proceedings 1998 - RECENT TRENDS 2016

Transkript

Recent Trends
in Charged Particle Optics and
Surface Physics Instrumentation
Proceedings
o f the 6lh International Sem inar,
held in Skalsky dvur near Brno, C zech Republic,
from June 29 to July 3, 1998,
organised by
the Institute o f Scientific Instrum ents AS C R and
the C zechoslovak Society for E lectron M icroscopy
Edited by Ilona Miillerová and Luděk Frank
IS B N 80-238-2333-7
P roceedings have been printed from the cam era-ready m anuscripts supplied by the authors
P ublished and distributed by the C zechoslovak Society for E lectron M icroscopy,
prin ted in C zech R epublic by A rtiq B rno
Czechoslovak Society for Electron Microscopy (CSEM), Královopolská 147, 612 64 Brno, Czech Republic;
fax +420 5 41514 402, e-mail [email protected], http: www.isibrno.cz/csem
© C SEM Brno 1998
All 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 sem inar on the Recent Trends in Charged
Particle O ptics and Surface Physics Instrum entation is again here, already the sixth one. The
history o f the m eeting w as described in the preface to the previous sem inar's proceedings. Let
us now sum m arise briefly the m ain points. The germ was the traditional sum mer sem inar held
nearly regularly in the Institute o f Scientific Instrum ents in Brno on the occasion o f visits o f
Professor Tom M ulvey from U niversity o f A ston in Birm ingham , UK. In the seventies and
eighties, this w as valuable enough for us and offered us the opportunity to m ake the sem inar
English spoken. In the sum m er o f 1989 we started to extend the participation, and the 1989
sem inar w as num bered the first. In 1990, there were as many as 30 participants from 5
countries. The third sem inar in 1992 w as m oved to hotel Skalsky dvur in H ighlands and the
next three sem inars organised there, each with around forty participants, had a sim ilar
schedule, at least from the point o f view o f non-scientific aspects o f organisation. The fifth
sem inar w as the first one to w hich the proceedings were published.
It seem s there have been no im portant events since the previous sem inar that are worth
adding to the sem inar history. This may be sim ply the consequence o f that the sem inar has
established a fully defined regularly repeating meeting and nothing is new about it except that
its serial num ber increases by one and the year by tw o and that the registered participation is
so num erous 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 w as claim ed many tim es at various occasions during the sem inars that their
prevailing orientation to charged particle optics w as and rem ains desirable owing to the lack
o f m eetings o f that kind. This argum ent is generally correct but this tim e m uch less than
usually: in 1998 the sem inar coincided with the CPO conference held in Europe, in April in
Delft. W e are really happy that this circumstance has not caused any reduction in the
participation in R ecent Trends. (To be exact, the "collision" appeared already earlier, in 1990,
w hen the C P 0 3 w as held in Toulouse but our second sem inar was then still sm aller and less
am bitious.)
O ur traditional and a bit unusual style o f the meeting, based on a not too large circle o f
personalities, know ing one another quite well, m ore and m ore seem s to be som ething that will
becom e usual in the future. Large congresses, aim ing at gathering hundreds or even thousands
o f anonym ous professional colleagues to one place to present their cofttributions to the crowd,
are m ainly organised because o f tradition. B ut in fact they are also already split into sym posia
o f a m oderate size, attended by groups sim ilar to ours. One surely cannot consider quite
unrealistic a vision that presentation o f scientific contributions w ill be fully replaced by
electronic conferences. B ut this w ill never be (as we hope) the case for personal face to face
m eetings and discussions.
The surface physics has apparently disappeared to a significant extent from our
program o f a m eeting o f people connected in different w ays w ith electron m icroscopy. No
wonder, the new est surface analytical m ethods, 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 m icroscopes that have those capabilities, are the only
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CON 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 environm ental SEM
Autrata R., J. Jirák, M. Michálek, J. Spinka
A m plification o f signal electrons in gas environment
Autrata R., J. Jirák, M. Michálek, J. Špinka
Conditions for specim en observation in environmental SEM
Barth J.E., M.D. Nykerk, M.J. Fransen
A pplication o f a tw o param eter bell distribution in charged particle optics
Delong A., V. Kolařík, D.C. Martin
Low voltage transm ission electron m icroscope LVEM-5
El-Gomati M.M.
Q uantitative surface analysis at high spatial resolution
Gerheim V., H. Rose
Q uadrupole projector system w ith variable m agnification for energy-filtering
transm ission electron m icroscopes
Hartei P., D. Preikszas, R. Spehr, H. Rose
Test o f a beam separator for a corrected PEEM / LEEM
v-
Hasselbach F., H. Kiesel, U. Maier
Recent advances in ion- and electron-biprism interferometry
Hejna J.
O ptim isation o f an im m ersion lens design in the BSE detector for the low voltage SEM
Hutař O.
N oncharging m icroscopy o f sem iconductor structures
Hutař O., R. Autrata
The separation o f secondary electrons in annular and planar detectors
Janzen R., E. Weimer
Study o f detection properties o f a M EDOL / GEM INI objective lens for secondary
electrons
Kahl F., H. Rose
O utline o f an electron m onochrom ator w ith 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. Miillerova
Distributed M onte Carlo: sm art way for com puting complex problems
Tsuno K., N. Handa, S. Matsumo to
An E+B+E beam separator for detecting secondary electrons in low voltage SEM
Tyc T.
A ntibunching o f electrons as a consequence o f the indistinguishableness o f fermions
Zadrazil M., M. El-Gomati
M easurem ents o f the secondary and backscattered electron coefficients in the very low
energy range
Zadrazil M., L. Frank, J. Norris
Im aging o f non-conducting specim ens by noncharging scanning electron microscopy
with m ethod for autom atically adjusted critical energies
D ETECTIO N OF B A C K SCA TTER ED ELECTRO NS IN ENV IRON M ENTA L SEM
R. A utrata, J. Jirák *, M. Klvac, V. Rom anovsky
Institute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno,
Czech Republic
Department o f Electrotechnology, Faculty o f Electrical Engineering and Computer Science,
Technical University Brno, Antonínská 1, CZ-612 64 Brno, Czech Republic
Scanning electron m icroscopy w orking w ith pressure in the specim en chamber that are
higher than 100 Pa enables investigation o f in-situ specimens and certain dynamic effects,
w hich is not possible in convential SEM.
In our case for the detection o f backscattered electrons (BSE) in environm ental
scanning electron m icroscope we use a paired scintillation detector YAG {yttrium aluminium
garnet) doped w ith Ce3+, provided w ith a central hole o f 300 to 500 fim in diam eter. The
detector acts simultaneously as a pressure limiting aperture, w hich allow s to achieving
different pressures in the specim en and differential chamber. The configuration o f the detector
ensures a large collection angle for the BSE signal and allow s the use o f the small working
distance o f the specim en from detector to ensure a sufficient signal even in high pressures in
the specim en cham ber w hen an increase num ber o f collisions o f electrons w ith the gaseous
m edium occurs. Theoretical calculations and
practical m easuring show ed 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 show s a decrease in the detection
efficiency o f the detector in relation to the working
distance. This effect is appreciable above all for
very sm all w orking distances o f the specim en from
the detector. For this reason a double paired
scintillation detector w as designed and constructed.
The principle o f the double paired detector
I
d [mm]
is evident from Figure 2. F or small working
distances d o f the specim en from detector 1 which
are com parable w ith the diam eter o f the hole D¡, the collection angle o f the detector 1
decreases rapidly and a considerable portion o f B SEs escapes through the hole into the
differential cham ber. The detector 2 is positioned here and it ensures the detection o f those
BSEs. The single crystals o f both detection stages are sym m etrically divided into the right and
the left half. The interface betw een them is provided w ith an optical reflecting layer. Then
both the halves are m echanically associated. B oth detection stages thus provide tw o paired
signals w ith the possibility o f further
processing signals.
The properties o f the detectors 1 and 2
w ere investigated by m easuring the signal and
noise levels in relation to the pressure in the
specim en cham ber and the specim en distance
d from detector 1. The signal levels were
m easured in the signal path behind the
photom ultiplier and preamplifier. A s the
m easuring specim en a carbon cylinder w ith a
Obr. 2
central hole coated with an Au - layer was
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IO NISATIO N D ETECTO R FOR THE ENVIRONM ENTAL SEM
R. A utrata, V. Romanovský, J. Jirák , M. Klvač
Institute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno.
Czech Republic
Department 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 cham ber under higher pressures. The group o f
these m icroscopes is usually called ESEM (environm ental scanning electron microscopy).
The value o f the working pressure in the specimen cham ber 609 Pa in 0 °C is tixed as the
limit for the groups o f m icroscopes SEM and ESEM.
The ESEM m icroscopes have wide application in observing biological specimens and
various types o f specim en o f insulation character. The observation biological specimens does
not require any special preparation technology. No charging phenom ena occur due to the
presence o f a gaseous medium. Consequently, the com plicated 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 specim en surface.
N ow adays scintillation detectors are usually used for the ESEM field. However, their
principle does not enable full application o f these m icroscopes for observing biological
specimens, i.e. specim ens containing a larger am ount o f w ater and especially in the lield o f
topography contrast, w hich is im portant, 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
E SEM m icroscopes, containing besides the reached functional configuration also optimisation
o f the working condition o f the
detector. In Figure 1 there is a
I Primary electrons
design o f a com bined detector,
T
w hich we used and w hich makes
use o f the features o f the
scintillation
and
ionisation
scintillation detector
detectors. With this configuration a
large collection angle is reached.
W hen designing the detector we
ionization detector
tried to find prim arily the optimal
w orking distance D and the
specimen
pressure in the specim en cham ber
p as you can see in Figure 2.
tig . 1 Geometrical configuration ot specimen anddeieciw
Keeping these optimal conditions,
it is possible to reach the maxim um possibilities offered by this detector.
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A M PLIFIC A TIO N O F SIG N A L ELECTRONS IN GAS ENVIRONM ENT
R. Autrata.*, J. Jirák, M. M ichálek, J. Špinka
* Institute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno, Czech
Republic
Environm ental scanning electron microscopes (ESEM ) enable the observation of specimens at
higher pressures than in ordinary SEM. The pressure in the specimen cham ber can be beween
10 -5.103 Pa. W orking at higher pressures, it is advantageous to use the ionization o f gas for
detection o f signal electrons. To am plify the signal, ionization detectors take advantage o f
ionization that occurs in the space betw een the specimen and the detector.
PRIMARY BEAM
F ig .l. A schem atic diagram o f the
parallel plate electrode system.
A - contribution o f prim ary electrons,
B - contribution o f secondary electrons
(SE), C - contribution o f backscattered
electrons (BSE) to the total detected
current.
d is the sam ple-to-detector distance, E
is the electric field intensity. Electrons
are
m ultiplied
through
ionizing
collisions in the gas (indicated by x).
d
SPECIMEN
1
The detected current is proportional to the num ber o f electrons em itted from the specimen.
W e assum e that the total detected current can be found by sum m ing the following
contributions:
(1)
w here I “
PE , I “E , I “SE are the contributions o f the prim ary electrons, the SEs, and the BSEs to
the total detected current, respectively.
A cording to [1] the total am plification is given by:
(2 )
where I;p is the part o f the prim ary beam current im pacting the specim en w ithout any
collisions w ith the gas evironm ent, p is the pressure, a and y are the Tow nsend first and
second ionization coefficients, respectively, s ^ and Sbse are the field-independent ionization
efficiencies o f the prim ary electrons and the BSEs, respectively, and 5 and T| are the SE and
BSE coefficients, respectively.
The calculation o f the am plification can only be done for a particular type o f the electrode
system. In the follow ing part, we consider the parallel plate electrode system as shown in
Fig. 1. F or the calculation it is also necessary to know the surface em issive properties and the
ionization properties o f the used gas. Usually, we consider that the environm ent which
surrounds the specim en is air, and that ionization takes place in this gas. H ow ever it is also
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CONDITIONS FO R SPECIM EN OBSERVATION IN ENVIRONM ENTAL SEM
R. Autrata.*, J. Jirák, M. M ichálek, J. Špinka
Institute o f Scientific Instruments ofASCR, Královopolská 147, CZ-612 64 Brno, Czech
Republic
Classical scanning electron m icroscopes (SEM) possess extraordinary properties (resolution,
im age sharpness, possibility o f elem ent analysis o f specimens, etc.) but they have certain
lim itations as regards vacuum that is necessary for their operation.
The exam ined specim ens should be:
- vacuum resistant: On exposing a specimen in vacuum conditions, its properties should not
be affected.
- vacuum inert:
The specim ens may not emit gases or vapours or particles into vacuum.
This could endanger successful operation.
- and electrically conducting.
In practice, not all specim ens m eet these demands. Therefore com plex m ethods, e.g. freezing,
fixation, etc., m ust be used to treat them. Specim ens having the character o f insulators must
be coated w ith m etal mostly.
In the environm ental SEM , where we work with pressures around 1000 Pa in the specimen
cham ber, we can fill the cham ber w ith suitable gases and vapours. From this it follows that it
is possible to exam ine hydrated specimens, to w atch the interaction o f specimens with the
gaseous or liquid atm osphere, and to observe dynamic processes, such as crystal growth,
wetting, corrosion processes, cem enting process. Charging effects are elim inated, owing to the
presence o f ionized particles o f a gas [1],
Conditions for the creation o f an optim um environm ent in the specimen cham ber that is
necessary for a successful observation o f specimens are different for different cases,
depending on the kind o f processes and specimens to be examined. Sometim es, some
"preparation" o f specim ens for ESEM is needed.
Let us focus on the m ost frequent case o f observation o f specimens containing w ater that is
carried out in the presence o f
water
vapour.
For
the
environm ental SEM , the most
suitable-, range of working
pressures and tem peratures
follows from the curves o f
relative humidity [2].
To cool specimens, it is
advantageous to use the Peltier
cell which m akes it possible to
achieve a tem perature diffe
rence as high as 40 K,
compared with the tem perature
o f the warm end. The setting
and control o f tem perature o f
----- ► tem perature ( °C)
the cell by a change in the
flowing current are advan
Fig. 1 Relative hum idity versus pressure and
tageous, and when needed, the
tem perature in the specimen chamber
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A PPLICA TIO N OF A TW O PA RA M ETER BELL DISTRIBUTION IN CHARGED
PA RTICLE OPTICS
J.E. Barth, M .D. N ykerk and M.J. Fransen
Delft University o f Technology, Department o f Applied Physics, Lorentzweg I, 262H ( \J Delft.
The Netherlands
For the sake o f sim plicity, the G aussian distribution exp(-w2x2) is used w henever the actual
distribution has m ore 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. H aving two param eters, a width m easure w and the pow er p, it can better lit a
variety o f real distributions than the Gaussian. For large p it approaches the Gaussian.
A practical m easure for the size o f the image o f a point blurred by chrom atic aberration is the
diam eter o f the circle containing 50% o f the particles,
d c = KcCc(AU/U)a.
W ith AU the full w idth h alf m axim um (FW HM ) o f the energy distribution the value o f K(
depends on the form o f the energy distribution. Kc = 0.34 for the G aussian and K, = 0.62 for
the Lorentzian distribution (bell with p = 1). It was found [1] that if instead o fth e FWHM the
FW 50 (50% o f the particles w ithin 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 FW 50 diam eter o f the source image.
Fransen has measured [2] the brightness o f an ultra sharp tungsten field em itter by analyzing
Frensel fringes occurring at sam ple edges in the point projection microscope. The fringe
intensity profile calculated when a point, Gaussian or Lorentzian distribution is assumed for
the source, w ill be shown.
W hen m aking num erical M onte Carlo simulations o f the Coulom b interaction deterioration o f
beam quality in a charged particle optics colum n it is necessary to make assum ptions as to the
properties o f the source as view ed from the extractor. Inclusion o f m ore 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 chrom atic aberration spot size on the form o f
the energy distribution o f the charged particles. In: Proc. o f the Fifth Int. Conf. on Charged
Particle O ptics, to be published in Nucl. Inst, and M ethods A
[2] M.J. Fransen: Electron em itters 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 o f sample preparation leads to regular lozenge shaped crystals, with a nominal thickness of
10 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 images (Figures 3,4) show the well known, lozenge shaped crystals associated with
the PE single crystal morphology. The regularity in the crystal faceting and presence o f 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.
References
1. Delong A., Low Voltage TEM, Electron M icroscopy 1992, V o l.l, 79-82, 1992.
2. Delong A., Hladil K., K olařík 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)
F ig .l: The Low Voltage TEM
Fig-2: Schematic Device Arrangement
Fig.3: LVTEM Image o f PE Single Crystals
Fig.4: LVTEM Image o f PE Single Crystals
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H igh voltage transm ission electron microscopy (STEM ), has been used in the past as the
prime tool for obtaining dim ensional (i.e. metrology) and crystallographic inform ation at high
spatial resolution. The technique rem ains 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 sam ple preparation. In addition, in the STEM , the whole sample
thickness contributes to the image formation, m aking the results obtained to be less reliable
even with the aid o f deconvolution methods. The use o f STEM s is therefore considered not to
be practical in on-line analysis o f large samples.
M etrology techniques currently available prim arily involve the use o f low voltage electron
m icroscopes (LVSEM ). A lthough there has been a great deal o f instrum ent developm ent in
LVSEM over the last decade, and where currently m ost m icroscope manufacturers offer SKM
operating around the 1 keV and lower, data analysis at these operating voltages is still in its
infancy stages. O ther probe m icroscopies, such as the various forms o f tunnelling m icroscopes
(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 som e activities. These, however, are again limited to electron energies around (he 5
keV region.
The present contribution w ill attem pt to highlight the areas o f developm ents in stirlace
m icroanalysis and high resolution electron microscopy. In particular the session is to address
the recent developm ents dem onstrating the successful use o f the cathode lens in scanning
electron m icroscopes (SLEEM ) [3] and the m easurem ents o f low energy secondary and
backscattered electron coefficients from clean solid surfaces for use in both LVSEM and
SLEEM [4], O f im portance in this respect is the correlation between the atom ic num ber
contrast obtainable in SLEEM and LVSEM as a function o f the incident electron energy.
W ork in com bining A uger analysis w ith low energy im aging as a step in the interpretation o f
the SLEEM contrast w ill be covered [5]. Recent developm ents in parallel data acquisition in
AES w ill also be addressed [6].
»-
References
[1] El Kareh B, 3rd International W orkshop on M easurem ents and C haracterisation-of U ltra-Shallow
D oping Profiles In Sem iconductors. M arch 1993, N . C arolina, U SA.
[2] See for exam ple Q uantitative surface A nalysis 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 G om ati M and A sa a ’d A, M icrochim ica A cta, (1998) In Press.
[5] El G om ati M , M ullerova I and Frank L, Proceeding o f the International C entennial Sym posium on
the Electron, C am bridge, UK, Septem ber (1997), In Press.
[6] Jacka M, K irk M , Prutton M and El G om ati M, 5th International C onference on C harged particle
O ptics, D elft, A pril (1998).
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an d astig m a tic im aging w ith any degree o f astig m atism (length o f th e line im age). A
single q u ad ru p o le trip le t generally form s cith er a first ord er d isto rte d stigm at ic im age or
two line im ages. T hese n o n -ro ta tio n a lly sy m m etric first-o rd er d eviations are co m p en
sa te d by th e second q u ad ru p o le trip le t. Since th e num ber o f th e individual q iiadrnpoles
is larger th a n t h a t required for stig m atic an d d isto rtio n free (first order) im aging, 1Inp a th of rays w ith in th e p ro jecto r system can be varied even if th e m agnification is fixed.
O w ing to th is behaviour, it is possible to a d ju st th e q u ad ru p o le stre n g th s in such a wa\
th a t th e chro m atic a b e rra tio n of m agnification a n d /o r th e th ird order d isto rtio n an
elim in ated or m inim ized, respectively.
For th e recording of th e energy loss sp ectru m , a ch ro m atic ab erra tio n p erp en d icu lar
to th e d irectio n of th e dispersion can be to le ra te d , as it only enlarges th e extension
of th e im age lines. T h e com p o n en t of th e axial chrom atic a b e rra tio n in th e direct,ion
of th e dispersion m ust be elim in ated by ap p ro p ria te ly read ju stin g th e stre n g th of the
hoxapoles w ith in th e energy filter. For recording th e filtered ach ro m atic im age of the
o b ject or th e diffraction plane, respectively, th e qu ad ru p o les are excited in such a wa\
th a t th e th ird -o rd e r d isto rtio n is m inim ized. A ny u n d u ly large rem aining com ponent
o f th e d isto rtio n can be com p en sated subsequently by an a d d itio n a l o ctu p o le field
D espite th e fact th a t th e q u ad ru p o le p ro je c to r system consists of a few m ore elem ents
th a n th a t com posed of ro ta tio n a lly sy m m etric lenses, its im proved perform ance and
v ariab ility outw eigh th is m inor d isad v an tag e by far. In ad d itio n , th e d istan ce between
th e recording plan e an d th e filter can be sho rten ed due to th e stro n g refraction powei
of th e q u ad ru p o le lenses.
References
[1] Rose, II ., C orrection of ab erra tio n s, a prom ising m eans for im proving jjie sp atial
a n d energy reso lu tio n of en erg y -filterin g electron m icroscopes, U ltram icroscopv 5<>
(1994) 11-25.
|2 |
U h lem an n , S. an d Rose, H., T h e M A N D O L IN E filter
a new high p e r f o r m a n c e
im aging filter for su b eV E F T E M , O p tik 9 6 (1994) 1G3 178.
[3] G erheim , V ., B erechnung eines variablen P ro jek tiv sy stem s für ein energiefilterndes
T ransm ission s E lektronenm ikroskop, D iplom T hesis, Fachbereich Physik. Institut
für A ngew andte Physik, Technische U n iv ersität D a rm s ta d t (1993).
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Instrum. 61(1990), 1072.
[19] S. Cova. M. Ghioni, F. Zappa: Optimum amplification of microchannel-plate photomul
tiplier 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 pho
ton timing with microchannel plate photomultipliers, Rev. Sei. Instrum. 64(1993), 118.
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(d) in Figs. 2 and 3 refer to versions (a) +
(d) in this figure._______________________
z, /mm
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Fig. 2. D ependence o f the spherical
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Fig. 3. D ependence o f the chromatic
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ELECTRODE
SPECIMEN
SPECIMEN ELECTRODE
Fig. 1. D esign o f the cathode lens
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Fig. 3. The B SE trajectories . E = 500eV
T ake-off angles 30, 35, 40, 60, 82, 86 degree
Fig. 4. The SE Trajectories. E = 5eV
Take-off angles 0, 40, 50, 60 degree
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References:
[1], Autrata, R.: Scanning M icroscopy, 1989,3, pp.739-763
[2]. Autrata, R., H ejna, J.: Scanning ,1991, 13, pp.275-287
p o le
p ie c e
\
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ITO lay er+ 1 0 k V
s p e c im e n
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g rld |-1 0 0 V )'
GUIDE
GRID {-100V)
GRID HOLDER
SPECIMEN
ITO LAYER
TUBE J_
Fig. 1. T he annular ( le f t ) and planar ( r ig h t) detector for low voltage operation
•is
: U scint;= lukg
5
1«
15
se
,
e
» 2-500V
20
25
I . . . . i . . . . I ..........,
Fig. 2. SE trajectories in annular and planar detector with a negatively biassed grid (-100V).
Fig. 3. Topographic contrast in BSE mode. A nnular detector ( le f t), planar detector (rig h t).
IC surface covered with the passivating S i0 2 A PCV D layer. E0 = 2,2keV.
Fig. 4. V oltage contrast in BSE + SE mode. A nnular detector.
Transistor KFY 18. W ithout passivation.
U BE = + 5V applied. The rest o f the circuit is grounded.
V oltage contrast is visible below IV.
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OUTLINE O F AN ELECTRON MONOCHROM ATOR W ITH SM ALL BOERSCH
EFFECT
F. Kahl and H. Rose
Institute o f Applied Physics, Technical University Darmstadt,
Hochschulstr. 6, D -64289 Darmstadt, Germany.
The attainable inform ation in electron microscopy and holography is ultim ately limited by
the chrom atic 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 vol
tages higher than about 200 kV, the energy width must not exceed 0.2 eV. Unfortunately, the
energy width of field-em ission guns lies in the range between 0.6 eV and 0.8 eV for beam cur
rents required in TEM . As shown by experiments, about 30 % of the electrons have an energy
deviation from the mean value sm aller than 0.1 eV for an em itted beam current of a few //.A.
If the rem aining 70 % o f the electrons could be filtered out by a m onochromator, one would
obtain a nearly m onochrom atic source with sufficient beam current. The acceleration volta
ge at the location o f the m onochrom ator should not exceed 3 - 5 kV to achieve a dispersion
which is sufficiently large for filtering. Hence the m onochrom ator 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 m onochrom ator was first proposed by
Plies [2], Unfortunately, his design consists o f a large num ber of elem ents and requires a large
extension of the height o f the m icroscope. The electrostatic Si-shaped m onochrom ator propo
sed by Rose [3] is significantly shorter. However, a com m on disadvantage o f both designs is
the formation o f several stigm atic interm ediate im ages 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 minim ize the Boersch effect, we recently analyzed the feasibility of i2-Jhaped mo
nochrom ators with astigm atic and virtual stigm atic interm ediate im ages of the source. The
line-shaped astigm atic im ages produce a much low er current density than stigm atic images.
The schem atic construction of this type o f m onochrom ator is sketched in figure 1. To avoid a
loss o f lateral coherence and brightness, the m onochrom ator m ust be free of dispersion at the
exit plane. H ence it is useful to m axim ize the dispersion at the sym metry plane z, and select
the energy there. The line im age in the energy selection plane is perpendicular to the direction
o f the dispersion. The dispersion shifts this im age 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 m isalignm ent of the source,
m ust be kept small in the direction o f the dispersion. To preserve the diam eter o f the source,
the second-order aberrations at the final im age plane z* must also be negligibly small. Owing
to the sym metry of the monochrom ator, 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 -s e c tio n and defocuses it in the yz-section. In order to focus the beam also in this section an
additional quadrupole field m ust be excited within each deflector which overcom pensates the
defocusing refraction of the dipole field in the yz-sectio n 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 o f 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 diffractionlimited situation, where our I (a) form is exact as a consequence o f 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. Optik
101
(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 K hursheed in
1997 in [3] or at C P 0 5 ). The same argum ents hold for the use o f graded meshes: if most users
see that the axial field behaves strangely at the places w here the mesh step change abruptly, the
m ost natural solution is the use o f sm oothly graded meshes. Another fact that nobody uses the
value o f the integral o f m agnetic field along the axis and/or around the lens as a check o f
correctness o f the m agnetic lens com putation is really difficult to understand.
N ext question is that o f com putation accuracy. The accuracy of any ‘m esh’ method
depends on the type o f mesh and the num ber o f mesh points used. 1 will in this respect briefly
mention an im portant but overlooked aspect o f checking the accuracy o f FEM computations, the
extrapolation to ‘infinite num ber o f points’; the first exam ple o f that for m agnetic lenses we
published already in 1994 [4], and I have discussed this in detail at C P 0 5 .
In the practical application o f any program, the aspect o f user friendliness and user
interface becom es im portant. W e have devoted to this aspect a lot o f attention in Brno as well
as in D elft in our softw are packages, that use a unified approach to magnetic and electrostatic
lenses and m ultipoles. The com putation 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 autom atically, and all results are shown or exported
graphically. The program packages thus meet most requirem ents from a user point o f view, in
spite o f leaving som e space for im provem ents, because the interfaces were written in a preW indow s time. The numerically obtained results are accurate enough to allow not only com put
ation o f paraxial properties and aberrations from axial potentials or fields but also ray tracing.
SO FE M by M unro 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 lim ited beams. In spite o f the considerable span of time since the introduction o f SOFEM,
hardly any attention is given to accuracy (an exception being the discussion o f the com putation
accuracy of axial potential in a two-cylinder lens by Munro in [4] and later by me at C P 0 4 where
it could be shown that the FO FEM produces competitive results). Electrostatic lens computations
seem to work, although the mirror results in [1] are surprisingly inaccurate (as discussed in 1996
at this sem inar). In magnetic lens com putations with SO FEM no lifhit o f m axim um number
o f points is ever m entioned (but it is known that it is im possible to calculate on large meshes).
No integral along the axis is computed, so the very basic check, if the result is correct, is missing.
Som e o f the SOFEM results on saturated lenses look strange [7]. W hat is published by Munro
on the com putation o f m ultipole com ponents with SO FEM is even ridiculous, and the same
error since [4] is in [1]. The FO FEM im plem ented by M unro does not w ork properly for the
computation o f hexapole field component in deflectors, in particular with small number o f points
and w ith large m esh step change at the place where the field is still strong and varying (the
com putations in meshes where the problem is stated last less than 1 s on obsolete 486 PC), and
th eir program does not w ork for 5th harm onic com ponent at all. It does not mean that this is a
problem that cannot be handled by FOFEM accurately [8]. As a sum mary I do not see SOFEM
as the ‘com petition’ o f FO FEM , and I would like to see more accuracy tests o f the method.
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program ) for three problem s where analytical solutions are known: spherical analyzer, thin
aperture betw een tw o regions o f constant field, and a two-cylinder lens, where com putation
accuracy was given against computation time. The results in 3D computation were added for the
presentation at C P 0 5 . One test was actually left out, which can be used as an ultimate test o f any
electrostatic program: the dipole mirror o f Preikszas and Rose (see the notes for 1996 seminar).
Conclusions
Even 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
o f the usual ‘hum an’ approach to computers and programs: some people tend to trust any result
produced by a com puter if it keeps them from thinking. Are there any ways how to prevent this?
A nother fact is that in the places where the actual research is done into com putational
m ethods and extrem e applications o f 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 o f services (W indows interfaces, on-line help,
full docum entation, many options im plem ented in a program), but is there som ebody really
w illing to pay for all these features? W hat should be in a good software for electron optics?
Acknowledgment
Supported 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. W isselink, M.
Lene, J. C hm elik (and recently w ith J. Zlám al) 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 m e also mention recent fruitful discussions started
with R. Becker, U. Frankfurt, and G. M artinez, U. Complutense, M adrid.
References
[1] Handbook of Charged Particle Optics, ed. Jon Orloff, CRC Press, 1997.
[2] Proc. o f C P 0 3 published in Nucí. Instr. M eth. A 298(1990), C P 0 4 in NIM A 363(1995).
[3] Proceedings o f SPIE 2014 (1993), 2522 (1995), 2858(1996) and 3^55(1997), respectively.
[4] W orkshop on C om puter 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, U ltram icroscopy 72(1998), 31-39.
[8] M. Lenc and B. Lencová, Rev. Sci. Instrum. 68(1997), 4409-4413.
[9] J. Zlám al, M Sc. Thesis, TU Brno 1996 (see also 1996 seminar).
[10] K. J. Binns, P. J. Lawrenson and C. W. Trow bridge, The analytical and numerical
solution of electric and magnetic fields (J. W iley & Sons, 1992).
111] A. von der W eth, D issertation FB Physik, U. Frankfurt/M ain (1997).
[12] D. Cubric, B. Lencová and F. H. Read, Proc. EM AG97. Inst. Phys. Conf. Ser. 153, 91-94.
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OPTIM AL SY NTHESIS OF CHARGED BEAM FO CU SIN G SYSTEM S
G M artinez(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 contem porary Science is a quick creation o f knowledge that
is frequently associated to the appearance o f new or more refined measurem ents There has
been a continuous im provem ent o f the existent instrum entation and a developm ent o f
sophisticated new devices that has made possible this outstanding progress.
To go on this tendency we need to prepare appropriate tools: m athematical and physical
models to sim ulate the behaviour o f a system and the w ay in w hich this behaviour can be
optimized. In this talk I will present a scheme o f w ork that w e are applying to the optimal
design o f electrostatic lenses. Even if this is a small area in Charged Particle Optics the
schem e could be extended to other beam guide systems
The direct m ethod for finding the optimal design would be to com pute simultaneously the
field and trajectories o f the particles through the quadruplet, but these trial and error tests
demand a huge am ount o f com puting time that is not possible to do in practise To overcom e
this problem w e use tw o 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
approxim ate differential equations are replaced by the linear equations in the space o f the
phase m om ents with the same approxim ation accuracy. Thus w e 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 tw o slits at the appropriate place before entering the lens
allow s to shape optim ally the initial beam and to obtain the minim um spot size aM he target
By this w ay it is possible to find the optimal param eters o f the system with minimum
com puting time
At the second stage w e apply an accurate version o f the boundary elem ent method which
sim ulates the geom etry o f the real system and perform s a very precise calculation o f the field
In fixing the initial conditions for ray tracing, w e use the inform ation provided by the
analytical model Thus, the com bination o f both techniques allows tfle synthesis o f the best
lens in a straightforw ard way.
As a first exam ple let us consider the optim ization o f electrostatic axisym m etric lenses
consisting o f multiple coaxial cylinders [2], A new analytical model o f the axial potential
distribution is applied w hich corresponds to realistic multiple cylinder systems. Using the
version o f BEM described in reference [3] to solve L aplace’s equation we obtain the
param eters o f the physical model that has the sam e axial potential distribution as the
analytical model The param eters o f the physical m odel are lengths and radii o f the cylinders,
the gaps betw een them, and the applied potentials. Figure 1 shows the com puted axial
potential for a 3-cylinder lens and the corresponding analytical function The coincidence
betw een the tw o profiles allows m atching the focal distance and the dem agnification within at
least three digits.
To analyse the beam spot size w e find the matrizant (or transfer matrix function) for the linear
and nonlinear equations o f motion using the effective recursive com putational method
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THE M ICR O A N A LY TIC PROSPECTS OF A HIGH RESOLUTION PEEM
M .M erkel(1), M .Escher(l>, O .Schm idt<2), C h.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 M ercury lamp we perform microspectroscopy
experim ents w ith a photoelectron m icroscope (FOCUS IS-PEEM ) equipped with an electron
energy analyser (FOCUS M ICRO -ESCA ). In this arrangem ent we are able to determine the
chemical com position o f solid surfaces with a high lateral resolution down to appr. 250 nm.
Sample
x/y adjustable
via piezo drives
| Objective
Contrast aperture
size and X/Y
adjustable via
piezo drives
Stigmator/Deflector
Iris Aperture
size adjustable
(mech. feedthr. )
First Projective
Second Projective
Channeltron J | 0
Energy Analyser
Multi Channel Plate
Fluorescent Screen
Im aging Device
H um an Eye, Foto,
Video o r Slow Scan
CCD Camera
Figure 1: FO C U S IS-PEEM equipped w ith the
H-ESCA energy analyser
The experim ental set-up is shown in F ig .l: The PEEM is used to get a lateral image o f the
chosen sam ple region w ith a resolution o f today down to about 20..25nm. To get chemical
inform ation o f a certain feature this region o f interest is centred in respect to the actual field o f
view by m eans o f the piezo driven x-y sam ple stage. N ow the field o f view is to be limited
using the iris aperture located at the first im age plane o f the m icroscope 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 m agnification o f the PEEM . The deflecting potentials o f the
analyser have to be sw itched on and choosing a suitable pass energy the energy spectrum o f
the selected region can be taken. M ore detailed inform ation is given elsewhere [1 j,[2 J .
For dem onstration o f the recent perform ance w e show in Fig.2 an example: This PEliM
m icrograph w as taken with a photon energy o f 95 eV at BESSY I (U ndulator IJ2 com bined to
a m ultilayer optics). The sam ple consists o f 20x20|im Pt-Co-Pt m ultilayer squares deposited
onto a silicon substrate. There are plotted three valence band spectra taken at different p-spot
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A C O H EREN CE FU N C TIO N APPRO ACH T O MULTISLICE THEORY
H. M üller and H. Rose
Institute of Applied Physics, Technical University Darmstadt,
Hochschulstrafie 6, D-64%89 Darmstadt, Germany.
T he sim ulation of high-resolution electron micrographs is a valuable tool for determ ining the
atom ic stru ctu re of objects by m eans of electron microscopical techniques. A lthough a number
of different sim ulation m ethods have been proven useful, a q u antitative correspondence between
HREM sim ulations and experim ental images has not yet been reached.
To take the step from qualitative to q u antitative HREM image sim ulation, a theory of image
form ation which is solely based on th e propagation of the stationary wave function of the
scattered electron proves to be insufficient. To avoid this shortcoming, we have proposed
a theory of im age sim ulation based on the propagation of the stationary m utual coherence
function [1 ]
Tc
(p,p',t) =
{'¡/{p,t)'¡>,(p',t-T))T.
( 1)
Here 1 is the electron wave function and (..
denotes the tim e average over the recording
tim e T of the m icrograph; p, p' are 2-dim ensional coordinate vectors perpendicular to tinoptical axis. T he recorded intensity in the image plane is given by I(p) = Tc(p , p' = p ,r = 0) —
(l'í'íp ,i) | 2)r- T he coherence function approach correctly accounts for the partially coherent
n atu re of the electron optical im aging 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 approxim ately described by the m utual
transm ission function
M (p ,p ',r) = exp (i(p i(p ) - Pi(p')) ~ g ( M p ) + M p ') ) + Pn(p, p \ r )) ■
(2)
T his transm ission function depends only on the first and second stochastical m om enta of the
projected slice potential considered as a tim e-dependent stochastic process. T his approach
considers the fact th a t for weak objects the ideal inelastic image represents the variance of the
projected potential [3]. The term s 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)
- p x(p')))T ■
The second relation ensures th a t our form ulation does not violate tKS optical theorem as it, is
th e case for th e conventional multislice theory which uses an absorption potential to account
for inelastic scattering. The inform ation about th e stochastical measures p i, p-¿, and p.\ \ can be
calculated from sim ple analytical models describing the elem entary quasi-elastic and inelastic
scattering processes w ith a sufficient degree of accuracy. C urrently we employ the Einstein
m odel of lattice dynam ics for therm al diffuse scattering and a modified R am an Com pton ap
proxim ation for inelastic electron scattering resulting in electronic excitations [1 ,2].
To dem onstrate the feasibility of our calculation m ethod we have sim ulated unfiltered diffrac
tion p attern s of Si (110) for different crystal thicknesses. The calculation considers the influence
of elastic, quasi-elastic, and inelastic scattering processes w ithin the object. The results are
com pared w ith experim ental diffraction p attern s of specimens of com parable thickness. The
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VARIA BLE M ODE RETA RD IN G FIELD ELEM ENT FOR LOW ENERGY S E M
I.M iillerová, 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 tow ard low electron energies in a SEM is motivated by reasons connected
solely w ith the specim en itself. A t low energy electron impact, the interaction volum e
dim inishes so that the information is better localized, the total electron yield is generally
higher and the specim en charging-up can be suppressed, and m oreover many new types o f
contrast appear. C ontrary to this, although significant progress has been m ade in designing
low voltage guns and electron optical colum ns, principal needs for keeping the beam energy
at least at few keV throughout the colum n 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. U sing the SEM designs em ploying
variable electron energy along their trajectory betw een the gun final anode and the specimen
can com bine both demands.
O ne im portant possibility is to use an integrated beam accelerator or booster [1,2]
w hich holds the beam, betw een the gun extractor and the objective lens, at an energy higher
than the landing one, w hich is given by the cathode potential with respect to the earthed
specimen. An im m ersion electrostatic lens, com bined with a normal objective lens, closes the
booster. The com bination lowers the aberrations and they even decrease with the increasing
im m ersion ratio or decreasing landing energy. A lternative is to apply a high negative bias to
the specim en and to low er the beam energy im mediately above the specim en surface with the
help o f a cathode lens [3,4]. This com bination is capable o f preserving a nearly constant
im age resolution throughout the energy scale and even comm ercial 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 m aximum reasonable immersion ratio o f
its closing lens - otherw ise it becomes too strong to form the probe [7], For a 4wo-aperture
lens w ith the aperture distance D and "sharp" field transitions in electrodes, we get, from a
sim ple analytical calculation [8], the lower focal point lying at the distance D below the lower
aperture already at an im m ersion ratio o f 7. C om puter 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 pow er 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 m ost o f the advantages m entioned above. N evertheless,
principally new contrasts appear below 50 eV w here the electron reflection yield acquires a
vector character, dependent on the specim en crystallinity, and w ave-optical contrasts become
possible. In addition, the probing depth starts to increase again, weakening the vacuum
dem ands. This range can be reached only with a cathode lens with the full field strength on
the specim en surface and difficulties connected with the specimen biasing.
A booster equipped SEM colum n (Fig. la ) offers a very efficient way o f com bining
both described m ethods. W hen insulating even the low er im m ersion lens electrode from the
colum n body, one can simply switch the retarding field to the cathode lens mode but with the
advantage o f the specim en earthed (Fig. lb ) - in-lens detector is then available only.
Furtherm ore, an insulated specim en holder enables one to use also a highly efficient
(retractable) anode/detector assem bly (Fig. lc).
The variable m ode arrangem ent m akes the full energy scale accessible with the
possibility to adjust the electric field on the specimen.
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SH ORT N O T E ON LO W -EN ERG Y S E M CONFIGURATIONS
I.M üllerová and L. Frank
Institute o f Scientific Instruments A S CR, Královopolská 147, 612 64 Brno, Czech Republic
There are good acknow ledged reasons to low er the landing energy o f primary
electrons incident onto a specim en in the SEM down to hundreds and even tens and units o f
eV. B ut there are equally good reasons to produce the prim ary electron beam at a high energy
o f tens o f keV. To satisfy both, SEM designs are desirable in w hich fast prim ary electrons are
decelerated som ew here in front o f the specimen surface.
M odifications o f this general principle, proved to date, can be divided according to
w here the deceleration field is applied. It can simply be between tw o bored electrodes o f an
electrostatic im m ersion lens fitted into the m agnetic objective lens so that the fields overlap.
A nother alternative is to replace the final electrode w ith the specimen, i.e. to use the cathode
lens. B oth approaches differ m ainly in the electric field intensity on the specimen surface. A
higher field causes a m ore effective collim ating o f the em itted electron tow ard the axis, which
affects the detection conditions. On the other hand, the specim en geometry, tilt and surface
quality becom e m ore critical. Some specimens can be even intolerant to a high electric field.
The m ain difference is that the aberration coefficients keep proportionally decreasing down to
the low est energies for the cathode lens [ 1 ] while for the im m ersion lens, it falls only down to
values sim ilar to its w orking distance [2,3].
B oth versions can be treated in the dependence on the w orking distance w o f the
electrostatic im m ersion lens, so that the cathode lens is for w=0; this is sim ilar to the
system atic approach in [4]. Fig. 1 shows the electric field on the specimen surface, as a
function o f w/D, w here D is both the diam eter and distance o f the electrodes. Obviously, the
surface field can easily range in tens o f per cent o f the m axim um while the aberration
coefficients still rem ain in tenths o f w while for the cathode lens they are roughly equal to D
divided by the im m ersion ratio. This speaks in favor o f the cathode lens w henever it is
applicable.
A further aspect is that for a compound lens com posed o f electrostatic and magnetic
lenses, both aberration contributions are generally comparable. For a cathode lens, the
focusing lens influence dim inishes 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.
Furtherm ore, the effect o f such an adaptation is enhanced due to the favorable property shown
in Fig. 3. If the beam aperture is kept constant at a value aligned for a certain landing energy,
the im age resolution rem ains acceptable and m oderately offset from the ultim ate value
throughout the energy scale.
From the practical point o f view, the landing energy is defined by a (sm all) potential
difference betw een the gun cathode and specim en w hile the (high) colum n energy can be
reached either by biasing both negatively or by biasing positively the w hole microscope
colum n. The second case is discussed elsewhere in this book [5], the first [6] can be even
applied to com m ercial SEMs. In a cathode lens, the full electron em ission is, in the anode
plane, collim ated to w ithin a diam eter 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 ED O L-type in-lens detection [7] w ith electrons passing through the anode opening,
and an anode/detector com bination w ith a very sm all central bore (m ade 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. D oubts have been m any tim es expressed as regards restrictions, put onto the specimen
surface properties when the specim en serves as the cathode in a cathode lens. Particularly, the
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A STUDY OF W AYS OF IM PROVING THE SPEED AND ACCURACY OF
C O M PU TIN G FIELDS, TRAJECTORIES AND ABERRATIONS IN ELECTRON OPTICS
E. Munro, X. Zhu, J. Rouse and H. Liu
Munro s Electron Beam Software Ltd, 14 Cornwall Gardens, London SW7 4AN, England.
Tel. & Fax: (+44) 171 581 4479 e-mail: [email protected]
The m ain objective in the com puter sim ulation o f electron optical systems is usually to predict
as accurately as possible the im age blurring and distortions o f an im aging or probe-form ing
system.
This essentially involves com puting fields, trajectories and aberrations.
The
traditional way o f doing this is to com pute the electrostatic and/or m agnetic 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.
A lthough this traditional m ethod has served electron optical designers well, the design o f
som e o f the latest instrum ents is straining the capabilities o f the standard simulation methods.
Exam ples that are hard to sim ulate by traditional m ethods include LEEM systems, aberration
correctors, electron m irrors, curved axis systems for beam separators, W ien filters, etc. In
LEEM system s, im ages are formed w ith electrons em itted from the sam ple surface with low
energies and large angles. A t such low energies and large angles, conventional aberration
analysis may becom e inadequate, the energy spread can dominate the initial energy, and the
concept o f chrom atic aberration coefficients may become alm ost meaningless. In aberration
correctors, analysis o f high-order and asym m etry aberrations may be needed, and this is very
com plicated using conventional aberration analysis methods. In m irror systems, conventional
aberration form ulations break dow n near the reversal point, and very involved theoretical
treatm ents 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 com plexity and enorm ous scope for mistakes.
To help address such problem s, the aim o f this paper is to investigate methods for improving
the speed and accuracy o f num erical field analysis and direct electron ray-tracing. The aim is
to identify areas w here im provem ents can be made in the sim ulation techniques. In particular,
w e aim to try to com pute 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 sim ulations with
conventional aberration results and try to assess the relative merits o f the various approaches.
The m ost difficult task, by far, in m ost electron optical sim ulations, is accurate field analysis,
since if the fields are know n accurately the trajectories can be computed with negligible
truncation errors, using high-order Runge-K utta or B ulirsch-Stoer methods [1|. For high
accuracy field analysis o f structures with rotational or m ultipolar symmetry, second order
finite elem ent m ethod (SOFEM ) [2] is in principle an attractive candidate. Isoparametric
second order finite elem ents use biquadratic basis functions for both the elem ent geometry
and the potential. The biquadratic elem ent geometry allows the elem ents to be curved, thus
allow ing accurate geom etrical m odelling o f structures w ith 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 num ber o f grid points.
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m uch faster with the interpolation polynom ials. The field com putation and the resulting
direct ray-tracing are both speeded up by at least a factor o f 20, for the sam e accuracy. A
typical trajectory can be com puted 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 m inutes. 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 )r 2 + c 4(z ) r 4 + ... + c 2</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 sm ooth, w ell-behaved functions. A ssum ing the potential obeys L aplace'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:
dÔ/dr2 = 2co
cf<t>/drA = 2Acn
Axial derivatives at r=0:
c^íVdz 2 = -4co
d4<I>/3z4 = 64c4
db<S>ldrb = 12()ch
5 6<t>/3z6 = -2 3 0 4 c (,
etc.
etc.
These functions can all be obtained directly from the radial polynom ial fits. Since the axial
derivatives are exactly the functions needed for com puting aberrations by the ordinary
integral m ethods, these functions can be used to evaluate the aberration integrals directly,
w ithout any need for integrations by parts, which greatly simplifies the formulae and their
program m ing. The aberration coefficients up to fifth order, or possibly even seventh order,
should be able to be com puted accurately in this way. We are in the process o f com paring the
aberration integral results with direct ray-tracing, for ordinary im aging systems, and hope to
present results o f this at the meeting.
Techniques for im proving the speed and accuracy o f the direct ray-tracing itself are also being
investigated.
Instead o f using a standard fourth-order R unge-K utta formula, we are
evaluating a fifth-order Runge-K utta form ula due to Cash and Karp [5], which involves six
field evaluations per step. This form ula is accurate to fifth-order term s in the Taylor series
expansion, but sim ultaneously also allows an estim ation o f truncation error on each step,
using an em bedded fourth-order Runge-Kutta formula. This can be incorporated into an
adaptive step-size control algorithm , that optim izes the step size to produce a fast ray-trace
with the truncation errors contained below a specified threshold. This typically enables < 10
nm cum ulative truncation error over an entire trajectory in < 100 steps.
We are also trying to apply the above techniques to the analysis o f m ultipole and curved axis
system s and hope to also present some initial results for these cases at the meeting.
References:
[1] W.H. Press et al., “N um erical Recipes in C”, 2nd Ed., Cam bridge University Press, 1992,
707-732.
[2] X. Z hu and E. M unro, Journal o f M icroscopy 179 (1995) 170-180.
[3] B. L encova and M. Lenc, Scanning Electron M icroscopy 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, A CM Transactions M athematical Software 16 (1990) 201-222.
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U LTIM ATE RESOLUTION: W HAT ARE THE NEEDS FOR FUTURE M ICROSCOPES?
Harald Rose
Institute 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 b y
far the most difficult problem encountered on the route towards sub-angstrom resolution.
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400
450
500
550
GOO
650
of PMT Photocathodes
700
450
wavelength (nm)
Figure 1 N orm alized cathodolum inescent spectra o f
single crystal scintillators fo r S(T)EM .
Table I
500
550
600
wavelength (nm)
Figure 2
N orm alized spectral response o f the
sensitivity o f the photocathodes used.
Spectral p roperties o f single crystals fo r S(T)E M
spectral characteristic
maximum"
FW H M '
S 20 PM T
S l l PM T
(nm)
(nm)
m atching'"’ (%)
m atching'"“ (% )
Y A G :C e
560
122
73
45
Y A P:C e
366
52
60
58
P47
420
77
85
80
CaF2:Eu
426
30
92
88
single crystal
‘position o f the m axim um o f the m ain em ission band.
" fu ll w idth o f the h alf m axim um o f the m ain em ission band
’“ m atching to the spectral response o f S 20 photocathode
“ "m a tc h in g to the spectral response o f S 11 photocathode
with alkali photocathodes. In the case o f 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 w ith the S 11 photocathode. In addition to the characteristic broad yellow em ission
band w ith a m axim um at 560 nm, the YAG:Ce shows a very weak em ission in the blue, violet
and U V spectrum regions. This weak em ission w hich is more m arked for specimens with a low
activator concentration has a sharp m axim um at 400 nm w hich is superim posed on the broad
em ission band w ith a m axim um in the UV region, i.e. beyond the capabilities of the measuring
device used.
Efficiency
For all applications in S(T)EM , high C L efficiency is required. The relative CL efficiency o f
the investigated single crystals is shown in T able H The values o f this quantity are always related
to the corrected value o f the Y A G .Ce single crystal. The as measured integral (spectrally non
decom posed) efficiency includes the influence o f the PM T photocathode spectral sensitivity. This
quantity is interesting from the view point o f application in scintillation detectors w here the
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Table III
D ecay properties o f single crystals fo r S(T)EM
tim e characteristic
single crystal
Y A G :C e
decay time"
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afterglow ” '
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(ns)
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110
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P47
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"c o rre c te d fo r the tim e response o f the m easuring equipm ent
" 'in te n s ity 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 o f the pulse o f
the excitation electron beam (5 ns) and the fall time o f PMT (2 ns), the short-term decay
com ponent m ust be corrected by subtracting approxim ately 7 ns o f the fall tim e o f the measuring
equipm ent. The short-term com ponent o f the CL decay o f both yttrium alum ínate single crystals
depends only negligibly on the duration o f excitation. On the contrary, the long-term com ponent
o f the C L decay depends strongly on the duration o f excitation, so that for a very short excitation
the afterglow o f 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
T V rate, because the im ages w ith a rich topographic content can be o f higher quality.
CONCLUSION
U nfortunately, all single crystals that have their CL decay tim e 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 m ost efficient o f the four chosen, has only limited applicability because its decay time
constant is 1.2 ps. The greatest advantage o f Y AP:Ce single crystals and P47 is that they are the
fastest (38 ns and 34 ns, respectively). Especially, they have no such a m arked com ponent o f long
persistent lum inescence as the Y AG:Ce single crystals have. The only disadvantage o f YAG:Ce
single crystals is their speed which can be behind the lim it for the'T V rate in som e cases. It is
therefore necessary to search for a way to shorten the decay tim e o f YAGtCe scintillators.
REFERENCES
[1] Schauer, P.; Autrata, R.: Inquiry o f D etector C om ponents for Electron M icroscopy., Fine
Mechanics and Optics, 42 (1997), 340-342.
[2] Robbins, D.J.: On Predicting the M axim um Efficiency o f Phosphor System s Excited by
Ionizing Radiation. J. Electorchem. Soc., 127 (1980), 2694-2702.
[3] Lempicki, A .; W ojtow icz, A.J.; Berman, E .: Fundam ental Limits o f Scintillator Performance.
Nucl. Instrum. Meth. Phys. Res. A, 333 (1993), 304-311.
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N O IX O a H ia 3 NO M I S IX V 3 H X
j o x j i h s a h v h x i s h v H x iM S N iaa s i x v - a i s v r a v A v j o a N i a x n o
SP EC T R O SC O P IC X-PEEM WITH EMPHASIS ON MAGNETIC CONTRAST
G. Schönhense
Institut 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 param eters for the control o f magnetic properties. Vertical
h eterostructures (multilayers) offer a wide range o f technical applications e g. in magnetic
sensor technology (read heads, position sensors) because o f the giant m agnetoresistance
(G M R) effect. H orizontal patterning is crucial for novel devices such as m agnetic tunnel
junctions for spin transistors being the basic units o f future non-volatile magnetic storage
elem ents (M RAM ). Also high-capacity hard discs require the controlled creation o f welldefined m agnetic domains with lateral dimensions down to the 100 nm range.
F o r all these systems there is an increasing demand o f powerful microanalytical tools in the
sub-micron range. F or patterned structures a resolution o f several 10 nm is desirable, for
multilayers it w ould be advantageous to view "buried layers", i. e. to look through a non
magnetic coating. M ost o f the above-mentioned materials are com posed o f several chemical
elem ents or intermetallic compounds. Since the constituents contribute differently to the
magnetic behavior, it is necessary to distinguish the various magnetically active com ponents in
a system. Consequently, an appropriate magnetic imaging technique must com bine magnetic
sensitivity with elem ent specificity.
The pioneering w ork o f Stöhr et al. [1] has dem onstrated 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 chrom atic aberration due to
the energy distribution will be addressed. The base resolution o f our instrument (FOCUS ISPE EM ) 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-ESC A 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 M icro-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
("m agnetisation ripple") being indicative o f its high intrinsic anisotropy and the polycrystalline
9
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T H R E E D IM EN SIO N A L SCANNING ELECTRON M ICROSCOPY
W. Slowko
Institute o f Microsystem Technology, Wroclaw University o f Technology, ul. Janiszewskiego
11, 50-327 Wroclaw, Poland
Introduction
Hum ans 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 m icro-topography is
one o f most essential problems in many fields o f science and technology, as for instance:
m icroelectronics, micromechanics or tribology o f magnetic media. Scanning electron
m icroscopy (SE M ) is a very im portant tool for inspection and measurements o f geometrical
issues o f sem iconductor 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. H owever, 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 crosssections o f the sample. Current investigations on the problem are focused on tw o groups o f
m ethods [ 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
m ethod shows some deficiencies and disadvantages, so three dimensional imaging still is not a
very popular technique.
Stereoscopic methods
The 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 m ethods 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 betw een tw o images registered
from tw o points o f view. The idea can be explained on the example showed in Fig. I, w here
different images can be obtained by shifting the sample or viewpoint. In this case, the elevation
difference H betw een 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 ,
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( 1)
w here S is the shift distance and Wd is the working distance.
Fig. 1. Characteristic dimensions used to estimate
the vertical height o f objects when the tilt or shift
o f 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 tw o images to change the
view directions (as in Fig. 1). This time, the
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probe m icroscopy (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 5 0
A fter proper operations the expression for the d e te c 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
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dz
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for 0 A = 0 and a- c/d
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w here 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.:
dx + Q
(7)
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 /).
F or 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 y z plane. Then, the final expression defining the surface
topography along successive scan lines takes the following shape :
st
z(x ,y t) = a j
dx +
I a + Ib
«J
Ic - I n )
■I c + I J
dy+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 -X q), as it has been shown in Fig. 4.
d ./c f
S'. 'V y=v,t
Figure 3. Quotient of the detector geometry
coefficients against the detector declination
angle ( - 4- O.lrad, -9 - 0.3rad, -0 - lrad).
Fig.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 tw o dimensional representation and can be
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O X T H E T H E O R E T IC A L U N D ER ST A N D IN G O F T H E W IE N F IL T E R IN AN
E L E C T R O N B IP R IS M IN T E R F E R O M E T E R
P eter S onnentag, H arald K iesel, a n d F ranz H asselbach
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 v isibility spectroscopy [1] has been realized suc
cessfully w ith electron waves in ste ad of lig h t waves [2], For th is, an electron b iprism is
used, an d as a c o u n te rp a rt o f th e different p a th len g th s of th e interfering b eam s in light
interferom etry, a W ien filter in its co m p en sated s ta te is em ployed (see Fig. 1). A W ien
filter consists of a crossed electric a n d m ag n etic field, b o th b eing p e rp e n d ic u lar to th e
o ptical axis. It is said to be in its co m p en sated or m atch ed s ta te if th e electric and m a
gnetic force for th e m ain energy com p o n en t of th e electron beam cancel each other. From
th e decrease in fringe c o n tra st w ith increasing e x citatio n of th e W ien filter, th e energy
w id th of th e source can be d eterm in ed , an d even th e form of th e energy d is trib u tio n can
be o b tain e d in case that, it is sy m m etrical to its centre.
If th e in itia l s ta te o f th e electro n is a pure s ta te , i.e. all electrons form identical wave
packets, th en th e actio n of th e W ien filter is to in tro d u ce a lo n g itu d in al sh ift betw een th e
two p a rtia l wave packets com ing from opp o site sides of th e b iprism filam ent. R eduction
of c o n tra st of th e interference fringes can th e n be explained by th e lack of overlap b et
ween th e two packets. T h e lo n g itu d in al shift is caused by th e different group velocities
inside the W ien filter b eing due to a different electric p o ten tial. If, on th e contrary, th e
electron beam is m ade up o f a sta tistic a l ensem ble of electrons being in different energy
eigenstates, th en - a t least for narrow energy d istrib u tio n s - th e loss of contrast, is th e
sam e as for a p u re s ta te w ith th e sam e energy sp read , b u t in th is case it is caused by
th e displacem ent of th e incoh eren tly su perim posed interference p a tte rn s relative to each
o ther. T h is com es from th e fact th a t for electrons w ith an energy differing from th e one
for w hich th e m atch in g co n d itio n is fulfilled th ere is a re su lta n t force an d therefore also
a phase shift. B u t in reality, we have n eith er a p u re sta te of th e electrons n or a m ixed
s ta te w hich is d iag o n al w ith resp ect to th e energy eigenstates, so th a t b o th m echanism s
o f th e red u ctio n of c o n tra st will be involved.
W hereas th e A haronov-B ohm effects yield phase shifts w ith o u t affecting th e centres
of th e wave packets, a n d th e S agnac effect or a hom ogeneous electric or m ag n etic field
in an electron in terfe ro m eter lead to b o th a sh ift of th e fringes and o f th e ir c o n trast,
th e W ien filter in its co m p en sated s ta te p roduces a wave packet shift without a phase
shift so th a t in th e m iddle o f th e fringe p a tte rn th ere is always a m ax im u m
an d this
is also a difference to F ourier spectroscopy w ith light. B ecause of th is special featu re of
th e W ien filter it seem ed w orthw hile to do th e calc u latio n of th e b iprism interferom eter
w ith W ien filter for th e case of a wave packet explicitly. T h is was done by using a form of
th e sem iclassical ap p ro x im atio n of th e F eynm an p a th integral for stro n g ly localized wave,
packets [3].
For monochromatic waves an d consequently also for incoherently su perim posed mo
n o ch ro m atic waves - th e elec tro n -o p tical b iprism can be replaced by two v irtu a l sources
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-[f»]
th e phase difference A tp(k) o f th e two interfering p a rts of an energy com ponent m ay be
ap p ro x im ated by th e first ord er term in th e deviation 8k o f th e wave n u m b er from its
m ain value ka. T h en , th e phase shift caused by th e W ien filter is equivalent to a difference
in th e geom etrical p a th len g th in vacuum , so th a t
is p ro p o rtio n a l to 7Vwp.
F o u rier-tran sfo rm spectroscopy d em an d s a variable p ro p o rtio n a l to
¿¿r-'>k>■ T here
fore, n eith er E nor N - w hich has been used so fa r [2] - is su itab le if th e high precision of
visibility spectroscopy shall be fully exploited. B ecause iVwp c an n o t be m easured directly,
we propose to use j as th e tra n sfo rm a tio n variable, w here s is taken from th e recorded
fringe p a tte rn s.
For th e case o f a wave packet, th e decrease in fringe co n trast w ith increasing ex citatio n
of th e W ien filter can also be in te rp re te d as being due to th e increasing (possibility of get
ting) “w elcher W eg” (w hich -p ath ) in fo rm atio n available from th e difference in arrival tim e
betw een th e tw o packets. A n o th e r way how com plem entarity, in p a rtic u la r w ave-particle
duality, m ay be enforced in “w elcher W eg” ex p erim en ts is en tan g lem en t w ith orthogonal
sta te s e ith er w ith th e enviro n m en t (e.g., m easurem ent device) or w ith an in tern al degree
of freedom (e.g., spin). T h e effect of th e W ien filter can, loosely speaking, as well be seen
as a kind of en tanglem ent: If we w rite th e o rd in ary s ta te space of th e p article as a tensor
p ro d u ct of th e s ta te space of positio n s on th e d etec tio n screen an d of th e s ta te space Z
of positions o rth o g o n al to th a t screen (i.e., along th e o ptical axis 2), th en because o f the
lo ngitudinal d istan ce A z o f th e positions o f th e m ax im a of th e p a rtia l wave packets we
have en tan g lem en t w ith resp ect to th e space Z .
H elpful discussions w ith R ich ard N eutze an d Tom áš Tyc are th an k fu lly acknowledged.
a)
b)
Fig. 1
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VARIABLE AXIS LENS WITH A N EXTREMELY LARGE
SCANNING AREA IN ONE DIRECTION
R. Spehr
Institute of Applied Physics, Technical University Darmstadt, Hochschulstrafie 6, D-6^289 Darm
stadt, Germany
In order to obtain a large writing area on a single line, we have developed an electron lens design
[lj quite different to th a 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 th at 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 th at 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. W hen 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 stigm ator 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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D ISTRIBU TED
PROBLEM
M O NTE
CARLO:
SM ART
W AY
FOR
COM PUTIN G
COM PLEX
R. Stekly, L. Frank and I. M ullerová
Institute o f Scientific Instruments A S CR, Královopolská 147, 612 64 Brno, Czech Republic
The aim o f this w ork w as to create an engine for the distribution o f an com putation
task in the TCT/IP network, to verify its operation and to achieve a low -cost great-volume
com putation pow er for sim ulations o f electron scattering using the M onte Carlo m ethod [1-3].
The available P C 's have a sufficiently high com putation output not only for office
w ork but also for sim pler scientific computations. The com putation output o f the best P C 's is
com parable w ith that o f the cheaper series o f the RISC w orkstation but their purchase cost is
h a lf that or less. M odem offices are being equipped w ith P C 's w ith the operating system
W in95 connected to the LAN network, which is often connected to the Internet.
A t interactive w ork, the processor is operated noncontinously and there are long
inactive periods. Typical exam ples are text and graphic editors, table calculators and Internet
brow sers. On average, for a sufficiently long period, the processor is never used 100%.
Therefore it has been decided to w rite a program that w ill make use o f the tim e-outs for its
own activity, will receive sim ple tasks via the network, make com putation and send back the
results [4], O perating systems w ith pre-em ptive m ultitasking can effectively w ork with
priorities o f processes and they are m ostly equipped with the m echanism that allows the action
o f program s during the inactive period o f the computer. The chosen platform W in95/NT
im plem ents this m echanism relatively well. The only problem is the back com patibility when
the 16-bit program s (D OS, W in3.11) are being started using the com puter em ulator w ith the
given operating system that causes the m echanism to stop because W 95/N T are not capable o f
determ ining the state o f the application w ith no im plem ented m echanism o f com m unication
w ith the given operating system.
The w ritten com putation program has very low demands on the operating memory,
typically 2.7M B com pared w ith the 30MB text editor, is easy to control, provides m axim um
inform ation about its state, and w orks autom atically w ithout any intervention o f the user.
A fter starting, the program becom es connected to the com puter that distributes the task,
receives the data and starts computation. A fter finishing the com puter work, the user m akes
the shutdow n o f the operating system, the program becomes logout from the com putation
process, sends the com puted 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
com puter, w hich is determ ined in advance. This com puter serves for data collection and
recording o f the current state o f computation.
The operation o f the engine w as tested in the internal netw ork o f the Institute o f
Scientific Instrum ents. The test task was a sim ple com putation o f electron scattering in Au
specim en at electron energy o f 1 keV. The entire task is divided into subtasks. The m axim um
num ber o f trajectories is lim ited so that all computers end the w hole task at the sam e time.
The com putation process w as running on the background, the test w as m ade during the
norm al w orking tim e, the users were asked not to change their working habits.
The follow ing form ulas were used for statistically processing the operation:
m ean value
x=
standard deviation
S trajectories
I time
ô = VZ>,
variance
variation factor
n
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AN
E+B+E
BEAM
SEPARATOR
FOR
DETECTING
SECONDARY ELECTRONS IN LOW VOLTAGE SEM
Katsu Tsuno, N obuo H anda and Sunao M atsumoto
JEOL Ltd., 1-2, Musashino 3-chome, Akishima, Tokyo 196-8558, Japan
tsuno(a)jeol.co.jp
1. INTRODUCTION
A m ong various proposals o f the objective lens for high resolution low voltage scanning
electron m icroscope (LVSEM ), an im mersion m agnetic lens called Snorkel lens [1,2] and a
com bined electric and m agnetic field lens[3] are now w idely used. We classified various
objective lenses for LVSEM and compared their electron optical perform ances [4—6]. For
designing the optical system o f SEM , not only spherical and chrom atic aberration coefficients
o f the objective lens for the incident beam but also efficiency o f collecting secondary
electrons are important. In the strong m agnetic field region ju st 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 com e up inside the bore, secondary electrons spread out
and hit the wall o f the lens, because there are no m agnetic field. It is useful to apply a
m agnetic field along the optical axis to bring up those electrons to the top o f the objective lens.
A w eak electro-static field is effective to pull up the electrons em itted with high angles.
In this investigation, w e further show electron
trajectories from the top o f the objective lens to the
detector. We use an usual Everhart-Thom ley detector,
w hich is inserted from the side o f the optical column.
High voltage 10 kV is applied to the detector. In the in
lens SEM w ith accelerating voltage o f 2 0 -5 0 kV, high
voltage applied to the detector captures the secondary
electrons w ithout influencing the prim ary beam.
However, in LVSEM, the detector must be set far
behind the optical axis o f the prim ary beam. In such the
case, it is necessary to introduce a beam separator to
deflect secondary electrons tow ards the direction o f the
detector. S ato[l] used the Wien filter as the beam
separator. In this investigation, w e propose a new beam
separator, w hich is sim ilar 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.
A s shown in Fig. 1, the new beam separator
consists o f the first electrodes, the m agnet and
the second electrodes. The length o f the magnet
is equal to the sum o f the length o f tw o
electrodes. The electro-static and magnetic
fields are calculated using E 0 3 D and M 0 3 D
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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A N TIB U N C H IN G OF ELEC TR O N S AS A CO N SEQ U EN CE OF THE
IN D ISTIN G U ISH A BLEN ESS OF FERM IONS
Tomáš Tyc
Dept, o f Theor. Physics and Astrophysics
K otlářská 2, 611 37 Brno
Czech Republic
T he principal indistinguishableness of identical particles has a fundam en
tal significance in quantum mechanics. One of its m ost im portant conse
quences for fermions is the Pauli principle. A nother consequence of the
qu an tu m indistinguishableness is th e difference of the statistics of arrival
tim es of coherent particles em itted from a therm al source to a detector, with
respect to th e statistics of classical particles. This phenom enon is called
bunching in th e case of bosons due to the fact th a t bosons come m ore likely
in groups of two, th ree etc. ( “bunches” ) than alone. In th e case of fermions
we deal w ith antibunching because the fermions avoid each other, i.e., do not
come to a detecto r even in pairs.
B unching of bosons was predicted theoretically [1] and proved experi
m entally [2] with photons already over 40 years ago. T he theory describing
this phenom enon is richly developed (e.g. [3]). On the contrary, the theory
of antibunching (e.g. [4, 5]) is quite incom plete and there are still many
problem s to be solved. M oreover, the antibunching of fermions has not been
experim entally proved until now.
In th e 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. H anbury Brown, R. Q. Twiss, Proc. Roy. Sac. London 242 (1957),
300
[3] L. M andel, E. Wolf: O ptical Coherence and Q uantum O ptics, Cam bridge
University Press, 1995
[4] M. P. Silverm an, 11 Nuovo C im enlo 9 7 B (1987), 200
[5] S. Saito, J. Endo, T. K odam a, A. Tonom ura, 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. Norris
Institute 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 chargingup fully develops. The final step in the method development consisted in closing an automated loop
formed by the following steps:
I:
2:
3:
4:
5:
6:
7:
measurement of the signal vs. time curve in series of pixels not illuminated before;
smoothing of the curves by using the polynomial rms fitting method;
curve integration with respect to its asymptotic level;
stepwise discarding of the curves most differing from the average;
determination of the average integral as the total charge measure;
determination of the next suitable value of the cathode lens excitation, i.e. the electron landing energy;
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 o f 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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proceedings 1998 - RECENT TRENDS 2016

Transkript

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