Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry
Structural changes in silicon single crystals irradiated with high-energy electrons (Е = 18 MeV) were studied. The peculiarities of diffraction reflection curve behaviour and changes in the profiles of isodiffusion lines in high-resolution reciprocal space maps (HR-RSMs) were found as a function...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2010
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| Цитувати: | Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry/ І.М. Fodchuk, V.V. Dovganyuk, Т.V. Litvinchuk , V.P. Kladko, М.V. Slobodian, O.Yo. Gudymenko, Z. Swiatek // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 2. — С. 209-213. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1182372017-05-30T03:05:49Z Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry Fodchuk, І.М. Dovganyuk, V.V. Litvinchuk, Т.V. Kladko, V.P. Slobodian, М.V. Gudymenko, O.Yo. Swiatek, Z. Structural changes in silicon single crystals irradiated with high-energy electrons (Е = 18 MeV) were studied. The peculiarities of diffraction reflection curve behaviour and changes in the profiles of isodiffusion lines in high-resolution reciprocal space maps (HR-RSMs) were found as a function of the radiation dose. The generalized dynamic theory of X-ray Bragg-diffraction in crystals comprising defects of several types (spherical and disc-shaped clusters as well as dislocation loops) and a damaged nearsurface layer was used for explanation. 2010 Article Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry/ І.М. Fodchuk, V.V. Dovganyuk, Т.V. Litvinchuk , V.P. Kladko, М.V. Slobodian, O.Yo. Gudymenko, Z. Swiatek // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 2. — С. 209-213. — Бібліогр.: 22 назв. — англ. 1560-8034 PACS 61.10.Kw, Nz, 61.72.Dd, Ff, 68.55.Ln http://dspace.nbuv.gov.ua/handle/123456789/118237 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| description |
Structural changes in silicon single crystals irradiated with high-energy
electrons (Е = 18 MeV) were studied. The peculiarities of diffraction reflection curve
behaviour and changes in the profiles of isodiffusion lines in high-resolution reciprocal
space maps (HR-RSMs) were found as a function of the radiation dose. The generalized
dynamic theory of X-ray Bragg-diffraction in crystals comprising defects of several types
(spherical and disc-shaped clusters as well as dislocation loops) and a damaged nearsurface
layer was used for explanation. |
| format |
Article |
| author |
Fodchuk, І.М. Dovganyuk, V.V. Litvinchuk, Т.V. Kladko, V.P. Slobodian, М.V. Gudymenko, O.Yo. Swiatek, Z. |
| spellingShingle |
Fodchuk, І.М. Dovganyuk, V.V. Litvinchuk, Т.V. Kladko, V.P. Slobodian, М.V. Gudymenko, O.Yo. Swiatek, Z. Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Fodchuk, І.М. Dovganyuk, V.V. Litvinchuk, Т.V. Kladko, V.P. Slobodian, М.V. Gudymenko, O.Yo. Swiatek, Z. |
| author_sort |
Fodchuk, І.М. |
| title |
Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry |
| title_short |
Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry |
| title_full |
Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry |
| title_fullStr |
Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry |
| title_full_unstemmed |
Structural changes in Cz-Si single crystals irradiated with high-energy electrons from data of high-resolution X-ray diffractometry |
| title_sort |
structural changes in cz-si single crystals irradiated with high-energy electrons from data of high-resolution x-ray diffractometry |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118237 |
| citation_txt |
Structural changes in Cz-Si single crystals
irradiated with high-energy electrons
from data of high-resolution X-ray diffractometry/ І.М. Fodchuk, V.V. Dovganyuk, Т.V. Litvinchuk , V.P. Kladko, М.V. Slobodian, O.Yo. Gudymenko, Z. Swiatek // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 2. — С. 209-213. — Бібліогр.: 22 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
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2025-07-08T13:36:26Z |
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2025-07-08T13:36:26Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 209-213.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
209
PACS 61.10.Kw, Nz, 61.72.Dd, Ff, 68.55.Ln
Structural changes in Cz-Si single crystals
irradiated with high-energy electrons
from data of high-resolution X-ray diffractometry
І.М. Fodchuk1, V.V. Dovganyuk1, Т.V. Litvinchuk1 , V.P. Kladko2, М.V. Slobodian2,
O.Yo. Gudymenko2, Z. Swiatek3
1Yu. Fed’kovych Chernivtsi National University, Chernivtsi, Ukraine
2 V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 03028 Kyiv, Ukraine
3Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Krakow, Poland
Abstract. Structural changes in silicon single crystals irradiated with high-energy
electrons (Е = 18 MeV) were studied. The peculiarities of diffraction reflection curve
behaviour and changes in the profiles of isodiffusion lines in high-resolution reciprocal
space maps (HR-RSMs) were found as a function of the radiation dose. The generalized
dynamic theory of X-ray Bragg-diffraction in crystals comprising defects of several types
(spherical and disc-shaped clusters as well as dislocation loops) and a damaged near-
surface layer was used for explanation.
Keywords: irradiation, high-energy electrons, Cz-Si, oxygen-containing defects, X-ray
diffraction.
Manuscript received 03.02.10; accepted for publication 25.03.10; published online 30.04.10.
1. Introduction
Among the methods of crystal research the methods
based on the analysis of the angular distributing of X-ray
intensity are the most informative [1-14]. The
determination of concentrations and sizes of micro-
defects, their type (interstitial or vacancy) and symmetry
of static distortion fields formed by them, is possible
from the analysis of the angular intensity distributions
[3-12].
In the method of X-ray two-crystal diffractometry
(TCD) the information about concentration-size
descriptions of defects is represented by the tails of
diffraction reflection curves, which are mainly formed
by X-ray diffuse scattering on microdefects [1-3, 8, 12].
However, only the three-crystal X-ray diffractometry
allows to separate diffuse intensity component of X-ray
scattering from the coherent one [3-8, 14].
Irradiation of silicon by high-energy particles
considerably influences on decomposition processes of
oxygen solid solution in Si and, consequently, changes
the character of X-ray scattering [9-11]. The presence
of a great number of different types of defects in the
irradiated samples significantly complicates construc-
tion of the model of imperfect structure, allowing to
correctly describe the obtained experimental results
[15-23].
Therefore, it is necessary to choose the basic types
of defects that provide dominant contribution to the
diffraction pattern. A similar attempt to construct such a
model was undertaken in the papers [9-11], where
assumptions of the imperfect system supposing a
presence of dislocation loops, ellipsoid clusters (SiO2
precipitates), point defects and thermal diffuse scattering
in the crystal are used.
The generalized dynamic theory of X-ray Bragg-
diffraction in a crystal containing the defects of several
types (spherical and disc-like clusters, dislocation loops)
was used in this work to research the dynamics of
changes of concentration and sizes of dominant defects
in crystals before and after irradiation by high-energy
electrons as well as their influence on coherent and
diffuse components of the diffraction reflection curve.
2. Objects of investigations
They were Czochralski-grown dislocation-free silicon
samples (Table 1) irradiated by different doses of high-
energy electrons (Е = 18 МeV). The oxygen concen-
tration in these samples was n 1018 cm-3, input surface
orientation (111), р-type of conductivity, boron-doped,
resistivity 7.5 Оhmсm. To eliminate the damaged layer,
crystals prior to and after irradiation were subjected to a
complete cycle of chemical and mechanical treatment.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 209-213.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
210
3. Experimental investigations
X-ray diffraction curves (Fig. 1) were measured in the
-2-scanning mode with a narrow detector window in
common Bragg geometry. The HR-RSMs (Figs 2
and 3) were measured using a triple-axis Х-ray
diffractometer „PANalytical X’pert Pro MRD XL” in a
coplanar diffraction geometry for (333) planes with a
rectangular cross-section using 4-fold Ge (220)
monochromator and 3-fold Ge (220) analyzer with the
angular discrepancy 12″.
Table 1. Samples under investigation.
Sample Radiation dose Thickness, mm
№1 Reference 4.271
№1а 1.8 kGray 4.263
№1b 3.6 kGray 4.261
Our analysis of experimental data in Fig. 1 shows the
following. The crystal №1а (Fig. 1) is characterized by
reduction of the full width at half maximum (FWHM) of
diffraction curves as compared to the initial sample for
both (111) and (333) reflections. Whereas in the case of
the crystal №1b for (333) reflection, the situation is
opposite. It is caused by different contributions of the
damaged near-surface layer to the general scattering
intensity for these reflections. Similar peculiarities are
observed for rocking curves obtained in the ω-scanning
mode [3-6].
-400 -300 -200 -100 0 100 200 300 400
100
101
102
103
104
105
106
, arc sec
N 1
N 1a
N 1b
TKS_Si(111)
I, pulses/s
-400 -300 -200 -100 0 100 200 300 400
100
101
102
103
104
105
, arc sec
N 1
N 1a
N 1b
TKS_Si(333)
I, pulses/s
Fig. 1. Experimental diffraction reflection curves, ω-2θ-
scanning (111) and (333) reflections of CuK1-radiation.
Monochromator – (220).
Fig. 2. Crystal №1 (reference). Distribution of diffuse
scattering intensity around the CuKα(333) reciprocal lattice
site.
a)
b)
Fig. 3. Crystal: a) №1а (1.8 kGray); b) №1b (3.6 kGray).
Distribution of the diffuse scattering intensity around the
CuKα(333) reciprocal lattice site.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 209-213.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
211
In the experimental maps (Figs 2 and 3), the
distribution of the diffuse scattering intensity is
manifested as certain changes in symmetry of profiles.
It is known that formation of isodiffuse profiles is
largely dependent on the type of defects, their location in
the lattice and symmetry of their displacement fields
[3-8]. General appearance of these profiles allows
establishing symmetry of the displacement field and
choosing between several possible configurations of a
defect structure.
4. Тheory
Monocrystalline Cz-Si is characterized by the presence
of relatively high concentrations of clusters and
dislocation loops. Certain processes, such as temperature
annealing, can cause intensive nucleation of new and
decay of genetic cluster formations with SiО2 precipitate
structure 12-16. Based on the evidence from [16-17],
the energy of formation of silicon-oxygen precipitates of
spherical or elliptical shape is higher than the formation
energy of these precipitates in a lamellar or disc shapes,
that is, their formation is a most probable [18-22].
However, under certain conditions, for example,
high-energy irradiation, different scenarios of defect
system reconstruction can occur in bulk silicon crystal.
Stimulated diffusion of oxygen from matrix to crystal
surface can cause a volume change in the area of
precipitate formation. It can account for a nucleation of
the dislocation Frank loop 12-16, as well as origination
of silicon-oxygen clusters in the (111) planes [16].
Oxygen atoms in these clusters are introduced into
interstitial positions between pairs of silicon atoms
located along the [111] directions. For a further growth
of oxygen-containing clusters, injection of interstitial
atoms to surrounding lattice is needed. When con-
centrations of interstitial atoms in these areas reach a
certain critical value, their condensation with formation
of the cluster surrounded by a dislocation loop may take
place. Such cluster formations have smaller effective
sizes than the dislocation loops.
To explain possible structural changes in crystals
irradiated with high-energy electrons, we used the
following model of interrelated and interacting dominant
microdefects typical for Si-Cz crystals [20-22]: disc-like
clusters, fine spherical clusters – SiО2 precipitates,
dislocation loops, point defects – silicon vacancies and
elastic bend of crystal reflecting (111)-planes.
To determine individual and combined effect of each
of the above defect types on the formation of diffraction
curves (Fig. 1), we used relationships of the generalized
theory of X-ray scattering in single crystals with
randomly distributed defects [3-6]. According to this
theory, the crystal diffraction curve is a sum of coherent
(Rcoh) and diffuse (Rdiff) components [3, 4]:
)()()( diffcoh RRR . (1)
Coherent component is assigned by the relationship [3]:
1)( 2LLRcoh , (2)
where L is the parameter taking into account absorption
of strong Bragg waves due to processes of nonelastic
scattering on defects and additional absorption of these
waves due to diffuse scattering on defects, is the
coefficient taking into account dispersion corrections for
Fourier-components of polarization χH .
The diffuse component of reflectivity R in the
presence of several types of randomly distributed defects
in crystal and in the absence of correlation between them
is of the form [3, 6]:
0000 /)()()( tkFR dyndiff , (3)
)()()( 000 tpkDS ,
tetp t 2/)1()( 2 , (4)
where t is the crystal thickness, γ0 is the direction cosine
of the wave vector of crystal incident wave.
The statistic Debye-Waller factor LH and absorption
coefficient due to diffuse scattering on defects μDS in
j-layer are a respective superposition on all defect types
and described by the expressions:
HH LL ,
DSDS . (5)
Here, α is used to number defect type. The factor LH
in (5) is related to characteristics of dominant defects by
the relationships [5]:
2/33
0
1
0 )(5.0 bHRcvLD
H – dislocation loops,
)100/)1(5.0 22
0 cnLK
H : )10( 2 – spherical,
2/3
0 cnLH : )10( 2 – disc-shaped clusters,
where с is the concentration for the respective type of
defects, 0 is the number of atoms in a matrix cubic
cell, R0 is the real defect radius, H is the vector of
reciprocal lattice, b is the Burgers vector of a dislocation
loop, 0n is the number of cluster-substituted matrix unit
cells, 2/0
3/1
00 Han , 2/2
00 phR , ph is the
cluster thickness, α0 is the lattice constant, ε is a
deformation at cluster boundary, 3/)1)(1( 1Г ,
ν is the Poisson coefficient.
The coefficient of absorption μDS due to diffuse
scattering is described by the relationship [4]:
)()()( 00
22
0 kJmECck jDS
,
20
0 /
4
rHHm , )exp( HLE , (6)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 209-213.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
212
where c is the value of defect concentration in the
layer under study, С is the polarization factor, ν0 is the
number of atoms in the matrix cubic cell, rH is the real
Fourier polarization component, λ is the wavelength,
)( 0kJ is the normalized coefficient of absorption due
to diffuse scattering.
For precipitates that can have the shape of ellipsoids,
plates or discs, we have used the relationship between
the radius Rd.cl and thickness hd.cl of disc-shaped
precipitate [3, 4]:
2
..1. / a
cldcldcld RLRah , (7)
where а1 = 3.96 and а2 = 0.5966 [4]. The parameter of
deformation at the interface between the precipitate and
Si matrix was assumed to be corresponding to SiO2
amorphous phase ε = 0.0242 [3-5].
5. Analysis of investigation results
Calculations performed on the basis of relationships (1)-
(6) made it possible to reach correspondence between
experimental and theoretical diffraction curves (Fig. 4).
It allowed evaluation of the sizes and concentrations
inherent to dominant types of defects (Table 2).
In particular, a change in the shape of diffraction
curve for the crystal №1а (Fig. 1) after following
irradiation with high-energy electrons is apparently
caused by increase in concentrations of disc-shaped
clusters and small-size dislocation loops with a
simultaneous decrease in concentrations of fine spherical
clusters (Table 2). As a rule, this is reflected accordingly
in the essential increase of diffuse component in the
integral intensity (Fig. 1).
A slight difference in diffraction reflection curves in
Fig. 1 for crystals №1b and №1 (initial sample) can be
explained by a decrease in the diffuse intensity
component due to reduction in the concentration of disc-
shaped clusters and dislocation loops. Also, their size
increase with the concentration of fine spherical clusters,
which contribution is commensurate to that of disc-
shaped clusters and dislocation loops. That is in
agreement with the results [8].
Тable 2. Concentrations and sizes of dominant types
of microdefects obtained in the process of
comparison between experimental and theoretical
diffraction reflection curves.
Sample
сd.cl.,
106
сm-3
Rd.cl.,
μm
сL,
106
сm-3
RL,
μm
сsph.cl.,
1013
сm-3
Rsph.cl.,
nm
№1 15 3.56 2.5 8.95 19.2 6.2
№1а 86 1.8 54.8 7.18 8.16 5.8
№1b 14 3.56 9.8 7.2 4.35 7.9
Fig. 4. Experimental and calculated rocking curves for the
reflection (333) of silicon crystals under study.
The character of scattered intensity distribution in
the experimental HR-RSMs (Figs 2, 3) is indicative of
the following. The microdefects with a positive power are
presented by disc-shaped clusters and fine spherical
clusters. The elongated profile of isodiffuse lines in qх,
direction testifies to the presence of prolonged regions of
nonuniform composition of oxygen solid solution in
silicon with a smeared coherent boundary. In our case, it
is interpreted by the Patel model of packing defects [14,
16, 17].
For the crystal №1а (Fig. 3), isodiffuse lines are
somewhat smeared and flattened, their curvature radius
is increased parallel to qx axis. This testifies to a
predominant process of increasing the concentration
inherent to disc-shaped clusters and small-size disloca-
tion loops on the background of reduced concentrations
of fine spherical clusters. Apparently, the energy
absorbed in crystal irradiated by the dose of 1.8 kGray is
sufficient to cause respective transformations in its
defective structure. However, this energy proved to be
insufficient to form a stable defective structure relaxed
after this high-energy “shock”.
A different situation arises for the crystal №1b. The
elliptical shape of profile isodiffuse lines and their
elongation in direction of positive qx values can bear
witness to a reduced concentration of disc-shaped
clusters and dislocation loops, and their size increases
with the growing concentration of fine spherical clusters.
On the whole, the model of defective structure
comprising several types of dominant microdefects
yields a more detailed description of the shape and
characteristics of diffraction reflection curves, the
profiles of isodiffuse lines. This allowed obtaining a
scenario of possible structural reconstructions in
defective system of silicon crystals irradiated with high-
energy electrons [4, 9-11].
6. Conclusions
In conformity with the selected model for description of
the defective system of Cz-Si crystals by several types of
dominant defects, the dynamics of changes in the
concentrations and sizes of microdefects prior to and
after their irradiation was studied:
– the observed change in the shape of diffraction
reflection curves for crystals irradiated by the dose
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 209-213.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
213
of 1.8 kGray (sample №1а) with high-energy
electrons can be explained by increased
concentrations of disc-shaped clusters and small-
size dislocation loops on the background of
reduced concentrations of fine spherical clusters;
– slight discrepancies in diffraction reflection curves
for crystals irradiated by the largest specific dose
844 Gray/mm (sample №1b) and reference (№1)
can be explained by the reduced diffuse intensity
component due to a reduced concentration of disc-
shaped clusters and dislocation loops as well as
their increased sizes with the growing
concentration of fine spherical clusters whose
contribution is commensurate to that of disc-shaped
clusters and dislocation loops.
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Silicon. Mir, Мoscow, 1984 (in Russian).
15. J.R. Patel, Computer-simulation methods in X-ray
topography // Acta cryst. A, 35, p. 21-28 (1979).
16. K.F. Kelton, R. Falster, D. Gambaro, M. Olma,
M. Cornara and P.F. Wei // J. Appl. Phys., 85,
p. 8097-8111 (1999).
17. W. Patrick, E. Hearn, W. Westdorp, A. Bohg,
Oxygen precipitation in silicon // J. Appl. Phys. 50,
p. 7156-7164 (1979).
18. H. Bender, Investigation of the oxygen-related
lattice defects in Czochralski silicon by means of
electron microscopy techniques // Phys. status
solidi (a), 86, p. 245-261 (1984).
19. W. Bergholz, M.J. Binns, G.R. Booker,
J.C. Hutchinson, S.H. Kinder, S. Messoloras, A
study of oxygen precipitation in silicon using high-
resolution transmission electron microscopy, small-
angle neutron scattering and infrared absorption //
Phil. Mag. B, 59, p. 499-522 (1989).
20. A.J.R. de Kock, Crystal growth of bulk crystals:
Purification, doping and defects, in: Handbook on
Semiconductor (vol. 3: Materials, Properties and
preparation). North-Holand and Publishing
Company, 1980, p. 247-333.
21. A.J.R. de Kock, P.J. Roksnoer, P.G.T. Boonen, The
introduction of dislocations during the growth of
floating-zone silicon crystals as a result of point
defect condensation // J. Cryst. Growth, 30(3),
p. 279-294 (1975).
22. S. Iida, Y. Aoki, Y. Sugita, T. Abe, H. Kawata,
Grown-in microdefects in a slowly grown
Czochralski silicon crystal observed by synchrotron
radiation topography // Jpn. J. Appl. Phys., 39,
p. 6130-6135 (2000).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 209-213.
PACS 61.10.Kw, Nz, 61.72.Dd, Ff, 68.55.Ln
Structural changes in Cz-Si single crystals
irradiated with high-energy electrons
from data of high-resolution X-ray diffractometry
І.М. Fodchuk1, V.V. Dovganyuk1, Т.V. Litvinchuk1 , V.P. Kladko2, М.V. Slobodian2,
O.Yo. Gudymenko2, Z. Swiatek3
1Yu. Fed’kovych Chernivtsi National University, Chernivtsi, Ukraine
2 V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 03028 Kyiv, Ukraine
3Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Krakow, Poland
Abstract. Structural changes in silicon single crystals irradiated with high-energy electrons (Е = 18 MeV) were studied. The peculiarities of diffraction reflection curve behaviour and changes in the profiles of isodiffusion lines in high-resolution reciprocal space maps (HR-RSMs) were found as a function of the radiation dose. The generalized dynamic theory of X-ray Bragg-diffraction in crystals comprising defects of several types (spherical and disc-shaped clusters as well as dislocation loops) and a damaged near-surface layer was used for explanation.
Keywords: irradiation, high-energy electrons, Cz-Si, oxygen-containing defects, X-ray diffraction.
Manuscript received 03.02.10; accepted for publication 25.03.10; published online 30.04.10.
1. Introduction
Among the methods of crystal research the methods based on the analysis of the angular distributing of X-ray intensity are the most informative [1-14]. The determination of concentrations and sizes of microdefects, their type (interstitial or vacancy) and symmetry of static distortion fields formed by them, is possible from the analysis of the angular intensity distributions [3-12].
In the method of X-ray two-crystal diffractometry (TCD) the information about concentration-size descriptions of defects is represented by the tails of diffraction reflection curves, which are mainly formed by X-ray diffuse scattering on microdefects [1-3, 8, 12]. However, only the three-crystal X-ray diffractometry allows to separate diffuse intensity component of X-ray scattering from the coherent one [3-8, 14].
Irradiation of silicon by high-energy particles considerably influences on decomposition processes of oxygen solid solution in Si and, consequently, changes the character of X-ray scattering [9-11]. The presence of a great number of different types of defects in the irradiated samples significantly complicates construction of the model of imperfect structure, allowing to correctly describe the obtained experimental results [15-23].
Therefore, it is necessary to choose the basic types of defects that provide dominant contribution to the diffraction pattern. A similar attempt to construct such a model was undertaken in the papers [9-11], where assumptions of the imperfect system supposing a presence of dislocation loops, ellipsoid clusters (SiO2 precipitates), point defects and thermal diffuse scattering in the crystal are used.
The generalized dynamic theory of X-ray Bragg-diffraction in a crystal containing the defects of several types (spherical and disc-like clusters, dislocation loops) was used in this work to research the dynamics of changes of concentration and sizes of dominant defects in crystals before and after irradiation by high-energy electrons as well as their influence on coherent and diffuse components of the diffraction reflection curve.
2. Objects of investigations
They were Czochralski-grown dislocation-free silicon samples (Table 1) irradiated by different doses of high-energy electrons (Е = 18 МeV). The oxygen concen-tration in these samples was n ( 1018 cm-3, input surface orientation (111), р-type of conductivity, boron-doped, resistivity 7.5 Оhm(сm. To eliminate the damaged layer, crystals prior to and after irradiation were subjected to a complete cycle of chemical and mechanical treatment.
3. Experimental investigations
X-ray diffraction curves (Fig. 1) were measured in the (-2(-scanning mode with a narrow detector window in common Bragg geometry. The HR-RSMs (Figs 2 and 3) were measured using a triple-axis Х-ray diffractometer „PANalytical X’pert Pro MRD XL” in a coplanar diffraction geometry for (333) planes with a rectangular cross-section using 4-fold Ge (220) monochromator and 3-fold Ge (220) analyzer with the angular discrepancy 12″.
Table 1. Samples under investigation.
Sample
Radiation dose
Thickness, mm
№1
Reference
4.271
№1а
1.8 kGray
4.263
№1b
3.6 kGray
4.261
Our analysis of experimental data in Fig. 1 shows the following. The crystal №1а (Fig. 1) is characterized by reduction of the full width at half maximum (FWHM) of diffraction curves as compared to the initial sample for both (111) and (333) reflections. Whereas in the case of the crystal №1b for (333) reflection, the situation is opposite. It is caused by different contributions of the damaged near-surface layer to the general scattering intensity for these reflections. Similar peculiarities are observed for rocking curves obtained in the ω-scanning mode [3-6].
-400
-300
-200
-100
0
100
200
300
400
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Dq
, arc sec
N 1
N 1a
N 1b
TKS_Si(111)
I
, pulses/s
-400
-300
-200
-100
0
100
200
300
400
10
0
10
1
10
2
10
3
10
4
10
5
Dq
, arc sec
N 1
N 1a
N 1b
TKS_Si(333)
I
, pulses/s
Fig. 1. Experimental diffraction reflection curves, ω-2θ-scanning (111) and (333) reflections of CuK(1-radiation. Monochromator – (220).
Fig. 2. Crystal №1 (reference). Distribution of diffuse scattering intensity around the CuKα(333) reciprocal lattice site.
a)
b)
Fig. 3. Crystal: a) №1а (1.8 kGray); b) №1b (3.6 kGray). Distribution of the diffuse scattering intensity around the CuKα(333) reciprocal lattice site.
In the experimental maps (Figs 2 and 3), the distribution of the diffuse scattering intensity is manifested as certain changes in symmetry of profiles.
It is known that formation of isodiffuse profiles is largely dependent on the type of defects, their location in the lattice and symmetry of their displacement fields
[3-8]. General appearance of these profiles allows establishing symmetry of the displacement field and choosing between several possible configurations of a defect structure.
4. Тheory
Monocrystalline Cz-Si is characterized by the presence of relatively high concentrations of clusters and dislocation loops. Certain processes, such as temperature annealing, can cause intensive nucleation of new and decay of genetic cluster formations with SiО2 precipitate structure (12-16(. Based on the evidence from [16-17], the energy of formation of silicon-oxygen precipitates of spherical or elliptical shape is higher than the formation energy of these precipitates in a lamellar or disc shapes, that is, their formation is a most probable [18-22].
However, under certain conditions, for example, high-energy irradiation, different scenarios of defect system reconstruction can occur in bulk silicon crystal. Stimulated diffusion of oxygen from matrix to crystal surface can cause a volume change in the area of precipitate formation. It can account for a nucleation of the dislocation Frank loop (12-16(, as well as origination of silicon-oxygen clusters in the (111) planes [16]. Oxygen atoms in these clusters are introduced into interstitial positions between pairs of silicon atoms located along the [111] directions. For a further growth of oxygen-containing clusters, injection of interstitial atoms to surrounding lattice is needed. When concentrations of interstitial atoms in these areas reach a certain critical value, their condensation with formation of the cluster surrounded by a dislocation loop may take place. Such cluster formations have smaller effective sizes than the dislocation loops.
To explain possible structural changes in crystals irradiated with high-energy electrons, we used the following model of interrelated and interacting dominant microdefects typical for Si-Cz crystals [20-22]: disc-like clusters, fine spherical clusters – SiО2 precipitates, dislocation loops, point defects – silicon vacancies and elastic bend of crystal reflecting (111)-planes.
To determine individual and combined effect of each of the above defect types on the formation of diffraction curves (Fig. 1), we used relationships of the generalized theory of X-ray scattering in single crystals with randomly distributed defects [3-6]. According to this theory, the crystal diffraction curve is a sum of coherent (Rcoh) and diffuse (Rdiff) components [3, 4]:
)
(
)
(
)
(
q
D
+
q
D
=
q
D
diff
coh
R
R
R
.
(1)
Coherent component is assigned by the relationship [3]:
÷
ø
ö
ç
è
æ
-
-
x
=
q
D
1
)
(
2
L
L
R
coh
,
(2)
where L is the parameter taking into account absorption of strong Bragg waves due to processes of nonelastic scattering on defects and additional absorption of these waves due to diffuse scattering on defects, ( is the coefficient taking into account dispersion corrections for Fourier-components of polarization χH .
The diffuse component of reflectivity R in the presence of several types of randomly distributed defects in crystal and in the absence of correlation between them is of the form [3, 6]:
0
0
00
/
)
(
)
(
)
(
g
m
q
D
=
q
D
t
k
F
R
dyn
diff
,
(3)
)
(
)
(
)
(
0
00
t
p
k
DS
×
m
m
=
q
D
m
,
t
e
t
p
t
×
m
-
=
×
m
×
m
-
2
/
)
1
(
)
(
2
,
(4)
where t is the crystal thickness, γ0 is the direction cosine of the wave vector of crystal incident wave.
The statistic Debye-Waller factor LH and absorption coefficient due to diffuse scattering on defects μDS in
j-layer are a respective superposition on all defect types and described by the expressions:
å
a
a
=
H
H
L
L
,
å
a
a
m
=
m
DS
DS
.
(5)
Here, α is used to number defect type. The factor LH in (5) is related to characteristics of dominant defects by the relationships [5]:
2
/
3
3
0
1
0
)
(
5
.
0
b
H
R
cv
L
D
H
×
»
-
– dislocation loops,
)
100
/
)
1
(
5
.
0
2
2
0
h
-
h
»
cn
L
K
H
:
)
10
(
2
<<
h
– spherical,
2
/
3
0
h
»
cn
L
H
:
)
10
(
2
>>
h
– disc-shaped clusters,
where с is the concentration for the respective type of defects,
0
n
is the number of atoms in a matrix cubic cell, R0 is the real defect radius, H is the vector of reciprocal lattice, b is the Burgers vector of a dislocation loop,
0
n
is the number of cluster-substituted matrix unit cells,
p
×
a
=
h
2
/
0
3
/
1
0
0
Ha
n
,
2
/
2
0
0
p
h
R
e
G
=
a
,
p
h
is the cluster thickness, α0 is the lattice constant, ε is a deformation at cluster boundary,
3
/
)
1
)(
1
(
1
-
n
-
n
+
=
Г
, ν is the Poisson coefficient.
The coefficient of absorption μDS due to diffuse scattering is described by the relationship [4]:
)
(
)
(
)
(
0
0
2
2
0
k
J
m
E
C
c
k
j
DS
a
a
a
=
m
,
(
)
2
0
0
/
4
l
c
pn
=
rH
H
m
,
)
exp(
H
L
E
-
=
,
(6)
where
a
c
is the value of defect concentration in the layer under study, С is the polarization factor, ν0 is the number of atoms in the matrix cubic cell,
rH
c
is the real Fourier polarization component, λ is the wavelength,
)
(
0
k
J
a
is the normalized coefficient of absorption due to diffuse scattering.
For precipitates that can have the shape of ellipsoids, plates or discs, we have used the relationship between the radius Rd.cl and thickness hd.cl of disc-shaped precipitate [3, 4]:
(
)
2
.
.
1
.
/
a
cl
d
cl
d
cl
d
R
L
R
a
h
=
,
(7)
where а1 = 3.96 and а2 = 0.5966 [4]. The parameter of deformation at the interface between the precipitate and Si matrix was assumed to be corresponding to SiO2 amorphous phase ε = 0.0242 [3-5].
5. Analysis of investigation results
Calculations performed on the basis of relationships (1)-(6) made it possible to reach correspondence between experimental and theoretical diffraction curves (Fig. 4). It allowed evaluation of the sizes and concentrations inherent to dominant types of defects (Table 2).
In particular, a change in the shape of diffraction curve for the crystal №1а (Fig. 1) after following irradiation with high-energy electrons is apparently caused by increase in concentrations of disc-shaped clusters and small-size dislocation loops with a simultaneous decrease in concentrations of fine spherical clusters (Table 2). As a rule, this is reflected accordingly in the essential increase of diffuse component in the integral intensity (Fig. 1).
A slight difference in diffraction reflection curves in Fig. 1 for crystals №1b and №1 (initial sample) can be explained by a decrease in the diffuse intensity component due to reduction in the concentration of disc-shaped clusters and dislocation loops. Also, their size increase with the concentration of fine spherical clusters, which contribution is commensurate to that of disc-shaped clusters and dislocation loops. That is in agreement with the results [8].
Тable 2. Concentrations and sizes of dominant types of microdefects obtained in the process of comparison between experimental and theoretical diffraction reflection curves.
Sample
сd.cl.,
106
сm-3
Rd.cl., μm
сL,
106
сm-3
RL, μm
сsph.cl., 1013 сm-3
Rsph.cl., nm
№1
15
3.56
2.5
8.95
19.2
6.2
№1а
86
1.8
54.8
7.18
8.16
5.8
№1b
14
3.56
9.8
7.2
4.35
7.9
Fig. 4. Experimental and calculated rocking curves for the reflection (333) of silicon crystals under study.
The character of scattered intensity distribution in the experimental HR-RSMs (Figs 2, 3) is indicative of the following. The microdefects with a positive power are presented by disc-shaped clusters and fine spherical clusters. The elongated profile of isodiffuse lines in qх, direction testifies to the presence of prolonged regions of nonuniform composition of oxygen solid solution in silicon with a smeared coherent boundary. In our case, it is interpreted by the Patel model of packing defects [14, 16, 17].
For the crystal №1а (Fig. 3), isodiffuse lines are somewhat smeared and flattened, their curvature radius is increased parallel to qx axis. This testifies to a predominant process of increasing the concentration inherent to disc-shaped clusters and small-size dislocation loops on the background of reduced concentrations of fine spherical clusters. Apparently, the energy absorbed in crystal irradiated by the dose of 1.8 kGray is sufficient to cause respective transformations in its defective structure. However, this energy proved to be insufficient to form a stable defective structure relaxed after this high-energy “shock”.
A different situation arises for the crystal №1b. The elliptical shape of profile isodiffuse lines and their elongation in direction of positive qx values can bear witness to a reduced concentration of disc-shaped clusters and dislocation loops, and their size increases with the growing concentration of fine spherical clusters.
On the whole, the model of defective structure comprising several types of dominant microdefects yields a more detailed description of the shape and characteristics of diffraction reflection curves, the profiles of isodiffuse lines. This allowed obtaining a scenario of possible structural reconstructions in defective system of silicon crystals irradiated with high-energy electrons [4, 9-11].
6. Conclusions
In conformity with the selected model for description of the defective system of Cz-Si crystals by several types of dominant defects, the dynamics of changes in the concentrations and sizes of microdefects prior to and after their irradiation was studied:
–
the observed change in the shape of diffraction reflection curves for crystals irradiated by the dose of 1.8 kGray (sample №1а) with high-energy electrons can be explained by increased concentrations of disc-shaped clusters and small-size dislocation loops on the background of reduced concentrations of fine spherical clusters;
–
slight discrepancies in diffraction reflection curves for crystals irradiated by the largest specific dose 844 Gray/mm (sample №1b) and reference (№1) can be explained by the reduced diffuse intensity component due to a reduced concentration of disc-shaped clusters and dislocation loops as well as their increased sizes with the growing concentration of fine spherical clusters whose contribution is commensurate to that of disc-shaped clusters and dislocation loops.
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15. J.R. Patel, Computer-simulation methods in X-ray topography // Acta cryst. A, 35, p. 21-28 (1979).
16. K.F. Kelton, R. Falster, D. Gambaro, M. Olma, M. Cornara and P.F. Wei // J. Appl. Phys., 85, p. 8097-8111 (1999).
17. W. Patrick, E. Hearn, W. Westdorp, A. Bohg, Oxygen precipitation in silicon // J. Appl. Phys. 50, p. 7156-7164 (1979).
18. H. Bender, Investigation of the oxygen-related lattice defects in Czochralski silicon by means of electron microscopy techniques // Phys. status solidi (a), 86, p. 245-261 (1984).
19. W. Bergholz, M.J. Binns, G.R. Booker, J.C. Hutchinson, S.H. Kinder, S. Messoloras, A study of oxygen precipitation in silicon using high-resolution transmission electron microscopy, small-angle neutron scattering and infrared absorption // Phil. Mag. B, 59, p. 499-522 (1989).
20. A.J.R. de Kock, Crystal growth of bulk crystals: Purification, doping and defects, in: Handbook on Semiconductor (vol. 3: Materials, Properties and preparation). North-Holand and Publishing Company, 1980, p. 247-333.
21. A.J.R. de Kock, P.J. Roksnoer, P.G.T. Boonen, The introduction of dislocations during the growth of floating-zone silicon crystals as a result of point defect condensation // J. Cryst. Growth, 30(3), p. 279-294 (1975).
22. S. Iida, Y. Aoki, Y. Sugita, T. Abe, H. Kawata, Grown-in microdefects in a slowly grown Czochralski silicon crystal observed by synchrotron radiation topography // Jpn. J. Appl. Phys., 39, p. 6130-6135 (2000).
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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