Double- and triple-crystal X-ray diffractometry of microdefects in silicon
The generalized dynamical theory of X-ray scattering by real single crystals allows to self-consistently describe intensities of coherent and diffuse scattering measured by double- and triple-crystal diffractometers (DCD and TCD) from single crystals with defects in crystal bulk and with strained...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2010
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| Цитувати: | Double- and triple-crystal X-ray diffractometry of microdefects in silicon / V.B. Molodkin, S.I. Olikhovskii, Ye.M. Kyslovskyy, E.G. Len, O.V. Reshetnyk, T.P. Vladimirova, V.V. Lizunov, S.V. Lizunova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 353-356. — Бібліогр.: 20 назв. — англ. |
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irk-123456789-1185772017-05-31T03:06:25Z Double- and triple-crystal X-ray diffractometry of microdefects in silicon Molodkin, V.B. Olikhovskii, S.I. Kyslovskyy, Ye.M. Len, E.G. Reshetnyk, O.V. Vladimirova, T.P. V.V. Lizunov, V.V. Lizunova, S.V. The generalized dynamical theory of X-ray scattering by real single crystals allows to self-consistently describe intensities of coherent and diffuse scattering measured by double- and triple-crystal diffractometers (DCD and TCD) from single crystals with defects in crystal bulk and with strained subsurface layers. Being based on this theory, we offer the combined DCD+TCD method that exhibits the higher sensitivity to defect structures with wide size distributions as compared with any of these methods alone. In the investigated Czochralski-grown silicon crystals, the sizes and concentrations of small oxygen precipitates as well as small and large dislocation loops have been determined using this method. 2010 Article Double- and triple-crystal X-ray diffractometry of microdefects in silicon / V.B. Molodkin, S.I. Olikhovskii, Ye.M. Kyslovskyy, E.G. Len, O.V. Reshetnyk, T.P. Vladimirova, V.V. Lizunov, S.V. Lizunova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 353-356. — Бібліогр.: 20 назв. — англ. 1560-8034 PACS 61.72.Dd http://dspace.nbuv.gov.ua/handle/123456789/118577 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
The generalized dynamical theory of X-ray scattering by real single crystals
allows to self-consistently describe intensities of coherent and diffuse scattering
measured by double- and triple-crystal diffractometers (DCD and TCD) from single
crystals with defects in crystal bulk and with strained subsurface layers. Being based on
this theory, we offer the combined DCD+TCD method that exhibits the higher sensitivity
to defect structures with wide size distributions as compared with any of these methods
alone. In the investigated Czochralski-grown silicon crystals, the sizes and concentrations
of small oxygen precipitates as well as small and large dislocation loops have been
determined using this method. |
| format |
Article |
| author |
Molodkin, V.B. Olikhovskii, S.I. Kyslovskyy, Ye.M. Len, E.G. Reshetnyk, O.V. Vladimirova, T.P. V.V. Lizunov, V.V. Lizunova, S.V. |
| spellingShingle |
Molodkin, V.B. Olikhovskii, S.I. Kyslovskyy, Ye.M. Len, E.G. Reshetnyk, O.V. Vladimirova, T.P. V.V. Lizunov, V.V. Lizunova, S.V. Double- and triple-crystal X-ray diffractometry of microdefects in silicon Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Molodkin, V.B. Olikhovskii, S.I. Kyslovskyy, Ye.M. Len, E.G. Reshetnyk, O.V. Vladimirova, T.P. V.V. Lizunov, V.V. Lizunova, S.V. |
| author_sort |
Molodkin, V.B. |
| title |
Double- and triple-crystal X-ray diffractometry of microdefects in silicon |
| title_short |
Double- and triple-crystal X-ray diffractometry of microdefects in silicon |
| title_full |
Double- and triple-crystal X-ray diffractometry of microdefects in silicon |
| title_fullStr |
Double- and triple-crystal X-ray diffractometry of microdefects in silicon |
| title_full_unstemmed |
Double- and triple-crystal X-ray diffractometry of microdefects in silicon |
| title_sort |
double- and triple-crystal x-ray diffractometry of microdefects in silicon |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118577 |
| citation_txt |
Double- and triple-crystal X-ray diffractometry
of microdefects in silicon / V.B. Molodkin, S.I. Olikhovskii, Ye.M. Kyslovskyy, E.G. Len, O.V. Reshetnyk, T.P. Vladimirova, V.V. Lizunov, S.V. Lizunova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 353-356. — Бібліогр.: 20 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 353-356.
PACS 61.72.Dd
Double- and triple-crystal X-ray diffractometry
of microdefects in silicon
V.B. Molodkin, S.I. Olikhovskii, Ye.M. Kyslovskyy, E.G. Len, O.V. Reshetnyk,
T.P. Vladimirova, V.V. Lizunov, S.V. Lizunova
G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine,
36, Academician Vernadsky Blvd. 03680 Kyiv, Ukraine,
Phone: (044)4229583, e-mail: len@imp.kiev.ua
Abstract. The generalized dynamical theory of X-ray scattering by real single crystals
allows to self-consistently describe intensities of coherent and diffuse scattering
measured by double- and triple-crystal diffractometers (DCD and TCD) from single
crystals with defects in crystal bulk and with strained subsurface layers. Being based on
this theory, we offer the combined DCD+TCD method that exhibits the higher sensitivity
to defect structures with wide size distributions as compared with any of these methods
alone. In the investigated Czochralski-grown silicon crystals, the sizes and concentrations
of small oxygen precipitates as well as small and large dislocation loops have been
determined using this method.
Keywords: dynamical scattering, triple-crystal diffractometer, double-crystal
diffractometer, microdefects.
Manuscript received 20.06.10; accepted for publication 02.12.10; published online 30.12.10.
1. Introduction
Silicon single crystals contain microdefects (MDs) of
different types and sizes ranged from nano- to
micrometers [1]. Such complicated defect structures
arise both during crystal growth and in consequence of
various technological treatments. Besides, disturbed or
distorted surface layers are present in these crystals with
strains caused by intentional modification or due to
natural surface relaxation, including strains due to
“mirror image forces” from point defects [2] and MDs
[3]. The consecutive and self-consistent description of
X-ray diffraction patterns from such crystals, which are
measured by high-resolution double- (DCD) or triple-
crystal (TCD) X-ray diffractometers, should take into
account the influence of all the above mentioned factors
on the reflectivities of investigated samples.
The TCD measurements provide the most complete
diffractometric characterization of both defects in the
crystal bulk [4-6] and strains in disturbed surface layer
[7]. However, when analyzing diffraction patterns, the
consideration is usually limited to the investigation of
the diffuse scattering (DS) intensity distributions only in
those reciprocal space regions where the coherent
component can be neglected [8-9]. Such approach can
cause systematical errors when determining defect
characteristics. There exist also restrictions connected
with the low sensitivity of reciprocal space maps
measured by TCD in the cases when MDs have very
small radii and corresponding DS intensity distributions
are very smooth, or MDs have very large radii and
corresponding DS peaks are located within the total
reflection range.
The DCD measurements provide more sensitive
characterization of MDs with very small radii due to the
additional integration of DS intensity over the horizontal
divergence. However, the determination of MD
characteristics and, especially, parameters of disturbed
surface layers by this method can be ambiguous [10, 11].
The circumstances stated above lead to the idea of joint
using both diffractometric methods with the aim to
compensate disadvantages of each of them by
advantages of the another one [12].
In this work, the analytical expressions for the
description of X-ray diffraction profiles measured by
DCD [13-16] and TCD [17-19] from single crystals with
homogeneously distributed defects of several types and
disturbed surface layers, which take into account also the
DS intensity from defects in monochromator and
analyzer, have been used to develop the combined
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
353
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 353-356.
method for the characterization of defect structures in
single crystals with joint treatment of DCD and TCD
profiles. It should be emphasized that the used approach
[13-19] allows to consider the X-ray scattering in
crystals containing MDs of arbitrary sizes due to account
for multiple DS effects in coherent and diffuse
components of the diffracted intensity.
-150 -100 -50 0 50
100
101
102
Δθ = −68 arc sec
a)
Δθ' (arc sec)
In
te
ns
ity
(c
ps
)
2. Experimental
The investigated Czochralski-grown silicon sample has
been cut from the central part of 10 cm wafer with (111)
surface plane perpendicular to the growth direction. The
wafer was of р-type conductivity with the resistance of
10.5 Ohm×сm. The thickness of sample after chemical
etching was 480 μm. The sample contained
and less than of oxygen
and carbon atoms, respectively, and was annealed at
750 °С for 50 h in argon atmosphere under 150 kPa
pressure.
318 cm101.1 −⋅ 317 cm10 −
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Measurements of diffraction profiles in the
symmetric Bragg reflection geometry have been carried
out near the reciprocal lattice point (111) in
dispersionless scheme (n, –n, n) by automated TCD with
widely open detector window. The RCs have been
measured when the investigated sample was mounted on
analyzer place and two monochromators in dispersion
position were mounted on first two axes. Thus, the
scheme of DCD measurements was (m, m, –n). At the
treatment of DCD profiles, vertical and horizontal
divergences as well as dispersion of X-ray beam were
taken into account.
3. Treatment and analysis of measurement results
The TCD method has a low sensitivity to small nm-sized
MDs (and to large MDs with sizes of the order of the
extinction length) because DS intensity from these MDs
is very weak in measured reciprocal space regions. On
the other hand, DCD method has high sensitivity to both
small and large MDs due to the additional integration of
DS intensity over the horizontal divergence, but has a
disadvantage of the wide uncertainty range for
characteristics of MDs with intermediate sizes, what is a
consequence of the same integration. The joint treatment
of TCD and DCD diffraction profiles (Fig. 1) allows to
increase the sensitivity to MD characteristics in the
whole size range from nano- to micrometers.
Such joint treatment of measured diffraction
profiles was carried out in the iterative way, when MD
characteristics determined from TCD profiles were used
as initial ones at the treatment of DCD profiles, and vice
versa. At the treatment of the measured diffraction
profiles, we used the model of a defect structure in the
investigated silicon sample, which supposed the
presence of randomly distributed disk-shaped oxygen
precipitates and chaotically oriented circular dislocation
loops with Burgers vectors b = 〈110〉/2 [1, 15, 18].
Fig. 1. Fitted diffraction profiles (solid lines) measured by
TCD (a) and DCD (b) for Si (111) reflection of CuKα1
radiation from Czochralski-grown silicon sample annealed at
750 °С for 50 h. Dashed and dotted lines describe DS
intensities from oxygen precipitates and dislocation loops,
respectively.
The proposed method has allowed to simultaneously
determine characteristics of small and large MDs in the
crystal bulk, namely, the characteristics of small oxygen
precipitates of the radius RP = (7.7 ± 0.2) nm, thickness
hP = (2.2 ± 0.05) nm, and numeric density
nP = (2.8 ± 0.3)×1013 3cm− , as well as characteristics of
large and small dislocation loops (see Fig. 2).
Additionally, the proposed approach has allowed for
the quantitative investigation of the strain in subsurface
layer, which is caused by “mirror image forces” from
point defects and MDs. This strain was described by the
exponential law ε⊥ = ε0⊥ exp(– z /t0 ), where z is a depth,
and the parameters determined by fitting the experimental
diffraction profiles are t0 = (7.0 ± 0.7) nm and
( ) 4
0 101.00.1 −
⊥ ×±=ε (see Fig. 3).
Besides, the quantitative description of the
asymmetrical behaviour of pseudo-peak heights on TCD
profiles measured at opposite deviation angles of the
investigated sample has allowed to determine the
characteristics of dislocation loops in TCD
monochromator, which has been made of Czochralski-
grown silicon crystal, namely, RL = (1.0 ± 0.03) μm and
nL = (1.1 ± 0.1)×108 . 3cm−
-200 -100 0 100
10-3
10-1
b)
Δθ (arc sec)
R
ef
le
ct
iv
ity
354
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 353-356.
0,01 0,1 1 10
108
1010
1012
0.1
N
um
er
ic
d
en
si
ty
(c
m
−3
)
Loop radius (μm)
0.01
Fig. 2. Determined numeric density of dislocation loops (sizes
of markers correspond to error bars).
0 10 20 30
0,00000
0,00003
0,00006
0,00009
0.00003
0.00006
ε
z, nm
0.00009
Fig. 3. The strain profile caused in a subsurface layer by
“mirror image forces” from point defects and MDs in the
investigated silicon single crystal.
In the whole, the proposed complex diffractometric
method with using the analytical formulas of the
generalized statistical dynamical theory for X-ray
scattering by real single crystals offers the new
possibilities for the extended quantitative
characterization of the defect structures in imperfect
single crystals.
4. Conclusion
Thus, the joint treatment of DCD and TCD diffraction
profiles can substantially improve the completeness and
uniqueness of characterization of complicated defect
structures in real single crystals. Of course, the key role
in the adequate treatment of measurement results is
played by applying the formulas of the generalized
statistical dynamical theory for X-ray scattering by real
single crystals, which allows to self-consistently
describe the coherent and diffuse scattering intensities.
The exclusive importance of account for the
simultaneous presence of various-type MDs for the
correct interpretation of diffraction patterns from silicon
crystals (see, e.g., also [6, 20, 15]) should be emphasized
as well.
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