Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals
The methods of numerical calculations based on the formulae of the X-ray dynamic scattering theory by real crystals and of the Takagi-Topin equations were used for investigation of the basic regularities of inherent to the Bragg diffraction in conditions of a strong and weak absorption. The mechanis...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
1999
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| Cite this: | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals / V.P. Klad'ko, D.O. Grigoriev, L.I. Datsenko, V.F. Machulin, I.V. Prokopenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 157-162. — Бібліогр.: 19 назв. — англ. |
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| author | Klad'ko, V. P. Grigoriev, D.O. Datsenko, L.I. Machulin, V.F. Prokopenko, I.V. |
| author_facet | Klad'ko, V. P. Grigoriev, D.O. Datsenko, L.I. Machulin, V.F. Prokopenko, I.V. |
| citation_txt | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals / V.P. Klad'ko, D.O. Grigoriev, L.I. Datsenko, V.F. Machulin, I.V. Prokopenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 157-162. — Бібліогр.: 19 назв. — англ. |
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| description | The methods of numerical calculations based on the formulae of the X-ray dynamic scattering theory by real crystals and of the Takagi-Topin equations were used for investigation of the basic regularities of inherent to the Bragg diffraction in conditions of a strong and weak absorption. The mechanisms of profile formation of a spatial intensity distribution of diffracted beams depending on an energy of radiation and on structural perfection parameters of crystals are discussed. The formulae for an analytical description of spatial intensity distribution profiles which take into account the dynamical corrections (coefficients of extinction) for coherent and incoherent components of the total reflectivity were used.
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157© 1999, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 1999. V. 2, N 1. P. 157-162.
Introduction
The Bragg diffraction in well known as an important
tool for developing effective nondestructuve techniques
in investigations of structure defects intrinsic to thin near-
surface layers of crystals widely used in microelectronics
[1]. Despite existing opinion about weak sensitivity of
methods based on the Bragg diffraction peaks intensity
to structure defects [2], considerable attention was paid
recently [3-6] for investigation of X-ray scattering in this
case.
The revival of investigators interest to the Bragg ge-
ometry for the indicated aims is due probably to the re-
sults of papers [7-9], carried out with use of short-wave
radiation, in which the high sensitivity of integral inten-
sity to structure defects is, however, shown to take place.
In particular, the total integrated reflectivity (TIR) was
shown to increase essentially with growth of a distor-
sion level in crystals with chaotically distributed defects
at the expense of a diffuse component [10]. The contri-
PACS 81.40.-Z,61.66.Bi
Influence of absorption level on mechanisms of Bragg-
diffracted x-ray beam formation in real silicon crystals
V. P. Klad�ko, D. O. Grigoriev, L. I. Datsenko, V. F. Machulin, I. V. Prokopenko
Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kyiv, 252028, Ukraine
Abstract. The methods of numerical calculations based on the formulae of the X-ray dynamic
scattering theory by real crystals and of the Takagi-Topin equations were used for investigation of
the basic regularities of inherent to the Bragg diffraction in conditions of a strong and weak ab-
sorption. The mechanisms of profile formation of a spatial intensity distribution of diffracted
beams depending on an energy of radiation and on structural perfection parameters of crystals are
discussed. The formulae for an analytical description of spatial intensity distribution profiles which
take into account the dynamical corrections (coefficients of extinction) for coherent and incoher-
ent components of the total reflectivity were used.
Keywords: X-ray beams, Bragg-diffraction , reflectivity, extinction and absorption lengths, dy-
namical theory of scattering, structure defects, clusters.
Paper received 10.02.99; revised manuscript received 06.05.99; accepted for publication 24.05.99.
bution of this component becomes noticeable already at
t ≥ Λ , ( t =1 0/ µ , µ 0 is normal photoelectric absorption
coefficient, Λ = ⋅ ⋅λ ϑ χsin / h C is length of an extinc-
tion). The series of experimental results [11,12] does not
find, nevertheless, a convincing explanation within the
framework of the existing theories of a scattering by real
crystals, especially under the conditions of strong absorp-
tion of radiation, for example, near the absorption K-
edges. It concerns, for example, to the excess of the X-
ray dynamic scattering level in an ideal crystal in com-
parison with an ideal - mosaic crystal.
The aim of this work consisted in discovering of char-
acter and basic mechanisms of intensity losses of the
Bragg diffraction peaks at variation of incident radia-
tion energy by methods of numerical calculations using
the formulae of the dynamical theory, developed for the
TIR of crystals with homogeneously distributed defects
[6] , as well as by the method of the Takagi-Taupin (TT)
equations solution.
V. P. Klad�ko et al.: Influence of absorption level on mechanisms of ...
158 SQO, 2(1), 1999
Object and methods of investigations
Convenient objects for solution of the posed problem
are the silicon crystals containing so-called Coulomb cen-
ters of strains (clusters), which sizes and concentrations
of which are suitable to change in wide reasonable lim-
its. Besides, utilization of silicon also allows to vary a
level of absorption for the known wavelengths of a char-
acteristic spectrum over a wide range. The analytical
calculations of the TIR and its components were carried
out under the formulae of the Braggdiffraction theory
[6] for homogeneously distributed clusters. The level of
distorsions and its influence on a character of scattering
was stimulated by introduction in to the formulae for an
ideal crystal [2] the known parameters of structural per-
fection, i.e., exponent of the Debye - Waller static factor
L , and coefficients of an extinction for coherent, µ ds ,
and diffuse, µ*
components of intensity, too. TIR for a
real crystal in case of the Bragg diffraction is known to
be the sum of two parts, i.e., the Bragg (coherent) , RiB ,
and diffuse (incoherent), RiD , components :
iKiiDiBi REERRRR ⋅−+⋅=+= )1( 2
0 , (1)
where Ri0 , RiK are the integral reflectivity (IR) of an ide-
al and ideal - mosaic crystals, respectively, and
E L= −exp( ) is the static Debye - Waller factor. The
values of the mentioned parameters of structural perfec-
tion ( L ds, , *µ µ ) were varied in a rather wide interval
(0< L <1, µ µds , * up to 0.3 µ 0 ). Except TIR, the change
of its components, RiB and RiD , were also analyzed as
those depending on an energy of incident radiation and
level of distorsions for clearing up their contributions in
Ri .
Theoretical [13,14] and the experimental [10] investi-
gations have shown, that the analysis of a spatial distri-
bution profiles of a diffracted beam I x( ) allows to gain
the reliable information up on structural perfection de-
gree of crystals. However, the approaches made in [7, 8],
allow to handle experimental results only at low levels
of distorsions, L <<1. Besides , the influence of coeffi-
cient of an extinction µ* for diffuse scattered waves was
not taken into account in the mentioned papers. The ne-
cessity of such an introduction for correct describing the
TIR for a real crystal was justified much later.
Respective alterations in the formulae [7,8] were made
taking into account the results of theoretical examina-
tions of the TIR for the Bragg diffraction peak [6]. With
this purpose, the expression for a spatial intensity distri-
bution profile of a diffracted beam in an ideal absorbing
crystal was used, following [14]:
)cos/exp(
)2/(
)(
)2sin(/)()(
02
2
1
0
ϑµ
α
α
ϑ
x
x
xJ
sQIxI B
⋅−⋅
⋅
⋅
×
×⋅⋅⋅=
. (2)
Here, I0 is the intensity of a primary beam,
Q d= ⋅ ⋅π ϑ2 2cos / Λ , Λ = ⋅ ⋅λ ϑ χsin / C h is an extinction
length, d = ⋅λ ϑ/ sin2 , J x1( )α ⋅ the Bessel function of the
first order, α χ ϑ= ⋅ ⋅ ⋅C K h / cos2 , K = ⋅2 π λ/ ,ϑ is the
Bragg angle, and s is a slit width at the detector, respec-
tively.
In a real crystal, the diminution of the coherent
component (2) happens at the expense of intensity tran-
sition in a diffuse background described by the factor
exp( / cos )− ⋅µ ϑds x . Besides, this diminution is pos-
sible to be taken into account also by renormalization of
the Fourier components of a suspectibility χ h on χ h E⋅
according to [6]. Intensity of diffuse background can be
submitted according to [5] as follows:
I x I R x xD o iD
kin( ) ( ) ( )= ⋅ ⋅ Π , (3)
where R x
Q s
E EiD
kin ( )
sin
( ) /= ⋅ ⋅ −
2
1 2 2
ϑ
and
[ ]Π( ) exp ( )*x x= − + ⋅µ µ0 .
Thus, distribution of a total intensity in the Bragg
profile of a reflected beam in crystals with defects can be
written as:
I x I x I xB D( ) ( ) ( )= + , (4)
taking into account the results of [6]. For analysis of
the profile of a possible intensity spatial distribution of
a diffracted beam and its evolution the calculations were
carried out by means of (2 - 4) and using the Takagi-
Topin (TT) equations solution [15,16] for specific peri-
odic (ultrasonic) strains. It was done for confirmation
of an admissibility of the offered analytical approach for
describing of regularities of scattering by a distorted crys-
tal. The extend and the amplitude of distortions in the
last case can be easily varied. The approach of the so-
called short wavelengths ( λ s << Λ ) was used. Such ap-
proach to modeling the structure distortions in relation
to their influence on a X-ray scattering corresponds most
closely to the case of homogeneously distributed lattice
defects. The level of a lattice distortions was character-
ized by dimensionless parameter HW ( H d= 1/ is a vec-
tor of reciprocal lattice, W is an amplitude). This value
was varied in the interval from 0 up to 2. The physical
sense of the parameter HW for a shortwave ultrasound
is virtually close to concept of the Debye-Waller static
factor [17] in real crystals with structure defects.
The calculations were carried out for the most strong
Bragg reflection, 111, and the following wavelengths of
X-rays: WK AgK MoK CuKα α α α, , , , as well as for soft radi-
ations with λ = 2 � and λ = 3�.
Results of numerical simulations
Let us consider first the behavior of TIR for various lev-
els of structure distortions in a crystal characterized by
an exponent of the Debye-Waller static factor, L . With
this purpose, the results of computation of the depen-
V. P. Klad�ko et al.: Influence of absorption level on mechanisms of ...
159SQO, 2(1), 1999
dences TIR, Ri , as a function of a wavelength of dif-
fracting radiation calculated using the formula (1) for
an ideal and for an ideal - mosaic (the kinematic limit)
crystals are given in the Table together with the TIR
Ri1 ÷ Ri3 for the samples with defects. The higher the level
of parameter L , the more the TIR value of a distorted
crystal. This does not contradict the majority of known
experimental results obtained by different authors for
the Bragg case of X-ray diffraction. Thus, the gaps be-
tween RiK and Ri0 , which make it possible to discrimi-
nate samples with various degrees of structural perfec-
tion, decrease with increasing wavelength, though the
absolute values of the TIR increase under these condi-
tions. Analysis of the Ri values for real crystals (with
structure defects ) shows that the level of the TIR with
growing λ (for example for λ > 2 �) is caused by an
essential enhancement of absorption, can be even small-
er, than R is . Such behaviour of intensity with increas-
ing a level of distortions was known earlier for the Laue
case of diffraction of X-rays in the approach of a thick
crystal, when the Borrmann effect is realized. One should
note that not only Ri0 , but also Ri1 ÷ Ri3 are less than
the relevant value of a kinematic reflectivity, RiK , in the
wide interval of wavelengths ranging from λ = 0.5593 �
to λ = 1.930 �.
The diagnostics of structural perfection degree of a
sample becomes impossible near the point, where
Ri1 ÷ Ri3 are equal to value Ri0 . It is important to note
that the diminution of the TIR for a longwave (soft)
radiation at some level of distortions characterized by
parameter L can take place instead of increase of this
characteristics. It means that the energy dependence
R fi = ( )λ in a wide interval of wavelengths is non-mono-
tonic. This peculiarity of considered dependence behav-
iour is observed at large values of the static factor, when
the known analytical expressions for the TIR require the
extra analysis [4]. One of the most important result fol-
lowing from the performed calculations consists in weak
influence of extinction parameter µ ds for hard radiation,
when the so-called one-parametric approach in describ-
ing of a TIR permissible, which was shown earlier in the
case of Laue-diffraction [18]. The carried out calculations
also show that the shortwave region of X-ray spectrum
at the Bragg diffraction is the most sensitive to structure
defects (because of greatest gap ∆r R RiK i= − 0 ). The im-
portant characteristics of a scattering for the analysis of
the TIR variations in the Bragg case of diffraction is also
the parameter g i rh= χ χ0 / [19], which characterizes a
relation of contributions of a scattering and absorption.
The analysis of character of energy dependence varia-
tions of this parameter shows, however, that more im-
portant for structural diagnostics is the decrement of R i ,
i.e., ∆R R Ri i= − 0 . Really, the ∆R decreases with increas-
ing of a wave length (see the Table) though the parame-
ter g grows (Fig. 1).
The Bragg spatial intensity distributions I x( ) calcu-
lated for the first time using the formula (4) for various
wavelengths are given for a set of structural perfection
parameters (Fig. 2). As it follows from the analysis of
the obtained results, enhacement of a lattice distortion
degree results in noticeable growth of diffuse scattering
intensity on large penetration depths of X-rays (t >> Λ ).
Thus, the dependences ln ( ) ( )I x f x= in the thickness re-
gion (t >> Λ ), which are not considered here for short-
nese, are linear with a slope ( )*µ µ0 + . It means that the
role of an extinction coefficient µ*
at a diffuse scattering
is essential. The magnitude of the Bragg maximum, i.e.,
the first Uragami peak, decreases in accord with the for-
mula (3). As the slope of the indicated function for a ki-
nematic limit of intensity is equal µ 0 , with growth of a
Table. The TIR values and increments ∆∆∆∆∆R for various wavelengths (reflection 111) in silicon crystals with a various structure
perfection degree.
λ, Å R i0×105
R i1×105,
∆R=R i1-R i0
×105
R i2×105,
∆R=R i2-R i0
×105
R i3×105,
∆R=R i3-R i0
×105
R iK×104,
∆R=R iK-R i0
×104
0.5593 1.49 1.74
0.26
1.95
0.46
1.94
0.45
7.49
7.341
0.709 1.88 2.12
0.24
2.33
0.45
2.31
0.43
6.09
5.902
1.54 3.88 4.01
0.13
4.11
0.23
3.985
0.1
2.8
2.412
1.93 4.75 4.82
0.07
4.87
0.12
4.65
-0.1
2.3
1.825
The note: reflectivities for ideal crystal; (R io ) and real crystals (R
i1
, L = 0.05; R
i2
, L = 0,1; R
i3
, L = 0, 1, µds = 0,3 µ 0 ).
Ideal-mosaic sample reflectivity is denoted by R ik .
V. P. Klad�ko et al.: Influence of absorption level on mechanisms of ...
160 SQO, 2(1), 1999
distortion degree in a crystal, the quantity µ* tends, re-
spectively, to zero, reducing the velocity of intensity
diminution with a depth. The diminishing contribution
of coherent component, observed at small values x (in
the limits of Uragami peak) also favors this process. From
the physical point of view, the drop of a level µ* is pos-
sible to treat, as diminution of a primary extinction for a
diffuse scattering at enhancement of lattice disordering
degree.
Most of typical profiles of a spatial intensity distri-
bution for a diffracted X-ray beam, obtained using the
numerical solution of the TT equations are given in the
Fig. 4 for the case of ultrasonic strains [16] considering
series of wavelengths and the parameter HW levels. Some
diminution of a coherent maximum and origin of a �dif-
fuse� scattering near its �pedestal� are observed at small
values of the HW in this figure. Its contribution increas-
es with diminution of a wavelength of used radiation. At
large HW values the diminution of maximum is more
considerable for the wavelengths λ > 2 �, where the val-
ues of diffuse component reach a maximum in such a
manner that its behaviour is described already by the
laws of a kinematical scattering.
Influence of possible X-ray scattering mechanisms on
the Bragg TIR
The fulfilled numerical experiments confirm that the TIR
of a real crystal in the Bragg case of diffraction is formed
as the sum of the coherent and incoherent components.
Thus, the presence both Coulomb centres of strain and
displacement caused by ultrasonic waves results in the
following diffraction phenomena:
� Diffuse smearing out of the reciprocal lattice points
(broadening of diffraction peaks);
� Appearance of interior sources of incoherent dif-
fracted beams due to again scattered radiation observed
in the case of ultrasonic strains [16];
� Drop of intensity of a coherent component, pro-
portional to exp( )−L , resulted in diminution of the co-
herent Uragami peak on curves of a spatial distribution
(Fig. 3).
The intensity of diffuse component of a TIR is there-
fore determined by the competition of two factors: 1) by
growth of the RiD with enhancement of scattering vol-
ume and level of distortions; 2) by its exponential ab-
sorption at the expense of the total factor of absorption
µ µ0 + * . Character of a relation of formation depths
of a coherent maximum and appearence of the �diffuse�
scattering �pedestal�, as a function of a wavelength, is
shown in the Fig. 4 which exhibits an advantage of utili-
zation just short wavelengths in an experiment follows.
Let us consider character of different TIR compo-
nents variations with a changing wavelength. In the case
of short wavelengths (weak absorption) the extinction
length increases, while the absorption constant sharply
drops ( µ ~ λ3 ). The curve I x( ) is essentially expanded
due to deep penetration of X-rays into a crystal. Defects,
beginning from some particular level of distortions, cre-
ated by them, result in diminution of coherent compo-
0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
111
333
[g
]
λ,
0,00 0,01 0,02 0,03 0,04 0,05
5,0x10-6
1,0x10-5
1,5x10-5
2,0x10-5
2,5x10-5
3,0x10-5
3,5x10-5
Si, AgKα
1
, 111
Perfect
HW=0.15
HW=0.5
HW=1
HW=1.5
HW=2
t, cm
R
i
Fig. 1. Dependence of the absorption and scattering relation
factor g for the reflections 111 and 333 in Si crystals on a wave-
length of X-rays.
Fig. 2. Profiles of a spatial intensity distribution of Bragg dif-
fracted beams, calculated with the help of the numerical solu-
tion of the Takagi-Topin equations for various levels of the
parameter HW. AgKα1 radiation, 111 reflection.
V. P. Klad�ko et al.: Influence of absorption level on mechanisms of ...
161SQO, 2(1), 1999
nent, which can not be compensated by the growth of a
incoherent part of the TIR registrated in our experiments,
because of very high values of the photoelectric absorp-
tion coefficient µ 0 in the case of longwave radiation.
As it follows from results of the carried out calcula-
tions, the peak value of intensity in the region of the
�pedestal� of a curve of spatial intensity distribution can
be described by some enveloping curve (formula (3)).
Thus, the behaviour of the TIR at high levels of absorp-
tion and lattice distortions is mainly determined by the
contribution of coherent part of scattering, as far as the
incoherent one reaches a maximum and then tends to
the limit described by the kinematic theory, where the
factor 2L defines a scattering volume of a crystal which
is situated in a reflecting position.
The effects, discussed in the paper, are the basis of
sensitivity of radiation with some wavelengths at Bragg
diffraction to structural distortions of a lattice. In this
connection utilization of diffuse scattering of soft radia-
tion, which is strongly absorbed in a crystal and does
not reach a surface, is not desirable for structural diag-
nostics of real crystals. It completely confirms conclu-
sions made earlier [5, 6].
Conclusions
1. Character of the X-ray interferential interaction
with a substance in geometry of Bragg diffraction is de-
termined by a value of the relation of imaginary and
real parts of the Fourier coefficient of a crystal succepti-
bility and essentially depends on a wavelength. The sen-
sitivity of a X-ray scattering to structure defects increas-
es with enhancement of this relation, though a difference
of the TIR values for a real (measured) and for a perfect
crystal is the most important for a structure diagnostics.
The modeling of influence of structure defects of a vari-
ous type (Coulomb centres, periodic strains) within the
framework of the dynamic theory of a scattering by crys-
tals with homogeneously distributed defects, or, as it has
been shown using the Takagi-Topin equations solutions,
the level of a kinematical scattering always exceeds the
dynamical one. Using a hard radiation, one can reach
rather high sensitivity of the intensity of the Bragg-re-
flections to lattice strain level described by the parame-
ter L , or HW . With increasing their level the gradual
transition I IB Kin→ is observed.
2. The dependence of the TIR on a level of distor-
tions has monotonous character for a Bragg diffraction
of soft radiation. With an increase of a distortion level,
the behaviour of the TIR in Bragg case of diffraction is
determined by the contribution of a coherent compo-
nent. Therefore, depending on a type, size and concen-
tration of defects, it is possible to reach an enhancement
(small values of µ ds ),as well as the diminution of the
TIR. The last on was known earlier for the Laue case
diffraction (Borrmann effect).
3. One can conclude, that particular caution in inter-
pretation of experimental results should be taken into
account by utilizing of soft radiation for structural diag-
0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
0
50
100
150
200
250
300
333
111
t/
Λ
λ,
Fig. 3. Profiles of a spatial intensity distribution of the Bragg-
diffracted beam of X-rays calculated under the formulae
(2) � (4) for different values of structural perfection parame-
ters: 1 � ideal crystal; 2 � real crystal (L = 0.05); 3 � real crystal
(L = 0.1, µ µds = ⋅0 3 0. ). AgKα1 radiation, 111 reflection .
Fig. 4. A relation of absorption and extinction lengths as func-
tion of a wavelength for the reflections 111 and 333 in Si crys-
tals.
0,000 0,005 0,010 0,015 0,020 0,025
0,0
2,0x10-5
4,0x10-5
6,0x10-5
R
i
1
2
3
t, cm
V. P. Klad�ko et al.: Influence of absorption level on mechanisms of ...
162 SQO, 2(1), 1999
nostics of boundary layers with the help of the TIR anal-
ysis.
4. Analytical calculations of curves of a spatial in-
tensity distribution of the Bragg diffraction peaks by
means of the dynamic theory of a scattering of radia-
tions by real crystals, are in the whole adequate to data
of the Takagi-Topin equations solution and describe sat-
isfactorily the behaviour of measured reflectivity as well
as the character of a spatial intensity distribution in a
wide interval of wavelengths and absorption levels.
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| id | nasplib_isofts_kiev_ua-123456789-119062 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T16:38:51Z |
| publishDate | 1999 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Klad'ko, V. P. Grigoriev, D.O. Datsenko, L.I. Machulin, V.F. Prokopenko, I.V. 2017-06-03T04:54:58Z 2017-06-03T04:54:58Z 1999 Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals / V.P. Klad'ko, D.O. Grigoriev, L.I. Datsenko, V.F. Machulin, I.V. Prokopenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 157-162. — Бібліогр.: 19 назв. — англ. 1560-8034 PACS 81.40.-Z,61.66.Bi https://nasplib.isofts.kiev.ua/handle/123456789/119062 The methods of numerical calculations based on the formulae of the X-ray dynamic scattering theory by real crystals and of the Takagi-Topin equations were used for investigation of the basic regularities of inherent to the Bragg diffraction in conditions of a strong and weak absorption. The mechanisms of profile formation of a spatial intensity distribution of diffracted beams depending on an energy of radiation and on structural perfection parameters of crystals are discussed. The formulae for an analytical description of spatial intensity distribution profiles which take into account the dynamical corrections (coefficients of extinction) for coherent and incoherent components of the total reflectivity were used. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals Article published earlier |
| spellingShingle | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals Klad'ko, V. P. Grigoriev, D.O. Datsenko, L.I. Machulin, V.F. Prokopenko, I.V. |
| title | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals |
| title_full | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals |
| title_fullStr | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals |
| title_full_unstemmed | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals |
| title_short | Influence of absorption level on mechanisms of Braggdiffracted x-ray beam formation in real silicon crystals |
| title_sort | influence of absorption level on mechanisms of braggdiffracted x-ray beam formation in real silicon crystals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119062 |
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