X-ray diffraction study of deformation state in InGaN/GaN multilayered structures
High resolution X-ray diffractometry (HRXRD) was used to investigate InxGa₁₋xN/GaN multilayered structures grown by the metal-organic chemical vapor
 deposition (MOCVD) method. Deformation conditions in the superlattice (SL) and its
 separate layers, degree of relaxation in the struc...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Дата: | 2010 |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2010
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | X-ray diffraction study of deformation state in InGaN/GaN
 multilayered structures / V.P. Kladko, A.V. Kuchuk, N.V. Safryuk, V.F. Machulin, A.E. Belyaev, R.V. Konakova, B.S. Yavich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 1. — С. 1-7. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860248078082113536 |
|---|---|
| author | Kladko, V.P. Kuchuk, A.V. Safryuk, N.V. Machulin, V.F. Belyaev, A.E. Konakova, R.V. Yavich, B.S. |
| author_facet | Kladko, V.P. Kuchuk, A.V. Safryuk, N.V. Machulin, V.F. Belyaev, A.E. Konakova, R.V. Yavich, B.S. |
| citation_txt | X-ray diffraction study of deformation state in InGaN/GaN
 multilayered structures / V.P. Kladko, A.V. Kuchuk, N.V. Safryuk, V.F. Machulin, A.E. Belyaev, R.V. Konakova, B.S. Yavich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 1. — С. 1-7. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | High resolution X-ray diffractometry (HRXRD) was used to investigate InxGa₁₋xN/GaN multilayered structures grown by the metal-organic chemical vapor
deposition (MOCVD) method. Deformation conditions in the superlattice (SL) and its
separate layers, degree of relaxation in the structure layers, as well as the period of the
SL, thicknesses of its layers and composition of InxGa₁₋x solid solution in active area
were determined. It was found that SL was grown on the relaxed buffer layer. SL layers
were grown practically coherent with slight relaxation of InGaN layer (about 1.5 %). The
role of dislocations in relaxation processes was established. Analysis of experimental
diffraction spectra in these multilayered structures within the frameworks of ParratSperiozu
was adapted for hexagonal syngony structures.
|
| first_indexed | 2025-12-07T18:39:41Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 1. P. 1-7.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
1
PACS 61.05.cp, 64.75.Nx, 78.55.Cr, -m, 78.67.De, Hc, 81.07.St
X-ray diffraction study of deformation state in InGaN/GaN
multilayered structures
V.P. Kladko, A.V. Kuchuk, N.V. Safryuk, V.F. Machulin, A.E. Belyaev, R.V. Konakova, B.S. Yavich1
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
1CJSC “Svetlana-Optoelectronics”, St.-Petersburg, POB 78, 194156 Russia
Abstract. High resolution X-ray diffractometry (HRXRD) was used to investigate
InxGa1−xN/GaN multilayered structures grown by the metal-organic chemical vapor
deposition (MOCVD) method. Deformation conditions in the superlattice (SL) and its
separate layers, degree of relaxation in the structure layers, as well as the period of the
SL, thicknesses of its layers and composition of InxGa1−x solid solution in active area
were determined. It was found that SL was grown on the relaxed buffer layer. SL layers
were grown practically coherent with slight relaxation of InGaN layer (about 1.5 %). The
role of dislocations in relaxation processes was established. Analysis of experimental
diffraction spectra in these multilayered structures within the frameworks of Parrat-
Speriozu was adapted for hexagonal syngony structures.
Keywords: high resolution X-ray diffractometry, multilayered structure, deformation
characteristics.
Manuscript received 15.08.09; accepted for publication 22.10.09; published online 04.12.09.
1. Introduction
Multilayered epitaxial structures (nanoheterostructures)
based on InGaN/GaN solid solutions are widely used to
fabricate light-emitting diodes (LED) for visible and UV
bands [1-3].
For these structures, large mismatches of lattice
parameters are typical, which are caused by strain fields
that results in appearance of strong piezoelectric fields
[4, 5]. In addition, a large density of dislocations,
interface roughness, composition fluctuations are
inherent to these structures. Such a situation results in
deterioration of optical properties of these structures.
Therefore, the rise of efficiency and broadening the
spectral band for LED is one of the main trends in
current technology of nanoheterostructures.
Consequently, the investigation of the defects nature
and deformation state of these systems is an urgent
problem for both production process providing layers with
different electron potential and understanding the
influence of these effects on electronic devices
performance. Growing the various intermediate buffer
layers makes it possible to compensate mismatch stresses
and improve crystalline perfection of heterostructures.
X-ray diffractometry is used to determine structural
(geometrical) parameters of multilayered systems, such
as composition and thickness of separate layers, as well
as sequence of their arrangement [6-10]. Besides, the
rocking curves contain information concerning the
sharpness of heteroboundaries (the presence of
transitional layers), the strain inside layers as well as
structural perfection of epitaxial layers and composition,
the type of defects and their parameters.
Some aspects of the X-ray diffractometry
implication for the investigation of InGaN/GaN
multilayered epitaxial structures and for determination of
structural and deformational parameters are considered
in this work.
2. Samples and experimental technique
X-ray study was carried for samples based on
InGaN/GaN grown by metal organic chemical vapor
deposition method of hybrid epitaxy (MOCVD) on
(0001) sapphire substrates. The quantum wells (QW)
composition was uniform and adjusted to emit the
wavelength close to 460 nm. Nominal composition of
InGaN was within the range of 12-15 % In content. The
samples consist of low temperature nucleation GaN-
layer grown on the sapphire substrate, 3.5-µm thick n-
GaN buffer layer, buffer five-periods SL (the thicknesses
of QW was 2.5 nm and GaN barrier – 4-5 nm), and
active region which contains five InGaN/GaN QWs, 20-
nm thick current locking р-AlGaN layer, and 0.1-µm
thick p-GaN-layer. The nominal thicknesses of QW and
quantum barrier were 2.5 and 9 nm, respectively.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 1. P. 1-7.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
2
The measurements were performed using
“PANalytical X’Pert PRO MRD” high resolution
diffractometer for symmetric (000l) and asymmetric (–
1–124) reflections. The experimental setup makes it
possible to obtain two cross-sections of the reciprocal
lattice nodes – transversal to the diffraction vector, ω-
scan, and in parallel to it, ω–2θ-scan. Triple-axis
diffractometry provides a mean for separation of the
effects of interplane spacing changes and atomic plane
rotation, therefore, analysis of the intensity distribution
in xq , yq coordinate system, directed along and normal
to H-vector, respectively, makes it possible to separate
each of these contributions separately [8, 9]. The
macrodeformations that cause the sample bending were
estimated by the system curvature radius determined by
the measurement of the changes in the reflection angles
from sapphire reflection during linear scanning of the
sample along X-ray beam [11].
The following structural parameters were used in
this work. GaN: a = 3.1896±0.0003 Å, c =
5.1855±0.0002 Å, c/a = 1.6258±0.0002; p = 0.53 [12];
InN: a = 3.5378±0.0001 Å, c = 5.7033±0.0001 Å, c/a =
1.6121±0.0001; p = 0.49 [13].
3. The model of X-ray diffraction for multilayered
structures (MS)
Superlattice (SL) represents periodical sequence of two
alternating layers with different composition. Coherent
two-layered superlattice with sharp heteroboundaries is
characterized by four main parameters: the period T, the
thickness ratio of two layers t1/t2, the compositions of the
layers х1 and х2, which determines the interplane spacing
in the layers d1 and d2 and their structural factors F1 and
F2. The number of parameters is reduced to two, if SL
consists of pure element layers (for example AlN/GaN).
Three parameters are used in the case when one of the
layers is a ternary solid solution (e.g., InxGa1–xN/GaN).
Typical rocking curve from SL has two systems of
oscillations – periodical intensity distributions
depending on the incident angle (see Fig. 1). The first
system represents the thickness oscillations which are
typical for any reflection from thin layer, and the second
one represents periodically distributed satellites, caused
by periodical distribution of the interplane spacing d(z)
and dispersion capacity F(z) throughout the crystal
depth.
In most cases, rocking curves elude analyzing
because of blurring of heteroboundary, close
compositions of layers, etc. Thus, obtaining the real
structural parameters from the rocking curves requires
the fitting calculation of diffraction reflections.
The reflection coefficient of MS in the semi-
kinematical approximation [14] is given by:
2
0 LiAAR , (1)
where А0 is the amplitude of dynamic reflection from the
substrate:
12
0 yyA , (2)
and AL is the kinematical amplitude of a surface structure
calculated as a sum of reflection amplitudes for
individual layers:
n
i
i
i
iii i
fy
Kufy
AL
1
)exp(
])sin[(
. (3)
The phase i takes into account individual phases
of each i-layer as well as phase progression inside lower
layers and can be calculated as:
1
1
)(2)(
i
k
kkiii ufyufy . (4)
/tu is the reduced thickness, – length of
extinction.
In the general case of asymmetric diffraction for
coherent systems, reduced angle displacement is equal to
HH
y
02sin
, (5)
where angle is reckoned from the substrate peak.
Reduced deformation
HH
HHj
zzjf
00 (6)
is the reflection centre of i-th layer in the y-scale, and the
thickness of layers u is expressed in fractions of the
extinction length. The quantities ||/|| 0FFK ii take
into account the difference of structural factors Fi of the
layer and F0 of the substrate.
For superlattices, summation (3) is carried out only
for two layers that make the period. Let us determine an
appropriate value as a structural factor for SL FSL, but the
total scattering amplitude is equal to:
])1(exp[
sin
sin
mi
m
FA SLSL , (7)
where
2211 ufyufy . (8)
If the denominator in (7) is equal to zero (Ф = n ),
we obtain the angle position of n-th satellite, if the
numerator is equal to zero, we obtain the position of
thickness oscillation.
As is seen from (7), the satellites intensity is
determined by FSL values in these angular positions.
According to [15], the intensity of zero satellite with the
angle position y0 is equal to:
22
21
22
22 )(
)(
))((sin
2
0 muu
ufy
ufy
J
. (9)
Quantity (y0 – f2) u2= – (y0 – f1) u1 (let us denote it
as В) can be expressed as:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 1. P. 1-7.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
3
cos
21
21
tt
tt
SB , (10)
where is the relative difference of interplane spacings
(normal to the surface) of two layers = 2(d2 –
d1) / (d2 + d1). The first factor in equation (4) shows
dependence of B on the order of reflection. Intensities of
other satellites can be analytically expressed as a
function of SL parameters. This function is proportional
to the total thickness of SL. But the relative intensity of
satellites with respect to the zero-satellite height will be
independent of the number of superlattice periods and
can be written as:
,
sin
)(
)()()(sin 22
0
B
B
anB
anaBK
a
naB
naB
J
Jn
(11)
where а = / (1 + t2/t1). The relative intensity of
satellites is the function of three unknown quantities: the
parameter of deformation В, the ratio of thicknesses of
two layers b = t2 / t1, and ratio of their structural factors
K = F2 / F1. Period T is involved implicitly through В
value. Using the expressions (10) and (11) makes it
possible to replace the intensity fitting of the whole
rocking curve from SL by calculation of intensity for
particular angular points, namely, the satellites maxima.
In the majority of cases, the parameter B exerts the
biggest influence on the shape of rocking curve from SL.
Its value can be increased due to the rise of both lattice
mismatch of two layers and SL period growth. Certainly,
absolute intensity values and their angle range will be
different. The higher B value, the higher is the intensity
of side satellites in comparison with zero satellite, all
other factors being equal, and for B > /2 zero satellite
can become lower than side satellites. In this case, a
problem with identification of zero satellite arises.
In another limiting case, for small values of B, the
intensity of side satellites decays fast, and at B < 0.1 only
the first order satellites can be observed. Reduction of В
is achieved not only by and T reduction, but also by
reduction of one of the layer thickness at a constant period.
For the SL parameter-matched solid solutions (В = 0),
side satellites appear at the expense of structural factors
difference. The relative intensity of these satellites is
expressed by a simple formula:
22
21
2
2
2
0
)1(
/
)/(sin
Ktt
Kt
Ttn
Ttn
J
Jn
. (12)
As the expression (12) suggests, the curve must be
symmetric, and the intensity of side satellites reduces
rather slowly, if one layer is much thinner than another
one.
There are two parameters of the superlattice that
can be determined directly from rocking curves. The
period Т can be obtained from satellites spacing , and
average interplane spacing d can be obtained from the
angle between the central superlattice (zero-satellite) peak
and substrate peak. We can calculate unknown values of B,
b, and k from relative satellites intensities (if their
number on the experimental curve exceeds three,
including zero-satellite). We need only these quantities
to calculate all four parameters of coherent SL.
However, it takes place for an ideal case only. The
sensitivity of satellites intensity to b and K values
depends on their change intervals. It can be very low that
prevents to determine peaks with a sufficient accuracy.
For the case when one of the layers is much thinner
than another (b << 1), which takes place in multilayered
quantum wells, the parameter B depends on product of
mismatch and thin layer thickness only, and represents
phase shift of waves, diffracted by thick layer and
caused by the presence of thin layer.
2tB . (13)
This product also determines an average interplanar
spacing in superlattice and angular position of zero-
satellite. Thus, the number of parameters that can be
obtained from a diffraction curve reduces to three.
Real structures will differ from the two-layered
system with sharp heteroboundaries. Possible blurring of
interfaces and the presence of additional buffer and
coating layers in the heterosystem effect on the shape of
diffraction rocking curve. However, in all cases the two-
layered structure can be considered as the first
approximation, which can be used to obtain initial
parameters for their further improvement by simulation
of curves and fitting procedure.
4. Results and discussions
The experimental double-crystal (1) and triple-axis (2)
diffraction rocking curves and calculated spectrum (3) of
symmetric reflection 0002 are presented in Fig. 1.
These rocking curves contain two systems of
satellites: system from main SL and that from buffer SL
with lower intensity and fewer satellites. Position of zero
satellite on this picture is blurred by buffer GaN peak
having a strong diffuse component.
Diffraction rocking curves from SL contain two
systems of oscillations – periodic intensity distribution
depending on the incidence angle – “fast” oscillations,
which are typical for reflection from the thin layer or the
whole structure, and periodically located satellites (Sn)
up to the second order, which testify good periodicity of
grown structures. The splitting of zero satellite observed
in the experimental rocking curve cannot be explained
by oscillations of the thickness. As we can see from
simulation results, this is the influence of the cover
layer, which provides reflection in the zero satellite
region of main SL. We cannot estimate indium content
inside QW of buffer SL from experimental spectra,
because it is under the influence of zero satellite region
of the active SL, coating layer and GaN buffer layer.
This issue can be solved by simulation of the structure
spectra. This simulation provides indium content of
about 8-10 %.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 1. P. 1-7.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
4
Fig. 1. –2-scans for symmetric reflection 0002 for
InxGa1–xN/GaN SL grown on buffer layer GaN and calculated
data. nS – satellites of active SL, nS – satellites of buffer SL.
The period T and the average interplanar spacing
d are obtained immediately from rocking curves of SL:
T – from the spacing between two satellites :
)2(sin B
hT , (14)
d – from the angle between the substrate peak and
central peak from SL (zero satellite):
h
h
Bd
dd
dd
0
2
)(tg/)/(
0
0 . (15)
For epitaxial structures of hexagonal syngony
grown in plane (0001)
)/(/)/( aapccdd , (16)
where p = 2c13/c33 (c and a are parameters of the
hexagonal unit cell).
Knowing these values will suffice to determine
parameters of superlattices consisting of pure
substances.
Let us note that there is no substrate peak on
rocking curves obtained from nitride films grown on
sapphire (the nearest reflection from sapphire is located
out of the measured angular interval). This substrate
peak usually serves as a datum point for determination
of buffer epitaxial layers deformation. Therefore, an
absolute scale of reflection angles should be used to
obtain a and c parameters. An analyzer was used to
measure the scattering angle 2 for GaN layer and
central SL peak.
For defect structures similar to the system under
investigation, the satellites are broadened due to the
influence of defects [16]. However, in actual practice all
satellites of SL are distorted in the same manner (if only
influence of defects, and not the mistakes in the SL
sequence are taken into account), that makes it possible to
compare the calculated curve (for ideal SL) and
experimental (distorted) rocking curves by relative height
of satellites or their integral intensity.
However, to obtain full information about structure
parameters one should calculate the reflectivity spectra.
The parameters of SL obtained using this method
and adjusted using the fitting procedure for experimental
and calculated curves are presented in Table.
The expression (15) holds if epitaxial layers have
coherent borders, i.e., the system is not relaxed. The
relaxation of elastic stresses (basically, mismatch and
thermal stresses) can proceed by different mechanisms
[17, 18]. The main one is appearance of mismatch
dislocations grid. In this case, the tangential mismatch
(d /d)|| appears in the vicinity of normal mismatch
(d /d). (For unrelaxed systems, the distances between
planes perpendicular to heterointerface are identical for
all the layers and the substrate). On the rocking curves,
the relaxation manifests itself in angular shift and
broadening the diffraction peaks in comparison with
those in elastically deformed system. However, from the
angular position of peaks for symmetric Bragg
reflections we cannot draw the conclusion that a certain
layer is elastically deformed or relaxed, if the
composition of this layer is unknown. From
measurements of asymmetric reflections, values of the
average parameter of superlattices a were determined
a = (a1t1 + a2t2) / T.
Then real parameters сi and ai were determined
from the values B, c and a for both layers of SL.
From these parameters, the In content in InGaN layer
and distribution of changes in the c parameter over the
SL thickness were established. All these data are
presented in Table and Fig. 2.
Table.
Layers
of the
structure
t,
nm
c, nm a, nm x c/a
InGaN-
SL1
3.5 0.52987 0.32309 0.01410 0.18 1.6400
GaN-
SL1
9.0 0.51744 0.31871 –
0.00561
– 1.6235
InGaN-
SL2
3.5 0.53007 0.32313 0.01560 0.07 1.6404
GaN-
SL2
3.8 0.51713 0.31887 –
0.00645
– 1.6217
The triple-axis geometry of diffraction makes it
possible to determine epitaxial structures using the
analysis of the so-called maps of the intensity distribution
around reciprocal space nodes (RSM) [19]. It is based on
the fact that the intensity of coherent scattering from
completely stressed epitaxial heterostructures is
distributed in the scattering plane in direction parallel to
the surface normal. In this direction, additional nodes,
such as the centers of reflection from separate layers, the
thickness oscillations, and satellites of superlattice, are
located.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 1. P. 1-7.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
5
Fig. 2. Schematic figure of the lattice parameter с distribution
with thickness inside strained SL InGaN/GaN grown on GaN
buffer layer. Dashed lines – с parameter for unstrained layers,
solid lines – average value of с parameter for the SL period.
This relaxation is fixed on maps of the intensity
distribution around reciprocal space nodes, which
correspond to asymmetric Bragg’s reflections, for which
the diffraction vector makes an angle with normal to
the surface n
. For completely relaxed structure nodes –
the centers of reflection of separate layers should lay along
the diffraction vector. In the case of partial relaxation,
they occupy some intermediate positions. Thus, if the
centers of intensity distribution, which correspond to two
adjacent layers or to a layer and substrate, are located on
the normal n , relaxation between them does not take
place and heterointerface is coherent. Opposite indicates
on the presence of relaxation. Our measurement of the
intensity distribution around 0002 node of the reciprocal
lattice using triple-axis diffractometry shows its
periodical character in the direction normal to the sample
surface (Fig. 3а). However, the degree of relaxation
cannot be determined from the analysis of the symmetric
RSM due to the reasons described above. RSM for 11-24
node reflection is presented in Fig. 3b.
Complete relaxation takes place if nodes lay in the
direction of the reciprocal lattice vector. In our case,
nodes (satellites) of SL lay along the surface normal, but
the whole system of satellites is shifted by some distance
from GaN buffer layer. The active SL was grown on the
buffer SL with a lower indium content. This fact testifies
that SL structure was grown on partially relaxed buffer
layer.
As A3-nitrides films grown on sapphire relax almost
completely at the growing temperature, and stresses
observed in them at room temperature are mainly
thermal, the previous reasoning can be applied to the
buffer layer, so, SL can be characterized by two
parameters of relaxation – relaxation of SL as a whole
with respect to the buffer layer and relaxation between
separate layers of SL.
(a)
(b)
Fig. 3. Intensity distribution around reciprocal lattice nodes
0002 (a) and 11-24 (b) in strained SL InGaN/GaN.
As for complete relaxation of the buffer layer, it is
related to the parameters of the lattice of the layer in free
condition and is determined with reference to the
substrate (the centers of reflection of the layer and substrate
lay along H direction). Let us note that these reasoning
relates to such structures with hexagonal syngony, in all
layers of which the ratio of dense packing c/a = 1.633
conserves.
Studied InxGa1−xN/GaN superlattices are
characterized by reasonable mismatch of lattice
parameters of two layers (more than 1 %) and relatively
small thickness of layers and total thickness of SL.
For wurtzite structures (InGaN and GaN layers)
that are grown along the hexagonal axis 0001, the
lattice parameter a determines the interplane distances in
the interface plane, parameter c – in plane perpendicular
to it. Let us designate measured parameters of i-th layer
in the system as ai and ci, and corresponding values for a
layer of the same composition in free (unstressed)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 1. P. 1-7.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
6
condition as b
ia and b
ic . The index i = 0 corresponds to
the buffer layer, and i = 1, 2 – to the first and the second
sublayers of SL. Elastic deformation of SL layers will be
equal to:
b
i
b
ii
i
a
aa
, (17)
and real parameter ci = cib(1 – p ii), where p = 2c13/c33 is
Poisson’s ratio. The relaxation of elastic deformations in
SL can be characterized by a jump of the lattice
parameter a – 1 iii aaa on the heterointerface or
by the relative level of relaxation
11
1
i
b
i
i
i
b
i
ii
i
aa
a
aa
aa
r . (18)
Values a1 and r1 correspond to the relaxation on
the lower heterointerface (between the buffer layer and
the first layer of СР), and a2 and r2 – to the relaxations
on borders between separate layers (Fig. 4). For stressed
coherent structure a1 = a2 = 0 and, respectively, rі = 0,
and for relaxed layers rі = 1. In our case, as follows from
Fig. 4, the growth of lattice parameter а in InGaN layers
is observed that points to partial relaxation of these
layers (rInGaN = 0.015).
In the case of preservation of the coherence of
appropriate layers of SL and its relaxation as a whole with
respect to the buffer a2 = 0, while a1 can be positive or
negative depending on the buffer layer composition. In
the general case for relaxed non-coherent SL, both jumps
of the parameter will not be equal to zero, thus to
preserve the periodicity of structure a2 should have the
same absolute values at all the borders between SL
layers.
As seen from Table and Fig. 2, GaN layers in SL
are subjected to stretching (Ga > 0), and layers of solid
solution are subjected to compression (InGa < 0), and it
takes place for all the investigated structures. The
stretching deformation in GaN layers is lower than the
compression one in InGaN layers. This difference is
mainly caused by the thickness of layers. For all SLs
under investigation, the relaxation on the lower
heterointerface, i.e., disappearing of stresses between the
SL as a whole and the buffer layer, takes place. This is
not surprising, taking into account the total thickness of
the buffer layer (about 3 μm) and relative mismatch
between SL as a whole and buffer layer of GaN (of the
order of 0.476 %, proceeding from average SL
composition x = 0.18), so the arising stresses far
exceed the critical ones.
Epitaxial layers of nitrides grown on the sapphire
substrates are characterized by a high density of
threading dislocations (up to -210 cm10 ), causing
considerable broadening the diffraction rocking curves.
Therefore, the classical diffraction pattern with satellites
is badly developed on curves of symmetric Bragg’s
reflections taken with widely open detector (Fig. 1,
curve 1). It is caused by a specific feature of defective
structure of nitride films, which is characterized by the
high density of threading dislocations, which grow
transversely to the surface. This leads to the fact that the
diffraction pattern is mainly broadened in a direction
parallel to the surface, and its broadening in transversal
direction is much lower [19]. The dislocation grids
localized on the heterointerface cause stretching the
diffraction pattern in the direction transversal to the
vector of the reciprocal lattice, regardless of the
direction of the latter (see Fig. 1).
The dislocation structure of SL consisting of nitride
layers is basically identical to the patterns for single-
layered nitride films [20]. As the additional reflection
centers (satellites) are distributed along the normal (in
the direction of periodic change of the crystal layer
composition) they can be fixed on the curves crossing
the nodes of the reciprocal lattice in the direction that
takes place for –2-scan in symmetric Bragg’s
geometry. Satellites are also seen on two-crystal curves
obtained in asymmetric grazing-incidence geometry, as
the diffracted intensity is integrated in the direction of the
greatest broadening (a tangent to Evald’s sphere is almost
parallel to the surface).
Epitaxial layers and grown monocrystals have
different defect structures. The relaxation of mismatch
elastic stresses arising due to the difference of lattice
parameters of the film and substrate or separate layers
among themselves is the basic source for generation of
defects in the epitaxial layers [21]. The structure of the
layers is characterized by more uniform distribution of
defects, high anisotropy of shift fields and appearance of
clearly expressed directions — along the surface of the
crystal plate (heterointerfaces) and normal to it.
Broadening transversely to the vector of diffraction is
associated with average turns of blocks and their
effective lateral size, the broadening along vector H is
associated with deformations inside blocks and their
sizes in normal direction n
.
Fig. 4. The lattice parameters of unstrained SL InGaN/GaN.
Solid line shows the relaxed value calculated from Vegard’s
law.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 1. P. 1-7.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
7
As follows from the analysis of regularities of
nodes broadening, dislocation structures of SL layers
have a lower dislocation density and more chaotic
distribution of dislocations. The stressed condition of SL
with respect to the buffer layer testifies the insignificant
influence of dislocations in layers of superlattice.
5. Conclusions
The investigation of multilayered structures based on
InGaN/GaN compounds that radiate in 460 nm spectral
range was carried out using high resolution X-ray
diffractometry. Deformation condition of SL and its
separate layers, degree of relaxation of the layers of the
structure, as well as the period of the SL, thicknesses of
the layers and composition of InxGa1−x solid solution in
active area were determined. The method of analysis of
experimental rocking curves from multilayered
structures with hexagonal symmetry was adapted within
the framework of the Parrat-Speriozu model. This made
it possible to improve structural parameters and
determine the deformation characteristics of the system.
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|
| id | nasplib_isofts_kiev_ua-123456789-117701 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T18:39:41Z |
| publishDate | 2010 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Kladko, V.P. Kuchuk, A.V. Safryuk, N.V. Machulin, V.F. Belyaev, A.E. Konakova, R.V. Yavich, B.S. 2017-05-26T12:13:38Z 2017-05-26T12:13:38Z 2010 X-ray diffraction study of deformation state in InGaN/GaN
 multilayered structures / V.P. Kladko, A.V. Kuchuk, N.V. Safryuk, V.F. Machulin, A.E. Belyaev, R.V. Konakova, B.S. Yavich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 1. — С. 1-7. — Бібліогр.: 21 назв. — англ. 1560-8034 PACS 61.05.cp, 64.75.Nx, 78.55.Cr, -m, 78.67.De, Hc, 81.07.St https://nasplib.isofts.kiev.ua/handle/123456789/117701 High resolution X-ray diffractometry (HRXRD) was used to investigate InxGa₁₋xN/GaN multilayered structures grown by the metal-organic chemical vapor
 deposition (MOCVD) method. Deformation conditions in the superlattice (SL) and its
 separate layers, degree of relaxation in the structure layers, as well as the period of the
 SL, thicknesses of its layers and composition of InxGa₁₋x solid solution in active area
 were determined. It was found that SL was grown on the relaxed buffer layer. SL layers
 were grown practically coherent with slight relaxation of InGaN layer (about 1.5 %). The
 role of dislocations in relaxation processes was established. Analysis of experimental
 diffraction spectra in these multilayered structures within the frameworks of ParratSperiozu
 was adapted for hexagonal syngony structures. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics X-ray diffraction study of deformation state in InGaN/GaN multilayered structures Article published earlier |
| spellingShingle | X-ray diffraction study of deformation state in InGaN/GaN multilayered structures Kladko, V.P. Kuchuk, A.V. Safryuk, N.V. Machulin, V.F. Belyaev, A.E. Konakova, R.V. Yavich, B.S. |
| title | X-ray diffraction study of deformation state in InGaN/GaN multilayered structures |
| title_full | X-ray diffraction study of deformation state in InGaN/GaN multilayered structures |
| title_fullStr | X-ray diffraction study of deformation state in InGaN/GaN multilayered structures |
| title_full_unstemmed | X-ray diffraction study of deformation state in InGaN/GaN multilayered structures |
| title_short | X-ray diffraction study of deformation state in InGaN/GaN multilayered structures |
| title_sort | x-ray diffraction study of deformation state in ingan/gan multilayered structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/117701 |
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