended primarily for basic and advanced training purposes. These were prepared with great care because von Borries placed substantial emphasis on educating the new generation, and he knew that motivation was an essential precondition of professional achievement. At the hard-coal conference in Essen and at the conference of the Leoben mining college at Graz Technical University at the end of 1955, von Borries delighted audiences with his lively lectures and obvious love of his subject. Drawing on his experiences in America, he used every opportunity to campaign for cooperation with experienced electron microscopists. He saw this as practically the only way for users to gain access to the routine skills on the electron microscope that were essential for fruitful results. He had repeatedly observed the success of this type of cooperation at the Diisseldorf Institute. Discussions with people from diverse backgrounds gave him a deep insight into many areas of application. The year 1956 began with a seminar in Tiibingen lasting several days. Bod0 von Borries expressed his firm belief that the uses of electron microscopy would continue to multiply since ultramicrotomy permitted the production of extremely fine sections. Furthermore, electron spectroscopy was still in its infancy. Work continued as energetically as ever alongside the efforts to push ahead with the new building for the Dusseldorf Institute. Development work was also progressing on the small magnetostatic microscope and the ultramicrotome with Leitz in Wetzlar. In March, Helmut Ruska came over from the USA. For some time he had wished to return to Germany, and now interviews had been arranged with several institutes. Regrettably, none of these negotiations was successful. I was able to accompany my husband to the general meeting of the founders’ association for German science on April 27th in Wiesbaden. Theodor Heuss, the federal president, gave an impressive opening address. The following weekend we visited colleagues and friends who lived in the area. On April 30th, after a meeting lasting several hours in the federal science ministry in Bonn, where von Borries was representing the AIF, we drove to Liege. The Belgian conference for applied electron microscopy was taking place there on May 2nd and 3rd. For the first time Russian scientists were in attendance. The Liege international trade fair was being held at the same time; at the fair, a Japanese electron microscope was presented in Europe for the first time. These events naturally provided a further opportunity to discuss plans for the international conference in Stockholm.

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Bod0 von Borries had accepted an invitation to give a lecture in Halle on May 1 lth. O n the 9th, he set off for Aachen at seven o’clock to adjudicate at an examination as well as give lectures and a seminar. This was followed by a detailed discussion. Having arrived home in Dusseldorf at four in the afternoon, he just had time for a short coffee break before setting off for Kassel and another meeting. He finally arrived at his sister’s in Gottingen at eleventhirty at night. He spent the following public holiday there with her family and prepared his lecture. To save time and avoid a detour, he had obtained permission to drive into East Germany away from the official border crossing point. On a section of road that had been ploughed up to demarcate the border zone, several border guards with live rifles got into his car and escorted him to Klettenburg barracks despite his valid permit. After consulting headquarters in Nordhausen, the guards apologized that they had not been notified in good time, invited him to eat in the officers’ mess and then sent him on his way. He arrived in Halle just in time. That night, following the lecture, a discussion and a meal, he drove on to Berlin. The next morning, the centenary celebrations of the Association of German Engineers began. With the lectures behind him, this gave von Borries an ideal opportunity of meeting esteemed figures from the world of science and technology of interest to him. The new building had become so urgent by Easter 1956 that von Borries had to conduct negotiations almost every day. Notice had been served on the previous premises some time before, as they were required for other purposes. As usual during the summer leading up to the vacation period, there were countless meetings, conferences, talks and excursions to attend. In view of this extremely full timetable, we were not surprised that my husband frequently woke up with a headache. However, since the pain disappeared shortly afterwards, it did not incovenience him unduly. On June 29, 1956, the final authorizations came through for the new Institute building. However, contrary to my expectations, my husband did not seem really delighted. He was simply too exhausted. That evening we visited theempty building that was going to house the Institute temporarily until the new premises were ready. We celebrated the final granting of permission with our three sons. The next morning my husband complained of a desperately severe headache. A few minutes later he suffered a brain haemorrhage. In hospital only his closest family was allowed to visit him. Convinced that he would be fully able to work again within a few weeks, his thoughts continued to revolve around the Institute. I was entrusted with explaining his ideas for the immediate future to a committee meeting and had to report to him in full on the outcome of the meeting. Although physically he was very weak, his mind

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was as active as ever. On July 9th, he was transferred to the care of Germany’s best brain surgeon in Cologne because an operation appeared inevitable. Within a few days of arriving in Cologne his condition improved greatly: He was even able to get up and go for a walk outside. I stayed in Cologne, and one or two of our children came to visit each day. My husband felt so much better that he no longer wished to have the operation. During this period he read proofs of papers, dictated letters to me and chatted to the doctors about electron microscopy. He also discussed convalescence plans with the surgeon. The professor asked me to explain to my husband why he had to operate now, while he was still well. It was certain that attacks would recur, and then it might be too late to save him. We talked about everything that might lie ahead for me. Although we were full of hope that the critical operation would be a success, given his good condition, we also knew that it was a matter of life or death. In all seriousness and very calmly, he asked me to convey all his thoughts to the executive committee as to the future of the Institute and suitable successors should he not survive. His last wish was that the Institute, for which detailed plans had been drawn up and which had at last been approved, should still be built after his death. He also wanted Helmut Ruska to return from America and become its director, to continue the work on applications. Lenz was initially to take over von Borries’ lecture courses in Aachen until a lasting appointment was made. Only the way ahead for development work was not quite clear. We also discussed how the family would survive on the small pension we would receive from his three and a half years as a state employee. He tried to reassure me by saying that I would be called to accept the Nobel prize, which he was sure of receiving, on his behalf immediately after his death. This award would safeguard the education of our five children. There was no doubt in his mind that this distinction would now be granted more than twenty years after the invention. After all these things had been discussed our cwfidence was restored and we were grateful for every hour spent together. Bodo’s sister arrived the day before the operation was due to take place, in order to be with us both at this difficult time. My husband did not survive the long operation the next morning. Even before he was buried, five members of the executive committee of the Diisseldorf Society visited me. They promised to provide an education allowance for the children, and I passed on my husband’s last wishes. Teaching activities initially continued in Aachen. Students preparing to take diploma examinations and postgraduates working for their doctorates were able to complete their studies. The Institute was built in Diisseldorf; the majority of the staff continued to work under temporary management until

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the new building was finished and Helmut Ruska had been appointed a full professor. He took over as head of the Institute in 1958. Ernst Ruska became president of the International Society in 1956 and thus assumed responsibility for the Stockholm and Tokyo conferences. The honorary doctorate he received in 1958 was the first of numerous distinctions. All that von Borries’ family was left with was heartfelt grief and memories. Bod0 von Borries exuded an exceptional enthusiasm for work and zest for life. His gifts comprised a happy combination of technical, organizational and intellectual abilities. This allowed him to pursue his objectives doggedly, even in adverse circumstances. His family had instilled in him a deep sense of obligation and belief in loyal behaviour. His gift of free speech and skill in capturing the imagination of others by his enthusiasm were the foundation of his extensive lecturing activities. Equally important were his warmheartedness, willingness to help and genuine interest in others. Many lifelong friendships came of these qualities. Friends and colleagues alike appreciated his ability to devote complete concentration to a conversation. His great love of nature helped him to relax: He enjoyed a short drive through the countryside or a few minutes watching the setting sun or the starlit sky. His pronounced sense of family values also originated in his parents’ home. His every free moment was spent with our five children, whom he loved deeply. He passed on to them his lively enthusiasm for art and culture; during our annual holidays, mainly by bicycle, he took his sons to beautiful churches, as well as to museums and the theatre. Even on business trips he managed to arrange similar excursions from time to time. His capacity to enjoy everything demonstrated his exceptional vitality. The following extracts from tributes from his fellow experts conclude this essay. “Bodo von Borries has been one of the chief founders of electron microscopy in the strictly scientific as well as in the organisational sphere.” (Cosslett, 1957) “In Bod0 von Borries, I feel we have lost the most active pioneer of electron microscopy ... in over 25 years of joint studies.. . . As early as 193 1, while still working on his doctoral thesis on “External recordings using the cathode-ray oscillograph”, he became fascinated by the prospects . . . of using the electron beam for microscopy. He . . . thus embarked on a career in which he was to produce such fruitful work, tirelessly dedicated to scientific, technical and organizational activity.” (Ruska, 1957) “Already then, both men were investigating the possibility of optical recording using electron beams. The cathode-ray oscillograph was used for experiments in this direction.” (N. N., 1956)

BOD0 VON BORRIES: PIONEER OF ELECTRON MICROSCOPY

173

“The hour of birth of electron microscopy came when Ruska and von Borries succeeded in producing pictures with a cathode-ray oscillograph using special pole-piece concentration coils (patented in 1932). The electron microscope was conceived unexpectedly from basic research on the development of a cathoderay oscillograph; the infant was watched over by its creators, Ernst Ruska and Bod0 von Borries”. (Grunewald, 1956)

“In 1932 B. von Borries and E. Ruska announced the decisive patent for the magnetic pole-piece lens, which forms the basis of high-resolution electron microscopy.” (N. N., 1956) “Von Borries’ first electron optics papers (in collaboration with E. Ruska) were published in 1932 and 1933. The second study in particular . . . belongs to the pioneering achievements of electron microscopy.” (Mahl, 1957) ... He was successful, with Dr Ernst Ruska, in obtaining in 1932 the first transmission pictures with an electron microscope.” (Cosslett, 1957)

“

“Von Borries had already at that time clearly recognised that electron microscopy would develop to become a valuable method of future research, and devoted his very charismatic personality to its promotion in lectures and papers.” (Ruska, 1957) “9. von Borries saw himself primarily as an engineer; his achievements originated in the fusion of scientific, technical and economic thinking and creation. His great love . . . was design.. . .” (Ruska, 1957)

“In 1940 he introduced the first usable method of depicting surfaces, known as electron reflection microscopy.. . .” (N. N., 1956) “These were not only major original contributions towards image formation in the electron microscope, surface microscopy under glancing incidence, intensity conditions in the electron microscope but also review articles.” (Boersch, 1956) “In January 1945 he also completed his postdoctoral thesis at the Technical University in Berlin with fundamental examinations of the “energy data and limits of electron microscopy”; these have since formed the basis for many studies in this field.” (N. N., 1956) “When the continued existence of the electron microscopy department . . . was repeatedly called into question during the war years, he successfully fought with great determination for the preservation of this workplace.” (Ruska, 1957). “When the post-war years interrupted experimental research, von Borries wrote . .. ‘Super microscopy: introduction, examination of its limits and outline of its results’.’’ (N. N., 1956)

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“His initiative succeeded in 1948 when the North Rhine-Westphalian Society for Super Microscopy was founded.. . . In addition to application work,. . . research and development also took place, for example on magneto-static electron microscopy.. . and ultra microtomy.. .. This has substantially added to the scope of items to be studied.” (N. N., 1956)

“It is a remarkable tribute to his vision and ability that he finally successfully formed and financed, almost entirely by his own efforts, the RheinischWestfalisches Instirut f u r Uberrnikroskopie in Diisseldorf.” (Cosslett, 1957) “His sphere of study and activity extended from inventive and design work to basic physical research and preparation technology . .. in extremely close cooperation with users.. . .” (Boersch, 1956) “He occupied himself with the applications as well as the design and operation of the instrument.” (Cosslett, 1957) “He made every . . . effort to introduce more and more circles to the application of electron microscopy in medicine, chemistry and metal research.”(N. N., 1956)

“. . . The idea of bringing electron microscopists together in order to facilitate the exchange of experiences led him to found the German Society for Electron Microscopy in 1949.” (Boersch, 1956) “The German Society for Electron Microscopy was established on his initiative in 1949.. . . In 1954 he was elected Chairman of the International Federation of Electron Microscope Societies, which he helped found.” (Mahl, 1957) “He . . . has worked hard to set up an effective international organisation for electron microscopy, and to ensure that his own country played a full part in it.” (Cosslett, 1957) “In Bod0 von Borries, the world has lost one of the most prominent representatives of electron microscopy . . . whose seemingly tireless, extremely tenacious capacity for work and study made a major contribution to electron microscopy’s regaining world importance so soon after Germany’s collapse.” (Mahl, 1957) “Over seventy publications originated from von Borries’ hand; in the years 1948 to 1956, the Institute had 145 papers published.” (N. N., 1956) “He applied himself. . . to basic problems of furthering research . . . far beyond his own field.” (N. N., 1956) “During the last years of his life, his vitality . . . seemed to reach new levels.. . . Despite an extremely heavy professional workload, he always found time for conversations . . . that never failed to benefit the participants.” (Boersch, 1956) “In 1953 .. . he was appointed a full professor at Aachen Technical University and was thus able-if only for a few years-to pass on his rich experience to the

B O D 0 VON BORRIES: PIONEER OF ELECTRON MICROSCOPY

175

upcoming generation as an enthusiastic and charismatic teacher.. . . He took a sincere, human interest in his students and colleagues.. .and offered help in word and deed.” (Ruska, 1957) “His ability to kindle enthusiasm . . . his unerring eye for research and development directions with great future potential formed the basis of the achievements of this unique personality, which was also characterized by so much human warmth.” (N. N., 1956) “His death has deeply shocked all those who knew him.. . . also in the contradiction between his irrepressible vitality and his sudden end.” (Boersch, 1956) “For more than 25 years von Borries worked passionately and tirelessly to further electron microscopy from its very beginnings. His harmonious family life provided a buffer for his constant mental effort.. . . We, his friends and colleagues, are deeply saddened by the sudden and premature departure of electron microscopy’s most active champion. We shall always remember the man and his life’s work.” (Ruska, 1957) “What his mind and his commitment have created is durable and will grow.. . . He was allowed to complete a life’s work that will only benefit and profit mankind.” (Grunewald, 1956) “His students will be obliged to take up his legacy and to conduct research into everything that can be researched for the good of mankind.” (N. N., 1956)

REFERENCES Boersch, H. (1956).Phys. Elafter 12,459. Cosslett, V. C. (1957).In Proceedings of the Stockholm Conference, p. 5 . Grunewald. H. (1956). VDI-Nachrichten 16,7. Knoll, M. (1935).Z. f .urztl. Forth. 32, pp. 644-647, 678-680. Knoll, M., and Ruska, E. (1931).Z. t e c h Phq’sik 12, p. 389-400.448. Mahl, H. (1957).Optik 14, p. 46. Matthias. A,, von Borries, B., and Ruska, E. (1933).Z. Phys. 85,336. Ruska, E. (1934).Z. Phys. 87,580. Ruska, E. (1957).In “Proceedings of the Stockholm Conference,” p. 3. Ruska, E. (1979). A c f a historica Leopoldina 12, Anhang D. Von Borries, B. (1935). Vortrage aus dem Haus der Technik Essen, 1 (Haus der Technik, D4300 Essen). Von Borries, B. (1948). Optik 3, pp. 321-377, 389-412. Von Borries, B. (1949).“Die Ubermikroskopie. Einfiihrung, Untersuchung ihrer Grenzen und Ubersicht iiber ihre Ergebnisse.” Werner Sanger, Berlin. Von Borries, B. (1952).Z. wiss. Mikroskopie 60, 329. Von Borries, B. (1954). In “Proc. Internat. Conf. on Electron Microscopy London,” p. 4. Von Borries, B. (1956).In “Rationalisierungskur. d. dt. Wirtschaft,” Auslandsdienst 44,HansenVerlag, Miinchen.

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Von Borries, B. (1957). Z. V D f 99,427. Von Borries, B., and Knoll, M. (1934). Phys. Z.35,279. Von Borries, B., and Ruska, E. (1932). Z. Phys. 76,649, and Archio f.Elektotechnik 27, 1933,227. Von Borries, B., and Ruska, E. (1932a). German Patent 680284, patented beginning March 17, 1932. Von Borries, B., and Ruska, E. (1932b). German Patent 679857, patented beginning March 17, 1932. Von Borries, B., and Ruska, E. (1933). Z. Phys. 83, 187. Von Borries, B., and Ruska, E. (1944a). VDI-Z. 88,686. Von Borries, B., and Ruska, E. (1944b). Phys. Z. 45,314, or Frequenz 2 (1948), 267. (1941). “Das Ubermikroskop als Forschungsmittel.” Walter de Gruyter & Co., Berlin. (1956). Arbeitsgemeinschaft fur Forschung des Landes Nordrhein Westfalen, Mitteilungsblatt, 8, p. 3., N. N., Druckhaus Deutz.

ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS,VOL. 81

Design Principles of an Optimized Focused Ion Beam System Y. L. WANG* A T&T Bell Laboratories, Murray Hill, New Jersey

and

ZHIFENG SHAO Department of Physiology, University of Virginia Charlottesidle. Virginia

I. Introduction

. . .

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11. Beam Profile and Beam Radius . . . . . . . . . . .

A. Spherical Aberration and Defocus . . . . . . . . . B. Chromatic Aberration . . . . . . . . . . . . . C. Spherical and Chromatic Aberrations and Defocus . . . D. Effect of Finite Source Size . . . . . . . . . . . E. Summary . . . . . . . . . . . . . . . . . 111. Optimization . . . . . . . . . . . . . . . . . A. General Considerations . . . . . . . . . . . . B. Optimization . . . . . . . . . . . . . . . . C. Special Cases: Further Simplification . . . . . . . . D. Summary . . . . . . . . . . . . . . . . . IV. Examples of Typical Ion Optical Systems . . . . . . . A. Case Study: UC-HRL FIB System. . . . . . . . . B. Sub-Micron Ultra-Low Energy Focused Ion Beam . . . C. High Voltage High Current Column with Both Aberrations V. Conclusion . . , . . . . , . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . References . . . . . . . . . . . . . . .

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182 188 190 . 192 . 193 . 194 . 195 . 197 ,201 .202 . 202 ,202 ,204 . 206 . 207 . 208 . 208

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I. INTRODUCTION

During the last decade, focused ion beam (FIB) has emerged as one of the most important tools for the fabrication and analysis of submicron structures. Researchers around the world have begun to take advantage of the small size and the large momentum of such an energetic beam for lithography [Seliger et al., 19791, direct milling [Harriot et al., 19861, deposition [Shedd et al., 1986; 177

* Current affiliation: Institute of Atomic and Molecular Sciences, Taipei, Taiwan

Copyright 01991 by Academic Press, Inc All nghts of reproduction in any form reserved ISBN 0-12-014681-9

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Y. L. WANG A N D ZHIFENG SHAO

Harriot and Vasile, 19881, implantation [Gamo et al., 1984; Ochiai et al., 19861, ion induced etching, and high spatial resolution secondary ion mass spectrometry [Levi-Setti et al., 1984; Liebel, 1983, 19851. Each of these applications requires certain beam energy, size, and current. Usually, the primary optical column of an FIB system, which focuses ions emitted from a source onto a target surface, is designed to meet these requirements. However, in many cases, these requirements cannot be satisfied simultaneously, and compromises are therefore inevitable. In this article, we will systematically discuss a set of guidelines for the design of an optimized optical column that provides the best and simplest practical approach, under the constraints of the present engineering limitations, to the desired specifications. Readers are assumed to be familiar with the basic nomenclatures of charged particle optics and have an access to some computer ray tracing programs, such as the one developed by Munro and his associates [Munro, 1973; Smith and Munro, 19871. A generic FIB system [Fig. 11 consists of an ion source, a condenser lens, a beam acceptance angle defining aperture, an optional ion species selector, a group of scanning octupoles and axial astigmatism corrector, and an objective lens, which is sometimes absent depending on the desired performance. Ions originating from the source are accelerated to the required energy and focused onto the target. Since the De Broglie wavelength (A = 0.29 (A)/

mlm

I/'

=Ill= (ccis

-

BEAM DEFINING APERTURE ION SPECIES SELECTOR OCTOPOLE DEFLECTOR AND ASTIGMATISM CORRECTOR OBJECTIVE LENS

c5i)

SAMPLE STAGE (S,,Vi,

J)

FIG. 1 . Illustration of a typical Focused Ion Beam (FIB) system. The crossover between the two lenses is not essential.

OPTIMIZED FOCUSED ION BEAM SYSTEM

179

J(E(eV)/m(amu)}) of an ion is very short (for a 50 k V proton, 2 = 0.001 A), diffraction effect is negligible. The factors affecting the beam spot size are the spatial and energy distributions of the source and the aberrations of the optical column. Therefore, better sources and columns are the two major thrust areas for FIB technology research. The latter is the subject of this article. Minimizing the aberrations of an electrostatic lens, and therefore the size of the beam it produces, has been a subject of both theoretical and experimental interests for a long time [Orloff and Swanson, 1979a; Szilagyi, 1983, 1985, 1986; Szilagyi and Szep, 1988; Wu and Shao, 19903. The most recent theoretical and computational progress has provided an algorithm for design of a complex lens that minimizes certain aberration coefficients of concern. Though there is still some unsettled issues [Glatzel and Lenz, 1988; Scheinfein and Galantai, 19861 about the proposed optimization algorithm and its results, these systematic efforts have begun to shed some light on the complex problem of designing an “optimized” lens. It appears to be possible to design an electrostatic lens with performance comparable to that of a magnetic lens. (It should be noted that for high voltage electron beams, electrostatic optical systems are genetically inferior to magnetic optical systems for the lack of strong lenses due to electrical breakdowns. But for ion optical systems, there is no strong lens that can be constructed in a practical way in either magnetic or electrostatic optical systems, except in a retarding electrostatic field.) However, because of its complexity and marginal improvement over the conventional design in some cases, no such optimized lens has been constructed to date. To our knowledge, all the existing FIB systems use an electrostatic lens with less than four electrodes of simple geometric shape to simplify the construction and alignment. Therefore, reducing the number of lens elements and simplifying the shape of the lens electrodes are the most important steps to be taken before these optimized multielectrode lenses become serious contenders. It will not only reduce the engineering effort and cost, but also simplify the operation of a system based on this kind of lens. While we are waiting for the design of a single optimized lens to reach maturity and its construction to become practical, it is beneficial to study how to optimize an optical column that consists of a few conventional, simple lenses and to push its performance to the extreme. It is apparent that these two approaches of optimization are complementary and will proceed in parallel. Eventually, one would like to have a completely optimized optical column with individually optimized condenser and objective lenses to achieve the best performance and flexibility. In order to make this article self-contained, and the meaning of the “system optimization” well-defined, we shall start with a discussion of the radius of a beam based on its profile and then proceed to the problem of system

180

Y. L. WANG AND ZHIFENG SHAO

optimization after briefly examining the relevance of such an optimization. Several examples will be presented to highlight the application of this optimization scheme to the design of FIB systems.

11. BEAMPROFILE AND BEAMRADIUS

In the long history of charged particle optics, several definitions for the characteristic beam size were proposed. However, none of them is overwhelmingly accepted by the community. The reason can be traced back to the ambiguity in the beam profile both theoretically and experimentally. Without such a precise mathematical description, one can only expect a “sloppy” definition of beam size. The beam profile is determined by the spatial and energy distributions of the ion source and by the spherical and chromatic aberrations of the optical column. Each of these undesirable defects degrades the profile from a delta distribution to an extended distribution of certain characteristic size. Unlike in electron optics, where the discussion should be based on wave optics [Crewe, 1987; Shao and Crewe, 1987, 19881, a discussion based on ray (geometric) optics here is adequate, for the wave length of an ion is exceedingly short. As normally defined, the minimum beam radius due to spherical aberration at the defocus Az = 3Csu2/4 inside the Gaussian image plane is 1 rs = - Csu3, 4

and the minimum beam radius due to chromatic aberration at the Gaussian image plane is 1 AV r =-C2 v, OLY where u is the semi-angle of convergence, Q AV is the mean energy spread of the ion beam and QV, is the nominal ion energy (Q is the total charge). The common practice in calculating the overall beam size is simply adding these individual sizes quadratically: rt2 = (Mr,)’ + r t + r:. (3) where M r , is the apparent source size at the image plane. Because the minimums of these contributing factors do not all occur at the Gaussian image plane, this common practice can only be taken as an intuitive approximation. The extent of its validity will be discussed as follows.

OPTIMIZED FOCUSED ION BEAM SYSTEM

181

It has been proposed that the root-mean-square [RMS] [Hart, 19731 radius be used to describe the characteristic size of a beam profile. For a symmetric distribution J ( r ) with total current I , , it is defined as

which is the square root of the second moment of the distribution. We will show in the following that the validity of the quadratic sum method can be applied most adequately for adding the RMS radii of the two profiles. An alternative is the fractional-current (FC) radius of a beam, which is defined as r ( p ) [Slowko, 19811:

It represents the radius ( r )of a disk containing 0 fraction of the total current. We now have two mathematical formulae to characterize the size of a beam. It is natural to ask if the conventional quadratic method can be used in both cases. Suppose that the beam profile is a convolution of two normalized distributions in n-dimensions, i.e.,

and both J , and Jb satisfy

Also suppose that one of the constituent profiles is totally symmetric, i.e., ,... - x , ,... x,) = J o o r b ( x l ,..x,,. . . .xn) for any m, the second moment of the combined profile, which is defined as

Aorb(X1

(X2)o*b

=

P

X2dXl"'dXn

#

Jb(y)J,(x - y ) d y , " ' d y , ,

(8)

has a quadratic form with each constituent profile. Proof by substituting z = x - y and changing the order of integration, Eq. 8 can be rewritten as (X2)olb =

$

Jb(y)dy,"'dynf ( y 2

+ 2 y . Z + z2)J,(z)dzl"'dz,.

(9)

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Y. L. WANG AND ZHIFENG SHAO

Because Ja(z) is a symmetric function of z , the integration of all the terms involving ( y z)Ja(z)is zero, and Eq. 9 is equivalent to

-

r

The RMS radius of a beam profile can then be readily calculated from that of its constituent profiles. Unfortunately, the profile of a beam with spherical and chromatic aberrations is not a convolution of the two constituent profiles, because of the interdependence of the two aberrations. Therefore, the above theorem is not directly applicable in this case, and both individual and combined profiles must be obtained in order to verify the validity of the quadratic sum method. There is no general method for calculating the FC radius from the corresponding radii of the constituent profiles either. Therefore, in the following discussion, we will derive the profile as well as the FC and RMS radii of a beam produced by an optical system with single and multiple aberrations. We then show how to calculate the FC and RMS radii of a beam by adding the corresponding radii of all the contributing profiles adequately. A. Spherical Aberration and Defocus

Figure 2 shows an idealized optical system that focuses the ions emitted from a source into a point of interest on the optical axis. A beam defining aperture, which serves to define a geometrical angle of convergence (a) of the beam at the image plane, has an equivalent aperture in the principle plane of the system. What we are concerned with is the profile of the beam in an

EOUIVALENT APERTURE

-I

PRINCIPAL PLANE IN THE

~,

OBSERVATION PLANE I GAUSSIAN I IMAGE ,, PLANE

OPTICAL AXIS

FIG.2. Illustration of an optical system that produces an ion microprobe in some observation plane. The aperture radius is A.

OPTIMIZED FOCUSED ION BEAM SYSTEM

183

observation plane at a distance Az inside the Gaussian image plane. According to the third order approximation of the ray equation, the radial position of a ray in the observation plane is related to that in the principal plane as

where R is the ray coordinate in the principal plane and r is the ray coordinate in the observation plane (or to say, the specimen surface). To simplify the notations, we use f = 1, y = r(Cs)'12,and x = R(Cs)'12 and rewrite Eq. 11 as = lbZx- 21,

(12)

where y and x are the reduced radial positions of a ray in the principal and the observation planes respectively. If we assume, to a good approximation, that the aperture plane is uniformly illuminated, in principle, the beam profile can be derived from Eq. 11 by solving the cubic equation directly. However, a more elegant method is to calculate the fractional current contained in a disk of radius r (i.e., P(r) in Eq. 5 ) and then use the result to derive the beam profile as

In general, Eq. 12 maps the aperture plane onto the observation plane with various overlapping. Thus it is necessary to discuss the probe profile separately in different regions. For xA( = A(Cs)'/2)in each of the four regions shown on the x-axis in Fig. 3, y can be in any of the three possible areas as

Y

FIG.3. The radial position (defined in Eq. 12) of a ray in the observation plane as the function of its position in the principal plane of the optical system.

184

Y. L. WANG AND ZHIFENG SHAO

c

shown on the y-axis (we define a dimensionless quantity = A.z/(Csa2) to represent defocus). In the following discussion, we will derive the FC radius in the four regions divided by x = 0, ( A . z / ~ ) ' / ~(A.z)'/~, , 2(A.z/3)'/', 00. Even though the results appear to be quite complicated, the underlying principles are straightforward.

c

1. For X, 2 2 ( A ~ / 3 ) ' /(or ~ I(3/4)). In this case, y can he in any of the areas partitioned by y = 0 , 2 ( A ~ / 3 ) ~yA, ' ~ ,M, where yA = x i - AzxA. a. For 0 I y 5 2 ( A ~ / 3 ) ~the / ~ ,fractional current contained in a disk of radius y is

2,( { 1 ' * d x BAY) =

+ j X T X d X+ j ; x d x ) ,Xi

Since xl, x2 and x3 are the roots of Eq. 12, they must satisfy x,

+ x2 - x3 = 0 -

~ 1 x 2 ~2x3 -~ 3 x= 1

x: - AZX,

+y =0

-Az.

By substituting Eq. 15 into Eq. 14 to eliminate xl, x2 and x3, we can express Y as

y=hx;J+. 2 In terms of more conventional notations, Eq. 16 can be rewritten as

By substituting y I 2 ( A ~ / 3 ) into ~ / ~ Eq. 17, we can show that i2 3ps/4. In other words, Eq. 17 only describes the fractional-current radius of the beam at a defocus satisfying 3 &/4 I iI 3/4. b. For 2 ( A . ~ ( 3 ) ~5" y 5 yA,we have

185

OPTIMIZED FOCUSED ION BEAM SYSTEM

Since y

= x i - Azx3, Eq.

18 is equivalent to

C,a3 r =(A

-$)a.

Similarly, it can be shown that Eq. 19 is valid for [ I38,/4 I3 For y 2 y,, all ions passing the aperture are included. Therefore 8, = 1.

c.

In the following, we will only present the results for x, in the other regions, because the derivations are similar to that shown above. 2. For (Az)”’ Ix, I2(Az/3j1/’(or 3/4 I[ I1j. Now, ycan be in any of the areas partitioned by y = 0, y,, 2 ( A ~ / 3 ) ~ a. ”, a. For 0 I y Iy,, it is easy to show that Eq. 17 is valid for 3/4 I1 I (8%- 28, + 4)/4 I1. b. For y, Iy I 2 ( A ~ / 3 ) ~Eq. ” , 14 yields

with x3 = x,. Therefore, r

- 21 -

3(1 - 8,)

c,cr’-

+ J(2[)’

- 3(1 - 8,)’

6 41

+ 3(1 - 8,) + J(2C)’

- 3(1 - 8,)’

6

(21)

Again, it can be shown that Eq. 21 is only valid for 3/4 I (8: - 28, 4)/4 s 1 I1. c. For y 2 2 ( A ~ / 3 ) ~we / ’ , have 8, = 1.

+

3. For (Az/3)’/* IX, I(Az)”’ (or 1 I [ I 3). We have

+ +

a. for 0 Iy Iy,, Eq. 18 is valid for 1 I1 8, I [ I 3; b. for y, Iy I2 ( A ~ / 3 ) ~Eq. ” , 21 is valid for 1 I[ I1 8, c. for y 2 2 ( A ~ / 3 ) ~8, ” , = 1.

+ +

I3;

4. For x, I(Az/3)’/’ (or ‘4 2 3). We now have a. for 0 Iy I y,, Eq. 18 is valid for 2 3; b. for y, Iy I2 ( A ~ / 3 ) ~ 8, / ’ ,= 1; c. for y 2 2 ( A ~ / 3 ) ~ 8, / ’ ,= 1. (For x, in region (4), i.e., Az 2 3C,a2, in Eq. 1 1 is no longer a good approximation; therefore, the result listed in (4.a.) should be treated with reservation.)

186

Y. L. WANG AND ZHIFENG SHAO 1 .O

.

cn

2

9

0.4

LL

0.2 0 0

0.5

4.0

1.5

2.0

D E F O C U S / ( C ~ Q) ~

FIG.4. The radius of a disk containing (a) loo%,(b) 75%, (c) SO%, and (d) 25% of the total current as a function of defocus in an optical system with only spherical aberration. The dotted curve represents the RMS radii of the beam, which has a minimum at [ = rather than 3 (the least confusion plane).

+

Figure 4 summarizes the above results in terms of r vs. Az for PS = 1, $, and 4 (iso-fractional-current contour of the beam profile). Curve (a) (P, = 1) is equivalent to the envelope of all the rays, which, as expected, has a minimum radius r = C,a3/4 in the plane Az = (3/4)C,aZ,the so-called least confusion plane (note: in our notation, positive defocus means inside the focal plane). The p r o k of the beam in this least confusion plane is of practical interest, which can be derived from Eqs. 13 and 17 as

where r = r,P,(3 - 2/3,)'12. To our knowledge, this is the first time the current density distribution of a spherical aberration limited probe is derived analytically for arbitrary C, and a. As shown by curve (a) in Fig. 5, this current density distribution has two singularities at r = 0 (P, = 0) and r = r,(Ps = 1). The former occurs because of the l/r factor that appears in Eq. 13; the latter occurs because Eq. 12 has a local maximum at x = (Az/3)'I2. These singularities are the direct consequence of the assumed point source and the third order approximation of the ray equation. In a real system, they will become finite (due to the convolution with the finite source size, as explained later) but local maxima should exist at these locations. It should be interesting if the existence of this singularity can be verified experimentally.

187

1

I

I

I

I

)

I

-

; ;10c .-

E

2

-

-

8-

0

0.2

0.4

0.6

0.8

4.0

RA D1 US /rs

FIG.5. The current density distribution of a beam produced by a system with only (a) spherical and (b) chromatic aberration. The singularities are the result of the assumption that the ion source is an ideal point. When the finite size of an ion source is included, these singularities will disappear, but the local maxima should still exist (see text).

The second moment of the beam profile can be written as

Using the notations defined in Eq. 12, we can rewrite the above equation as

Since the aperture is assumed to be uniformly illuminated, it is much easier to perform the integration on the aperture plane, i.e., to use variable x rather than y . However, y is not a one-to-one function of x (Eq. 12); different functional dependence must be used for the variable transformation when different amount of defocus is present. For example, consider the case where (Az)l12 Ix, 5 2(Az/3)'I2. We have J,(Y)Y dY

= 1x1dxi

I + 1x2 dx21 + 1x3 dx31,

(25)

Y. L. WANG AND ZHIFENG SHAO

188

and Eq. 24 is transformed into

s{

(AZ/ 3) '1'

(Azx, - x:)2x,dxl -

(Azx, - x;)'x,

dx,

(Az)'j2

+

{

2

XA

(Azx, - x : ) ~ xd~x 3 } = C,2a2 sOxA(Azx- x3)%dx}.

(Az)'12

(26) It can be shown that the simple result in Eq. 26 is valid for x, in all four regions as discussed before. This is why we prefer to evaluate the RMS radius on the aperture plane, even though the same result can be obtained by using the direct current distribution on the image plane. In terms of real quantities R and A , the second moment of the profile is

2n

loA

(AzR - CSR3),Rd R

s=

lTA2

for any given defocus C. The dotted line in Fig. 4 shows the RMS radii of a spherical aberration limited probe. It is 2r, in the Gaussian image plane = 0) and r , / a in the least confusion plane = i), and it has a minimum of 2r,/3 at = 4. Clearly, the least confusion plane does not provide the minimum RMS probe. The above results can be summarized by defining a generalized radius for the spherical-aberration disk

(c

c

rgs

=V s ,

(r

(28)

where q is a dimensionless quantity that reflects the type of radius under consideration. For example, q = (27/32)'12 when rgsis the 75% FC radius in the least confusion plane; q = 4 when rgsis the least RMS radius. B. Chromatic Aberration

It is well known that different energy ions will be focused at different planes in an optical system. In particular, the radial positions of an ion in the aperture plane ( R ) and in the Gaussian image plane (r) of an optical system are related by the following equation to the first order approximation:

OPTIMIZED FOCUSED ION BEAM SYSTEM

189

where C , is the chromatic aberration coefficient, f is the focal length, Vo is the mean landing energy of all ions emitted from the source, and V is the energy of those ions under consideration. If we assume that ions of one energy illuminate the virtual aperture uniformly, the relative intensity distribution of these ions in the image plane is

where I , is a normalization constant, f = 1 and V’ = ( V - V,)/V,. If we further assume that the energy distribution of the ion source is a Gaussian with a spread of AV, the current density distribution on the image plane can be written as

By substituting Eq. 30 into Eq. 31 and changing the integration variable from V’ to u = 2V0V’/AV, the current distribution can be rewritten in the following form

where rc is the conventional radius of the chromatic aberration disk (Eq. 2). This current density distribution is shown in Fig. 4. It has an expected singularity at r = 0. The fraction of the total current contained in a disk of radius r can be derived from Eq. 32 as

In terms of the reduced radius y tained as

= r / r c , the

result of the integration is ob-

where erf(y) is the error function. For r = rc (or y = l), p, = 0.94. In other words, the conventional chromatic aberration disk contains 94% of the total current if the ion source has a Gaussian energy distribution. It is obvious that the FC radius for p, = 1 would be infinite.

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Y. L. WANG AND ZHIFENG SHAO

The second moment of J,(r) is ( r 2 ) , = rE Jrn ! l r t 3dr' J;;o = -1

:{

1

-;-2exp(-u2) du

2

(35)

4rc.

Therefore, the RMS radius of a chromatic aberration limited probe is (+)re. Similarly, we can define a generalized radius of chromatic aberration disk as rgc

= KIC,

(36)

where K is, again, a dimensionless quantity that reflects the type of radius under consideration. For example, K = 1 when rgcis the 94%FC radius; K = 4 when it is the RMS radius. C. Spherical and Chromatic Aberrations and Defocus

We now consider the case where both spherical and chromatic aberrations are present. For a ray leaving the principal plane at a radial position R, it

FIG.6. A subspace (shaded area) of the u-u (energy-radius)space is mapped by Eq. 38 into a disk of radius r on the observationplane. For each different value of r, a similar map can be drawn. The functions v + ( u ) are defined in the text.

191

OPTIMIZED FOCUSED ION BEAM SYSTEM

intercepts the plane of observation at a radial position [Zworykin et al., 19451

=

I(/

v - v,

AZ

+ c c - ) RVO

(37)

- Cs$l.

By substituting Az = (Csaz, rs = (a)Csa3,f = 1, R = au, and (V - V,) = u(AV/2)into the preceding equation, we can rewrite Eq. 37 as

As shown by the shaded area in Fig. 6, a subspace of the o - u plane is mapped by Eq. 38 into a disk of radius r on the observation plane. The boundaries of this subspace are defined by u* = (4rs/rc)(u2- [) f (r/rcu). If we assume that the ion source has a Gaussian energy distribution, the fraction of the total current contained in a disk of radius r can be written as 3

L

Psc(r)= J;t

ri

rv+

udu J

exp( - u z ) du.

(39)

v-

By performing an integration by part with respect to u, the double integral can be transformed into a summation of integrals that are easier to handle numerically. The result is exp(-u2)du

- ysC

lo1

1

u3[exp( - 0:) - exp( - u!)] du ,

where ysc = rc/4rs.Equation 40 enables us to calculate the FC radius of the beam, provided that the defocus ((), the ratio of the chromatic and the spherical aberrations ( y s c ) are given. The same technique used to derive Eq. 27, the second moment of a spherical aberration limited beam profile, can also be used to obtain the second moment of the beam profile here. We have

192

Y. L. WANG AND ZHIFENG SHAO

where Eq. 38 has been used. u and v are defined as before. Because the integration of the terms that are odd with respect to v vanishes, Eq. 41 can be readily integrated to give

= (r2>,

+ (r2>,,

(42)

which is exactly the quadratic sum of the second moments of the constituent profiles. Note that the validity of this quadratic sum depends only on the symmetric property of the energy distribution rather than its actual functional form. Furthermore, (r2),, has a minimum at a defocus of c = 5 where the minimum of (r2), also occurs, irrespective of the existence of the chromatic aberration. Therefore, the RMS radius of a beam with both spherical and chromatic aberrations is ((2r,/3)2+ (rc/2)2)1/2, which is significantly different from the usual beam size of (rf + r;)’I2. Even though it is straightforward to derive Js,(r) from Eq. 40 we will not show the lengthy result. Instead, we derive the FC radius of the beam from Eq. 40 for any given P,, and verify if this radius is comparable to the radius derived from the quadratic sum of the corresponding FC radii of its constituent profiles. Specifically, we like to compare r( /$,) with rr;,(P,

= Psc)

+ ric(Pc =

Psc)1”2,

(43)

which can be derived from Eqs. 17 and 34. Since the discrepancy between these two radii is expected to be largest when the sizes of spherical and chromatic aberrations are comparable, we choose to evaluate it for rs = r,. Also, in order to calculate the discrepancy numerically, C is chosen to be 3, where the RMS radius of the beam reaches its minimum. As shown in Fig. 7, for any fractional current, the results derived from the quadratic sum (curve b) do not deviate more than 20%from the exact values derived from Eq. 40 (curve a).This result explains why the common practice has been giving reasonable estimates of the beam spot size. D . Effect of Finite Source Size

Because the source profile is independent of the aberrations of an optical system, the profile of a beam produced from a source of finite size is a convolution of the source profile and the profiles of the aberrations. Mathematically, we have

4(r) = j p ( Y V S & -m

-Y

) O l dY2,

(44)

OPTIMIZED FOCUSED ION BEAM SYSTEM

193

0

0

04

0 8

1.2

RADIUS/-

FIG. 7. (a) The fractional-current radii of a beam produced by an optical system with both spherical and chromatic aberration (with ysc = 1 and ( = 5). (b) The square root of the quadratic sum of the corresponding fractional-current radii of the spherical-aberration disk and that of the chromatic-aberration disk. As shown, the maximum deviation between the two approaches is less than 209d.

where J , ( y ) is the source profile and J&) can be derived from Eq. 40. In principle, the profile J,(r)can be calculated if J,( y ) is known. Unfortunately, the profiles of most ion sources are not known, which makes it impossible to discuss the FC radii of the ion source in detail. However, by the experience we gained from calculating the error involved in the radius derived from the quadratic sum of the FC radii (Fig. 6), we expect that Eq. 43 can be generalized to include the contribution of the source with comparable error, i.e.,

= Cr:AP, = P ) + r f ( P c = B ) + M 2 r : o ( P o = 8)1’/2?

rgm

(451

where rg,(flo = p) is the radius of a disk containing Po fraction of the total ions emitted from the ion source. As for the RMS radius of the beam, we can readily apply the theorem Eq. 10 and state that the RMS radius of the beam must be

r,.(RMS) = [ r i s ( R M S )+ r % ( R M S ) + M2r:o(RMS)]”2.

(46)

E . Summary

We have analytically derived the current density distribution of an ion beam produced by an optical system with spherical and/or chromatic aberrations. The RMS radius of an ion beam is a good measure not only because it reflects the size and the profile of the beam, but also because it can

194

Y. L. WANG AND ZHIFENG SHAO

be exactly calculated simply by quadratically adding the RMS radii of the constituent profiles that are the results of the individual aberrations. It was also shown that the fractional current (FC)radius can be approximated by the quadratic sum of the corresponding FC radii of all contributing profiles. This approximation is normally adequate for most practical applications. The detailed current distribution of an aberration limited probe provides insight to the design of ion deposition and microfabrication instruments where control over the profile of the desired features is important.

111. OPTIMIZATION After the beam size is clearly defined, we can now proceed to the problem of optimization based on the results of Section 11. So far, the design of an optical column has been mostly empirical [Orloff and Swanson, 1979b; Orloff and Whitney, 1988; Clear and Ahmed, 1981; Kurihara, 1985a; Parker et al., 1985; Tsumagari et al., 1988; Aihara et al., 19891. A designer usually spends long hours in front of a computer terminal trying to come up with a set of boundary conditions (i.e., the shape and potentials of all the lens electrodes), which either gives record-low aberration coefficients or produces a desired ion beam current density and spot size. As expected in an engineering design, these boundary conditions have to abide by the constraints due to the availability and cost of materials needed for the construction. The maximum electric field strength has to be below the specification, and the diameter of the electrode bore has to be big enough for the required field of view, etc. These restrictive yet important realities have to be dealt with before one can produce a practical design. With this in mind, we can then ask ourselves if there is a systematic way to achieve the design goals by using only conventional simple lenses. Although there has been a large quantity of detailed work on individual lens [Orloff and Swanson, 1979a; Saito et al., 1986;Szilagyi and Szep, 19881 or specific system [Orloff, 1987a, 1987b] designs, very little effort has been made to formulate some guideline principles at the system level in general [Shao and Wang, 19901. It is important to have some sense of what would be needed for the objective or the condenser lens for the desired performance, such as minimum current density and maximum beam spot size at a given beam energy and ion source, before actually going into detailed design work on lens electrodes and potential distributions. It is conceivable, in view of the large amount of available data, that one can often look into the database to find the most suitable lens geometry with no or little modification. We will first address the issue of optimization at the system level in an abstract sense and then apply the optimization scheme to specific system designs. The following discussion

OPTIMIZED FOCUSED ION BEAM SYSTEM

195

is not aimed at providing a complete algorithm for the design of an ion optical column; rather it is aimed at providing a platform for the detailed design to proceed and a platform for the discussion of feasibility for achieving desired performance. A . General Considerations

There are two types of design goals. The first is required by a specific application, and the second is created by the desire to improve the FIB technology. As an example of the first case, a system for x-ray mask repair would require a beam size smaller than 0.1 pm and a beam current larger than 100 PA. For the second case, it is a challenge to design a system with a current density much higher than a few Amp/cm2, which is the present limitation of FIB technology. It is well known that the current density must be improved by a factor of a thousand or so, before ion beam lithography can become a practical production tool. In the following, we systematically go through a list of specific design goals and leave the second type to the readers who are interested in taking the challenge. From a practical point of view, beam energy is the first parameter to be determined before an optical system design can start. Because the attainable electric field strength is limited, the physical length and the cost of a column depends strongly on the beam energy. A word of caution is that a lens can only be designed to have good optical properties in limited energy range. Therefore, it is a good practice to have a clear energy range in mind, based on a specifically desired application. According to the type of dominant ion-solid interaction, we can roughly divide the beam energy into four regions of interest: (1) less than a few hundred eV; (2) between a few hundred eV and a few keV; (3) between a few keV and several lo's of keV; and (4) above several lo's of keV. Obviously, each of these corresponds to a category of applications. For the first region, the physics and chemistry of beam-sample interaction is little, or not at all, understood. However, one expects that the damage caused by the ion bombardment to be significantly reduced and the beam induced physical and chemical surface process to be important. This type of extremely low energy FIB is expected to find its application in the areas of direct ion deposition, beam induced deposition, and low damage beam induced etching. For the second region, the ions transfer their energies primarily to the electrons in the solids, and their range is only a few nanometers. A feasible application is focused ion beam scattering for localized surface analysis. For the third region, nuclear stopping is the dominant process, and the sputtering yields for the most projectile-target combinations are maximized. Among the known applications are high spatial resolution ion microscopy, micromachining, and patterning of oxide mask for in situ processing [Wang et al.,

196

Y. L. WANG AND ZHIFENG SHAO

19901.For the fourth region, electron stopping takes over again, and the range of ions can reach several thousand A. The applications are ion implantation and beam induced disordering. Next, the desired probe size and minimum current density at the target surface are usually determined. For clarity, we will always use the probe diameter (rather than probe radius used in Section 11) to represent probe size, which is labeled by 6 with appropriate subscripts. Therefore the formulae derived in the following can be readily applied to a practical problem. The total probe current can be approximately written as

I,

%

(n/4)Jdi,

(47)

where J is the current density at the center of the probe and 6, is the probe diameter. As we can see, depending on definition (see Section 11), the total current could have a somehow different value. If J,(Amp/sr) is the angular emission intensity of an ion source, the required acceptance angle (ao)at the emitter must be the following: a: E (634)(5/5*).

(48)

The semi-angle of convergence ai at the target side and the linear magnification M are related by the Helmoltz-Lagrange equation [Zworykin et al., 19451 ai = ( l / M ) r n ao.

(49)

We will always refer to the target side by subscript i and the source side by o in this article. For the two lens optical system shown in Fig. 1, the total aberration coefficients at the target side can be written as

+ Cc,M2(v/V0)3’2 C, = cSi +C,,M~(~/V~)~’~,

Cc = Cci

(50)

(51)

where C,, and C,, are aberrations of the condenser lens at the source side and CSiand Cciare those of the objective lens at the target side. In particular, if the condenser lens produces a parallel beam output, the magnification has a rather simple form M =C A / f O ) r n , (52) where fi is the focal length of the objective lens at the target side and fo is the focal length of the condenser at the source side. Using the general results presented in Section I1 (Eqs. 45 and 46), we have the probe size at the target side as s; = (MS,,)2 s: 6:

+ + = (MS,,)2 + ( ~ C , / 2 ) ~ a+?(KC, AV/r/r)za2,

(53)

OPTIMIZED FOCUSED ION BEAM SYSTEM

197

where 6,, = 2rgo,6 , = 2rgcand 6, = 2rgs.Substituing Eqs. 50 and 51 into the above equation, we have the rather bulky expression 312 2 V, J 3 6,’ = (M6,,)2 (3’(Csi CS0M4($) V, Jn

+

+

) (- -) &

(54)

For a given ion source operating at an extraction voltage V,, its energy spread QAV, virtual source size 6,, and angular emission intensity Jn are fixed parameters. K and q are constants (their values are chosen according to the type of probe diameter of interest) and the ion beam energy V, at the target is also determined. Only the spherical and chromatic aberration coefficients and the magnification remain to be determined. We like to point out that off-axis aberrations, such as coma and astigmatism, are not included in this expression, because by dynamic scanning, all off-axis third order aberrations can be eliminated simultaneously (Crewe and Parker, 1976) and anisotropic aberrations do not exist in pure electrostatic optical systems [Zworykin et al., 19451. Before we try to find the optimized conditions from Eq. 54, we must first justify its validity and clarify the meaning of the following optimization process. It is well known that M and all aberration coefficients are interrelated, which means that we are not free to choose arbitrary combinations of these parameters. However, since we are seeking predesign guidance to these parameters, we could arbitrarily fix a number of parameters and find the “optimized” value for the remaining parameters under the given constraints. The result would be a set of values that provide the best performance. This procedure of optimization implies that the optimized values may not be accessible to a particular system. This possibility also implies that an overall optimum design might not be found in practice for the chosen optical system. It is from this point of view that a two lens system is easier to design, because it is often the case that the aberrations of the entire system are dominated by one of the lenses. Therefore, we can vary the magnification of the system over some range without significantly changing the total aberrations of the system. It is also from this point of view that the following optimization scheme provides general guidelines for further detailed engineering design.

B. Optimization

Although we can directly use d ( 6 , ’ ) / d M 2= 0 with Eq. 54 to find the optimum value for M that gives the smallest probe size for a fixed set values of CcirC,,, CSiand C,, (which can be shown always exists), it is easier to tackle the

198

Y. L. WANG AND ZHIFENG SHAO

problem from a different perspective. We understand that in practice, the total aberrations are often dominated by either the condenser lens or the objective lens. For the former (it happens in electron optical system for low resolution lithography with a field emission source), Eq. 54 can be simplified as

In this approximation, there is no local optimum. The trivial solution M = 6, = 0 has no practical interest. For the latter, it is often the case that the objectives must provide large enough working distance at a higher ion energy, which leads to much larger aberration coefficients (it is common to have an objective with C , of a few hundred millimeters). Equation 54 can now be simplified to the following form (note: we have omitted the subscript i in the following discussion for simplicity):

(56)

If we define

=c

> 0, a = (~2/44)~,2(J/Jn)3(Vo/2 ~ ) 0, 3

(57)

and b = ( K ~ / ~ ) C , ~ ( J / J ~ ) ( V , / & ) (2A0, V/K)~

(58)

and Eq. 54 can then be written in a very convenient form: M66i = cM8 + bM46i

+ ad:.

(59)

Now minimize 6, with respect to magnification M . We require d(Gi)/dM = 0. Under the assumption that C, and C, depend weakly on M , i.e., dC,/dM << C,/M and dCs/dM << C J M , we can derive the optimum conditions as 6 ; = 4cM4/(3M2 - 2b).

(60)

Since both 8,’ and c are positive, this imposes a restraint on the value of M 2 , namely, M 2 > 2b/3. Equations 59 and 60 are the basic functions that relate the different parameters in the subspace of the optimized conditions. We now substitute Eq. 60 into Eq. 59 to obtain the optimum magnification for the given spherical and chromatic aberration coefficients. We have ( M 2 - 2b)(3M2 - 2b)‘ = 4 3 a ~ 2 M 4 .

(61)

OPTIMIZED FOCUSED ION BEAM SYSTEM

199

Substituting y = 2b/M into the above expression, we now have the following reduced form: (1 - y)(3 - r)2/Y

(62) The left-hand side of the above equation is a universal function of y, a quantity related to the chromatic aberration. In explicit terms, the right-hand side can be written as 43ac2 2b

p=-=-

= P.

S,",q2 (Cs J V o ) 2 2 0, --2~~ C, Jn A V

which represents the relative magnitude of spherical and chromatic aberrations. Since p is positive and finite for all practical systems, we have the following requirement for y: (64)

O
The left-hand side of Eq. 62 is given a name F(y)and is plotted in Fig. 8. Some typical values of this function for corresponding p and y are also presented in Table I. The value of M 2 is then obtained through y, which is derived by matching the specific p value in Table I or on Fig. 8. The value of the optimized probe diameter can then be reached by substituting M 2 into Eq. 60. In general, this optimization procedure can be readily applied to a specific design problem in the following manner. When the ion source and the values of 1, and 6, are chosen, one should first assume a value for the chromatic aberration coefficient. A good starting point is to take C, to be a value that is a

1000

7

0

0.2

0.4

0.6

0.8

4.0

Y

FIG.8. Plot for the universal function F ( y ) for the valid range 0 < y I 1

200

Y. L. WANG AND ZHIFENG SHAO TABLE I

FUNCTION F(y)

1 100 485 360 240

I80 140 100 60 30 15 10 5 3 2

I 0.4 0.2 0.1 0

0.008 0.018 0.024 0.036 0.046 0.058 0.079 0.121 0.206 0.323 0.402 0.546 0.648 0.719 0.825 0.9 16 0.954 0.976 1.OOo

few times larger than the working distance for a nonimmersion objective lens. In fact, the value of C, is always in the same order of magnitude compared with the image distance; thus, it is always longer than the working distance in a nonimmersion lens (this is valid for both magnetic and electrostatic lenses). To check if such a C, is compatible with the desired performance, we have the following criterion. By substituting y = 2 b / M 2 into Eq. 60 and solving for y, we have the following solution:

The one with the negative sign is the proper solution to use, for it satisfies y _< 1. Since the argument under a square root must be positive, we obtain an upper limit for acceptable C, value:

If this condition is not satisfied, there will be no solution possible and one will have to relax the prechosen design parameters. This condition is also consistent with the result of Eq. 60. After a value of y is obtained that only contains C, and M, Fig. 8 or Table I can be used to obtain the correspond-

OPTIMIZED FOCUSED ION BEAM SYSTEM

20 1

ing value of p that gives the required value of C,. In practice, it is often necessary to calculate a number of values for C, and M at different C,. When the acceptable range of these values (for the given performance) is established, Munro or other optics programs can then be used to calculate details for a chosen practical system. If the optimum conditions cannot be satisfied after a reasonable effort, some modification on the original goal must be made. Another round of calculation can then be initiated. C. Special Cases: Further Simplijicution

Although the procedure discussed so far can be applied to most practical designs, it is rather awkward to use the graphical method to obtain the optimum magnification when p is too large or too small. From Eq. 63, one can see that the former corresponds to spherical aberration and the latter to chromatic aberration. Under both circumstances, the optimization can be simplified. Most FIB systems to date are limited by the chromatic aberration because of the rather large energy spread of liquid metal ion sources, Q A V 2 10 eV. In this case, we can simply assume a = 0 in Eq. 59. We have the following solution for M : M 2 = 2b and

M 2 = 2b/3.

(67)

Since 3M2 > 26 (Eq. 60), we must have

Substituting this result into Eq. 60, we have 6; = 4bc. In more explicit terms, it becomes

For any given values of J , 6 , 6, and ion source parameters, it is a simple exercise to find the required values of C, and M. The other limiting case is where the spherical aberration becomes the limiting factor, as in the case of high voltage and large probe current. If we assume b = 0 in Eq. 60, we have 6,” = 4cM2/3. Using this result in Eq. 59, we have M 2 = 3 ~ ( 4 ) ~In c ~conventional . terms, the above expressions can be written as

202

Y. L. WANG AND ZHIFENG SHAO

It is seen that in this case, finding the optimized values of C, and M for a given system is also much simplified. The application of these results will be presented in the next section.

D. Summary

It has been shown that under certain conditions, a local optimum for an ion optical column dominated by the objective lens can indeed be found. For single aberration cases, these optimum conditions are rather simple and straightforward. These results can be used as a basis for selecting the “ultimate” optical elements for the design of a desired FIB system, from either commercial sources or published data. Combined with an optical software package, such as the Munro program or the program developed at Peking University (Ximen et al., 1988, 1990), the design procedure is complete and relatively easy to implement in most research or industrial laboratories.

Iv. EXAMPLES OF TYPICAL ION OPTICAL SYSTEMS In this section, we will devote our attention to the application of the principles derived so far to several practical problems in ion optical systems of importance. It is important to understand that the following examples are chosen mostly based on our personal preference and that not all of the important topics in current ion optical research are included. The main purpose here is to demonstrate how to apply these rules in a practical process. In all the following examples, a liquid metal ion source (LMIS) is always assumed and the parameters are set as the following: Jn = 20 pA/sr, 6,, = 0.05 pm and Q AV = 10 eV. All values of probe diameter are in the sense of RMS, so that IC = $ and q = 3 will be used. A. Case Study: UC-HRL FIB System

The twin scanning ion microscopes (SIM) developed jointly by the University of Chicago and Hughes Research Laboratories in the early eighties [Levi-Setti, 1977, 1984; Levi-Setti and Fox, 1980; Seliger et al., 19791 are still among the best FIB systems in the world. We will apply the optimization

OPTIMIZED FOCUSED ION BEAM SYSTEM

203

procedure to analyze these systems and to try to understand the reason behind their excellent performance. We hope that this case study can demonstrate the benefit of the optimization in reducing the effort involved in searching for the best performance. Because these systems are limited by the chromatic aberration, Eqs. 68 and 69 can be readily used to derive the optimum magnification and probe size. Using the typical operating parameters for the SIM at Chicago, Vo = 8 kV, F = 40 kV and the values given at the beginning of this section, in terms of total probe current, we have the optimum magnification:

and

The major uncertainty in this equation comes from the source size dss. There has not been a serious attempt to measure this quantity. If we simply take the typical estimation of 50 nm, the optimum magnification is 0.19 (Eq. 72) for a 1.6 pA beam with a total chromatic aberration 200 mm, which is calculated from the Munro program. Figure 9 shows a picture of the eye of a fruit fly taken by Professor R. LeviSetti at University of Chicago, using a In' beam with his system operating at

FIG.9. A secondary ion image of the eye of a fruit fly obtained from the Chicago SIM system using an 1.6 pA Int ion beam. The full scale is 5 p n and the smallest resolved feature is about 0.02 pm. Courtesy of Professor R. Levi-Setti.

204

Y. L. WANG AND ZHIFENG SHAO

an optimum condition found by a systematic experimental search. With the same chromatic aberration and probe current used in our calculation, the magnification was found to be 0.2, which is surprisingly close to the theoretical prediction. The RMS probe size calculated from Eq. 73 is 13.4 nm, which is compatible to the size of the smallest resolvable feature (- 20 nm) shown in Fig. 9, given the expected more than 20% uncertainty in the 6,, used in the calculation. Although we do not know the detailed operating parameters used by the researchers at Hughes Research Laboratories for fabricating the 12 nm features on a resist-coated gallium arsenide wafer except the greatly reduced working distance (about 30% of that of the UC-SIM) and = 50 kV, the reported magnification (0.14)is also very close to our calculation (Eqs. 72 and 73, assuming all other parameters are the same as the UC-SIM): M 0.13 and 6, 9 nm. Total chromatic aberration is now reduced to about 120 mm, according to our calculations. (In both cases, less than 30% of the total aberration comes from the gun lens.) The larger probe found in the experiments seems to indicate a larger source size than expected, if we can attribute these differences entirely to the uncertain source size, although other factors such as current density, angular distribution of the source, etc. can also contribute to this deviation. If we used 6,, = 75 nm (rather than 50 nm), we would have 6, = 19.5 nm for the UC-SIM and 6, = 13.5 nm for the Hughes system. Therefore, we consider this optimization procedure well-founded and useful for the design of a new system as well as the improvement of existing systems.

-

-

B. Sub-Micron Ultra-Low Energy Focused Ion Beam

Ion beam direct and induced deposition have become promising techniques in processing semiconductor wafers. However, high resolution capabilities of ion beams have not yet been fully explored. Submicron ion beam deposition may become a useful tool for the correction of VLSI chips. In a dedicated ion beam deposition machine, one often requires a very fine probe at very low energies. This has been proven difficult to achieve because of the rather large energy spread of available ion sources. Thus, designing a better ion optical column has become a difficult but important research project at many institutions and industrial laboratories. For example, we need a system capable of producing a 0.1 pm probe at a landing energy at the target surface in the range of 0.1 kV to 1 kV with a current density between 1-2 Amp/cm2. Using the source parameters given above (assuming V, = 10 kV) and Eqs. 68 and 69, the required chromatic aberration coefficients and magnifications at several typical voltages are calculated. The results are shown in Table 11. The contribution from the

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OPTIMIZED FOCUSED ION BEAM SYSTEM

4

S

k

FIG. 10. Illustration of an einzel lens-retarding field assembly for low energy focused ion beam deposition. See text for actual dimensions.

spherical aberration is negligible. Although the magnification is larger than one in all cases, the objective lens is still the major source of aberration in the system. In addition, we wish to keep at least 10 mm distance between the target surface and the focusing lens to accommodate a microchannel plate for signal collection. This requires a rather long working distance, and therefore a fairly weak lens. To our knowledge, only retarding field optics can be used to produce such small aberrations [Narum and Pease, 1988; Munro et al., 19881. Using a modified Munro program [Shao, 19881, we calculated the performance of the einzel lens retarding field assembly shown in Fig. 10. The results are presented in Table 111. The following parameters are used in the calculation: t = 1 mm, s = 3 mm, D, = 2 mm, D, = 3 mm and L = 15 mm. The potentials on the central electrode (V,) required for adequate focusing are also shown. It is noted that this lens assembly actually produces smaller aberrations than those required in Table 11, which is actually necessary to allow some contributions from the condenser lens to the total aberrations of

TABLE I1 OPTIMUM CONDITIONS AT DIFFERENT ENERGIES FOR LOW ENERGY FIB

0.2 0.1 0.1 0.1

0.I

50

100 500 500 lo00

1 .o 1 .0 1 .o 2.0 2.0

0.13 0.18

2 1.43 4.1

2.8 1.4 1.4 I .4 1.4

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Y. L. WANG AND ZHIFENG SHAO TABLE 111

OPTICALPROPERTIES OF THE EINZELLENSRETARDING FIELDASSEMBLY r/; (volt) 50 100 500 loo0

loo00

S, (mm)

C, (mm)

V , (volt)

2.26 3.22 6.82 9.17 19.7

0.054 0.13 0.82 2.18

24350 24450 24860 21960 22930

25.1

V,

=

Vo (volt)

1 so00 1 so00 1 so00 loo00 loo00

the system. To be practical, the maximum surface field strength at the target was kept below 1 kV/mm, and the maximum field strength between electrodes was kept below 5 kV/mm. With a properly designed condenser lens, such a low voltage FIB system is feasible. With a tentative design of a four element zoom lens, it is possible to design a system at optimum conditions for landing energies from 50 eV to 10 keV with a probe size of 0.2 pm (50 eV) to 0.05 pm (10 keV) at a minimum current density of 1 Amp/cm2 (3 Amp/cm2 at 10 keV). Details of this design will be available in a future publication.

C . High Voltage High Current Column With Both Aberrations We now consider a case where both spherical and chromatic aberrations must be considered. Suppose we need a focused ion probe at 100 kV with a current density of J = 10 Amp/cm2. The desired probe size is no bigger than 0.02 pm. Furthermore, the objective lens must have a minimum working distance of 5 cm. Based on this information, we can assume C, = 35 cm as the starting point. A large chromatic aberration is assumed due to the fact that at high beam voltages, a strong lens is difficult to achieve. From Eq. 65, y would be 0.92 and its corresponding magnification is 0.29. From Eq. 63, the p value is calculated as 0.38,which gives a required value of C, I 1831 cm. It is obvious that even at this beam voltage, the ion probe is still chromatic aberration limited. This value of spherical aberration coefficient appears to be possible to achieve. After these parameters are known, we can verify if they can be satisfied in a practical system by performing detailed calculations on a chosen system. Some modifications may be made, and subsequently a new value of C, must be used. Since M 2 ( v / 1 / 0 ) 3 / 2 2.7, one may question if the objective lens is still the dominant factor. In practice, one should use the system developed by N

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Kurihara (1985b), where the chromatic aberration of the gun lens could be made as small as 10 mm. Therefore, the contribution from the gun lens is only about 27 mm, 10% of the total aberration. It is seen that we must be very careful in assuming this initial value to allow enough room for contributions from the condenser lens or the gun lens. It is always a good practice to use the best possible gun lens whenever possible to ensure that the objective lens is indeed the dominant element in the system. This example also shows that some improvement at higher beam voltages can still be achieved by pushing for better optical design. If on the other hand, both C, and C,are known for an existing system, we can first calculate p and then find the corresponding magnification and the smallest possible probe size by using Eqs. 63 and 60. V. CONCLUSION

We have shown that the concepts of root-mean-square and fractionalcurrent diameter are most adequate for defining the beam size based on the actual current distribution. The conventional method of adding several contributing factors quadratically is valid only when the diameters of each aberration are defined consistently. In most cases, the RMS diameter is preferred because it has a simple geometric meaning and the quadratic sum method is exactly applicable. Based on these general discussions of beam profile and diameter, we have derived a set of guidelines for the design of an optimized ion optical column. We have shown that such an optimization procedure can be applied to the design of several practical systems, as well as the analysis of existing systems. These guidelines provide estimations of the required parameters for achieving the desired performance without going into the details of a specific design. Therefore, this optimization procedure can be considered the preliminary step toward a real system design and should be used only as a guideline for choosing the design parameters. We should point out that the space charge effects are not included in this discussion of optimization. Apparently, this effect may be too important to be overlooked in many cases. This problem has been subjected to extensive studies in the past [Yau et al., 1983;Narum and Pease, 19863.It is obvious that the space charge effect will inevitably degrade the final probe. When this proves to be the case, one should first determine the required aberration coefficients and magnification. After a tentative design is found, the Monte Carlo technique can then be used to estimate the effect [Narum and Pease, 19861. If the performance is seriously affected, the procedure will have to be repeated for further refinement by using different parameters.

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ACKNOWLEDGMENTS The authors wish to thank Professors R. Levi-Setti and A. V. Crewe for their invaluable support in the past many years. Z. Shao wishes to acknowledge financial supports from NIH, Whitaker Foundation for Biomedical Engineering Research and the University of Virginia, and particularly the support from Professor A. P. Somlyo. Y. L. Wang wishes to acknowledge the support of the management of AT&T Bell Laboratories during this work. We are also grateful to Professor P. W. Hawkes for his constant encouragement.

REFERENCES Aihara, R., Sawaragi, H., Thompson, B. and Shearer, N. J. (1989).Nucl. Instrum. Meth. B. 37-38, 212. Clear, J. R. A,, and Ahmed, H. [1981]. J. Vac. Sci. Technol. B6,1035. Crewe, A. V. [1987]. Ultramicroscopy 23, 159. Crewe, A. V. and Parker, N. W. [1976]. Optik 46, 183. Gamo, K., Takakura, N., Samoto, N., Shimizu, R. and Namba, S. [1984]. Jpn. J. Appl. Phys. 23, L293. Glatzel, U.,and Lenz, F. [1988]. Optik 79, 15. Harriott, H. L., and Vasile, M. J. [1988]. J. Vac. Sci. Technol. B6, 1035. Harriott, L. R., Wagner, A. and Fritz, F. [1986]. J . Vac. Sci. Technol. W,181. Hart, K. J. [1973]. J. Vac. Sci. Technol. 10, 1098. Kurihara, K. [1985a]. J. Appl. Phys. (Japan) 24,225. Kurihara, K. [1985b]. J. Vac. Sci. Technol. B3,41. Levi-Setti, R. [1977]. In “Advances in Electronics and Electron Physics.”(Septier, ed.),Suppl. 13A, p. 261. Academic Press, New York. Levi-Setti, R. [1984]. AFOSR/AFSC Final Technical Report, DTIC Document AD-A 149-992. Levi-Setti, R.,and Fox, T. R. [1980]. Nucl. Instrum. Meth. 168, 139. Levi-Setti, R., Wang, Y. L. and Crow, G. [1984]. J . Phys. [Paris] 45, C9-197. Liebel, H. [ 19831. Vacuum 33, 525. Liebel, H. [1985]. “Scanning Electron Microscopy 11” (0.Johari, ed.),p. 519. SEM Inc., AMF OHare, Chicago, Illinois. Munro, E. [ 19731. In “Image Processing and Computer Aided Design in Electron Optics (P. W. Hawkes, ed.), p. 284. Academic Press, London. Munro, E., OrloR, J., Rutherford, R. and Wallmark, J. [l988]. J. Vac. Sci. Technol. 86, 1971. Narum, D. H., and Pease, R. F. [1986]. J. Vac Sci. Technol. B4,154. Narum, D. H., and Pease, R. F. [1988]. J . Vac. Sci. Technol. B6,966. Ochiai, Y., Shihoyama, K., Shiokawa, T., Toyoda, K., Masayama, A,, Gamo, K. and Namba, S. [1986]. J . Vac. Sci. Technol. B4,333. Orloff, J. [1987a]. J . Vac. Sci. Technol. B5, 175. Orloff, J. [1987b]. Microelectronic Eng. 6, 327. Orloff, J., and Swanson, L. W. [1979a]. J . Appl. Phys. 50,2494. Orloff, J., and Swanson, L. W. [1979b]. Scanning Electron Microscopy 1, 39.

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Orloff, J., and Whitney, J. [1988]. Proc. SPIE, Electron-Beam X - R a y , and Ion Beam Technology .for Submicrometer Lithography V I I , 923, 121. Parker, N. W., Robinson, W. P., Levi-Setti, R.. Wang, Y. L. and Crow, G . [1985]. Proc. SPIE., Electron-Beam, X - R a y and Ion-Beam Techniques f o r Submicrometer Lithography I V, 537,117. Saito, K., Okubo, T. and Takamoto, K. [1986]. J . Vac. Sci. Technol. A4,226. Scheinfein, M., and Galantai, A. [1986]. Optik 74, 154. Seliger, R. L., Kubena, R. L., Olney, R. D., Ward, J. W. and Wang V. [1979]. J . Vac. Sci. Technol. 16, 1610. Shao, 2. [1988]. Reti. Sci. Instrum. 59, 1985. Shao, Z., and Crewe, A. V. [1987]. Ultramicroscopy 23, 169. Shao, 2.. and Crewe, A. V. [1988]. Optik 79, 105. Shao, 2.. and Wang, Y. L. [1990]. J. Vac. Sci. Technol. B8,95. Shedd, G . M., Lezec, H., Dubney. A. D. and Melngailis, J. [1986]. Appl. Phys. Lett. 49, 1584. Slowko, W. [1981]. J . Vac. Sci. Techno/. BI, 1137. Smith, M. R., and Munro, E. [1987]. J . Vac. Sci. Techno/. B5, 161. Szilagyi, M. [1983]. J . Vac. Sci. Technol. B1, 1137. Szilagyi, M. [1985]. Proc. I E E E 73,412. Szilagyi, M. [1986]. Appl. Phys. Lett. 44. 7. Szilagyi, M., and Szep, J. [1988]. J. Vac. Sci. Techno/. B6,953. Tsumagari, T., Ohiwa, H. and Noda, T. [1988]. J. Vac. Sci. Technol. B6.949. Wang, Y. L., Harriott, L. R., Hamm, R. A. and Temkin. H. [1990]. Appl. Phys. Lett. 56, 749. Wu, X. D., and Shao, Z. [1990]. Optik 84,66. Ximen, J . [ 19881. Optik 80,2. Ximen, J. [1990]. J. Appl. Phys. 67, 1643. Yau, Y. W., Groves, T. R. and Pease, R. F. [1983]. J. Vac. Sci. Technol. BI, 1141. Zworykin, V. K., Morton, G. A,, Ramberg, E. G., Hillier, J. and Vance, A. W. [1945]. "Electron Optics and Electron Microscope." Wiley, New York.

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOL. 81

Electron Microscopy in Berlin 1928-1945 C. WOLPERS Lubeck Federal Republic of Germany

The city of Berlin was, in the middle of the twenties, a growing metropolis of 4 million inhabitants. It was a thrilling, hectic state at that time; a city without fatigue, a melting pot for all newcomers, with a widespread cultural, intellectual and scientific life, with a flamboyant luxury beside a depressing poverty. In 1928, a student at the “Technische Hochschule” in Berlin, Ernst Ruska, (Fig. l), under the guidance of Max Knoll, assistant at the high tension institute of Professor Matthias, began an investigation of the lens effect of magnetic fields acting on fast electron beams (Ruska and Knoll, 1931).At the same time, Manfred von Ardenne installed in the south of Berlin (von Ardenne, 1972) his private laboratory for electronic techniques. Finally, the university instructor Ernst Briiche (Schimmel, 1985),working in the research institute of the AEG (“Allgemeine Elektrizitatsgesellschaft”) in the north of Berlin, as a coworker of professor Ramsauer (Ramsauer, 1943), commenced electron optical research into the northern lights (Briiche, 1971). The future Nobel prize winner Dennis Gabor from Hungary, predecessor of Max Knoll, had just finished his doctoral thesis on measurements of lightning with the cathode ray oscillograph. Together with his friend Leo Szilard he made plans for the future. The latter urged: “Build an electronmicroscope.” Gabor answered: “That is useless. The electronic beam would burn all objects to ashes. In addition, objects couldn’t stand the vacuum,” an opinion that was widespread among physicists (Sommerfeld and Schemer, 1934) and electron microscopists (Gabor, 1957; Knoll, 1935a; Marton, 1968, 1976) during this time. Beginning, 1929-1932

In the depressing time between 1929 and 1932, the number of unemployed in the humiliated Germany had risen from 2 to 6 million, the rightist “Hamburger Front” and the leftist “Iron Front” were continually engaged in bad bloody fights, seething with hatred, and the worldwide economic crisis led to loss of wages and to deductions from salaries, as well as to price control and 21 1 Copyright 01991 by Academic Press, Inc. All rights of reproduction in any form reserved.

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(a) (b) FIG. 1. (a) Ernst Ruska (1986). Courtesy of Mrs. M. Kischke from the F.H.I. of the Max Planck Gesellschaft, Berlin. (b) Bod0 von Borries (1956). Courtesy of Mrs. H.von Borries, Diisseldorf.

foreign exchange control; despite these conditions Knoll and Ruska finished in the spring of 1931 the construction of the first two-stage transmission electron microscope with magnetic lenses. Their report consisted of 85 printed pages (Knoll and Ruska, 1932a, 1932b).It became the basis for further constructions worldwide. In June of 1931, Knoll reported the concerted result to the experts of Berlin. In that account, the term “electron microscopy” was used with reserve, because with that apparatus only a 17-fold magnification was reached. Five days before this lecture, the chief electrician of the Siemens company, Riidenberg (who was at the same time university teacher of Ernst Ruska, and who had been specially informed by a previous visit of his assistant, Max Steenbeck, to Knoll) applied for a patent “for the magnifying electronic copy of objects”. Although Riidenberg had never built an electron microscope himself, he always defended his worldwide applications for these patents. It was later suggested that Riidenberg was thinking faster and more comprehensively than Knoll and Ruska (Freundlich, 1963; Rudenberg, 1932, 1943; Ruska, 1986), but see also Ruska (1979, 1980, 1984). Independently of this lengthy controversy with Riidenberg, a publication of six pages by Briiche and

ELECTRON MICROSCOPY IN BERLIN 1928-1945

213

Johannsen (1 932) about an emission electron microscope, appeared seven months after the report of Knoll. This microscope provided a magnified image of the emissive surface of the cathode by means of a one-step electric lens. For decades the struggle between electrical and magnetic lenses in the electron microscope remained a stimulus. The Revaluation of All Values

With some help from the bourgeoisie, taking advantage of the weakness of the 85-year-old president, in 1933 Hitler suddenly reached a powerful position, although his unquestioning adherents were only 34%. Two months later, the dictatorial regime had a firm seat and interfered with growing pressure in the habits of life of everybody within the practically closed frontiers. Adaptation, retirement and distrust led us to adopt a pragmatic behaviour. By spring 1932, Knoll had left Ruska, the electron microscope and the university. The friend of Ruska, Bod0 von Borries (Fig. l), also tutored by Knoll, became for one year the successor of Knoll, while Ernst Ruska (Fig. 1, on the right) as a scholarship-holder, started in 1933 on the construction of his second electron microscope (Ruska, 1934a, 1934b, 1979, 1980, 1987). The improved design of the magnetic lenses by Bod0 von Borries and Ernst Ruska was an essential feature. At the end of 1933 the second electron microscope was finished and ready to work. Ruska then accepted a salaried position elsewhere, leaving his newly built apparatus in the Institute. Two students of engineering, H. 0. Muller and E. Driest, used Ruska’s instrument for their diploma thesis to show the chitin wings of a common fly in a excellent manner (Driest and Muller, 1935). After this intermezzo, an assistant of Professor Matthias, Dipl. ing. Czemper, provided his cousin, the 21-year-old medical student Friedrich Krause, with the chance to work with Ruska’s instrument from 1935 to 1938 (temporarily together with Dr. Beischer, assistant at the “Kaiser Wilhelm Institute for Physical Chemistry”). Krause interrupted his university studies. His first aim was to test the performance of Ruska’s instrument by examination of the diatom Pleurosigma angulatum, already studied by light microscopy (Krause, 1936).In spite of the support of a physicist from the Zeisswerke/Jena, Dr. Kohler, the result remained unsatisfactory. The complicated fine structure of this diatom could only be cleared up later (Muller and Pasewaldt, 1942). In 1936 Krause demonstrated to the physicists gathered in Salzbrunn (Krause, 1937a, 1937b) his first pictures of animal cells (from the skin of the epithelium of the salamander), influenced by Marton’s pictures of plant cells (Marton, 19341937).After chromfixation, one saw formations similar to mitochondria in the cytoplasma. The light microscope image of a similar specimen was, however,

214

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more impressive. Together with Beischer, Krause worked on problems of colloidal chemistry (Beischer, 1938; Beischer and Krause, 1937).The improvement of Ruska’s instrument, especially the smoothing of the high voltage, and the broadening of the preparative technique (freezing of the objects, shading off the beam, negative staining, ultrasound microtomy, print-off methods) were the aim of Krause (Krause, 1937a, 1937b, 1939, 1944a, 1944b; Krause and Mahl, 1943). In 1939 Krause continued his university studies, then was obliged to do military service and was wounded in the war, where he went missing as a medical officer in 1945. Stimulated by an idea of Knoll (Knoll, 1935b), in 1937 von Ardenne had devoted his interest to electron microscopy and constructed the first scanning electron microscope (von Ardenne, 1938a, 1938b), he also built the “Keilschnittmikrotom” (wedge-cutting) (von Ardenne, 1938c, 1940),which was not well received in practice. Not until 27 years later was the scanning electron microscope developed into a commercial model (Oatley et al., 1965). In 1934 Bod0 von Borries returned to Berlin, and together with Ernst Ruska he tried energetically to launch the series production of electron microscopes for research laboratories, as well as for applications establishments. After frustrating efforts (1934- 1936),the detailed and positive approval of Richard Siebeck, chief and professor of the first clinic for internal medicine at the university hospital of the Charite in Berlin, the chief of Helmut Ruska and the author, convinced the hitherto hesitant companies Zeiss (Jena) and Siemens (Berlin) to take the risk (Ruska, 1979, 1980). Because of the fact that Riidenberg’s patents belonged to Siemens, and that von Borries was already a cooperator of Siemens, Ernst Ruska himself decided in favour of that company (von Borries, 1949). Helmut Ruska (Fig. 2) was the younger brother of Ernst Ruska and the sixth child of Julius Ruska and Elisabeth Ruska, nee Merx. Julius Ruska was chief of the Department of History of the Natural Sciences, a specialist on alchemy in the Arabic world during the middle ages, at first at the University of Heidelberg, later on at the University of Berlin. Elisabeth Ruska was the daugther of the chief of the institute for Theological Sciences at the University of Heidelberg. During the first world war Elisabeth Ruska was a nurse. The younger sister of Ernst and Helmut Ruska was Hede Ruska. She married Bod0 von Borries. The fact that the development of the transmission electron microscope into a commercial model required only six years is chiefly the merit of Helmut Ruska, with whom the author worked in Berlin from 1936 till 1945. Helmut Ruska was a contemplative, tolerant and modest person with far-reaching interest in medicine, natural sciences and history. During his school time he was already a tutor for ornithology in Heidelberg. After finishing his medical

ELECTRON MICROSCOPY IN BERLIN 1928-1945

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FIG.2. Helmut Ruska. About 1969.

education, he worked as a medical doctor in the Department for Internal Medicine at the University of Heidelberg and as a research fellow at the Kaiser Wilhelm Institute for Medical Research in Heidelberg, at the former working place of Warburg and Meyerhoff. The human relations between Ernst and Helmut Ruska remainded always brotherly and cordial. During the critical time, between 1932 and 1937, as Max Knoll, Ernst Ruska and Bod0 von Borries had abandoned their electronic toy, Helmut Ruska persistently urged his brother in particular, to return to the development of the electron microscope. As a medical doctor he saw every day the necessity to surmount the frontier of the light microscope, predicted by Abbe in 1876 (Ruska, 1980). The fact that the physicist Marton had tried to penetrate biological objects with the electron beam and the medical student Krause had tried to improve technologically the old, second Ruska microscope encouraged Helmut Ruska to move in 1936 from Heidelberg to Berlin, to inspire his former chief Richard

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Siebeck to write a positive approval for the development of a commercial model, which set the ball rolling (Ruska, 1979, 1980). In 1937 the building for the production of Siemens electron microscopes was equipped in BerlinSpandau, Zitadellenweg 23. In 1938 first experimental apparatus was ready for use. In his approval, Siebeck had promised to support the application of the electron microscope by providing a member of his staff. Helmut Ruska started a full-time job, the author a half-time job. At the congress of cell research in 1938in Zurich, Helmut Ruska reported (Ruska, 1939)comprehensively on the first objects studied: bacterial flagellates, bacterial nucleosides (Piekarski and Ruska, 1939a, 1939b), the square form of the myxoma virus in rabbits (von Borries et al., 1938; Ruska et al., 1939),the rod-shaped tobacco mosaic virus (Kausche et al., 1939), the chloroplast structure (Kausche and Ruska, 1940) and the variation of shape in thrombocytes with the structure of fibrin during coagulation (Wolpers and Ruska, 1939). In the laboratory of the AEG, work was concentrated until 1937 mostly on emission electron microscopy and on other questions. In October 1938, Miiller from the Siemens group published his opinion that, because of fundamental causes, the efficiency of a light microscope could not be exceeded by the electron microscope with electric lenses (Miiller, 1938). In 1939 Mahl (Fig. 3) demonstrated the performance of a two-step transmission electron microscope with electric lenses and high resolution and showed that Miiller, despite his prestige, was wrong (Mahl, 1939). The electric lens of this Mahl apparatus was built by Boersch and Mahl together. In 1939 the application of this instrument was demonstrated by pictures of bacteria (Briiche and Haagen, 1939; Jakob and Mahl, 1940).

“On Call” With the outbreak of the war the fundamental demands of the government on individuals were essentially increased. However, as there alternated in this time short periods of attacks with longer periods of regeneration, some people obtained “leave on call” to continue interrupted research. In 1940 Siemens had created an applications laboratory led by Helmut Ruska, with four electron microscopes that were also used by foreigners. In spite of the fact that Berlin in the first three years of the war was bombed 70 times (Girbig, 1977), we were able to study successfully important medical objects such as: bacteriophages (Ruska, 1942),glycogen molecules (Husemann and Ruska, 1940), chloroplasts (Kausche and Ruska, 1940),pathologically changed thrombocytes (Wolpers, 1941a),the membrane of erythrocytes (Wolpers, 1941b) and malaria parasites in erythrocytes (Wolpers, 1942).The finding of the cross striation of the slowly developing fibrin in the liquor of tuberculous meningitis was at that time perfectly unexpected (Ruska and Wolpers, 1940). Beside the Ruska brothers

ELECTRON MICROSCOPY IN BERLIN 1928-1945

217

FIG.3. Hans Mahl, 1950

and Bod0 von Borries, the following scientists cooperated often in the Siemens group: Eitel and Radczewski (mineralogy), Kausche (virology), Meldau (dust), Muller (electron optics), Piekarski (bacteriology), Wolpers (blood) and Zahn (fibre). Under the guidance of Hans Mahl the laboratory of the AEG was also active in this time (1940-1942). Their interest focused on metallurgy (Mahl, 1942) and medicine (Krause and Mahl, 1943). Jakob examined bacteria, bacteriophages, cancer cells and the sporozoites of malaria (Emmel et al., 1942; Jakob, 1942; Ramsauer, 1942). Helmcke examined zoological objects (Ramsauer, 1942).Kinder built in 1941 the first transmission apparatus from the AEG with magnetic lenses (Kinder, 1941). The controversy about magnetic and electrical lenses in the electron microscope was not yet decided, as in 1941 the “Preussische Akademie der Wissenschaften” in Berlin gave the silver Leibniz medal as a distinction to each of the following: Knoll, Ernst

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Ruska, von Borries, Bruche (Fig. 4), Boersch, Mahl and von Ardenne (Fig. 5 ) . The award was made in the above order, without any evaluation, with a view to reconciliation. It was only in 1956 that Zeiss, as successor of AEG, halted the construction of electron microscopes with electric lenses (Partsch, 1986) and turned over to the use of magnetic lenses. For von Ardenne, the years from 1940- 1942 were especially successful ones. Four contracts (with Siemens, Reichspost, Krupp and Forschungsgemeinschaft) assured economically the existence of his private laboratory and exempted him from serving in the army. He got a bomb-proofed air-raid shelter, which enabled him to wait for the end of the war in Berlin. In 1940 his universally accepted book, Elektronenubermikroskopie (von Ardenne, 1940) was published with a lot of technical data, but also with applications, which he had obtained with the operators at several Kaiser Wilhelm Institutes and with his efficient transmission electron microscope with magnetic lenses. Here Beischer continued his examinations on colloid chemistry (von Ardenne and Beischer, 1940; Beischer, 1938). Friedrich-Freksa and Schramm pursued biological research (von Ardenne and Friedrich-Freksa, 1941; von Ardenne et al., 1941). Hofmann e'xamined dust and minerals. Menke worked in the field of botany (1940) and Weber on muscle protein (von Ardenne and Weber, 1941).

FIG.4. Manfred von Ardenne. About 1939.

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219

FIG.5. Ernst Briiche, 1944.

End-Phase of the War (1943-1945) The numerous military reverses generated support for hitherto neglected basic sciences. Conversely the bombing of the bigger towns meant that the backward zone now belonged to the war zone. As a result of an order of the “Sanitatsinspektion of the Wermacht,” the medical officers Helmut Ruska and the author Wolpers (Fig. 6) were transferred from the eastern front back to Berlin, to continue their electron microscopical studies at Siemens. They could choose their own topics. Helmut Ruska dedicated himself to the examination of bacteriophages (Ruska, 1941, 1942), viruses (Ruska, 1943) and rickettsia1 diseases (Eyer and Ruska, 1944),while the author turned to the analysis of the fibres in the intercellular space. The methods available at that time for producing extremely thin sections (von Ardenne, 1938c; Krause, 1944b; Sjostrand, 1943)promised no satisfying results. Under the pressure of the war

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FIG.6. Carlheinrich Wolpers, 1960.

situation, a simpler way had to be found (Frey-Wyssling, 1938).Aware of this, we renounced all work on cells and concentrated on fibres in the intercellular space (collagen, Wolpers, 1944a), elastic tissue and muscle (Wolpers, 1944b). We avoided embedding, and mostly fixed especially with osmium. We prepared thin sections with the freezing microtome and pulled the sections apart with the low-frequency ultrasound, produced in the magnetostrictive way (under cooling) (Pohlmann and Wolpers, 1944). With the centrifuge we separated the fibre elements from the other tissue parts (Wolpers, 1944~).The 2600 pictures thus obtained of collagen (normal from different species or pathological-myxomatosis, rheumatics, Arthus phenomenon), elastic fibres and muscles were destroyed by the air raid on October 6, 1944. From January 1943 until October 6, 1944, we endured in Berlin 135 air raids, in 1943 mostly at night, in 1944 day and night (Girbig, 1977). The research institute of the AEG was evacuated in the middle of 1943. The attempt to continue near Dresden with two electron microscopes that had been transferred was without results. On the flight towards the west, the coworkers were caught in the air raid on Dresden, where men were lost. Those

ELECTRON MICROSCOPY IN BERLIN 1928-1945

22 1

who survived were soon able to build an excellent microscope in Mosbach (Baden),with the aid of Zeiss and under the guidance of Briiche (Briiche, 1971; Partsch, 1986). The magnetic instrument of Kinder (Kinder, 1941) remained near Dresden. In the spring of 1944 the main laboratory building of von Ardenne was destroyed (von Ardenne, 1972). In his deep air-raid shelter one electron microscope and one cyclotron were preserved. For the scanning electron microscope and the 200 k V instrument, there was no more space. They were destroyed. Von Ardenne occupied himself with the separation of isotopes (von Ardenne, 1944) while waiting for the war to end and afterwards led a research institute in Russia (von Ardenne, 1972). The war and the postwar time also splintered the Siemens group. The laboratory for application in BerlinSpandau (Figs. 7 and 8) was destroyed, but not the rooms for production in the

FIG. 7. The first Siemens electron microscope, 1938.

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FIG.8. The former Siemens Laboratory for electron microscopy in Berlin-Spandau, 19371945. Courtesy of Dr. Tesche, Berlin 1989.

same building. Before this event von Borries had already transported electron microscopes and archival material into western Germany. Ernst Ruska remained in Berlin and at the end of February 1945 assembled the 38th electron microscope for Professor Thiessen in Berlin. At the end of the war, there were still three instruments being set up. The whole manufacturing plant (including numerous experienced coworkers) disappeared in the eastern direction. Ernst Ruska managed to hide. Helmut Ruska and the author found a refuge with two functioning electron microscopes and with coworkers inside the “Reichsforschungsanstalt fur Viruskrankheiten der Tiere” on the isle of Riems near Greifswald, which remained active up to the very end of the war. Then, taking one electron microscope with them, they too fled towards the west. The publication of results was very difficult, as the printing offices and the publishing houses were destroyed too. In addition, access to literature, especially from abroad, was difficult, if not impossible. From 1938 till 1945, the three groups presented 206 scientific publications (von Ardenne 15%, AEG 15% and Siemens 70%). Let us look back: Three hundred years ago in Delft (Holland) the first steps were taken to overcome the natural limits of the human eye, looking into the microcosmos. The second stage, which eventually enabled Man to look at molecules and atoms, started fifty years ago in Berlin (Fig. 9).

ELECTRON MICROSCOPY IN BERLIN 1928-1945

223

Ib) FIG.9. Early electron micrographs, of considerable importance for morphology: (a) crossstriations of fibrin (1939); (b) human erythrocyte membrane (1941); (c) cross-striations of collagen ( 1943). \

,

224

C. WOLPERS

Fates of the Electron Microscopes Built in Berlin during Wartime, 1939 till 1945

Ernst Ruska, before his death on May 27, 1988, sent me a list of the 38 electron microscopes that Siemens manufactured during wartime. (Table I). TABLE I SPECIFICATIONS OF THE WARTIME ELECTRON MICROSCOPES BUILTBY SIEMENS, ARRANGED BY ERNSTRUSKA(1988)

No. 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Year of delivery

Voltage (kV)

Localization (primary)

Field of research

1938 1939 1939 1939 1940 1940 1940 1940 I940 1940 1941 1941 1941 1942 1942 1942 1942 1942 1942 1942 1943 1943 1943 1943 1943 1943 1943 1943 1944 1944 1944 1944 1944 1944 1944 1944 1944 1945

60 60 120 70 70 85 70 70 85 220 70 70 85 85 85 120 85 85 85 85 85 85 100 100 100

Berlin Berlin Berlin Frankfurt Berlin Berlin Leverkusen Danzig Heidelberg Berlin Bitterfeld Berlin Jena Wolfen Tiibingen Berlin Freiburg Rome Heidelberg Hamburg Stuttgart Kiel Riems Vienna Vienna Uppsala Strasbourg Frankfurt Vienna Berlin Essen Geisweid Strasbuorg Riems Berchtesgaden Vienna Berlin Berlin

experimental experimental experimental chemical industry chemical research morphological research chemical industry physical research virus research experimental chemical industry chemical research optical industry chemical industry medical research experimental chemical research medical research physical research physical research metallurgical research medical research virus research chemical research chemical research chemical research medical research biophysical research chemical industry military research metallurgical research metallurgical research chemical research medical research medical research medical research chemical research chemical research

100

100 100 100 100 100 100

100 100 100

100 100 100

225

ELECTRON MICROSCOPY I N BERLIN 1928-1945

He asked me to ascertain the fates of these instruments. Nearly 50 years after the event, the results were disappointing, because it was not possible to penetrate the "iron curtain", behind which 36% of the electron microscopes disappeared. Also the fast development of this specialty implied that most of the instruments were meanwhile scrapped. This was ascertained for nos. 7,9, 12, 21 and 28 of Table 1 . The numbers 3, 4, 26 and 35 are now standing in museums in Berlin, Muenich, Stockholm and Washington D.C. The bombardments demolished 6.4% of the 47 instruments (Table 11). The destruction of one instrument with a hammer in Vienna was tragic. Three young chemical scientists lost their lives by shooting and by suicide. During the entry of the Russian troops, two scientist wished to preserve and one to

TABLE I1 POSTWAR

DISTRIBUTION OF THE 47 ELECTRON MICROSCOPES BUILTIN BERLINDURING wAR(l939-1945) A. Siemens ( n

Country

=

38)

Number of microscopes

No."

Austria France Great-Britain Sweden USA West-Germany

25, 29, 36 15, 27. 33 6, 20, 22, 31, 32 (temporarily 34) 26 35 3.4, 7, 9, 12, 18, 19, 21, 28, (34)

Destroyed by bombardment by hammer

17 24

Missing in East-Germany and in the Soviet Union

1,2, 5.8, 10, I I , 13, 14, 16,23,30,37, 38 B. AEG ( n

In West-Germany Destroyed by transportation Missing

=

3 3 5-6 1 1 9-10

13

5)

two

2

one two

I 2 C. von Ardenne

Destroyed by bombardment Missing See Table I.

two two

THE

2 2

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C. WOLPERS

destroy the instrument. The distribution of the 47 electron microscopes built in wartime in Berlin can be seen in Table 11.

REFERENCES Beischer, D. (1938). “Bestimmung der Kristallgrosse in Metall und Metall-Oxyd-Rauchen aus Rontgen- und Elektronenbeugungsdiagrammen und aus Elektronenmikroskopbildern,” Z . Elektrochem. 44,375. Beischer, D. and Krause, F. (1937).“Das Elektronenmikroskop als Hilfsmittel der Kolloidforschung,” Naturwissenschaften 25, 825. Briiche, E. (1971).Aus dem Leben eines Physikers. Mosbach. Briiche, E. and Haagen, E. (1939). “Ein neues, einfaches Ubermikroskop und seine Anwendung in der Bakteriologie,” Naturwissenschaften 27,809. Briiche, E. and Johannson, H. (1932). “Elektronenoptik und Elektronenmikroskop. Naturwissenschaften 20, 353. Driest, E. and Miiller, H. (1935). “Elektronenmikroskopische Aufnahmen (Elektronenmikrogramme) von Chitinobjecten,” Z . wiss. Mikrosk. 52, 53. Emmel, L., Golz, E. and Jakob, A. (1942). “Elektronenoptische Untersuchungen an MalariaSporoziten,” Dtsch. tropenmed. Z . 46, 254, 257. Eyer, H. and Ruska, H. (1944).“Uber den Feinbau der Fleckfieber-Rickettsien,” Z . H y g . 125,483. Freundlich, M. M. (1963).“Origin of the electron microscope,” Science 142, 185. Frey-Wyssling, A. (1938). Submikroskopische Morphologie des Protoplasmas und seiner Derivate. Borntrager, Berlin. Gabor, D. (1957). “Die Entwicklungsgeschichte des Elektronenmikroskops,” Elektrotech. Z . A 78, 522. Girbig, W. (1977).Im Anjug auf die Reichshauptstadt. Motorbuch, Stuttgart. Husemann, E. and Ruska, H. (1940). “Die Sichtbarmachung von Molekiilen des pJodbenzoylglykogens,” Naturwissenschaften 28, 534. Jahrbuch der Preussischen Akademie der Wissenschaften (194l), 248. Jakob, A. (1942). “Untersuchungen iiber die Struktur der Tumorasciteszellen mit dem Ubermikroskop,” Z . Krebsforsch. 52,412. Jakob, A. and Mahl, H. (1940). “Strukturdarstellung bei Bakterien (Anerobier),” Arch. exp. Zellforsch. 24, 87. Kausche, G . A. and Ruska, H. (1940). “Zur Frage der Chloroplastenstruktur,” Naturwissenschaften, 28,303. Kausche, G. A,, Pfankuch, E. and Ruska, H. (1939). “Die Sichtbarmachung von pflanzlichem Virus in Ubermikroskop,” Naturwissenschaften 27,292. Kinder, E. (1941). “Jochlinsen-Ubermikroskop. Anwendung in der Kolloidchemie,” Kolloid Z . 95, 328. Knoll, M. (1935a).“Das Elektronenmikroskop,” Z . arzt. Fortbild (Jena) 32,679. Knoll, M. (1935b). “Aufladepotential und Sekundaremissiom elektronenbestrahlter Korper,” Z . tech. Phys. 16,467. Knoll, M. and Ruska, E. (1932a). “Beitrag zur geometrischen Elektronenoptik,” Ann. Phys. (Leipzig) 12,607 and 641. Knoll, M. and Ruska, E. (1932b). “Das Elektronenmikroskop,” Z . Physik 78,318. Krause, F. (1936). “Elektronenoptische Aufnahmen von Diatomeen mit dern magnetischem Elektronenmikroskop,” Z . Physik 102,417.

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Krause, F. (1937a). “Das magnetische Elektronenmikroskop und seine Anwendung in der Biologie,” Naturwissenschafien 25.81 7. Krause, F. (1937b). “Neuere Untersuchungen mit dem magnetischem Elektronenmikroskop,” in Beitriiger zur Elektronenoptik (Busch, H. and Briiche, E., eds.), p. 55. Barth, Leipzig. Krause, (1939). “Die Anwendung des Elektronenmikroskops in Biologie und Medizin,” Arch. exp. Zelljorsch. 22, 668. Krause, F. (1944a). “Die Darstellung von Geweben mit dem Elektronenmikroskop,” Disch. med. Wochenschr. 70,532. Krause, F. (1944b).“Die Erzielung iibermikroskopischer Elektronenbilder von Gewebeschnitten. Virchows Arch. path. Anat. 312, 346. Krause, F. and Mahl, H. (1943). “Die ubermikroskopische Oberflachenabbildung medizinischbiologischer Objecte nach dem Abdruckverfahren,” Kolloid 2. 105, 53. Mahl, H. (1939). “Uber das elektrostatische Elektronenmikroskop hoher Auflosung,” 2. k c h . Phys. 20, 316. Mahl, H. (1942). “Die iibermikroskopische Oberflachendarstellung mit dem Abdruckverfahren,” Naturwissenschaften 30,207. Marton, L. (1934- 1937). La microscopie electronique des objects biologiques,” Bull. Acad. roy. Belg. Cl. Sci. (1934) 20,439; (1935) 21,553; (1936) 22, 1336; (1937) 23,672. Marton, L. (1968). Early History of the Electron Microscope. San Francisco Press, San Francisco. Marton, L. (1976). “Early application of electron microscopy to biology,” Ultramicroscopy 1,281. Menke, W. (1940). “Untersuchungen iiber den Feinbau des Protoplasmas mit dem UniversalElektronenmikroskop,” Protoplasma (Wien)35, 11 5. Miiller, H. 0. (1938). “Grundlagen und Entwicklung des Ubermikroskops,” Elektrotech. 2. 59, 1 189. Miiller, H. 0. and Pasewaldt, C. W. A. (1942).” Der Feinbau der Test-Diatomee Pleurosigma angulatum WSn. nach Beobachtungen und stereoskopischen Aufnahmen im Ubermikroskop,” Naturwissenschaften 30,55. Oatley, C. W., Nixon, W. C. and Pease, R. F. W. (1965). “Scanning electron microscopy,” Ado. Electronics Electron Phys. 21, 181. Partsch, R. 0.(1986). “The history of electron microscopy at Carl Zeiss,” in History of Electron Microscopes; Xlth International Congress on Electron Microscopy, (Fujita, H., ed.). Kyoto. Piekarski, G. and Ruska. H. (1939a). “Ubermikroskopische Darstellung von Bakteriengeisseln,” Klin. Wochenschr. 18,383. Piekarski, G . and Ruska, H. (1939b). “Ubermikroskopische Untersuchungen an Bakterien unter besonderen Beriicksichtigung der sogenannten Nucleoide,” Arch. Mikrobiol. 10, 302. Pohlmann, R. and Wolpers, C. (1944). “Uber das Verhalten histologischer Suspensionen im Ultraschallfeld,” Kolloid 2. 109, 106. Ramsauer, C. (1942). “Europaische Studienmappe. Geometrische Elektronenmikroskopie,” Universitat Heidelberg, Studentischer Kulturaustausch. Ramsauer, C. (1943). Elektronenmikroskopie. 3. Aujiage. Springer, Berlin. Riidenberg, R. (1932). “Elektronenmikroskop,” Nururwissenschuften 20,522 Riidenberg, R. (1943). “The early history of the electron microscope,” J . Appl. Phys. 14, 434. Ruska, E. ( 1934a). “Das Elektronenmikroskop als Ubermikroskop,” Forsch. Fortschr. dtsch. Wiss. 10, 8. Ruska, E. (1934b). “Uber Fortschritte in Bau und in der Leistung des magnetischen Elektronenmikroskops,” 2. Physik 87,580. Ruska, E. (1979).“Die fruhe Entwicklung der Elektronenlinsen und der Elektronenmikroskopie,” Acta Historicu Leopoldina, No. 12. Halle/Saale. Ruska, E. (1980). The Early Development of Electron Lenses and Electron Microscopy. Hirzel, Stuttgart. Translation of Ruska (1979) by Thomas Mulvey.

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Ruska, E. (1986).“The emergence of the electron microscope,” J. Ultrastruct. Res. M,3. Ruska, E. (1987). “Die Entstehung des Elektronenmikroskops und der Elektronenmikroskopie,” Phys. Bl.43, 27 1. Ruska, E. (1984). “Die Entstehung des Elektronenmikroskops (Zusammenhang zwischen Realisierung und erster Patentanmeldung, Dokumente einer Erfindung),” Arch. Geschichte Naturwiss. 11/12, 525-551. Ruska, E. and Knoll, M. (1931).“Die magnetische Sammelspule fur schnelle Elektronenstrahlen,” Z. techn. Physik 12,389. Ruska, H. (1939). “Ubermikroskopische Darstellung organischer Strukturen,” Arch. exp. Zellforsch. 22,673. Ruska, H.(1941).“Uber Grenzfragen aus dem Gebiet der Strukturforschung und Mikrobiologie,” Dtsch. med. Wochenschr. 67,281. Ruska, H. (1942).“Morphologische Befunde bei der bakteriophagen Lyse,” Arch. ges. Virusforsch. (Arch. Virol.) 2, 345. Ruska, H. (1943).“Uber das Virus der Vancellen und des Zosters,” Klin. Wochenschr. 22,703. Ruska, H., von Borries, B. and Ruska, E. (1939). “Die Bedeutung der Ubermikroskope fur die Virusforschung,” Arch. ges. Virusforsch. (Arch. Virol.) 1, 155. Ruska, H. and Wolpers, C. (1940).“Zur Struktur des Liquorfibrins,” Klin. Wochenschr. 19,695. Schimmel, G. (1985).“Ernst Bruche zum Gedenken,” Optik 70, 130. Sjostrand, F. (1943). “Eine neue Methode zur Herstallung sehr dunner Objectschnitte fur die elektronenmikroskopische Untersuchungyon Gewebe,” Ark. Zool. 35A, 1. Sommerfeld, A. and Scherzer, 0. (1934). “Uber das Elektronenmikroskop,” Muench. Med. Wochenschr. 81, 1860. Von Ardenne, M. (1938a). “Das Elektronen-Rastermikroskop:Theoretische Grundlagen,” Z. Phys. 109,553. Von Ardenne, M. (1938b).“Das Elektronen-Rastermikroskop: Praktische Ausfuhrung,” 2. Techn. Phys. 19,407. Von Ardenne, M. (1938~).“Die Keilschnittmethode, ein Weg zur Herstellung von Mikrotomschnitten mit weniger als lo-’ mm Starke fur elektronenmikroskopische Zwecke,” Z. Wiss. Mikrosk. 56, 8. Von Ardenne, M. (1940).Elektronen- Ubermikroskopie. Springer, Berlin. Von Ardenne, M. (1944).Die physikalischen Grundlagen der Anwendung radioaktiuer oder stabiler Isotopen als Indikatoren. Springer, Berlin. Von Ardenne, M. (1972).Memoiren. Kindler, Munchen. Von Ardenne, M. and Beischer, D. (1940). “Untersuchungen von Katalysatoren mit dem Universal-Elektronenmikroskop,” Angew. Chem. 53, 103. Von Ardenne, M. and Friedrich-Freksa, H. (1941). “Die Auskeimung der Sporen von Bacillus vulgatus nach vorheriger Abbildung im 200 k V Universal-Elektronenmikroskop,” Naturwissenschaften 29, 523. Von Ardenne, M. M., Friedrich-Freksa, H. and Schramm, G. (1941). “Elektronenmikroskopische Untersuchung der Pracipitinreaktion von Tabakmosaikvirus mit Kannichenantiserum,” Arch. ges. Virusforsch. (Arch. Virol.) 2, 72. Von Ardenne, M. and Weber, H. H. (1941). “Elektronenmikroskopische Untersuchung des Muskeleiweisskorpers ‘Myosin’,” Kolloid 2.W,322. Von Borries, B. (1949).Die Ubermikroskopie. Saenger, Berlin. Von Borries, B., Ruska, E. and Ruska, H. (1938). “Bakterien und Virus in iibermikroskopischer Aufnahme,” Klin. Wochenschr. 17,921. Wolpers, C. (1941a).“Die Blutplattchen bei Thrombozytopenie,” Dtsch. med. Wochenschr. 67,515. Wolpers, C . (1941b). “Zur Feinstruktur der Erythrocytenmembran,” Naturwissenschafen 29, 416.

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Wolpers. C. (1942). “Zur elektronenoptischen Darstellung der Malaria tertiana,” Klin. Woschmschr. 21, 1049. Wolpers. C. (1944a). “Die Querstreifung der kollagenen Bindegewebsfibrille,” Virchows Arch. path. Anat. 312, 292. Wolpers, C. (l944b). “Zur elektronenmikroskopischen Darstellung elastischer Gewebselemente,” Klin. Wochenschr. 23, 169. Wolpers, C. (1944~). “Die Darstellung von Gewebe mit dem Elektronenmikroskop (Bemerkung zum Vortrag Krause.” Dtsch. med. Wochenschr. 70, 435. Wolpers, C. and Ruska, H. (1939). ”Strukturuntersuchungen zur Blutgerinnung,” Klin. Wochenschr. 18, 1077, 1I 1 I .

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ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS. VOL. 81

Canonical Theory in Electron Optics JIYE XIMEN Department of Radio-Electronics Peking University Beijing. China

1. Introduction. . . , . . . . . . . . . . . , . , . . . . , . . , A. Historical Review. . . . . . . , . . . . . . , . . . . . , , . B. Theoretical Background . . . . , . . . . . . , . . , . . . . . 11. Conventional Aberration Theory in Lagrangian Representations. . . . . . . , 111. Canonical Aberration Theory in Hamiltonian Representations . . . . , . . , 1V. Applications of Canonical Aberration Theory . . . . . . . . . . . . . . A. Canonical Higher Order Aberration in Electromagnetic Round Lenses . . . . B. Canonical Higher Order Aberration in Electromagnetic Multipoles . . . . . V. Canonical Electron Beam Optics. , . . . . . . . . . . . . . . . . . A. Electron Beam Optics in Round Lenses . . . . . . , . . . . , . . , B Electron Beam Optics in a Combined System Consisting of Round, Quadrupole and Octopole Lenses. . . . , . . . . . . . . . . . . . . . . . C. Electron Beam Optical Computations in Round Electrostatic Lenses . . . . . VI. Conclusion and Discussion. . . . . . . . . . . . . . . . . . . . . A. Theoretical Conclusion . . , . . . . . . . . . . . . . . , . . . B. Concluding Discussion . . , . . . . . . . . . . . . . . , . . . Appendix. . . . . . . . . , . . . . . . . . . . . . . . . . . A. Fifth Order Aberration Coefficients in Round Lenses . . . . . . . . . . B. Aberration Formulae for Sextopole, Octopole, Decapole, Twelvepole, and Fourteenpole Systems . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . , . . . . . . . . . . . . . . . . . . , . . . References . . . . . . . . . . . . . . . . . . . . . . . . . ,

23 1 23 I 234 236 239 245 245 241 255 255 258 262 264 265 261 268 268 270 215 215

I. INTRODUCTION A . Historical Review

Charged particle optics was born in the 1920s and the study of electron lens aberration is almost as old as electron optics itself. Indeed, in the history of electron optics, theory of aberration played a great role in the development of instruments and devices. The calculation of aberrations may be performed in two different ways: trajectory method and eikonal method. The trajectory method is straightforward. Using Lorentz force, one may derive the electron 23 1 Copynght Ql991 by Academic Press. Inc. All rights of reproduction in any Corm reserved. ISBN 0- 12-014681-9

232

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motion equation and then convert it into trajectory equation. By means of successive approximation, one can solve the first order Gaussian trajectory and then solve the third order aberrations by variation of parameters. The eikonal method is somewhat abstract in form but general in nature. Knowing the electron optical refractive index or electron optical variational function and expanding it into power series, one can solve, step by step, the EulerLagrange equation, which describes the electron trajectory in an electromagnetic system. The eikonal method has a distinct advantage: different order aberrations can be universally expressed by gradients of corresponding order eikonal functions. The first calculation of aberration coefficientswere made in the early 1930s by Schemer (1933, 1936a,b, 1937), who preferred the trajectory method, and by Glaser (1933a,b, 1935, 1936a,b, 1937, 1938), who introduced the eikonal method into electron optics and established the eikonal aberration theory in his famous book (Glaser, 1952). It was Seman (1958),who strictly proved the equivalences and relationships between the trajectory method and the eikonal method in calculating electron optical aberrations. Sturrock (1951a,b, 1952, 1955) developed Glaser’s eikonal aberration theory and founded a firm theoretical foundation for calculating higher order aberrations. The basic aberration theory was again reformulated by Rose (1968, 1968/69), who discussed higher order aberrations. The eikonal method does provide the possibility for treating all the branches of electron and ion optics in such a unified way that practically all the results can be derived from Maxwell’s basic equations and Hamilton’s variational principle. The author (Ximen, 1983, 1986) employed the eikonal method to investigate rotationally symmetric imaging systems, electromagnetic deflection systems, electromagnetic multipole systems and ion optical systems. The previously mentioned review is restricted to some important work in electron lens aberration theory. Many contributions of comparable importance have not been cited. Fortunately, P. W. Hawkes and E. Kasper (Hawkes and Kasper, 1989) have published their encyclopedic book, where the fundamentals of electron and ion optics have been presented in great detail, and the original articles devoted to aberration theory have also been reviewed in detail. In summary, it is to be noted that most of the studies in the field of eikonal aberration theory are restricted to the Lagrangian representation using the position and slope configuration space. Although, over the decades, Glaser (1952), Sturrock (1955) and Hawkes and Kasper (1989) have touched the electron optical Hamiltonian function, the Hamiltonian representation using the position and momentum phase space has not been explored to analyze electron optical aberration.

CANONICAL THEORY IN ELECTRON OPTICS

233

In the present paper, based on the theory of classic mechanics (Arnold, 1978; Goldstein, 1980), the electron trajectories and aberrations will be described in the generalized position and momentum representations and will be derived by the Hamiltonian function and the canonical equations (Ximen, 1990a,b). This Hamiltonian approach may be regarded as canonical aberration theory and has several advantages. First the momentum aberrations are simpler than the same order slope-aberrations, so that the calculation of higher order aberrations is facilitated (Ximen, 1990a,b). Secondly, the canonical aberration expressions enable us to calculate position and momentum aberrations, including axial and off-axial aberrations, at any observation plane in an electromagnetic system with rectilinear or curvilinear axes. Finally, the canonical electron optics can be utilized to analyze the transport characteristics of electron beams in an electron optical system possessing aberrations. Although a theory of electron beam optics in phase space has been developed (Brown, 1972, 1981), it is basically restricted to the first order linear theory. Recently, Dragt and Forest (1986) employed Lie algebraic tools for characterizing charged particle optical systems and computing aberrations. Obviously, the Lie algebraic theory presented in Dragt’s paper and the canonical theory in the present article have physical equivalences and mutual complemen ts. The remaining sections of this paper are devoted to canonical aberration theory and canonical electron beam optics. Section I1 provides a,brief account of conventional aberration theory, using Lagrangian representation, in a rotationally symmetric electromagnetic system. This content will provide a preliminary knowledge for further studies. Section 111 describes canonical aberration theory, using Hamiltonian representation, also in a rotationally symmetric electromagnetic system. In comparison with Section 11, Section I11 clarifies the main advantages of canonical aberration theory. In Section IV, we will deal with some applications of canonical aberration theory. Section 1V.A derives higher order aberration in a round lens, while Section 1V.B deduces higher order aberration in electromagnetic multipoles. Section V is devoted to canonical electron beam optics and is divided into three parts: A. Electron beam optics in round lenses (Ximen, 1987a). B. Electron beam optics in a combined system consisting of round, quadrupole and octopole lenses (Ximen, 1988b). C , Electron beam optical computations in round electrostatic lenses (Ximen and Liu, 1991).

Finally, Section VI presents both theoretical conclusion (i.e., Liouville’s theorem, symplectic conditions, Poisson brackets) and concluding discussion (possible applications and future developments).

234

JIYE XIMEN

B. Theoretical Background

Lagrange mechanics (Arnold, 1978) describes a particle’s motion in a mechanical system by means of an n-dimensional coordinate space, Let q = ( 4 , ,. . .,4”) be generalized coordinates in a mechanical system having n degrees of freedom and q = ( q l , . . . ,4,) be the generalized velocities. According to Hamilton’s principle of least action, the motion of a particle from to to t , in a mechanical system makes the action an extremum.

where L is Lagrangian function. For this variational problem, the Euler equation is the electron’s trajectory equation:

Since q is a vector in the n-dimensional coordinate space, Eq. (2) is n second order equations, and its solution depends on 2n arbitrary constants; for example, the 2n conditions q ( t o ) = qo and q ( t o ) = qo are used for solving Eq. (2). Hamiltonian mechanics (Arnold, 1978) describes a particle’s trajectory by means of a 2n-dimensional phase space (coordinate-momentum space). It is well known that a Lagrangian system of second order differential equations, such as Eq. (2), can be converted into a remarkably symmetrical system of 2n first order equations called canonical equations (Goldstein, 1980). We consider the system of Lagrangian equations as follows:

where p and p are the generalized momentum and its time rate of change. It is to be shown that the system of Lagrange’s equations (n second order equations) is equivalent to the system of Hamiltonian equations (2n first order equations):

where the Hamiltonian H associated with a Lagrangian L is defined by the Legendre transformation H(q, 4, t ) = P * 4 - L(q, 4, t).

(5)

235

CANONICAL THEORY IN ELECTRON OPTICS

By definition, H is to be expressed as a function of q, p, t , and its total differential is given by

-

Equation (6) is equal to the total differential of p q - L for p

=

dL/aq:

Both expressions for dH must be the same, so that we get

So far we have deduced Hamilton’s Eq. (4) by applying Lagrange’s Eq. (3). Consequently, we have seen that, if q satisfies Lagrange’s equation, then p(t) and q(t) satisfy Hamilton’s equation. The converse can be similarly proved. Therefore, the systems of Lagrange and Hamilton are equivalent. The Lagrangian theory allows us to solve a series of important mechanical problems, including problems in charged particle optics. However, Lagrangian mechanics is contained in Hamiltonian mechanics as a special case. The Hamiltonian theory allows us to solve a series of more general mechanical problems, and it has greater value for seeking approximate solutions to perturbation theory, for understanding the general characteristics of motion in a complicated mechanical system, and finally for developing canonical aberration theory and charged particle beam optics. It is to be noted that in usual Lagrangian-Hamiltonian formulations, the time t plays the role of an independent variable and all conjugated generalized variables, i.e., the canonical variables 4, and p,(i = 1, . . . , n), are dependent variables, which are viewed as functions of the independent variable t . In some cases of interest (Dragt, 1981), it is more convenient to take some coordinate to be the independent variable rather than the time. For example, in electron optics, we always choose the z-coordinate along a rectilinear or curvilinear optical axis to be the independent variable for the trajectory equation. Indeed, suppose H(q, p, t ) is a Hamiltonian function for a system having n degrees of freedom, and i1 = L7H/tJp1# 0 for some interval of time and in some phase region of the 2n-dimensional phase space (q,,pi) (i = 1,. . ., n). Then in this time interval and this phase region, 41 can be introduced as an independent variable in place of time. Moreover, the equation of trajectory with q1 as an independent variable can be obtained from a transformed Hamiltonian function also with q1 as an independent variable.

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In the following sections, we will consider the Lagrangian and Hamiltonian functions with the axial z-coordinate as an independent variable.

11.

ABERRATION THEORY IN LAGRANGIAN REPRESENTATIONS

CONVENTIONAL

According to Hamilton’s principle of least action, we obtain the following variational description:

[

p d s -,extremum.

(9)

In Eq. (9), p is the electron optical index of refraction:

where 4 and A are electrostatic potential and magnetic vector potential, respectively, and r = (x,y) is the transversal position vector along the electron’s trajectory. For the sake of mathematical simplicity, we will discuss a rotationally symmetric electromagnetic system. If the axis of symmetry is the z-axis and the independent variable is z, then Eqs. (9) and (10) will be rewritten as

s

F dz -+ extremum

where r = (x2 + y2)l/’ and the magnetic vector potential only has an azimuthal component A. The electrostatic potential 4 and magnetic vector potential A can be expanded into a power series (Glaser, 1952; Ximen, 1983, 1986):

-

1 4 = V(z) - -1 V”(z)(r r) + V4)(r r)2 0

4

A r

-=

1 2

64

1 16

- B,(z) - -Bg(z)(r

9

r) +

~

1 ~

36 x 64

12 x 32

V@)(r r)3 + . . . (13)

Br)(r .r)’

+ ...,

(14)

where V(z) and B,(z) are axial distributions of electrostatic potential and magnetic induction respectively.

CANONICAL THEORY IN ELECTRON OPTICS

237

Substituting Eqs. (13) and (14) into Eq. (12), one can expand the variational function F into a power series up to the sixth order (Wu, 1957; Li, 1986; Ximen, 1990b).

F

=

Fo

+ F2 + F4 + F6 + ...

(15)

F0 -- V1/2

r11/2

-___ flL4)(r *

12 x 32

r)2(r x r’).

For this variational problem, the Euler-Lagrange equation is the electron’s trajectory equation:

For calculating first order Gaussian optical properties and aberrations, we have to introduce a rotating rectangular coordinate system (ux,u,,z) instead of the original coordinate system (x, y, z) fixed in the laboratory (Glaser, 1952; Ximen, 1983,1986):

u

= (uxruy),

u, = xcosx

r = (x,y),

+ ysinx,

u = r exp( -ix)

uy = -xsinx

+ ycosx

(18) (19)

238

JIYE XIMEN

By performing laborious mathematical calculations, one may transform the variational functions F,, F4, and F6 in the fixed coordinate system into corresponding functions F*2, F’4, and F*6 in the rotating coordinate system:

FAr, r’, 2 )

F,

= F23

F4, F6.

F*,(u, u’, z )

(21)

F*n = F*2, F*4, F*6-

(22)

+

First, by substituting the second order function F*, into Eq. (17), we obtain the first order Gaussian trajectory equation.

Equation (23) is a linear homogeneous second order differential equation, whose general solution is given by

u

=

u,rp + u&r,

u’ = uarb + u&r&, where ra and r p are well known particular solutions to the Gaussian trajectory equation (Glaser, 1952; Ximen, 1983, 1986), which satisfy following initial conditions at the initial plane z,:

r,(z,) = 0,

r&(z,)= 1,

rp(z,) = 1,

r;(z,) = 0.

(25)

Secondly, by substituting up to the fourth order function F*2 + F*4 into Eq. (17), we obtain the third order position and slope aberrations (Ximen, 1983, 1986)

where {F*4}G indicates that the entry F*4 must assume its Gaussian value. We will adopt this notation in future sections. In Eqs. (27) the last gradient can be derived by means of the following gradient identity:

whose entry F*n may be F*,, F*4, or F*6.

CANONICAL THEORY IN ELECTRON OPTICS

+

Finally, by substituting up to the sixth order function F*2 F,, Eq. (17), we obtain the fifth order position and slope aberrations

239

+ Fy6into

It is to be emphasized (Ximen, 1990b) that in Eqs. (29) and (30) the gradient operators d/&, d/au;, a/du‘ must not act onto the lower order aberrations Au, and Au;. Obviously, for calculating fifth order aberrations, in conventional Lagrangian representation, see Eqs. (29) and (30); the third order slope aberration AU; in Eq. (27) always contains an additional gradient (l/V1’2)(dF,,/du’) that makes the product Au; (dF,,/du’) too complicated to be dealt with. In order to get rid of this difficulty, we will introduce canonical aberration theory using Hamiltonian representation.

.

111. CANONICAL ABERRATION THEORY IN HAMILTONIAN REPRESENTATION

Based on theory of classic mechanics, the canonical aberration theory has been discussed in the author’s previous papers (Ximen, 1990a,b).In the present section, a rotationally symmetrical electron optical system will be discussed. All symbols and notations will follow the same convention as used in Section 11. Let the transversal component of position vector and momentum vector be r = (x, y) and p = ( px, p,) respectively. The Hamiltonian function H is defined as follows (Glaser, 1952; Sturrock, 1955; Hawkes and Kasper, 1989; Ximen, 1990a,b):

where r

-

= ( - y , x).

240

JIYE XIMEN

According to classic mechanics (Arnold, 1978; Goldstein, 1980), the canonical equation is the electron’s trajectory equation:

Using Eqs. (13) and (14), we can expand the Hamiltonian function H into a power series

H = Ho + H2 + H4 + H6 + . * * Ho = - V’I2

-

H2 = M(r r)

L H4 = -(r 4

1 + -(p. 2V’12

(33)

p) + 2Q(r x p)

1 .r)’ + -(p - P ) +~ K(r x p)’ 8 V312

+ JYr * r)(r x

P)

M Q +y (r * r)(p * P) + 7(P ’ p)(r x

P)

+ p ( r - r)(P * P)2 + M,(r * r)2(r x P) L3

+ -(r N1 2V1I2

- r)(r x p)2 + -(p 2

N2 v3’2

- p)(r x p12 + -(r3v N3

x pl3

(34) where K, L, M, P, and Q are electromagnetic field distribution functions for describing third order aberrations (Glaser, 1952; Ximen, 1983, 1986); while L,, L,, L 3 , M,,M,, M 3 , N,, N 2 , and N3 are corresponding functions for characterizing fifth order aberrations (Wu, 1957; Ximen, 1990b):

K = -1- V G 8 V312

1

1 1 L=--[ -(V” + 18;)’- V‘4’ - 4 ~ E , , E ~ 32V1/’ V 1 M = -(V” 8V1‘2

+v B ~ )

CANONICAL THEORY IN ELECTRON OPTICS

-(V"

+ qBi)

-

B:

1 q'"B, Q=--

24 1

1 (35)

4 V1'2

3B2 + q2B$V" - q B i ( V " ) 2 - ( V " ) ' ]

[3q2B;: + 2qB6 V"

-

(V")2]

+V

The canonical position and momentum vectors r and p can be combined into the four-dimensional vector X ; meanwhile the differential vector r' and p' can be combined into X ' :

Introducing an antisymmetric fundamental matrix J (Goldstein, 1980), 1

J=

1 -1

-1

242

JIYE XIMEN

we can transfer Eq. (32) into the four-dimensional representation

In the first order approximation, by substituting H z into Eq. (32), we obtain the first order Gaussian canonical equations

Similarly, we can transfer Eq. (40) into the four-dimensional representation

where subscript g indicates first order Gaussian approximation and T is a 4 x 4 matrix describing first order optical properties (Ximen, 1990a,b):

Therefore, the first order trajectory and momentum can be solved: rg

= rurp

+ Par0

(43)

pg = r a P z r b + paV1”rh,

where r, and rg are well known particular solutions to Gaussian trajectory equation, which satisfy following initial conditions at z,: r,(z,) = 0,

r;(za)=

rs(z,) = 1,

rb(z,) = 0.

(44)

It is to be stressed that the previously defined r,(z) is different from the ordinary one; see Eq. (25).The Wronsky determinant is given by V’’Z(r;rfl- lark) = 1.

(45) Equation (43) can be transformed into a four-dimensional representation: X,

=

GX,

243

CANONlCAL THEORY IN ELECTRON OPTICS

Since the first order quantities r,, p,, and X , can be tacitly understood, the subscript g will be omitted from here on. In up to the fifth order approximation, by substituting H, + H, + H , into Eq. (39),we obtain the canonical position and momentum aberrations (X

(? + AX)' = T(X + AX) + J-{H4 + A,(r,p)H, + If,} ?JX

AX

=

AX3 + AX5 = ( A I - ~ , A P+~ (Ar5rAp5)T )~

(48) (49)

In Eq. (49) superscript T indicates a transposed matrix. Obviously, the linear homogeneous part in Eq. (48) is exactly the Gaussian trajectory Eq. (41), while the nonlinear inhomogeneous part results in the third order and fifth order aberrations; see Eq. (49). This first order differential Eq. (48), with known nonlinear terms assuming their Gaussian values, can be solved by a variation of parameters:

where the entry of { ...} must assume its Gaussian value. This notation will be adopted in future expressions. The initial aberrations are specified as follows: AX, = 0,

AX;

+ A,(r,p)H, + H , ) ]

=J

.

(52)

za

The gradient identity Eq. (28) can be transformed into a four-dimensional representation

whoseentry may be H,. A,(r,p)H,, H,. Substituting thisidentity into Eq. (51), one obtains the canonical aberration formulae. {H,

+ A3(r,p)H4+ € I 6 ) dz

(54)

244

JIYE XIMEN

Equation (54)is the most important aberration expression, being general in nature and compact in form, which can be converted into conventional twodimensional vector representations:

Ar,

= - I,-

a ara

{:

{H,} dz

+ ra- a .

{H,} dz

(55)

aPa

{H,} dz

jza

a . {H,} dz + V1%' dpa

(56)

It is to be stressed again that the lower order aberrations Ar, and Ap, in Eqs. (57)-(58) must not be acted upon by the gradient operators a/ar, and d/dpa. So far we have presented up to the sixth order Hamiltonian functions H,, H,, and H,. We have also derived canonical position and momentum vector X, and up to the fifth order aberrations AX3 and AX5. The main advantages of canonical aberration theory using Hamiltonian generalized position and momentum representation may be illustrated as follows:

(i) Both canonical trajectory equations and aberration expressions are remarkably symmetric with respect to position variables (x, y) and momentum variables ( p x , p,,). (ii) In Eqs. (33) and (34), the power series of H(q,p,z) only contains scalar or vector products (r r), (p p), (r x p), which are rotationally invariant quantities. Therefore, employing the Hamiltonian function enables us to avoid introducing rotating coordinate systems and performing laborious calculations. (iii) Canonical equations for trajectories and aberrations are first order differential equations and thus easy to solve; Euler-Lagrange equations are second order differential equations and thus elaborate to handle. (iv) Comparing the third order and fifth order slope-aberrations in Eqs. (27) and (30) with the same order momentum aberrations in Eqs. (56) and (58), one may conclude that the momentum aberrations are much simpler than the slope aberrations. Therefore, calculation of higher order aberrations is greater facilitated, which will be shown in Section IV.

-

245

CANONICAL THEORY IN ELECTRON OPTICS

Iv. APPLICATIONS OF CANONICAL ABERRATION THEORY A. Canonical Higher Order Aberration in Electromagnetic Round Lenses

In Section 111, Eq. (54) describes the canonical aberrations in an electromagnetic round lens, which is divided into three parts (Ximen, 1990b): {H4}dz = GJ-,884

c4 = j:{H4}dz,

(59)

axa where AX3 is third order aberration and

E,

is fourth order eikonal, and

where (AXS)intr and are fifth order intrinsical and combined aberrations respectively. Utilizing Eqs. (50),(53), and (59), the operator A3(rrp)in Eq. (61) can be rewritten as

Inserting Eq. (62) into Eq. (61), we get an appropriate combined fifth order aberration expression:

It is to be noted that in Eq. (63), the gradient a/aXa (i.e., a/&, and a/apa) must not act onto the lower order aberrations, i.e., a ~ , / a rand ~ d&,/apa(Ximen, 1990b). Utilizing the theoretical methods in a previous paper (Ximen, 1990a) and performing cumbersome mathematical calculations, we have obtained the fifth order aberrations (Ximen, 1990b):

(AX5)intr = G{(ra ra)' AII

+ 2(ra * ra)(ra * Pa)A12 + 2(ra. ra)(ra X

+ 2(ra ' ra)(pa ' pa) A14 + (ra ' pa)' A22 + 2(ra ' + 2(ra * Pa)(Pu ' P u ) A24 + (ra Pal2 A33 + 2(ra

+ (~a*pa)~A44jXa

Pa)A1\13

Pa) Pa)(Pa ' Pa) A34

(64)

246 (Ax5)C0111b

JIYE XIMEN

+ '11) + ' + 2(ru ru)(ra P ~ ) ( ~ 1+3 n13) + 2(ru + (ra + '22) + 2(ru ' + 2(ru * Pu)(Pu ' p ~ r ) ( ~ 2+4 n24) + (ru + x Pa)(Pa * P a ) ( A 3 4 + '34) + (P. * PA2(A44 + n 4 4 ) I x a .

= G{(rU

' rU)2(A11

rU)(rU

2(rU

PU)(A12

+ '12)

' ra)(Pu ' P

+

~ ) ( ~ 1 4 '14)

+ p 1 1 ) ' ( ~ 3 3 + '33)

P ~ ) ( ~ 2 3 n23)

(65)

In Eq. (64) the intrinsical aberration is expressed by the 4 x 4 matrix Aij (i, j = 1,. . .,4), which can be universally described as follows: 64

Aij=[

62

-63

-:: -;:

( i , j = 1,***34)*

-6164

(66)

- 6,

The entries of Aij (i.e., 6,, 6,, d3, d4 for different indices i, j ) involve altogether 20 fifth order geometrical aberration coefficients G, H , I, J, S, T, g, h, s, t, u, u, n, etc. (Wu, 1957; Li, 1986; Li and Ni, 1988; Ximen, 1990b). In Appendix A, the expressions for matrices Aij and for aberration coefficients G, H, I,. . .,u, u, n, etc. will be given in detail. are expressed by the 4 x 4 In Eq. (65) the combined aberrations (AX5)comb matrices Aij and llij(i, j = 1,. .. ,4), which can be described as follows:

;

+

A.. = "

nl1= nl2= n1-3=

s:j:u.

(i I j = 1,2,3,4)

(2Ea; - A a ; ) d z

((2C

:j

+ D)c\ - Ea; - Aak)dz

{ca\ - ea;} dz

s:j:a.

{Fa; - Eak} dz

n14

=

n22

=4

n23 =

(ciaj a>ai)dz,

{Fa; - Eak} d Z

2 [:u {fa; - eok} dz

= 4n14

(67)

CANONICAL THEORY IN ELECTRON OPTICS

247

where A , B, C, D,E, F, and c, e, f are well known third order geometrical aberration coefficients for round lenses (Glaser, 1952; Ximen, 1983, 1986, 1990a). Moreover, in Eqs. (67) and (68), a,, a;,. . .,a4, are 4 x 4 matrices and can be similarly described as follows: -03

"4

0 3

"2 "2

"4

- "1

-04

r

--"I

0 3

( i = 1, ..., 4)

-wJ -m4.

-"; -0;

1 wj

-mi

(69)

The entries of hi (i.e., wl, 02,03,o, for different indices i ) involve altogether nine third order geometrical aberration coefficients and will also be given in Appendix A. So far, the third order and fifth order canonical position and momentum aberration formulae have been derived and are more general and more concise than those in literature (Wu, 1957; Li, 1986; Li and Ni, 1988).

B. Canonical Higher Order Aberration in Electromagnetic Multipoles

In 1936, Scherzer proved an important theorem (Scherzer, 1936b): the third order spherical aberration coefficient must always have the same sign, if the electrostatic or magnetic fields of an electron lens have rotational symmetry, are independent of time and free of space charge. Since then, many attempts based on Scherzer's theorem have been made to eliminate third order spherical aberration either by using a quadrupole-octopole system (Scherzer, 1947; Seeliger, 1949; Koops, 1978) or by using sextupole system (Beck, 1979;

248

JIYE XIMEN

Crewe and Kopf, 1980a,b; Rose, 1981; Ximen and Crewe, 1985). The hypothesis that a 2N-pole system could be used to correct the Nth order spherical aberration of a round lens was put forward and discussed (Crewe and Kopf, 1980a; Hawkes, 1980). Recently, sextupole, octopole, decapole, twelvepole, and fourteenpole systems have been investigated, and their spherical aberrations from lower to higher order have been derived (Shao, 1987; Shao and Crewe, 1987; Shao, 1988; Shao et al., 1988). However, the fully general aberration theory in any integer 2N-pole electromagnetic system has not been established. The author believes that canonical aberration theory is just the appropriate theoretical tool for completely investigating axial and off-axial aberrations in any integer 2N-pole electromagnetic system. In the author’s previous paper (Ximen, 1990c), the general algebraic expressions of aberrations from lower to higher order (i-e., the order of N - 1, N + 1, 2N - 3, 2N - 1,3N - 5 ) in an arbitrary integer 2N-pole electromagnetic system have been derived. For a 2N-pole electromagnetic system, electrostatic potential 4 and magnetic vector potential A (which only possesses axial component) can be expressed by (Ximen, 1983,1986) 1 N

4 = u + - $NrNCOS NO

(70)

where U is the electron’s constant energy (apart from a physical constant e) and 4, and A, are the constant strengths of multipoles (with a scaling factor l/N). In Eqs. (70) and (71) cylindrical coordinates (I,@) are related to rectangular coordinates (x, y): x = rcos0,

r N cos NO = Re(x

y = rsinO

+ iy)”.

The electron optical Hamiltonian function H is now defined as follows: H = -($ - p,” - p ; ) l i 2

+ u’I2A.

(72)

Substituting Eqs. (70) and (71) into Eq. (72),one can expand the Hamiltonian function H into a power series: H = Ho

+ HN +

+ H2p +

H4p

+ HNp.

(73)

For a 2N-pole electrostatic system, Hamiltonian functions are given by Ho = - u’I2,

249

CANONICAL THEORY IN ELECTRON OPTICS

1 1 -(HN)2 2 U'i2

H2N

=-

H2P

=-

H4P

=

HNP

=

1 1 2 --(PI U", 1

+ Pi)

1

2@H2d2 (74)

For a 2N-pole magnetic system, Hamiltonian functions are given by Ho

=

H N --

-U1l2,

(i) + Re(x

-u'/2

iy)N,

112

k=

(t)

A,

Hi.. = o 1

1

1

1

2 $7z(H2P)2

H4P

=

HNp

= 0.

(75)

In the first order approximation, by substituting the second order Hamiltonian function H , , into canonical equations (see Eq. (32)) we obtain the Gaussian optical properties x, =

P xp

y'=-

PY u"2.

P i = 0,

PI

= 0.

(76)

Obviously, for 2N-pole multipoles, if N 2 3, then first order trajectory is a straight line: x

= xo

+ z-LP/ x1 o/ 2 '

PYO

Y =yo+zU'/z

where subscript "o'' indicates the initial values of position, slope and momentum at the initial or input plane zo = 0. Because the object point is usually assumed to be a real or virtual point source on the optical axis, the initial slope xb, yb can be expressed in terms of the initial position xo, yo (Shao

250

JIYE XIMEN

and Crewe, 1987; Shao et al., 1988): xb = xop yb = yap, p = const. Therefore, the Gaussian optical properties are given as follows: y = ro sin 8(1 + z p ) x = ro cos 8(1 + zp), Px u”2

PXO

- u”2 = pro cos 0,

& $ =

= pro sin 8.

(79)

In Eq. (79) the ititial rectangular coordinate (xo, y o ) is expressed in terms of cylindrical coordinates (ro cos 8, ro sin 8). Now we will apply canonical aberration theory (Ximen, 1990a,b) to electromagnetic multipoles, where the first order trajectory is a straight line. Using the canonical aberration equation (e.g., Eq. (54)), one can directly and exactly obtain general aberrations for an arbitrary integer 2N-pole electromagnetic system (Ximen, 1990~):

where two-dimensional vector notations are defined as follows: Ar = (Ax, Ay),

-=(-,-), a a 8x0 aro

a

dY0

AP = ( A P n APY)

-=(”, a ’). apo

(82)

JPxo JPyo

Note that the aberration equations, i.e., Eqs. (80) and (81), may be solved by successive approximation; having calculated the lower order aberrations Ar,

CANONICAL THEORY IN ELECTRON OPTICS

25 1

Ap and substituting them into the right-hand side parts, one can thus obtain the left-hand side higher order aberrations Ar, Ap by conventional integration procedures. In Eqs. (80) and (81) the gradients a/&,, d/dpo must not act onto the lower order aberrations Ar, Ap. According to different properties of Hamiltonian functions HN, H4p,H2N, HNp, the aberrations can be divided into four groups. 1. Aberrations Due to HN in Both Electric and Magnetic Multipoles

The lowest order ( N - 1) position and momentum aberrations are given by Alr = -z{i-

x {(ZP

a

+

{-}dz HN

dr

u1I2

+

1)N+’ -

a

HN

{F}dz

(N

+ l)(zb + 1) + N }

(85)

For calculating the higher order aberrations in the following paragraphs, only the lowest order aberrations Alr and Alp will appear in the integrations; meanwhile the gradients d/dr and a/dp must not act onto Alr and Alp. The medium order (2N - 3) and higher order (3N - 5) aberrations due to HNare given as follows:

- 2(2N

+ l)(ZD +

I)N+ 1

+ 2N(2N + 1) ( Z P + (N

-

1)

252

JIYE XIMEN

cos(N + l)B k 3 r i N - ' ( N - 1)(N - 2) {(zfl sin(N + l ) e 6 N 3 ( N + 1)'(3N + 1)p6

)

(:;i)N=(

- 3(N

+

+

1)(3N 1) 2N+1 (zp + l ) (2N 1)

+

+

+ 1)3~+1

3N(3N + '1 (2N - 1)

+ l)ZN+ 3(N + 1)(3N + l)(zfl + l ) N + l 3N3(3N + 1) - 6 N ( N + 1)(3N + 1) x (zfl

(zp + llN + ( N - 1)(N - 2)

( N - 1) x (zp

+ l ) N - l + A(zfl + 1) + B }

(91)

+ 1)'(3N + 1)(5N + 2)/[(2N - 1)(N - 1)(N - 2)] B = 3N(5N + l)(N + 1)/[(2N + 1)(N - l)].

A

=

-(N

All these aberration expressions contain some truncated zp-polynomials that appeared in Eqs. (85), (87), (89) and (91) and terminated at (zp)', (zfl)', (zfl),, ( ~ f lrespectively. )~ 2. Aberrations Due to H,, in Both Electric and Magnetic Multipoles

The lower order (N + 1) and higher order (2N - 1) aberrations due to H,, are given as follows:

~ C O S ( N-

-2sin(N x

{(ZP

+

i)e + COS(N i)e l)e + sin(N + l)O

-

+ l ) N + '- ( N + l)(zp + 1) + N }

(93)

CANONICAL THEORY I N ELECTRON OPTICS

253

1 k2,.2N- 1 0

1 N2(2N + sin8 - -sin(2N - l)8 2

- (2N

1)p2

+ l ) ( z f l+ 1) - ( N + 1) ~

(95)

Some truncated zfl-polynomials appear in Eqs. (93) and (95) and terminate at (zfl), and ( z B ) respectively. ~ 3. Aberrations Due to H 2 , Only in Electric Multipoles Only ( 2 N - 1) order aberrations due to H , , are given:

-cos(N x

{ ( ~ f+l

-

-

l)8 cos N 8 - (2N

+ l)(zfl + 1) - 2 N ) .

(97)

A truncated polynomial appears in Eq. (97) and terminates at (zfl)'. 4. Aberrations Due to HNp Only in Electric Multipoles

The lower order ( N are given by

+ 1)and higher order ( 2 N - 1) aberrations due to H N p

JIYE XIMEN

+ +

c o s ( ~ i)e [(zp sin(N 1)O)

{( +

f cos(N \-sin(N -lle 1)0)"N

- 2(2N

+ l)N+' - 13

+1)4}

(99)

+ 1)(N + 1)(zp + 1)N+' + 2N(2N + 1)( Z P + (3N + 1) + 1)

(3N

+ 1)" + + (2N(3N + 1)

+

1) -

-

++

cos(N - 1)0 cos NO )"zp -sin(N - 1 ) O . cos NO

+ - 2(2N

"(zp (N + 1) +

"I

2N(N (3N 1)

+ 1)2N+'

1

+ l ) N + '+ (2N + l)(zp + 1) - (N2NZ + 1)

-

A truncated polynomial appears in Eq. (99) and terminates at (zp)'; three truncated polynomials appear in Eq. (101) and terminate at (ZB)~,( ~ 8 )and ~. ( Z P ) ~respectively. So far we have derived the general algebraic expressions of aberrations from lower to higher order (i.e., the order of N - 1, N + 1,2N - 3,2N - 1, 3N - 5) in an arbitrary integer 2N-pole electromagnetic system. These results and expressions basically cover those presented in literature (Beck, 1979; Crewe and Kopf, 1980a,b; Ximen, and Crewe, 1985; Shao, 1987; Shao and Crewe, 1987; Shao, 1988; Shao et al., 1988) and allow us to investigate aberrations at any observation plane, to deduce angular dependencies of different aberrations, and to examine the possibility for spherical correction of a round lens by using multipoles. Therefore, introducing Hamiltonian function

CANONICAL THEORY IN ELECTRON OPTICS

255

and developing the canonical aberration theory have remarkable advantages for completely calculating higher order aberrations in multipoles. In Appendix B, the numerical formulae for aberrations in sextupole, octopole, decapole, twelvepole, and fourteenpole electromagnetic systems ( N = 3,4, 5, 6, 7) will be given in detail.

V. CANONICAL ELECTRON BEAMOPTICS In past decades, the theory of charged particle beam optics in phase space has been developed for designing high energy accelerators, beam transport and guidance systems (Banford, 1966; Brown, 1972,1981). However, the theory of beam optics is basically restricted to the first order linear theory, and the influences of aberrations have not drawn much attention. Recently, the Lie algebraic theory of beam optics has been developed for investigating charged particle optical systems possessing up to fifth order aberrations (Dragt and Forest, 1986). Meanwhile, a comparable study on electron beam optics for electron optical systems possessing third order or higher order aberrations has been developed in the author’s recent papers. Several general cases have been discusseed, including rotationally symmetrical systems (Ximen, 1987a), combined magnetic round lens and sextupole systems (Ximen, 1988a), combined systems consisting of round, quadrupole, and octopole lenses (Ximen, 1988b), and combined electromagnetic focusing-deflection systems with rectilinear or curvilinear axes (Ximen, 1987b, 1988~).In the previous papers, based on Liouville’s theorem (Arnold, 1978; Goldstein, 1980), canonical aberration theory has been utilized to discuss the transport characteristics of an electron beam, including transfer matrix, envelope and orientation of phase ellipsoid, beam emittances, etc. A . Electron Beam Optics in Round Lenses

As shown in Section 111, the first order description of an electron beam in four-dimensional phase space is given by Eq. (46):

x = GXa,

x = (X,Px,Y7P,)T9

x u

= (Xa,Pxa?Ya,Pya)T

256

JIYE XIMEN

where superscripts indicates transposed matrix, G is first order Gaussian transfer matrix, and its determinant is equal to 1. According to classic mechanics (Arnold, 1978; Goldstein, 1980), the motion of a particle (e.g., an electron) is simply the evolution of a canonical transformation generated by Hamilton's equations and is specifically called the phase flow. Liouville's theorem states that the phase flow of Hamilton's equations preserves phase volume. Based on Liouville's theorem, the volumes of phase diagram (i.e., phase ellipsoid) in the current plane z and in the initial plane z, are conserved:

xTa-'x= X:G~O-~GX,= x,o;~x, = 1,

(103) where the a-matrix and a,-matrix are the characteristic matrices of an electron beam in the z plane and z, plane respectively.

Considering Eq. (104), we obtain the transfer formula between a and a,: a;' = GTa-'G, a = GnmGT. (105) It is to be noted that (Brown 1972, 1981) quantities 0:{' (or a:{:), a;' (or ):;a and a12(or a12,)characterize the position envelope, the momentum envelope and the orientation of the phase ellipsoid respectively. It is evident that the volume of the ellipsoid in phase space is conserved: 011022 -

af2= a11,a22a- a:2a = constant

(106) where E is a kinematic constant called beam emittance. The main purpose of this paragraph is to investigate the influences of third order aberrations upon the transport characteristics of an electron beam. As shown in Section 111, up to the third order description of an electron beam in four-dimensional phase space may be given as follows: E',

X = G(I + AM)X,. (107) I is a 4 x 4 identity matrix, while AM is a 4 x 4 perturbation matrix consisting of all third order aberration coefficients A , B, C, D,E, F, c, e, and f (Ximen, 1990a):

AM=

257

CANONICAL THEORY IN ELECTRON OPTICS

AM11 = -AM22 = E(ra * ra)

*

pa)

+ C(ra

x

Pa)

+ F(P,

*

Pa)

+ 2 m a x Pa) + W P a * Pa) AM13 = AM24 = e ( r a * ra) + ~ ( r a* p a ) + f ( p a * Pa) AM21 = -A(ra .ra) - 2E(ra . pa) - W ,x Pa) - D ( P ~* PA AM12

= D(ra

ra)

*

+2

+ 2C(r,

m a * Pa)

( 109)

It is to be emphasized that (Ximen, 1987a,b, 1988a,b,c) the perturbation matrix AM generates the third order aberration AX = GAMX, and equivalently results in perturbation to transfer matrix AG = G AM and perturbation to characteristic matrix Aa. From Eq. (109)it is evident that the trace of AM is equal to zero, and then the determinant IZ + AM1 is equal to 1 (Arnold, 1 9 7 8 ) : Tr(AM) = AMll

+ AM22 = 0,

II

+ AM1 = 1.

(1 10)

Therefore, even if third order aberrations exist in an electron optical system, the determinant of transfer matrix is always equal to 1: J G ( I + AM)I

=

IGJ* 11

+ AM1 = 1.

(1 11)

This is what Liouville's theorem states (Ximen, 1981). Based on Liouville's viewpoint, the volumes of phase ellipsoid in up to the third order approximation are also conserved: XT(o+ Aa)-'X = X,T(G + GAM)T(a+ Aa)-'(G

+ GAM)Xa

= xao,'xa = 1.

(1 1 2 )

Thus, we have a,' (a

= (G

+ G A M ) T (+~ Ao)-'(G + CAM)

+ AD) = (G + GAM)aa(G+ GAM)T.

(1 13)

Neglecting the higher order perturbation, we obtain (a

+ Aa) = GaaGT+ G(AMaa + aaAMT)GT.

( 1 14)

If Aaa and Aa are defined as

then the transfer formula between a order approximation is given by

+ Aa and aa+ Aaa in up to the third

8SZ

259

CANONICAL THEORY IN ELECTRON OPTICS

1 A , = - Yy;xy2 4

1 4

A

= - - y‘x 2 y

A = -1 y x Z - - 1y 2 y 2 = 2 2

+

-Y;

+ Y4

)

2

(A’?;

- Y4)x4 - 6 Y 4 x 2 y 2

y4.

In above formulae, the field distribution functions are defined as follows: -axial potential of an electrostatic round lens; a),-second and fourth order harmonic potentials of electrostatic quadrupole and octopole lenses respectively; and Y 2 ,Y4-second and fourth order harmonic potentials of magnetic quadrupole and octopole lenses respectively.

a)

Q2,

The Hamiltonian function H is defined by

H

-{4 -(p, +

-(p,

+ q1/2Ay)z}1’2+ q1’2Az.

(123) Substituting Eqs. (121) and (122) into Eq. (123), we obtain the power series expansion of Hamiltonian function (Ximen, 1990a)

H, =

=

-m1l2

1 H4 = - L 1 x 4 4

= -2N

( 124)

1 + -21 L x z y 2 + -41L , y 4 + -(pE + pi)(M,x2+ M2yZ) 2a)

where K , L , , L 2 , M , , M 2 , and N are functions of electromagnetic field distributions defined in a previous paper (Ximen, 1988b). Substituting Eq. (125) into the Hamiltonian Eq. (32), one obtains the first order Gaussian trajectory equation

+ (2M, + ql’2Y2)x = 0 (@”*y’)’ + (2M2 - q 1 / 2 Y 2 ) y= 0.

(a)1’2x’)’

(127)

Let two pairs of linearly independent particular solutions of Eq. (127) be g,, h,, g,, h,, which satisfy the similar initial conditions as Eq. (44).

260

JIYE XIMEN

Therefore, the first order Gaussian transfer matrix is given by (Ximen, 1988b) = [V1I2g: 9,

V1'2h: hX

gY 1/1/2g;

hY

V1/2h' Y

I

JGJ= 1.

(128)

The main purpose of this paragraph is to discuss electron beam optics in the x and y direction dually symmetric system, which is different from the rotationally symmetric system, as shown in Section V.A. At first, the first order description of an electron beam and the conservation of phase ellipsoid in the combined system are given as follows: X = GXa,

X = ( x , P ~ , Y , P ~ ) ~X,a = (Xa,Pxa,ya,Pya)T

xTa-lx= X , T G ~ ~ - ~ G X ,= X , ~ ; ~ X ,= 1.

(129) (1 30)

Secondly, up to the third order description is given by X = G(I

+ AM)Xa,

(131)

where AM is a 4 x 4 perturbation matrix consisting of all third order aberration coefficients D1, D,, D,,D4 (distortion); El, E2, E3 (super distortion outside Gaussian image plane); A,, A,, A, (astigmatism); F,, F,, F3,F4 (field curvature); C,, C,, C3,C4 (coma); and S , , S2,S3(spherical aberration) (Ximen, 1988b):

1

26 1

CANONICAL THEORY IN ELECTRON OPTICS

Therefore, in up to the third order approximation, the determinant of transfer matrix is always equal to 1 : IG(Z

+ AM)I = IGI

*

II

+ AM1 = 1.

(136)

This is what Liouville's theorem states (Ximen, 1981). In up to the third order approximation, the characteristic matrices a + A a and a, + An, are given as follows:

i

011

a+A.a=

a12

+ A% + A012

+ AOlh 012u + A012a

%a

a,

+ Aaa =

[

+ A012 + A022

A012 a22

a12, 022,

a33

+ A033

a34

+ A034

+ A034 a44 + A044 a34

+ A012a + A"22a + Aa33a + Aa34a

~33a 034,

1

(137)

+ Aa34a 044u + AfJ44, 034.

I*

(138)

The transfer formula is given by (a

+ Aa) = G(au+ Aa,)GT Aa, = AMa, + auAMT,

Aa

=

GAa,GT

- d2,) = ~22aA~l+ l . ~ I l a A Q 2 2 u- 2%2,A~12, A(011~~22 - 0 f 2 ) = 022 A011 + 011 A022 - 2a12 A012 = 0

A(~llu022a

A(a33aa440

- d 4 , ) =,,a

A033a

+ 033, A%.4u

A ( o ~ ~ o , - az4)=,a A o + ~ a,, ~ Aa,

- 2a34,

(139)

=0

Aa34,

=0

( 140)

- 2a3, Aa34 = 0.

From Eq. (140), we conclude that the x and y direction projected square emittances are conserved, even if third order aberrations exist in the combined system : (011

+ A011)(022 + A022) - (012 + Aa12)2 = (%a

+ h a ) ( % 2 a + Ag22,)

= a11a22 - a:, (a33

+ A033)(044 + A

(k. + Aa12a)2

= ~ , , , c T ~ ~-, of2, = constant E:

d

= (03301 + A033,)(%4, =

-

- (0334

(141)

+ Aa34I2

+ A 0 4 4 a ) - (034. + Aa34A2

a3,a, - ai4 = a33aa,a -

= constant E:.

(142)

262

JIYE XIMEN

C . Electron Beam Optical Computations in Round Electrostatic Lenses

Based on the theory of electron beam optics, as shown in Section V.A, the electron beam optical computations for rotationally symmetric immersion lenses and unipotential lenses have been performed: (i) an immersion lens consisting of two equiradial ( R = 1) coaxial cylinders ( L , = L , = 20.1) with a gap S = 0.2, while V, = 1, V, = 40 (all quantities measured in relative units). (ii) A unipotential lens consisting of three equiradial ( R = 1) coaxial cylinders ( L , = 19.34, L, = 1.2, L , = 19.34) with equi-gap S , = S2 = 0.26, while F,,,, = 10, V,,,,, = 20 (all quantities measured in relative units).

By successive overrelaxation method (Ximen, 1983, 1986), we can obtain the potential distribution in the meridional plane with high precision. Therefore, the axial distribution of electrostatic potential and its first, second and third order derivates can be accurately calculated by numerical derivative method. Using fourth order Runge-Kutta method (Munro, 1975; Ximen, 1983, 1986), we have solved the particular solutions to Gaussian trajectory equations. By using Simpson’s integration method (Munro, 1975; Ximen, 1983, 1986), all third order aberration coefficients for electrostatic lenses (i) and (ii) are obtained. For some typical initial phase diagram, i.e., a twodimensional ellipse with the major and minor radii x, = 0.25,pxa = 0.125 and y, = 0, pya = 0 respectively, we have calculated a series of phase diagrams at different observation p l a n e s , ~= -5.05, -4.04, -3.03, -2.02, - 1.01,0,1.01, 2.02, 3.03,4.04, 5.05 respectively. The characteristics for a phase diagram expressed in a polar coordinate system (p,d) include (a) p,,,-maximum polar radius; (b) &,,,-the corresponding polar angle at pmax;and (c)E - the phase area of the ellipse, which is defined as the emittances (Lawson, 1983):

The phase diagram computations for electrostatic lenses (i) and (ii) either with or without third order aberrations are listed in Table I-IV, under the previously mentioned initial conditions. Comparing the computed beam emittances with the theoretical emittances, &,heor = Z X , ~ ~=, 9.81747

x lo-,.

(144)

Therefore, we can find that beam emittances in two-dimensional phase space is conserved within the precision of about 1%.

TABLE I PHASEDIAGRAM CALCULATION FOR IMMERSIONLENS(i) WITHOUT ABERRATIONS z

Pmax

omax

E

-0.505000E+01 - 0.404000E+ 01 -0.303WE +01 -0.202000E +01 -0.101000E +01 0.000000E +00 0. lOlOOOE + 01 0.202000E+01 0.303000E+ 01 0.404000E+ 01 0.505000E+01

0.250000E+ 00 0.286367E+ 00 0.3633268 +00 0.430851E + 00 0.4997078 + 00 0.836919E +00 0.748415E +00 0.7598968+ 00 0.789035E+ 00 0.83241 1E + 00 0.889791E+00

0.000000E + 00 0.219034E+00 0.2339848+00 0.121149E+00 0.24 1023E + 0 1 0.490853E+ 01 0.473837E+ 01 0.457086E+ 01 0.44 1953E + 0 1 0.428043E+ 01 0.415693E+Ol

0.980100E-01 0.979578E-01 0.970473E-01 0.978717E-01 0.978478E-01 0.979797E-01 0.977862E -0 1 0.968628E -01 0.976614E-01 0.977812E- 01 0.978277E-01

TABLE I1 PHASEDIAGRAM CALCULAT~ON FOR IMMERSION LENS(i) WITHABERRATIONS Z

-0.505OOOE +01 - 0.404000E+01

-0.303OOOE +01 - 0.202000E + 01 -0.101000E+W 0.000000E+ 00 0.101OOOE + 01 0.202000E+ 0 1 0.303000E+ 01 0.404000E+ 01 0.505000E+ 01

Pma.

omas

&

0.250000E + 00 0.2863488 + 00 0.363441E+00 0.433539E+ 00 0.497294E +00 0.867071E+00 0.790423E+ 00 0.809496E+ 00 0.84291 1E + 00 0.891195E+ 00 0.954242E + 00

0.000000E+ 00 0.2186608 +00 0.233782E+ 00 0.130808E+ 00 0.243340E + 01 0.489114E +01 0.47 1544E +01 0.455481E + 01 0.440371E + 01 0.4265368+ 01 0.4 14299E + 01

0.974345E-01 0.973867E - 01 0.966752E - 01 0.972956E -01 0.972979E- 01 0.974469E -01 0.974532E-01 0.973951E- 01 0.973555E -01 0.973132E -01 0.9727478-01

TABLE 111 PHASEDIAGRAM FOR UNIPOTENTIAL LENS(ii) WITHOUT ABERRATIONS z

Pmsx

omax

&

-0.505000E + 0 1 -0.404000E + 01 - 0.303OOOE + 01 - 0.202000E+01 - 0. lOlOOOE 01 0.000000E+ 00 0.101000E+01 0.202000E 01 0.303000E+Ol 0.404000E+ 01 0.505000E 01

0.250000E+ 00 0.252087E+00 0.258365E+ 00 0.271335E+OO 0.320357E+00 0.3175968 + 00 0.313079E+00 0.292896E + 00 0.2983928 + 00 0.3064OOE + 00 0.315992E+00

0.000000E+ 00 0.651194E-01 0.129760E+ 00 0.2239298 + 00 0.477614E +00 0.912 126E -01 0.598959E+Ol 0.532644E-?2 0,9451638 - 01 0.139948E + 00 0.136017E + 00

0.980018E-01 0.9799 1 1E -01 0.979745E -01 0.979446E -01 0.974713E- 01 0.979780E - 0 1 0.979856E-01 0.97929 1E -01 0.979874E- 01 0.979678E-01 0.978161E-01

+

+ +

264

JlYE XIMEN TABLE IV PHASEDIAGRAM FOR UNIPOTENTIAL LENS(ii) WITHABERRATIONS z

-0.505000E + 01 -0.404OOOE+ 01 -0.303WE +01 - 0.202000E + 01 - 0.lOlOOOE + 01 0.000000E+ 00 O.lOlOOOE+Ol 0.202000E+Ol 0.303000E+ 01 0.404000E + 01 0.505OOOE+ 01

PIWlll

0.250000E +00 0.2520868 + 00 0.258354E+00 0.271197E+OO 0.321285E+00 0.318073E+00 0.314493E+00 0.2900878 + 00 0.293764E + 00 0.300727E+00 0.309485E + 00

&

t?n,x

0.000000E+ 00 0.651024E-01 0.129565E + 00 0.222548E+ 00 0.484207E +00 0.837809E-01 0.596043E + 01 -0.162972E - 01 0.733876E-01 0.122692E+ 00 0.164149E + 00

0.979731E -01 0.979624E -01 0.979459E - 01 0.979172E -01 0.973588E-01 0.97956 1 E -0 1 0.979388E - 01 0.979095E-01 0.979353E - 01 0.97957lE-01 0.977949E -01

Based on these computations, one can conclude that the electron beam emittances in phase space is conserved, even if third order aberrations exist. However, for the larger initial values (i.e., for larger aberrations), the shape of the phase diagram will be deformed by some nonlinear distortions, but the emittance is still conserved within definite precision.

AND DISCUSSION VI. CONCLUSION

The main points of the previous sections may be summarized as follows. The theory of canonical electron optics has been extensively developed in generalized position and momentum representations (see Section 111). Electron optical Hamiltonian function and canonical equations have been fully utilized to derive higher order aberrations in electromagnetic round lenses and multipoles (see Section IV). Finally, canonical aberration theory has been further extended in order to discuss electron beam optical characteristics in phase space for an electromagnetic round lens or a combined system consisting of round, quadrupole and octopole lenses (see Section V). In this final section, we will draw some important theoretical conclusions (i.e., Liouville’s theorem, symplectic conditions and Poisson brackets) that govern the behaviours of an electron beam traveling through an optical system. Meanwhile, some possible applications and future developments will also be supplemented within the scope of canonical electron optics.

CANONICAL THEORY IN ELECTRON OPTICS

265

A . Theoretical Conclusion We are going to show that the generalized canonical representations for describing electron beams satisfy the following classic mechanical relations. As shown in Section IV.A, V.A, and V.B, in up to the fifth order approximation, the canonical position and momentum vector X in four-dimensional phase space can be rewritten as follows:

AX3 = G J -(354 ,

ax,

(147)

c4 = j l { H 4 ) d z

Combining Eqs. (145)-(149), we get

x = GX, + G J - dE , ax,

E

= E4

+ + &6c

&6.

( 150)

According to classic mechanics (Arnold, 1978; Goldstein, 1980), the Jacobin matrix is defined as aX/aX,, which can be derived by means of Eq. (1 50):

Then the determinant of Jacobin matrix is given by

Evidently, a2c/aX: is a symmetric matrix:

ax: = (5) ax: ji) ( i , j = I ,..., 4). (5) ij

(153)

266

JIYE XlMEN

Obviously, a product of an arbitrary symmetric matrix and the antisymmetric fundamental matrix J (see Eq. (38)) has a zero trace: Tr( J $ )

= 0.

(154)

From Eq. (154), it is easy to show that

Consequently, the determinant of Jacobin matrix is given by

Irl=I G I .111

= 1.

(156)

Therefore, even if third order and fifth order aberrations exist, the determinant of the Jacobin matrix is equal to 1. This is what Liouville’s theorem states. In the first order approximation, the Jacobin matrix is equal to the Gaussian transfer matrix G (see Eqs. (47), (102), (128), which satisfies the symplectic condition (Arnold, 1978; Goldstein, 1980) GTJG = J, (157) where the antisymmetric fundamental matrix J satisfies J T = - J . Now we will extend the symplectic condition to higher order approximation. From Eqs. (151), (153), and (157), we obtain matrices T T and TT J T :

r T J r = J. Therefore, even if the third order and fifth order aberrations exist, the symplectic conditions hold. Noticing Eq. (151), i.e., r = aX/aX,, we can transform Eq. (1 58) into the generalized form

This symplectic matrix identity describes the important and invariant property under a canonical transformation X , -+ X and vice versa. In order to explain the symplectic structure of a canonical transformation, we will transform the canonical position and momentum representations into the equivalent Poisson bracket descriptions.

CANONICAL THEORY IN ELECTRON OPTICS

267

In classical mechanics, the Poisson bracket of two functions V and V with respect to the canonical variables X = (r,p)* or Xu = (r,,p,)* is defined as follows (Arnold, 1978; Goldstein, 1980):

au av av av

-

[V, V l x = [V, V]r,p = - - - - - = ( & ) * J ( E ) ap a r a r ap

(160)

where the square bracket denotes a Poisson bracket and the superscript denotes a transposed matrix. Using Eqs. (160) and (161), the symplectic condition Eq. (159) can be equivalently expressed in terms of Poisson bracket:

[ [ X , X I D = J = [[Xa,XuIJI. (162) The double brackets denote a square matrix consisting of different Poisson brackets. Precisely speaking, the ij element of this square matrix is a Poisson ]. Eq. (162) states that the funbracket [ X i , X j ] or [ ( X u ) i , ( X u ) jConsequently, damental Poisson brackets are invariant under the canonical transformation Xa -,X and vice versa. In fact, it is equivalent to state that canonical transformation is a group in phase space. B. Concluding Discussion

It has been shown in Section IV that canonical aberration theory has remarkable advantages for completely calculating higher order geometrical and chromatic aberrations in rotationally symmetric or multipole electromagnetic systems and for fully examining the possibility in correction of spherical and chromatic aberrations. It has been demonstrated in Sections V.A and V.B that canonical electron beam optics not only can deal with primary order and higher order perturbations to both transfer matrix and characteristic matrix for electron beam, but also can investigate influences of aberrations upon the transport of electron beams. It is worth noting that electron beam optics for combined electromagnetic focusing deflection systems with rectilinear or curvilinear axis has already been discussed in complex six-dimensional phase space (Ximen, 1987b, 1988c). It is obvious that canonical electron optics possessing symplectic structures and group properties enables us to develop a general theory for describing electron optics in different types of electromagnetic systems (for example, Dragt, 1981, Dragt and Forest, 1986).

268

JIYE XIMEN

APPENDIX A. Fifth Order Aberration CoefJicients in Round Lenses In Eq. (66), the 4 x 4 matrix A, has been defined, whose entries S,, 8,, for different indices i, j are listed as follows: For All, 6, = G, 62 = I, 6 3 = 9, 6, = H

a3, and 6, For A 1 2 9

6, = 2H,

6,

= 2S,

6,

= 2h,

6,

= 25

For A13

6, = 29,

6, = 2s,

63

=42,

84

= 2h

6, 6,

= I,

62 =

6, = s,

6,

=

= 45,

6, = 4 J t ,

6,

6, = 4 T

= 4h,

6, = 4ht,

d3 = V ,

For

7

9

For A 2 2 9

For A23

9

It,

= 4t,

s

6,= 4t

For

61 = 2St,

62 = 2 H t ,

63

= 2ht,

6, = 2Jt

For A 3 3 9

6,

= u,

6,

= Ut,

6,

= n,

6,

=0

For A349

6,

= 2st,

6, = 2g',

6,

= ut/2,

6,

= 2h'

(163)

For A,,, 6, = It, 63=g t 6, = H t . 62 = Gt, In Eq. (691, the 4 x 4 matrices aiand 0 : have been defined, whose entries wl, w 2 , a,,and w, for different indices i are listed as follows: 1

For aland a;

w1 = A,

w2 = D,

w3 = e ,

w, = E

For a, and a;

o1= 2E,

w2 = 2F,

w3 = c,

w, = 2C

For a, and a;

o1= e,

w, = f ,

w3

=o,

0,=

For a, and a:

w1 = D,

~2

~3

=f,

a4

=E,

c

(164)

= F.

In Eq. (163), G, H, I, J , S, T, g, h, s, t, u, u, n, etc. are fifth order geometrical aberration coefficients, which can be expressed in terms of three general aberration integration functions:

CANONICAL THEORY IN ELECTRON OPTICS

269

where K ~ K, ~ K, ~ K, ~ K~, are the dummy arguments, which are constituted by different combinations of ro, r B , rk, rh. Therefore, we obtain altogether 20 fifth order geometrical aberration coefficients: G = FL(r;,2r;rh2,rb4; r;,r?) Gt

H

=

FL(r:, 2r,2rh2,rk4;r:, rk2)

= FL(r;,2rirh2,r$

rarB,r&)

Ht = FL(r:, 2r,2rk2,ri4; rarp,r&) I = FL(r;, 2 r i r 7 , rb4;rz, rL2) I t = FL(r:, 2r:rk2, rk4;r;, 12)

J

=

FL(r:r;, 2rarpr&, rL2rh2;r;, r?)

= FL(r:r;,

2rursr(zr;l,rL2r?; r;, rk2)

S

= &,(r,2r;,

rb2r,2 + rirk2,rk2r$ rarB,r&) = S'

T

=

FL(r:r;, 2rararkrh,ri2rh2;r,rB, rhrb) = Tt

g

=

FM(r&2r$rb2,r;)

J

(166)

g t = FM(r:, 2r,2rk2,rk4)

h = F M [ r i r a rBrh(rarp)', , r;dr&]

h+ = FM[r,jrB,ruri(rarB)',rL3rb] s = FM(r:r;, r?rL2

+ rirh2,rk2 r?)

= st

t = ~,(rzrg, 2rarpr~r;P, rk2r;pZ)= t + u = F,(r;,r?),

ut

=

F,(r;, ri2)

v = FN(rarB,r&),

n

= J;(N3,v)dz = n t .

In the above formulae, G and G t etc., denote a pair of associated coefficients, in which the dummy arguments in functions F',,,'F FN are interchanged as follows: Ki(ra,rh, rB,rb) * Ki(rB,rh, r a ,rh),

(i

=

1,. . . , 5 ) .

(167)

270

JIYE XIMEN

B. Aberration Formulae for Sextupole, Octopole, Decapole, Twelvepole, and Fourteenpole Systems Obviously, all kinds of aberrations in multipoles may be expressed by a universal truncated zp-polynomial with descending power:

P:(zB; a J ,a,-

19.

* . a,+ 1, a,) 9

+

+ ... +

= u J ( z ~ ) ~~ J - l ( z p ) " - '

where a,, a J P l , . . . ,ar+,, a,(J > J - 1 2 constants.

+ a,(zp)',

U~+~(Z~)'+'

2I

+ 1 >I)

are numerical

1. Electronmagnetic Sextupoles ( N = 3)

HN

-u',2-

N);:(

= =

(:;) (

'OS 28 -sin28

k 3

--(x3

-

3xy2)

)3 12p2

P:(zP; 1,4,6)

P:(zp; 1, 7, 21, 21) = (cos48)

k3r:

PAo(zp; 1, 10,45, 720/7, 108) sin48 12960p6 2 cos 28 + cos 48 -2sin28+sin48

A2y (A2x)

(;::>,

=

[

1

cos 8 + -COS 58 $P:(,B;

1,7,21,63/2, 21)

sin 8 - -sin 58 P;(zp; 1, 7, 21, 35, 35, 21)

CANONICAL THEORY IN ELECTRON OPTICS ?lx) AIY N P

=

2{

1,7,21, 147/5,84/5)

-(fz:)P:(z/?;

P:(z/?; 1, 7,21,63/2,21) -

8.5

(

c0s28 )P:(,8; 1, 7, 21, 35, 35,21) -sin28

2. Electromagnetic Octopoles (N = 4)

k 4

H N

u1,2 - - --(x"

=

(

cos 30 -sin38

-

6x2y2+ y")

)3 20B2

P:(zB; 1, 5, 10, 10)

Pz(z/?;1,9, 36, 84,108, 60)

(A2x) = ( c o s 5 8 ) k3r2 A2y N sin58 20800p6

Pi3(z/?;1, 13,78,286, 2080/3, 7800/7, 7800/7, 520)

x

2cos 38 + cos 50

P$(z/?; 1,9, 36, 84, 612/5, 108,48)

=(

- cos 30

?ox)

Aoy

NN

AOY

NP =

>-

- cos 48

sin3O-cos48

-:

k 'r;

2888'

P:(z/?; 1,9, 36, 84, 126, 126, 84, 36)

{ ( : z i : ) P ; ( z / ? ; 1,5, 10,10,5)

+

-sin 38

27 1

272

JIYE XIMEN

("") AIY

NP

- 13k2r' --

{ - ( ~ ~ i ) P ~ ( z f i1,9,36, ; 84, 1548/13, 1260/13,480/13)

2880b2 )P;(zp; 1,9, 36, 84,612/5, 108,48) -

2o ( 'OS3' )P:(zp; 13 -sin38

3. Electromagnetic Decapoles (N

=

(A,") Aly

(A,") A2y

(

'OS4'

-sin48

)

=

1,9,36,84, 126, 126,84,36)

5)

S P : ( z p ; 1,6, 15,20, 15) 30p2

=(cosO) k2r; P:'(zp; 1, 1 1 , 55, 165, 330,440, 715/2, 275/2) sin6 825p4 60) k3rh0 PA6(zp; 1, 16, 120, 560, 1820,47760/11, sin68 36000p6

= (cos

2324013, 30800/3, 9750,6000, 5580)

1, 6, 15,20, 15)

P:'(zp; 1, 11, 55, 165, 330, 1375/3,

440,275, 275/3) P:'(zp; 1, 11, 55, 165, 330, 462,

462,330, 165,55)

(i:')Np-2 =

{ ( ~ ~ ~ ~ ) P f1,6, ( z 1520, p ; 15,6)

+ (-'OSsin4848) - 6zp]

CANONICAL THEORY IN ELECTRON OPTICS

{ -(f::)P:'(z&

=

'ly

NP

273

1, 11, 55, 165, 330, 1815/4,

335518, 1925/8,275/4)

P:'(zp; 1, 11, 55, 165, 330, 1375/3, 440,275,275/3) -

32 (-sin40 )f'il(zfl; 1, 11, 55, 165, 330, 462,462, 330, 165, 55) 'OS4'

4. Electronmagnetic Twelvepoles ( N

HN - --(x6 k -u,,z

= 6)

+ 15xZy4- y 6 )

- 15x4yZ

6

Pi3(zp;1, 13, 78, 286, 715, 1287, 1690, 7826/5,4641/5, 273)

5k3rh3 PAg(zB; 1, 19, 171,969, 3876, 11628, sin78 301644p6 352317/13,550221/11,809172/11,85652, 77273, 51471,

= (cos76)

Azy (A2x)

22743,25 173/5) 2 cos 58 + cos 10 -2sin58+sin78

1, 7,21, 35, 35, 21)

Pi3(zp;1, 13, 78, 286, 715, 1287, 11986/7, 1368, 1209, 585, 156) (A(+) Aoy

NN

=(

-cos 50 cos 68 k2rh' P13(zB;1, 13, 78, 286, 715, 1287, sin58-cos68 936p2 +

)-

1716, 1716, 1287,715,286,78)

274

JIYE XIMEN

cos 8

Pi3(zP; 1, 13, 78, 286,715, 1287,

32422119, 31486/19,21567/19,9555/19,2184/19) cos 5 8 . cos 68 )Pi3(z/3; 1, 13, 78, 286, 715, 1287, -k 19(-sin 58 cos68 14

-

1198617, 1690, 1209,585, 156)

- 28

(

‘OS

19 -sin58

)Pi3(zP; 1,13,78,286,715,1287, 1716,1716,

1287, 715, 286, 78) 5. Electromagnetic Fourteenpoles ( N = 7)

HN - - 4k x 7 - 21X5y2 + 3 w Y 4 - 7xy6) -u1,2

rox)(t:;) =

AOY

N

(t:;)N ):(: =

7

=

(

‘OS 68 -sin68

) -!6P:(zP; 56b2

196084Pf(zly; k2rh’

1, 8, 28, 56,70, 56,28)

1,15, 105,455, 1365,3003,5005,6405,

6230,4410,2058,490)

5k3r;6 PE2(z/3;1,22,231, 1540,7315,26334,74613, sin88 482944P6 852544/5,4150608/13,6424880/13,633864,670320,2882572/5,

= (c0~88)

A2y (A ~x)

392392,200508,68992,60368/5) 2 cos 68 + cos 88 - P ; ( Z ~ ; 1, 8, 28, 56, 70, 56, 28) -2sin68+sin88

P:’(zP; 1, 15, 105,455, 1365, 3003,

5005,25725/4,6405,4900,2793,2205/2,245)

CANONICAL THEORY IN ELECTRON OPTICS

275

P:’(zp; 1, 15, 105, 455, 1365, 3003, 5005,6435,6435,5005,3003, 1365,455, 105)

{

kr: (cos 88) Py(zp; 1, 8, 28, 56, 70, 56, 28, 8) 112 sin88 - sin 60 1

1

~

3 COS 8 P:’(zg; 1, 15, 105,455, 1365, 3003, 5005, {-(sin 8)

70665/11, 69930/11, 52430/11, 28518/11, 10290/11, 1960/11) cos 68 cos 78 11(-sin 68 cos 70 P:’(zp; 1, 15, 105,455, 1365, 3003, 8

-

5005, 25725/4,6405,4900,2739,2005/2,245) -

‘6 11

(

c0s68 ) P i 5 ( z F ; 1, 15, 105,455, 1365,3003,5005,6435, -sin60

6435,5005,3003,1365,455, 105)

ACKNOWLEDGMENTS The author is extremely grateful to Prof. Y. Li of Shanghai Institute of Mechanical Engineering for providing the Scientific Word Processor Software and also wishes to thank Asst. Prof. Z. Liu of Peking University for participating in electron beam optical computations.

REFERENCES Arnold, V. 1. (1978).“Mathematical Method of Classical Mechanics.” Springer-Verlag,New York. Banford, A. P. (1966).“The Transport of Charged Partical Beams.” E. & F. N. Spon Ltd., London. Beck, V.D. (1979). Optik 53,241. Brown, K. L. (1972). SLAC Report No. 75. Brown, K. L. (1981).Nucl. Instr. Meth. 187, 51. Crewe, A. V., and Kopf, D. (1980a). Optik 55, 1. Crewe, A. V., and Kopf, D. (1980b). Optik 56, 391.

276

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Dragt, A. J. (1981). “Lectures on Nonlinear Orbit Dynamics.” In Physics of High Energy Particle Accelerators. (Carrigan, R. A., Huson, F. R. and Month, M., eds.). Amer. Inst. of Phy., New York. Dragt, A. J., and Forest, E. (1986).“Lie Algebraic Theory of Charged Partical Optics and Electron Microscopes.” In Ado. in Electronics and Electron Physics (P. W. Hawkes, ed.) Vol. 67. Academic Press, Orlando. Glaser, W. (1933a).Z. Physik 81,647. Glaser, W. (1933b).Z. Physik 83, 104. Glaser, W. (1935).Z. Physik 97, 177. Glaser, W. (1936a).Z. Tech. Phys. 17,617. Glaser, W. (1936b). Z. Physik 104, 157. Glaser, W. (1937). In “Beitrage Zur Elektronenoptik.” (Busch, H. and Bruche, E., eds.) Barth, Leipzig. Glaser, W. (1938).Z. Physik 109, 700. Glaser, W. (1952).“Grundlagen der Elektronenoptik.” Springer, Wien. Goldstein, H. (1980).‘‘Classical Mechanics.” (2nd Ed.). Addison-Wesley Pub. Comp., California. Hawkes, P. W. (1980). Optik 56, 123. Hawkes, P. W., and Kasper, E. (1989). “Principles of Electron Optics.” Academic Press, London. Koops, H. (1978). Electron Microscopy, 9th Int. Congr. on Electr. Micro., 111, 185. Lawson, 3. D. (1983).In “Adv. in Electronics and Electron Physics.” (Septier, A. ed.) Suppl. 13C. Academic Press, New York. Li, Y. (1986).Optik 74,65. Li, Y., and Ni, W. (1988). Optik 78,45. Munro, E. (1975). “A Set of Computer Programs for Calculating the Properties of Electron Lenses.” Cambridge Univ. Eng. Dept., Report No. CUED/B-ELECT/TR45. Rose, 0.(1968). Optik 27, 466, 497. Rose, 0.(1968/69). Optik 28,462. Rose, 0.(1981).Nucl. Instr. Meth. 187, 187. Scherzer, 0. (1933). Z. Physik 80, 193. Scherzer, 0.(1936a). Z. Physik 101,23. Scherzer, 0.(1936b). Z. Physik 101,593. Scherzer, 0.(1937). In “Beitrage Zur Elektronenoptik.” (Busch, H. and Bruche, E., eds.) Barth, Leipzig. Scherzer, 0.(1947). Oprik 2, 114. Seeliger, R. (1949).Optik 5,490. Seman, 0.I. (1958).“Theoretical Basis of Electron Optics.” Higher Education Press, Beijing. Shao, Z. (1987).Optik 75, 152. Shao, Z. (1988).Reo. Sci. Instr. 59, 2429. Shao, Z., and Crewe, A. V. (1987).Journ. Appl. Phys. 62, 1149. Shao, Z., Beck, V. and Crewe, A. V. (1988). Journ. Appl. Phys. 64, 1646. Sturrock, P. A. (1951a).Proc. Roy. Soc. (London) A210,269. Sturrock, P. A. (1951b). Phil Trans. Roy. Soc. (London) A243, 387. Sturrock, P. A. (1952). Phil. Trans. Roy. Soc. (London)A245, 155. Sturrock, P. A. (1955). “Static and Dynamic Electron Optics.” University Press, Cambridge. Wu, M. (1957). Acta Phys. Sinica 13, 181. Ximen, J. (1981).Optik 60,93. Ximen, J. (1983).“Principles of Electron and Ion Optics and Introduction to Aberration Theory.” Science Press, Beijing. Ximen, J. (1986). “Aberration Theory in Electron and Ion Optics.” In Ado. in Electronics and Electron Physics (Hawkes, P. W., ed.) Suppl. 17., Academic Press, New York.

CANONICAL THEORY IN ELECTRON OPTICS Ximen, J. (1987a). Optik 76, 32. Ximen. J. (1987b). Optik 76, 89. Ximen, J. (1988a). Optik 78,95. Ximen, J. (1988b). Optik 79, 165. Ximen, J. (1988~).Optik 80, 141. Ximen, J. (1990a). Optik 84,83. Ximen, J. (1990b).(to be published in Journ. Appl. Phys. in Dec. 15, 1990). (to be published in Journ. Appl. Phys. in Dec. 15, 1990). Ximen, J. (1990~). Ximen, J. and Crewe, A. V. (1985). Optik 69, 141. Ximen, J. and Liu, Z. (1991).(to be published in Journ. of Electronics, China).

277

This Page Intentionally Left Blank

Subject Index A

the four laboratories for electron microscopy, 211, 216, 217, 218, 220, 221, 222, 224. 225 Bethe ridge, 57, 109 Bleisteiner, 164 Boersch, H., 146, 154, 159, 173, 174, 175, 216, 218 Bruche, E., 146, 158, 211, 213, 218, 219, 22 1

Abbe, E., 215 Aberration, 231-233 chromatic, 83, 188 of fifth order, 239-240, 244-245 combined, 245-246 intrinsical, 245-246 of higher order, 232-233, 244-245, 247 from lower to higher order, in 2N-pole system, 248, 254 spherical, 182 of third order, 238, 240, 244-245 for 2N-pole electromagnetic system, 250 in electric and magnetic multipole, 251-252 in electric multipoles, 253 Aberration coefficient, 231 fifth order geometrical, 246, 269 in round lens, 231, 268 third order, geometrical, 247, 256, 260 Aberration formula, 231, 270 for decapoles, 272 for fourteenpoles, 274 for octopoles. 271 for sextupoles, 270 for twelvepoles, 273 AEG Company (Allgemeine Elektrizitats Gesellschaft), 140, 158, 211, 216. 219, 220, 221, 225 Antisymmetric fundamental matrix, 241. 266 Application laboratory, 144, 145, 148

Calculation of aberration, 231 by eikonal method. 231-232 by trajectory method, 231-232 Canonical aberration theory, 231, 233, 239, 244, 250, 255: 264 Canonical electron beam optics, see Electron beam optics Canonical higher order aberration, 231 in electromagnetic multipole, 231, 247 in electromagnetic round lens, 231, 245 Canonical theory in electron optics, 231-274 Canonical transformation. 266-267 Cathode-ray oscillograph, 128, 130-132. 137, 143, 148. 152, 162. 172, 173 Characteristic matrix, 256-257. 261, 267 Classic mechanics, 233, 239-240, 256, 265 Compton angle. 57 peak. 58. 109 Conventional aberration theory, 231, 233, 236 Convolution, 181 Cosslett, 155. 159. 164. 165, 172, 173 Cranz colloquium, 129

B Beam energy spread, 189 fractional current radius, 181. 186 root mean square radius, 181, 188, 100, 192 profile, 180, 186, 187 Beischer, D., 213. 214, 218 Berlin, wartime air raids, 216, 220, 225

D

Defocus, 180, 182 Discontinuity of potential, 2-3 Diisseldorf Society, see Gesellschaft f i i I Ubermikroskopie 279

280

SUBJECT INDEX

E Electromagnetic system, 232-233 deflection, 232 focusing-deflection, 255, 267 with curvilinear axis, 233, 255, 267 with rectilinear axis, 233, 255, 267 rotationally symmetric, 232-233, 236, 239 Electron beam optics, 233, 255, 267 in focusing-deflection system, 255, 267 with curvilinear axis, 233, 255, 267 with rectilinear axis, 233, 255, 267 in magnetic round lens and sextupole system, 255 in rotationally symmetric system, 255 in round lens, 231, 233, 255 in round, quadrupole and octopole lenses, 231, 233, 255, 258 Electron beam optical computation, 231, 233, 262 in round electrostatic lens, 231, 233, 262 Electron energy-loss spectroscopy (EELS) angular and spatially resolved, 73 modes, 71 transmission electron microscope, 69 spectrum contributions, 49 ionization of inner shells, 56 cross-sections, 57 energy loss near edge structure (ELNES), 56 extended energy loss find structure (EXELFS), 56 partial cross-sections, 58, 104 plasmon-loss region, 54 cut-off angle O,, 55 dielectric theory, 54 mean-free-path, 58, 104 Poisson distribution, 58 surface plasmon, 55 Electron filter lenses, 64 Castaing-Henry filter, 66 Mollenstedt analyzer, 65 0-filter, 67 Electron microscope (wartime, Berlin) electric lenses, 213, 216, 218 emission type, 213, 216 laboratories for applications, 211, 216, 218 for construction, 211, 214, 216, 221, 224, 225

magnetic lenses, 211, 212, 213, 214, 216-218 magnification of the first instrument, 212 patents, 212, 214 serial production, 214, 224 transmission type, 212, 214 Electron microscopy (wartime, Berlin) comments on the future (1931), 211 objects bacteria, 216, 218 bacteriophages, 216, 219 cancer cells, 217 chloroplast, 216 colloids, 214 collagen, 219, 220 diatom, 213 epithelium, 213 erythrocytes, 216, 223 fibers, 217, 219, 220, 223 fibrin, 216, 223 fly, 213 mitochondria, 214 molecules, 216 protein of muscle, 218 rickettsial, 219 surface of metals, 217 thrombocytes, 216 virus, 216, 218, 219 preparation techniques, 213, 214, 215, 219, 220 Electron optical refractive index, 232, 236 Electron optics laboratory, 144, 145, 147, 148, 150, 152 Electron scattering elastic, 44, 76 characteristic angle &, 48 mean-free-path, 47 inelastic, 47, 76 characteristic angle & , 48 mean ionization potential, 48 ratio of total inelastic to elastic cross-sections, 49 multiple, 58 most probable energy loss, 61 top-bottom effect, 101 Electron spectrometer prism, 62, 68 Wien filter, 63 Electron spectroscopic diffraction, 71, 105 amorphous films, 105 Compton scattering, 109 Debye-Scherrer rings, 108

28 1

SUBJECT INDEX single-crystals, 111 ALCHEMI. 117 Kikuchi lines, 113 bands, 113 Laue-zones. 116 streaks, 115 small-angle diffraction, 107 Electron spectroscopic imaging (ESI), 70, 75 contrast tuning, 99 elemental mapping, 102 most probable loss imaging, 100 plasmon-loss imaging, 91 contrast transfer function. 93 phase contrast, 93 scattering contrast, 91 selective, 95 structure-sensitive imaging, 96 zero-loss imaging, 76 Bragg contrast, 85 contrast enhancement, 79 dark-field, 84 lattice defects. 88 Lorentz contrast, 90 scattering contrast, 76 transmission. 76 Z-ratio contrast, 89 Electrostatic potential, 236, 248, 258 Emittance, 256, 261-262, 264 EM, magnetostatic, 158-160, 164, 165, 168, 169, 174 EM Society, German, 157, 158, 160, 174 EM Society, international, 165, 168, 172, 174 Energy-filtering transmission electron microscope, 43

Four-dimensional phase space, 255-256, 265 representation, 242-243 Freundlich, M.M., 128, 131, 134, 137-139, 213

G Gabor, D., 211 Gaussian canonical equation, 242, 259 optical property, 237, 249-250 trajectory equation, 238, 242, 259 transfer matrix, 256, 260, 266 Generalized oscillator strength (GOS), 47, 57 Gesellschaft fur Ubermikroskopie e. V. zu Diisseldorf, 156-158, 160-162, 166, 171, 174 Glaser, 144, 153, 159, 166 Griinewald, 173, 175

H Hamiltonian equation, 234-235 function, 233-235, 239-240, 244, 248-249, 254, 259 mechanics, 234-235 representation, 232-233, 239 in position and momentum phase space, 232

I

F Four-aperture lens. 22-36 axial potential, 22, 23-24 energy scanning, 31-36 focal and midfocal lengths, 24-31, 33, 35 linear magnification, 24, 31, 33, 34, 35, 36 polynomials for voltage ratios, 33-35 reflection symmetry, 23 retarding, 24, 35-36 spherical aberration coefficients, 24, 31, 32, 33, 35. 36

Integral equation accuracy of results, 40 for conducting and dielectric bodies, 3-5 for conductors, 3, 22-23 for ion channel, 17, 19, 20 numerical solution, 6-15, 17, 19, 23, 38 for space-charge problems, 37 International Federation of Electron Microscope Societies, see EM Society. international Ion optical column, 178 source size, 192

282

SUBJECT INDEX

Ion channel, 16-22 dipolar effects, 20-22 electric field, 19 energy barrier, 16, 20-21 image potential, 16-18 potential drop, 19 potential profile, 21

J Jacobin matrix, 265-266

K Kinder, E., 217, 221 Knoll, M., 128-130, 134, 137, 146, 175, 176, 211, 212, 213, 214, 217 Krause, F., 213-215

L Lagrangian equation, 234-235 function, 234 mechanics, 234-235 representation, 232-233, 239 in position and slope configuration space, 232 Leitz, 159, 161, 169 Lie algebraic theory, 233, 255 Liouville’s theorem, 255-257, 261, 264, 266

M Magnetic induction, 236 Magnetic vector potential, 236, 248, 258 Mahl, H . , 146, 159, 164, 173-175, 214, 216, 217, 218 Marton, L., 211, 213, 215 Matthias, A , , 128, 130-132, 137, 139, 175, 211 Method of moments, see Moment method Moment method basis function, 6, 40 coefficients, 7, 17, 19, 23, 38 analytical evaluation of, 7, 8-15 physical meaning of, 8 nonuniform division, 6, 40 circular annular subarea, 8-9, 12-13, 14 cylindrical subarea, 8, 9-10, 13, 14

volume element, 6 cylindrical, 10-12, 14-15 weighting function, 6 Muller, H.O., 213, 216 Multipole system, 232 decapoles, 248, 270 fourteenpoles, 248, 270 octopoles, 248, 270 sextupoles, 248, 270 twelvepoles, 248, 270 of 2N-pole, 248. 250 electrostatic, 248 magnetic, 249

N Neubabelsberg, 132, 140 North Rhine-Westphalian Society for Super Microscopy, see Gesellschaft fur Ubermikroskopie 0

Optimization of lens, 194 of optical system, 195, 197

P Patents, 127, 129, 133, 137, 139, 140, 142, 158-160, 173 Perturbation matrix, 256-257, 260 Perveance, 37, 39 Petersen, 156, 160, 164 Phase diagram calculation, 263-264 for immersion lens, 263 for unipotential lens, 263-264 Philips, 166, 168 Picht equation, 24 Poisson bracket, 264, 266-267 equation, 1 Position and momentum aberrations, 233, 243 and slope aberrations, 238 Power series expansion, 236-237 of electrostatic potential, 236, 258 of Hamiltonian function, 240, 248 of magnetic vector potential, 236, 258 of variational function, 237

283

SUBJECT INDEX

R Radiation damage, 105 Ramsauer, C., 21 1 RCA. 154, 155, 160. 166 Reflexion electron microscopy, 146, 173 Riems. 148, 150, 153 Rudenberg, R . , 140, 141, 142. 212. 214 Ruska. E., 127-129, 137-139, 144-146, 157-159, 166, 168, 172, 173, 175, 176, 211-214, 218, 222-224 Ruska, H., 127, 140, 141, 143-145, 147, 151-154, 157. 166, 169, 171-172, 214-216, 219, 222 Ruska. Elisabeth. Hede, Julius, 214

S

Scanning electron microscope, 214 Scanning transmission electron microscope (STEM), 67 Scherzer’s theorem, 247 Siebeck, R., 141, 145, 152, 214, 216 Siemens & Halske, 142-144, 151-153, 156-158, 164, 167-168 Siemens Company, 212, 216, 217, 221-225 Siemens-Schuckert , 133- 135, 137, 140- 141 SIMS lens, 37-39 Sjdstrand, 146, 165 Space-charge effects, 2, 8. 16, 36-39. 207 on ion beam profile, 38-39 Steenbeck, M., 212 Surface microscopy, see Reflexion electron microscopy Symplectic condition. 264, 266 Szilard, L., 21 1

T Trajectory computation, 24, 37, 38-39 Transport characteristics, 255-256

U Ultra microtome, 167, 168, 169 Ultra microtomy, 174

V Variational function, 232, 237-238 von Ardenne. M.. 146, 211, 214, 218, 221, 222, 225 von Borries, B . , 212, 213, 214, 218. 222, 224 von Buol, 141, 142, 144, 148, 149, 150 von Laue, 143, 154, 159, 162-163 von Siemens, Carl Fredrich, 143 von Siemens, Ernst, 152, 153 von Siemens, Hermann, 142-144, 157

W Wolpers, C., 146. 147, 153. 159, 214. 216, 217, 219, 220, 222, 223, 225 Wronsky determinant, 242

2

Zeiss Company, 142, 214, 218, 221

This Page Intentionally Left Blank

Cumulative Author Index, Volumes 1-81 A

Ables, H. D.: see Kron, G. E. Abraham, George: Multistable semiconductor devices and integrated circuits, XXXV, 270 Abraham, J. M., Wolfgang, L. T., and Inskeep, C. N.: Application of solid-state elements to photoemissive devices, XXII B, 671 Abraham, E.: Relaxation processes in ferromagnetism, VI, 47 Adams, J . : X-ray detection by channel electron multipliers, XXII A, 139 Adams, K. M., Deprettere, E. F. A,, and The gyrator in Voorman, J. 0.: electronic systems, XXXVII, 80 Ahmad, N., Gale, B. C., and Key, M. H.: Time resolution limitations in single-stage image converter photography, XXVIII B, 999 Aikens, R.: see Hynek, J. A . Airey, R. W.: see McGee, J. D.; Morgan, B. L. Alexander, J. W. F., and Burtt, R. B.: Bombardment-induced conductivity targets for image orthicons, XVI, 247 Allan, F. V., and Garfield, B. R. C.: The study of photocathode composition by microbalance methods, XVI, 329 Allen, J. Denton: see Malling, L. R. : The Mariner IV spacecraft television system, XXII V, 849 Alpern, M., Bijaoui, A,, and Duchesane, M.: Sur le gain en sensibilitk, dans I’infra-rouge Proche, de la camera Clectronique par rapport a la photographie classique, XXII A, 5 Amboss. K.: The analysis of dense electron beams, XXVI, 1 An, M., Gertner, I., Rofheart, M., and Totimieri, R.: Discrete fast Fourier transform algorithms: a tutorial survey, LXXX, 1 Anderson, A . E.: see Wachtel, M. M. , and Schneeberger, R. J.:

Limitations to resolving power in electronic imaging, XVI, 299 Anderson, D. G . : see Flanagan, T. P. Anderton, H.: An x-ray image intensification system for use with a point projection x-ray microscope, XXII B, 919 , and Beyer, R. R.: Dynamic imaging with television cameras, XXVIII A, 229 Arsac, J., Galtier, Ch., Ruggiu, G., Van Khai, Tran, Vasseur, J . P.: The Edelweiss system, XLVIII, 202 Asano, M.: see Hirashima, M. Ashworth, F.: Field emission microscopy, 111, 1 Aslam, M.: see McGee, J . D. Aukerman, L. W.: see Seib, D. H. Auld, B. A.: see Meeks, Steven W.

B Bacik, H., see McGee, J . D. Baier, P. W., and Pandit, M.: Spread spectrum communication systems, LIII, 209 Bakken, G . S.: see Jordan, J. A,, Jr. Bakos, G.: see Hynek, J. A. Bakos, J. S . : Multiphoton ionization gf atoms, XXXVI, 58 Baldinger, E., and Franzen, W.: Amplitude and time measurement in nuclear physics, VIII, 255 Balk, Ludwig Josef: Scanning electron acoustic microscopy, LXXI, 1 Ball, Jack, Niklas, Wilfrid F., Dolon, Paul J., and Ter-Pogossian, M.: Image intensifying chains for medical scintillation cameras, XXII B, 927 Baranova, L. A , , and Yavor, S. Ya.: The optics of round and multipole electrostatic lenses, LXXVI, 3 Bargellini, P. L., and Rittner, E. S.: Advances in satellite communications, XXXI, 119

285

286

CUMULATIVE AUTHOR INDEX. VOLUMES 1-81

Barlow, G . E., Overstone, J. A., and Thonemann, F. F.: Automatic data processing in the physical sciences, XI, 185 Barnes, Aaron: Theoretical studies of the large-scale behavior of the solar wind, XXXVI, 1 Barnett, M. E., Bates, C. W . , Jr., and England, L.: Electron optics of a photoconductive image converter, XXVIII A , 545 Barton, G.: see Hynek, J. A. Barybin, A. A.: Electrodynamic concepts of wave interactions in thin-film semiconductor structures. I, XLIV, 99 : Electrodynamic concepts of wave interactions in thin-film semiconductor structures. 11, XLV, 1 Baskett, J. R.: see Liu, J. D. Bastard, G., Delalande, C . , Guldner, Y., and Voisin, P.: Optical characterization of 111-V and 11-VI semiconductor heterolayers, LXXII, 1 Bates, C. W., Jr.: see Barnett M. E. -: Scintillation processes in thin films of CsI(Na) and CaI(T1) due to low energy x-rays, electrons and protons, XXVIII A, 451 Bates, David J., Knight, Richard I . , Spinella, Salvatore, and Silzars, Ark: Electron-bombarded semiconductor devices, XLIV, 221 Bates, R. H. T., and Mnyama, D.: The status of practical Fourier phase retrieval, LXVII, 1 Batey, P. H., and Slark, N. A , : Performance of the transmission secondary-electron image intensifier, XXII A, 63 Baud, C.: see Rougeot, H. Baum, P. J., and Bratenahl, A.: Magnetic reconnection experiments, LIV, 1 Baum, W. A.: see Frederick, L. W.; see Hall, J. S.; see McGee, J. D.; see Wilcock, W. L. : A critical comparison of image intensifiers for astronomy, XXVIII B, 753 : Laboratory evaluation of image tubes for astronomical purposes, XVI, 391 : Magnetic focusing of image tubes, XXII A, 617

The potentialities of photoelectronic imaging devices for astronomical observations, XII, 1 Baumgartner, W.: A light amplifier with high light output, XXVIII A , 151 Beckman, J. E.: Application of information theory to the evaluation of two image intensifier tubes, XXII A, 369 , and Egan, D. W.: A search for molecular hydrogen in the interstellar medium, XXVIII B, 801 Beesley, J., and Norman, D. J.: High-resolution phosphor screens, XXII A, 551 Bell, A. E.: see Swanson, L. W . Bellier, Mlle M.: see Wltrick, G. BL.nC, G. J.: see Geneux, E. BenC, Georges J.: Foundations and preliminary results on medical diagnosis by nuclear magnetism, XLIX, 86 Berenyi, D.: Recent applications of electron spectroscopy, XLII, 55 : Spectroscopy of electrons from high-energy ion-atom collisions, LVI, 41 1 Berg, A. D., Smith, R. W . , and Prosser, R. D.: An electron image store and analyser, XXII B, 969 Berger, Harold, see Niklas, Wilfrid F. Bergeson, H. E., and Cassiday, George L.: On the teaching of electronics to scientists, XLV, 253 Berry, R. Stephen: Elementary attachment and detachment processes, I, LI, 137 , and Leach, Sydney: Elementary attachment and detachment processes, 11, LVII, 1 Bertero, M.: Linear inverse and ill-posed problems, LXXV, 2 Bescos, Julian: see Cristobal. Gabriel Beurle, R. L . , Daniels, M. V., and Hills, B. L.: Image intensifier design and visual performance at low light-levels, XXVIII B, 635 , and Jenkinson, G. W.: A charge image storage tube for character recognition, XXVIII B, 1043 , and Slark, N . A.: An experimental image storage tube for the detection of weak optical images of low contrast. XII. 247

-:

CUMULATIVE AUTHOR INDEX. VOLUMES 1-81 , and Wreathall, W. M.: Aberration in magnetic focus systems, XVI, 333 Beyer, R. R.: see Anderton, H.; Boerio, A. H.; Collins, P. R. , and Goetze , G . W. : An optically scanned SEC camera tube, XXII A, 241 , Green, M., and Goetze, G. W.: Point-source imaging with the SEC target, XXII A, 251 Bied-Charreton, P., Bijaoui, A,, Duchesne, M , , and Le Contel, J. M. : Sur quelques progrks recents apportes a la camera Clectronique a focalisation Clectrostatique et sur son application en physique et en astronomic, XXVIII A , 27 Bijaoui, A,: see Alpern, M.; Bied-Charreton, P. Billig, E., and Holmes, P. J.: Defects in diamond-type semiconductor crystals, X, 71 Binnie, D. M., Jane, M. R., Newth, J. A., Potter, D . C., and Walters, J . : Work, at Imperial College, London, on the use of image intensifiers in nuclear physics, XVI, 50 I Biondi, Manfred A,: Atomic collisions involving low energy electrons and ions, XVIII, 67 Birnbaum, George: Optical masers, Suppl. 2 Blake, J . , and Burtt, R. B.: Image orthicons with magnesium oxide targets, XVI, 213 Blamoutier, M.: Un tube de prise de vues sensible aux rayons X, XXVII A, 273 Blewett, John P.: Recent advances in particle accelerators, XXIX, 223 Bloch, F.: see Brillouin, L. Blum, Emile-Jacques: Radioastronomy on millimeter wavelengths, LVI, 98 Boato, G., and Cantini, P.: Diffraction of neutral atoms and molecules from crystalline surfaces, LX, 95 Boerio, A. H.: see Goetze, G . W . -, Beyer, R. R., and Goetze, G. W.: The SEC target. XXII A, 229 Bogdanov, E. V.: see Kislov, V. Ya. Boischot, A,, and Denise, J. F.: Solar radio astronomy, XX, 147 Boksenberg, A,, and Newton, A. C.: An electromechanical picture signal generating device, XXVIII A, 297 Bostanjoglo, 0.:Electron microscopy of fast processes, LXXVI, 209

287

Boulmer, J.: see Delpech, J.-F. Boussuge, C.: see Rosch, J. Boutot, J . P., Nussli, J., and Vallat, D.: Recent trends in photomultipliers for nuclear physics, LX, 223 Bouwers, A , : Low brightness photography by image intensification, XVI, 85 Bowen, J. S.: see Dennison, E . W. Bowers, Michael, T., and Su, Timothy: Thermal energy ion-molecule reactions, XXXIV, 223 Bowers, Raymond: see Frey, Jeffrey. Bowhill, S. A,, and Schmerling, E. R.: The distribution of electrons in the ionosphere, XIX, 55 Bowles, K. L.: Radio wave scattering in the ionosphere, XIX, 55 Boyce, J. F., and Murray, L. R.: Signal analysis in seismic studies, LXXVII, 210 Boyer, L. A,: see Flory, L. E. Bradley, D. J., and Majumdar, S.: Application of electron-optical deflexion and storage techniques to time-resolved interference spectroscopy, XXII B, 985 Brand. P. W. J. L.: see Smyth, M. J . , and Smyth, M. J.: Use of a Lenard-window image tube for astronomical spectrophotometry. XXII B. 741 , and Wolstencroft, R. D.: Recent astronomical applications of a Spectracon, XXVIII B, 783 Branscomb, L. M.: Negative ions, IX, 43 Bratenahl, A,: see Baum, P. J . Brau, Charles A.: Free-electron lasers, Suppl. 22 Brauer, W.: see Hachenberg, 0. Braun, P., Riidenauer, F., and Viehbock, F. P.: Surface analysis using charged-particle beams, LVII, 231 Bremmer, H.: see Bugnolo, D. S. Brillouin, L.: Electronic theory of the plane magnetron, 111, 85 , and Bloch, F.: Electronic theory of the cylindrical magnetron, 111, 15 Brittain. James E.: Power electronics at General Electric: 1900-1941, L. 412 Brodersen, Robert W., and White, Richard M.: Charge transfer and surface acoustic-wave signal-processing techniques, LI, 265

288

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Broerse, P. H.: Electron bombardment induced conductivity in lead monoxide, XXII A , 305 Brooks, F. P., Jr.: Recent developments in computer organization, XVIII, 45 Brooks, H.: Theory of the electrical properties of germanium and silicon, VII, 85 Broussaud, G., and Simon, J. C.: Endfire antennae, XIX, 255 Brown, J . : Microwave optics, X, 107 Bruin, Frans: The autodyne as applied to paramagnetic resonance, XV, 327 Bube, Richard H., and Fahrenbruch, Alan L.: Photovoltaic effect, LVI, 163 Bugnolo, D. S . , and Bremmer, H.: The Wigner distribution matrix for the electric field in a stochastic dielectric with computer simulation, LXI, 300 Burns, J., and Neumann, M. J.: The channeled image intensifier, XII, 97 Burstein, E., and Egli, P. H.: The physics of semiconductor materials, VII, 1 Burtt, R . B.: see Alexander, J. W. F.; Blake, J. Byatt, D.: Bright displays for radar applications, XVI, 265

C

Cailler, M., Ganachaud, J. P., and Roptin, D.: Quantitative Auger electron spectroscopy, LXI, 162 Calderwood, J. H.: see Smith, C. W. Caldwell, D. 0.: see Hill, D. 0. : Scintillation chamber comparisons: fibers v . NaI and image intensifiers v . orthicons, XVI, 469 Campagna, M., Pierce, D. T., Meier, F., Sattler, K., and Siegmann, H. C.: Emission of polarized electrons from solids, XLI, 113 Cantini, P.: see Boato, G. Cappellini, V.: Two-dimensional digital filters and data compression, LXVI, 141 Carinena, Jose F., and Santander, Mariano: Dimensional analysis, LXXII, 182 Carlemalm, E., Colliex, C . , and Kellenberger, E.: Contrast formation in

electron microscopy of biological material, LXIII, 270 Cassiday, George L.: see Bergeson, H. E. Castaing, Raymond: Electron probe microanalysis, XIII, 317 Catchpole, C . E.: see McGee J. D. -. . Measurement of the spatial frequency response of image devices, XXII A, 425 -: X-ray image intensification using multistage image intensifiers, XVI, 567 Celotta, R. J.: see Pierce, D. T. Champion, R. L.: Collisional detachment of negative ions, LVIII, 143 Chan, F. T., Lieber, M., Foster, G., and Williamson, W., Jr.: Applications of the Glauber and eikonal approximations to atomic collisions, XLIX, 134 Charles, D . R.: see Guillard, C. -, and Duchet, M.: Visible and x-ray image devices working on the induced conductivity principle, XXII A , 323 Charman, W. H.: Cosmic rays and image intensifier dark current, XXIII B, 705 Charman, W. N . , and Hewitt, A. V.: The influence of temperature on the performance of a cascade image intensifier, XXII A, 101 Charrier. Mlle. S.,and Wleick, G.: Proprietes des photocathodes IiberCes dans un vide elbve, XVI, 5 Chatterton, P. A,: see Smith, W. A. Chenette, E. R.: see van der Ziel, A. -. . Noise in semiconductor devices, XXIII, 303 Chernov, Z. W.: see Kislov, V. Ya. Chizeck, Howard J., and Trott, Mitchell D.: Algebraic systems, trellis codes, and rotational invariance, LXXIX, 1 Chodorow, M.: see Warnecke, R. R. Christophorou, L. G.: The lifetimes of metastable negative ions, XLVI, 56 Churchill, J. L. W., and Curran, S. C.: Pulse amplitude analysis, VIII, 317 Churchill, J. N . : see Collins, T. W. -, Holmstrom, F. E., and Collins, T. W.: Modeling of irradiation-induced changes in the electrical properties of metal-oxide-semiconductor structures, Lvrrr, I Clayton, R. H., and Gumnick, J. L.: Use

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 of the image dissector in photocathode research, XXII A , 507 Cohen, M.: see Kahan. E. Cohen, Marvin L.: Electrons at interfaces, LI, 1 Cole, F. T., and Milla, F. E.: Recent progress in particle accelerators, LXXI, 75 Coles, D. K.: Microwave spectroscopy, 11, 300 Colliex, C.: see Carlemalm, E. Collings. P. R., Beyer, R. R., Kalafut, J. S . . and Goetze, G. W.: A family of multi-stage direct-view image intensifiers with fiber-optic coupling, XXVIII A, 105 Collins, T. W.: see Churchill, J. N. , Churchill, J . N., Holmstrom, F. E., and Moschwitzer, A.: Modeling of the transient response of an MIS capacitor, XLVII, 267 Combes, M., Felenbok, P., Guerin, J., and Picat, J . P.: Electronic cameras for space research, XXVIII A, 39 Condon, P. E.: Image tubes in nuclear physics, XII, 123 Conrad, A. C., Jr.: see Jordan, J. A , , Jr. Cooper, A. W.: see Oleson, N . L. Cooper, R., and Elliott, C. T.: Pre-breakdown light emission from alkali halide crystals, XXII B, 995 Cope, A. Danforth, and Luedicke, Eduard: The development of camera tubes for recording astronometric images, XXII A, 175 Corney, A.: The measurement of lifetimes of free atoms, molecules, and ions, XXIX, 115 Corps, R. J.: see Groves, P. R . Cowley, J. M.: Electron microdiffraction, XLVI, 1 Cozens, J . R.: see von Engle, A. Cram, Lawrence E.: Solar physics, LIV, 141 Cranstoun, G . K. L.: The application of high-gain image intensification and closed-circuit television to field-ion microscopy, XXVIII B, 875 Cristobal, Gabriel, Gonzalo, Consuelo, and Bescos, Julian: Image filtering and analysis through the Wigner distribution, LXXX, 309

289

Crompton, R. W.: The contribution of swarm techniques to the solution of some problems in low energy electron physics, XXVII, 1 Culshaw, W.: Millimeter wave techniques, XV. 197 Curran, S. C.: see Churchill, J. L. W. Curzon. A. E., and Lisgarten, N. D.: The electron-beam shadow method of investigating magnetic properties of crystals, XXIV, 109 Cusick, Danny R.: see Kelly, Robert J. Czekalowski, G . W. A , , and Hay, G. A , : A quadrature spatial-frequency Fourier analyser, XXVIII B, 653

D Danforth, W. E.: Thorium oxide and electronics, V. 169 Daniels, M. V.: see Beurle, R. L. Danilatos, G . D.: Foundations of environmental scanning electron microscopy, LXXI, 110 : Theory of the gaseous detector device in the ESEM, LXXVIII, 2 David, D.-J.: Microprocessor systems, LVII, 41 1 Davies, Anthony J.: Microprocessors and their use in physics, XLVII, 51 Davies, J. G.: Radio observation of meteors, IX, 95 Davis, G. P.: Experiences with magnetically focused cascade image intensifiers, XVI, 119 Davis, Robert J.: The use of the Uricon-Celescope television system for ultra-violet astronomical photometry, XXII B, 875 Dawson, P. H.: Ion optical properties of quadrupole mass filters, LIII, 153 -, and Kimbell, G. H.: Chemical lasers, XXXI, 1 , and Whetten, N. R.: Mass spectroscopy using rf quadrupole fields, XXVII, 59 Day, J. E.: Recent developments in the cathode-ray oscilloscope, X, 239 De Baere, W.: Einstein-Podolsky-Rosen paradox and Bell’s inequalities, LXVIII, 235

290

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Dean, R . J.: see Jennings, A. E. Decker, R. W.: Decay of S.20 photocathode sensitivity due to ambient gases, XXVIII A, 357 , and Mestwerdt, H.: Large-image electronographic camera, XXVIII A, 19 Declerck, Gilbert J.: see Muls, Paul A. DeCorpo, J. J.: see Saalfeld, F. E. de Haan, E. F.: Signal-to-noise ratio of image devices, XII, 291 Delalande, C.: see Bastard, G . Delcroix, Jean-Loup, and Trindade, Armando Rocha: Hollow cathode arcs, XXXV, 88 Delpech, J.-F.: see Gauthier, J.-C. , Boulmer, J., and Stevefelt, J.: Low-temperature rare-gas stationary afterglows, XXXIX, 121 Deltrap, J. H. M., and Hanna, A. H . : Image intensifier system using reflective photocathode, XXVIII A, 443 De Man, Hugo J.: see Mertens, Robert P. De Mey, Gilbert: Potential calculations in Hall plates, LXI, 2 Denise, J. F.: see Boischot, A . Dennison, E. W.: The image orthicon applied to solar photometry, XVI, 447 -: An isophote converter for u5e with signal-generating image tubes, XII, 307 -: A microphotometer for use with photographic and electronographic recording image tubes, XXII A, 435 , Schmidt, M., and Bowen, J. S.: An image-tube spectrograph for the Hale 200-in. telescope, XXVIII B , 767 Deprettere, E. F. A,: see Adams, K. M. Deutscher, K.: see Kossel, D. De Witt, John H . , Jr.: A report on the image orthicon using slow readout, XVI, 419 Doe, L. A , : see Livingston, W. C. Dolan, W. W.: see Dyke, W. P. Dolizy, P., and Legoux, R.: A new technology for transferring photocathodes, XXVIII A, 367 Dolon, Paul J.: see Ball, Jack; Niklas, Wilfrid F. Donal, J. S . : Modulation of continuous-wave magnetrons, IV, 188 Donati, S . , Gatti, E., and Svelto, V.: The statistical behavior of the scintillation

detector: theories and experiments, XXVI, 251 Donelli, G . , and Paoletti, L.: Electron micrograph analysis by optical transforms, XLIII, 1 Doolittle, R. F., 11, and Graves, C. D.: The application of scintillation chambers to space research, XVI, 535 , and Graves, C. D.: Further developments in the application of scintillation chambers to space research, XXII B, 823 Doughty, D. D.: see Schneeberger, R. J.; Wachtel, M. M. : Ultra-violet sensitive camera tubes incorporating the SEC principle, XXII A, 261 Dow, W. G.: The general perturbational theory of space-harmonic traveling-wave electron interaction, XVII, 1 : Nonuniform D-C electron flow in magnetically focused cylindrical beams, x, 1 Dracass, J.: see Flanagan, T. P. Dragoun, 0.:Internal conversion-electron spectroscopy, LX, 1 Dragt, Alex J., and Forest, Etienne: Lie algebraic theory of charged-particle optics and electron microscopes, LXVII, 65 Driard, B.: see Guyot, L. F. -: ContriBle des monocristeaux par tube intensificateur de luminance, XXVIII B, 931 Duchesne, M.: see Alpern, M.; Bied-Charreton, P.; Lallemand, A. : Sur la rtalisation d’une camCra Clectronique de grandissement 1/7, XVI, 27 : Sur une nouvell technique d’utilisation de la camtra Clectronique, XVI, 19 , and HCzard, C.: Sur la realisation d’un objectif 51 immersion B lentilles cylindriques croisees en vue de son utilisation comme systbme focalisateur de la camtra Clectronique: rCsultats prkliminaires, XXII A, 609 Duchet, M.: see Charles, D. R. : Time-response of photocathodes, XXII A, 499

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 Dunham, Theodore, Jr.: Performance of image tubes in the coude spectrograph at Mount Stromlo observatory, XXII B, 729 Dunlap, J.: see Hynek, J . A. Dunning, F. B., and Stebbings, R. F.: Rydbery atom collision processes, LIX. 79 Dupre, Mile M.: see Wltrick, G. Dvoiak, M.: Some properties of the trialkali Sb-K-Rb-Ca photocathode, XXVIII A , 347 Dyke, W. P., and Dolan, W. W.: Field emission, VIII, 89

E Edgecumbe. J.: see Garwin, E . L. Egan, D. W.: see Beckman, J. E. Egli, P. H.: see Burstein, E. Eichmeier, J . : see Knoll, M. Einstein, P. A,: see Haine, M. E. Eisenstein, A. S . : Oxide coated cathodes, I. 1 El-Kareh, A. B.: see Marton, L. Elliott, C . T.: see Cooper, R.; Smith, W. A. Elvey, C. T.: Aurora borealis, IX, 1 Emberson, C. J.: see Wheeler, B. E. Emberson, D. L.: A comparison of some properties of image intensifiers of the transmitted secondary emission multiplication type and of the cascade type, XXII A , 129 , and Long, B. E.: Some aspects of the design and manufacture of a fiber-optic coupled cascade image intensifier, XXVIII A, 119 , Todkill, A., and Wilcock, W . L.: Further work on image intensifiers with transmitted secondary electron multiplication, XVI, 127 Emeleus, K. G.: Plasma oscillations, XX, 59 England, L.: see Barnett, M. E. Ennos, A. E.: see Haine, M. E. Eom. Kie-Bum: see Kashyap, R. L. Erbudak, M.: see Siegmann, H. C. Erickson, William C., and Kerr, Frank J.: Technology and observations in radio astronomy, XXXII, 1

29 1

Eschard, G., and Graf, J.: Quelques problemes concernant les multiplicateurs canalists pour intensificateur d’image, XXVIII A, 499 , and Polaert, R.: Tubes obturateurs pour photographie ultra-rapide au temps de pose d’une nanoseconde, XXVIII B, 989 Essig, Sanford E.: Field emission in image tubes, XII, 73 Evans, H. D.: see McGee, J . D.

F Fahrenbruch, Alan L.: see Bube, Richard H. Farago, P. S . : The polarization of electron beams and the measurement of the gfactor anomaly of free electrons, XXI, 1 Fawcett, J. M.: see Jensen, A. S. Fay, Clifford E.: see Von Aulock, Wilhelm H. Fay, Theodore D . : see Frederick, Lawrence W. Feibelman, W. A , : see Schneeberger. R. J . Feinstein, David L.: see Granatstein, V. L. Felenbok, P.: see Combes, M. Ferguson, Eldon E.: Thermal energy ion-molecule reactions, XXIV, 1 Ferry, D. K.: Materials considerations for advances in submicron very large scale integration, LVIII, 312 Ferwerda, Hedzer A,: see Slump, Cornelis H. Fiermans, L., and Vennik, J . : Electron beams as analytical tools in surface research: LEED and AES, XLIII, 139 Filby, R. S . , Mende, S. B., and Twiddy, N. D.: A television camera-tube using a low density potassium chloride target, XXII A , 273 Fink, Jorg: Recent developments in energy-loss spectroscopy, LXXV, 122 Finn, Bernard S.: Thermoelectricity, L, 176 Fisher, Arthur D.: see Lee, John N. Flanagan, T. P., Anderson, D. G., Noe, E. H., and Dracass, J . : Properties and applications of glass scintillators, XVI, 547 Fleming, W. J., and Rowe, J. E.: Acoustoelectric interactions in 111-V compound semiconductors, XXXI, 162

292

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Flinn, E. A,: see McGee, J. D. : Progress report on a channelled image intensifier, XVI, 155 Flory, L. E., Pike, W. S . , Morgan, J . M., and Boyer, L.A.: A programmable integrating television system for use with the stratoscope, XXII B , 885 Folkes, J. R.: see Garfield, B. R. C. : Introduction of pre-formed photocathodes into vacuum systems, XVI, 325 Fonseca, Strgio Barroso de Assis, and Giarola, Attilio Jost: Dyadic Green’s functions and their use in the analysis of microstrip antennas, LXV, 2 Foote, D. P.: see Kaxan, B. Ford, W. K., Jr.: see Frederick, L. W.; Hall, J . S. : Astronomical uses of cascade intensifiers, XXII B, 697 Foreman, P. H . , and Thumwood, R. F.: An image intensifier tube using the multipactor principle, XVI, 163 Forest, Etienne: see Dragt, Alex J. Foster, G . : see Chan, F. T. Fowler, Richard G . : Electrons as a hydrodynamical fluid, XX, 1 -: Nonlinear electron acoustic waves. Part I, XXXV, 1; Part 11, XLI, 1 Fowweather, F., and Harbour, J.: The application of image storage tubes to the observation of optical diffraction patterns, XII, 311 Frank, K.: see Hambrecht, F. T. Franks, J.: Ion beam technology applied to electron microscopy, XLVII, 1 Franzen, W.: see Baldinger, E . , and Porter, John H.: Energy spectrum of electrons emitted by a hot cathode, XXXIX, 73 Frederick, L. W., Hall, J . S., Baum, W. A , , and Ford, W. K., Jr.: Some astronomical uses of image intensifying tubes, XVI, 403 Frederick, Lawrence W., Fay, Theodore D., and Johnson, Hollis R.: Infra-red stellar spectroscopy with a mica-window, XXII B, 723 Freeman, A. J.: see Wimmer, E. Freeman, K. G.: see Taylor, D. G .

Frey, Jeffrey, and Bowers, Raymond: The impact of solid state microwave devices: a preliminary technology assessment, XXXVIII, 148 Fritz, Edward F., Jr.: Recent advances in electron beam deflection, XLIX, 299 Frohlich, H.: The biological effects of microwaves and related questions, LIII, 85 Frolich, H., and Simpson, J. H.: Intrinsic dielectric breakdown in solids, 11, 185 Fromm, W. E.: The magnetic airborne detector, IV, 258 Fujioka, H.: see Ura, K. G Gagnepain, Jean-Jacques: Resonators, detectors, and piezoelectrics, LXXVII, 84 Gale, B. C.: see Ahmad, N. Galtier, Ch.: see Arsac, J. Ganachaud, J. P.: see Cailler, M. Ganson, A,: see McGee, J . D. Gardiol, Fred E.: see Mosig, Juan R. : Open-ended waveguides: principles and applications, LXIII, 140 Garfield, B. R. C.: see Allan, F. V . , Folkes, J . R., and Liddy, B. T.: Improvements to photocathodes for pulse operation, XXVIII A, 375 , and Thumwood, R. F.: A microbalance study of the Cs-Sb and Na-K-Sb photocathodes, XXII A , 459 Garlick, G. F. J.: Cathodoluminescence, 11, 152 : Recent developments in solid state image amplifiers, XVI, 607 Garrett, C. G . B.: The electron as a chemical entity, XIV, 1 Garthwaite, E.: X-ray image intensifier using image orthicon tubes, XII, 379 Garwin, E. L., and Edgecumbe, J.: Response of low-density KCI foils to multi-meV electrons, XXII A, 635 Gatti, E . : see Donati, S. Gauthier, J.-C., and Delpech, J.-F.: Time-resolved laser fluorescence spectroscopy for atomic and molecular excited states: kinetic studies, XLVI, 131

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 Gebel, R. K. H.: The fundamental infrared threshold in thermal image detection as affected by detector cooling and related problems, XXVIII B, 685 : Low-energy quanta image transducers using a controlled recombination mode, XXII A. 189 : The potentialities of electronically scanned photoconductive image detectors for astronomical uses, XVI, 451 , and Deval, Lee: Some early trails of astronomical photography by television methods, XII, 195 Geneux, E . , Ben&,G. J., and Perrenoud, J.: Magnetic coherence resonances and transitions at zero frequency, XXVII, 19 Georges, A . T., and Lambropoulos, P.: Aspects of resonant multiphoton processes, LIV, 191 Gertner, I.: see An, M. Geurts, A , : see Kiihl, W. Chose, D . , and Karmohjapatro, S. B.: Topography of solid surfaces modified by fast ion bombardment, LXXIX, 73 Giardina. Charles R.: The universal imaging algebra, LXVII, 121 Giarola, Attilio Jose: see Fonseca, Sergio Barroso de Assis Gibson, Jerry D., and Sayood, Khalid: Lattice quantization, LXXII, 259 Giese, R.: see Gildemeister, 0. , Gildemeister, O., and Schuster, G.: Test of a high-resolution cerenkov chamber with a four-stage image intensifier, XXVIII B, 919 Gildemeister, 0.:see Giese, R. , and Giese, R.: An image intensifier for track recording, XVI, 113 Ginzton, E. L.: see Warnecke. R. R. Gnadinger, A. P.: Electronic watches and clocks, LI. 183 Goetze, G . W.: see Beyer, R. R.; Boerio, A . H.; Collings, P. R. : Secondary electron conduction (SEC) and its application to photoelectric image devices, XXII A , 219 : Transmission secondary emission from low density deposits of insulators, XVI, 145 , and Boerio, A. H.: SEC

293

camera-tube performance characteristics and applications, XXVII A , 159 , Taylor, A . : Recent applications of transmission secondary emission amplification, XVI, 557 Goldberg, Seymour, and Rothstein, Jerome: Hydrogen thyratrons, XIV, 207 Goldstein, L.: Electrical discharge in gases and modern electronics, VII, 399 Gonzalo, Consuelo: see Cristobal, Gabriel Gopinath, A.: Voltage measurement in the scanning electron microscope, LXVIX, 1 Gordon, A . W.: see Raffan, W. P. Gorlich, P.: Problems of photoconductivity, XIV, 37 : Recent advances in photoemission, XI, 1 Goto, S.: see Sasaki, T. Graf, J.: see Eschard, G. Granatstein, V. L., and Feinstein, David L.: Multiple scattering and transport of microwaves in turbulent plasmas, XXXII, 312 Graves, C. D.: see Doolittle, R. F. Greatorex, C. A , : Image intensification using a flying-spot x-ray tube, XII, 317 : Image storage techniques applied to diagnostic radiology, XVI, 593 Green, M.: see Beyer, R. R. , and Hansen, J. R.: The application of SEC camera tubes and electrostatic image intensifiers to astronomy, XXVIII B, 807 Greenspan, Donald: Discrete mathematical physics and particle modeling, LXIII, 189 Grivet, P.: Electron lenses, 11, 48 : Sixty years of electronics, L, 89 Grivet. P. A . , and Malnar, L.: Measurement of weak magnetic fields by magnetic resonance, XXIII, 39 Grosch, G . A , , and Krieser, J. K.: Leistungagrenze eines sichtsystems mit bildverstarker, XXVIII B, 603 Grosse, Achilles: see WICrick, Gerard Groves, P. R., and Corps, R. J . : Applications of the image isocon tube, XXVIII B, 827 Grubin, H. L.: see Shaw, M. P. Guenard, P. R.: see Warnecke, R. R. Guerin, J.: see Combes, M.

294

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Guest, A , : see Manley, B. W. Guillard, C., and Charles, D. R.: On some properties of electron bombardment induced conductivity, XXII A, 315 Guillemin, E. A,: A summary of modern methods of network synthesis, 111, 261 Guldner, Y.: see Bastard, G. Gumnick, J. L.: see Clayton, R. H. Guyot, L. F.: Derniers developements sur les intensificateurs d’image rayons X B grand gain et les tubes convertisseurs d’image, XVI, 91 -, Driard, B . , and Sirou, F.: Tubes intensificateurs d’image pour observation des phenomtnes lumineux rapidement kvolutifs, XXII B, 949

H Hachenberg, O., and Brauer, W.: Secondary electron emission from solids, XI, 413 Hahn, E.: Methods of calculating the properties of electron lenses, LXXV, 233 Haine, M. E.: The electron microscopea review, VI, 295 , Ennos, A. E., and Einstein, P. A , : An image intensifier for the electron microscope, XII, 317 Hall, J. S . : see Frederick, L. W. -, Ford, W. K., Jr., and Baum, W. A , : Astronomical tests of barrier-membrane image converters, XII, 21 Hambrecht, F. T., and Frank, K.: The future possibilities for neural control, XXXVIII, 55 Handel, Peter H.: see Hora, Heinrich Hanna, A. H.: see Deltrap, J. H. M. Hansen, J . R.: see Green, M. Hanson, Delon C.: Fiber optics in local area network applications, LVII, 145 Hanszen, K.4.: Holography in electron microscopy, LIX, 2 Harbour, J.: see Fowweather, F. Harmuth, Henning F.: Acoustic imaging with electronic circuits, Suppl. 11 : Antennas and waveguides for nonsinusoidal waves, Suppl. 15

: From the flat earth to the topology of space-time, L, 261 : Generation of images by means of two-dimensional, spatial electric filters, XLI, 168 : Nonsinusoidal waves for radar and radio communication, Suppl. 14 -- : Propagation of nonsinusoidal electromagnetic waves, Suppl. 18 -, . Radiation of nonsinusoidal electromagnetic waves, Suppl. 23 -. , Research and development in the field of Walsh functions and sequency theory, X M V I , 195 : Sequency theory: foundations and applications, Suppl. 9 Harth, W.: see Schaff, F.; Unger, H.-G. Hartmann, P.: see Vernier, P. Hase, Takashi, Kano, Tsuyoshi, Nakazawa, Eiichiro, and Yamamoto, Hajime: Phosphor materials for cathode-ray tubes, LXXIX, 271 Hasegawa, S.: Resolving power of image tubes, XXVIII B, 553 Hasted, John B.: Inelastic collisions between atomic systems, XIII, 1 Hawkes, P. W . : Quadrupoles in electron lens design, Suppl. 7 -. . The beginnings of electron microscopy, Suppl. 16 Haus, Hermann A.: see Pucel, Robert A . Hay, G . A.: see Ozekalowski, G . W. A. -: The image orthicon in diagnostic radiology, XVI, 581 -: X-ray image intensification using optical television methods, XII, 363 Hayward, R. W.: Beta-ray spectrometers, v, 97 Heimann, W.: Experiments with a simple photo-electronic storage tube, XII, 235 -. . Possibilities of reducing image defects in electron-optical imaging devices using electrostatic lenses, XXII A, 601 , and Hoene, E. L.: Improvement of signal-to-noise ratio of image converters with S.1 photocathodes, XXVIII B, 677 , and Kunze, C.: Development of an

CUMULATIVE AUTHOR INDEX. VOLUMES 1-81 infra-red vidicon-type pick-up tube with a lead sulphide target, XVI, 217 Heinrich, Hans: see Stahnke, Ingeborg Heinzl, J . , and Hertz, C. H.: Ink-jet printing, LXV. 91 Herbatreit. J . W.: see Rice, P. L. : Cosmic radio noise, I, 347 Herrmann. M., and Kunze, C.: A new multiplier system with forty separate channels, XXVIII B. 955 Hersey, J. B.: Electronics in oceanography, IX, 239 Herstel, W.: The assessment of image quality in medical fluoroscopy, XXII A, 363 : The observation of moving structures with x-ray image intensifiers, XXVIII B, 647 : Some experiences with x-ray image intensifiers and television channels, XVI, 610 Hertz, C. H.: see Heinzl, J. Hess. K.: Aspects of high-field transport in semiconductor heterolayers and semiconductor devices, LIX, 239 Hewitt, A. V.: see Charman, W. N . ; Kron. G. E. Hezard, C.: see Duchesne, M. Higatsberger, Michael J . : Solid surfaces analysis, LVI, 291 Hill, D. A , , Caldwell, D. O., and Schluter, R. A,: Performance of an image intensifier system, XVI, 475 , and Porter, N. A.: Photography of extensive air showers in the atmosphere, XVI. 531 Hills, B. L.: see Beurle, R. L. Hiltner, W. A , , and Niklas, W. F.: A low background image tube for electronography, XVI, 37 , and Pesch, Peter: Image tube research at Yerkes Observatory. XII. 17 Hinder, G. W.: see Iredale, P. Hirashima, M.: Optimum conditions for activating silver-magnesium alloy dynodes in water vapour, XXII A, 661 , and Asano, M.: Effects of caesium vapour upon target glass of image orthicon, XXII A , 651; XXVIII A, 309

29 5

, and Asano, M.: Reaction of caesium vapour with gold, XXII A , 643 -, and Asano, M.: Some better materials for caesium vapour, XXVIII A, 38 1 Hirayama, T.: see Kajiyama. Y . Hirschberg, K.: see Kossel, D. Hirsh, C. J.: A review of recent work in color television, V, 291 Hobson. J . P.: see Redhead, P. A. Hoene, E. L.: see Heimann. W . Hok. G . : The microwave magnetron, 11, 220 Holloway, Paul H.: Fundamentals and applications of Auger electron spectroscopy, LIV, 241 Holmes, R. T.: see Manley, B. W . Holmshaw, R. T.: see Manley, B. W . Holmstrom, F. E.: see Churchill, J . N . ; Collins, T. W. Hooper. E. B., Jr.: A review of reflex and Penning discharges, XXVII, 295 Hopmann. W.: The image orthicon in high-speed photography, XXII B, 1011 : The influence of photocathode resistance and space charge on the resolution of magnetic focus systems, XXII A 591 Hora, Heinrich, and Handel, Peter H.: New axperiments and theoretical development of the quantum modulation of electrons (Schwarz-Hora effect), LXVIX, 55 Hori, H., Tsuji, S . , and Kiuchi, Y . :An infra-red sensitive vidicon with a new type of target, XXVIII A, 253 Houston, J . M.: see Vosburgh, Kirby G . , and Webster, H. F.: Thermionic energy conversion, XVII, 125 Hubbard, Edward L.: Linear ion accelerators, XXV, 1 Huebener, R. P.: Scanning electron microscopy at very low temperatures, LXX, I Huggett, J. M.: Scanning electron microscopy in the petroleum exploration industry, LXXVII, 140 Hunt, B. R.: Digital image processing, LX, 161

296

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Huston, A. E.: Image tube high-speed cameras, XXII B, 957 , and Walters, F. W.: Electron tubes for high-speed photography, XVI, 249 Hutter, E. C.: see Vance, A. W. Hutter, R. G. E.: The deflection of beams of charged particles, I, 167 : Traveling-wave tubes. VI, 371 Hynek, J. A., Bakos, G., Dunlap, J., and Powers, W.: Advances in the application of the image orthicon to astronomy, XXII B, 713 , Barton, G., Aikens, R., and Powers, W.: Potentialities and limitations of image scanning techniques in astronomy, XVI, 409 I I l k , V. P., Kateshov, V. A., Kulikov, Yu. V., and Monastyrsky, M. A.: Emission-imaging electron-optical system design, LXXVIII, 156 Inghram, M. G.: Modern mass spectroscopy, I, 219 Inskeep, C. N . : see Abraham, J. M. Ioanovichiu, D.: Ion optics, LXXIII, 1 Iredale, P., Hinder, G. W., and Smout, D. W. S . : Position-sensitive photon counters, XXVIII B, 965 , Hinder, G. W . , Parham, A. G., and Ryden, D. J.: The observation of cerenkov ring images with an image intensifier system of high gain, XXII B, 80 1 , and Ryden, D. J.: On the quality of photographic images recorded with the use of image intensifiers, XXVIII B, 589 h e y , Henry F.: Electroluminescence and related effects, Suppl. 1 -: Space charge limited currents, VI, 137

J Jackson, F. W.: see Wardley, J . Jackson, R. N . , and Johnson, K. E.: Gas discharge displays: a critical review, XXXV, 191 Jain, S. C.: see Tewary, V. K.

,Winters, K. H., and Van Overstraeten, R., LXXVIII, 104 Jane, M. R.: see Binnie, D. M. Jansen, G . H.: Coulomb interactions in particle beams, Suppl. 21 JareS, V., and Novotnp, B.: Two methods for the determination of the imaging properties of electron-optical systems with a photocathode, XXVIII A, 523 Jaumot, Frank E . , Jr.: Thermoelectricity, XVII, 207 JedliEka, M.: Research on photocathodes in Czechoslovakia, XXVIII A, 323 , and Vilim, P . : Some properties of the Sh;sb;Rb;sb;Cs photocathode, XXII A, 449 Jeffers, S . , and McGee, J. D.: On the transmission of medium energy electrons through mica, XXII A, 41 Jenkinson, G. W.: see Beurle, R. L. Jennings, A. E., and Dean, R. J . : Sensitization of electrostatically focused image converters, XXII A, 441 Jensen, A . S . , and Fawcett, J . M.: Measurement of TV camera noise, XXVIII A, 289 , Reininger, Walter G., and Limansky, Igor: The grating storage target, XXII A, 155 Jiye, Ximen: Aberration theory in electron and ion optics, Suppl. 17 Johnson, Hollis R.: see Frederick, Lawrence W. Johnson, J . M.: see Sackinger, W. M. Johnson, K. E.: see Jackson, R. N. Jones, L. W., and Perl, Martin L.: Two high-energy physics experiments using the luminescent chamber, XVI, 513 Jones, Lawrence W.: see Perl, Martin L. , and Loo, Billy W.: The use of image intensifiers with streamer chambers, XXII B, 813 Jones, R. Clark: Performance of detectors for visible and infrared radiation, V, 1 : Quantum efficiency of detectors for visible and infrared radiation, XI, 87 Jordan, J . A., Jr., Bakken, G. S . , and Conrad, A. C., Jr.: A cascade image intensifier camera for beam-foil spectroscopy, XXVIII B, 907

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 Jory, H. R.: see Symons, R. S. Jullien, Graham A . : Number theoretic techniques in digital signal processing, LXXX, 69

K Kahan, E.: see McGee, J . D. , and Cohen, M.: Comparison of the efficiency of image recording with a Spectracon and with Kodak IIa-0 emulsion, XXVIII B, 725 Kaiser, Michael: Derivation of a focusing criterion by a system-theoretic approach, LXXV, 329 Kajiyama, Y., Kawahara, T., and Hirayama, T.: Newly developed image orthicon tube with a MgO target, XXVIII A, 189 Kalafut, J. S . : see Collings, P. R. Kan, S. K.: see Sauzade, M. D. Kano, Tsuyoshi: see Hase, Takashi Kao, K. C.: see Smith, C. W. Karady, George: High-power electronic devices, XLI, 311 Karmohapatro, S. B.: see Ghose, D. : Laboratory isotope separators and their applications, XLII, 113 Kashyap, R. L., and Eom, Kie-Bum: Robust image models and their applications, LXX, 79 Kateshov, V. A.: see Win, V. P. Kaufman, Harold R.: Technology of electron-bombardment ion thrusters, XXXVI, 266 Kaufmann, U., and Schneider, J.: Point defects in Gap, GaAs, and InP, LVIII, 81 Kaw, Predhiman Krishan: see Sodha, Mahendra Singh Kawahara, T.: see Kajiyama, Y. Kawakami, H.: see Uno, Y. Kay, Eric: Impact evaporation and thin film growth in a glow discharge, XVII, 245 Kazan, B.: .see Knoll, J. , and Foote, D. P.: Recent developments in field-effect image storage panels, XXVIII B, 1059 Keen, Ralph S . : see Schnable, George L.

297

Kellenberger, E.: see Carlemalm, E. Kelly, John: Recent advances in electron beam addressed memories, XLIII, 43 Kelly, Robert J.: see Redlien, Henry W. , and Cusick, Danny R.: Distance measuring equipment and its evolving role in aviation, LXVIII, 1 Kennedy, David P.: Semi-conductor device evaluation, XVIII, 167 Kennedy, S. W.: see Weingartner, H. C. Kerr, Frank J.: see Erickson, William C. Kerwin, L.: Mass spectroscopy, VIII, 187 Key, M. H.: see Ahmad, N. Keyes, Robert W.: Physical limits in information processing, LXX, 159 Khogali, A.: see McGee, J . D. Kidger, M. J . : see Wynne, C. G. Kimbell, G. H.: see Dawson, P. H . King, J . G . , and Zacharias, J . R.: Some new applications and techniques of molecular beams, VIII, 1 Kislov, V. Ya., Bogdanov, E . V., and Chernov, Z. S.: Physical foundations of plasma applications for generation and amplification of microwaves, XXI, 287 Kistemaker, J.: see Snoek, C. Kiuchi, Y.: see Hori, H. Klein, N.: Electrical breakdown in solids, XXVI, 309 Knight, Richard I.: see Bates, David J. Knoll, M., Eichmeier, J., and Schon, R. W.: Properties, measurement, and bioclimatic action of “small” multi-molecular atmospheric ions, XIX, 178 , and Kazan, B.: Viewing storage tubes, VIII, 447 Kohashi, T., Nakamura, T., Maeda, H., and Miyaji, K.: A fast-response solid-state image converter, XXII B, 683 -, Nakamura, T., Nakamura, S., and Miyaji, K.: Recent developments in solid-state infra-red image converters, XXVIII B, 1073 Kohl, H . , and Rose, H.: Theory of image formation by inelastically scattered electrons in the electron microscope, LXV, 173 Komrska, Ji€i: Scalar diffraction theory in electron optics, XXX, 139

298

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Konigsberg, R. L.: Operational amplifiers, XI, 225 Konrad, G . T., and Rowe, J . E.: Harmonic generation and multisignal effects in nonlinear beam plasma systems, XXIX, 1 Kornelsen, E. V.: see Redhead, P. A. Kossel, D., Deutscher, K., and Hirschberg, K.: Interference photocathodes, XXVIII A, 419 Krakauer, H.: see Wimmer, E. Krieser, J . K.: see Grosch, G. A. Kron, G. E.: Advantages of a bakeable electronographic plate, XVI, 35 : A modified Lallemand image tube, XVI, 25 , Ables, H. D., and Hewitt, A. V.: A technical description of the construction, function, and application of the U.S. Navy electronic camera, XXVIII A, 1 , and Papiashvili, I. I.: Progress in the development of the Lick-Stromlo electronic camera, XXII A , 59 Kulikov, Yu. V.: see I l k , V. P. Kulkarni, A. D.: Digital processing of remotely sensed data, LXVI, 310 Kunze, C.: see Heimann, W.; Herrmann, M. Kunze, W . , Meyerhoff, K., and Retzlaff, G.: The useful luminance gain of image intensifier systems with respect to noise limitations, XXVIII B, 629 Kusak, Lloyd: Basic concepts of minicomputers, XLIV, 283 Kiihl, W., Geurts, A , , and van Overhagen, J . : Information transfer with high-gain image intensifiers, XXVIII B, 615 Kyser, David F.: see Murata, Kenji

L Labeyrie, A.: An image-tube Fourier spectrograph, XXVIII B, 899 LainC, D. C.: Advances in molecular beam masers, XXXIX, 183 Lallemand, A.: Perfectionnement de la camera Cltctronique-application a l’infra-rouge, XXII A , 1

Quelques reflexions sur la camkra tlCctronique, XVI, 1 -, Duchesne, M., and Wlkrick, G.: La photographic Cltctronique, XII, 5 Lambropoulos, P.: see Georges, A. T. Lamport, D. L.: see Stark, A . M. Landolt, M.: see Siegmann, H. C. Lansiart, A , , and Roux, G.: Spark chambers and image intensifiers used in the scanning of radioactive objects, XXII B, 941 Laques, P.: Photographic des Ctoiles doubles au moyen de la camtra ClCctronique Lallemand, XXII B, 755 Lashinsky, Herbert: cerenkov radiation at microwave frequencies, XIV, 265 Lawless, W.L.: Developments in computer logical organization, X, 153 Le Carvennec, F.: Recherche d’un dispositif nouveau de ttltvision thermique, XXVIII A, 265 Le Contel, J. M.: see Bied-Charreton, P. Leach, Sydney: see Berry, R . Stephen Lechmann, J.: see Vance, A. W. Leder, L. B.: see Marton, L. Lee, John N., and Fisher, Arthur D.: Device developments for optical information processing, LXVIX, 115 Legoux, R.: see Dolizy, P. Leifer, M., and Schreiber, W . F.: Communication theory, 111, 306 Lenz, F.: see Garfield, B. R. C . Li, Ming Chiang: Electron interference, LIII, 269 Lieber, M.: see Chan, F. T. Liebmann, G.: Field plotting and ray tracing in electron optics: A review of numerical methods, 11, 102 Limansky, Igor: see Jensen, Arthur S. Linden, B. R.: A survey of work at CBS laboratories on photoelectronic image devices, XVI, 311 Lindgren, Allen G., and Rattey, Paul A.: The inverse discrete radon transform with applications to tomographic imaging using projection data, LVI, 360 Lindsay, P. A.: Velocity distribution in electron streams, XIII, 181 Lisgarten, N. D.: see Curzon, A. E. Liu, I. D., and Baskett, J . R.: A high-gain -:

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 time-resolving spectrograph for diagnostics of labortory simulated re-entry objects, XXVIII B, 1021 Livingston, M. S.: Early history of particle accelerators, L, 2 : Particle accelerators, I, 269 Livingston, W. C.: Properties and limitations of image intensifiers used in astronomy, XXIII, 347 : Stellar photometry with an image orthicon, XVI, 431 -, Lynds, C. R., and Doe, L. A.: Recent astronomical research utilizing a high gain image intensifier tube, XXII B, 705 Long, B. E.: see Emberson, D. L. Low, W.: Electron spin resonance-a tool in mineralogy and geology, XXIV, 51 Lowrance, J . L., and Zucchino, P. M.: Integrating television sensors for space astronomy, XXVIII B, 851 Luedicke, Eduard: see Cope, A. Danforth Lynds, C. R.: see Livingston, W. C. Lynds, R.: see Powell, J. R. Lynton, E. A., and McLean, W. L.: Type I1 superconductors, XXIII, 1

M McCombe, Bruce D., and Wagner, Robert J.: Intraband magneto-optical studies of semiconductors in the far infrared. Part I, XXXVII, 1; Part 11, XXXVIII, 1 McDermott, D. B.: see Marshall, T. C. McGee, J. D.: see Jeffers, S . ; Smith,

c. w.

, Airey, R. W., and Aslam, M.: High quality phosphor screens for cascade image intensifiers, XXII A, 571 , Airey, R. W., Aslam, M., Powell, J. R., and Catchpole, C. E.: A cascade image intensifier, XXII A, 113 , Airey, R. W., and Varma, B. P . : Cascade image intensifier developments, XXVIII A, 89 , Airey, R. W., and Wheeler, B. E.: Thin-window image intensifier with phosphor output, XVI, 61 -, Aslam, M., and Airey, R. W.: The

299

evaluation of cascade phosphorphotocathode screens, XXII A, 407 , Flinn, E. A,, and Evans, H. D.: An electron image multiplier, XII, 87 , Khogali, A., and Ganson, A,: Electron transmission through mica and the recording efficiency of the spectracon, XXII A, 31 , Khogali, A . , Ganson, A . , and Baum, W. A,: The spectracon-an electronographic image recording tube, XXII A, 11 , McMullan, D . , Bacik, H., and Oliver, M.: Further developments of the spectracon, XXVIII A, 61 , McMullan, D., and Kahan, E.: Photo-electronic image devices, XXII A; XXII B; XXXIII A; XXXIII B , McMullan, D., Kahan, E., and Morgan, B. L.: Photo-electronic image devices, XXVIII A; XXVIII B , and Wheeler, B. E.: An image tube with Lenard window, XVI, 47 , Wilcock, W. L., Mandel, L.: Photo-electronic image devices, XVI McKay, K. G.: Secondary electron emission, I, 66 McKee, J. S. C., and Smith; G. R.: Proton microprobes and their applications. LXXIII, 93 McLane, W. L.: see Lynton, E. A. McMullan, D.: see McGee, J. D.; Morgan, B . L. , and Towler, G. 0.:Some properties of SEC targets, XXVIII A, 173 McNish, A . G.: Ionospheric research, I, 317 Maeda, H . : see Kohashi, T.; Miyazaki, E.; Uno, Y . Majumdar, S.: see Bradley, D. J . Malherbe, A., Tessier, M., and Veron, S . : Spectral response of S . 1 photocathodes in the near infra-red. XXII A. 493 Malling, L. R., and Allen, J. Denton: The slow-scan vidicon as an interplanetary imaging device, XXII B, 835 Malnar, L.: see Grivet. P. A . Mandel, L.: see McGee, J. D . Manley, B. W., Guest, A., and Holmshaw,

300

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

R. T.: Channel multiplier plates for imaging applications, XXVIII A, 471 , and Schagen, P.: The tenicon: A high resolution information storage tube, XVI, 287 Manson, Steven T.: Atomic photoelectron spectroscopy. Part I, XLI, 73; Part 11, XLIV, 1 Marshall, F. B., and Roane, G. D.: Performance comparison of the SEC camera tube and the image orthicon, XXII A, 291 Marshall, T. C., Schlesinger, S. P., and McDermott, D. B.: The free-electron laser: a high-power submillimeter radiation source, LIII, 48 Martin, Andre: Cathode ray tubes for industrial and military applications, LXVLI, 183 Martin, R.: see Wise, H. S. Martinez, G., and Sancho, M.: Application of the integral equation method to the analysis of electrostatic potentials and electron trajectories, LXXXI, 1 Marton, C.: see Marton, L. Marton, L.: see Tousimis, A. J . , and El-Kareh, A. B.: Electron beam and laser beam technology, Suppl. 4 , Leder, L. B . , and Mendlowitz, H.: Characteristic energy losses of electrons in solids, VII, 183 , and Marton, C.: Evolution of the concept of the elementary charge, L, 449 Massey, H. S. W.: Electron scattering in solids, IV, 2 Masuda, Kohzoh: see Namba, Susumu Matare, Herbert F.: Light-emitting devices. Part I: methods, XLII, 179; Part 11: device design and applications, XLV, 40 Mayer, H. F.: Principles of pulse code modulation, 111, 221 Medved, David B., and Strausser, Y . E.: Kinetic ejection of electrons from solids, XXI, 101 Meeks, Steven W., and Auld, B. A,: Optical and acoustic device applications of ferroelastic crystals, LXXI, 251 Meier, D. T.: see Campagna, M. Meier, F.: see Siegmann, H. C.

Mellini, Marcello: High resolution transmission electron microscopy and geology, LXXVI, 282 Melton, B. S.: Contributions of electronics to seismology and geomagnetism, IX, 297 Mende, S. B.: see Filby, R. S. Mendlowitz, H.: see Marton, L. Mertens, Robert P., Van Overstraeten, Roger J., and De Man, Hugo J.: Heavy doping effects in silicon, LV, 77 Mestwerdt, H.: see Decker, R. W. Metson, G. H.: On the electrical life of an oxide-cathode receiving tube, VIII, 403 Meyerhoff, K.: see Kunze, W. Midgley, D.: Recent advances in the Hall effect: research and application, XXXVI, 153 Miller, D. E.: see Wilcock, W. L. Miller, Thomas M.: Photodetachment and photodissociation of ions, LV, 119 Mills, F. E.: see Cole, F. T. Milnes, A. G . : Impurity and defect levels (experimental) in gallium arsenide, LXI, 64 Misell, D. L.: Image formation in the electron microscope with particular reference to the defects in electron-optical images, XXXII, 64 Miyaji, K.: see Kohashi, T.; Miyazaki, E. Miyashiro, S., and Nakayama, Y . : Electronic zooming with the image orthicon television pick-up tube, XVI, 195 -, and Nakayama, Y.:Some methods of minimizing the black-border effect in the image orthicon television pick-up tube, XVI, 171 -, and Shirouzo, S.: Electrostatically scanned image orthicon, XXVIII A , 191 Miyazaki, E.: see Uno, Y. , Maeda, H., and Miyaji, K.: The evoscope-a fixed-pattern generator using a Au-Si diode, XXII A, 331 MladjenoviC, Milorad S.: Recent advances in design of magnetic beta-ray spectrometers, XXX, 43 Mnyama, D.: see Bates, R. H. T.

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 Mockler, Richard C.: Atomic beam frequency standards, XV, 1 Mollenstedt, G . , and Lenz, F.: Electron emission microscopy, XVIII, 251 Monastyrsky, M. A , : see Win, V. P. Moreno. T.: High-power axial-beam tubes, XIV, 299 Morgan, B. L.: see McGee, J. D . : Photo-electronic image devices, LXIV A; LXIV B, LXXIV , Airey, R. W., and McMullan, D.: Photo-electronic image devices. XL A; XL B , and McMullan, D.: Photo-electronic image devices, LII , Smith, R. W., and Wilson, G . A , : A storage image tube for optoelectronic computing, XXVIII B, 1051 Morgan, J. M.: see Flory, L. E. Morozumi, Shinji: Active-matrix thin-film transistor liquid-crystal displays, LXXVII, 2 Morton, G. A.: The scintillation counter, IV, 69 , and Ruedy, J. E.: The low light level performance of the intensifier orthicon, XII, 183 Moschwitzer, A,: see Collins, T. W. Mosig, Juan R . , and Gardiol, Fred E.: A dynamical radiation model for microstrip structures, LIX. 139 Moss, H.: Cathode ray tube progress in the past decade with special reference to manufacture and design, 11. 2 : Narrow angle electron guns and cathode ray tubes, Suppl. 3 Motz, H., and Watson, C. J.: The radio-frequency confinement and acceleration of plasmas, XXIII, 153 Miiller, Erwin W.: Field ionization and field ion microscopy, XIII, 83 Muller. J . : Photodiodes for optical communication, LV, 189 Muls, Paul A , , Declerck, Gilbert J., and Van Overstraeten, Roger J.: Characterization of the MOSFET operating in weak inversion, XLVII, 197 Murata, Kenji, and Kyser, David F.: Monte Carlo methods and

30 1

microlithography simulation for electron and x-ray beams, LXVIX, 176 Murray, L. R.: see Boyce. J. F.

N Nagai, Keinosuke: Synthetic aperture ultrasonic imagery, LXX, 215 Nakamura, S . : see Kohashi, T. Nakamura, T.: see Kohashi, T.; Sasaski, T. Nakayama, Y . : see Miyashiro, S . Nakazawa, Eiichiro: see Hase, Takashi Namba, Susumu, and Masuda, Kohzoh: Ion implantation in semiconductors, XXXVII, 264 Narcisi. Rocco S . , and Roth, Walter: The formation of cluster ions in laboratory sources and in the ionosphere, XXIX, 79 Nassenstein, H.: The boundary layer image converter, XVI, 633 Needham, M. J., and Thumwood, R. F.: A proximity-focused image tube, XXVIII A. 129 Nelson, P. D.: The development of image isocons for low-light applications, XXVIII A , 209 Neumann, M. J.: see Burns, J. Newbury, D. E.: see Williams, D. B. Newth, J. A.: see Binnie, D. M. Newton, A. C.: see Boksenberg, A. Niklas, W . F.: see Ball, Jack; Hiltner, W. A. , Dolon, Paul J., and Berger, Harold: A thermal-neutron image intensifier, XXII B, 781 Ninomiya, T., Taketoshi, L., and Tachiya, H.: Crystal structure of multialkali photocathodes, XXVIII A, 337 Niquet, G . : see Vernier, P. Nixon, W. C.: see Oatley, C. W. Noe. E. H.: see Flanagan, T. P. Norman, D. J.: see Beesley, J. Norton, K. A.: Propagation in the FM broadcast band, I . 381 Novice, M.: see Szepesi, Z . Novotny. B.: see JareS, V. Nozawa, Y . : Characteristics of a television photometer, XXVIII B, 891

302

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

: A digital television system for a satellite-borne ultra-violet photometer, XXII B, 865 Nudelman, S.: Intensifiers: detective quantum efficiency, efficiency contrast transfer function and the signal-to-noise ratio, XXVIII B, 577 Nussli, J.: see Boutot, J. P.

0 Oatley, C. W., Nixon, W. C., and Pease, R. F. W.: Scanning electron microscopy, XXI, 181 O’Keefe, T. W., and Vine, J.: A high-resolution image tube for integrated circuit fabrication, XXVIII A, 47 Okress, E. C.: Magnetron mode transitions, VIII, 503 Oleson, N. L., and Cooper, A. W.: Moving striations, XXIV, 155 Oliver, M.: see McGee, J . D. Olson, Sandra L.: Applications of scanning electron microscopy in archaeology, LXXI, 357 Oman, R. M.: Electron mirror microscopy, XXVI, 217 Ovenstone, J. A.: see Barlow, G . E .

P Pandit, M.: see Baier, P. W. Paoletti, L.: see Donelli, G. Papiashvili, I. I.: see Kron, Gerald E. Parham, A. G.: see Iredale, P. Paro, L., and Taneja, I. J.: Information energy and its applications, LXXX, 165 Pawley, M. G . , and Triest, W. E.: Multi-channel radio telemetering, IV, 301 Pease, R. F. W.: see Oatley, C. W. Penman, J.: Dual complementary variational techniques for the calculation of electromagnetic fields, LXX, 315 Per], Martin L.: see Jones, L. W. , and Jones, Lawrence W.: The regenerative image intensifier and its application to the luminescent chamber, XII, 153

Perrenoud, J.: see Geneux, E. Pesch, Peter: see Hiltner, W. A. Petley, C. H.: see Taylor, D. G. Picat, J. P.: see Combes, M. Pickering, H . W.: see Sakurai, Toshio Pierce, D. T.: see Campagna, M. , and Celotta, R. J.: Spin polarization in electron scattering from surfaces, LVI, 219 Pierce, J. A.: Electronic aids to navigation, I, 425 Pike, W. S.: see Flory, L. E. Pinsker, Z. G . : Electron diffraction structure analysis and the investigation of semiconducting materials, XI, 355 Pippard, A. B.: Metallic conduction at high frequencies and low temperatures, VI, 1 Polaert, R.: see Eschard, G . Porter, John H.: see Franzen, Wolfgang Porter, N. A,: see Hill, D. A. Potter, D. C . : see Binnie, D. M. Poultney, Sherman K.: Single photon detection and timing: experiments and techniques, XXXI, 39 Powell, J. R.: see McGee, J. D. -, and Lynds, R.: Methods of increasing the storage capacity of high-gain image intensifier systems, XXVIII B, 745 Powers, W.: see Hynek, J. A. Pratt, William K.: Image transmission techniques, Suppl. 12 Prosser, R. D.: see Berg, A. D. Pucel, Robert A., Haus, Hermann A,, and Statz, Hermann: Signal and noise properties of gallium arsenide microwave field-effect transistors, XXXVIII, 195 Pulfrey, D. L.: see Smith, W. A.

R Rado, G. T.: Ferromagnetic phenomena at microwave frequencies, 11, 251 Raffan, W. P., and Gordon, A. W.: The development and application of interference photocathodes for image tubes, XXVIII A, 433 Ramsdale, P. A.: Wire antennas, XLVII, 123

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 Randall, R. P.: Charge integration experiments with a C.P.S. Emitron, XII, 219 -. . Dark current scintillation of cascade image intensifiers, XXVIII B, 713 : Operating characteristics of a four-stage cascade image intensifier, XXII A, 87 Rattey, Paul A,: see Lindgren, Allen G. Redhead, P. A., Hobson, J. P., and Kornelson, E. V.: Ultra-high vacuum, XVII, 323 Redlien, Henry W., and Kelly, Robert J.: Microwave landing system: the new international standard, LVII, 311 Reimer, L.: Energy-filtering transmission electron microscopy, LXXXI, 43 Reininger, Walter G.: see Jensen, Arthur S. Reisner, John H.: An early history of the electron microscope in the United States, LXXIII, 134 Retzlaff, G.: see Kunze, W. Reynolds, G. T.: The distribution of single electron multipliers, and single electron detection, XXII A, 71 -. . Photon interference experiments utilizing photoelectric devices, XXVIII B, 939 -. . Sensitivity of image intensifier-film systems for observing weak light sources, XXII A, 381 Reynolds, T. T., Scarl, D. B., Swanson, R. A., Waters, J. R., and Zdanis, R. A,: Filament scintillation chamber experiments at Princeton University, XVI, 487 Riblet, Henry B.: Radio telernetering, XI, 287 Rice, P. L., and Herbstreit, J. W.: Tropospheric propagation, XX, 199 Richards, E. A.: Contrast-enhancement in imaging devices by selection of input photosurface spectral response, XXVIII B, 661 Richards, E. W.’ T.: see Wise, H. S. Rindfleisch, T., and Willingham, D.: A figure of merit measuring picture resolution, XXII A, 341

303

Ritter, G. X.: Recent developments in image algebra, LXXX, 243 Rittner, E. S.:see Bargellini, P. L. : Recent advances in silicon solar cells for space use, XLII, 41 Roach, F. E.: The nightglow, XVIII, 1 Roane, G. D.: see Marshall, F. B. Roberts, Arthur: Amplification of transient images in high-gain photocathodephosphor image intensifier systems, X I , 135 Robinson, L. C.: Generation of far-infrared radiation, XXVI, 171 Rofheart, M.: see An, M. Ronchi, L., and Scheggi, A. M.: Beam waveguides and guided propagation, LI, 64 Roptin, D.: see Cailler, M. Rosch, J.: see Wltrick, G. : Le gain possible de rksolution dans l’observation astronomique par I’emploi de la camtra eltctronique de Lallemand, XII, 113 , Wlkrick, G., and Boussuge, C.: Photographie des &toilesdoubles au moyen de la camtra tltctronique, XVI, 357 Rose, A.: Television pick-up’ tubes and the problem of vision, I, 131 Rose, D. C.: Intensity variations in cosmic rays, IX, 129 Rose, H.: see Kohl, H. Rosencwaig, Allan: Photoacoustic spectroscopy, XLVI, 208 Rosensweig, Ronald E.: Fluid dynamics and science of magnetic liquids, XLVIII, 103 Roth, Walter: see Narcisi, Rocco S. Rothstein, Jerome: see Goldberg, Seymour Rougeot, H., and Baud, C.: Negative electron affinity photoemitters, XLVIII, 1 Roux, G.: see Lansiart, A. Rowe, E. G.: On some aspects of tube reliability, X, 185 Rowe, J. E.: see Fleming, W. J.; Konrad, G. T. Rowlands, Richard 0.: Electronic engineering in river and ocean technology, XXXI, 267

304

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Riidenauer, F.: see Braun, P. Ruedy, J. E.: see Morton, G . A. Russell, L. A,: High-speed magnetic-core memory technology, XXI, 249 Ryden, D. J.: see Iredale, P. Ryssel, Heiner: Ion implantation for very large scale integration, LVIII, 191 Rzhanov, A. V . , Svitashev, K. K.: Ellipsometric techniques to study surfaces and thin films, XLIX, 1

S

Saalfeld, F. E., DeCorpo, J . J., and Wyatt, J . R.: Mass spectroscopy, XLII, 2 Sabatier, P. C.: Inverse problems: an interdisciplinary study, Suppl. 19 Sackinger, W. M., and Johnson, J. M.: An analysis of the low-level performance of channel multiplier arrays, XXVIII A, 487 -, and Johnson, J. M.: Effects of vacuum space charge in channel multipliers, XXVIII A , 507 Sakai, A,: see Sakurai, Toshio Sakurai, Toshio, Sakai, A., and Pickering, H. W.: Atom-probe field ion microscopy and its applications, Suppl. 20 Sancho, M.: see Martinez, G. Santander, Mariano: see Carinena, Jose F. Sasaki, T., Nakamura, T . , and Goto, S.: Experiments on a wire-electrode type image intensifier using electroluminescence, XVI, 621 Sattler, K.: see Campagna, M. Sauzade, M. D., and Kan, S. K.: High resolution nuclear magnetic resonance spectroscopy in high magnetic fields, XXXIV, 1 Saxton, W. 0.: Computer techniques for image processing in electron microscopy, Suppl. 10 Sayood, Khalid: see Gibson, Jerry D. Scarl, F., and Harth, W.: Computation of imaging properties of image tubes from an analytic potential representation, XXVIII A, 535 Schaffner, J.: Junction transistor applications, V , 367

Schagen, P.: An image intensifier system for direct observation at very low light levels, XVI, 75 Schagen, P., and Turnbull, A. A.: New approaches to photoemission at long wavelengths, XXVIII A, 393 Schagen, P.: see Manley, B. W.; Woodhead, A. W. Scharfe, M. E., and Schmidlin, F. W.: Charged pigment xerography, XXXVIII, 83 Scheggi, A. M.: see Ronchi, L. Schiek, B.: see Schilz, W. Schilz, W., and Schiek, B.: Microwave systems for industrial measurements, LV, 309 Schlesinger, S. P.: see Marshall, T. C. Schluter, R . A,: see Hill, D . A. Schmerling, E. R.: see Bowhill, S. A. Schmidlin, F. W.: see Scharfe, M. E. Schmidt, M.: see Dennison, E. W. Schnable, George L., and Keen, Ralph S.: On failure mechanisms in large-scale integrated circuits, XXX, 79 Schneeberger, R. J.: see Anderson, A. E. , Skorinko, G., Doughty, D. D., and Feibelman, W. A.: Electron bombardment induced conductivity including its application to ultra-violet imaging in the Schuman region, XVI, 235 Schneider, J.: see Kaufmann, U. Schooley, Allen H.: Electronic instrumentation for oceanography, XIX, 1 Schon, R. W.: see Knoll, M. Schumacher, Berthold W.: Dimensional terms for energy transport by radiation and for electromagnetic quantities-comments on the SI system, LXV, 229 Schuster, G.: see Giese, R. Seib, D. H., and Aukerman, L. W.: Photodetectors for the 0.1 to 1.0 p n spectral region, XXXIV, 95 Sekunova, L. M.: see Yakushev, E. M. Septier, A.: Applied charged particle optics, Suppl. 13 -: Strong-focusing lenses, XIV, 85

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 SCquin, Carlo H., and Tompsett, Michael F.: Charge transfer devices, Suppl. 8 Shao, Zhifeng: see Wang, Y. L. Shapiro, G.: Subminiaturization techniques, 111, 195 Shaw, M. P., Grubin, H. L., and Solomon, P. R.: Gunn-Hilsum effect electronics, LI, 310 , and Yildirim, N . : Thermal and electrothermal instabilities in semiconductors, LX, 307 Shirouzo, S.: see Miyashiro, S. Shrager, Peter G., and Suskind, Charles: Electronics and the blind, XX, 261 Siegmann, H. C.: see Campagna, M. , Meier, F., Erbudak, M., and Landolt, M.: Spin-polarized electrons in solid-state physics, LXII, 2 Silzars, Ark: see Bates, David J. Simon, J. C.: see Broussaud, G . Simpson, J. H.: see Frohlich, H. Singer, J. R.: Masers and other quantum mechanical amplifiers, XV, 73 Sirou, F.: see Guyot, L. F. Skorinko, G.: see Schneeberger, R. J. Slark, N. A.: see Batey, P. H.; Beurle, R. L. , and Woolgar, A. J.: A transmission secondary emission image intensifier, XVI, 141 Slump, Cornelis H., and Ferwerda, Hedze: A.: Statistical aspects of image handling in low-dose electron microscopy of biological material, LXVI, 202 Smiley, V. N . : Recent advances in high-power tunable lasers (UV, visible, and near IR) LVI, 2 Smit, J., and Wijn, H. P. J.: Physical properties of ferrites, VI, 69 Smith, C. V. L.: Electronic digital computers, IV, 157 Smith, C. W.: An x-ray sensitive photoconductive pick-up tube, XII, 345 , Kao, K. C . , Calderwood, J . H., and McGee, J . D.: A study of pre-breakdown phenomena in n-hexane using an image intensifier tube, XXII B, 1003 Smith, G . R.: see McKee, J . S. C.

305

Smith, R. W.: see Berg, A. D.; Morgan, B. L. : The application of the electron image store and analyser to high-speed photography, XXVIII B, 1011 Smith, W. A., Chatterton, P. A., Elliott, C. T., and Pulfrey, D. L.: A high speed photographic study of the electrical breakdown of small gaps in vacuum, XXVIII B, 1041 Smith-Rose, R. L.: Radiowave propagation: A review, IX, 187 Smout, D. W. S.: see Iredale, P. Smyth, M. J.: and Brand, P. W. J . L.: Linearity of electronographic emulsions, XXVIII B, 737 Smyth, M. J.: see Brand, P. W. J. L. Snoek, C . , and Kistemaker, J.: Fast ion scattering against metal surfaces, XXI, 67 Sodha, Mahendra Singh, and Kaw, Predhiman Krishan: Theory of the generation of harmonics and combination frequencies in a plasma, XXVII, 187 Soethout, L. L., van Kempen, H., and van de Walle, G. F. A , : Scanning tunneling microscopy: a mature surface-science technique, LXXIX, 155 Solomon, P. R.: see Shaw, M. P. Southon, M. J.: see Whitmell, D. S. Spinella, Salvatore: see Bates, David J. Stahnke, Ingeborg, and Heinrich, Hans: Special problems in measuring the modulation transfer function of x-ray image intensifiers, XXII A, 355 Stark, A. M., Lamport, D. L., and Woodhead, A. W.: Calculation of the modulation transfer function of an image tube, XXVIII B, 567 Statz, Hermann: see Pucel, Robert A . Stebbings, R. F.: see Dunning, F. B. Sternheimer, R. M.: Parity nonconservation in weak interactions, XI, 31 Stevefelt, J.: see Delpech, J.-F. Stone, H. D.: Preparation of highresolution phosphor screens, XXII A, 565 Stoudenheimer, R. G.: Image intensifier

306

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

developments in the RCA electron tube division, XII, 41 Strausser, Y. E.: see Medved, David B. Stricker, S.: The Hall effect and its applications, XXV, 97 Stiirimer, W.: Some applications of solid state image converters (SSIC), XVI, 613 Su, Timothv: see Bowers, Michael T. Susskind, C.: See Shrager, Peter G. -: Electron guns and focusing for high-density electron beams, VIII, 363 -: Ferdinand Braun: forgotten forefather, L, 241 Svelto, V.: see Donati, S. Svitashev, K. K.: see Rzhanov, A. V. Swank, Robert K.: see Vosburgh, Kirby G . Swanson, R. A.: see Reynolds, G. T. Symons, R. S., and Jory, H. R.: Cyclotron resonance devices, LV, 2 Syms, C. H. A,: Gallium arsenide thin-film photocathodes, XXVIII A, 399 Szepesi, Z., and Novice, M.: Solid-state radiographic amplifiers and infra-red converters, XXVIII B, 1087

T Tachiya, H.: see Ninomiya, T. Taketoshi, K.: see Ninomiya, T. Taneja, I. J.: see Pardo, L. Taneja, Inder, Jeet: On generalized information measures and their applications, LXXVI, 328 Taylor, A.: see Goetze, G. W. Taylor, D. G.: see Schagen, P.; Woodhead, A. W. -. . The measurement of the modulation transfer functions of fluorescent screens, XXII A, 395 -, Petley, C. H., and Freeman, K. G.: Television at low light-levels by coupling an image intensifier to a Plumbicon, XXVIII B, 837 Taylor, S.: An infra-red-sensitive television camera tube, XII, 263 te Winkel, J.: Past and present of the charge-control concept in the characterization of the bipolar transistor, XXXIX, 253

Tepinier, M.: see Vernier, P. Ter-Pogossian, M.: see Ball, Jack Tessier, M.: see Malherbe, A. Teszner, J. L.: see Teszner, S. Teszner, S., and Teszner, J . L.: Microwave power semiconductor devices. Part I, XXXIX, 291; Part 11, XLIV, 141 Tewary, V. K., and Jain, S. C.: Open-circuit voltage decay in solar cells, LXVII, 329 Theile, R.: On the signal-to-noise ratio in television storage tubes, XII, 277 Theodorou, D. G.: Research on photocathode surfaces at the Bendix Corporation Research Laboratories Division, XXII A, 477 Thonemann, F. F.: see Barlow, G. E. Thornton, P. R.: Electron physics in device microfabrication. Part I General background and scanning systems, XLVIII, 272; Part I1 Electron resists, x-ray lithography, and electron beam lithography update, LIV, 69 Thumwood, R. F.: see Foreman, P. H.; Garfield, B. R. C.; Needham, M. J. Timan, H.: A survey of recent advances in the theory and practice of vacuum photoemitters, LXIII, 73 Todkill, A.: see Emberson, D. L. Toepfer, Alan J.: Particle beam fusion, LIII, 1 Tolimieri, R.: see An, M. TomoviC, R.: Systems approach to skeletal control: concept of the system, XXX, 273 Tompsett, Michael F.: see SCquin, Carlo H . Tousimis, A. J., and Marton, L.: Electron probe microanalysis, Suppl. 6 Towler, G. 0.:see McMullan, D. Triest, W. E.: see Pawley, M. G. Trindade, Armando Rocha: see Delcroix, Jean-Loup Trolander, Hardy W., and Veghte, James H.: Recent advances in biological temperature measurements, XXX, 235 Trott, Mitchell D.: see Chizeck, Howard J . Trunk, G. V.: Radar signal processing, XLV, 203 Tsuji, S.: see Hori, H.

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 Turnbull, A. A , : see Schagen, P. Twiddy, N . D.: see Filby, R. S. Twiss, R. Q.: On the steady state theory of the magnetron. V, 247

U Unger, H.-G., and Harth, W.: Physics and applications of MIS varactors, XXXIV, 281 Uno, Y.,Kawakami, H., Maeda, H., and Miyazaki, E.: Cathode-ray tube with thin electron-permeable window, XXVIII A, 81 Ura, K., and Fujioka, H.: Electron beam testing, LXXIII, 234 V

Vallat, D.: see Boutot, J. P. van den Handel, J.: Paramagnetism. V1, 463 van der Polder, L. J.: Beam-discharge lag in a television pick-up tube, XXVIII A, 237 van der Ziel, A,: Flicker noise in electronic devices, XLIX, 225 : Fluctuation phenomena, IV, 110 : History of noise research, L, 351 , and Chenett, E . R.: Noise in solid state devices, XLVI. 314 van de Walle. G . F. A , : see Soethout, L. L. van Dyck, D.: Image calculations in high-resolution electron microscopy: problems, progress, and prospects, LXV. 296 van Kempen, H . : see Soethout, L. L. Van Khai, Tran: see Arsac, J. van Overhagen, J.: see Kiihl, W. van Overstraeten, R.: see Jain, S. C. van Overstraeten, Roger J.: see Mertens, Robert P.; Muls, Paul A. van Roosmalen. J . H. T.: Adjustable saturation in a pick-up tube with linear light transfer characteristics, XXVIII A, 281 Vance, A. W . , Hutter, E. C., Lehmann, J . , and Wadlin, M. L.: Analog computers, VII. 363

307

Varma, B. P.: see McGee, J. D Vasseur, J . P.: see Arsac, J. Veghte, James H.: see Trolander, Hardy W. Vennik. J . : see Fiermans. L. Vernier. P., and Hartmann, P.: Resultats obtenus a I’aide de la camera electronique Lallemand dans I’etude de I’emission photoelectrique, XXII A , 519 -, Hartmann, P., Niquet, G., and Tepinier. M.: Etude de I’emission photoelectrique des structures metal-isolant-metal, XXVIII A, 409 Veron. S.: see Malherbe. A. -: Quelques aspects des essais de depAt de photocathodes S.20 et d’ecrans Huorescents sur fibres optiques. XXVIII A. 461 Verwey. J. F.: Nonvolatile semiconductor memories, XLI, 249 Viehbock, F. P.: see Braun, P. Vilim, P.: see JedliEka, M. Vine. J.: see O’Keefe, T. W. -: The design of electrostatic zoom image intensifiers, XXVIII A, 537 Vodovnik, L.: Functional electrical stimulation of extremities, XXX, 283 Vogl, P. : Predictions of deep-impurity-level energies in semiconductors, LXII, 101 Voisin, P.: see Bastard, G . Von Aulock, Wilhelm H . , and Fay, Clifford E.: Linear ferrite devices for microwave applications, Suppl. 5 von Borries, Hedwig: Bod0 von Borries: pioneer of electron microscopy, LXXXI, 127 von Engel, A,, and Cozens, J . R.: Flame plasmas, XX, 99 Voorman, J . 0.:see Adams, K. M. Vosburgh. Kirby G.. Swank. Robert K.. and Houston, John M.: X-ray image intensifiers, XLIII, 205

W Wachtel. M. M., Doughty, D . D., and Anderson, A. E.: The transmission secondary emission image intensifier, XII, 59

308

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81

Wadlin, M. L.: see Vance, A. W. Wagner, K. H.: Application of image intensifiers and shutter tubes to the study of gas discharges, XXVIII B, 1033 Wagner, Robert J . : see McCombe, Bruce D. Wait, James R.: Recent theoretical advances in the terrestrial propagation of ULF electromagnetic waves, XXV, 145 Walker, M. F.: Performance of the Spectracon in astronomical spectroscopy, XXVIII B, 773 -: Recent astronomical observations obtained with the Lallemand electronic camera, XVI, 241 -: Recent progress in the use of the Lallemand electronic camera in astronomical spectroscopy, XXII B, 761 Walsh, John E.: Stimulated cerenkov radiation, LVIII, 271 Walters, F. W.: see Huston, A . E. Walters, J . : see Binnie, D. M. Wang, Y. L., and Shao, Zhifeng: Design principles of an optimized focused ion beam system, LXXXI, 177 Wanson, L. W., and Bell, A. E.: Recent advances in field electron microscopy of metals, XXXII, 194 Wardley, J . : A high-resolution ruggedized half-inch vidicon, XXII A , 211 -. . An improved ultra-violet sensitive vidicon, XVI, 227 -, and Jackson, F. W.: A 13-mm all-electrostatic vidicon, XXVIII A, 247 Warnecke, R. R., Chodorow, M., Guenard, P. R., and Ginzton, E. L.: Velocity modulated tubes, 111, 43 Waters, J. R.: see Reynolds, G. T. Watson, C. J.: see Motz, H. Webster, H. F.: see Houston, J. M. Webster, W. M.: A comparison of analogous semiconductor and gaseous electronic devices, VI, 257 Wechsler, Harry: Invariance in pattern recognition, LXVIX, 262 Wehner, G . K.: Sputtering by ion bombardment, VII, 239 Weimer, P. K.: Image sensors for solid state cameras, XXXVII, 182

: Television camera tubes: a research review, XIII, 387 Weingartner, H. C., and Kennedy, S. W.: Modern vacuum pumps in electronics manufacturing, V, 213 Welton, T. A , : A computational critique of an algorithm for image enhancement in bright field electron microscopy, XLVIII, 37 Wendt, G.: INTIC, an image intensifying, integrating and contrast-enhancing storage tube, XXVIII A, 137 Wheeler, B. E.: see McGee, J . D. , and Emberson, C. J . : Some measurements on the direct recording of electron images using thin windows, XXII A, 51 Whelm, M. J . : Electron diffraction theory and its application to the interpretation of electron microscope images of crystalline materials, XXXIX, 1 Whetten, N . R.: see Dawson, P. H. White, J . E.: Tube miniaturization, 111. 183 White, Richard M.: see Brodersen, Robert W . Whitmell, D. S . , and Southon, M. J.: Image intensification in field-ion microscopy, XXII B, 903 Wijn, H. P. J . : see Smit, J. Wilcock, W. L.: see Emberson, D. L.; McGee, J. D. -: Routine measurement of the responsive quantum efficiency of photoemissive cathodes, M I 1 A, 535 -. . Statistics of transmitted secondary electron multiplication, XXII A, 629 -, and Baum, W. A.: Astronomical tests of an imaging photomultiplier, XVI, 383 , and Miller, D. E.: Statistics of transmitted secondary electron emission, XXVIII A , 513 Wild, J. P.: Observational radio astronomy, VII, 299 Williams, D. B . , and Newbury, D. E.: Recent advances in the electron microscopy of materials, LXII, 162 Williams, F. E.: Solid-state luminescence, V, 137

CUMULATIVE AUTHOR INDEX, VOLUMES 1-81 Williams, Gareth F.: Lightwave receivers, LXXV, 389 Williamson, W . , Jr.: see Chan, F. T. Willingham, D.: see Rindfleisch, T. Wilson, G. A,: see Morgan, B. L. Wimmer, E., Krakauer. H., and Freeman, A. J.: Theory of surface electronic structure, LXV, 358 Winkler, Gernot, M. R.: Timekeeping and its applications, XLIV, 34 Winters, K. H.: see Jain, S. C. Wise, H. S . , Richards, E. W. T., and Martin, R.: Digital read-out of an image intensifier using a vidicon or a scanning spiral slit plus a digital memory oscilloscope, XXVIII B, 981 Wlerick, G.: see Charrier, Mlle S . ; Lallemand, A , ; Rosch, J . : Etudes d'astres faibles en lumiere totale avec la camera tlectronique, XXVIII B, 787 , and Grosse, Achilles: La camCra electronique: u n recepteur d'images sans lumiere diffusee, XXII A, 465 , Rosch J., Dupre, Mlle M., and Bellier, Mlle M.: La photographie electronique des planetes et ses applications photometriques, XVI, 371 Wolfgang, L. G.: see Abraham, J. M. Wolpers, C.: Electron microscopy in Berlin, LXXXI, 211 Wolstencroft, R. D.: see Brand, P. W. J . L. Woodhead, A. W.: see Schagen, P.; Stark, A. M. , Taylor, D. G . , and Schagen, P.: A two-stage electrostatic image intensifier with a large photocathode area, XVI, 105 Woolgar, A. J.: see Slark, N. A. Woonton, G. A , : Relaxation in diluted paramagnetic salts at very low temperatures, XV, 163 Wreathall, W. M.: see Beurle, R. L. -: Aberrations of diode image tubes, XXII A, 583

309

Wyatt, J . R.: see Saalfeld, F. E. Wynne. C. G., and Kidger, M. J.: The design of optical systems for use with image tubes, XXVIII B, 759 v

A

Ximen, Jiye: Canonical theory in electron optics, LXXXI, 231

Y Yakushev, E. M., and Sekunova, L. M.: Theory of electron mirrors and cathode lenses, LXVIII, 337 Yamamoto, Hajime: see Hase, Takashi Yang, Edward S . : Current saturation mechanisms in junction field-effect transistors, XXXI, 247 Yaroslavskii, L. P.: Applied problems of digital optics, LXVI, 1 Yavor, S . Ya.: see Baranova, L. A. Yildirim, N.: see Shaw, M. P. Yu, Francis, T. S.: Recent advances in white-light image processing, LXIII, 1

Z

Zacharias, J . R.: see King, J . G. Zacharov, B.: A demagnifying image tube for nuclear physics applications, XVI, 99 -: Image resolution in thin-window intensifiers using homogeneous fields, XVI. 61 -, and Dowden, S.: An image intensifier with a thin end-window, XII, 31 Zalm, P.: Thermionic cathodes, XXV, 211 Zdanis, R. A,: see Reynolds, G . T. Zeitler, E.: Resolution in electron microscopy, XXV, 277 Zimmerman, Bodo: Broadened energy distributions in electron beams, XXIX, 251 Zucchino, P. M.: see Lowrance, J . L.

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Cumulative Subject Index, Volumes 1-81 A

Aberration correctors, electrostatic lenses, LXXVI, 187 Aberration models, cathode lenses, LXXVIII, 158 Aberration theory electron and ion optics, Suppl. 17 Lagrangian representations, LXXXI, 236 ac arrays, XXXV, 235 Accelerators linear ion, XXV, 1 particle, I, 269 history, L, 2 Acoustic devices, using NPP periodic domain wall gratings, LXXI, 327 Acoustic imaging, electronic circuits, SUPPI. 11 Acoustic waves interaction with ferroelastic domain walls, LXXI, 256 nonlinear electron, XXXV, 1; XLI, 1 Acoustoelectric interactions 111-V compound semiconductors, XXXI, 162 off-axis, XXXI, 166 Aids to navigation, electronic, I, 425 Airborne detector, magnetic, IV, 258 Algebraic systems, LXXIX, 1 Alkali halide crystals, pre-breakdown light emission from, XXII B, 995 Alternating gradient accelerators, L, 65 Amorphous carbon, energy-loss spectroscopy, LXXV. 181 Amplification gaseous detector device, LXXVIII, 60 of transient images, XII, 135 transmission secondary emission, XVI, 557 Amplifiers beam-maser, XXIX, 219 noise, L, 397 operational, XI, 225 quantum mechanical, XV, 73 solid-state traveling-wave, design and analysis, XLIV, 100 31 1

Amplitude measurement in nuclear physics, VIII, 256 pulse, analysis. VIII, 317 variation, with offset, signal analysis. seismic studies, LXXVII, 298 Analog computers, VII. 353 Analog signal processors, charge-transfer sensors as, XXXVII, 247 Angular momentum transfer, solar wind, XXXVI, 52 Annealing, electrical properties and, XXXVII, 299 Antennas active, XLVII, 172 endfire, XIX, 255 microstrip, see Microstrip antennas millimeter radioastronomy, LVI, 133 nonsinusoidal waves, Suppl. 15 passive loaded, XLVII, 163 selection, XLVII, 187 unloaded, XLVII. 152 wire, XLVII, 123 Archaeological specimens, preparation, LXXI. 359 Archaeology, SEM applications, LXXI. 357 Arithmetic operations, universal imaging algebra, LXVII, 144 ARMA model, LXX, 84 AR model, LXX, 84 Array, size reduction. XLI, 200 Astronometric images, camera tubes for recording, XXII A, 175 Astronomy comparison of image intensifiers for, XXVIII B, 753 image scanning techniques in, XVI, 409 observational radio, VII, 299 observations, recent, obtained with Lallemand electronic camera, XVI, 34 1 radio, XXXII, 1 solar radio, XX, 147 tests of barrier-membrane image converters, XII, 21

312

CUMULATIVE SUBJECT INDEX. VOLUMES 1-81

Astronomy (Continued) tests of imaging photomultiplier, XVI, 383 uses of image intensifying tubes, XVI, 403 Atomic collisions, XVIII, 67 Glauber and Eikonal approximations, XLIX, 134 Rydberg processes, LIX, 79 Atomic photoelectron spectroscopy, XLI, 73; XLIV, 1 Atomic reactants, collisional detachment of negative ions, LVIII, 148 Atomic targets, Rydberg atom collision processes, LIX, 88 Atom-probe field ion microscopy, Suppl. 20 Atoms multiphoton ionization, XXXVI, 58 neutral, diffraction from crystalline surfaces, LX, 95 Atom-surface scattering, quantum theory, LX, 111 Attachment, LI, 137; VXII, 1 Auger electron, voltage measurement schemes, LXIX, 24 Auger electron spectroscopy applications, LIV, 287 elastic collisions, LXI, 185 fundamentals, LIV, 241 quantitative, LIV, 280, LXI, 162 sample damage, LIV, 285 surface research, XLIII, 164 Auger emission, quantitative description, LXI, 213 Auger transitions, in solids, LXI, 187 Aurora borealis, IX, 1 Automatic data processing, XI, 185 Autoregressive models, robust estimation, LXX, 109 Avalanche device integrated, XXXV, 312 physics, X M V , 289 Aviation, distance measuring equipment, LXVII1,I Axial-beam tubes, XIV, 299

Band structure, submicron VLSIs, LVIII, 361 Barrier-membrane image converters, astronomical tests of, XII, 21 Beams, see also specific types deflection of, I, 167 high density electron, VIII, 363 magnetically focused cylindrical, X , 1 molecular, new applications and techniques, VIII, 1 Beam waveguides, guided propagation, LI, 64 Bell’s inequalities, LXVIII, 273 Beta-ray spectrometers, V, 97 Betatron, L, 34 Biological effects, microwaves, LIII, 85 Biological material aldehyde-fixed, contrast, LXIII, 294 electron microscopy contrast formation, LXIII, 270 low-dose, image handling, LXVI, 202 Biological temperature measurements, XXX, 235 Biology, photoacoustic spectroscopy, XLVI, 280 Biopsis, NMR, XLIX, 109 Bipolar transistors charge-control concept, XXIX, 253 three-terminal, XLIV, 141 Boundary-element method, Hall plates, LXI, 18 Braun, Ferdinand, L, 241 Bright field electron microscopy algorithm for image enhancement, XLVIII, 37 image theory, XLVIII, 39 Bucket brigade registers, charge-transfer sensors, XXXVII, 208 Bulk charge storage, electron beam addressed memories, XLIII, 81 Bulk diodes, microwave power, XXIX, 293 Bus architecture, minicomputers, XLIV, 295 C

B Band-gap narrowing, measurement, heavily doped silicon, LV, 87

Cache memory, minicomputers, XLIV, 299 Caesium vapor effects upon target glass, XXII A, 651; XXVIII A, 309

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 getter materials for, XXVIII A, 381 reaction with gold, XXII A , 643 Cameras color, self-scanned sensors, XXXVII, 25 1 solid state, image sensors, XXXVII, 182 Canonical theory, electron optics, LXXXI, 231 Canterbury algorithm, LXVII, 40 Carrier resonances. bound. XXXVIII. I Carriers, interaction of free and bound with collective excitations, XXXVIII, 19 Carrier stream surfaces, nondegenerate semiconductor plasmas. XLV, 1 Carrier transport bulk silicon and weak silicon inversion layers, LXXVIII, 104 MOSFET weak-inversion region, LXXVIII, 117 Cascade image intensifier, XXII A , 113; XXVIII A, 89 astronomical uses, XXII B, 697 comparison with transmission secondary emission type, XXII A , 129 dark current scintillations of, XXVIII B, 713 fibre-optic coupled, XXVIII A , 119 four-stage, characteristics of, XXII A , 87 influence of temperature on, XXII A , 101 magnetically focused, XVI, 113 Cascade phosphor-photocathode screens, evaluation, XXII A , 407 Cathode arcs, hollow, XXXV, 88 Cathode lenses aberration models, LXXVIII. 158 theory, LXVIII, 337 Cathode ray oscilloscopes, recent developments, X, 239 Cathode ray tubes contrast enhancement, color tubes, LXXIX, 353 design, 11, 26 with electron-permeable window. XXVIII A , 81 excitation processes. LXXIX, 289 industrial and military applications, LXVII, 183 manufacture and design, 11, 2 narrow angle, Suppl. 3

313

phosphors, LXXIX, 271 characteristics, LXXIX, 359 progress, 11, 2 screen fabrication techniques, LXXIX, 332 Cathodes hot. energy spectrum of electron emission, XXXIX, 73 oxide coated, I, 1 thermionic, XXV, 211 Cathodoluminescence, 11, 152 terenkov chamber, with four-stage image intensifier, XXVIII B, 919 terenkov radiation at microwave frequencies, XIV, 265 stimulated, LVIII, 271 Chalcogenide, thin films, thermal and electrothermal instabilities, LX, 332 Channelled image intensifier, XII, 97 progress report on, XVI, 155 Channel multiplier for imaging applications, XXVIII A , 471 low-level performance of, XXVIII A , 487 problems concerning, XXVIII A , 499 vacuum space charge in, XXVIII A , 507 x-ray detection by, XXII A , 139 Characteristic energy losses, of electrons in solids, VII, 183 Charge-control concept, bipolar transistor, XXIX, 253 Charge-coupled device characteristics, XXXVII, 213 performance limitations, LI, 270 principles, LI, 266 transversal filters, LI, 287 Charged-particle beams, surface analysis, LVII, 231 Charged-particle optics, Lie algebraic theory, LXVII, 65 Charged particles, collisions with, LIX, 122 Charged pigment xerography, XXXVIII, 83 Charge integration experiments, XII, 219 Charge particle beams, deflection of, I, 167 Charge particle optics, applied, Suppl. 13 Charge transfer reactions, XXXIV, 231 scanning by, XXXVII, 202 surface acoustic-wave signal-processing, LI, 265

314

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Charge-transfer devices, Suppl. 8 Charge-transfer sensors as analog signal processors, XXXVII, 247 bucket brigade registers, XXXVII, 208 Chemical analysis, electron microscopy, LXII, 263 Chemical lasers, XXXI, 1 Chemistry, photoacoustic spectroscopy, XLVI, 256 Circuits, computer-aided analysis, charge-control concept, XXIX, 284 Circuit transients, impulsive, LIV, 58 Clocks, XLIV, 43 electronic, LI, 186 Cluster ions, in laboratory and ionosphere, XXIX, 79 Coherence quantum modulation of electrons, LXIX, 77 white-light image processing, LXIII, 7 Coherent processing, radar signal, XLV, 204 Coherent sources, nonlinear, tunable lasers, LVI, 60 Colliding beams, L, 82 Collisional detachment, negative ions, LVIII, 143 Collisions, inelastic, between atomic systems, XIII, 1 Color cameras, self-scanned sensors, XXXVII, 251 Color center lasers, LVI, 54 Color images, thin-film transistor liquid-crystal displays, LXXVII, 57 Color television, recent work in, V, 291 Combination frequencies, in plasma, 187 Communications radar and radio, nonsinusoidal waves, Suppl. 14 satellite, XXXI, 119 spread spectrum systems, LIII, 209 Communication theory, 111, 306 Composite edge detection, LXX, 139 Computer-aided design, fast scanning system, XLVIII, 341 Computer architecture, trends, XLVIII, 203 Computer logical organization, X , 153

Computer organization, recent developments in, XVIII, 45 Computers analog, VII, 363 electronic digital, IV, 157 Computer techniques, EM image processing, Suppl. 10 Conductance, thermally induced negative differential, LX, 321 Conduction mechanism, nonvolatile semiconductor memories, XLI, 264 Conduction, metallic, at high frequencies and low temperatures, VI, 1 Conductivity, electron bombardment induced, XVI, 235 Conductors, integral equations, LXXXI, 2 Consoles, minicomputers, XLIV, 310 Continuous jets, ink-jet printing, LXV, 132 Continuous random variables, information energy and energy gain, LXXX, 176 Continuous-wave magnetrons, modulation of, IV, 188 Contrast enhancement cathode ray tubes, LXVII, 288 color cathode ray tubes, LXXIX, 353 in imaging devices, XXVIII B, 661 Contrast formation, electron microscopy, biological material, LXIII, 270 Contrast mechanisms, scanning electron acoustic microscopy, LXXI, 4 Cooley-Tukey algorithms, tensor product formulation, LXXX, 4 Cosmic radio noise, I, 347 Cosmic rays and image intensifier dark current, XXVIII B, 705 intensity variations in, IX, 129 CoudC spectrograph, performance of image tubes in, XXII B, 729 Coulomb interactions, particle beams, Suppl. 21 Counter, scintillation, IV, 69 CPU, minicomputer, XLIV, 285 CramCr-Rao bound, LXVI, 305 Crossed electrostatic lenses, LXXVI, 174 Crystal-lattice anharmonicities, LXXVII, 98 Crystalline surfaces, neutral atom and molecule diffraction, LX, 95 Crystallography, electron microscope, LXII, 247

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Crystals diffraction, electron interference, LIII, 274 electron-beam investigating of, XXIV. 109 magnetic properties of, XXIV, 109 Current density distribution, electrostatic lenses, LXXVI, 69 generation, photovoltaic effect, LVI, 189 space-charge-limited, VI, 138 Cyclotron resonance devices, LV, 2 Cylindrical beams, nonuniform D-C electron flow in, X, 1 Cylindrical magnetron, electronic theory of. 11, 15

D Data checking, minicomputers, XLIV, 293 Data compress, two-dimensional digital filters, LXVI, 141 Data entry, minicomputers, XLIV, 313 Data processing, automatic, in physical sciences, XI, 185 Data set interfaces, minicomputers, XLIV, 320 Data transmission, invasion of privacy and interception of, XXXVIII, 191 dc arrays, XXXV, 204 dc discharge cells, characteristics, XXXV, 195 D-C electron flow, nonuniform, in magnetically focused beams, X, 1 Deblurring, LX, 163 Deconvolution, two-dimensional data, XXXII, 183 Deep-impurity-level energy, semiconductors, predictions, LXII, 101 Deep trap, LXII, 104 Defects diamond-type semiconductor crystals, X , 71 GaAs levels, LXI, 64 implanted, concentration profiles, XXXVII, 271 molecular picture, LXII, 105

315

Deflection amplification, industrial and military applications. LXVII, 209 beams of charge particles, I , 167 device microfabrication, XLVIII, 352 electron beams. XLIX, 299 Detachment, LI, 137; VXII, 1 Detective quantum efficiency, of intensifiers, XXVIII B, 577 Detectors design, LXXVII, 125 magnetic airborne, IV, 258 noise. L. 397 piezoelectricity, LXXVII, 84 quantum efficiency of, XI, 87 for visible and infrared radiation, V, 1 Developments, image intensifier, XII, 41 Diagenesis, reservoir, SEM, LXXVII. 156 Dielectric breakdown in solids, intrinsic, 11, 185 Dielectric rods and fibers, LI, 80 Dielectrics, integral equations, LXXXI, 2 Dielectric structures, two-dimensional, LI, 91 Dielectric theory. inelastic collisions of electrons in solids, LXI, 173 Diffraction neutral atoms and molecules, from crystalline surfaces, LX, 95 tomography, LXX, 290 Diffusion coupled equations, open-circuit voltage decay, LXVII, 383 enhanced, ion implantation, XXXVII, 289 Digital circuits, filter implementation, XLI. 216 Digital computers, electronic, IV, 157 Digital filters, two-dimensional, LXVI, 141 Digital image processing, LX, 161 Digital imaging system, LXX, 283 Digital memory oscilloscope, XXVIII B, 9R 1 Digital optics applied problems, LXVI, 1 automatic localization of objects, LXVI, 68 Digital processing, remotely sensed data, LXVI, 310

316

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Digital signal processing, number theoretic techniques, LXXX, 69 Digital ultrasonic imaging, LXX, 253 Dimensional, analysis, LXXII, 182 kinematic groups, LXXII, 226 mathematical foundations, LXXII, 199 physical meaning, LXXII, 216 symmetries of differential equations, LXXII, 234 Dimensional terms, LXV, 229 Diode image tubes, aberrations, XXII A, 583 Diodes, noise, XLVI, 320 Direct voltage accelerators, L, 11 Discharges, electrical, in gases, VII, 401 Discrete coordinate systems applied to space-time, L, 285 multidimensional, L, 306 Discrete fast Fourier transform algorithms, LXXX, 1 Discrete Fourier transforms, digital signal processing, LXXX, 75 Discrete mathematical physics, particle modeling, LXIII, 189 Discrete random variables, information energy and energy gain, LXXX, 167 Disk operating systems, minicomputers, XLIV, 325 Disk systems, minicomputers, XLIV, 315 Dispersion equations, solution, XXXIX, 68 Distance measures equipment, aviation, LXVIII, 1 generalized, LXXVI, 352 Divergence measures, generalized, LXXVI, 359 DME/N system, LXVIII, 118 Doping, silicon, heavy doping, LV, 77 Drain current model, MOSFET, XLVII, 201 Drift velocity, bulk silicon, LXXVIII, 109 Drop-on-demand methods, ink-jet printing, LXV, 111 Dual complementary variation techniques, electromagnetic fields, LXX, 315 Dyadic coordinate systems, L, 324 Dyadic functions, definition and properties, LXV, 7 Dyadic Green’s function expansion, LXV, 11

free-space, LXV, 7 microstrip antenna analysis, LXV, 2 Dyadic metric, L, 310 Dye lasers, LVI, 3 Dynamical radiation model, microstrip structures, LIX, 139

E Earth from flat to spherical, L, 261 three-dimensional space, L, 264 Ebers-Moll model, derived from charge-control concept, XXIX, 269 Edelweiss system, XLVIII, 202 Efficiency contrast transfer function, of intensifiers, XXVIII B, 577 Eikonal approximation, atomic collision applications, XLIX, 134 Einstein-Podolsky-Rosen paradox, LXVIII, 245 Ejection, kinetic, of electrons from solids, XXI, 101 Elastic collisions, Auger electron spectroscopy, LXI, 185 Elastic diffraction, structural information, LX, 129 Elasticity, fundamental equations, LXXVII, 85 Elastic scattering physics, LXXXI, 44 spin dependence, LXII, 52 Electrical properties annealing and, XXXVII, 299 irradiation-induced change modeling, metal-oxide-semiconductor structures, LVIII, 1 Electric field correlations, differential equation, LXI, 303 Wigner distribution matrix, stochastic dielectric, LXI, 300 Electrodynamic concepts of wave interactions, thin-film semiconductors, XLIV, 99; XLV, 1 Electroluminescence, Suppl. 1, XVI, 621 Electromagnetic deflection, industrial and military applications, LXVII, 222 Electromagnetic fields, dual complementary variation techniques, LXX, 315

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Electromagnetic waves, nonsinusoidal propagation, Suppl. 18 radiation, Suppl. 23 Electromagnetic waves, nonsinusoidal, XXXVI, 245 Electromechanical picture signal generating device, XXVIII A, 297 Electron as a chemical entity, XIV, 1 distribution, in ionosphere, XV, 265 energy distribution, surface barrier effect, XXIX, 75 as hydrodynamic fluid, XX, 1 interactions with matter, LXXVI, 211 at interfaces, LI, 1 and ions, low energy, atomic collisions involving, XVIII, 67 quantum modulation, LXIX, 55 Schwarz-Hora effect, LXIX, 55 Electron acoustic waves, nonlinear, XXXV, 1 ; XLI, 1 Electron beam as analytical tools in surface research, XLIII, 139 broadened energy distributions, XXIX, 257 canonical optics, LXXXI, 255 deflection, XLIX, 299 dense, analysis, XXVI, 1 focused, interaction with resist-covered wafer, LIV, 73 high density, VIII, 363 interaction with resist-coated substrate, XLVIII, 280 parameters, low temperature SEM, LXX, 8 polarization, XXI, 1 profiles, environmental scanning electron microscopy, LXXI, 138 relativistic, pulsed intense, properties, LIII, 57 relativistic, scattering from, LIII, 48 technology, Suppl. 4 Electron beam addressed memories, XLIII, 43 Electron beam lithography device microfabrication, LIV, 133, XLVIII, 275 pattern analyses applications, LXIX, 208

317

Electron-beam pulsing, scanning electron microscope, LXIX, 33 Electron beam testing, LXXIII, 234 electron optical column, LXXIII, 270 Electron-bombarded semiconductor devices, XLIV, 221 Electron bombardment induced conductivity image devices working on, XXII A , 323 properties, XXII A, 315 Electron-bombardment ion thrusters, XXXVI, 266 Electron-diffraction problem, systematic approach, LXV, 308 Electron diffraction structure analysis, XI, 355 Electron diffraction theory, interpretation of electron microscope images of crystalline materials, XXXIX, 1 Electron emission electron-bombardment ion thrusters, XXXVI, 345 hot cathode, energy spectrum, XXIX, 73 polarized, from solids, XLI, 113 secondary, I , 66; XI, 413 Electron emission microscopy, XVIII, 251 Electron flow, in magnetically focused beams, X , 1 Electron guns for high density electron beams, VIII, 363 industrial and military applications, LXVII, 186 narrow angle, Suppl. 3 spherically symmetric, XXIX, 95 Electron-hole carrier transport, acoustoelectric interaction, XXXI, 234 Electronic aids to navigation, I, 425 Electronic camera, XVI, 1 , 19 astronomical spectroscopy, XXII B, 76 1 diffused light, XXII A, 465 double-star photography, XVI, 357; XXII B, 755 electrostatically focused, in physics and astronomy, XXVIII A , 27 for enlargement 1/7, XVI, 27 focusing with cylindrical lens, XXII A, 609

318

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Electronic camera (Continued) infra-red application, XXII A, 1 new technique for utilization, XVI, 19 photoelectric emission study, XXII A, 519 relation to standard photography, XXII A, 5 for space research, XXVIII A, 39 weak stars study, XXVIII B, 787 Electronic circuits, acoustic imaging, Suppl. 11 Electronic devices flicker noise, XLIX, 225 gaseous, comparison with semiconductors, VI, 257 high-power, XLI, 311 Electronic energy levels, heavily doped silicon, LV, 80 Electronic engineering, river and ocean technology, XXXI, 267 Electronic imaging, limitations to resolving power, XVI, 299 Electronic photography, planets, XVI, 371 Electronics and the blind, XX, 261 contributions to seismology and geomagnetism, IX, 297 at General Electric, early history, L, 412 Gum-Hilsum effect, LI, 310 history, L, 89 modern, and electrical discharges in gases, VII, 401 modern vacuum pumps in, V , 213 in oceanography, IX, 239 postwar development, L, 124 prewar achievements, L, 91 teaching to scientists, XLV, 253 thorium oxide and, V , 169 World War 11, L, 106 Electronic states, symmetry, LXII, 34 Electronic structure, surface, theory, LXV, 358 Electronic systems, gyrator in, XXXVII, 80 Electronic theory cylindrical magnetron, 111, 15 plane magnetron, 111, 185 Electronic zooming, XVI, 195 Electron image direct recording, using thin windows, XXII A, 51

multiplier, XII, 87 store and analyser, XXII B, 969 Electron interaction, space-harmonic traveling-wave, XVII, 1 Electron interference, LIII, 269 Electron irradiation, electron beam testing, LXXIII, 258 Electron lens, 11, 48 coupling between field and basis, LXXV, 246 differential equation of trajectories, LXXV, 237 equation of motion, LXXV, 235 iteration cycle, LXXV, 255 micro-lenses, LXXV, 269 property calculation, LXXV, 233 quadrupoles, Suppl. 7 optics, LXXV, 294 trajectory representation, LXXV, 250 Electron-liquid model, Hall effect, LXXVIII, 140 Electron microdiffraction, XLVI, 1 Electron micrograph analysis, optical transforms, XLIII, 1 Electron microscopy, VI, 269; XII, 317 assimilation, LXXIII, 222 in Berlin, LXXXI, 211 biological material contrast formation, LXIII, '270 low-dose, image handling, LXVI, 202 bright field, algorithm for image enhancement, XLVIII, 37 chemical analysis, LXII, 263 crystallographic information, LXII, 247 development at General Electric, LXXIII, 154 at RCA, LXXIII, 163 Farrand Optical Co., LXXIII, 215 fast processes, LXXVI, 209 high-resolution, image calculations, LXV, 296 history, Suppl. 16 Bod0 von Borries, LXXXI, 127 early U. S . , LXXIII, 134 holography, LIX, 2 image formation, XXXII, 64; XLIII, 2 inelastically scattered electrons, LXV, 173 image processing, computer techniques, Suppl. 10

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 imaging developments, LXII, 179 instrumentation, LXII, 162 interpretation of crystalline materials images, XXXIX, 1 ion beam technology applications, XLVII, 1 Lie algebraic theory of charged-particle optics, LXVII, 65 mirror, XXVI, 217; LXVIII, 372 modes, LXXVI, 216 off-axis holography, LIX, 35 optical processing, XLIII, 12 real-time fast laser-induced processes, LXXVI, 260 space-time resolution, LXXVI, 273 resolution, XXV, 277 time resolved, LXXVI, 223 Electron mirror, LXXV, 258 axially symmetric, electron-optical properties, LXVIII, 350 theory, LXVIII, 337 Electron mirror microscopy, XXVI, 217; LXXIII, 372 Electron-molecule collisions, Glauber approximation applications, XLIX, 216 Electron multiplication, secondary image intensifiers, XVI, 127 Electronographic camera, large-image, XXVIII A, 19 Electronographic emulsions, linearity, XXVIII B, 737 Electronographic plate, bakeable, advantages, XVI, 35 Electron optical column automatic control system, LXXIII, 291 electron beam testing, LXXIII, 270 Electron-optical deflexion and storage techniques, XXII B, 985 Electron-optical images, defects, XXXII, 64 Electron optical instrumentation, LXII, 162 Electron-optical systems electron beam addressed memories, XLIII, 112 imaging properties, XXVIII A, 523 Electron optics aberration theory, Suppl. 17 canonical theory, LXXXI, 231

319

field plotting and ray tracing, 11, 102 scalar diffraction, XXX, 139 x-ray image intensifiers, XLIII, 216 Electron physics, device microfabrication, XLVIII, 272; LIV, 69 Electron probe microanalysis, Suppl. 6; XIII, 317 voltage contrast, LXXIII, 247 Electron resists, device microfabrication, LIV, 69 Electron scattering angular and energy distributions, XXXII, 66 from ions, XLIX, 199 Monte Carlo modeling, LXIX, 177 neutral atoms, XLIX, 148 in solids, IV, 2; VII, 183 from surfaces, spin polarization, LVI, 219 Electron spectroscopy applications, XLII, 55 diffraction, LXXXI, 105 high-energy ion-atom collisions, LVI, 411 imaging, LXXXI, 75 internal conversion, LX, 1 Electron spin resonance, in mineralogy and geology, XXIV, 51 Electron streams, velocity distribution, XIII, 181 Electron theories, thermoelectricity, L, 231 Electron trajectories, integral equation method, LXXXI, 1 Electron tubes, high-speed photography, XVI, 249 Electron wave, LIII, 271 theories, XLI, 50 Electrostatic acceleration, electron-bombardment ion thrusters, XXXVI, 289 Electrostatic deflection electron beams, XLIX, 323 industrial and military applications, LXVII, 209 Electrostatic field, dual complementary variational techniques, LXX, 342 Electrostatic image intensifiers, application to astronomy, XXVIII B, 807 Electrostatic lens aberration correctors, LXXVI, 187

320

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Electrostatic lens (Continued) aberrations, LXXVI, 36 crossed, LXXVI, 174 current density distribution, LXXVI, 69 frequency-contrast characteristics, LXXVI, 69 paraxial optics concepts, LXXVI, 20 quadrupole, LXXVI, 115 reducing defects in imaging devices using, XXII A, 601 round and multipole, LXXVI, 3 transaxial, LXXVI, 159 two-dimensional cylindrical, LXXVI, 148 Electrostatic potentials, integral equation method, LXXXI, 1 Electrothermal instabilities, semiconductors, LX, 307 Elementary charge, concept evolution, L, 449 Ellipsometry, surface and thin film studies, XLIX, 1 Emission field, 111, 1; VIII, 90; XII, 73 transmission secondary, XII, 59 Emission-imaging electron-optical system cathode lenses, LXXVIII, 158 design, LXXVIII, 156 Emitron, C. P. S., charge integration experiments, XII, 219 Emitter open-circuit voltage decay effect, LXVII, 370 quasi-static approximation, LXVII, 383 Endfire antennae, XIX, 255 Energy band model, XXXIV, 283 Energy conversion, thermionic, XVII, 125 Energy density magnetic field, LXV, 27 numerical values, LXV, 292 Energy distribution, angular, XLVIII, 21 Energy-filtering transmission electron microscopy, LXXXI, 43 Energy levels heavily doped silicon, LV, 80 semiconductor heterolayers, LXXII, 4 Energy losses, electrons in solids, VII, 183 Energy-loss spectroscopy, LXXV, 122 amorphous carbon, LXXV, 181 conducting polymers, LXXV, 187 instrumentation, LXXV, 148

rare gas bubbles in metals, LXXV, 167 sample preparation, LXXV, 157 superconductors, LXXV, 215 Energy spectrum, electrons emitted by hot cathode, XXXIX, 73 Energy transport, by radiation, electromagnetic quantities, LXV, 229 Engineering, field problems, LXX, 331 Entropy generalized, multivariate probability distributions, LXXVI, 368 graph, LXXVI, 410 Environmental scanning electron microscopy, LXXI, 110 applications, LXXI, 238 beam radiation effects, LXXI, 223 contrast and resolution, LXXI, 217 detection, LXXI, 193 electron beam profiles, LXXI, 138 gas state, LXXI, 115 interactions, LXXI, 134 Equation of motion charged particles, LXXVI, 9 electron lenses, LXXV, 235 electron mirrors and cathode lenses, LXVIII, 338 ESEM, gaseous detector device theory, LXXVIII, 2 Evaluation, semiconductor device, XVIII, 167 Evaporation, impact, glow discharge, XVII, 245 Evoscope, fixed pattern generator, XXII A, 331 Excitation collective, interaction of free and bound carriers with, XXXVIlT, 19 normal-mode, generalized theory, XLIV, 110 Excited states kinetics studies, time-resolved laser fluorescence spectroscopy, XLVI, 132 population, stationary afterglow, XXIX, 160 relaxation, chemical lasers, XXXI, 16 EXEL, principles, XLVIII, 207 Extraterrestrial mineralogy, E M ,LXXVI, 317

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 F Far infrared, semiconductors, intraband magneto-optical studies, XXXVII. 1 ; XXXVIII, 1 Farrand Optical Co., electron microscope, LXXIII, 215 Fast Fourier transform algorithms, digital signal processing, LXXX, 77 Ferrites. physical properties, VI, 70 Ferroelastic crystals, optical and acoustic device applications, LXXI, 251 Ferroelastic domain walls, LXXI, 256 Ferromagnetic materials. spin-dependent scattering, LVI, 261 Ferromagnetic phenomena at microwave frequencies, 11, 251 Ferromagnetism, relaxation processes, VI, 47 Fiber optics, local area networks, LVII, 145 Fibers, dielectric, LI, 80 Field-effect image storage panels, XXVIII B. 1059 Field-effect transistors gallium arsenide microwave, XXXVIII, 195 intrinsic, XXXVIII, 204 with parasitic resistances, XXXVIII, 224 three-terminal, XLIV, 174 Field electron microscopy, metals, XXXII. 194 Field emission, VIII, 90 image tubes, XII, 73 microscopy, 111, 1 Field emitter cathodes, fast scanning system, XLVIII, 326 Field ionization, XIII, 83 Field ion microscopy, XIII, 83 atom-probe, Suppl. 20 image intensification, XXII B, 903 Field plotting, electron optics, 11, 102 Filament scintillation chamber, XVI, 487 Filtering, white-light image processing, LXIII, 36 Filters high-Q, surface acoustic-wave, LI, 301 quadrupole mass, ion optical properties, LIII, 153

32 1

signals with two space variables, XXXVI, 218 two-dimensional, spatial electric, XLI, 168 Finite algebras, digital signal processing, LXXX, 80 Fishing. electronic engineering, XXXI, 293 Flame plasmas, XX, 99 Flanged waveguide, radiating into infinite homogeneous medium, LXIII, 162 Flicker noise electronic devices, XLIX, 225 resistors, XLIX, 244 vacuum tubes, XLIX, 234 Floating-gate devices, XLI, 294 Floppy disks, minicomputers, XLIV. 316 Fluctuation phenomena, IV, 110 Fluid dynamics, magnetic liquids, XLVIII, I03 Fluorescence spectroscopy medical, image quality, XXII A , 363 pulsed-laser, XLVI. 143 time-resolved laser, XLVI, 131 Flux transfer, impulsive, LIV, 58 FM broadcast band, propagation, I , 381 Focused cylindrical electron beams, magnetically, X, 1 Focused ion beam system, LXXXI, 177 Focusing criterion, system-theoretic approach, LXXV, 329 high density electron beams, VIII, 363 by plane radiators, LXXV, 348 in stratified media, LXXV, 363 Fourier optical treatment, electron microscopical holography, LIX, 5 Fourier phase retrieval, LXVII, 1 Fourier theorem, noise, L, 369 Fourier transform low-dose image, electron microscopy, LXVI, 297 symmetric, LXXX, 51 x-ray crystallography, LXXX, 40 Fraunhofer in-line holography, LIX, 24 Free atoms, lifetimes, XXIX, 115 Free carrier resonances, XXXVII, 28 Free-electron laser, Suppl. 22 submillimeter radiation source, LIII, 48 Frequency high metallic conduction at, VI, 1

322

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Frequency (Continued) microwave, XIV, 265 multipliers, MIS varactor, XXXIV, 312 standards, atomic beam, XV, 1 Functional electrical stimulation of extremities, XXX, 283 Fusion, particle beam, LIII, 1 Fuzzy sets theory, information energy, LXXX, 224

G Gallium arsenide Group I impurities, LXI, 108 Group IV as dopants, LXI, 118 Group VI shallow donors, LXI, 127 impurity and defect levels, LXI, 64 irradiation and defect levels, LXI, 81 microwave field-effect transistors, signal and noise properties, XXXVIII, 195 minority-carrier recombination, LXI, 131 oxygen in, LXI, 123 point defects, LVIII, 81 semi-insulating, LXI, 91 shallow acceptors, LXI, 116 thin-film photocathodes, XXVIII, 399 transition metal effects, LXI, 100 traps from DLTS studies, LXI, 76 Gap, point defects, LVIII, 81 Gas discharge displays, review, XXXV, 191 Gaseous detector device amplification, LXXVIII, 60 discharge characteristics, LXXVIII, 42 physical parameters, LXXVIII, 16 scintillation, LXXVIII, 80 signal spectroscopy, L M V I I I , 84 theory in ESEM, LXXVIII, 2 Gaseous electronic devices, VI, 257 Gases electrical discharges in, VII, 401 photoacoustic effect, XLVI, 211 Gate capacitance expression, derivation, XXXVIII, 261 General Electric early power electronics, L, 412 electron microscope development, LXXIII, 154

Geology, high resolution transmission electron microscopy, LXXVI, 282 Geomagnetism, contributions of electronics to, IX, 297 Geometry from Euclidean to non-Euclidean, L, 265 metric and differential, L, 269 Germanium, electrical properties, VII, 87 g-factor anomaly, free electrons, XXI, 1 Glass scintillators, XVI, 547 Glauber approximation atomic collision applications, XLIX, 134 electron-molecule collisions, XLIX, 216 Glow discharge, impact evaporation and thin film growth, XVII, 245 Gradual channel approximation, saturation in JFETs, XXXI, 251 Grating storage target, XXII A , 155 Gray-valued mathematical morphology, LXVII, 167 Green’s function dyadic, microstrip antenna analysis, LXV, 2 Koster-Slater method, LXII, 108 microstrip structures, LIX, 165 Green’s theorem, Hall plates, LXI, 54 Group I, GaAs impurities, LXI, 108 Group IV, as GaAs dopants, LXI, 118 Group VI shallow donors, GaAs, LXI, 127 Gunn-Hilsum effect electronics, LI, 310 Guns, electron, high density, VIII, 363 Gyrator, in electronic systems, XXXVII, 80 Gyro device theory, LV, 7 Gyrokystron, LV, 39 Gyrotron oscillator, LV, 14 Gyro-TWT, LV, 45

H Hale 200-in. telescope, image-tube spectrograph, XXVIII B, 767 Hall effect applications, XXV, 97 electron-liquid model, LXXVIII, 140 research and applications, XXXVI, 153 three-dimensional, LXI, 49 Hall plates boundary-element method, LXI, 18 conformal mapping, LXI, 10 current, magnetic field and, LXI, 58

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 potential calculations, LXI, 2 relaxation methods, LXI, 15 Hamiltonians canonical aberration theory, LXXXI, 239 charged-particle optics, LXVII, 75 Harmonic generation nonlinear beam plasma systems, XXIX, 1 plasma, XXVII, 187 Helium speech processing, XXXI, 295 Heterojunction, light-emitting devices, XLII, 222 n-Hexane, pre-breakdown using image intensifier, XXII B, 1003 High-current effects, device microfabrication, XLVIII, 367 High density electron beams, VIII, 363 High-field transport, semiconductor heterolayers and devices, LIX, 239 High frequencies, metallic conduction at, VI, 1 High-gain image intensifier, XII, 135 field-ion microscopy, XXVIII B, 875 increasing storage capacity, XXVIII B, 745 High injection, FCVD effects, LXVII, 395 High-power electronic devices, XLI, 311 High-power tubes, XIV, 299 High-power tunable lasers, LVI, 2 High-resolution electron microscopy, image calculations, LXV, 296 High resolution transmission electron microscopy geology, LXXVI, 282 microstructure, LXXVI, 292 High-speed photography electron store and analyser application, XXVIII B, 1011 image orthicon, XXII B, 1011 High temperature studies, mass spectroscopy, XLII, 25 Hollow cathode arcs, XXXV, 88 Holograms, synthesis. LXVI, 92 Holography adaptive correction of distortions, LXVI, 5 electron microscopy, LIX, 2 in-line, LIX, 5 off-axis, LIX, 35 single-sideband, LIX, 28 theory and application, LXX, 223

323

Homatons, finite group, LXXIX, 37 Hybrid-pi equivalent circuit, XXIX, 266 Hydrodynamical fluid, XX, 1 Hydrogen thyratrons, XIV, 207 I ICF particle beam generators, LIII, 8 power flow and energy requirements, LIII, 2 targets, intense beam interaction, LIII, 37 IEEE standard digital interface, minicomputers, XLIV, 319 11-VI semiconductors, heterolayers, optical characterization, LXXII, 1 111-V semiconductors acoustoelectric interactions, XXXI, 162 heterolayers, optical characterization, LXXII, 1 Ill-posed problems, regularization theory, LXXV, 67 Image algebra, developments, LXXX, 243 Image amplifiers, solid state, recent developments, XVI, 607 Image converter barrier-membrane, astronomical tests, XII, 21 boundary layer, XVI, 633 electrostatically focused, XXII A, 441 solid state applications, XVI, 613 fast response, XXII B, 683 Image data compression, LX, 192 Image detectors, photoconductive, astronomical uses, XVI, 451 Image devices signal-to-noise ratio, XII, 291 spatial frequency response, XXII A, 425 Image filtering, Wigner distribution, LXXX, 309 Image formation electron microscopy, XXXII, 64; LXV, 297; XLIII, 2 incoherent theory, XXXII, 165 inelastically scattered electrons, electron microscope, LXV, 173 Image generation by linear transformations, XLI, 172

324

CUMULATIVE SUBJECT INDEX. VOLUMES 1-81

Image generation (Continued) two-dimensional spatial electric filters, XLI, 168 Image intensification, XII, 327 low brightness photography, XVI, 85 Image intensifier, XVI, 75, 475 in astronomy, XXIII, 347 cerenkov Ring observation, XXII B, 801 channeled, XII, 97; XVI, 155 developments, XII, 41 digital read-out, XXVIII B, 981 electron microscope, XII, 317 electrostatic, two-stage, XVI, 105 electrostatic zoom, XXVIII A, 537 fiber-optic coupling, XXVIII A, 105 gas discharge application, XXVIII B , 1033 high gain, astronomical research utilizing, XXII B, 705 information transfer with, XXVIII B, 615 luminescent chamber application, XII, 153 magnetically focused cascade, experiences with, XVI, 119 multi-stage, XVI, 567 rapid luminescence phenomena observation, XXII B , 949 scanning radioactive objects, XXII B, 941 secondary emission, XII, 59 sensitivity, XXII A, 381 streamer chambers, XXII B, 813 thermal-neutron, XXII B, 781 thin end-window, XII, 31 thin window image resolution, XVI, 67 with phosphor output, XVI, 61 track recording, XVI, 113 transmission, XVI, 141 transmitted secondary electron multiplication, XVI, 127 use in nuclear physics, XVI, 501 visual performance at low light, XXVIII B, 635 wire-electrode type, experiments, XVI, 621 x-ray, XII, 379; XLIII, 205 experiences with, XVI, 601 Image intensifying tubes astronomical uses, XVI, 403 multipactor principle, XVI, 163 single-crystal, XXVIII B, 931

Image isocon tube, XXVIII B, 827 Image models, robust, LXX, 79 Image multiplier, electron, XII, 87 Image orthicon, XVI, 447, 581 astronomy applications, XXII B, 713 bombardment-induced conductivity targets, XVI, 247 comparison of SEC camera tube, XXII A , 291 magnesium oxide targets, XVI, 213 stellar photometry, XVI, 431 using slow readout, XVI, 419 Image processing digital, LX, 161 electron microscopy, computer techniques, Suppl. 10 white-light, LXIII, 1 Image reconstruction, from projections, LX, 207 Image recording, comparison of efficiency, XXVIII B, 725 Image restoration, LX, 163 robust image modelling techniques, LXX, 121 Image sampling, white-light image processing, LXIII, 36 Image scanning in astronomy, potentialities and limitations, XVI, 409 Image sensors charge-coupled, XXXVII, 225 performance limitations, XXXVII, 236 multiplexed scanning, XXXVII, 187 solid state cameras, XXXVII, 182 XY, XXXVII, 193 Image storage techniques, XVI, 593 Images, transient, in high-gain photocathode-phosphor intensifier systems, XII, 135 Image transducers, low energy quanta, XXII A, 189 Image transmission, Suppl. 12 Image tube analysis, XXVIII B, 603 computation of imaging properties, XXVIII A, 535 demagnifying, nuclear physics applications, XVI, 99 diode, XXII A, 583 field emission, XII, 73

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Fourier spectrograph, XXVIII B , 899 high-resolution, for integrated circuit fabrication, XXVIII A , 47 high-speed cameras, XXII B, 957 high-speed photography, XXVIII B, 989 intensifier, evaluation, XXII A , 369 laboratory evaluation, astronomical purposes, XVI, 391 Lallemand, modified, XVI, 25 Lenard window, XVI, 47 for astronomical spectrophotometry, XXII B, 741 low background, electronography, XVI, 37 magnetic focusing, XXII A, 617 modulation transfer function, XXVIII B, 567 orthicon, XII, 379 proximity-focused, XXVIII A, 129 research, XII, 17 resolving power, XXVIII A, 553 signal generating, XII, 307 storage application, XII, 311 character recognition, XXVIII B, 1043 experimental, XII, 247 for optoelectronic computing, XXVIII B, 1051 Imaging, quadrupole mass filter, LIII, 205 Imaging algebra, universal, LXVII, 121 Imaging system adaptive correction of distortions, LXVI, 5 spherical aberration, LXVII, 92 Impurities deep, g factors, LXII, 120 energy levels, heavily doped silicon, LV, 80 GaAs levels, LXI, 64 Incoherent theory, image formation, XXXII, 165 Industrial electronics cathode ray tubes, LXVII, 183 General Electric history, L, 432 Industrial measurements, microwave systems, LV, 309 Inelastic collisions between atomic systems, XIII, 1 electrons in solids, dielectric theory, LXI, 173

325

Inelastic scattering image formation by, electron microscope, LXV, 173 physics. LXXXI, 44 Information, representation. LXX, 161 Information energy, LXXX, 165 statistical aspects, LXXX, 188 weighted, LXXX, 234 Information measures, generalized, LXXVI, 328 Information processing, physical limits, LXX, 159 Information theory applied to space-time, L, 277 inverse problems, LXXV, 96 Infra-red converters, XXVIII B, 1087 Infrared radiation, detectors, V, 1 quantum efficiency, XI, 87 Infra-red stellar spectroscopy, with mica-window tube, XXII B, 723 Infra-red television camera tube, XII, 263 Injection mechanism, nonvolatile semiconductor memories, XLI, 264 Injection process, light-emitting devices, XLII, 189 Ink-jet printing, LXV, 91 InP, point defects, LVIII, 81 Instability, thermal and electrothermal, semiconductors, LX, 307 Instruction repertoire, minicomputers, XLIV, 287 Instrumentation, electronic, oceanography, XIX, 1 Insulators, low density deposits, XVI, 145 Integral equation method, electrostatic potential and electron trajectory analysis, LXXXI, 1 Integrated circuits microwave, XXXVIII, 169 multistable, XXXV, 270 INTELSAT system, XXXI, 123 Intensifier orthicon, performance, XII, 183 Intensity variations, cosmic rays, IX, 129 Interactions, weak, parity nonconservation in. XI, 31 Interfaces, electrons at, LI, 1 Interference, electron, LIII, 269 Internal conversion environmental effects, LX, 71 theory, LX, 3

326

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Internal conversion-electron spectroscopy, LX, 1 Interrupt structure, minicomputers, XLIV, 300 Interstellar medium, transition of outer solar wind, XXXVI, 39 INTIC, image storage tube, XXVIII A, 137 Intraband magneto-optical studies, semiconductors in far infrared, XXXVII, 1; XXXVIII, 1 Intrinsic dielectric breakdown in solids, 11, 185 Invariance, pattern recognition, LXIX, 262 Inverse discrete radon transform, tomographic imaging applications, LVI, 360 Inverse problems infomation theory, LXXV, 96 interdisciplinary study, Suppl. 19 Ion-atom collisions, high-energy, electron spectroscopy, LVI, 411 Ion beams electron microscopy applications, XLVII, 1 focusing in space, LXXIII, 2 in time, LXXIII, 74 intense, production and formation, XLII, 118 production, XLVII, 2 profile and radius, LXXXI, 180 Ion bombardment processes, LXXIX, 76 solid surface modification, LXXIX, 73 sputtering by, VII, 239 Ion erosion, scanning electron microscopy, XLVII, 45 Ionic population, stationary afterglow, XXIX, 140 Ionic structure, determination, XXXIV, 269 Ion implantation annealing of layers, LVIII, 210 nondoping and other applications, LVIII, 231 range distributions of ions, LVIII, 193 semiconductors, XXXVII, 264 VLSI, LVIII, 191 Ionization field, XIII, 83

mass spectroscopy, XLII, 12 multiphoton, atoms, XXXVI, 58 neutral atoms, by electron collisions, XLIX, 183 Ion microscopy, field, XIII, 83 Ion-molecule reactions, thermal energy, XXXIV, 223 Ion-molecule studies, mass spectroscopy, XLII, 19 Ion motion, quadrupole, LIII, 155 Ion optics, LXXIII, 1 aberration theory, Suppl. 17 quadrupole mass filters, LIII, 153 Ionosphere radio wave scattering, XIX, 55 research, I, 317 Ion-permanent dipole reactions, XXXIV, 246 Ions acceleration, isotope separators, XLII, 135 electron scattering from, XLIX, 199 implanted, concentration profiles, XXXVII, 271 lifetimes, XXIX, 115 negative, see Negative ions photodetachment and photodissociation, LV, 119 production, electron-bombardment ion thrusters, XXXVI, 267 “small” multimolecular atmospheric, XIX, 177 thinning, transmission electron microscopy, XLVII, 30 Ion scattering, against metal surfaces, XXI, 67 Irradiation, GaAs impurity and defect levels, LXI, 81 Isophate converter, XII, 307 Isotope separators, applications, XLII, 113 Iteration cycle, electron lenses, LXXV, 255

J Junction currents, photovoltaic effect, LVI, 193 Junction diodes, microwave power, XXIX, 320

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Junction field-effect transistors noise, XLVI, 356 saturation mechanisms, XXXI, 247 Junction formation, light-emitting devices, XLII, 246

K Kodak IIa-0 emulsion, comparison of image recording with, XXVIII B , 725 Koster-Slater Green’s function method, LXII, 108

L

Lagrangians aberration theory, LXXXI, 236 charged-particle optics, LXVII, 75 Lallemand electronic camera, astronomical observation, XII, 113; XVI, 341 Lallemand image tube, modified, XVI, 25 Large-scale integrated circuits, failure, xxx, 79 Large-signal charge-control model, XXIX, 271 Laser beam, technology, Suppl. 4 Laser fluorescence spectroscopy, time-resolved, XLVI, 131 Lasers chemical, XXXI, 1 color center, LVI, 54 free-electron, Suppl. 22 high-power tunable, LVI, 2 technology progress, XLV, 70 Lattice quantization, LXXII, 259 scalar, LXXII, 262 Lead monoxide, electron bombardment induced conductivity, XXII A, 305 Lens cathode, LXVIII, 337 electron, 11, 48 strong-focusing, XIV, 85 Lick-Stromlo electronic camera, development, XXII A, 59 Lie algebraic theory, charged-particle optics, LXVII, 65 Lie algebraic tools, LXVII, 68

327

Lie calculus, LXVII, 81 Light amplifier, with high light output, XXVIII A , 151 Light control devices, optical information processing, LXIX, 123 Light-emitting devices, XLII, 179; XLV, 40 materials, XLII, 195 Light ion beam, LIII, 33 Light sources, optical information processing, LXIX, 117 Lightwave receivers, LXXV, 389 active-feedback circuits, LXXV, 431 first- and second-generation, LXXV, 422 noise, LXXV, 395 Lightwave systems, receiver and device requirements, LXXV, 393 Line algorithm, LXXX, 26 Linear accelerators, L, 48 Linear ferrite devices, microwave applications, Suppl. 5 Linear inverse problems, LXXV, 10 with discrete data, LXXV, 36 Linear ion accelerators, XXV, 1 Linvill lumped model, XXIX, 275 Liquid-crystal displays active-matrix thin-film transistor, LXXVII, 2 thin-film transistor-addressed applications, LXXVII, 69 characteristics, LXXVII, 28 color-image, LXXVII, 57 driving schemes, LXXVII, 47 evolution and history, LXXVII, 12 key factors, LXXVII, 17 performance, LXXVII, 65 Liquids, photoacoustic effect, XLVI, 241 Lithography, photon and electron beam, XLVIII, 275 Local area networks, fiber optics, LVII, 145 Local space operators, LXVI, 152 Logic high-speed, switching, LVIII, 340 limitations, ULSIs, LVIII, 375 Longitudinal structures, LI, 73 Low background image tube, XVI, 37 Low density deposits, transmission secondary emission, XVI, 145 Low energy electron diffraction, surface research, XLIII, 141

328

CUMULATIVE SUBJECT INDEX. VOLUMES 1-81

Low energy electron physics, swarm techniques, XXVII, 1 Lowest order perturbation theory, multiphoton ionization, XXXVI, 61 Low light levels, direct observation, image intensifier, XVI, 75 Low-temperature experimental-edge model, LXXVIII, 134 Low temperatures, metallic conduction at, VI, 1 LSI circuits, XLVII, 54 Luminance gain, image intensifier systems, XXVIII B, 629 Luminescence, solid-state, V, 137 Luminescent chamber, XII, 153 high energy physics experiments, XVI, 513 M Macroscopic inhomogeneity model, LXXVIII, 138 Magnetic airborne detector, IV, 258 Magnetically focused electron beams, X, 1 Magnetic beta-ray spectrometers, XXX, 43 Magnetic coherence resonances, at zero frequency, XXVII, 19 Magnetic-core memory technology, high-speed, XXI, 249 Magnetic dipole, relaxation, water of biological substances, XLIX, 95 Magnetic field Hall-plate current contributions, LXI, 58 high, high resolution NMR, XXXIV, 1 measurement by magnetic resonance, XXIII, 39 quantities and dimensions, LXV, 247 structure and properties, XLVIII, 103 Magnetic focus systems aberrations, XVI, 333 photocathode resistance on resolution, XXII A, 591 Magnetic liquids in devices, XLVIII, 157 fluid dynamics, XLVIII, 103 processes based on, XLVIII, 186 Magnetic reconnection experiments, LIV, 1 Magnetic tapes, minicomputers, XLIV, 314 Magnetism in metals, LXII, 11

systems with localized magnetic moments, LXII, 21 Magnetization curves, surface, LXII, 81 Magnetochemistry, surface, LXII, 74 Magnetostatic deflection, electron beams, XLIX, 303 Magnetostatics, LXX, 336 Magnetron continuous-wave, modulation, IV, 188 cylindrical, electronic theory, 111, 15 microwave, 11, 220 mode transitions, VIII, 503 plane, electronic theory, 111, 85 steady state theory, V, 247 Manufacture, cathode ray tubes, 11, 2 Many-beam electron-diffraction calculations, LXV, 299 formulations, LXV, 316 Mariner IV spacecraft television system, XXII B, 849 Masers, XV, 73 molecular beam, XXIX, 183 optical, Suppl. 2 Mask inspection, LXIX, 248 Mass analyzers, isotope separators, XLII, 137 Mass spectroscopy, I, 219; VIII, 188; XLII, 2 using RF quadrupole fields, XXVII, 59 Material constants, LXXVII, 93 Mathematical morphology, universal imaging algebra, LXVII, 127 Mechanical valves, ink-jet printing, LXV, 161 Medicine diagnosis by nuclear magnetism, XLIX, 86 photoacoustic spectroscopy, XLVI, 298 scintillation cameras, image intensification, XXII B, 927 Memory cache, minicomputers, XLIV, 299 direct access, minicomputers, XLIV, 305 electron beam addressed, XLIII, 43 high-speed magnetic-core, XXI, 249 interleaving, minicomputers, XLIV, 298 microprocessors, XLVII, 75 nonvolatile semiconductor, XLI, 249 protect, minicomputers, XLIV, 298 MESFETs, submicron, LVIII, 332

CUMULATIVE SUBJECT INDEX. VOLUMES 1-81 Metal-insulator-metal structure, photoemission from, XXVIII A, 409 Metallic conduction, at high frequency and low temperature, VI, 1 Metallic waveguides, LI, 73 Metal-oxide-semiconductor structures, irradiation-induced change modeling, LVIII, 1 Metals field electron microscopy, XXXII, 194 magnetism in, LXII, 11 nearly-free-electron, LXXV, 160 rare gas bubbles, LXXV, 167 surfaces, ion scattering against, XXI, 67 Metastable negative ions, lifetimes, XLVI, 56 Meteors, radio observation, IX, 95 Mica, electron transmission through, XXII A , 31, 41 Microanalysis, electron probe, XIII, 317, Suppl. 6 Microbeams, quality, LXXIII, 105 Microdiffraction. electron, XLVI. 1 Micro-lenses, LXXV, 269 Microlithography simulation, electron and x-ray beams, LXIX, 176 Microphotometer, photographic and electronographic image tubes, XXII A, 435 Microprocessors, LVII, 41 1 architecture, XLVII, 61 components, LVII, 424 design, LVII, 462 development, LVII, 454 linking physics experiment to, XLVII, 88 revolution, LVII, 411 trends, XLVII, 109 use in physics, XLVII, 51 Microprogrammable systems, minicomputers, XLIV, 306 Microscopy electron emission, XVIII, 251 field emission, 111, 1 field ion, XIII. 83 theories, thermoelectricity, L, 2 17 Microstrip antennas analysis, dyadic Green’s function, LXV, 2

329

disk radiation pattern, LXV, 32 space waves and directivity, LXV, 66 properties and applications, LXV. 4 ring. radiation characteristics, LXV, 42 wraparound, radiation patterns, LXV, 55 Microstrip structures dynamical radiation model, LIX, 139 fundamentals, LIX, 142 Microstructure measurement. electron beam testing, LXXIII, 307 minerals, TEM, LXXVI, 292 structural control over, TEM, LXXVI, 297 Microwave biological effects, LIII, 85 linear ferrite devices, Suppl. 5 multiple scattering and transport, turbulent plasmas, XXXII, 312 plasma generation and amplification, XXI, 287 solid state sources, XXXVIII, 153 Microwave devices, solid state, XXXVIII, 148 Microwave diagnostics, stationary afterglow, XXIX, 132 Microwave frequencies terenkov radiation, XIV, 265 ferromagnetic phenomena, 11, 251 Microwave integrated circuits, XXXVIII, 169 Microwave landing system, new international standard, LVII. 31 1 Microwave magnetron, 11, 220 Microwave measuring systems industrial, LV, 309 physical basis, LV, 312 Microwave optics, X, 107 Microwave power semiconductor devices, XXIX, 291; XLIV, 141 Microwave spectroscopy, 11, 300 Migration, signal analysis, seismic studies, LXXVII. 277 Military electronics cathode ray tubes, LXVII, 183 General Electric history, L, 432 Millimeter wavelengths, radioastronomy , LVI, 98 Millimeter wave techniques, XV, 197

330

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Minerals extraterrestrial, TEM, LXXVI, 317 reactions, TEM, LXXVI, 305 structure and microscopy, TEM, LXXVI, 292 Miniaturization, tube, 11, 183 Minicomputers applications, XLIV, 328 basic concepts, XLIV, 283 Minority carrier lifetime, heavily doped silicon, LV, 95 recombination, GaAs, LXI, 131 MIOS devices, XLI, 274 Mirror electron microscope, LXVIII, 372 MIS capacitor flatband to inversion transient simulation, XLVII, 279 transient response modeling, XLVII, 267 MIS varactors, physics and applications, XXXIV, 281 Mixed dynamic form factor, electron microscope, LXV, 174 Mobility-edge model, LXXVIII, 134 Modems, minicomputers, XLIV, 320 Modulation continuous-wave magnetrons, IV, 188 pulse code, 111, 221 satellite communications, XXXI, 134 Modulation transfer function fluorescent screens, XXII A, 395 image tube, XXVIII B, 567 x-ray image intensifiers, XXII A, 355 Molecular beam masers, XXIX, 183 Molecular beams, new applications and techniques, VIII, 2 Molecular hydrogen, interstellar medium, XXVIII B, 801 Molecular reactants, collisional detachment of negative ions, LVIII, 177 Molecular targets, Rydberg atom collision processes, LIX, 105 Molecules lifetimes, XXIX, 115 neutral, diffraction from crystalline surfaces, LX, 95 Monte Carlo modeling electron scattering, LXIX, 177 photo- and Auger electron production, LXIX, 197

Monte Carlo simulation, electron and x-ray beams, LXIX, 176 MOSFET current saturation, XXXI, 263 drain current model, XLVII, 201 noise, XLVI, 356 operation in weak inversion, XLVII, 197 submicron, LVIII, 314 weak-inversion region, carrier transport and mobility, LXXVIII, 117 Multialkali photocathodes, crystal structure, XXVIII A, 337 Multichannel radio telemetering, IV, 301 Multidimensional algorithms, Fourier transform, LXXX, 16 Multidynode electron multipliers, single electron pulse sizes from, XXII A , 71 Multilayer reflecting systems, relative reflectivity coefficient, XLIX, 6 Multi-MeV electrons, KCI foil response, XXII A, 635 Multiphoton ionization, atoms, XXXVI, 58 Multiphoton processes formal theory, LIV, 194 resonant, LIV, 191 Multiple access, satellite communications, XXXI, 134 Multiplexed photodiode arrays, XXXVII, 198 Multiplexed scanning, image sensors, XXXVII, 187 Multiplexing satellite communications, XXXI, 134 sequency, XXXVI, 201 Multiplication, transmitted secondary electron, XXII A, 629 Multiplier electron image, XII, 87 forty channel, XXVIII B, 955 Multipole electrostatic lenses, optics, LXXVI, 3 Multisignal effects, nonlinear beam plasma systems, XXIX, 1 Multistable integrated circuits, XXXV, 270 Multistable semiconductor devices, XXXV, 270 Multistable states, generation, XXXV, 272

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Multivariate probability distributions, generalized entropies, LXXVI, 368

N Narrow angle electron guns and cathode ray tubes, Suppl. 3 Navigation electronic aids, I, 425 electronic engineering, XXXI, 280 Nearly-free-electron metals, energy-loss spectroscopy, LXXV, 160 Negative differential mobility circuits and boundaries, LI, 329 semiconductors, LI, 310 Negative electron affinity photoemitters, XLVIII, 1 Negative ions, IX, 43 collisional detachment, LVIII, 143 double charged, autodetachment lifetimes, XLVI, 122 metastable, lifetime, XLVI, 56 Negative resistance interactions, XXXV, 356 Network synthesis, methods, 111, 261 Neural control, future possibilities, XXXVIII, 55 Neutral atoms electron scattering, XLIX, 148 ionization, by electron collisions, XLIX, 183 Neutralization, electron-bombardment ion thrusters, XXXVI, 336 Newtonian mechanics, particle modeling, LXIII, 190 Nightglow, XVIII, 1 Noise amplifiers, L, 397 cosmic radio, I , 347 detectors, L, 397 diodes, XLVI, 320 flicker, XLIX, 225 Fourier theorem, L, 369 GaAs microwave FETs, XXXVIII, 228 JFETs, XLVI, 356 lightwave receivers, LXXV, 395 MOSFETs, XLVI, 356 research history, L, 351 solid state devices, XLVI, 314

33 1

sources, XLVI, 314 transistors, XLVI, 335 Noncoherent processing, radar signal, XLV, 224 Nonconservation, parity, in weak interactions, XI, 31 Nonradiative recombination, light-emitting devices, XLII, 185 Nonreflective cell, solar, XLII, 50 Nonsinusoidal waves antennas and waveguides, Suppl. 15 electromagnetic propagation, Suppl. 18 radiation, Suppl. 23 radar and radio communication, Suppl. 14 Nonvolatile semiconductor memory. XLI, 249 NPP, periodic domain walls and ferroelastic bubbles, LXXI, 256 Nuclear magnetic resonance spectroscopy biological tissue application, XLIX, 109 high resolution, high magnetic fields, XXXIV, 1 medical diagnosis by, XLIX; 86 Nuclear physics amplitude and time measurements, XIII, 256 demagnifying image tube, XVI, 99 image intensifiers, XVI, 501 photomultipliers, LX, 223 Nuclear spectroscopy, internal conversion, LX, 61 Number theoretic techniques, digital signal processing, LXXX, 69 Numerical field plotting, ray tracing, electron optics, 11, 102

0

Object wave reconstruction, LXVI, 213 Observational radio astronomy, VII, 299 Observations astronomical, photo-electronic imaging devices, XII, 1 of meteors, radio, IX, 95 Ocean currents, XXXI, 277

332

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Oceanography, electronics in, IX, 239 engineering, XXXI, 267 instrumentation, XIX, 1 Open-circuit voltage decay, solar cells, LXVII, 329 Open-ended waveguides, LXIII, 140 Operating systems, general-purpose, XLVIII, 203 Operational amplifiers, XI, 225 Optical communications fiber optics in LANs, LVII, 145 photodiodes, LV, 189 Optical devices, using NPP periodic domain wall gratings, LXXI, 327 Optical diffraction patterns, XII, 311 Optical images, low contrast, detection, XII, 247 Optical information processing, device developments, LXIX, 115 Optical masers, Suppl. 2 Optical processing, electron microscopy, XLIII, 12 Optical systems, for image tubes, XXVIII €3, 759 Optical television methods, XII, 363 Optical transforms, electron micrograph analysis, XLIII, 1 Optical waves, interaction with ferroelastic domain walls, LXXI, 256 Optics electron, 11, 102 microwave, X, 107 Orbita system, XXXI, 127 Oscillations, plasma, XX, 59 Oscillator beam-maser, XXIX, 221 gyrotron, LV, 14 surface acoustic-wave, LI, 301 Oscilloscope, cathode ray, X , 239 Oxide-cathode receiving tubes, electrical life, VII, 404 Oxide coated cathodes, I, 1 Oxygen, in GaAs, LXI, 123

P Pair tunneling, LXX, 18 Paleontology, SEM, LXXVII, 185 Paramagnetic resonance, XV, 327

Paramagnetic salts, diluted, relaxation, XV, 163 Paramagnetism, VI, 463 Parametric amplifiers, MIS varactor, XXXIV, 321 Parasitic resistances, FETs, XXXVIII, 224 Paraxial map, solenoidal lens, LXVII, 86 Paraxial optics, concepts, LXXVI, 20 Parity nonconservation, in weak interactions, XI, 31 Partial coherence bright field electron microscopy, XLVIII, 47 Particle accelerator, I , 269; XXIX. 223; LXXI, 75 beam environment, LXXI, 87 history, L, 2 statistical methods and quality control, LXXI, 90 superconducting technology, LXXI, 92 Particle beam Coulomb interactions, Suppl. 21 formation and focusing, LIII, 26 fusion, LIII, 1 generator, ICF, LIII, 8 number for characterization, LXV, 278 phase-space approach, LXXVI, 51 Particle modeling, discrete mathematical physics, LXIII, 189 Pattern recognition invariance, LXIX, 262 statistical, information measures, LXXVI, 386 Peierls dispersion, Varshalovich-Dyakonov correction, LXIX, 86 Penning discharges, XXVII, 295 Peripheral circuits, solid state sensors, XXXVII, 253 Peripheral devices microprocessors, XLVII, 75 minicomputers, XLIV, 310 Petrography, reservoir, SEM, LXXVII, 156 Petroleum exploration industry, scanning electron microscopy, LXXVII, 140 Petrophysics, SEM, LXXVII, 192 Phase retrieval, Fourier, LXVII, 1 Phase-space approach, particle beams, LXXVI, 51

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Phonon ballistic signal, LXX, 58 structural defect imaging, LXX, 71 focusing, SEM, LXX, 64 Phosphors aging, LXXIX, 349 cathode-ray tubes, LXXIX. 271 cathodoluminescence emission spectral distribution curves, LXXIX, 361 characteristics, LXXIX, 359 industrial and military applications, LXVII, 254 input, x-ray image intensifiers, XLIII, 207 luminescent processes, LXXIX. 273 output thin window image intensifier. XVI, 61 x-ray image intensifiers, XLIII, 226 powder synthesis methods, LXXIX. 325 specific applications, LXXIX. 307 Phosphor screens high resolution, XXII A, 551 cascade image intensifiers, XXII A, 571 preparation, XXII A , 565 special, LXXIX, 337 Photoacoustic effect gases, XLVI, 211 history, XLVI, 209 liquids, XLVI, 241 solids, XLVI, 214 Photoacoustic spectroscopy, XLVI. 208 future trends, XLVI, 306 Photocathode composition, study by microbalance methods, XVI. 329 Cs-Sb and Na-K-Sb, microbalance study, XXII A, 459 image dissector, XXII A , 507 improvements for pulse operation, XXVIII A, 375 interference, XXVIII A, 419 for image tubes, XXVIII A , 433 near infra-red spectral response, XXII A, 493 NEA technology, XLVIII, 22 new technology for transferring, XXVIII A, 367

333

physical properties, LXIII, 83 pre-formed introduction into vacuum systems, XVI, 325 properties, liberated in high vacuum, XVI, 5 reflection, XLVIII, 9 image intensifier system using. XXVIII A, 443 research in Czechoslovakia, XXVIII A, 323 responsive quantum efficiency, XXII A, 535 S 20, and fibre optic plates. XXVIII A, 46 1 Sb-Rb-Cs, XXII A, 449 sensitivity, decay, XXVIII A , 357 stability, LXIII, 75 surfaces, research, XXII A, 477 time response, XXII A, 499 using negative electron affinity. XLVIII. 2 Photoconductive detectors, 0.1 to 1.0 mm spectral region, XXXIV, 191 Photoconductive image converter, electron optics, XXVIII A , 545 Photoconductive image detectors, electronically scanned, potentialities, XVI, 451 Photoconductive tube x-ray sensitive, XII. 345 Photoconductivity. problems of, XIV, 37 Photodetachment, ions, LV, 119 Photodetector optical information processing, LXIX. 161 0.1 to 1.0 mm spectral region, XXXIV. 95 Photodiodes materials and design, LV, 245 multiplexed arrays. XXXVII, 198 optical communication, LV, 189 physics, LV, 192 semiconductor, XXXIV, 163 special applications, LV, 287 Photodissociation. ions, LV, 119 Photoelectric image devices, survey of work, XVI, 31 1 Photoelectron, angular distributions, XLIV, 15 3

334

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Photo-electronic image devices, XL B; LII; LXIV A; LXIV B; LXXIV; XVI; XXII A; XXII B; XXXIII A; XXXIII B; XL A Photo-electronic imaging devices, potentialities, XII, 1 Photo-electronic storage tube, experiments, XII, 235 Photoelements, self-scanned sensors, XXXVII, 183 Photoemission detectors, 0.1 to 1.0 mm spectral region, XXXIV, 96 enhancement, LXIII, 99 at long wavelengths, XXVIII A, 393 recent advances, XI, 1 spin-polarized, XLI, 130 stability and dark current, XLVIII, 31 strong field, XXXVI, 124 by transmission, XLVIII, 17 Photoemitters negative electron affinity, XLVIII, 1 solid-state application, XXII B, 671 vacuum, LXIII, 73 Photographic images, recorded with image intensifiers, XXVIII B, 589 Photography astronomical, television methods, XII, 195 double stars, by electronic camera, XVI, 357; XXII B, 755 electronic, XII, 5 extensive air showers, in atmosphere, XVI, 531 high-speed, electron tubes, XVI, 249 low brightness, image intensification, XVI, 85 Photoionization chamber detectors, 0.1 to 1.0 mm spectral region, XXXIV, 204 cross sections, atomic photoelectron spectroscopy, XLIV, 1 theoretical description, XLI, 75 Photometric applications, and electronic photography of planets, XVI, 371 Photomultiplier characteristics, LX, 262 imaging, astronomical tests, XVI, 383 notation, XXXI, 114 nuclear physics, LX, 223 technology, LX, 224

Photon, single, XXXI, 39 Photon beam lithography, device microfabrication, XLVIII, 275 Photon counters, position-sensitive, XXVIII B, 965 Photon interference, XXVIII B, 939 Photoreceptor subsystem, charged pigment xerography, XXXVIII, 100 Photovoltaic cell, Hall-effect, LXI, 57 Photovoltaic effect, LVI, 163 Physical properties, ferrites, V1, 70 Physics microprocessor use, XLVII, 51 photoacoustic spectroscopy, XLVI, 256 Pick-up tube infra-red vidicon-type, development, XVI, 217 with linear light transfer, XXVIII A, 281 television, I, 131 Picosecond tunable sources, LVJ, 38 Picture resolution, figure of merit measuring, XXII A, 341 Piezoelectricity, fundamental equations, LXXVII, 85 Piezoelectrics, LXXVII, 84 Plane interfaces, wave propagation, seismic studies, LXXVII, 229 Plane magnetron, electronic theory, 111, 85 Plane radiators, focusing by, LXXV, 348 Plasma experimental turbulence, XXX, 1 flame, XX, 9 generation and amplification of microwaves, XXI, 287 harmonics and combination frequencies, XXVII, 187 nondegenerate semiconductor, carrier stream surfaces, XLV, 1 oscillations, XX, 59 radio-frequency confinement and acceleration, XXIII, 153 turbulent, microwave multiple scattering and transport, XXXII, 312 Point defects assessment, LVIII, 84 donors and acceptors, LVIII, 86 Gap, GaAs, and InP, LVIII, 81 intrinsic, LVIII, 96 trap-level energies, LXII, 119 Poisson’s equation, solution, XXJX, 87

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Polarization, multiphoton ionization of atoms, XXXVI, 136 Polarized electron emission, from solids, XLI, 113 Polymers, conducting, energy-loss spectroscopy, LXXV, 187 Pore studies, qualitative, SEM, LXXVII, 185 Potential calculations, Hall plates, LXI, 2 Power-fail protection, minicomputers, XLIV, 297 Preprocessing remotely sensed data, LXVI, 319 signal analysis, seismic studies, LXXVII, 244 Prestack deconvolution, signal analysis, seismic studies, LXXVII, 244 Printing devices ink-jet, LXV, 91 minicomputers, XLIV, 312 Privacy, invasion of, data transmission, XXXVIII, 191 Process control peripherals, minicomputers, XLIV, 317 Programming, trends, XLVIII, 205 Propagation in FM broadcast band, I, 318 guided, beam waveguides, LI, 64 tropospheric, XX, 199 Proton microprobes, LXXIII, 93 applications, LXXIII, 123 high energy, LXXIII, 128 microbeam quality, LXXIII, 105 Pulse amplitude analysis, VII, 317 Pulse code modulation, 111, 221 Pulsed-laser fluorescence spectroscopy, XLVI, 143

Q Quadrature spatial-frequency Fourier analyser, XXVIII B, 653 Quadrupole ion motion, LIII, 155 RF-only, LIII, 202 Quadrupole electron lenses, Suppl. 7 Quadrupole electrostatic lenses, LXXVI, 115 Quadrupole fields, distorted, LIII, 193 Quadrupole mass filters, ion optical properties, LIII, 153

335

Quadrupole optics, electron lenses, LXXV, 294 Quantum efficiency of detectors, XI, 87 Quantum mechanical amplifiers, XV, 73 Quantum mechanics, particle modeling, LXIII, 259 Quantum modulation, electrons, LXIX, 55 Quantum theory atom-surface scattering, LX, 111 resonant two-photon processes, LIV, 200 Quasiparticle tunneling, LXX, 26

R Radar applications, bright displays for, XVI, 265 nonsinusoidal waves, Suppl. 14 signal processing, XLV, 203 Radiation detectors, V , 1 energy transport by, electromagnetic quantities, LXV, 229 far-infrared, generation, XXVI, 171 nonsinusoidal electromagnetic waves, Suppl. 23 re-emission, quantum-modulated beam, LXIX, 93 submillimeter source, LIII, 48 Radiative recombination, light-emitting devices, XLII, 185 Radiative transport equation, XXXII, 320 Radio astronomy millimeter wavelengths, LVI, 98 development, LVI, 99 observational, VII, 299 technology and observations, XXXII, 1 Radio communication, nonsinusoidal waves, Suppl. 14 Radiology, diagnostic, image orthicon, XVI, 581 image storage techniques applied to, XVI, 593 Radio noise, cosmic, I, 347 Radio observation, meteors, IX, 95 Radio telemetering, XI, 287 multichannel, IV, 301 Radiotelescope, fundamentals, LVI, 124 Radio-wave propagation, IX, 187 Radon transform continuous pair, LVI, 362

336

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Radon transform (Continued) far-beam projection sampling, LVI, 388 inverse discrete, LVI, 360 parallel-beam projection sampling, LVI, 380 properties, LVI, 376 Rare gas bubbles, metals, LXXV, 167 Ray tracing, LI, 128 electron optics, 11, 127 RCA, electron microscope development, LXXIII, 163 Reactive species, sampling, mass spectroscopy, XLII, 28 Real-space method, image calculations, LXV, 324 Real-time electron microscopy fast laser-induced processes, LXXVI, 260 space-time resolution, LXXVI, 273 Receivers lightwave, LXXV, 389 millimeter radioastronomy, LVI, 142 Receiving tubes, oxide-cathode, electrical life, VIII, 404 Reciprocity, in physical systems, XXXVII, 80 Recom bina tion GaAs minority carriers, LXI, 131 heavily doped silicon, LV, 95 light-emitting devices, XLII, 185 Reconnection magnetic, LIV, 1 theory, LIV, 14 Reconstruction algorithm bright field electron microscopy, XLVIII, 67 tomographic imaging, LVI, 372 Reflex discharges, XXVII, 295 Registration mark detection, electron-beam lithography, LXIX, 248 Regularization theory, ill-posed problems, LXXV, 67 Relative reflectivity coefficient determination, XLIX, 20 multilayer reflecting systems, XLIX, 6 Relativistic mechanics, particle modeling, LXIII, 242 Relaxation in diluted paramagnetic salts, XV, 163 Hall plates, LXI, 15

Remotely sensed data digital processing, LXVI, 310 enhancement, LXVI, 326 Reprogrammable read-only memory devices, XLI, 262 Residue number systems, digital signal processing, LXXX, 121 Resistors, flicker noise, XLIX, 244 Resonance acceleration, L, 22 Resonant multiphoton processes, LIV, 191 Resonant two-photon processes, quantum theory, LIV, 200 Resonators piezoelectricity, LXXVII, 84 simple linear model, LXXVII. 103 surface acoustic-wave, LI, 301 RF quadrupole fields, mass spectroscopy using, XXVII, 59 River technology, electronic engineering, XXXI, 267 Rods, dielectric, LI, 80 Rotational invariance, LXXIX, 51 Round electrostatic lenses, optics, LXXVI, 3 Rydberg atom collision processes, LIX, 79 S

Saddle point method, dyadic Green’s function, LXV, 1 1 Satellite communications, XXXI, 119 Saturation mechanisms, junction field-effect transistors, XXXI, 247 Scalar diffraction, electron optics, XXX, 139 Scalar radiation problems, system-theoretic approach, LXXV, 335 Scan magnification, electron beams, XLIX, 349 Scanning, by charge transfer, XXXVII, 202 Scanning electron acoustic microscopy, LXXI, 1 Scanning electron microscope electron-beam pulsing, LXIX, 33 qualitative voltage contrast, LXIX, 6 stroboscopic and sampling-mode operation, LXIX, 44 voltage measurement, LXIX, 1 Scanning electron microscopy, XXI, 181 archaeology applications, LXXI, 357

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

337

environmental, LXXI, 110 SEC camera tube ion erosion, XLVII, 45 astronomy application, XXVIII B, 807 petroleum exploration industry, LXXVII, compared with image orthicon, XXII A , 140 29 1 very low temperatures, LXX, 1 optically scanned, XXII A, 241 Scanning system, fast, development, Secondary electron XLVIII, 300 conduction, photoelectronic image Scanning tunneling microscopy, LXXIX, devices, XXII A, 219 155 emission, I , 66; XI, 413 applications, LXXIX, 203 spin-polarized, LXII, 67 construction and electronics, LXXIX, SEC target, XXII A , 229 168 point-source imaging with, XXII A , 251 theory, LXXIX, 188 Seismology Scattering contributions of electronics, IX, 297 amplitudes, Eikonal approximations, signal analysis, LXXVII, 210 XLIX, 137 Self-consistent solution, space charge, atom-surface, quantum theory, LX, 111 XXIX, 90 cross sections, EM of biological material, Self-scanned sensors LXIII, 286 color cameras, XXXVII, 251 electron, in solids, IV, 2; VIII, 183 photoelements, XXXVII, 183 model, quantum modulation, LXIX. 89 Semiconductor multiple, microwaves, XXXII, 312 current filaments and turbulence, LXX, radio wave, in ionosphere, XIX, 55 49 from relativistic electron beams, LIII, deep-impurity-level energy predictions, 48 LXII, 101 stimulated, theory. LIII. 59 in far infrared, intraband magneto-optical Schwarz-Hora effect, LXIX. 55 studies, XXXVII, I ; XXXVIII. 1 Scientists, teaching electronics to, XLV, ion implantation, XXXVII, 264 253 negative differential mobility, LI, 310 Scintillation, in CsI(Na) and CsI(TI), due nondegenerate plasmas, carrier stream to low energy, XXVIII A, 451 surfaces, XLV, 1 Scintillation chambers nonvolatile memory, XLI, 249 fibers versus NaI, XVI, 469 surfaces, electrons, LI, 2 image intensifiers versus orthicons, XVI, thermal and electrothermal instabilities, 469 LX, 307 space research application, XVI, 535; thin-film XXII B, 823 electrodynamic concepts of wave Scintillation counter, IV, 69 interactions, XLIV, 99; XLV, I Scintillation detector, statistical behavior, without magnetic field, modes, XLV, XXVI, 251 19 Scintillation gaseous detector device, Type 11. XXIII, 1 LXXVIII, 80 Semiconductor crystals, diamond-type, Screens, cathode ray tube defects, X, 71 high resolution, XXII A, 551 Semiconductor devices cascade image intensifiers, XXII A. compared with gaseous electronic devices. 571 VI, 257 preparation, XXII A . 565 electron-bombarded, XLIV, 221 industrial and military applications, evaluation, XVIII. 167 LXVII, 254 high-field transport, LIX, 239 special, LXXIX. 337 high-power, XLI, 313

338

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Semiconductor devices (Continued) microwave power, XXIX, 291; XLIV, 141 trends and future development, XLIV, 216 multistable, XXXV, 270 noise, XXIII, 303 three-terminal, XLIV, 141 Semiconductor heterolayers energy levels, LXXII, 4 high-field transport, LIX, 239 111-V and 11-VI, optical characterization, LXXII, 1 Semiconductor materials investigation, XI, 355 photodiode design, LV, 245 physics, VII, 1 Semiconductor-metal interfaces, LI, 13 Semiconductor photodiodes, XXXIV, 163 Semiconductor-semiconductor interfaces, electrons, LI, 32 Sequency multiplexing, XXXVI, 201 Sequency theory, Suppl. 9 research and development, XXXVI, 195 Shallow acceptors, GaAs, LXI, 116 Shannon’s entropy, generalized, LXXVI, 329 Shutter tubes, gas discharge application, XXVIII B, 1033 Signal analysis, seismic studies, LXXVII, 210 GaAs microwave FETs, XXXVIII, 195 generation, scanning electron acoustic microscopy, LXXI, 4 processing, digital, number theoretic techniques, LXXX, 69 radar, processing, XLV, 203 Signal spectroscopy, gaseous detector device, LXXVIII, 84 Signal-to-noise ratio, XII, 277, 291; XXVIII B, 1033 with S 1 photocathodes, XXVIII B , 677 Silicon bulk carrier transport, LXXVIII, 104 drift velocity, LXXVIII, 109 heavy doping, LV, 77 band-gap narrowing, LV, 87 device applications, LV, 106

electronic and impurity energy level changes, LV, 80 recombination and minority carrier lifetime, LV, 95 solar cells, space use, XLII, 41 theory of electrical properties, VII, 87 weak inversion layers carrier transport, LXXVIII, 104 mobility and saturation velocity, LXXVIII, 112 Silver-magnesium alloy dynodes, in water vapour, XXII A, 661 Single electron pulse sizes, distribution, XXII A, 71 Single photons detection, XXXI, 39 fast timing with, XXXI, 69 Single-sideband holography, LIX, 28 Single-stage image converter, photography, XXVIII B, 999 SI system, peculiar aspects, LXV, 235 Skeletal control systems, XXX, 273 “Small” multimolecular atmospheric ions bioclimatic action, XIX, 177 measurement, XIX, 177 properties, XIX, 177 Software microprocessors, XLVII, 83 minicomputers, XLIV, 321 Solar activity, LIV, 179 Solar atmosphere, LIV, 160 Solar cells open-circuit voltage decay, LXVII, 329 silicon, XLII, 41 Solar interior, LIV, 144 Solar photometry, image orthicon applied to, XVI, 447 Solar physics, LIV, 141 Solar radio astronomy, XX, 147 Solar wind, large-scale behavior, XXXVI, 1 Solenoidal lens paraxial map, LXVII, 86 second- and third-order effects, LXVII, 88

Solids Auger transitions, LXI, 187 characteristic electron energy losses, VIII, 183 electrical breakdown, XXVI, 309 electron scattering, IV, 2

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 intrinsic dielectric breakdown, 11, 185 kinetic ejection of electrons, XXI, 101 photoacoustic effect, XLVI, 214 polarized electron emission, XLI, 113 secondary electron emission, XI, 413 Solid state cameras, image sensors, XXXVII, 182 Solid state devices, noise, XLVI, 314 Solid state image amplifiers, XVI, 607 Solid state image converters, XVI, 613 infra-red, XXVIII B, 1073 Solid-state luminescence, V, 137 Solid state microwave devices, XXXVIII, 148 Solid-state physics, spin-polarized electrons, LXII, 2 Solid state radiographic amplifiers, XXVIII B, 1087 Solid state sensors, peripheral circuits. XXXVII, 253 Solid-state traveling-wave amplifiers, design and analysis, XLIV, 100 Solid surfaces analysis, LVI, 291 modified by fast ion bombardment, LXXIX, 73 Sonar, river and ocean technology, XXXI, 283 Source encoding, white-light image processing, LXIII, 36 Space, dimension, L, 308 Space charge density, spherical cathode, XXIX, 83 limited currents, VI, 138 self-consistent solution. XXIX, 90 Space harmonic traveling wave electron interaction, general perturbational theory, XVII, 1 Space research, application of scintillation chambers, XVI, 535 Space-time, L, 272 Space (time)-frequency representations, Wigner distribution, LXXX. 372 Spatial electric filters, two-dimensional, image generation, XLI, 168 Spectracon astronomical applications, XXVIII B, 783 astronomical spectroscopy, XXVIII B, 773

339

compared with image recording, XXVIII B , 725 electronographic image recording tube, XXII A, 11 electron transmission through mice, XXII A. 31 further developments, XXVIII A , 61 Spectral analysis, noise, L, 369 Spectrograph, high-gain, for simulated re-entry, XXVIII B, 1021 Spectrometers, beta-ray, V, 97 Spectroscopy beam-maser, XXIX, 199 laser fluorescence, time-resolved, XLVI, 131 mass, I. 129; VIII, 188 microwave, 11, 300 photoacoustic, XLVI, 208 time resolved interference, XXII B, 985 Spherical aberration correction, LXVII, 96 imaging system, LXVII, 92 Spherical cathode, space-charge density, XXIX, 83 Spherical wavefronts, focusing, XLI, 197 Spin-orbit interaction, spin-dependent scattering, LVI, 240 Spin polarization, electrons scattering from surfaces, LVI, 219 solid-state physics, LXII, 2 Spin-polarized photoemission, XLI, 130 Spread spectrum basic techniques, LIII, 214 communication systems, LIII, 209 Sputtering, XLVII, 13 by ion bombardment, VII, 239 Standing waves, topology characterization, L, 318 Static fields arbitrarily oriented, acoustoelectric interaction, XXXI, 185 collinear, acoustoelectric interaction, XXXI, 176 Stationary afterglow, low-temperature rare-gas, XXIX. 121 Steady-state theory of magnetron, V, 247 Stellar photometry, XVI, 431 Stochastic dielectric, Wigner distribution matrix for electric field, LXI, 300

340

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Stochastic transport equation, Wigner distribution functions, LXI, 354 Storage media, electron beam addressed memories, XLIII, 51 Storage rings, L, 82 Storage tube high resolution information, XVI, 287 photo-electronic, XII, 235 television, signal-to-noise ratio, XII, 277 viewing, VIII, 448 Stratified media, focusing in, LXXV, 363 Striations, moving, XXIV, 155 Strong-focusing lens, XIV, 85 Structure analysis, electron diffraction, XI, 355 Submicron MESFETs, LVIII, 332 Submicron MOSFETs, LVIII, 314 Submicron VLSIs, LVIII, 312 Subminiaturization techniques, 111, 195 Subpicosecond tunable sources, LVI, 38 Superconducting microbridges, hotspots, LXX, 41 Superconducting technology, particle accelerators, LXXI, 92 Superconducting tunnel junctions arrays, LXX, 39 pair tunneling, LXX, 18 quasiparticle tunneling, LXX, 26 Superconductors, energy-loss spectroscopy, LXXV, 215 Superlattices, 11-VI, LXXII, 151 Surface acoustic-wave oscillators, resonators, and high-Q filters. LI, 301 principles, LI, 279 transversal filters, LI, 295 Surface acoustic-wave signal-processing, charge transfer, LI, 265 Surface analysis, charged-particle beams, LVII, 231 Surface charge storage, electron beam addressed memories, XLIII, 56 Surface electronic structure, theory, LXV, 358 Surface lattice dynamics, information on, LX, 146 Surface potential well, information on, LX, 138 Surfaces adsorption, XXXII, 258

clean, characteristics, XXXII, 223 ellipsometry, XLIX, 1 mass spectroscopy studies, XLII, 5 state density determination, XLVII, 224 waves, XXXI, 274 Synchronous accelerators, L, 38 Synthetic aperture ultrasonic imagery, LXX, 215 System-theoretic approach, focusing criterion, LXXV, 329

T Tape cassettes, minicomputers, XLIV. 315 Target conductivity, bombardment-induced, image orthicons, XVI, 247 lead sulphide, XVI, 217 magnesium oxide, XVI, 213 Target glass, effects of caesium vapour on, XXVIII A , 309 Telemetering multichannel, IV, 301 radio, XI, 287 Television closed-circuit, and field-ion microscopy, XXVIII, B, 785 at low light-levels, XXVIII B , 837 Television camera noise, measurement, XXVIII A, 289 Television camera tube, XII, 203; XXVIII A, 265 C. P. S. Emitron, XII, 203 infrared, XII, 263 review, XIII, 387 using potassium chloride target, XXII A, 273 x-ray sensitive, XXVIII A, 273 Television channels, experiences with, XVI, 601 Television color, V, 291 Television methods, optical, XII, 363 Television photometer, XXVIII B, 891 Television pickup tube, I , 131 electronic zooming with, XVI, 195 image orthicon effect, XVI, 171 minimizing black-border effect, XVI, 171 Television sensors, space astronomy, XXVIII B, 851

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 Television storage tubes, signal-to-noise ratio, XII, 277 Television system stratoscope use. XXII B, 885 ultra-violet astronomical photometry, XXII B, 865, 875 Temperature high, mass spectroscopy, XLII, 25 very low, SEM, LXX, 1 Tenicon, high resolution information storage tube, XVI, 287 Tensor product formulation, cooley-Tukey algorithms, LXXX, 4 Thermal cathodes, fast scanning system, XLVIII, 326 Thermal energy ion-molecule reactions, XXIV, 1 Thermal image detection, infra-red threshold, XXVIII B, 685 Thermal instabilities, semiconductors, LX, 307 Thermionic cathodes, XXV, 211 Thermionic energy conversion, XVII. 125 Thermistor, thermal and electrothermal instabilities, LX, 310 Thermodynamics, experimental tests, L. 198 Thermoelectricity, L, 176, XVII, 207 electron theories, L, 231 microscopic theories, L, 217 Thin films growth, gow discharge, XVII, 245 ellipsometry, XLIX, 1 semiconductor, without magnetic field, modes, XLV, 19 Thomson, William, L, 184 Thorium oxide, electronics and, V , 169 Thyratrons, hydrogen, XIV, 207 Thyristor systems, high-power, XLI, 336 Tides. XXXI, 276 Tight-binding method, LXII, 109 Time determination, XLIV, 73 measurements, nuclear physics, VIII, 256 synchronization, XLIV, 77 three dimensions, L, 308 Timekeeping applications, XLIV, 34 history, LI, 184

34 1

Time resolved electron microscopy, LXXVI, 223 Tomography diffraction, LXX, 290 inverse discrete radon transform applications, LVI, 360 Topological operations, universal imaging algebra, LXVII, 150 Tracking system, radar signal, XLV, 236 Track recording, image intensifier, XVI, 1 I3 Trajectories, differential equation, electron lenses, LXXV, 237 Transaxial electrostatic lenses, LXXVI, 159 Transducer array, properties, LXX, 267 Transient response modeling, MIS capacitor, XLVII, 267 Transistor active-matrix thin-film liquid-crystal displays, LXXVII, 2 applications, junction, V , 367 computer-aided analysis, charge-control concept, XXIX, 284 information processing, LXX, 175 noise, XLVI, 335 secondary breakdown, LX, 354 thin-film, characteristics, LXXVII, 28 Transition metals GaAs effects, LXI, 100 impurities, chemical trends, LXII, 153 3d, point defects, LVIII, 109 Transitions, at zero frequency, XXVII, 19 Transmission, image, Suppl. 12 Transmission electron microscopy energy-filtering, LXXXI, 43 high resolution, geology, LXXVI. 282 ion thinning, XLVII, 30 Transmission secondary emission, XVI, 145 amplification, XVI, 557 image intensifier, XII, 59; XVI, 141 statistics, XXVIII A, 513 Transmission secondary image intensifiers compared with cascade type, XXII A , 129 performance, XXII A , 63 Transport, microwaves, in turbulent plasmas, XXXII, 312 Transport equations, heavily doped silicon, LV. 102

342

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81

Transversal filters charge-coupled device, LI, 287 surface acoustic-wave, LI, 295 Transverse structures, wave guiding by, LI, 94 Traveling-wave deflection, electron beams, XLIX, 345 Traveling wave tubes, VI, 372 Trellis codes, LXXIX, 1 designing, LXXIX, 28 structure, LXXIX, 18 Trialkali Sb-K-Rb-Cs photocathode, properties, XXVIII A, 347 Tropospheric propagation, XX, 199 Tube, see also specific tubes axial-beam, high-power, XIV, 299 electron, XVI, 249 high-power, XIV, 299 image converting, XVI, 91 image orthicon, XII, 379; XXII A, 291 image isocon, XXVIII B, 827 image storage, XXVIII A, 137 infra-red television camera, XII, 263 Lallemand, XVI, 25 mica-window, XXII B , 723 miniaturization, 11, 183 oxide-cathode receiving, VII, 404 photoconductive pickup, XII, 345 reliability, X, 185 television storage, XII, 277 traveling wave, VI, 372 vacuum, XLIX, 234; L, 416 velocity modulated, 111, 43 x-ray, XII, 327 Tube miniaturization, 111, 183 Two-beam electron interference, LIII, 281

U ULSI, logic limitations, LVIII, 375 Ultrahigh vacuum, XVII, 323 Ultrasonic imaging digital, LXX, 253 synthetic aperture, LXX, 215 Ultra-violet camera tubes, incorporating SEC, XXII A, 261 Ultra-violet imaging, electron bombardment conductivity application, XVI, 235

Ultra-violet sensitive vidicon, XVI, 227 Upconverters, MIS varactors, XXXIV, 326 U. S. Navy electronic camera, XXVIII A, 1

V Vacuum breakdown, high-speed photographic study, XXVIII B, 1041 power flow, LIII, 21 pumps, electronics manufacturing, V, 213 Vacuum photoemitters, LXIII, 73 Vacuum systems, performed photocathode introduction into, XVI, 325 Vacuum tubes flicker noise, XLIX, 234 General Electric history, L, 416 Vanadium dioxide, thermal and electrothermal instabilities, LX, 358 Van Der Pauw method, Hall plates, LXI, 7 Varactors, MIS, XXXIV, 281 Varshalovich-Dyakonov correction, peierls dispersion, LXIX, 86 Velocity distribution, XIII, 181 Velocity-field determination, seismic studies, LXXVII, 263 Velocity modulated tubes, 111, 43 Vibrational transition, chemical lasers, XXXI, 5 Vibrations, in water molecules, model, LXIII, 259 Vidicon digital read-out of image intensifier using, XXVIII B, 981 high-resolution ruggedized half-inch, XXII A , 211 interplanetary imaging device, XXII B, 835 ultra-violet sensitive, improved, XVI, 227 Viewing storage tubes, VIII, 448 Violet cell, solar, XLII, 42 Visible radiation, detectors, V, 1 quantum efficiency, XI, 87 Vision, problem of, I, 121 VLF electromagnetic waves, terrestrial propagation, XXV, 145 VLSI finite algebraic system implementation, LXXX, 140

CUMULATIVE SUBJECT INDEX, VOLUMES 1-81 ion implantation, LVIII, 191 submicron, materials, LVIII, 312 Voltage, open-circuit decay, solar cells. LXVII, 329 Voltage contrast electron probe, LXXIII, 247 scanning electron microscope, LXIX, 6 synchronous and asynchronous pulsed beams, LXIX, 47 von Borries, Bodo, LXXXI, 127

W Walsh functions, research and development, XXXVI, 195 Watches, electronic, LI, 186 Water of biological substances, magnetic dipole relaxation, XLIX, 95 quality, measurement, XXXI, 268 Water moelcule, vibration model, LXIII, 259 Wave equation, seismic studies, LXXVII, 214 Wave-function reconstruction, weak scatterers, LXVI, 230 Waveguides active, polarized-medium, normal-mode excitation, XLIV, 110 infinite sample, LXIII, 182 nonsinusoidal waves, Suppl. 15 open-ended, LXIII, 140 two-dimensional, with metallic walls, LI, 88 Wave guiding, by transverse structures, LI, 94 Wave propagation, across plane interfaces, seismic studies, LXXVII, 229 Waves, electrodynamic concepts of interactions, thin-film semiconductors, XLIV, 99; XLV, 1 Wave techniques, millimeter, XV, 197 Weak inversion, MOSFET operation, XLVII, 197 White-light image processing, LXIII, 1

343

Wiener spectrum, object set, XLVIII, 94 Wigner distribution functions asymptotic equations, LXI, 330 coherent, LXI, 347 equation derivations, LXI, 313 image filtering, LXXX, 309 stochastic transport equation, LXI, 354 Wigner distribution matrix, electric field in stochastic dielectric, LXI, 300 Wind, solar, large-scale behavior, XXXVI, 1 Wire antennas, XLVII, 123 Wiring, information processing, LXX, 198 WKB approximation, modal propagation in slab, LI, 130

X Xerography, charged pigment, XXXVIII, 83 X-ray crystallography, Fourier transform, LXXX, 40 X-ray image intensification, XII, 363; XVI, 567 x-ray microscope, XXII B, 919 X-ray image intensifier, XII, 379; XLIII, 205 future, XLIII, 238 moving structures with, XXVIII B, 647 X-ray lithography device microfabrication, LIV, 95 pattern analyses applications, LXIX, 243 photo- and Auger electron production, LXIX, 197 X-ray sensitive photoconductive pick-up tube, XII, 345 X-ray tube, flying-spot, XII, 327

Z

Zero frequency magnetic coherence resonances, XXVII, 19 transitions, XXVII, 19

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