Recent Trendsin Charged Particle Optics and

Surface Physics Instrumentation

Proceedingso f the 6lh International Seminar,

held in Skalsky dvur near Brno, Czech Republic, from June 29 to July 3, 1998,

organised by the Institute o f Scientific Instrum ents AS CR and

the C zechoslovak Society for Electron M icroscopy

Edited by Ilona Miillerová and Luděk Frank

ISB N 80-238-2333-7

Proceedings have been printed from the camera-ready m anuscripts supplied by the authors Published and distributed by the C zechoslovak Society for Electron M icroscopy,

printed in Czech Republic by A rtiq Brno

Czechoslovak Society for Electron Microscopy (CSEM), Královopolská 147, 612 64 Brno, Czech Republic; fax +420 5 41514 402, e-mail csem@isibrno.cz, http: www.isibrno.cz/csem

© CSEM Brno 1998All rights reserved. No part o f this publication may be reproduced without the prior written permission of the publisher.

PREFACE

Two years have quickly elapsed and the seminar on the Recent Trends in Charged Particle Optics and Surface Physics Instrumentation is again here, already the sixth one. The history o f the meeting was described in the preface to the previous seminar's proceedings. Let us now summarise briefly the main points. The germ was the traditional summer seminar held nearly regularly in the Institute o f Scientific Instruments in Brno on the occasion o f visits o f Professor Tom Mulvey from University o f Aston in Birmingham, UK. In the seventies and eighties, this was valuable enough for us and offered us the opportunity to make the seminar English spoken. In the summer o f 1989 we started to extend the participation, and the 1989 sem inar was numbered the first. In 1990, there were as many as 30 participants from 5 countries. The third seminar in 1992 was moved to hotel Skalsky dvur in Highlands and the next three seminars organised there, each with around forty participants, had a similar schedule, at least from the point o f view o f non-scientific aspects o f organisation. The fifth seminar was the first one to which the proceedings were published.

It seems there have been no important events since the previous seminar that are worth adding to the sem inar history. This may be simply the consequence o f that the seminar has established a fully defined regularly repeating meeting and nothing is new about it except that its serial number increases by one and the year by two and that the registered participation is so numerous and high-quality one as it was expected. This could be a sign o f stability and tradition and we do hope that this is the explanation.

It was claimed many times at various occasions during the seminars that their prevailing orientation to charged particle optics was and remains desirable owing to the lack o f meetings o f that kind. This argument is generally correct but this time much less than usually: in 1998 the seminar coincided with the CPO conference held in Europe, in April in Delft. We are really happy that this circumstance has not caused any reduction in the participation in Recent Trends. (To be exact, the "collision" appeared already earlier, in 1990, when the C P03 was held in Toulouse but our second seminar was then still smaller and less ambitious.)

Our traditional and a bit unusual style o f the meeting, based on a not too large circle o f personalities, knowing one another quite well, more and more seems to be something that will become usual in the future. Large congresses, aiming at gathering hundreds or even thousands o f anonymous professional colleagues to one place to present their cofttributions to the crowd, are mainly organised because o f tradition. But in fact they are also already split into symposia o f a moderate size, attended by groups similar to ours. One surely cannot consider quite unrealistic a vision that presentation o f scientific contributions will be fully replaced by electronic conferences. But this will never be (as we hope) the case for personal face to face meetings and discussions.

The surface physics has apparently disappeared to a significant extent from our program o f a meeting o f people connected in different ways with electron microscopy. No wonder, the newest surface analytical methods, various scanning probe microscopies but not only them , exhibit surface sensitivities unachievable by electron beams. A few o f us, operating the low energy electron microscopes that have those capabilities, are the only

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C ON TEN TS

Autrata R., J. Jirák, M. Klvač, V. Romanovský Detection o f backscattered electrons in environmental SEM

Autrata R., V. Romanovský J. Jirák, M. Klvač,Ionisation detector for the environmental SEM

Autrata R., J. Jirák, M. Michálek, J. Spinka Amplification o f signal electrons in gas environment

Autrata R., J. Jirák, M. Michálek, J. ŠpinkaConditions for specimen observation in environmental SEM

Barth J.E., M.D. Nykerk, M.J. FransenApplication o f a two param eter bell distribution in charged particle optics

Delong A., V. Kolařík, D.C. MartinLow voltage transmission electron microscope LVEM-5

El-Gomati M.M.Quantitative surface analysis at high spatial resolution

Gerheim V., H. RoseQuadrupole projector system with variable magnification for energy-filtering transmission electron microscopes

Hartei P., D. Preikszas, R. Spehr, H. RoseTest o f a beam separator for a corrected PEEM / LEEM v-

Hasselbach F., H. Kiesel, U. MaierRecent advances in ion- and electron-biprism interferometry

Hejna J.Optimisation o f an immersion lens design in the BSE detector for the low voltage SEM

Hutař O.Noncharging microscopy o f semiconductor structures

Hutař O., R. AutrataThe separation o f secondary electrons in annular and planar detectors

Janzen R., E. WeimerStudy o f detection properties o f a MEDOL / GEMINI objective lens for secondary electrons

Kahl F., H. RoseOutline o f an electron monochromator with small Boersch effect

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Spehr R.Variable axis lens with an extremely large scanning area in one direction

Slekly R., L. Frank, I. MiillerovaDistributed Monte Carlo: smart way for computing complex problems

Tsuno K., N. Handa, S. Mat sumo toAn E+B+E beam separator for detecting secondary electrons in low voltage SEM

Tyc T.Antibunching o f electrons as a consequence o f the indistinguishableness o f fermions

Zadrazil M., M. El-GomatiMeasurements o f the secondary and backscattered electron coefficients in the very low energy range

Zadrazil M., L. Frank, J. NorrisImaging o f non-conducting specimens by noncharging scanning electron microscopy with method for automatically adjusted critical energies

DETECTION OF BACKSCATTERED ELECTRONS IN ENVIRONMENTAL SEM

R. Autrata, J. Jirák *, M. Klvac, V. RomanovskyInstitute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno,Czech RepublicDepartment o f Electrotechnology, Faculty o f Electrical Engineering and Computer Science,

Technical University Brno, Antonínská 1, CZ-612 64 Brno, Czech Republic

Scanning electron microscopy working with pressure in the specimen chamber that are higher than 100 Pa enables investigation o f in-situ specimens and certain dynamic effects, which is not possible in convential SEM.

In our case for the detection o f backscattered electrons (BSE) in environmental scanning electron microscope we use a paired scintillation detector YAG {yttrium aluminium garnet) doped with Ce3+, provided w ith a central hole o f 300 to 500 fim in diameter. The detector acts simultaneously as a pressure limiting aperture, which allows to achieving different pressures in the specimen and differential chamber. The configuration o f the detector ensures a large collection angle for the BSE signal and allows the use o f the small working distance o f the specimen from detector to ensure a sufficient signal even in high pressures in the specimen chamber when an increase number o f collisions o f electrons with the gaseous m edium occurs. Theoretical calculations and practical measuring showed that a considerable portion o f the BSE signal escapes through the hole o f the scintillator and is not detected by the detector. Figure 1 shows a decrease in the detection efficiency o f the detector in relation to the working distance. This effect is appreciable above all for very small working distances o f the specimen from the detector. For this reason a double paired scintillation detector was designed and constructed.

The principle o f the double paired detector I d [mm]is evident from Figure 2. For small working distances d o f the specimen from detector 1 whichare comparable with the diam eter o f the hole D¡, the collection angle o f the detector 1 decreases rapidly and a considerable portion o f BSEs escapes through the hole into the differential chamber. The detector 2 is positioned here and it ensures the detection o f those BSEs. The single crystals o f both detection stages are symmetrically divided into the right and the left half. The interface between them is provided with an optical reflecting layer. Then both the halves are mechanically associated. Both detection stages thus provide two paired

signals with the possibility o f further processing signals.

The properties o f the detectors 1 and 2 were investigated by measuring the signal and noise levels in relation to the pressure in the specimen chamber and the specimen distance d from detector 1. The signal levels were measured in the signal path behind the photomultiplier and preamplifier. As the measuring specimen a carbon cylinder with a central hole coated with an Au - layer wasObr. 2

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IONISATION DETECTOR FOR THE ENVIRONMENTAL SEM

R. Autrata, V. Romanovský, J. Jirák , M. KlvačInstitute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno.Czech RepublicDepartment o f Electrotechnology, Faculty o f Electrical Engineering and C 'omputer Science,

Technical University Brno, Antonínská I, CZ-612 64 Brno. Czech Republic

One o f the relatively new trends in the field o f scanning electron microscopy focuses on observing specimens placed in the specimen chamber under higher pressures. The group o f these microscopes is usually called ESEM (environmental scanning electron microscopy). The value o f the working pressure in the specimen chamber 609 Pa in 0 °C is tixed as the limit for the groups o f microscopes SEM and ESEM.

The ESEM microscopes have wide application in observing biological specimens and various types o f specimen o f insulation character. The observation biological specimens does not require any special preparation technology. No charging phenomena occur due to the presence o f a gaseous medium. Consequently, the complicated and long coating o f the specimen is no longer needed. The coating usually causes the loss o f information on the material consistence o f the specimen surface.

Nowadays scintillation detectors are usually used for the ESEM field. However, their principle does not enable full application o f these microscopes for observing biological specimens, i.e. specimens containing a larger amount o f water and especially in the lield o f topography contrast, which is important, above all, for the already mentioned field ol biological specimens.

The configuration o f this detector described and used is already fully functional and enables the detection o f the low energy electrons, thanks to which we have approached to the possibility o f the better detection o f the topography contrast which we have lacked when observing certain specimens. In our case, a gaseous medium surrounding the specimen is used as an amplifier. In this medium an avalanche o f electrons occurs, produced byvxillision o f signal particles w ith a gaseous medium.

The aim o f the project was a design and construction o f the ionisation detector lor the ESEM microscopes, containing besides the reached functional configuration also optimisation o f the working condition o f the detector. In Figure 1 there is a design o f a combined detector, which we used and which makes use o f the features o f the scintillation and ionisation detectors. With this configuration a large collection angle is reached.When designing the detector we tried to find primarily the optimal working distance D and the pressure in the specimen chamber p as you can see in Figure 2.Keeping these optimal conditions,it is possible to reach the maximum possibilities offered by this detector.

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scintillation detector

ionization detector

specimen

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AM PLIFICATION OF SIGNAL ELECTRONS IN GAS ENVIRONMENT

R. Autrata.*, J. Jirák, M. Michálek, J. Špinka* Institute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno, Czech RepublicDepartment o f Electrotechnology, Faculty o f Electrical Engineering and Computer Science, Technical University Brno, Antonínská 1, CZ-612 64 Brno, Czech Republic

Environmental scanning electron microscopes (ESEM) enable the observation of specimens at higher pressures than in ordinary SEM. The pressure in the specimen chamber can be beween 10 -5.103 Pa. W orking at higher pressures, it is advantageous to use the ionization of gas for detection o f signal electrons. To amplify the signal, ionization detectors take advantage of ionization that occurs in the space between the specimen and the detector.

The detected current is proportional to the number of electrons emitted from the specimen. W e assume that the total detected current can be found by summing the following contributions:

where I “PE , I “E , I “SE are the contributions of the primary electrons, the SEs, and the BSEs to the total detected current, respectively.Acording to [1] the total amplification is given by:

collisions with the gas evironment, p is the pressure, a and y are the Townsend first and second ionization coefficients, respectively, s ^ and Sbse are the field-independent ionization efficiencies o f the primary electrons and the BSEs, respectively, and 5 and T| are the SE and BSE coefficients, respectively.The calculation of the amplification can only be done for a particular type of the electrode system. In the following part, we consider the parallel plate electrode system as shown in Fig. 1. For the calculation it is also necessary to know the surface emissive properties and the ionization properties o f the used gas. Usually, we consider that the environment which surrounds the specimen is air, and that ionization takes place in this gas. However it is also

PRIMARY BEAM Fig .l. A schematic diagram o f the parallel plate electrode system.

dd is the sample-to-detector distance, E is the electric field intensity. Electrons are multiplied through ionizing collisions in the gas (indicated by x).

A - contribution o f primary electrons, B - contribution of secondary electrons (SE), C - contribution o f backscattered electrons (BSE) to the total detected current.

SPECIMEN1

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CONDITIONS FOR SPECIMEN OBSERVATION IN ENVIRONMENTAL SEM

R. Autrata.*, J. Jirák, M. Michálek, J. Špinka Institute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno, Czech

RepublicDepartment o f Electrotechnology, Faculty o f Electrical Engineering and Computer Science, Technical University Brno, Antonínská 1, CZ-612 64 Brno, Czech Republic

Classical scanning electron microscopes (SEM) possess extraordinary properties (resolution, image sharpness, possibility o f element analysis o f specimens, etc.) but they have certain limitations as regards vacuum that is necessary for their operation.The examined specimens should be:- vacuum resistant: On exposing a specimen in vacuum conditions, its properties should not

be affected.- vacuum inert: The specimens may not emit gases or vapours or particles into vacuum.

This could endanger successful operation.- and electrically conducting.In practice, not all specimens meet these demands. Therefore complex methods, e.g. freezing, fixation, etc., must be used to treat them. Specimens having the character o f insulators must be coated with metal mostly.In the environmental SEM, where we work with pressures around 1000 Pa in the specimen chamber, we can fill the chamber with suitable gases and vapours. From this it follows that it is possible to examine hydrated specimens, to watch the interaction of specimens with the gaseous or liquid atmosphere, and to observe dynamic processes, such as crystal growth, wetting, corrosion processes, cementing process. Charging effects are eliminated, owing to the presence o f ionized particles o f a gas [1],Conditions for the creation of an optimum environment in the specimen chamber that is necessary for a successful observation of specimens are different for different cases, depending on the kind of processes and specimens to be examined. Sometimes, some "preparation" o f specimens for ESEM is needed.Let us focus on the most frequent case o f observation of specimens containing water that is

carried out in the presence o f water vapour. For the environmental SEM, the most suitable-, range of working pressures and temperatures follows from the curves o f relative humidity [2].To cool specimens, it is advantageous to use the Peltier cell which makes it possible to achieve a temperature diffe­rence as high as 40 K, compared with the temperature of the warm end. The setting and control o f temperature of the cell by a change in the flowing current are advan­tageous, and when needed, the

-----► tem perature ( °C)

Fig. 1 Relative humidity versus pressure and temperature in the specimen chamber

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APPLICATION OF A TWO PARAM ETER BELL DISTRIBUTION IN CHARGED PARTICLE OPTICS

J.E. Barth, M.D. Nykerk and M.J. FransenDelft University o f Technology, Department o f Applied Physics, Lorentzweg I, 262H ( \J Delft. The Netherlands

For the sake o f simplicity, the Gaussian distribution exp(-w2x2) is used whenever the actual distribution has more or less such a form. Real distributions often have tails which fall off more slowly than a Gaussian. A, still simple, bell shaped distribution that can model this is 1/(1 + w2x2)p. Having two parameters, a width measure w and the power p, it can better lit a variety o f real distributions than the Gaussian. For large p it approaches the Gaussian.

A practical measure for the size o f the image o f a point blurred by chromatic aberration is the diam eter o f the circle containing 50% o f the particles,

dc = KcCc(AU/U)a.

With AU the full width half maximum (FWHM) o f the energy distribution the value o f K( depends on the form o f the energy distribution. Kc = 0.34 for the Gaussian and K, = 0.62 for the Lorentzian distribution (bell with p = 1). It was found [1] that if instead o fthe FWHM the FW 50 (50% o f the particles within AU) is used for the measure o f AU that the coefficient K, is very nearly independent o f the distribution form; K<; = 0.61 +/- 0.01.

A practical definition o f source reduced brightness is

B = I[/(V(ro'4)dI2).

In is the angular current density, V the energy and d, the FW50 diameter o f the source image. Fransen has measured [2] the brightness o f an ultra sharp tungsten field emitter by analyzing Frensel fringes occurring at sample edges in the point projection microscope. The fringe intensity profile calculated when a point, Gaussian or Lorentzian distribution is assumed for the source, will be shown.

When making numerical Monte Carlo simulations o f the Coulomb interaction deterioration of beam quality in a charged particle optics column it is necessary to make assumptions as to the properties o f the source as viewed from the extractor. Inclusion o f more realistic distributions for the initial energy spread and source profile should allow better analysis o fth e effects o f adjusting the beam configuration in the column.

[1] J.E. Barth, M.D. Nykerk: Dependence o f the chromatic aberration spot size on the form of the energy distribution o f the charged particles. In: Proc. o f the Fifth Int. Conf. on Charged Particle Optics, to be published in Nucl. Inst, and Methods A

[2] M.J. Fransen: Electron emitters for electron microscopes, PhD. thesis, Delft University o f Technology, to be published.

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suspension to crystallize by cooling to room temperature. It is known from previous studies that this method of sample preparation leads to regular lozenge shaped crystals, with a nominal thickness of10 nm. The crystals were deposited from the suspension onto an amorphous carbon coated sheet of cleaved mica and susequently floated onto the surface of distilled water, where they were retrieved onto copper finder grids.

the PE single crystal morphology. The regularity in the crystal faceting and presence of overgrowths at their edges are similar to previous observations o f these same samples by conventional high voltage TEM and scanning tunnelling microscopy [3]. The estimated resolution of these images is on the order of 2 nm. The images show that variations in contrast are perceptible up to three or four layers thick, corresponding to the penetration o f the low voltage electron beam through samples with an estimated mass thickness (pt) o f 4 x 10'5 kg/m2.

1. Delong A., Low Voltage TEM, Electron Microscopy 1992, V ol.l, 79-82, 1992.2. Delong A., Hladil K., Kolařík V., A Low Voltage Transmission Electron Microscope, Microscopy & Analysis,

27(Europe), January 1994.3. R. Piner, R. Reifenberger, D. C. Martin, E. L. Thomas, and R. Apkarian, J. Poly. Sci.:C: Poly. Lett., 28, 399, (1990)

The images (Figures 3,4) show the well known, lozenge shaped crystals associated with

References

Fig .l: The Low Voltage TEM Fig-2: Schematic Device Arrangement

Fig.3: LVTEM Image of PE Single Crystals Fig.4: LVTEM Image of PE Single Crystals

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High voltage transmission electron microscopy (STEM), has been used in the past as the prime tool for obtaining dimensional (i.e. metrology) and crystallographic information at high spatial resolution. The technique remains to be so for fundamental research, but is considered less favourable to use in industry and particularly in quality control because o f its destructive nature during the course o f sample preparation. In addition, in the STEM, the whole sample thickness contributes to the image formation, making the results obtained to be less reliable even with the aid o f deconvolution methods. The use o f STEMs is therefore considered not to be practical in on-line analysis o f large samples.

M etrology techniques currently available primarily involve the use o f low voltage electron microscopes (LVSEM). Although there has been a great deal o f instrument development in LVSEM over the last decade, and where currently most microscope manufacturers offer SKM operating around the 1 keV and lower, data analysis at these operating voltages is still in its infancy stages. Other probe microscopies, such as the various forms o f tunnelling microscopes (STM, AFM etc.) are very slow and are therefore ruled out for the foreseeable future. Energy dispersive x-ray analysis (EDX) at low incident electron energies is an area o f research which is seeing some activities. These, however, are again limited to electron energies around (he 5 keV region.

The present contribution will attempt to highlight the areas o f developments in stirlace microanalysis and high resolution electron microscopy. In particular the session is to address the recent developments demonstrating the successful use o f the cathode lens in scanning electron microscopes (SLEEM ) [3] and the measurements o f low energy secondary and backscattered electron coefficients from clean solid surfaces for use in both LVSEM and SLEEM [4], O f importance in this respect is the correlation between the atomic number contrast obtainable in SLEEM and LVSEM as a function o f the incident electron energy. W ork in combining Auger analysis with low energy imaging as a step in the interpretation o f the SLEEM contrast will be covered [5]. Recent developments in parallel data acquisition in AES will also be addressed [6]. »-

References

[1] El Kareh B, 3rd International W orkshop on M easurements and Characterisation-of U ltra-Shallow Doping Profiles In Sem iconductors. M arch 1993, N. Carolina, USA.

[2] See for exam ple Q uantitative surface Analysis Seah and Briggs[3] M ullerova I and Lenc M, U ltra m icroscopy, 41, (1992) 399, and

M ullerova I and Frank L, Scanning, 15, (1993) 193.[4] El Gom ati M and A saa’d A, M icrochim ica A cta, (1998) In Press.[5] El Gom ati M, M ullerova I and Frank L, Proceeding o f the International Centennial Symposium on

the Electron, Cam bridge, UK, Septem ber (1997), In Press.[6] Jacka M, Kirk M, Prutton M and El Gomati M, 5th International Conference on Charged particle

Optics, Delft, A pril (1998).

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and astigm atic im aging w ith any degree of astigm atism (length of the line image). A single quadrupole tr ip le t generally forms cither a first order d isto rted stigm at ic image or two line im ages. These non -ro ta tiona lly sym m etric first-o rder deviations are com pen­sa ted by the second quadrupole trip le t. Since the num ber of the individual qiiadrnpoles is larger th an th a t required for stigm atic and disto rtion free (first order) im aging, 1 In- p a th of rays w ith in the p rojector system can be varied even if the magnification is fixed. Owing to th is behaviour, it is possible to ad just the quadrupole streng ths in such a wa\ th a t th e chrom atic aberra tion of m agnification an d /o r the th ird order d istortion an elim inated or m inim ized, respectively.

For the recording of th e energy loss spectrum , a chrom atic aberration perpendicular to the d irection of the dispersion can be to lerated , as it only enlarges the extension of the im age lines. T he com ponent of the axial chrom atic aberra tion in the direct,ion of the dispersion m ust be elim inated by appropriately readjusting the strength of the hoxapoles w ith in th e energy filter. For recording th e filtered achrom atic im age of the object or the diffraction plane, respectively, the quadrupoles are excited in such a wa\ th a t the th ird -o rd e r d is to rtion is m inim ized. Any unduly large rem aining component of th e d is to rtion can be com pensated subsequently by an additional octupole field

D espite th e fact th a t the quadrupole pro jector system consists of a few more elem ents th a n th a t com posed of ro ta tionally sym m etric lenses, its im proved perform ance and variability outw eigh th is m inor d isadvantage by far. In addition , the d istance between the recording plane and the filter can be shortened due to the strong refraction powei of the quadrupole lenses.

References

[1] Rose, I I ., C orrection of aberrations, a prom ising m eans for im proving jjie spatial and energy resolution of energy-filtering electron microscopes, U ltram icroscopv 5<> (1994) 11-25.

| 2 | U hlem ann, S. and Rose, H., The M ANDOLINE filter a new high p e r f o r m a n c e

im aging filter for sub eV E FTE M , O ptik 96 (1994) 1G3 178.

[3] G erheim , V., B erechnung eines variablen P rojektivsystem s für ein energiefilterndes Transm issions E lektronenm ikroskop, D iplom Thesis, Fachbereich Physik. Institut für A ngew andte Physik, Technische U niversität D arm stad t (1993).

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objective cham ber o f the LEO DSM 960

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Fig. 2 - Test facilities for the beam separator

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In sum m ary, Fig. 2a shows diffraction a t th e edges of the biprism filam ents, and Fig. 2b shows b iprism interference fringes of He+-ions. In order to reduce noise the in­teg ra ted in tensities I n of about 50 successive lines perpendicular to th e fringe direction are given in Fig. 2a,b. No additional filtering was applied in th e diagram s on top. All bu t one of the crucial s tab ility requirem ents for ions w ith sub-pm wavelengths are m et by th e in terferom eter. T he only exception is for th e ion source whose emission site tends to move uncontro llably in la tera l direction during the long exposure tim e. Lateral cohe­rence is destroyed and, w ith it, th e fringe visibility. Im provem ent of source stab ility and brightness are the next im p o rtan t goals on the way to an ion in terferom eter as a research tool.

im age intensifier

Fig. 1: Schematical set-up of the ion interferometer

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[6] Hanson G.R., Siegel B.M., •/. Vac. Set. Technol. 16(1979), 1875-1878; Börret R., Böhringer K., Kalbitzer S., J. Phys. D23(1990), 1271-1277.

[7] D. Gabor: Light and Information, Progress in Optics 1(1961), 109, Ed. E.Wolf, North Holland, Amsterdam.

[8] M.L.Goldberger, H.W.Lewis, Iv.M.Watson: Use of intensity correlation to determine the phase of scattering amplitude, Phys. Rev. 132(1963), 2764.

[9] E. Zeitler: Coherence in scanning transmission microscopy, SEM, Chicago (1975), 671-678.

[10] E. Zeitler: Zusammenhänge, die mit der Kohärenz Zusammenhängen, Optik 77(1987), 13.

[11] H. Rose. R. Spehr: Energy broadening in high-density electron and ion beams: The Boersch effect, Adv. in Electronics and Electron Phys. Suppl. 13C(1983), 475.

[12] M.P. Silverman: Fermion ensembles th a t show statistical bunching, Phys. Lett. A 124(1987), 27.

[13] M.P. Silverman: Distinctive quantum features of electron intensity correlation interfero­metry, II Nuovo Cimento 97B(1987), 200.

[14] M.P. Silverman: Second order temporal and spatial coherence of thermal electrons, II Nuovo Cimento 99(1987), 227-245.

[15] M.P. Silverman: On the feasibilitity of observing electron ant.ibunching in a field-emission beam, Phys. Lett. A 120(1987), 442.

[16] M.P. Silverman: Application of photon correlation technique to fermions, OSA Procee­dings on Photon Correlation Techniques and Applications 1 (1988), 26-34, Eds. J .B.Abbiss, A.E.Smart, OSA Washington DC.

[17] M.P. Silverman: Quantum interference effects on fermion clustering in a Fermion interfe­rometer, Physica fí 151(1988), 291. v' ■

[18] S. Cova, M. Ghioni, F. Zappa: Improving the performance of ultrafast microchannel- plate photomultipliers in time-correlated photon counting by pulse pre-shaping, Rev. Sei. Instrum. 61(1990), 1072.

[19] S. Cova. M. Ghioni, F. Zappa: Optimum amplification of microchannel-plate photomul­tiplier pulses for picosecond photon timing, Rev. Sei. Instrum. 62(1991), 2596.

[20] S. Cova, M. Ghioni, F. Zappa, A. Lacaita: Constant-fraction circuits for picosecond pho­ton timing with microchannel plate photomultipliers, Rev. Sei. Instrum. 64(1993), 118.

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Fig . 2. Image o f the positive resist pattern on A1 surface. PE landing energy 620cV

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References:[1], Autrata, R.: Scanning Microscopy, 1989,3, pp.739-763[2]. Autrata, R., Hejna, J.: Scanning ,1991, 13, pp.275-287

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Fig. 1. The annular ( le f t ) and planar ( r ig h t) detector for low voltage operation

Fig. 2. SE trajectories in annular and planar detector with a negatively biassed grid (-100V).

Fig. 3. Topographic contrast in BSE mode. Annular detector ( le f t), planar detector (r ig h t). IC surface covered with the passivating S i0 2 APCVD layer. E0 = 2,2keV.

Fig. 4. Voltage contrast in BSE + SE mode. Annular detector. Transistor KFY 18. W ithout passivation.U BE = + 5V applied. The rest o f the circuit is grounded. Voltage contrast is visible below IV.

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OUTLINE OF AN ELECTRON MONOCHROMATOR WITH SMALL BOERSCH EFFECT

F. Kahl and H. RoseInstitute o f Applied Physics, Technical University Darmstadt,Hochschulstr. 6, D-64289 Darmstadt, Germany.

The attainable information in electron microscopy and holography is ultimately limited by the chromatic aberration. For round lenses this defect can only be reduced by decreasing the energy width of the incident electron beam [1]. To push the information limit below I A at vol­tages higher than about 200 kV, the energy width must not exceed 0.2 eV. Unfortunately, the energy width of field-emission guns lies in the range between 0.6 eV and 0.8 eV for beam cur­rents required in TEM. As shown by experiments, about 30 % of the electrons have an energy deviation from the mean value smaller than 0.1 eV for an emitted beam current of a few //.A. If the remaining 70 % of the electrons could be filtered out by a monochromator, one would obtain a nearly monochromatic source with sufficient beam current. The acceleration volta­ge at the location of the monochromator should not exceed 3 - 5 kV to achieve a dispersion which is sufficiently large for filtering. Hence the monochromator must be placed immediately behind the source. Due to the high voltage to ground (a few hundred kV) in a TEM, a purely electrostatic design is mandatory. Such an electrostatic monochromator was first proposed by Plies [2], Unfortunately, his design consists o f a large number of elements and requires a large extension of the height o f the microscope. The electrostatic Si-shaped monochromator propo­sed by Rose [3] is significantly shorter. However, a common disadvantage of both designs is the formation of several stigmatic intermediate images of the source within the system. The high current density in the surrounding o f these images produces a large Boersch effect [4,51 which significantly increases the energy width of the beam.

To minimize the Boersch effect, we recently analyzed the feasibility of i2-Jhaped mo­nochromators with astigmatic and virtual stigmatic intermediate images of the source. The line-shaped astigmatic images produce a much lower current density than stigmatic images. The schematic construction of this type of monochromator is sketched in figure 1. To avoid a loss o f lateral coherence and brightness, the monochromator must be free of dispersion at the exit plane. Hence it is useful to maximize the dispersion at the symmetry plane z, and select the energy there. The line image in the energy selection plane is perpendicular to the direction of the dispersion. The dispersion shifts this image away from the axis by a distance which is proportional to the energy deviation. By properly adjusting the width of the selection slit, all electrons with too large energy deviations can be filtered out. To allow for an accurate filtering, the second-order aberrations, especially the aberrations caused by misalignment of the source, must be kept small in the direction of the dispersion. To preserve the diam eter of the source, the second-order aberrations at the final image plane z* must also be negligibly small. Owing to the symmetry of the monochromator, the aperture aberrations and the distortions vanish at this plane.

The dipole field o f each deflector curves the optic axis, focuses the electron beam in the iz -sec tio n and defocuses it in the yz-section. In order to focus the beam also in this section an additional quadrupole field must be excited within each deflector which overcompensates the defocusing refraction of the dipole field in the yz-section and reduces the focusing effect in the other section. The required quadupole field can be obtained by an appropriate curvature of

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DIFFERENT WAYS OF ADDING THE ABERRATIONS

Robert Kolařík and Michal Lenc Dept. ofTheor. Physics and Astrophys.Kotlářská 2, 611 37 Brno Czech Republic

In our paper [1] the main idea was to get a general expression for the resolution o r (when considering unavoidable axial aberrations - spherical and chromatic - and the finite source size) in terms o f wave optics. The resulting expression enables to choose an arbitrary criterion for the resolving power and to seek for the maximum resolution (optimization is being performed with respect to defocus and image aperture angle) in an analytical way. Our predictions for the resolution were compared with the results o f Mory [2] and Barth [3]. Hammel and Rose studied similar problems in [4],

The discussion in fl] did not concentrate on another result - a form of the intensity distribution function I (ct) (ct being the radial coordinate in the observation plane). This function depicts the probe profile in the observation plane. The main effort o f our present work has been directed to study the possibility o f verifying the validity o f I (a) experimentally. Basic idea was to design an appropriate optical alignment, whose optical parameters would enable us to measure the probe profile on the screen (the CCD camera is supposed as a detector). In order to get a sufficient magnification within the optical distance, where disturbing effects can be neglected, we have to work with a multi-lens system. We have considered a column with three lenses working in different modes. Using the computation program ELD [5], we were trying to design lenses suffering from very large spherical and chromatic aberration coefficients for given focal distances and magnifications. In such case we should obtain measurably wide probe spot close to the diffraction- limited situation, where our I (a) form is exact as a consequence of used approximation.

We assume that it is possible to derive similar formulae for the other experimental configurations, where only one aberration term becomes dominant.

[1] R. Kolařík, M. Lenc: An expression for the resolving power o f a simple optical system. Optik 106(1997) 135-139.

[2] C. Mory, M. Tence, C. Colliex: Theoretical study o f the characteristics o f the probe for a STF.M with a field emission gun. J. Microsc. Spectrosc. Electron. 10 (1985) 381-387.

[3] J. E. Barth, P. Kruit: Addition o f different contributions to the charged particle probe size. Optik101 (1996) 101-109.

[4] M. Hammel, H. Rose: Resolution and optimum conditions for dark-ficld STEM and CTEM imaging. Ultramicroscopy 49 (1993) 81-86.

[5] B. Lencová: Computation o f electrostatic lenses and multipoles by the first order finite element method. Nucl. Instr. Meth. A363 (1995) 190-197.

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Surprisingly, it is still possible to find references to problems with the use and accuracy o f the FOFEM with small meshes (e.g. Tsuno in his chapter on magnetic lenses in [ 1 ] or Khursheed in 1997 in [3] or at C P05). The same arguments hold for the use o f graded meshes: if most users see that the axial field behaves strangely at the places where the mesh step change abruptly, the most natural solution is the use of smoothly graded meshes. Another fact that nobody uses the value o f the integral o f magnetic field along the axis and/or around the lens as a check of correctness o f the magnetic lens computation is really difficult to understand.

N ext question is that of computation accuracy. The accuracy of any ‘m esh’ method depends on the type of mesh and the number o f mesh points used. 1 will in this respect briefly mention an important but overlooked aspect of checking the accuracy of FEM computations, the extrapolation to ‘infinite number of points’; the first example of that for magnetic lenses we published already in 1994 [4], and I have discussed this in detail at C P05.

In the practical application of any program, the aspect o f user friendliness and user interface becomes important. We have devoted to this aspect a lot o f attention in Brno as well as in Delft in our software packages, that use a unified approach to magnetic and electrostatic lenses and multipoles. The computation times are reasonably short, and cheap and available personal computers are used for the computations. In the user interface graphical editing is used, the generation o f graded fine mesh is done automatically, and all results are shown or exported graphically. The program packages thus meet most requirements from a user point o f view, in spite o f leaving some space for improvements, because the interfaces were written in a pre- Windows time. The numerically obtained results are accurate enough to allow not only comput­ation of paraxial properties and aberrations from axial potentials or fields but also ray tracing.

SOFEM by Munro group was introduced 10 years ago, and it is often put as a competitor to FOFEM. This seems to be the case of their program SOURCE for calculating guns and space charge limited beams. In spite o f the considerable span of time since the introduction of SOFEM, hardly any attention is given to accuracy (an exception being the discussion of the computation accuracy of axial potential in a two-cylinder lens by Munro in [4] and later by me at C P 04 where it could be shown that the FOFEM produces competitive results). Electrostatic lens computations seem to work, although the mirror results in [1] are surprisingly inaccurate (as discussed in 1996

at this seminar). In magnetic lens computations with SOFEM no lifhit o f maximum number o f points is ever mentioned (but it is known that it is impossible to calculate on large meshes). No integral along the axis is computed, so the very basic check, if the result is correct, is missing. Some of the SOFEM results on saturated lenses look strange [7]. W hat is published by Munro on the computation of multipole components with SOFEM is even ridiculous, and the same error since [4] is in [1]. The FOFEM implemented by Munro does not work properly for the computation o f hexapole field component in deflectors, in particular with small number of points and w ith large mesh step change at the place where the field is still strong and varying (the computations in meshes where the problem is stated last less than 1 s on obsolete 486 PC), and their program does not work for 5th harmonic component at all. It does not mean that this is a problem that cannot be handled by FOFEM accurately [8]. As a summary I do not see SOFEM as the ‘com petition’ o f FOFEM , and I would like to see more accuracy tests o f the method.

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program) for three problems where analytical solutions are known: spherical analyzer, thin aperture between two regions o f constant field, and a two-cylinder lens, where computation accuracy was given against computation time. The results in 3D computation were added for the presentation at C P05. One test was actually left out, which can be used as an ultimate test o f any electrostatic program: the dipole mirror of Preikszas and Rose (see the notes for 1996 seminar).

ConclusionsEven the best software for electron optics cannot solve all problems. A ‘dedicated’ user

can produce ANY result - including often the biggest nonsense. Sometimes this is a consequencc of the usual ‘human’ approach to computers and programs: some people tend to trust any result produced by a computer if it keeps them from thinking. Are there any ways how to prevent this?

Another fact is that in the places where the actual research is done into computational methods and extreme applications of programs, nobody is actually interested in having a nice program as an output. Should the universities do more to finish the software into a commercial product? Everyone implicitly requires a full range of services (Windows interfaces, on-line help, full documentation, many options implemented in a program), but is there somebody really willing to pay for all these features? W hat should be in a good software for electron optics?

AcknowledgmentSupported by a grant o f Acad. Sci. o f the Czech Republic No. A 1065804. Software for

FEM is distributed by Delft Particle Optics foundation [5] - cooperation with G. Wisselink, M. Lene, J. Chmelik (and recently with J. Zlámal) acknowledged. F. H. Read and D. Cubric from U. M anchester were involved in the comparison o f electrosatic programs; the project was supported by a grant o f Royal Society. Let me also mention recent fruitful discussions started with R. Becker, U. Frankfurt, and G. Martinez, U. Complutense, Madrid.

References[1] Handbook of Charged Particle Optics, ed. Jon Orloff, CRC Press, 1997.

[2] Proc. o f C P 03 published in Nucí. Instr. Meth. A298(1990), C P 04 in NIM A363(1995).[3] Proceedings of SPIE 2014 (1993), 2522 (1995), 2858(1996) and 3^55(1997), respectively.[4] W orkshop on Computer Assisted Design of Particle Optics Instrumentation, Delft, June 1994.[5] http://cpo.tn.tudelft.nl/bbs/cposis.htm.[6] http://chaos.fullerton.edu/mhslinks.html.[7] K. Tsuno, Ultramicroscopy 72(1998), 31-39.[8] M. Lenc and B. Lencová, Rev. Sci. Instrum. 68(1997), 4409-4413.[9] J. Zlámal, MSc. Thesis, TU Brno 1996 (see also 1996 seminar).[10] K. J. Binns, P. J. Lawrenson and C. W. Trowbridge, The analytical and numerical

solution of electric and magnetic fields (J. W iley & Sons, 1992).111] A. von der W eth, Dissertation FB Physik, U. Frankfurt/Main (1997).[12] D. Cubric, B. Lencová and F. H. Read, Proc. EMAG97. Inst. Phys. Conf. Ser. 153, 91-94.

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OPTIMAL SYNTHESIS OF CHARGED BEAM FOCUSING SYSTEMS

G Martinez(a), A D Dymnikov<b) and A H. Azbaid(J>(a)Dept. Física Aplicada III, Fac. de Física, Universidad Complutens, E-2H040 Madrid, Spain ^ C.I.KM.A.T., Avda. Complutense 22, E2H040Madrid, Spain

One o f the main characteristics o f contemporary Science is a quick creation o f knowledge that is frequently associated to the appearance o f new or more refined measurements There has been a continuous improvement o f the existent instrumentation and a development o f sophisticated new devices that has made possible this outstanding progress.To go on this tendency we need to prepare appropriate tools: mathematical and physical models to simulate the behaviour o f a system and the way in which this behaviour can be optimized. In this talk I will present a scheme o f work that we are applying to the optimal design o f electrostatic lenses. Even if this is a small area in Charged Particle Optics the scheme could be extended to other beam guide systems

The direct method for finding the optimal design would be to compute simultaneously the field and trajectories o f the particles through the quadruplet, but these trial and error tests demand a huge amount o f computing time that is not possible to do in practise To overcome this problem we use two models: an analytical model and a numerical field model The first one utilises analytical functions for the axial electrostatic potential and its partial derivatives W ith these functions it is possible to obtain the analytical solution in matrix form up to the desired order approximation, in our case up to third order. In the analytical model the initial approximate differential equations are replaced by the linear equations in the space o f the phase moments with the same approximation accuracy. Thus we can use all the advantages o f linear differential equations over non-linear ones, including the independence o f the matrizant o f the choice o f the initial point o f the phase space [ 1],

An interesting finding is that placing two slits at the appropriate place before entering the lens allows to shape optimally the initial beam and to obtain the minimum spot size aM he target By this way it is possible to find the optimal parameters o f the system with minimum computing time

At the second stage we apply an accurate version o f the boundary element method which simulates the geometry o f the real system and performs a very precise calculation o f the field In fixing the initial conditions for ray tracing, we use the information provided by the analytical model Thus, the combination o f both techniques allows tfle synthesis o f the best lens in a straightforward way.

As a first example let us consider the optimization o f electrostatic axisymmetric lenses consisting o f multiple coaxial cylinders [2], A new analytical model o f the axial potential distribution is applied which corresponds to realistic multiple cylinder systems. Using the version o f BEM described in reference [3] to solve Laplace’s equation we obtain the parameters o f the physical model that has the same axial potential distribution as the analytical model The parameters o f the physical model are lengths and radii o f the cylinders, the gaps between them, and the applied potentials. Figure 1 shows the computed axial potential for a 3-cylinder lens and the corresponding analytical function The coincidence between the two profiles allows matching the focal distance and the demagnification within at least three digits.

To analyse the beam spot size we find the matrizant (or transfer matrix function) for the linear and nonlinear equations o f motion using the effective recursive computational method

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THE MICROANALYTIC PROSPECTS OF A HIGH RESOLUTION PEEM

M .M erkel(1), M .Escher(l>, O.Schmidt<2), Ch.Ziethen(2), G.Schönhense<2)

(,):Focus GmbH, Am Birkhecker Berg 20, D655I0 Hünstetten-Görsroth, Germany (2>: Universität Mainz, Institut fü r Physik, Staudinger Weg 7, D55099 Mainz, Germany

Using synchrotron radiation at BESSY or a Mercury lamp we perform microspectroscopy experiments with a photoelectron microscope (FOCUS IS-PEEM) equipped with an electron energy analyser (FOCUS MICRO-ESCA). In this arrangement we are able to determine the chemical composition o f solid surfaces with a high lateral resolution down to appr. 250 nm.

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Iris Aperturesize adjustable (mech. feedthr. )

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Figure 1: FOCUS IS-PEEM equipped with the H-ESCA energy analyser

The experimental set-up is shown in F ig .l: The PEEM is used to get a lateral image o f the chosen sample region with a resolution o f today down to about 20..25nm. To get chemical information o f a certain feature this region o f interest is centred in respect to the actual field o f view by means o f the piezo driven x-y sample stage. Now the field o f view is to be limited using the iris aperture located at the first image plane o f the microscope objective lens. The iris aperture can be closed giving an effective field o f view o f down to about 250nm depending on the actual total magnification o f the PEEM. The deflecting potentials o f the analyser have to be switched on and choosing a suitable pass energy the energy spectrum of the selected region can be taken. More detailed information is given elsewhere [1 j,[2 J .For demonstration o f the recent performance we show in Fig.2 an example: This PEliM micrograph was taken with a photon energy o f 95 eV at BESSY I (Undulator IJ2 combined to a multilayer optics). The sample consists o f 20x20|im Pt-Co-Pt multilayer squares deposited onto a silicon substrate. There are plotted three valence band spectra taken at different p-spot

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A COHERENCE FUNCTION APPROACH TO MULTISLICE THEORYH. Müller and H. RoseInstitute of Applied Physics, Technical University Darmstadt,Hochschulstrafie 6, D-64%89 Darmstadt, Germany.

The simulation of high-resolution electron micrographs is a valuable tool for determining the atomic structure of objects by means of electron microscopical techniques. Although a number of different simulation methods have been proven useful, a quantitative correspondence between HREM simulations and experimental images has not yet been reached.To take the step from qualitative to quantitative HREM image simulation, a theory of image formation which is solely based on the propagation of the stationary wave function of the scattered electron proves to be insufficient. To avoid this shortcoming, we have proposed a theory of image simulation based on the propagation of the stationary m utual coherence function [1 ]

T c(p,p',t) = {'¡/{p,t)'¡>,(p',t-T))T . ( 1 )

Here 1 is the electron wave function and (.. denotes the time average over the recording tim e T of the micrograph; p, p' are 2-dimensional coordinate vectors perpendicular to tin- optical axis. The recorded intensity in the image plane is given by I(p) = Tc(p, p' = p ,r = 0) — (l 'í 'íp ,i ) |2)r- The coherence function approach correctly accounts for the partially coherent nature of the electron optical imaging process and the quasi-elastic and inelastic scattering processes w ithin the object. The propagation of the coherence function through the object can be calculated efficiently by a generalized multislice formalism [1,2]. In this formulation the scattering properties of each thin object slice are approximately described by the mutual transmission function

M (p ,p ',r) = exp (i(p i(p ) - Pi(p')) ~ g ( M p) + M p ') ) + Pn(p, p \ r )) ■ (2)

This transmission function depends only on the first and second stochastical momenta of the projected slice potential considered as a tim e-dependent stochastic process. This approach considers the fact th a t for weak objects the ideal inelastic image represents the variance of the projected potential [3]. The terms in the exponent are explicitly given by

p\{p) = (x (p,*))t , M p) = Mil (P,ff — PiT — 0),(3)

pn(p,p!,r) = ((x(p, t) - pi{p))(x(p', t - t) - px(p')))T ■

The second relation ensures th a t our formulation does not violate tKS optical theorem as it, is the case for the conventional multislice theory which uses an absorption potential to account for inelastic scattering. The information about the stochastical measures pi, p-¿, and p.\ \ can be calculated from simple analytical models describing the elementary quasi-elastic and inelastic scattering processes w ith a sufficient degree of accuracy. Currently we employ the Einstein model of lattice dynamics for therm al diffuse scattering and a modified Raman Compton ap­proximation for inelastic electron scattering resulting in electronic excitations [1 ,2].To dem onstrate the feasibility of our calculation method we have simulated unfiltered diffrac­tion patterns of Si (110) for different crystal thicknesses. The calculation considers the influence of elastic, quasi-elastic, and inelastic scattering processes within the object. The results are compared w ith experimental diffraction patterns of specimens of comparable thickness. The

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VARIABLE MODE RETARDING FIELD ELEMENT FOR LOW ENERGY S E M

I.Miillerová, L. Frank and E. Weimer*Institute o f Scientific Instruments AS CR, Královopolská 147, 612 64 Brno, Czech Republic LEO Elektronenmikroskopie GmbH, 73446 Oberkochen, Germany

Today's trend toward low electron energies in a SEM is motivated by reasons connected solely with the specimen itself. At low energy electron impact, the interaction volume diminishes so that the information is better localized, the total electron yield is generally higher and the specimen charging-up can be suppressed, and moreover many new types o f contrast appear. Contrary to this, although significant progress has been made in designing low voltage guns and electron optical columns, principal needs for keeping the beam energy at least at few keV throughout the column cannot be avoided. These include suppression o f influences o f both the external stray fields and the mutual interactions o f the beam electrons, and extraction o f a sufficient current from the cathode. Using the SEM designs employing variable electron energy along their trajectory between the gun final anode and the specimen can combine both demands.

One important possibility is to use an integrated beam accelerator or booster [1,2] which holds the beam, between the gun extractor and the objective lens, at an energy higher than the landing one, which is given by the cathode potential with respect to the earthed specimen. An immersion electrostatic lens, combined with a normal objective lens, closes the booster. The combination lowers the aberrations and they even decrease with the increasing immersion ratio or decreasing landing energy. Alternative is to apply a high negative bias to the specimen and to lower the beam energy immediately above the specimen surface with the help o f a cathode lens [3,4]. This combination is capable o f preserving a nearly constant image resolution throughout the energy scale and even commercial SEMs can be adapted to this mode, provided a special detector is fitted [5,6].

The operation o f the booster is limited by a maximum reasonable immersion ratio o f its closing lens - otherwise it becomes too strong to form the probe [7], For a 4wo-aperture lens with the aperture distance D and "sharp" field transitions in electrodes, we get, from a simple analytical calculation [8], the lower focal point lying at the distance D below the lower aperture already at an immersion ratio o f 7. Computer simulation [9] brings the ratio o f 36 for both aperture diam eters equal to D while the field strength on the specimen reaches already 5% o f the full value. The focusing power is further increased by the magnetic lens so that one can consider this principle viable down to electron landing energies p f 200-500 eV only. I his energy range brings already most o f the advantages mentioned above. Nevertheless, principally new contrasts appear below 50 eV where the electron reflection yield acquires a vector character, dependent on the specimen crystallinity, and wave-optical contrasts become possible. In addition, the probing depth starts to increase again, weakening the vacuum demands. This range can be reached only with a cathode lens with the full field strength on the specimen surface and difficulties connected with the specimen biasing.

A booster equipped SEM column (Fig. la) offers a very efficient way o f combining both described methods. W hen insulating even the lower immersion lens electrode from the column body, one can simply switch the retarding field to the cathode lens mode but with the advantage o f the specimen earthed (Fig. lb ) - in-lens detector is then available only. Furthermore, an insulated specimen holder enables one to use also a highly efficient (retractable) anode/detector assembly (Fig. lc).

The variable mode arrangement makes the full energy scale accessible with the possibility to adjust the electric field on the specimen.

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SHORT NOTE ON LOW -ENERGY S E M CONFIGURATIONS

I.M üllerová and L. FrankInstitute o f Scientific Instruments AS CR, Královopolská 147, 612 64 Brno, Czech Republic

There are good acknowledged reasons to lower the landing energy o f primary electrons incident onto a specimen in the SEM down to hundreds and even tens and units o f eV. But there are equally good reasons to produce the primary electron beam at a high energy o f tens o f keV. To satisfy both, SEM designs are desirable in which fast primary electrons are decelerated somewhere in front o f the specimen surface.

M odifications o f this general principle, proved to date, can be divided according to where the deceleration field is applied. It can simply be between two bored electrodes o f an electrostatic immersion lens fitted into the magnetic objective lens so that the fields overlap. Another alternative is to replace the final electrode with the specimen, i.e. to use the cathode lens. Both approaches differ mainly in the electric field intensity on the specimen surface. A higher field causes a more effective collimating o f the emitted electron toward the axis, which affects the detection conditions. On the other hand, the specimen geometry, tilt and surface quality become more critical. Some specimens can be even intolerant to a high electric field. The main difference is that the aberration coefficients keep proportionally decreasing down to the lowest energies for the cathode lens [ 1 ] while for the immersion lens, it falls only down to values similar to its working distance [2,3].

Both versions can be treated in the dependence on the working distance w o f the electrostatic immersion lens, so that the cathode lens is for w=0; this is similar to the systematic approach in [4]. Fig. 1 shows the electric field on the specimen surface, as a function o f w/D, where D is both the diameter and distance o f the electrodes. Obviously, the surface field can easily range in tens o f per cent o f the maximum while the aberration coefficients still remain in tenths o f w while for the cathode lens they are roughly equal to D divided by the immersion ratio. This speaks in favor o f the cathode lens whenever it is applicable.

A further aspect is that for a compound lens composed o f electrostatic and magnetic lenses, both aberration contributions are generally comparable. For a cathode lens, the focusing lens influence diminishes at very low energies and the resolution is mainly governed by the axial electric field (see Fig. 2). Consequently, if a cathode lens can be fitted into an existing SEM, good results can be obtained irrespectively o f the original SEM performance. Furthermore, the effect o f such an adaptation is enhanced due to the favorable property shown in Fig. 3. I f the beam aperture is kept constant at a value aligned for a certain landing energy, the image resolution remains acceptable and moderately offset from the ultimate value throughout the energy scale.

From the practical point o f view, the landing energy is defined by a (small) potential difference between the gun cathode and specimen while the (high) column energy can be reached either by biasing both negatively or by biasing positively the whole microscope column. The second case is discussed elsewhere in this book [5], the first [6] can be even applied to commercial SEMs. In a cathode lens, the full electron emission is, in the anode plane, collimated to within a diameter o f 4w(k-l)',/2 where k= Ep/EL is the ratio o f primary and landing energies. This enables one to employ, for the cathode lens based configurations, both the EDOL-type in-lens detection [7] with electrons passing through the anode opening, and an anode/detector combination with a very small central bore (made e.g. from the YAG crystal). The latter type has a very high efficiency but needs a working distance o f 8 mm at least. Doubts have been many times expressed as regards restrictions, put onto the specimen surface properties when the specimen serves as the cathode in a cathode lens. Particularly, the

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A STUDY OF WAYS OF IMPROVING THE SPEED AND ACCURACY OF COM PUTING FIELDS, TRAJECTORIES AND ABERRATIONS IN ELECTRON OPTICS

E. Munro, X. Zhu, J. Rouse and H. LiuMunro s Electron Beam Software Ltd, 14 Cornwall Gardens, London SW7 4AN, England.Tel. & Fax: (+44) 171 581 4479 e-mail: mebs@compuserve.com

The main objective in the computer simulation o f electron optical systems is usually to predict as accurately as possible the image blurring and distortions o f an imaging or probe-forming system. This essentially involves computing fields, trajectories and aberrations. The traditional way o f doing this is to compute the electrostatic and/or magnetic field distribution along the system axis and then evaluate the primary aberration coefficients with a set o f aberration integrals involving the paraxial rays, axial fields and their axial derivatives.

Although this traditional method has served electron optical designers well, the design o f some o f the latest instruments is straining the capabilities o f the standard simulation methods. Examples that are hard to simulate by traditional methods include LEEM systems, aberration correctors, electron mirrors, curved axis systems for beam separators, Wien filters, etc. In LEEM systems, images are formed with electrons emitted from the sample surface with low energies and large angles. At such low energies and large angles, conventional aberration analysis may become inadequate, the energy spread can dominate the initial energy, and the concept o f chromatic aberration coefficients may become almost meaningless. In aberration correctors, analysis o f high-order and asymmetry aberrations may be needed, and this is very complicated using conventional aberration analysis methods. In mirror systems, conventional aberration formulations break down near the reversal point, and very involved theoretical treatments are needed unless direct ray-tracing is used. For curved axis systems and Wien filters, the expansion o f field functions, paraxial rays and aberrations o f various orders about a general curved optical axis involves great complexity and enormous scope for mistakes.

To help address such problems, the aim o f this paper is to investigate methods for improving the speed and accuracy o f numerical field analysis and direct electron ray-tracing. The aim is to identify areas where improvements can be made in the simulation techniques. In particular, we aim to try to compute field distributions very accurately (off-axis as well as on the axis), and to see how fast and accurately we can directly compute rays through these fields, without resorting to aberration theories. We then compare the results o f these simulations with conventional aberration results and try to assess the relative merits o f the various approaches.

The most difficult task, by far, in most electron optical simulations, is accurate field analysis, since if the fields are known accurately the trajectories can be computed with negligible truncation errors, using high-order Runge-Kutta or Bulirsch-Stoer methods [1|. For high accuracy field analysis o f structures with rotational or multipolar symmetry, second order finite elem ent method (SOFEM) [2] is in principle an attractive candidate. Isoparametric second order finite elements use biquadratic basis functions for both the element geometry and the potential. The biquadratic element geometry allows the elements to be curved, thus allowing accurate geometrical modelling o f structures with curved cathodes, electrodes, polepieces, grids, etc. The biquadratic potential functions allow a closer fit to real potential distributions than linear basis functions do, for a given number o f grid points.

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much faster with the interpolation polynomials. The field computation and the resulting direct ray-tracing are both speeded up by at least a factor o f 20, for the same accuracy. A typical trajectory can be computed in about 0.016 seconds with less than 10 nm truncation error. This enables 10,000 trajectories for a LEEM system to be computed, and the results plotted, all in < 3 minutes. Results illustrating the technique will be presented.

In general, using the above method, the potential near the axis o f a round lens is expressed in the form:

O ( r ,z ) = c„(z) + c2(z)r2 + c4(z ) r4 + . . . + c2</v-i>(z ) ''2t^ l)

c'o(z) represents the axial potential, cifz) is related to the second radial derivative at the axis, C4(z) to the fourth radial derivative, and so on. These functions have been plotted as functions o f z and are very smooth, well-behaved functions. Assuming the potential obeys Laplace's equation, both the radial and axial derivatives o f the potential, at the axis, can be directly derived from these functions:

Radial derivatives at r=0: d^O/dr2 = 2co cf<t>/drA = 2Acn db<S>ldrb = 12()ch etc.

Axial derivatives at r=0: c^íVdz2 = -4co d4<I>/3z4 = 64c4 56<t>/3z6 = -2304c(, etc.

These functions can all be obtained directly from the radial polynomial fits. Since the axial derivatives are exactly the functions needed for computing aberrations by the ordinary integral methods, these functions can be used to evaluate the aberration integrals directly, without any need for integrations by parts, which greatly simplifies the formulae and their programming. The aberration coefficients up to fifth order, or possibly even seventh order, should be able to be computed accurately in this way. We are in the process o f comparing the aberration integral results with direct ray-tracing, for ordinary imaging systems, and hope to present results o f this at the meeting.

Techniques for improving the speed and accuracy o f the direct ray-tracing itself are also being investigated. Instead o f using a standard fourth-order Runge-Kutta formula, we are evaluating a fifth-order Runge-Kutta formula due to Cash and Karp [5], which involves six field evaluations per step. This formula is accurate to fifth-order terms in the Taylor series expansion, but simultaneously also allows an estimation o f truncation error on each step, using an embedded fourth-order Runge-Kutta formula. This can be incorporated into an adaptive step-size control algorithm, that optimizes the step size to produce a fast ray-trace with the truncation errors contained below a specified threshold. This typically enables < 10 nm cumulative truncation error over an entire trajectory in < 100 steps.

We are also trying to apply the above techniques to the analysis o f multipole and curved axis systems and hope to also present some initial results for these cases at the meeting.

References:

[1] W.H. Press et al., “Numerical Recipes in C”, 2nd Ed., Cambridge University Press, 1992, 707-732.

[2] X. Zhu and E. Munro, Journal o f Microscopy 179 (1995) 170-180.[3] B. Lencova and M. Lenc, Scanning Electron Microscopy 86/111 (1986) 897.[4] B. Lencova, Nucl. Instr. and Meth. In Phys. Res. A 363 (1995) 190-197.[5] J.R. Cash and A.H. Karp, ACM Transactions Mathematical Software 16 (1990) 201-222.

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ULTIMATE RESOLUTION: WHAT ARE THE NEEDS FOR FUTURE MICROSCOPES?

Harald RoseInstitute of Applied Physics, Technichal University Darmstadt, D-64289 Darmstadt, Germany

To fully understand the properties of solid objects, a detailed knowledge of the atomic structure, the chemical composition and the local electronic states is necessary. The atomic stucture of nonperiodic details can be determined in principle by means of tomography provided that the resolution limit can be lowered to about 0.06nm. In order to achieve quantitative information, a high-performance imaging energy filter with an energy resolution of at least 0.2 eV at a voltage of 200 kV is mandatory. If such a filter is incorporated in a combined STEM-TEM, it will become possible to elucidate the bonding of segregant atoms and the local distribution of electonic states near interfaces or defects.

For achieving sub-angstrom and sub-ev resolution, an entirely new generation of electron microscopes must be developed. The ideal future microscope will be a combined STEM-TEM operating at voltages between 150 and 300kV. It will consist of a field emission gun followed by a monochromator yielding an energy width below 0.2 eV. The condenser system must provide genuine Koehler illumination for the TEM mode and a spot size of about ,2nm for the STEM mode. This system also enables selected-area diffraction with variable cone angle if the diameter of the illuminated area is large compared to the diffraction-limited spot size. The spherically corrected aplanatic objective lens will consist of coma-free round lens and an integrated hexapole corrector. The formation of a spatially extended energy loss spectrum is performed by the highly dispersive aberration-free MANDOLINE-filter which has by far the highest transmissivity and the best overall performance of all filters proposed so far. The filtered intermediate image or the energy loss spectum are imaged onto a CCD array by means of an aberration-free projector system consisting of several lenses. For obtaining sub-angstroem resolution it is a "conditio sine qua non" that the incoherent defects resulting from parasitic mechanical and electromagnetic instabilities are reduced to such an extent that the information limit is pushed below 0.06 nm. The realization of this ambitious task is by

far the most difficult problem encountered on the route towards sub-angstrom resolution.

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Table I Spectral properties o f single crystals for S(T)EM

single crystal maximum"

(nm)

FW H M '

(nm)

spectral characteristic

S20 PM T

matching'"’ (%)

S l l PM T

m atching'"“ (%)

Y AG:Ce 560 122 73 45

YA P:Ce 366 52 60 58

P47 420 77 85 80

CaF2:Eu 426 30 92 88

‘position o f the m axim um o f the main emission band.

"fu ll w idth o f the half m axim um o f the main em ission band ’“ m atching to the spectral response o f S20 photocathode

“ "m atch ing to the spectral response o f S 11 photocathode

with alkali photocathodes. In the case of YAG:Ce, it is necessary to use the S 20 photocathode (its long wave spectrum region differs from that o f S 11). All other single crystals investigated can also w ork with the S 11 photocathode. In addition to the characteristic broad yellow emission band with a m aximum at 560 nm, the YAG:Ce shows a very weak emission in the blue, violet and UV spectrum regions. This weak emission which is more marked for specimens with a low activator concentration has a sharp maximum at 400 nm which is superimposed on the broad emission band with a maximum in the UV region, i.e. beyond the capabilities of the measuring device used.

EfficiencyFor all applications in S(T)EM, high CL efficiency is required. The relative CL efficiency of

the investigated single crystals is shown in T able H The values of this quantity are always related to the corrected value of the YAG.Ce single crystal. The as measured integral (spectrally non­decomposed) efficiency includes the influence of the PMT photocathode spectral sensitivity. This quantity is interesting from the viewpoint o f application in scintillation detectors where the

Figure 1 Norm alized cathodolum inescent spectra o f single crystal scintillators fo r S(T)EM .

of PMT PhotocathodesEmission Spectra of Single Crystal Scintillators for S(T)EM

450 500 550 600

wavelength (nm)

Figure 2 N orm alized spectral response o f the sensitivity o f the photocathodes used.

400 450 500 550 GOO 650 700

wavelength (nm)

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Table III Decay properties o f single crystals for S(T)EM

single crystal decay time"

(ns)

time characteristic

corrected decay tim e"

(ns)

afterglow ” '

(%)

YA G :Ce 110 103 2

Y AP:Ce 45 38 0.5

P47 41 34 unm easurable

C aF2:Eu 1200 1200 1.3

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" 'in ten sity m easured 5 p s after the end o f excitation

and the afterglow amounts to less than 1 %. In fact, with respect to the fall time of the pulse of the excitation electron beam (5 ns) and the fall time o f PMT (2 ns), the short-term decay component must be corrected by subtracting approximately 7 ns of the fall time of the measuring equipment. The short-term component o f the CL decay o f both yttrium alumínate single crystals depends only negligibly on the duration of excitation. On the contrary, the long-term component o f the CL decay depends strongly on the duration of excitation, so that for a very short excitation the afterglow of YAG:Ce and YAP:Ce can be one order and at least two orders lower, respectively. This is advantageous for applications in S(T)EM electron detectors operating at the TV rate, because the images with a rich topographic content can be of higher quality.

CONCLUSIONUnfortunately, all single crystals that have their CL decay time shorter than 100 ns (which

is the condition when the TV scan frequency is used) contain oxygen and just thiS*group o f single crystals belongs to those with the least efficiency [2,3]. This means that calcium fluoride, which is the most efficient o f the four chosen, has only limited applicability because its decay time constant is 1.2 ps. The greatest advantage o f YAP:Ce single crystals and P47 is that they are the fastest (38 ns and 34 ns, respectively). Especially, they have no such a marked component o f long persistent luminescence as the YAG:Ce single crystals have. The only disadvantage o f YAG:Ce single crystals is their speed which can be behind the limit for the'TV rate in some cases. It is therefore necessary to search for a way to shorten the decay time of YAGtCe scintillators.

REFERENCES[1] Schauer, P.; Autrata, R.: Inquiry of Detector Components for Electron Microscopy., Fine

Mechanics and Optics, 42 (1997), 340-342.[2] Robbins, D.J.: On Predicting the M aximum Efficiency of Phosphor Systems Excited by

Ionizing Radiation. J. Electorchem. Soc., 127 (1980), 2694-2702.[3] Lempicki, A .; W ojtowicz, A.J.; Berman, E .: Fundamental Limits o f Scintillator Performance.

Nucl. Instrum. Meth. Phys. Res. A, 333 (1993), 304-311.

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SPECTRO SCO PIC X-PEEM WITH EMPHASIS ON MAGNETIC CONTRAST

G. SchönhenseInstitut für Physik, Johannes Gutenberg-Universität, D - 55099 Mainz

Structural tayloring o f magnetic films is a rapidly growing field o f research and development because it offers additional parameters for the control o f magnetic properties. Vertical heterostructures (multilayers) offer a wide range o f technical applications e g. in magnetic sensor technology (read heads, position sensors) because o f the giant magnetoresistance (GMR) effect. Horizontal patterning is crucial for novel devices such as magnetic tunnel junctions for spin transistors being the basic units o f future non-volatile magnetic storage elements (MRAM). Also high-capacity hard discs require the controlled creation o f well- defined magnetic domains with lateral dimensions down to the 100 nm range.

For all these systems there is an increasing demand o f powerful microanalytical tools in the sub-micron range. For patterned structures a resolution o f several 10 nm is desirable, for multilayers it would be advantageous to view "buried layers", i. e. to look through a non­magnetic coating. M ost o f the above-mentioned materials are composed o f several chemical elements or intermetallic compounds. Since the constituents contribute differently to the magnetic behavior, it is necessary to distinguish the various magnetically active components in a system. Consequently, an appropriate magnetic imaging technique must combine magnetic sensitivity with element specificity.

The pioneering w ork o f Stöhr et al. [1] has demonstrated that Synchrotron-based photoelectron emission microscopy in the soft X-ray range (X-PEEM) is a highly promising technique to attack these problems. I f the magnetic X-ray circular dichroism (M XCD) as investigated by Schütz et al. [2] is exploited by using circularly polarised Synchrotron radiation, the magnetic contrast o f a selected element becomes visible.

This contribution will give an introduction into the technique [3] and illustrate its performance by means o f several typical examples. Technical problems like the chromatic aberration due to the energy distribution will be addressed. The base resolution o f our instrument (FOCUS IS- PEEM ) is less than 20 nm, visible in threshold photoemission at hv = 4.9 eV [4] Operation in the soft X-ray regime results in an effective energy distribution o f the imaged secondary electrons with a width o f 5-10 eV. This width has been confirmed by spectroscopy using the M icro-ESCA analyser [5], The energy width leads to a significant chromatical aberration yielding a total resolution o f 120 nm. Approaches to improve the resolution e g means o f a novel Time-Of-Flight mode o f operation [6] will be discussed.

Typical results [7,8] are shown in Figure 1 Micro-patterned layers o f permalloy (left), a Co/Pt multilayer (middle) and an epitaxial Co-film on Cu(100) (right) have been viewed by means o f the magnetic circular dichroism contrast at the iron and cobalt L-edges. Despite o f their similar dimensions, the three structures exhibit completely different domain patterns The permalloy squares show a simple flux closure structure with very few exceptions (like the defect-induced distortion near the centre o f the left image). This general behavior reflects the small magneto crystalline anisotropy and the tendency to minimize the magnetic stray field. The Co/Pt multilayer o f 7 periods (2.1nm Pt / 2.5nm Co) shows a complicated domain pattern ("magnetisation ripple") being indicative o f its high intrinsic anisotropy and the polycrystalline

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THREE DIM ENSIONAL SCANNING ELECTRON MICROSCOPY

W. SlowkoInstitute o f Microsystem Technology, Wroclaw University o f Technology, ul. Janiszewskiego11, 50-327 Wroclaw, Poland

IntroductionHumans and all higher animals are two-eyed so three-dimensional viewing the surface

topography should be an expected standard for most electron optical instruments. The subject has also very practical meaning. Quantitative characterisation o f surface micro-topography is one o f most essential problems in many fields o f science and technology, as for instance: microelectronics, micromechanics or tribology o f magnetic media. Scanning electron microscopy (SEM ) is a very important tool for inspection and measurements o f geometrical issues o f semiconductor structures (e.g. critical dimensions). Apart from its high lateral resolution, main advantages o f SEM are that it imagines the surface topography in the way preferred by human eyes and is very operative to find out some subtle peculiarities in large surface areas. However, it still gives limited information about the third dimension o f the surface objects and to measure their elevation and side slopes it is necessary to make cross- sections o f the sample. Current investigations on the problem are focused on tw o groups o f methods [ 1 , 2]: those based on principles o f stereoscopy or making use o f the specific angular distribution o f back scattered and secondary electrons (BSE & SE). Unfortunately, each method shows some deficiencies and disadvantages, so three dimensional imaging still is not a very popular technique.

Stereoscopic methodsThe utility o f a stereoscopic view o f the world to communicate depth information

resulted in the use o f stereo cameras to produce “stereopticon” slides for viewing. The stereoscopic methods o f a quantitative characterisation o f the surface topography are based on the same rules but they apply strict analysis o f the relations between two images registered from tw o points o f view. The idea can be explained on the example showed in Fig. I , where different images can be obtained by shifting the sample or viewpoint. In this case, the elevation difference H between the tw o points, A&B, results from the parallax (cl/ - d2), i.e. from the distance o f the tw o points measured in the horizontal direction:

H - Wd (d, - d2)/S , ^ ( 1 )where S is the shift distance and Wd is the working distance.

Fig. 1. Characteristic dimensions used to estimate the vertical height of objects when the tilt or shift of the viewpoints is applied

Much greater displacement o f the viewpoints can be achieved when it is obtained by changing inclination angles o f the view directions rather than by their parallel shift For instance, the sample stage may be tilted by angle P between the two images to change the view directions (as in Fig. 1). This time, the

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probe microscopy (SPM) and confocal microscopy (SCLM). In this field better results can be expected when the secondary electron signal is applied.

Secondary electrons are generated with Lambert’s distribution, so the current collected by one o f the detectors shown in Fig.2 can be written in the simple form [6, 7]:

/ / i = | iocosy sec cppdSl , (4)n<

where: ig is a maximum angle density o f the secondary current, proportional to the e-beam current and secondary electron yield 50After proper operations the expression for the d e tec to r^ current takes the form:

Ia = io\d-tg(pp-co^®A - 0 P)+cJ , (5)

that leads to the following eq. for the relative difference o f signals o f the detector A and B Ia - 1 b dz

(6)for 0 = 0 and a-A

c/d

dx + Q (7)

Ia + Ib dx ’where c and d are coefficients o f material and topographic contrast respectively. They depend

on the detector geometry, as it has been shown in Fig.3. Finally, an integral o f the expression represents the surface profile along x axis, i.e.:

where: x x - are co-ordinates o f the beginning and end o f the scan line, Q -is an integral constant equal with the surface profile height at the beginning o f each scan line (numbered /). For the tw o detector system all lines have to start from the same level. A fully three dimensional image can be obtained when the second pair o f detectors (C, D) is used to provide information about surface slopes in yz plane. Then, the final expression defining the surface topography along successive scan lines takes the following shape :

z(x ,y t) = a jI a + Ib

dx +st

«JIc - I n )

■ I c + I Jd y + c n ( 8 )

The second integral reconstructs the surface profile in t h e / direction (beginning with the initial altitude Cr) along start points o f all lines (x -Xq), as it has been shown in Fig. 4.

d ./c f

Figure 3. Quotient of the detector geometry coefficients against the detector declination angle ( -4- O.lrad, -9 - 0.3rad, -0 - lrad).

S'. 'V y=v,tFig.4. Scheme of the three-dimensional reconstruction of the surface geometry

The formulas for signal processing, (7) and (8), can be realised both in analog and com puter systems . Analog systems seem more suitable for the reconstruction o f the surface topography in a shape o f profiles which is a form o f two dimensional representation and can be

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OX T H E T H E O R E T IC A L U ND ERSTANDING O F T H E W IEN FIL T ER IN AN ELEC TR O N B IPR ISM IN T E R FE R O M E T E R

P eter Sonnentag, H arald Kiesel, and Franz Hasselbach Institut fü r Angewandte Physik der Universität Tübingen A u f der Morgenstelle 10, D-72076 Tübingen, Germany

In recent years, A. A. M ichelson’s visibility spectroscopy [1] has been realized suc­cessfully w ith electron waves instead of light waves [2], For th is, an electron biprism is used, and as a coun te rpart o f th e different p a th lengths of the interfering beam s in light interferom etry, a W ien filter in its com pensated s ta te is employed (see Fig. 1). A Wien filter consists of a crossed electric and m agnetic field, b o th being perpendicular to the optical axis. I t is said to be in its com pensated or m atched s ta te if the electric and m a­gnetic force for the m ain energy com ponent of the electron beam cancel each other. From the decrease in fringe con trast w ith increasing excitation of the W ien filter, the energy w idth of the source can be determ ined, and even the form of the energy d is tribu tion can be obtained in case that, it is sym m etrical to its centre.

If the in itia l s ta te o f th e electron is a pure s ta te , i.e. all electrons form identical wave packets, then th e action of th e W ien filter is to in troduce a longitudinal shift between the two partia l wave packets com ing from opposite sides of the biprism filam ent. R eduction of con trast of the interference fringes can then be explained by the lack of overlap bet­ween the two packets. T he longitudinal shift is caused by th e different group velocities inside the W ien filter being due to a different electric potential. If, on th e contrary, the electron beam is m ade up of a s ta tis tica l ensemble of electrons being in different energy eigenstates, then - a t least for narrow energy d is tribu tions - the loss of contrast, is the sam e as for a pure s ta te w ith the sam e energy spread, b u t in th is case it is caused by the displacem ent of th e incoherently superim posed interference p a tte rn s relative to each other. T his comes from th e fact th a t for electrons w ith an energy differing from the one for which the m atch ing condition is fulfilled there is a resu ltan t force and therefore also a phase shift. B u t in reality, we have neither a pure sta te of the electrons nor a mixed s ta te which is d iagonal w ith respect to the energy eigenstates, so th a t bo th mechanisms of th e reduction of con trast will be involved.

W hereas th e A haronov-B ohm effects yield phase shifts w ithout affecting the centres of the wave packets, and th e Sagnac effect or a homogeneous electric or m agnetic field in an electron in terferom eter lead to bo th a shift of the fringes and of their contrast, the W ien filter in its com pensated s ta te produces a wave packet shift without a phase shift so th a t in th e m iddle of the fringe p a tte rn there is always a m axim um and this is also a difference to Fourier spectroscopy w ith light. Because of th is special feature of th e W ien filter it seem ed w orthw hile to do the calculation of the biprism interferom eter w ith W ien filter for th e case of a wave packet explicitly. T his was done by using a form of the sem iclassical approx im ation of the Feynm an p a th integral for strongly localized wave, packets [3].

For monochromatic waves and consequently also for incoherently superim posed mo­nochrom atic waves - th e electron-optical biprism can be replaced by two v irtua l sources

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the phase difference Atp(k) of th e two interfering p a rts of an energy com ponent m ay be approxim ated by the first order term in the deviation 8k of the wave num ber from its m ain value ka. T hen, the phase shift caused by the W ien filter is equivalent to a difference in the geom etrical p a th length in vacuum , so th a t is p roportional to 7Vwp.

Fourier-transform spectroscopy dem ands a variable proportional to ¿¿r-'>k> ■ There­fore, neither E nor N - which has been used so far [2] - is suitable if the high precision of visibility spectroscopy shall be fully exploited. Because iVwp cannot be m easured directly, we propose to use j as th e transform ation variable, where s is taken from the recorded fringe patterns.

For the case of a wave packet, th e decrease in fringe con trast w ith increasing excitation of the W ien filter can also be in terp re ted as being due to the increasing (possibility of get­ting) “welcher Weg” (w hich-path) inform ation available from the difference in arrival tim e between th e two packets. A nother way how com plem entarity, in particu lar wave-particle duality, m ay be enforced in “welcher Weg” experim ents is entanglem ent w ith orthogonal sta tes e ither w ith th e environm ent (e.g., m easurem ent device) or w ith an in ternal degree of freedom (e.g., spin). T he effect of the W ien filter can, loosely speaking, as well be seen as a kind of entanglem ent: If we w rite the ordinary s ta te space of the partic le as a tensor product of the s ta te space of positions on the detection screen and of th e s ta te space Z of positions orthogonal to th a t screen (i.e., along the optical axis 2), then because of the longitudinal d istance A z of the positions of th e m axim a of the p artia l wave packets we have entanglem ent w ith respect to the space Z .

Helpful discussions w ith R ichard N eutze and Tomáš Tyc are thankfully acknowledged.

a) b)

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VARIABLE AXIS LENS WITH AN EXTREMELY LARGE SCANNING AREA IN ONE DIRECTIONR. Spehr

Institute of Applied Physics, Technical University Darmstadt, Hochschulstrafie 6, D-6^289 Darm­stadt, Germany

In order to obtain a large writing area on a single line, we have developed an electron lens design [lj quite different to tha t of usual variable axis lenses based on a round lens. The electrodes and the polepieces are formed by three parallel slits which in the x-direction are extending infinitely, at least in principle. Thus the geometry of the lens is translation invariant with respect to the x-axis as it is customary for a cylinder lens. For stigmatic focussing we combine two different fields, both fields being consistent with this geometry. Using a negative (or a positive) potential on the middle slit, we get a retarding (or an accelerating) electrostatic cylinder lens focussing in the yz-section [2J. In addition we superimpose a magnetic quadrupole field, which is oriented in such a way that focussing in the xz-section is achieved. This field is produced by fabricating the three slits out of magnetic material ( p.r » 105 ) and by placing windings on both halves of the middle slit, which carry constant current density. In this three-dimensional arrangement the magnetic scalar potential is given by

Umag = <3 X F (y ,z) . (1)

The function F (y, z) depends on the geometry of the slit in the yz-section and can be calculated by a suitable charge simulation procedure, which only needs to be two-dimensional. From eq.(1; we 6ee that the form of the magnetic potential does not change when moving into the x-direction, while its value increases linearly. In practice the slits must have a final length. Then the magnetic material should enclose the opening of the slit and we need two additional coils situated at both ends of the middle slit which carry the opposite Ampere windings as the polepigces do.

The magnetic quadrupole field focusses in the xz-section, but defocusses in the yz-section. To obtain stigmatic focussing, the electrostatic cylinder lens needs twice the refractive power as the quadrupole. When the axis of the quadrupole field lies within the xz-section, this axis coincides with the lens axis of the whole arrangement. The axis of the quadrupole field can be shifted over the whole length of the slit into the x-direction simply by transfering some current from the coil at one end of the slit to the coil at the other end. Thus our lens„acts as a variable axis lens. In principle the displacement of the axis with respect to the x-direction can be infinite without changing the imaging properties of the lens.

Like a round lens this lens does not show any aberrations lower than of third order due to its high symmetry. Furthermore there is no need for a separate stigmator as stigmatic focussing is achieved by balancing its cylinder lens field against its quadrupole field. Different to round lenses we have to distinguish between the x- and the y-direction when looking at its aberration coefficients. For instance the spherical aberration is given by three coefficients Caoca , Cppp and Ca0/3 = Ca<x0 j where a and /3 are the angles of convergence with respect to the xz- and the yz-section respectively.

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DISTRIBUTED MONTE CARLO: SMART WAY FOR COMPUTING COMPLEX PROBLEM

R. Stekly, L. Frank and I. MullerováInstitute o f Scientific Instruments AS CR, Královopolská 147, 612 64 Brno, Czech Republic

The aim o f this work was to create an engine for the distribution o f an computation task in the TCT/IP network, to verify its operation and to achieve a low-cost great-volume computation power for simulations o f electron scattering using the Monte Carlo method [1-3].

The available PC 's have a sufficiently high computation output not only for office work but also for simpler scientific computations. The computation output o f the best PC 's is comparable w ith that o f the cheaper series o f the RISC workstation but their purchase cost is ha lf that or less. M odem offices are being equipped with PC 's w ith the operating system W in95 connected to the LAN network, which is often connected to the Internet.

At interactive work, the processor is operated noncontinously and there are long inactive periods. Typical examples are text and graphic editors, table calculators and Internet browsers. On average, for a sufficiently long period, the processor is never used 100%. Therefore it has been decided to write a program that will make use o f the time-outs for its own activity, will receive simple tasks via the network, make computation and send back the results [4], Operating systems with pre-emptive multitasking can effectively work with priorities o f processes and they are mostly equipped with the mechanism that allows the action o f programs during the inactive period o f the computer. The chosen platform Win95/NT implements this mechanism relatively well. The only problem is the back compatibility when the 16-bit programs (DOS, W in3.11) are being started using the computer emulator with the given operating system that causes the mechanism to stop because W 95/NT are not capable o f determining the state o f the application with no implemented mechanism o f communication w ith the given operating system.

The written computation program has very low demands on the operating memory, typically 2.7M B compared with the 30MB text editor, is easy to control, provides maximum information about its state, and works automatically without any intervention o f the user. A fter starting, the program becomes connected to the computer that distributes the task, receives the data and starts computation. After finishing the computer work, the user makes the shutdown o f the operating system, the program becomes logout from the computation process, sends the computed part o f the task and becomes ended. The program is used as resident but the user can end it manually. The task distribution is carried out from one computer, which is determined in advance. This computer serves for data collection and recording o f the current state o f computation.

The operation o f the engine was tested in the internal network o f the Institute o f Scientific Instruments. The test task was a simple computation o f electron scattering in Au specimen at electron energy o f 1 keV. The entire task is divided into subtasks. The maximum num ber o f trajectories is limited so that all computers end the whole task at the same time. The computation process was running on the background, the test was made during the normal working time, the users were asked not to change their working habits.

The following formulas were used for statistically processing the operation:

mean value x =S trajectories

varianceI time n

standard deviation ô = VZ>, variation factor5

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AN E+B+E BEAM SEPARATOR FOR DETECTING

SECONDARY ELECTRONS IN LOW VOLTAGE SEM

Katsu Tsuno, Nobuo Handa and Sunao MatsumotoJEOL Ltd., 1-2, Musashino 3-chome, Akishima, Tokyo 196-8558, Japan tsuno(a)jeol.co.jp

1. INTRODUCTIONAmong various proposals o f the objective lens for high resolution low voltage scanning

electron microscope (LVSEM), an immersion magnetic lens called Snorkel lens [1,2] and a combined electric and magnetic field lens[3] are now widely used. We classified various objective lenses for LVSEM and compared their electron optical performances [4—6]. For designing the optical system o f SEM, not only spherical and chromatic aberration coefficients o f the objective lens for the incident beam but also efficiency o f collecting secondary electrons are important. In the strong magnetic field region just above the specimen, secondary electrons are spiral up into the bore o f the objective lens when the Snorkel lens is used. However, once the electrons come up inside the bore, secondary electrons spread out and hit the wall o f the lens, because there are no magnetic field. It is useful to apply a magnetic field along the optical axis to bring up those electrons to the top o f the objective lens. A weak electro-static field is effective to pull up the electrons emitted with high angles.

In this investigation, we further show electron trajectories from the top o f the objective lens to the detector. We use an usual Everhart-Thomley detector, which is inserted from the side o f the optical column.High voltage 10 kV is applied to the detector. In the in­lens SEM with accelerating voltage o f 20 -50 kV, high voltage applied to the detector captures the secondary electrons w ithout influencing the primary beam.However, in LVSEM, the detector must be set far behind the optical axis o f the primary beam. In such the case, it is necessary to introduce a beam separator to deflect secondary electrons towards the direction o f the detector. Sato[l] used the Wien filter as the beam separator. In this investigation, we propose a new beam separator, which is similar but not the same as the Wien filter. Recently, Philips announced a new beam separator with 3 stage electrode system[7].

2. ELECTRON TRAJECTORY CALCULATION IN THE SEPARATOR.

As shown in Fig. 1, the new beam separator consists o f the first electrodes, the magnet and the second electrodes. The length o f the magnet is equal to the sum o f the length o f two electrodes. The electro-static and magnetic fields are calculated using E 03D and M 03D and the electron trajectories are calculated using C 03D [8].

Fig. 2. Electro-static field distribution on xz plane and the primary beam trajectory

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ANTIBUNCHING OF ELECTRONS AS A CONSEQUENCE OF THE

INDISTINGUISHABLENESS OF FERMIONS

Tomáš TycDept, o f Theor. Physics and Astrophysics Kotlářská 2, 611 37 Brno Czech Republic

The principal indistinguishableness of identical particles has a fundam en­tal significance in quantum mechanics. One of its most im portant conse­quences for fermions is the Pauli principle. Another consequence of the quantum indistinguishableness is the difference of the statistics of arrival times of coherent particles em itted from a therm al source to a detector, with respect to the statistics of classical particles. This phenomenon is called bunching in the case of bosons due to the fact th a t bosons come more likely in groups of two, three etc. ( “bunches” ) than alone. In the case of fermions we deal with antibunching because the fermions avoid each other, i.e., do not come to a detector even in pairs.

Bunching of bosons was predicted theoretically [1] and proved experi­m entally [2] with photons already over 40 years ago. The theory describing this phenom enon is richly developed (e.g. [3]). On the contrary, the theory of antibunching (e.g. [4, 5]) is quite incomplete and there are still many problems to be solved. Moreover, the antibunching of fermions has not been experim entally proved until now.

In the talk will be given a brief introduction to the theory oPímti bunching for electrons and its application to an interesting case of an electrostatic biprism interferom eter.

[1] E. Purcell, Nature 178 (1956), 1449[2] R. Hanbury Brown, R. Q. Twiss, Proc. Roy. Sac. London 242 (1957), 300[3] L. Mandel, E. Wolf: Optical Coherence and Q uantum Optics, Cambridge University Press, 1995[4] M. P. Silverman, 11 Nuovo Cimenlo 97B (1987), 200[5] S. Saito, J. Endo, T. Kodama, A. Tonomura, A. Fukuhara, K. Ohbayashi, Phys. Lett. A 162 (1992), 442 - 448

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IMAGING OF NON-CONDUCTING SPECIMENS BY NONCHARGING SCANNING ELECTRON MICROSCOPY WITH METHOD FOR AUTOMATICALLY ADJUSTED CRITICAL ENERGIES

M. Zadražil, L. Frank, J. NorrisInstitute o f Scientific Instruments AS CR, Královopolská 147, 612 64 Brno, Czech Republic

The total emitted electron current in the SEM is normally lower than the primary beam current so that some negative charge is dissipated into the specimen. In the case of a non-conductive specimen, the charge stays localised at the surface. It creates a unipolar electric field which deflects the primary beam and influences the trajectories of the signal electrons before their detection, and can also cause discharges, etc. Thus, non-conductors cannot be observed at normal energies. Between the critical primary energies at, say, 0.5 to 4 keV, the total electron yield exceeds the unity level and the positive surface charge attracts back a part of slow secondaries so that a balance is established with a potential of a few volts only.

The non-charging microscopy method [2,3] consequentially utilises the critical energies to avoid any charge dissipation. The difficult task to determine a critical energy at absolute minimum surface charge-up (see [4]), is solved by quick acquisition of the signal development in time after a pixel is illuminated for the first time. The method was realised in a cathode lens equipped SEM which enables one to adjust easily the electron landing energy and even to roughly align the SEM at a different energy. The drawback is that the cathode lens extracts the secondaries off the surface so that also the positive charging- up fully develops. The final step in the method development consisted in closing an automated loop formed by the following steps:

I: measurement of the signal vs. time curve in series of pixels not illuminated before;2: smoothing of the curves by using the polynomial rms fitting method;3: curve integration with respect to its asymptotic level;4: stepwise discarding of the curves most differing from the average;5: determination of the average integral as the total charge measure;6: determination of the next suitable value of the cathode lens excitation, i.e. the electron landing energy;7: adjustment of the specimen bias by the electronically controlled HV supply and approximate automatic

prefocusing based on tabulated data (this step is not ready yet, such that partly manual control is necessary).

The loop is preceded by definitions of pixels prescribed for the critical energy measurements and determination of the working distance, it is closed when a total charge rtieasure falls below a pre-selected limit, and finally, a single-shoot picture at the critical energy is taken from the unused part of the view field.

The method was tested on two different ceramics materials. For both of them, signal vs. time curves were taken, and the curve integral was calculated. The sample (a) embodies only one critical energy (see Fig. 1), which means that the sample is compact of materials with close values of critical energies. There was no problem in observing this sample with the SEM’s landing energy set to the calculated value (1.6keV). On the contrary, we found two mutually distant critical energies on the sample(b) (Fig. 1). Under the latter circumstances, the method presented here cannot produce truly noncharged micrographs; a specimen of this kind of heterogeneity consists of domains, parts of which charge-up at any electron energy selected.

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