Advances in Electronics and Electron Physics, Volume 81

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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.

ACADEMIC PRESS, INC. 1250 Sixth Avenue, San Diego, CA 92101

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


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


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)


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


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


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


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


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


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


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


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


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,.


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


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.


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


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


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

> '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).


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.


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


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.)


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).

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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).


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):


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


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.

72

L. REIMER

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.


73

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

74

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).


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.

76

L. REIMER

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-


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.

78

L. REIMER X=Qt-

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):


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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L. REIMER

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.


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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L. REIMER

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.,


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,( 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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L. REIMER

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)

-


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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L. REIMER

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,


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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L. REIMER

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.


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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L. REIMER

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

The author thanks his students A. Bakenfelder, I. Baumann, I. Fromm, P. Hirsch, R. Oelgeklaus, R. Rennekamp, M. Ross-Messemer, and U. Zepke for their contributions to this review, and Peter Hawkes for revising the English. REFERENCES Adamson-Sharpe, K. M., and Ottensmeyer, F. P. (1981).J . Micr. 122,309-314. Ahn, C . C., and Krivanek, 0. C. (1983).“EELS Atlas,” Gatan Inc., Warrendale, PA. Ajika, N., Hashimoto, H., Yamaguchi, K., and Endoh, H. (1985). Jap. J. Appl. Phys. 24, L41-44. Andersen, W. H. J. (1967). Brit. J . Appl. Phys. 18, 1573-1579. Arsenault, A. L., and Ottensmeyer, F. P. (1983). Proc. Nat. Acad. Sci. U S A 80, 1322-1326. Arsenault, A. L., and Ottensmeyer, F. P. (1984). J. Micr. 133, 69-72. Ashley, J. C., and Ritchie, R. H. (1970). Phys. Stat. Sol. 40,623-630. Auerhammer, J., Rez, P., and Hofer, F. (1989). Ultramicroscopy 30,365-370. Badde, H. G., and Reimer, L. (1970).Z. Naturforschung 25,760-765. Bakenfelder, A., Fromm, I., and Reimer, L. (1990a).J. Micr. 159, 161-177. Bakenfelder, A,, Reimer, L., and Rennekamp. R. (1990b). “Proc. XIIth Int. Congr. for Electron Microscopy,” San Francisco Press, Vol. 2, pp. 62-63. Barckhaus, R. H., Fromm, I., Hohling, H. J., and Reimer, L. (1990).“Proc. XIIth Int. Congr. for Electron Microscopy,” San Francisco Press, Vol. 2, pp. 362-363. Barckhaus, R.H., Hohling, H. J., Fromm, I., Hirsch, P., and Reimer, L.(1991).J. Micr. (submitted) Batson, P. E. (1985). Rev. Sci. Instr. 57,95-98. Batson, P. E. (1986). “Proc. 11th Intern. Congr. on Electr. Micr. (Kyoto),” Vol. 1, pp. 95-98. Bauer, R. (1988). In Methods in Microbiology (F. Mayer, ed.), Vol. 20, pp. 113-146, Academic Press, London. Bauer, R., Hezel, U. and Kurz, D. (1987). Optik 77, 171-174.


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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)


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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HEDWIG VON BORRIES

“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


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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177

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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.


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)

182


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.


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


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


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)


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:


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.

190


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


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


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)


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


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


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


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)


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


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

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