Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images
A new method of experimental determination of the amplitude contrast value of electron-microscopic images for amorphous materials is suggested. The mathematical relations for calculating the contributions of different mechanisms of electron scattering by the object under study to the contrast on the...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
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irk-123456789-879802015-11-06T03:02:02Z Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images Bobyk, M.Yu. Ivanitsky, V.P. Ryaboshchuk, M.M. Svatyuk, O.Ya. A new method of experimental determination of the amplitude contrast value of electron-microscopic images for amorphous materials is suggested. The mathematical relations for calculating the contributions of different mechanisms of electron scattering by the object under study to the contrast on the basis of the relevant electron-diffraction patterns are obtained. The shares of contribution of elastically coherently, elastically incoherently, and inelastically scattered electrons to the contrast are determined experimentally for the amorphous As40Se60 films. Запропоновано новий метод експериментального визначення амплітуди контрастного значення електронно-мікроскопічних зображень для аморфних матеріалів. Були одержані математичні співвідношення для розрахунку внесків різних механізмів розсіювання електронів на досліджуваному об’єкті в контраст на основі відповідних електронограм. Для аморфних плівок As40Se60 були знайдені експериментально частки внесків пружньо когерентно, пружньо некогерентно та непружньо розсіяних електронів у контраст. Предложен новый метод экспериментального определения амплитуды контрастного значения электронно-микроскопических изображений для аморфных материалов. Были получены математические соотношения для расчёта вкладов различных механизмов рассеяния электронов на изучаемом объекте в контраст на основе соответствующих электронограмм. Для аморфных плёнок As40Se60 были найдены экспериментально доли вкладов упруго когерентно, упруго некогерентно и неупруго рассеянных электронов в контраст. 2015 Article Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images / M.Yu. Bobyk, V.P. Ivanitsky, M.M. Ryaboshchuk, O.Ya. Svatyuk // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2015. — Т. 13, № 1. — С. 85–97. — Бібліогр.: 13 назв. — англ. 1816-5230 PACS numbers: 07.78.+s, 61.05.J-, 61.05.jd, 61.43.Dq, 68.37.Lp, 68.55.jd, 87.64.Ee http://dspace.nbuv.gov.ua/handle/123456789/87980 en Наносистеми, наноматеріали, нанотехнології Інститут металофізики ім. Г.В. Курдюмова НАН України |
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A new method of experimental determination of the amplitude contrast value of electron-microscopic images for amorphous materials is suggested. The mathematical relations for calculating the contributions of different mechanisms of electron scattering by the object under study to the contrast on the basis of the relevant electron-diffraction patterns are obtained. The shares of contribution of elastically coherently, elastically incoherently, and inelastically scattered electrons to the contrast are determined experimentally for the amorphous As40Se60 films. |
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Article |
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Bobyk, M.Yu. Ivanitsky, V.P. Ryaboshchuk, M.M. Svatyuk, O.Ya. |
spellingShingle |
Bobyk, M.Yu. Ivanitsky, V.P. Ryaboshchuk, M.M. Svatyuk, O.Ya. Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images Наносистеми, наноматеріали, нанотехнології |
author_facet |
Bobyk, M.Yu. Ivanitsky, V.P. Ryaboshchuk, M.M. Svatyuk, O.Ya. |
author_sort |
Bobyk, M.Yu. |
title |
Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images |
title_short |
Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images |
title_full |
Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images |
title_fullStr |
Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images |
title_full_unstemmed |
Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images |
title_sort |
different electron-scattering mechanisms’ contribution to the formation of the amplitude contrast of electron-microscopic images |
publisher |
Інститут металофізики ім. Г.В. Курдюмова НАН України |
publishDate |
2015 |
url |
http://dspace.nbuv.gov.ua/handle/123456789/87980 |
citation_txt |
Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images / M.Yu. Bobyk, V.P. Ivanitsky, M.M. Ryaboshchuk, O.Ya. Svatyuk // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2015. — Т. 13, № 1. — С. 85–97. — Бібліогр.: 13 назв. — англ. |
series |
Наносистеми, наноматеріали, нанотехнології |
work_keys_str_mv |
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first_indexed |
2025-07-06T15:39:30Z |
last_indexed |
2025-07-06T15:39:30Z |
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fulltext |
85
PACS numbers: 07.78.+s, 61.05.J-, 61.05.jd, 61.43.Dq, 68.37.Lp, 68.55.jd, 87.64.Ee
Different Electron-Scattering Mechanisms’ Contribution
to the Formation of the Amplitude Contrast of Electron-
Microscopic Images
M. Yu. Bobyk, V. P. Ivanitsky, M. M. Ryaboshchuk, and O. Ya. Svatyuk
National University of Uzhhorod,
Narodna Place, 3,
88000 Uzhhorod, Ukraine
A new method of experimental determination of the amplitude contrast value
of electron-microscopic images for amorphous materials is suggested. The
mathematical relations for calculating the contributions of different mecha-
nisms of electron scattering by the object under study to the contrast on the
basis of the relevant electron-diffraction patterns are obtained. The shares of
contribution of elastically coherently, elastically incoherently, and inelas-
tically scattered electrons to the contrast are determined experimentally for
the amorphous As40Se60 films.
Запропоновано новий метод експериментального визначення амплітуди
контрастного значення електронно-мікроскопічних зображень для амор-
фних матеріалів. Були одержані математичні співвідношення для розра-
хунку внесків різних механізмів розсіювання електронів на досліджува-
ному об’єкті в контраст на основі відповідних електронограм. Для аморф-
них плівок As40Se60 були знайдені експериментально частки внесків пру-
жньо когерентно, пружньо некогерентно та непружньо розсіяних елект-
ронів у контраст.
Предложен новый метод экспериментального определения амплитуды
контрастного значения электронно-микроскопических изображений для
аморфных материалов. Были получены математические соотношения для
расчёта вкладов различных механизмов рассеяния электронов на изучае-
мом объекте в контраст на основе соответствующих электронограмм. Для
аморфных плёнок As40Se60 были найдены экспериментально доли вкладов
упруго когерентно, упруго некогерентно и неупруго рассеянных электро-
нов в контраст.
Key words: electron microscopy, electron diffraction, amplitude contrast,
amorphous material, morphology of films, microstructure.
Наносистеми, наноматеріали, нанотехнології
Nanosystems, Nanomaterials, Nanotechnologies
2015, т. 13, № 1, сс. 85–97
2015 ІÌÔ (Іíñòèòóò ìåòàëîôіçèêè
іì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàїíи)
Надруковано в Óкраїні.
Ôотокопіювання дозволено
тільки відповідно до ліöензії
86 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK
(Received 27 February, 2015)
1. INTRODUCTION
The bright field-imaging mode is the most common mode of operation
in the transmission electron microscopy. The results of such electron
microscopy (EM) experiments are fixed in a form of the two principal
complementary sources of information: the electron diffraction pat-
terns (i.e. electronograms, diffractograms, microelectronograms,
nanoelectronograms) and the EM images of different areas of the ob-
ject under study.
In most cases, the subject of analysis of the EM images of crystalline
materials is the diffraction contrast elements. They arise due to the
coherently scattered electrons that interfere making the correspond-
ing diffraction pattern. Therefore, when studying the crystal micro-
structure, the analysis of the relevant EM images and that of the elec-
tronograms are closely related [1].
The microstructure and the nanostructure of the amorphous speci-
mens are studied in accordance with their EM images only. In this case,
it is assumed that in such images the amplitude contrast is mainly
formed [2]. It is assumed here, as a rule, that inhomogeneities of the
EM images are determined mainly by the difference in the thicknesses
or masses of the local areas of the specimen under study [3]. In the ex-
perimental studies, such contrasts in the EM images are called the
‘mass–thickness’ contrast and describe them mainly qualitatively, i.e.
determine the image homogeneity or heterogeneity, provide qualita-
tive and several quantitative geometric parameters of heterogeneities.
Such a theoretical approach to the analysis of the amplitude contrast of
amorphous materials is very limited and does not take into account a
number of factors that affect essentially the processes of the EM image
formation. The principal of the above factors is the character of the
spatial distribution of all the waves scattered by the specimen under
study.
In general, for each chemically and structurally homogeneous local
area of the amorphous specimen, the electron wave (or the electron
flux) intensity that forms the EM image of this area could be set by a
simple relation [3]:
II0exp(–Qd), (1)
where Q is the parameter that characterizes the ability of this area to
scatter electrons outside the aperture diaphragm. Therefore, finding
the relationship between the electron beam intensity at a certain EM
image point with integral scattering property Q of the relevant local
ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 87
area of homogeneous specimen and the geometric thickness d of this
area makes a ground of the amplitude contrast analysis. If one reduces
the intensity I in (1) to a single atom and to the unit intensity of the
incident beam I0, then the presence of variation of the scattering prop-
erty of atoms for various areas of the object under study and their
thicknesses will be definitive for production of the EM contrast. Scat-
tering property variations could arise due to the differences in the
structure of these areas, i.e. different atomic density, chemical compo-
sition, structure of the short-range and medium-range order, nanopo-
rosity, etc. Therefore, it is advisable to have the experimental methods
of determining contribution of the differences of each of above param-
eters of the amorphous material structure into the amplitude contrast.
In this paper, we suggest one of the possible approaches to the solution
of such problem of the applied electron microscopy. It is based on the
fact that, for each amorphous material, the contrast observed in EM is
formed by electrons scattered by the atoms of the specimen under
study according to the three physical mechanisms, i.e. the elastic co-
herent, the elastic incoherent and the inelastic ones.
2. EXPERIMENTAL TECHNIQUE
Thin amorphous films were obtained by a method of discrete thermal
evaporation of the As40Se60 glass with vapour condensation onto the
substrate made of the NaCl single crystal. The substrates were not
heated and were kept at the room temperature. Condensation rate was
of 5–7 nm/s. Condensed film thickness was of 50–60 nm. The speci-
mens for the EM studies were prepared according to the standard tech-
nique of substrate dilution in the distilled water with film material
trapping by the golden grids. As for the use of the copper grids, this
resulted in the uncontrolled fast changes of the film atomic structure
during the EM experiments not allowing their reliable diffractograms
to be obtained.
The EM studies of the amorphous As40Se60 films were carried out us-
ing the transmission electron microscope JEM-2010 at the 100 kV ac-
celerating voltage. The images and electronograms were detected by
the Catan Ultrascan 4000SP CCD camera and processed by the comput-
er software.
The EM studies included several stages.
1. The general electronogram of the amorphous film was detected in
the diffraction mode at one picture. Then, the aperture diaphragm was
introduced ‘cutting out’ the central beam together with the adjacent
area of scattered electrons and the second picture was taken fixing the
diaphragm location against the electronogram background. Comparing
these two pictures enabled us to determine the scattering angle value a
that corresponds to the edges of the aperture diaphragm.
88 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK
2. The microstructure and the nanostructure of the specimens were
studied in the common light field mode. Such studies allowed the local
areas to be found in the amorphous film differing by their microstruc-
ture.
3. The microstructurally homogeneous areas of the specimen were
selected by the microdiffraction diaphragm and their microdiffraction
patterns were detected. Microdiffractograms of 5–7 different areas
were fixed in the same experiment for the same specimen. The data ob-
tained were compared with each other and then the average micro-
diffractogram of the areas under study was calculated using the com-
puter program. Further computer processing of this microdiffracto-
gram allowed it to be presented in a form of the intensity of electrons
scattered by the local area as a function of scattering angle, I(). The
function I() was determined reliably in the relative units within the
range of scattering angle variation from 2 mrad to 30 mrad with the
0.3 mrad discretization step. The scattering angle () axis scale was
determined with the help of the ‘embedded’ thin golden films.
The normalizing factor is a significant parameter of electrono-
gram and microdiffractogram processing at the EM studies. Having
found its value, one could easily transit from the relative to the abso-
lute units of electron scattering intensity. This allows the correct and
reliable comparison of diffractograms of the amorphous films of dif-
ferent chemical compositions to be done as well as the reliable calcula-
tions of electron fluxes forming the EM images of the objects under
study to be carried out on their basis. We have determined the normal-
izing factor and divided the total intensity I() into the elastic compo-
nent and the incoherent background using the method described in [4].
The initial tabulated values of atomic scattering amplitudes F() were
taken for calculations from tables quoted in [5].
3. CONTRIBUTION OF DIFFERENT SCATTERING TYPES INTO
THE CONTRAST
It has been shown [6] that the contrast between the EM images of the
two local areas of the object under study could be conveniently found
as
K(12)/112/1/1, (2)
where 1 and 2 are the integral fluxes of the electron waves scattered
by the two local areas outside the aperture diaphragm (it is assumed
here that 12).
In order to find experimentally the flux , one has to integrate the
intensity І() (see Fig. 1) over the entire space beyond the aperture dia-
phragm used to obtain the EM image patterns. An arrow in Figure 1
ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 89
indicates the scattering angle value that corresponds to the aperture
diaphragm boundary. Accordingly, integration should be carried out
within the scattering angle range amax, where max is the bounda-
ry scattering angle value up to which the intensity І() was measured.
In these conditions, one may write for each local area:
max
2 ( )sin
a
I d
. (3)
According to Figure 1, the integral intensity I() for each local area
could be resolved into components, i.e. into the elastic coherent Ik(),
the elastic incoherent Ie() and the inelastic In() ones. Then, relation
(3) takes a form:
max max max
2 ( ) sin 2 ( ) sin 2 ( ) sin
,
a a a
k e n
k e n
I d I d I d
(4)
where k, e, n are the electron fluxes of the relevant electron waves
scattered beyond the aperture diaphragm. Obviously, it is expedient to
determine quantitatively the amplitude contrast from (2) by analysing
each of the above-mentioned fluxes separately.
To solve the problem of the quantitative analysis of the amplitude
EM contrast on the basis of expressions (1)–(4), one has to use approx-
Fig. 1. Microdiffractogram of the 60 nm thick amorphous As40Se60 film (curve
1) with selected different scattering components: the elastic coherent (2), the
elastic incoherent (3) and the inelastic (4) ones. The intensities are reduced to
a single scattering atom.
90 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK
imations adequate to the real conditions.
The idea of one of approximations is that the EM image is considered
a result of ‘imposition’ of intensities of the electron scattering by a
great number of atoms. Therefore, formation of such image could be
mathematically set in a form of summating all the electron waves scat-
tered by separate atoms according to the laws specific both for the co-
herent and incoherent electron waves. The procedure of summation
could be substantially simplified by introducing the electron scatter-
ing parameters averaged over a certain macrovolume of the specimen
into consideration. Obviously, this approximation confidence will be
determined by the rules of averaging.
Let us analyse the contribution of different types of electron scatter-
ing by the object under study to the EM contrast.
4. ELASTIC INCOHERENT SCATTERING
Consider the first component of the electron flux e that is due to the
processes of incoherent scattering of the probing beam electrons by the
atoms of the specimen under study. The intensity of this component is
equal to the sum of effects of independent scattering by separate atoms
from the selected local area. The spatial distribution of the intensity of
the electron beam scattering by a single i-th atom is defined by its
atomic factor
2
( )
i
F , where ( )
i
F is the amplitude of electron scatter-
ing by the above atom. Therefore, the intensity Ie() of elastic incoher-
ent scattering by a certain local area of the specimen of the complex
chemical composition could be determined via the atomic factor F
2()
averaged over this area volume:
Ie()NF2() 2 2
1 1
( ) ( )
N m
i j j
i j
F N c F
, (5)
where N is the number of atoms included into the local area, m is the
number of different chemical elements in the local area, сj are the rela-
tive shares of different chemical elements of the local area. Thus, vari-
ations of intensity of the elastic incoherent electron scattering by dif-
ferent local areas will be determined by the changes in the number of
atoms N and relative concentrations сj of different chemical elements
in these local areas. The flux e due to the above processes could be
consequently calculated from (4) as:
max
2
2 ( )sin
a
e
N F d
. (6)
Let us analyse the process of formation of the flux e in more detail.
To do this, we will introduce the following approximation: the whole
volume of the specimen local area will be considered uniformly filled
ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 91
with the atoms having the average atomic density 0. For the substanc-
es with a complex chemical composition, this density is a sum of the
partial atomic densities of different chemical elements 0і, i.e.
0 0
1
m
i
i
, (7)
where 0ісі0. In these conditions, 0іSldx atoms of the і-th chemical
element will take part in the electron scattering inside the local area
volume with the thickness dx, where Sl is the cross section of the local
area of the object under study. In such a case, dnі electrons will be elas-
tically scattered by the atoms of a certain i-th chemical element beyond
the aperture diaphragm at the electron beam transmission through
this specimen area. This quantity ratio to the total number of not yet
scattered electrons n will be as follows:
0
0
ei i li
ei i
l
Sdxdn
dx
n S
, (8)
where ei
is the cross section of the elastic electron scattering by the
atoms of a certain i-th chemical element beyond the aperture dia-
phragm.
The further theoretical consideration of the electron scattering pro-
cesses in the objects with a complex chemical composition should be
carried out having introduced the elastic scattering cross section per a
single atom averaged over all the chemical elements in the local area e
.
In our opinion, such procedure could be correctly realized by applying
the physical essence of the elastic incoherent scattering process, i.e. the
total electron scattering intensity is equal to the sum of independent
electron scatterings by atoms of different chemical elements. Then,
taking into account (8), we have:
0
1 1
m m
i
ei i
i i
dndn
dx
n n
. (9)
Taking into account relation (7), the derived expression could be
written as follows:
0 0
1 1
m m
ei i i ei
i i
dn
c dx c dx
n
. (10)
It follows from the last equation that it is expedient to define the
elastic scattering cross section per a single atom averaged over all the
chemical elements of the specimen e
as:
1
m
e i ei
i
c
. (11)
Solving a simple differential equation (10) with the assumed defini-
92 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK
tion (11) gives the dependence of the number of electrons not scattered
beyond the aperture diaphragm on the thickness of the local area х
passed by them:
0 0
exp
e
n n x , (12)
where n0 is the number of probing beam electrons falling onto the se-
lected area.
Thus, the electron beam flux retarded by the aperture diaphragm
and not involved in the formation of the EM image of the local speci-
men area due to elastic incoherent scattering will be determined by the
quantity n0 n at the exit from this local area. Therefore, one may
write down that this flux is equal to
0 0
1 exp( )
e e
d , (13)
where 0 is the value of the probing beam electron flux at the object.
Comparison of this relation with equation (1) shows that the scatter-
ing property of the object area Q due to the elastic incoherent scatter-
ing is determined by the product of the three main parameters: the av-
eraged cross section of elastic electron scattering by the local area at-
oms beyond the aperture diaphragm e
, the average atomic density of
the specimen local area 0 and the geometric thickness of this area d. In
the applied electron microscopy of amorphous substances with complex
chemical composition, any of the above parameters may vary when go-
ing from one local area to another, giving, thus, its own contribution
to the EM image contrast. In this case, the e
variation occurs due to
that of the local area chemical composition, 0 variation takes place due
both to that of the chemical composition and to the presence of differ-
ent continual heterogeneities in the local areas in a form of nanopores,
while d variation is due to the specific features of the specimen surface
topology.
5. ELASTIC COHERENT SCATTERING
The elastic coherent scattering Ik is a second by its role in forming the
amplitude contract of the EM images of the amorphous substances. It
reflects the diffraction effects related to the interaction and interfer-
ence of electron waves scattered by different atoms. The value and the
spatial distribution of the elastic coherent scattering are determined
by the parameters of the short-range and medium-range orders of dis-
ordered atomic network. Therefore, the contribution of the coherent
scattering to the EM image formation is sometimes called the ‘struc-
tural’ contrast.
The structural factor S() of the intensity distribution of the coher-
ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 93
ent elastic scattering by the amorphous object beyond the aperture di-
aphragm is a basic characteristic that defines its character [7]. There-
fore, one may state with quite high accuracy that the amplitude con-
trast of the EM images due to the elastic coherent electron scattering
will be expressly determined by the S() function differences beyond
the aperture diaphragm for different local specimen areas. According-
ly, the variations of the short-range and medium-range order parame-
ters of the amorphous substance atomic network at the transitions
from one local area to other ones will be responsible for its appearance.
Within the framework of the approximations assumed above, the
distribution of the intensity Ik of the elastic coherent electron scatter-
ing by the amorphous substance with complex chemical composition
could be set as follows [8]:
Ik()NF2()[S()1]. (14)
As shown above, the function S() is easily determined experimen-
tally by detecting electronograms from the object areas under study.
From the viewpoint of contrast formation, we are interested in the dif-
ference in electron scattering by different local areas of the same spec-
imen. The minimal dimensions of such local areas in modern nano-
materials and nanosystems are of the units of nanometres. Therefore,
to use relation (14), one has to apply the electronographic methods that
allow separate diffractograms to be obtained from the specimen areas
with nanometric size. The electron diffraction method with strong
electron beam focusing [9, 10] complies with these requirements. It
allows the atomic structure of the nanoareas with size more than 5 nm
to be studied. Such specimen areas could be exactly distinguished in
the EM image.
Having the nanoelectronograms from different local nanoareas of
the object obtained in the strong focusing mode according to the tech-
nique suggested above, one might calculate their structural factors
S() and, accordingly, obtain the spatial distributions of the coherent
elastic electron scattering from these local areas from relation (14). As
a result, now, it is possible to calculate the contribution of the differ-
ences in atomic structure of amorphous specimens into the EM image
contrast in a form of a relevant flux k:
max
2
2 ( ) ( ) 1 sin
k
a
N F S d
. (15)
It should be noted here that the function S() must be exactly deter-
mined from the nanoelectronogram in the large-angle electron scatter-
ing region. In this region, the nanoelectronograms have low intensity,
and this may affect considerably the result of the contrast analysis.
94 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK
6. INCOHERENT SCATTERING
When analysing the EM image contrast one has also to take into ac-
count the electron energy losses in the specimen, i.e. to take into ac-
count the inelastic scattering as well. By its nature, it is incoherent
and depends on the number of atoms in the area under study.
Theoretical principles of the influence of inelastic electron scatter-
ing on the EM image contrast formation are much more complicated as
compared to those on case of elastic scattering. This is due to a number
of reasons [11].
1. Such scattering is very sensitive to the change in the state of the
atomic electron orbits and electron density at large distances from
atomic nuclei. Therefore, the scattering characteristics determined for
certain atoms strongly differ from those for the case of the inelastic
atom scattering in the condensed matter.
2. Unlike the elastic scattering, inelastic electron scattering differs
drastically from the inelastic X-ray Compton scattering.
3. A share of inelastic scattering is especially large in the low s re-
gion, where its intensity In may exceed that of the elastic scattering by
several orders of magnitude. Only this region corresponds to the aper-
ture diaphragm transmission and plays an important role in the ampli-
tude EM contrast formation.
Simultaneous and complex action of the above factors stipulates
traditionally preferable use of experimental methods of determining
the spatial intensity distribution In() in order to consider inelastic
scattering in the applied electron microscopy and electronography
[12]. Knowing this distribution found using the above-mentioned
technique, one may calculate the electron flux that is responsible for
the formation of the inelastic scattering contribution into the con-
trast:
max
2 ( )sin
a
n n
N I d
. (16)
Note that, in the applied electron microscopy, the In() component of
intensity includes also the ‘parasite’ background electron scattering by
the residual gas molecules in the microscope column, at the diaphragm
edges, etc.
7. RESULTS AND THEIR ANALYSIS
Figure 1 presents the distributions of the integral electron scattering
intensity I (curve 1) and its components as the functions of the scatter-
ing angle for the amorphous As40Se60 film. The above intensities corre-
spond to the scattering by a single ‘averaged’ atom of the specimen.
ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 95
The scattering angle value 3.8 mrad corresponds to the location of
the aperture diaphragm edges when obtaining the EM pictures in our
experiments. Based on these experimental data and using relations (6),
(15) and (16), we have determined the relative fluxes e1, k1, n1 of
electrons scattered beyond the aperture diaphragm according to dif-
ferent mechanisms per a single averaged atom of the specimen under
study: e1 6.610
6, k15.110
6, n1 9.110
6. These quantitative
data indicate that, in the 50–60 nm amorphous thick As50Se50 films,
almost a half of the scattered electrons appear to be scattered beyond
the aperture diaphragm. At the same time, approximately same num-
ber of electrons are scattered elastically coherently and elastically in-
coherently.
The above relations were obtained in the single electron-specimen
scattering approximation. However, the total intensity I(s) involves a
large part of multiply scattered electrons, i.e. those, for which the
number of interactions with atoms during their passing the specimen
exceeds a unit but is less than that necessary to describe the scattering
processes by a normal Gauss distribution. The latter holds true in case
of a multiple scattering.
A strict account of the multiple scattering influence using known
theoretical expressions is an unsolvable problem until now [11]. Com-
plexity of its solution is related to the fact that in each scattering act
one of the three above analysed mechanisms of electron interaction
with the specimen under study could be realized. For example, triply
scattered electron may take part in the elastic coherent, elastic inco-
herent, and inelastic scattering in the three serial interactions with the
specimen atoms. The studies of such processes and their contributions
to the EM contrast are an independent problem of the theory and prac-
tice of the modern electron microscopy. However, taking into account
the high intensity of the multiple electron scattering by the objects
with a thickness of several dozens of nanometres [13], one may state
that for such specimens the fluxes k, e, and, especially, n include
also a substantial part of the above multiple scattering. In our opinion,
only the multiple scattering contribution stipulates such a large part
of electrons being incoherently scattered by the specimens under study
beyond the aperture diaphragm.
If the heterogeneities of any origin are present in the specimen un-
der study, then, the relevant fluxes k, e, n will differ from each
other. Such differences will cause the appearance of the relevant con-
trasts between the different areas of the heterogeneous object in the
EM image. Using the method suggested above and the above relations,
one may find on the quantitative analysis level the real nature of nano-
heterogeneities present in the amorphous objects. If one takes into ac-
count that the EM pictures reliably demonstrate the 2–3% contrast
values, then for their appearance, the above fluxes k, e, n (or their
96 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK
sum) from the two local areas of the heterogeneous specimen must dif-
fer just by this value.
8. CONCLUSIONS
The electron wave intensity distribution in the plane of formation of
the EM image amplitude contrast is due to the probing electron beam
scattering by the object and consists of three main parts. The first part
is determined by the elastic incoherent scattering Ie(s) and equals to
the sum of scattering effects related to each separate atom inde-
pendently of any other atoms. The second part is the elastic coherent
scattering Ik(s) that causes formation of the diffraction pattern from
material. And the third intensity, In(s), results from the inelastic elec-
tron scattering processes. The spatial distribution and the intensity
Ie(s) are determined by the averaged cross section of electron scatter-
ing by atoms of the specimen under study, its average atomic density,
and geometric thickness. It seems expedient to calculate the coherent
scattering contribution Ik(s) via the experimental structural factor de-
fined by the short-range and medium-range orders of the atomic net-
work in the object under study. The inelastic scattering component
In(s) could be found from the results of the diffraction experiments in
the course of normalizing the intensity of the coherent electron scat-
tering by the specimen under study. Based on the intensities found,
one may calculate the electron fluxes that form the EM images of dif-
ferent local areas of the specimen under study and find the real physi-
cal and chemical nature of its nanoheterogeneities on the quantitative
level.
REFERENCES
1. B. Fultz and J. Howe, Transmission Electron Microscopy and Diffractometry of
Materials (Heidelberg: Springer: 2007).
2. P. Hawkes, The Beginnings of Electron Microscopy (Orlando: Academic Press:
1985).
3. D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook
for Materials Science (New York: Springer: 2009).
4. N. G. Nakhodkin, A. P. Bardamid, and A. I. Novoselskaya, Thin Solid Films,
112, No. 2: 267 (1984).
5. R. Herman and R. Hofstadter, High-Energy Electron Scattering Tables
(Stanford: Stanford University Press: 1966).
6. M. Yu. Bobyk, E. І. Bоrkach, V. P. Ivanytskyy, and V. І. Sabov, Nanosistemi,
Nanomateriali, Nanotehnologii, 10, No. 3: 423 (2012) (in Ukrainian).
7. B. E. Warren, X-Ray Diffraction (New York: Dower: 1990).
8. A. C. Wright, J. Non-Cryst. Solids, 123, No. 1: 129 (1990).
9. Y. Hirotsu, M. Ishimaru, T. Ohkubo, T. Hanada, and M. Sugiyama, J. Electron
http://jmicro.oxfordjournals.org/search?author1=Manabu+Ishimaru&sortspec=date&submit=Submit
http://jmicro.oxfordjournals.org/search?author1=Tadakatsu+Ohkubo&sortspec=date&submit=Submit
http://jmicro.oxfordjournals.org/search?author1=Takeshi+Hanada&sortspec=date&submit=Submit
http://jmicro.oxfordjournals.org/search?author1=Masaaki+Sugiyama&sortspec=date&submit=Submit
ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 97
Microscopy, 50, No. 6: 435 (2001).
10. W. McBride, D. J. H. Cockayne, and K. Tsuda, Ultramicroscopy, 94, Nos. 3–4:
305 (2003).
11. L. Reimer and H. Kohl, Transmission Electron Microscopy: Physics of Image
Formation (New York: Springer: 2008).
12. Z. L. Wang, Elastic and Inelastic Scattering in Electron Diffraction and
Imaging (New York: Plenum Press: 1995).
13. H. Lipson and S. G. Lipson, J. Appl. Cryst., 5, No. 2: 239 (1972).
http://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Lipson,%20H.
http://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Lipson,%20S.G.
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