Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios
Dependence of deformation characteristics changing in superlattice (SL) structures AlxGa₁₋xN/GaN with Al (~10%) on the well-barrier thickness ratio in period was studied in this work. The deformation state of SL and individual layers, relaxation level and periods, layers’ thickness and compositio...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автори: | , , , , , , , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2014
|
| Назва видання: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/118414 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios / V.P. Kladko, N.V. Safriuk, H.V. Stanchu, A.V. Kuchuk, V.P. Melnyk, A.S. Oberemok, S.B. Kriviy, Z.V. Maksymenko, A.E. Belyaev, B.S. Yavich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2014. — Т. 17, № 4. — С. 317-324. — Бібліогр.: 26 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-118414 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1184142017-05-31T03:03:27Z Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios Kladko, V.P. Safriuk, N.V. Stanchu, H.V. Kuchuk, A.V. Melnyk, V.P. Oberemok, A.S. Kriviy, S.B. Maksymenko, Z.V. Belyaev, A.E. Yavich, B.S. Dependence of deformation characteristics changing in superlattice (SL) structures AlxGa₁₋xN/GaN with Al (~10%) on the well-barrier thickness ratio in period was studied in this work. The deformation state of SL and individual layers, relaxation level and periods, layers’ thickness and composition of AlxGa₁₋xN layers were analyzed using high-resolution X-ray diffractometry. It was ascertained that the buffer layer and SL layers are compressed in all the investigated structures. Thus, it has been shown that deformation of the SL period depends on the well/barrier thickness ratio. Thicknesses of individual layers in SL strongly depend on the deformation state of the whole system. Increasing the deformation level leads to the increase of the barrier layer thickness. 2014 Article Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios / V.P. Kladko, N.V. Safriuk, H.V. Stanchu, A.V. Kuchuk, V.P. Melnyk, A.S. Oberemok, S.B. Kriviy, Z.V. Maksymenko, A.E. Belyaev, B.S. Yavich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2014. — Т. 17, № 4. — С. 317-324. — Бібліогр.: 26 назв. — англ. 1560-8034 PACS 61.05.cp, 64.75.Nx, 78.55.-m, 78.67.Hc, 78.55.Cr, 78.67.De, 81.07.St http://dspace.nbuv.gov.ua/handle/123456789/118414 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 |
| collection |
DSpace DC |
| language |
English |
| description |
Dependence of deformation characteristics changing in superlattice (SL)
structures AlxGa₁₋xN/GaN with Al (~10%) on the well-barrier thickness ratio in period
was studied in this work. The deformation state of SL and individual layers, relaxation
level and periods, layers’ thickness and composition of AlxGa₁₋xN layers were analyzed
using high-resolution X-ray diffractometry. It was ascertained that the buffer layer and
SL layers are compressed in all the investigated structures. Thus, it has been shown that
deformation of the SL period depends on the well/barrier thickness ratio. Thicknesses of
individual layers in SL strongly depend on the deformation state of the whole system.
Increasing the deformation level leads to the increase of the barrier layer thickness. |
| format |
Article |
| author |
Kladko, V.P. Safriuk, N.V. Stanchu, H.V. Kuchuk, A.V. Melnyk, V.P. Oberemok, A.S. Kriviy, S.B. Maksymenko, Z.V. Belyaev, A.E. Yavich, B.S. |
| spellingShingle |
Kladko, V.P. Safriuk, N.V. Stanchu, H.V. Kuchuk, A.V. Melnyk, V.P. Oberemok, A.S. Kriviy, S.B. Maksymenko, Z.V. Belyaev, A.E. Yavich, B.S. Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kladko, V.P. Safriuk, N.V. Stanchu, H.V. Kuchuk, A.V. Melnyk, V.P. Oberemok, A.S. Kriviy, S.B. Maksymenko, Z.V. Belyaev, A.E. Yavich, B.S. |
| author_sort |
Kladko, V.P. |
| title |
Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios |
| title_short |
Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios |
| title_full |
Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios |
| title_fullStr |
Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios |
| title_full_unstemmed |
Deformation state of short-period AlGaN/GaN superlattices at different well-barrier thickness ratios |
| title_sort |
deformation state of short-period algan/gan superlattices at different well-barrier thickness ratios |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118414 |
| citation_txt |
Deformation state of short-period AlGaN/GaN superlattices
at different well-barrier thickness ratios / V.P. Kladko, N.V. Safriuk, H.V. Stanchu, A.V. Kuchuk, V.P. Melnyk, A.S. Oberemok, S.B. Kriviy, Z.V. Maksymenko, A.E. Belyaev, B.S. Yavich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2014. — Т. 17, № 4. — С. 317-324. — Бібліогр.: 26 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT kladkovp deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT safriuknv deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT stanchuhv deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT kuchukav deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT melnykvp deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT oberemokas deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT kriviysb deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT maksymenkozv deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT belyaevae deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios AT yavichbs deformationstateofshortperiodalgangansuperlatticesatdifferentwellbarrierthicknessratios |
| first_indexed |
2025-07-08T13:56:08Z |
| last_indexed |
2025-07-08T13:56:08Z |
| _version_ |
1837087296536444928 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
317
PACS 61.05.cp, 64.75.Nx, 78.55.-m, 78.67.Hc, 78.55.Cr, 78.67.De, 81.07.St
Deformation state of short-period AlGaN/GaN superlattices
at different well-barrier thickness ratios
V.P. Kladko, N.V. Safriuk, H.V. Stanchu, A.V. Kuchuk, V.P. Melnyk, A.S. Oberemok, S.B. Kriviy,
Z.V. Maksymenko, A.E. Belyaev, B.S. Yavich1
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
1OАS “Svetlana-Optoelectronics”, 78, St.-Petersburg, 194156, Russian Federation
Abstract. Dependence of deformation characteristics changing in superlattice (SL)
structures N/GaNGaAl x1x with Al (10%) on the well-barrier thickness ratio in period
was studied in this work. The deformation state of SL and individual layers, relaxation
level and periods, layers’ thickness and composition of NGaAl x1x layers were analyzed
using high-resolution X-ray diffractometry. It was ascertained that the buffer layer and
SL layers are compressed in all the investigated structures. Thus, it has been shown that
deformation of the SL period depends on the well/barrier thickness ratio. Thicknesses of
individual layers in SL strongly depend on the deformation state of the whole system.
Increasing the deformation level leads to the increase of the barrier layer thickness.
Keywords: superlattice structure, gallium nitride, X-ray diffractometry, deformation
characteristics.
Manuscript received 23.06.14; revised version received 14.08.14; accepted for
publication 29.10.14; published online 10.11.14.
1. Introduction
Multilayered structures based on alloys AlxGa1–xN/GaN,
the so-called superlattices (SL), are widely used for light
emitting and laser diodes in UV and visible spectral
ranges as well as for high-power and high-temperature
field-effect transistors [1, 2]. These structures were
thoroughly investigated for the latter ten years by
various groups of researchers.
Despite many efforts to grow these structures of
high quality with specified properties they still are
failed. In previous works [3-6], it was shown that at
epitaxial growth of nitride structures they relaxed by
formation of dislocations and other defects also by
changing of well-barrier thicknesses in SL from
technological thicknesses. The deformation state,
thickness fluctuation and defects in SL negatively
affect on the devices performance changing their
wavelength, carrier transport and carrier lifetime [7-9].
Intrinsic electrostatic fields in nitride structures are an
important factor that influences the optical properties
of these structures, they leads to huge polarization,
roughness of surface and interfaces AlxGa1–xN/GaN.
These fields strongly depend on the deformation state
[10, 11]. As it was shown previously [12], deformation
in AlxGa1–xN/GaN SL can cause the shift of irradiation
area changing its electron properties. Structures of III-
nitrides have high piezoelectric constant in 0001
direction. Strain in SL layers leads to increasing of
piezoelectric fields, which changes the potential profile
and cause the red shift of emission well known as the
Stark effect.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
318
Taking into account previous facts,
investigation of the deformation state and variation of
the layer thickness is very important for optimization of
nitride structure growth.
High-resolution X-ray diffractometry (HRXD) is
one of nondestructive diagnostic methods widely used to
determine structural parameters of multilayered
structures such as composition, thickness of appropriate
layers, SL period, interface sharpness (existence of
transitional layers), deformation in layers and type of
defects [13, 14].
The reasons of origin and relaxation of mechanic
strain in AlGaN and GaN layers of SL at different ratios
of these thicknesses were investigated in this work. The
investigated samples were test samples with AlGaN
layers parameters for designing blue light diodes. We
study dependence of structure parameters on the growth
regime. In turn, parameters of nanosized layers are more
convenient to be defined in SL. All the values were
obtained from very precise measurements by using
HRXD, X-ray reflectometry and secondary neutral
mass-spectrometry (SNMS).
2. Theory
As usual, III-nitride films grown on the sapphire
substrate are fully relaxed at the growth temperature, and
their deformations at room temperature have mostly a
thermal character. Taking into account this fact, one can
describe relaxation by two parameters – relaxation of SL
with respect to the substrate and relaxation of each layer
with respect to other layers in SL.
For wurtzite structures (typical for AlGaN and
GaN) that grow along hexagonal axes 0001, the lattice
parameter а defines the interplanar distance in the
interface plane, while the lattice parameter c – in the
direction perpendicular to the interface. Let us denote
real (measured) lattice parameters as ai and ci for each i-
layer, b
ia and b
ic – corresponding values for the layer in
unstrained state, where the index i = 0 corresponds to the
buffer layer, indexes i = 1, 2 correspond to AlGaN and
GaN SL’s sub-layers. Elastic deformation in SL layers is
given by:
b
i
b
ii
i
a
aa
. (1)
The real parameter )1( i
b
ii pcc , where
p = 2c13/c33 is the Poisson ratio. Thus, strain relaxation in
SL can be characterized by deformation jump
1 iii aaa of lattice parameter а at the interface,
i.e., the so-called relaxation level:
11
1
i
b
i
i
i
b
i
ii
i
aa
a
aa
aa
r . (2)
The parameters 1a and r1 correspond to relaxation
on the bottom interface (between the buffer layer and
first layer of SL), parameters 2a and r2 – relaxation at
the interfaces of subsequent layers (Fig. 1). For a
strained coherent structure 012 aa . When
subsequent layers grow coherently and relax with
respect to the buffer layer as a whole 02 a , 1a can
be higher or lower than 0, which depends on the
composition of the buffer layer. In general, in the case of
relaxed incoherent SL both jumps can be no equal to
zero, at the same time 2a must be equal at all
interfaces in SL.
Lattice parameters’ mismatch in SL can be
obtained using the equation:
a
aa
a
a bb
AlGaNGaN
, (3)
where 2AlGaNGaN
bb aaa .
The average lattice parameter а in SL is equal:
AlGaNGaN
AlGaNAlGaNGaNGaN
tt
atat
a
bb
SL
. (4)
In case of symmetrical SL (tGaN = tAlGaN),
parameters are equal aaSL .
For SL AlGaN/GaN, which growth is pseudomorph
to that of the buffer layer, the jumps of lattice parameters
are 01 a and 02 a between layers in SL and
between buffer layer and SL, correspondingly. In this
case, deformations in AlGaN and GaN layers can be
described as:
0GaN ;
a
a
AlGaN . (5)
The average lattice parameter а in SL period is
equal:
,AlGaN
AlGaNGaN
AlGaNAlGaN
AlGaNGaN
AlGaNAlGaNGaNGaN
T
t
a
a
tt
t
tt
tt
SL
(6)
here T = tGaN + tAlGaN. When SL is partly relaxed, we
must use both parameters of relaxation. The first
parameter AlGaNGaN1 aaa is a jump of the lattice
parameter between individual layers AlN and GaN in
SL. These jumps must be equal on all the interfaces, if
relaxation doesn’t change periodicity of SL. Another
parameter 2a is the jump of the lattice parameter a at
the interface buffer – first layer of SL. This parameter
describes relaxation of SL.
Lateral deformation in AlGaN and GaN layers and
average deformation in SL period are given by:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
319
1
1
AlGaN
1
aa
aa
a
a
a
, (7)
T
t
a
aa
SL
AlGaN1
. (8)
Average deformation in SL period is
aaaSL 2/ , when layers AlN and GaN in
SL have equal thicknesses. As soon as deformation in
SL reach a critical value when thickness increases, there
appears situation when SL relaxes as a whole with the
deformation jump a . This relaxation (partly in
general) leads to average lateral deformation:
T
t
a
aa
k
T
t
a
a
kSL
AlGaN2AlGaN
, (9)
where the coefficient k is –1 ≤ k ≤ 1. In case when k = 0,
SL is fully relaxed, while 1k and 1 describe the
cases when layers of SL have lateral parameters of AlN
or GaN buffer layers, respectively. Three parameters of
relaxation are related as:
a
a
a
a
k
T
t
a
a
1AlGaN . (10)
Relaxation of SL as a whole leads to changes of the
average SL parameters and, correspondly, to the shift of
the diffraction picture (curve) with respect to the SL
peak. But this relaxation doesn’t change the intensity
ratio of the satellites. Relaxation between layers leads to
changes in deformation , which can be given as:
,
GaN
2
GaN
GaNAlGaN
GaN
GaNAlGaN
a
a
px
a
aa
p
x
c
cc
(11)
where cGaN, аGaN and сAlGaN, аAlGaN are table lattice
parameters of GaN and AlGaN, respectively. The
Poisson ratio p = 2c13/c33 is equal for GaN and AlGaN
layers.
3. Experimental
10-period AlхGa1–хN/GaN SL obtained by МОСVD
were investigated in this work. SL structures were grown
on complex GaN-buffer layer that contain GaN:Si
(3.5 µm) layer, GaN layer with intrinsic conductivity
(0.5 µm) and low-temperature nucleated GaN layer
(20 nm) grown on c-plane of sapphire. The first series of
SL (S1) consisted of barriers NGaAl x1x with the
nominal thickness close to 6.6 nm with nominal
composition Al ~ 10% and GaN well with the nominal
thickness near 9 nm. In the second series (S2) the
NGaAl x1x nominal thickness of barriers was
approximately 10 nm, the GaN well thickness was close
to 6 nm. Thickness values were calculated from the
growth time of SL layers.
Investigation of the samples was performed using
high-relosution X-ray diffractometer PANalytical X’Pert
PRO MRD. The reciprocal space map (RSM) and
diffraction curves (DC) obtained in triple-axis scheme
were used to analyze structural parameters. For
calculation of deformation in the buffer layer GaN
experimental DC were normalized to 0006 reflection of
the sapphire substrate at 2θ = 41.680°. Theoretical DC
were calculated using the plane wave methods [15, 16].
Ideal structural parameters for all the layers were taken
from the papers [17, 18]. Dislocation density
measurements were performed like to those in works
[19, 20]. The thickness of individual layers in SL and its
period were controlled using X-ray reflectivity and
secondary neutral mass-spectrometry (SNMS).
The layer-by-layer depth analysis of dopant
distribution in N/GaNGaAl x1x SL was carried out
using SNMS. Measurements were performed in high-
frequency (HF) regime of sputtering the sample by Ar+
ions with 330 eV in INA-3 (Laybold-Heraeus)
equipment. Ions were generated due to the application of
HF voltage in the form of rectangular pulses between
samples and wall of HF plasma at low pressure
( mbar1026.3 2 ). The voltage frequency was 50 kHz.
The area of sputtering was limited by the tantal
diaphragm with the internal diameter 3 mm. Selected
parameters of sputtering allowed to provide step-by-step
analysis with high resolution ~1 nm for the depth
100 nm. The dispersion speed of AlGaN and GaN layers
was estimated from the ratio between the crater etching
depth and dispersion time for each layer. The crater
etching depth was obtained using atomic force
microscopy (AFM) (NanoScope IIIa Dimension 3000).
The crater etching depth and thickness of individual
layers were determined using the methods from the
work [21].
aAlGaN aav aGaN
compressive
buffera1
a2
tensile
AlGaN
GaN
Fig. 1. Distribution of the lattice parameter a along the depth
of SL AlGaN/GaN grown on the buffer layer GaN. The dashed
layer corresponds to the parameter a for unstrained layers and
average parameter over SL.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
320
Fig. 2. RSM 4211 for SL AlGaN/GaN: S1 (a), S2 (b). Qу and Qx are reciprocal space coordinates perpendicular and parallel
to the surface, respectively. H
is the diffraction vector, n
– surface normal vector, SL0 – position of SL0 satellite.
Fig. 3. ω–2θ-scans for symmetrical reflex 0002 from SL AlGaN/GaN: а) S1, b) S2. Experiment – lower (red) curve, fitting–
upper (black) curve. SLn – satellites of SL.
4. Results
Series of RSM in the vicinity of reflexes 4211 and
5110 for all structures were analyzed. RSM for 4211
reflex of both structures S1 and S2 is presented in Fig. 2.
Information about the relaxation level in heterostructures
can be obtained from asymmetric RSM where the
diffraction vector makes the angle φ with surface. The
intensity of coherent distribution for additional nods
(from individual layers, thickness oscillations and SL
satellites) for the fully relaxed structure lay in the
diffraction plane parallel to the surface normal [20].
Such growth must be provided to obtain structures
suitable for application in devices. For the fully relaxed
samples, diffraction nods are placed along the diffraction
vector. When they are partly relaxed, nods are located in
an intermediate position.
Thus, in case when intensity distribution from SL
and substrate are placed on the surface normal, it shows
coherent interface, on the other hand, another placement
of intensity distribution corresponds to some relaxation
level of SL with respect to the substrate [20].
A small shift between SL satellites and buffer layer
in the vertical direction, which indicates partial
relaxation at this boundary ( 01 a ), was observed in
our work. Moreover, for S1 sample relaxation level is
higher (r1 = 0.047) than for the sample S2 (r1 = 0.037).
Interesting fact was noticed from RSM: peak
position of GaN indicates a compressed state. Thus, the
buffer layer wasn’t fully relaxed. The average lattice
parameter а of SL is bigger than that parameter of the
buffer layer. It indicates that pseudomorphic growth of
SL is corrupted and appearance of satellites shows the
coherent growth.
Broad intensity distribution from the buffer layer
GaN and satellites from SL AlxGa1–xN/GaN is depicted
in Fig. 2. As one can see from this figure, intensity
maxima from the buffer layer GaN are wider in Qx
direction, which indicates presence of defects (point
defects, dislocations). It is well known that the epitaxial
layer of III-nitride is often grown on a sapphire substrate
and has a high dislocation density of threading
dislocation (109 cm–2), which leads to broadening of
diffraction maxima in the direction parallel to surface
[21, 22]. In our case, the dislocation density in
N/GaNGaAl x1x SL is extremely lower ( 27cm10 ).
Also, from analysis of Fig. 2 one can observe
broadening of satellites in direction along the diffraction
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
321
Table 1. Technological (nominal) and experimental parameters of AlхGa1–хN/GaN.
Sample
Layers of
SL
Tnomin,
nm
tXRD,
nm
tSIMS,
nm
Тnomin/TXRD/Тrefl, nm xSIMS/xXRD, %
Ns,
27 cm10
Rcurv,
m
GaN 9 10 10
S1
AlGaN 6.6 7 8
15.6/17/17.2 9/10 8.37 6.8
GaN 6 5.5 6.5
S2
AlGaN 10 13.2 12.66
16/18.7/18 10/10 6.00 6.6
Table 2. Lattice parameters of the buffer layer and SL: ideal and calculated values.
S
am
pl
e
id
SLa , nm id
SLc , nm idaGaN , nm idcGaN , nm aSL, nm cSL, nm bufaGaN , nm bufcGaN , nm
S1 0.318598 0.51767 0.31892 0.51850 0.316422 0.520625 0.316314 0.521985
S2 0.318368 0.51708 0.31892 0.51850 0.315526 0.521079 0.315417 0.522979
vector. This indicates a stronger effect of mosaicity in
SL than in the buffer layer.
Modeling of experimental DC for the symmetrical
reflex 0002, being based on the dynamical diffraction
theory, was used for a more precise analysis of
N/GaNGaAl x1x parameters (Fig. 3) [11]. In Fig. 3, the
sharp peak corresponds for 0002 reflex from the buffer
layer GаN, broader peaks (satellites) corresponds to SL
N/GaNGaAl x1x . The peak position of SL depends on
both composition of SL and the ratio of layer thickness.
δθ is the distance between satellites, which marks
both SL–1 and SL0, corresponds to the SL period (T =
twell + tbarrier = B2sinh , where λ is the X-ray
wavelength, γh – directing cosines of the X-ray beam,
more frequent fringes are caused be the total thickness of
SL. The relative intensity of the satellites was used to
obtain the thickness ratio, and then the composition of
solid solution NGaAl x1x [23]. Parameters of SL were
obtained from RSM and refined by a procedure of fitting
experimental and calculated DC [14, 15]. They are given
in Table 1.
Vertical lattice parameters c of buffer layers GaN
were calculated from relative changes of the peak
position between the buffer layer GaN (0002) and
sapphire substrate (0006). The sapphire peak height was
used as a reference value. The parameters c from DC
were 5.1856 Å for S1 sample and 5.1859 Å for S2
sample. These values were used for calculation of the
perpendicular strain (perpendicular to the growth plane)
εzz by using the formula:
εzz = (c – c0)/c0, (12)
where c0 = 5.1855 Å lattice parameter for unstrained
layer GaN [18]. Perpendicular strain has tensile
character as for S1 εzz = 1.9·10–5 as for S2 εzz =
5107.7 , respectively. The parallel strain was
calculated using the following relation:
εxx = (a – a0)/a0, (13)
where a0 = 3.1891 Å. The lattice parameters a were
obtained from asymmetric scans for 5110 and 4211
reflections, a = 3.1631 Å and a = 3.1542 Å for S1 and
S2, respectively. The parallel compressing strains are εxx
= 3101.8 for S1 and εxx = 2101.1 for S2. Let us
note that the initial parameters for the buffer layer GaN
were the same for all the structures.
SNMS depth profiles of Al and Ga elements in
AlxGa1–xN/GaN SL within the upper three periods for S1
and S2 samples are presented in Fig. 4. We observed the
increase of the GaN well layer thickness by 0.5 nm for both
samples. In both samples, the NGaAl x1x barrier layer
thickness is different, with deviation from nominal value of
0.5 to 1.5 nm. The barrier layer thickness deviation with
depth was observed to be equivalent in each period for S1.
On the other hand, for S2 we observed reducing the barrier
layer thickness in each dipper period. All the thickness
values are presented in Table 1.
5. Discussion
AlхGa1–хN/GaN SL were grown on the buffer layer GaN,
which are in the compressed state that is partly relaxed.
The difference between the buffer GaN and average SL
lattice parameters a indicates partial relaxation on
interface buffer layer – SL, i.e. relaxation on the bottom
interface, which was observed for all SL. The calculated
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
322
Fig. 4. SNMS depth profiles of Al and Ga elements in N/GaNGaAl x1x SL: а) S1, b) S2. Upper (red) curves – Ga distribution,
lower (black) curves – Al distribution.
lattice parameters obtained from asymmetric RSM
4211 are summarized in Table 2. From these results,
both SL are compressed, but the strain is less than that in
the buffer layer. Difference of average SL lattice
parameter for S1 and S2 caused by changes in the layer
thickness ratio. It influences on the strain state of the
buffer and whole system.
As it follows from these results, GaN wells as well
as the barrier NGaAl x1x in SL are in the compressed
state (xx < 0) for all the structures (Table 2). The buffer
layer also is in the compressed state and leads to the
respective state of SL. But in SL this deformation is
bigger in well GaN than in the barrier NGaAl x1x .
However, the compressing strain is less for S1 than for
S2, which is caused by the different thickness ratio
(well-barrier). This behavior in the SL period can be
explained from determination of average parameters.
Average lattice parameters in the SL period were
calculated from the equations (1)-(6). From these
equations, one can see that those SL periods are strongly
dependent on the thickness ratio well-barrier and on
barrier composition.
Deformation profiles with depth of SL calculated
with respect to the ideal values of GaN and NGaAl x1x
are presented in Fig. 5.
The parameter of each SL layer tends to reach the
average SL parameter SL0_real, since it tends to reach
the real parameter value of the buffer layer GaN (Fig. 5).
Layers in S2 are more strained with respect to the
average SL parameter than those in S1. It well correlates
with broadening of RSM (0.0064 rlu and 0.0048 rlu, for
S1 and S2, respectively (Fig. 1)) as well as with the
dislocation density that is less in the more strained
structure S2.
The strain level of whole SL with respect to buffer
layer depends on type of SL. Relaxation is slower for SL
with a thick well because of the smaller lattice parameter
mismatch between SL and GaN buffer. Compression of
the buffer layer affects the strain level in the SL layer
and average lattice parameters in the period. But
deformation jump at the interfaces of SL layer remains
the same, only weak changes of the ratio of strain
between the SL layers were observed.
The difference of parameters Δt = texp – ttechn
corresponding to the difference between technological
and experimental layer thicknesses are probably caused
by different deformation state of the system. As one can
see from Fig. 6 for the NGaAl x1x barrier, the increase
of deformation leads to enhancement of the growth rate,
on the other hand, we observed the opposite process in
the GaN layer. The same changes in the growth rate for
the NGaAl x1x barrier under reducing of mechanical
strains were observed in [24]. Explanation of thickness
changes with those of deformation was deduced from the
first principles for AlxGa1–xN/GaN SL [25].
Fig. 5. Deformation profiles alternating with depth of SL in S1
and S2 samples.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
323
Fig. 6. Dependence of the growth rate V of SL layers
AlxGa1–xN and GaN on the deformation level.
As it follows from Table 1, deformation changes in
SL do not lead to significant changes in the dislocation
density Ns and curvature radius Rcurv for each sample. Thus,
at the practically equal curvature radius and small deviation
of dislocation density we observed different relaxation
states for S1 and S2 samples. But, to explain this difference
in the relaxation state only due to formation of dislocation is
impossible. It indicates that thickness changes of
NGaAl x1x and GaN layers can be additional relaxation
channel in these SLs. Moreover, the process of relaxation
and formation of defects are strongly interrelated [26].
5. Conclusions
The deformation state of short-period SL and its
individual layers, relaxation state, period and layer
thickness, composition of NGaAl x1x were obtained
using the X-ray diffraction methods.
It was ascertained that the buffer layer as well as
SL layers are compressed in all the investigated
structures. Thus, it was shown that deformation of SL
period depends on the well-barrier thickness ratio. It, to
some extent, determines the relaxation state of whole SL
with respect to the buffer layer. However, relaxation
state of buffer layer strongly affects deformation of the
whole system. The dependence between the growth rate
of individual layer and deformation state has been
shown. The increase in deformation leads to
enhancement of the growth rate for the barrier.
Thus, structural, optical and electro-physical
properties of SL are determined by the process of elastic
strain relaxation that leads to changing the well and
barrier thickness.
This study was supported by the National Academy
of Sciences of Ukraine within the framework of the
scientific-technological programs “Nanotechnology and
Nanomaterials” №3.5.1.12 and №3.5.1.30.
References
1. H. Morkoç, Handbook of Nitride Semiconductors
and Devices: Electronic and Optical Processes in
Nitrides. Berlin, Wiley-VCH, 2008.
2. P. Ruterana, M. Albrecht, J. Neugebauer, Nitride
Semiconductors: Handbook on Materials and
Devices. Berlin, Wiley-VCH, 2003.
3. V.P. Kladko, S.V. Chornen’kii, A.V. Naumov,
A.V. Komarov, M. Tacano, Yu.N. Sveshnikov,
S.A. Vitusevich, and A.E. Belyaev, Interface
structural defects and photoluminescence properties
of epitaxial GaN and AlGaN/GaN layers grown on
sapphire // Semiconductors, 40, p. 1060 (2006).
4. V.P. Kladko, A.F. Kolomys, M.V. Slobodian,
V.V. Strelchuk, V.G. Raycheva, A.E. Belyaev,
S.S. Bukalov, H. Hardtdegen, V.A. Sydoruk,
N. Klein, and S.A. Vitusevich, Internal strains and
crystal structure of the layers in AlGaN/GaN
heterostructures grown on sapphire substrate // J.
Appl. Phys., 105, 063515 (2009).
5. V.P. Kladko, A.V. Kuchuk, N.V. Safryuk,
V.F. Machulin, A.E. Belyaev, H. Hardtdegen,
S.A. Vitusevich, Mechanism of strain relaxation by
twisted nanocolumns revealed in AlGaN/GaN
heterostructures // Appl. Phys. Lett. 95, 031907
(2009).
6. V.P. Kladko, A.V. Kuchuk, P.M. Lytvyn,
O.M. Yefanov, N.V. Safriuk, A.E. Belyaev,
Yu.I. Mazur, E.A. DeCuir Jr, M.E. Ware, and
G.J. Salamo, Substrate effects on the strain
relaxation in GaN/AlN short-period superlattices //
Nanoscale Res. Lett. 7, p. 289 (2012).
7. H. Amano, K. Hiramatsu, and I. Akasaki,
Heteroepitaxial growth and the effect of strain on
the luminescence properties of GaN films on
0211 and 0001 sapphire substrates // Jpn. J.
Appl. Phys., 27, L1384 (1988).
8. A. Bykhovski, B. Gelmont, and M. Shur, The
influence of strain-induced electric field on the
charge distribution in GaN-AlN-GaN structure // J.
Appl. Phys. 74, p. 6734 (1993).
9. F. Bernardini, V. Fiorentini, and D. Vanderbilt,
Spontaneous polarization and piezoelectric constant
of III-V nitrides // Phys. Rev. B, 56, R10024
(1997).
10. P.K. Kandaswamy, F. Guillot, E. Bellet-Amalric,
E. Monroy, L. Nevou, M. Tchernycheva,
A. Michon, F.H. Julien, E. Baumann,
F.R. Giorgetta, D. Hofstetter, T. Remmele,
M. Albrecht, S. Birner, and Le Si Dang, GaN/AlN
short-period superlattices for intersubband
optoelectronics: A systematic study of their
epitaxial growth, design, and performance // J.
Appl. Phys. 104, 093501 (2008).
11. P.K. Kandaswamy, C. Bougerol, D. Jalabert,
P. Ruterana, and E. Monroy, Strain relaxation in
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
324
short-period polar GaN/AlN superlattices // J. Appl.
Phys. 106, 013526 (2009).
12. A. Sarua, Hangfeng Ji, M. Kuball, M.J. Uren, T.
Martin, K.J. Nash, K.P. Hilton, and R.S. Balmer,
Piezoelectric strain in AlGaN/GaN heterostructure
field-effect transistors under bias // Appl. Phys.
Lett. 88, 103502 (2006).
13. O.M. Yefanov, V.P. Kladko, V.F. Machulin,
V.B. Molodkin, Dynamical Diffraction of X-rays
in Multilayered Structures. Naukova Dumka,
Kyiv, 2008.
14. P.F. Fewster, X-Ray Scattering from Semi-
conductors. London, Imperial College Press, 2000.
15. O.M. Yefanov, V.P. Kladko, The solution of the
dispersion equation in an explicit format for a case
of two strong waves // Metallofizika i Noveishie
Tekhnologii, 28, p. 227-244 (2006).
16. V.B. Molodkin, S.I. Olikhovskii, E.G. Len, E.N.
Kislovskii, V.P. Kladko, O.V. Reshetnyk, T.P.
Vladimirova, B.V. Sheludchenko, Sensitivity of
triple-crystal X-ray diffractometers to microdefects
in silicon // phys. status solidi (a), 206(8), p. 1761-
1765 (2009).
17. M. Yamaguchi, T. Yagi, T. Sota, T. Deguchi,
K. Shimada, and S. Nakamura, Brillouin scattering
study of bulk GaN // J. Appl. Phys. 85, p. 8502
(1999).
18. W. Paszkowicz, X-ray powder diffraction data for
indium nitride // Powder Diffract., 14, p. 258
(1999).
19. H. Heinke, V. Kirchner, S. Einfeldt, A. Hommel,
X-ray diffraction analysis of the defect structure in
epitaxial GaN // Appl. Phys. Lett. 77, p. 2145
(2000).
20. N.V. Safriuk, G.V. Stanchu, A.V. Kuchuk,
V.P. Kladko, A.E. Belyaev, V.F. Machulin, X-ray
diffraction investigation of GaN layers on Si(111)
and Al2O3(0001) substrates // Semiconductor
Physics, Quantum Electronics & Optoelectronics,
16(3), p. 265-272 (2013).
21. Yu.P. Pershin, V.A. Sevtyukova, Ye.N. Zubarev,
A.S. Oberemok, V.P. Melnyk, B.M. Romanyuk,
V.G. Popov, P.M. Lytvyn, Investigation of the
phase interfaces in periodic multilayer Mo/Si
structures, using the method of mass-spectrometry
of neutral particles // Metallofizika i Noveishie
Tekhnologii, 35(12), p. 1617-1627 (2013).
22. M.A. Moram, M.E. Vickers, X-ray diffraction of
III-nitrides // Repts. Progr. Phys. 72, 036502 (2009).
23. V. Srikant, J.S. Speck, D.R. Clarke, Mosaic
structure in epitaxial thin films having large lattice
mismatch // J. Appl. Phys. 82, p. 4286 (1997).
24. R.N. Kyutt, M.P. Shcheglov, V.Yu. Davydov, A.S.
Usikov, Deformation of layers in superlattices
AlGaN/GaN according to XRD analysis // Fizika
Tverd. Tela, 46, p. 353 (2004), in Russian.
25. Y. Kotsar, B. Doisneau, E. Bellet-Amalric, A. Das,
E. Sarigiannidou, and E. Monroy, Strain relaxation
in GaN/ NGaAl x1x superlattices grown by plasma
molecular-beam epitaxy // J. Appl. Phys. 110,
033501 (2011).
26. A.V. Kuchuk, V.P. Kladko, T.L. Petrenko, V.P.
Bryksa, A.E. Belyaev, Yu.I. Mazur, M.E. Ware,
E.A. DeCuir Jr, and G.J. Salamo, Mechanism of
strain-influenced quantum well thickness reduction
in GaN/AlN short-period superlattices //
Nanotechnology, 25, 245602 (2014).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 4. P. 317-324.
PACS 61.05.cp, 64.75.Nx, 78.55.-m, 78.67.Hc, 78.55.Cr, 78.67.De, 81.07.St
Deformation state of short-period AlGaN/GaN superlattices
at different well-barrier thickness ratios
V.P. Kladko, N.V. Safriuk, H.V. Stanchu, A.V. Kuchuk, V.P. Melnyk, A.S. Oberemok, S.B. Kriviy,
Z.V. Maksymenko, A.E. Belyaev, B.S. Yavich1
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
1OАS “Svetlana-Optoelectronics”, 78, St.-Petersburg, 194156, Russian Federation
Abstract. Dependence of deformation characteristics changing in superlattice (SL) structures
N/GaN
Ga
Al
x
1
x
-
with Al ((10%) on the well-barrier thickness ratio in period was studied in this work. The deformation state of SL and individual layers, relaxation level and periods, layers’ thickness and composition of
N
Ga
Al
x
1
x
-
layers were analyzed using high-resolution X-ray diffractometry. It was ascertained that the buffer layer and SL layers are compressed in all the investigated structures. Thus, it has been shown that deformation of the SL period depends on the well/barrier thickness ratio. Thicknesses of individual layers in SL strongly depend on the deformation state of the whole system. Increasing the deformation level leads to the increase of the barrier layer thickness.
Keywords: superlattice structure, gallium nitride, X-ray diffractometry, deformation characteristics.
Manuscript received 23.06.14; revised version received 14.08.14; accepted for publication 29.10.14; published online 10.11.14.
1. Introduction
Multilayered structures based on alloys AlxGa1–xN/GaN, the so-called superlattices (SL), are widely used for light emitting and laser diodes in UV and visible spectral ranges as well as for high-power and high-temperature field-effect transistors [1, 2]. These structures were thoroughly investigated for the latter ten years by various groups of researchers.
Despite many efforts to grow these structures of high quality with specified properties they still are failed. In previous works [3-6], it was shown that at epitaxial growth of nitride structures they relaxed by formation of dislocations and other defects also by changing of well-barrier thicknesses in SL from technological thicknesses. The deformation state, thickness fluctuation and defects in SL negatively affect on the devices performance changing their wavelength, carrier transport and carrier lifetime [7-9]. Intrinsic electrostatic fields in nitride structures are an important factor that influences the optical properties of these structures, they leads to huge polarization, roughness of surface and interfaces AlxGa1–xN/GaN. These fields strongly depend on the deformation state [10, 11]. As it was shown previously [12], deformation in AlxGa1–xN/GaN SL can cause the shift of irradiation area changing its electron properties. Structures of III-nitrides have high piezoelectric constant in (0001( direction. Strain in SL layers leads to increasing of piezoelectric fields, which changes the potential profile and cause the red shift of emission well known as the Stark effect.
Taking into account previous facts, investigation of the deformation state and variation of the layer thickness is very important for optimization of nitride structure growth.
High-resolution X-ray diffractometry (HRXD) is one of nondestructive diagnostic methods widely used to determine structural parameters of multilayered structures such as composition, thickness of appropriate layers, SL period, interface sharpness (existence of transitional layers), deformation in layers and type of defects [13, 14].
The reasons of origin and relaxation of mechanic strain in AlGaN and GaN layers of SL at different ratios of these thicknesses were investigated in this work. The investigated samples were test samples with AlGaN layers parameters for designing blue light diodes. We study dependence of structure parameters on the growth regime. In turn, parameters of nanosized layers are more convenient to be defined in SL. All the values were obtained from very precise measurements by using HRXD, X-ray reflectometry and secondary neutral mass-spectrometry (SNMS).
2. Theory
As usual, III-nitride films grown on the sapphire substrate are fully relaxed at the growth temperature, and their deformations at room temperature have mostly a thermal character. Taking into account this fact, one can describe relaxation by two parameters – relaxation of SL with respect to the substrate and relaxation of each layer with respect to other layers in SL.
For wurtzite structures (typical for AlGaN and GaN) that grow along hexagonal axes (0001(, the lattice parameter а defines the interplanar distance in the interface plane, while the lattice parameter c – in the direction perpendicular to the interface. Let us denote real (measured) lattice parameters as ai and ci for each i-layer,
b
i
a
and
b
i
c
– corresponding values for the layer in unstrained state, where the index i = 0 corresponds to the buffer layer, indexes i = 1, 2 correspond to AlGaN and GaN SL’s sub-layers. Elastic deformation in SL layers is given by:
b
i
b
i
i
i
a
a
a
-
=
e
.
(1)
The real parameter
)
1
(
i
b
i
i
p
c
c
e
-
=
, where p = 2c13/c33 is the Poisson ratio. Thus, strain relaxation in SL can be characterized by deformation jump
1
-
-
=
D
i
i
i
a
a
a
of lattice parameter а at the interface, i.e., the so-called relaxation level:
1
1
1
-
-
-
-
D
=
-
-
=
i
b
i
i
i
b
i
i
i
i
a
a
a
a
a
a
a
r
.
(2)
The parameters
1
a
D
and r1 correspond to relaxation on the bottom interface (between the buffer layer and first layer of SL), parameters
2
a
D
and r2 – relaxation at the interfaces of subsequent layers (Fig. 1). For a strained coherent structure
0
1
2
=
D
=
D
a
a
. When subsequent layers grow coherently and relax with respect to the buffer layer as a whole
0
2
=
D
a
,
1
a
D
can be higher or lower than 0, which depends on the composition of the buffer layer. In general, in the case of relaxed incoherent SL both jumps can be no equal to zero, at the same time
2
a
D
must be equal at all interfaces in SL.
Lattice parameters’ mismatch in SL can be obtained using the equation:
a
a
a
a
a
b
b
AlGaN
GaN
-
=
D
,
(3)
where
(
)
2
AlGaN
GaN
b
b
a
a
a
+
=
.
The average lattice parameter а in SL is equal:
AlGaN
GaN
AlGaN
AlGaN
GaN
GaN
t
t
a
t
a
t
a
b
b
SL
+
×
+
×
=
.
(4)
In case of symmetrical SL (tGaN = tAlGaN), parameters are equal
a
a
SL
=
.
For SL AlGaN/GaN, which growth is pseudomorph to that of the buffer layer, the jumps of lattice parameters are
0
1
=
D
a
and
0
2
=
D
a
between layers in SL and between buffer layer and SL, correspondingly. In this case, deformations in AlGaN and GaN layers can be described as:
0
GaN
=
e
;
a
a
D
-
=
e
AlGaN
.
(5)
The average lattice parameter а in SL period is equal:
,
AlGaN
AlGaN
GaN
AlGaN
AlGaN
AlGaN
GaN
AlGaN
AlGaN
GaN
GaN
T
t
a
a
t
t
t
t
t
t
t
SL
×
D
-
=
+
×
e
=
=
+
×
e
+
×
e
=
e
(6)
here T = tGaN + tAlGaN. When SL is partly relaxed, we must use both parameters of relaxation. The first parameter
AlGaN
GaN
1
a
a
a
-
=
D
is a jump of the lattice parameter between individual layers AlN and GaN in SL. These jumps must be equal on all the interfaces, if relaxation doesn’t change periodicity of SL. Another parameter
2
a
D
is the jump of the lattice parameter a at the interface buffer – first layer of SL. This parameter describes relaxation of SL.
Lateral deformation in AlGaN and GaN layers and average deformation in SL period are given by:
(
)
1
1
AlGaN
1
a
a
a
a
a
a
a
D
-
D
-
=
D
+
D
-
=
e
,
(7)
(
)
T
t
a
a
a
SL
AlGaN
1
×
D
-
D
-
=
e
.
(8)
Average deformation in SL period is
(
)
a
a
a
SL
2
/
¢
D
-
D
-
=
e
, when layers AlN and GaN in SL have equal thicknesses. As soon as deformation in SL reach a critical value when thickness increases, there appears situation when SL relaxes as a whole with the deformation jump
a
¢
¢
D
. This relaxation (partly in general) leads to average lateral deformation:
(
)
T
t
a
a
a
k
T
t
a
a
k
SL
AlGaN
2
AlGaN
×
D
-
D
×
=
×
D
×
=
e
¢
,
(9)
where the coefficient k is –1 ≤ k ≤ 1. In case when k = 0, SL is fully relaxed, while
1
-
=
k
and 1 describe the cases when layers of SL have lateral parameters of AlN or GaN buffer layers, respectively. Three parameters of relaxation are related as:
(
)
a
a
a
a
k
T
t
a
a
¢
¢
D
+
¢
D
=
+
×
D
1
AlGaN
.
(10)
Relaxation of SL as a whole leads to changes of the average SL parameters and, correspondly, to the shift of the diffraction picture (curve) with respect to the SL peak. But this relaxation doesn’t change the intensity ratio of the satellites. Relaxation between layers leads to changes in deformation
^
e
, which can be given as:
,
GaN
2
GaN
GaN
AlGaN
GaN
GaN
AlGaN
a
a
p
x
a
a
a
p
x
c
c
c
D
-
-
+
+
-
=
e
D
^
(11)
where cGaN, аGaN and сAlGaN, аAlGaN are table lattice parameters of GaN and AlGaN, respectively. The Poisson ratio p = 2c13/c33 is equal for GaN and AlGaN layers.
3. Experimental
10-period AlхGa1–хN/GaN SL obtained by МОСVD were investigated in this work. SL structures were grown on complex GaN-buffer layer that contain GaN:Si (3.5 µm) layer, GaN layer with intrinsic conductivity (0.5 µm) and low-temperature nucleated GaN layer (20 nm) grown on c-plane of sapphire. The first series of SL (S1) consisted of barriers
N
Ga
Al
x
1
x
-
with the nominal thickness close to 6.6 nm with nominal composition Al ~ 10% and GaN well with the nominal thickness near 9 nm. In the second series (S2) the
N
Ga
Al
x
1
x
-
nominal thickness of barriers was approximately 10 nm, the GaN well thickness was close to 6 nm. Thickness values were calculated from the growth time of SL layers.
Investigation of the samples was performed using high-relosution X-ray diffractometer PANalytical X’Pert PRO MRD. The reciprocal space map (RSM) and diffraction curves (DC) obtained in triple-axis scheme were used to analyze structural parameters. For calculation of deformation in the buffer layer GaN experimental DC were normalized to 0006 reflection of the sapphire substrate at 2θ = 41.680°. Theoretical DC were calculated using the plane wave methods [15, 16]. Ideal structural parameters for all the layers were taken from the papers [17, 18]. Dislocation density measurements were performed like to those in works [19, 20]. The thickness of individual layers in SL and its period were controlled using X-ray reflectivity and secondary neutral mass-spectrometry (SNMS).
The layer-by-layer depth analysis of dopant distribution in
N/GaN
Ga
Al
x
1
x
-
SL was carried out using SNMS. Measurements were performed in high-frequency (HF) regime of sputtering the sample by Ar+ ions with 330 eV in INA-3 (Laybold-Heraeus) equipment. Ions were generated due to the application of HF voltage in the form of rectangular pulses between samples and wall of HF plasma at low pressure (
mbar
10
26
.
3
2
-
×
). The voltage frequency was 50 kHz. The area of sputtering was limited by the tantal diaphragm with the internal diameter 3 mm. Selected parameters of sputtering allowed to provide step-by-step analysis with high resolution ~1 nm for the depth 100 nm. The dispersion speed of AlGaN and GaN layers was estimated from the ratio between the crater etching depth and dispersion time for each layer. The crater etching depth was obtained using atomic force microscopy (AFM) (NanoScope IIIa Dimension 3000). The crater etching depth and thickness of individual layers were determined using the methods from the work [21].
Рис. 4 . Схематическое распределение параметра решетки a по глубине сверхрешетки AlGaN/GaN
на буферном слое GaN. Пунктирные линии соответствуют параметру a для ненапряженных слоев и
a
AlGaN
a
av
a
GaN
compressive
buffer
a
1
a
2
tensile
AlGaN
GaN
Fig. 1. Distribution of the lattice parameter a along the depth of SL AlGaN/GaN grown on the buffer layer GaN. The dashed layer corresponds to the parameter a for unstrained layers and average parameter over SL.
4. Results
Series of RSM in the vicinity of reflexes
(
)
4
2
11
and
(
)
5
1
10
for all structures were analyzed. RSM for
(
)
4
2
11
reflex of both structures S1 and S2 is presented in Fig. 2. Information about the relaxation level in heterostructures can be obtained from asymmetric RSM where the diffraction vector makes the angle φ with surface. The intensity of coherent distribution for additional nods (from individual layers, thickness oscillations and SL satellites) for the fully relaxed structure lay in the diffraction plane parallel to the surface normal [20]. Such growth must be provided to obtain structures suitable for application in devices. For the fully relaxed samples, diffraction nods are placed along the diffraction vector. When they are partly relaxed, nods are located in an intermediate position.
Thus, in case when intensity distribution from SL and substrate are placed on the surface normal, it shows coherent interface, on the other hand, another placement of intensity distribution corresponds to some relaxation level of SL with respect to the substrate [20].
A small shift between SL satellites and buffer layer in the vertical direction, which indicates partial relaxation at this boundary (
0
1
¹
D
a
), was observed in our work. Moreover, for S1 sample relaxation level is higher (r1 = 0.047) than for the sample S2 (r1 = 0.037).
Interesting fact was noticed from RSM: peak position of GaN indicates a compressed state. Thus, the buffer layer wasn’t fully relaxed. The average lattice parameter а of SL is bigger than that parameter of the buffer layer. It indicates that pseudomorphic growth of SL is corrupted and appearance of satellites shows the coherent growth.
Broad intensity distribution from the buffer layer GaN and satellites from SL AlxGa1–xN/GaN is depicted in Fig. 2. As one can see from this figure, intensity maxima from the buffer layer GaN are wider in Qx direction, which indicates presence of defects (point defects, dislocations). It is well known that the epitaxial layer of III-nitride is often grown on a sapphire substrate and has a high dislocation density of threading dislocation ((109 cm–2), which leads to broadening of diffraction maxima in the direction parallel to surface [21, 22]. In our case, the dislocation density in
N/GaN
Ga
Al
x
1
x
-
SL is extremely lower ((
2
7
cm
10
-
). Also, from analysis of Fig. 2 one can observe broadening of satellites in direction along the diffraction vector. This indicates a stronger effect of mosaicity in SL than in the buffer layer.
Modeling of experimental DC for the symmetrical reflex 0002, being based on the dynamical diffraction theory, was used for a more precise analysis of
N/GaN
Ga
Al
x
1
x
-
parameters (Fig. 3) [11]. In Fig. 3, the sharp peak corresponds for 0002 reflex from the buffer layer GаN, broader peaks (satellites) corresponds to SL
N/GaN
Ga
Al
x
1
x
-
. The peak position of SL depends on both composition of SL and the ratio of layer thickness.
δθ is the distance between satellites, which marks both SL–1 and SL0, corresponds to the SL period (T = twell + tbarrier =
(
)
dq
q
l
g
B
2
sin
h
, where λ is the X-ray wavelength, γh – directing cosines of the X-ray beam, more frequent fringes are caused be the total thickness of SL. The relative intensity of the satellites was used to obtain the thickness ratio, and then the composition of solid solution
N
Ga
Al
x
1
x
-
[23]. Parameters of SL were obtained from RSM and refined by a procedure of fitting experimental and calculated DC [14, 15]. They are given in Table 1.
Vertical lattice parameters c of buffer layers GaN were calculated from relative changes of the peak position between the buffer layer GaN (0002) and sapphire substrate (0006). The sapphire peak height was used as a reference value. The parameters c from DC were 5.1856 Å for S1 sample and 5.1859 Å for S2 sample. These values were used for calculation of the perpendicular strain (perpendicular to the growth plane) εzz by using the formula:
εzz = (c – c0)/c0,
(12)
where c0 = 5.1855 Å lattice parameter for unstrained layer GaN [18]. Perpendicular strain has tensile character as for S1 εzz = 1.9·10–5 as for S2 εzz =
5
10
7
.
7
-
×
, respectively. The parallel strain was calculated using the following relation:
εxx = (a – a0)/a0,
(13)
where a0 = 3.1891 Å. The lattice parameters a were obtained from asymmetric scans for
5
1
10
and
4
2
11
reflections, a = 3.1631 Å and a = 3.1542 Å for S1 and S2, respectively. The parallel compressing strains are εxx =
3
10
1
.
8
-
×
-
for S1 and εxx =
2
10
1
.
1
-
×
-
for S2. Let us note that the initial parameters for the buffer layer GaN were the same for all the structures.
SNMS depth profiles of Al and Ga elements in AlxGa1–xN/GaN SL within the upper three periods for S1 and S2 samples are presented in Fig. 4. We observed the increase of the GaN well layer thickness by 0.5 nm for both samples. In both samples, the
N
Ga
Al
x
1
x
-
barrier layer thickness is different, with deviation from nominal value of 0.5 to 1.5 nm. The barrier layer thickness deviation with depth was observed to be equivalent in each period for S1. On the other hand, for S2 we observed reducing the barrier layer thickness in each dipper period. All the thickness values are presented in Table 1.
5. Discussion
AlхGa1–хN/GaN SL were grown on the buffer layer GaN, which are in the compressed state that is partly relaxed. The difference between the buffer GaN and average SL lattice parameters a indicates partial relaxation on interface buffer layer – SL, i.e. relaxation on the bottom interface, which was observed for all SL. The calculated lattice parameters obtained from asymmetric RSM
(
)
4
2
11
are summarized in Table 2. From these results, both SL are compressed, but the strain is less than that in the buffer layer. Difference of average SL lattice parameter for S1 and S2 caused by changes in the layer thickness ratio. It influences on the strain state of the buffer and whole system.
N/GaN
Ga
Al
x
1
x
-
As it follows from these results, GaN wells as well as the barrier
N
Ga
Al
x
1
x
-
in SL are in the compressed state ((xx < 0) for all the structures (Table 2). The buffer layer also is in the compressed state and leads to the respective state of SL. But in SL this deformation is bigger in well GaN than in the barrier
N
Ga
Al
x
1
x
-
. However, the compressing strain is less for S1 than for S2, which is caused by the different thickness ratio (well-barrier). This behavior in the SL period can be explained from determination of average parameters. Average lattice parameters in the SL period were calculated from the equations (1)-(6). From these equations, one can see that those SL periods are strongly dependent on the thickness ratio well-barrier and on barrier composition.
Deformation profiles with depth of SL calculated with respect to the ideal values of GaN and
N
Ga
Al
x
1
x
-
are presented in Fig. 5.
The parameter of each SL layer tends to reach the average SL parameter SL0_real, since it tends to reach the real parameter value of the buffer layer GaN (Fig. 5).
Layers in S2 are more strained with respect to the average SL parameter than those in S1. It well correlates with broadening of RSM (0.0064 rlu and 0.0048 rlu, for S1 and S2, respectively (Fig. 1)) as well as with the dislocation density that is less in the more strained structure S2.
The strain level of whole SL with respect to buffer layer depends on type of SL. Relaxation is slower for SL with a thick well because of the smaller lattice parameter mismatch between SL and GaN buffer. Compression of the buffer layer affects the strain level in the SL layer and average lattice parameters in the period. But deformation jump at the interfaces of SL layer remains the same, only weak changes of the ratio of strain between the SL layers were observed.
The difference of parameters Δt = texp – ttechn corresponding to the difference between technological and experimental layer thicknesses are probably caused by different deformation state of the system. As one can see from Fig. 6 for the
N
Ga
Al
x
1
x
-
barrier, the increase of deformation leads to enhancement of the growth rate, on the other hand, we observed the opposite process in the GaN layer. The same changes in the growth rate for the
N
Ga
Al
x
1
x
-
barrier under reducing of mechanical strains were observed in [24]. Explanation of thickness changes with those of deformation was deduced from the first principles for AlxGa1–xN/GaN SL [25].
Fig. 5. Deformation profiles alternating with depth of SL in S1 and S2 samples.
Fig. 6. Dependence of the growth rate V of SL layers
AlxGa1–xN and GaN on the deformation level.
As it follows from Table 1, deformation changes in SL do not lead to significant changes in the dislocation density Ns and curvature radius Rcurv for each sample. Thus, at the practically equal curvature radius and small deviation of dislocation density we observed different relaxation states for S1 and S2 samples. But, to explain this difference in the relaxation state only due to formation of dislocation is impossible. It indicates that thickness changes of
N
Ga
Al
x
1
x
-
and GaN layers can be additional relaxation channel in these SLs. Moreover, the process of relaxation and formation of defects are strongly interrelated [26].
5. Conclusions
The deformation state of short-period SL and its individual layers, relaxation state, period and layer thickness, composition of
N
Ga
Al
x
1
x
-
were obtained using the X-ray diffraction methods.
It was ascertained that the buffer layer as well as SL layers are compressed in all the investigated structures. Thus, it was shown that deformation of SL period depends on the well-barrier thickness ratio. It, to some extent, determines the relaxation state of whole SL with respect to the buffer layer. However, relaxation state of buffer layer strongly affects deformation of the whole system. The dependence between the growth rate of individual layer and deformation state has been shown. The increase in deformation leads to enhancement of the growth rate for the barrier.
Thus, structural, optical and electro-physical properties of SL are determined by the process of elastic strain relaxation that leads to changing the well and barrier thickness.
This study was supported by the National Academy of Sciences of Ukraine within the framework of the scientific-technological programs “Nanotechnology and Nanomaterials” №3.5.1.12 and №3.5.1.30.
References
1.
H. Morkoç, Handbook of Nitride Semiconductors and Devices: Electronic and Optical Processes in Nitrides. Berlin, Wiley-VCH, 2008.
2.
P. Ruterana, M. Albrecht, J. Neugebauer, Nitride Semiconductors: Handbook on Materials and Devices. Berlin, Wiley-VCH, 2003.
3.
V.P. Kladko, S.V. Chornen’kii, A.V. Naumov, A.V. Komarov, M. Tacano, Yu.N. Sveshnikov, S.A. Vitusevich, and A.E. Belyaev, Interface structural defects and photoluminescence properties of epitaxial GaN and AlGaN/GaN layers grown on sapphire // Semiconductors, 40, p. 1060 (2006).
4.
V.P. Kladko, A.F. Kolomys, M.V. Slobodian, V.V. Strelchuk, V.G. Raycheva, A.E. Belyaev, S.S. Bukalov, H. Hardtdegen, V.A. Sydoruk, N. Klein, and S.A. Vitusevich, Internal strains and crystal structure of the layers in AlGaN/GaN heterostructures grown on sapphire substrate // J. Appl. Phys., 105, 063515 (2009).
5.
V.P. Kladko, A.V. Kuchuk, N.V. Safryuk, V.F. Machulin, A.E. Belyaev, H. Hardtdegen, S.A. Vitusevich, Mechanism of strain relaxation by twisted nanocolumns revealed in AlGaN/GaN heterostructures // Appl. Phys. Lett. 95, 031907 (2009).
6.
V.P. Kladko, A.V. Kuchuk, P.M. Lytvyn, O.M. Yefanov, N.V. Safriuk, A.E. Belyaev, Yu.I. Mazur, E.A. DeCuir Jr, M.E. Ware, and G.J. Salamo, Substrate effects on the strain relaxation in GaN/AlN short-period superlattices // Nanoscale Res. Lett. 7, p. 289 (2012).
7.
H. Amano, K. Hiramatsu, and I. Akasaki, Heteroepitaxial growth and the effect of strain on the luminescence properties of GaN films on
(
)
0
2
11
and
(
)
0001
sapphire substrates // Jpn. J. Appl. Phys., 27, L1384 (1988).
8.
A. Bykhovski, B. Gelmont, and M. Shur, The influence of strain-induced electric field on the charge distribution in GaN-AlN-GaN structure // J. Appl. Phys. 74, p. 6734 (1993).
9.
F. Bernardini, V. Fiorentini, and D. Vanderbilt, Spontaneous polarization and piezoelectric constant of III-V nitrides // Phys. Rev. B, 56, R10024 (1997).
10.
P.K. Kandaswamy, F. Guillot, E. Bellet-Amalric, E. Monroy, L. Nevou, M. Tchernycheva, A. Michon, F.H. Julien, E. Baumann, F.R. Giorgetta, D. Hofstetter, T. Remmele, M. Albrecht, S. Birner, and Le Si Dang, GaN/AlN short-period superlattices for intersubband optoelectronics: A systematic study of their epitaxial growth, design, and performance // J. Appl. Phys. 104, 093501 (2008).
11.
P.K. Kandaswamy, C. Bougerol, D. Jalabert, P. Ruterana, and E. Monroy, Strain relaxation in short-period polar GaN/AlN superlattices // J. Appl. Phys. 106, 013526 (2009).
12.
A. Sarua, Hangfeng Ji, M. Kuball, M.J. Uren, T. Martin, K.J. Nash, K.P. Hilton, and R.S. Balmer, Piezoelectric strain in AlGaN/GaN heterostructure field-effect transistors under bias // Appl. Phys. Lett. 88, 103502 (2006).
13.
O.M. Yefanov, V.P. Kladko, V.F. Machulin, V.B. Molodkin, Dynamical Diffraction of X-rays in Multilayered Structures. Naukova Dumka, Kyiv, 2008.
14.
P.F. Fewster, X-Ray Scattering from Semiconductors. London, Imperial College Press, 2000.
15.
O.M. Yefanov, V.P. Kladko, The solution of the dispersion equation in an explicit format for a case of two strong waves // Metallofizika i Noveishie Tekhnologii, 28, p. 227-244 (2006).
16.
V.B. Molodkin, S.I. Olikhovskii, E.G. Len, E.N. Kislovskii, V.P. Kladko, O.V. Reshetnyk, T.P. Vladimirova, B.V. Sheludchenko, Sensitivity of triple-crystal X-ray diffractometers to microdefects in silicon // phys. status solidi (a), 206(8), p. 1761-1765 (2009).
17.
M. Yamaguchi, T. Yagi, T. Sota, T. Deguchi, K. Shimada, and S. Nakamura, Brillouin scattering study of bulk GaN // J. Appl. Phys. 85, p. 8502 (1999).
18.
W. Paszkowicz, X-ray powder diffraction data for indium nitride // Powder Diffract., 14, p. 258 (1999).
19.
H. Heinke, V. Kirchner, S. Einfeldt, A. Hommel, X-ray diffraction analysis of the defect structure in epitaxial GaN // Appl. Phys. Lett. 77, p. 2145 (2000).
20.
N.V. Safriuk, G.V. Stanchu, A.V. Kuchuk, V.P. Kladko, A.E. Belyaev, V.F. Machulin, X-ray diffraction investigation of GaN layers on Si(111) and Al2O3(0001) substrates // Semiconductor Physics, Quantum Electronics & Optoelectronics, 16(3), p. 265-272 (2013).
21.
Yu.P. Pershin, V.A. Sevtyukova, Ye.N. Zubarev, A.S. Oberemok, V.P. Melnyk, B.M. Romanyuk, V.G. Popov, P.M. Lytvyn, Investigation of the phase interfaces in periodic multilayer Mo/Si structures, using the method of mass-spectrometry of neutral particles // Metallofizika i Noveishie Tekhnologii, 35(12), p. 1617-1627 (2013).
22.
M.A. Moram, M.E. Vickers, X-ray diffraction of
III-nitrides // Repts. Progr. Phys. 72, 036502 (2009).
23.
V. Srikant, J.S. Speck, D.R. Clarke, Mosaic structure in epitaxial thin films having large lattice mismatch // J. Appl. Phys. 82, p. 4286 (1997).
24.
R.N. Kyutt, M.P. Shcheglov, V.Yu. Davydov, A.S. Usikov, Deformation of layers in superlattices AlGaN/GaN according to XRD analysis // Fizika Tverd. Tela, 46, p. 353 (2004), in Russian.
25.
Y. Kotsar, B. Doisneau, E. Bellet-Amalric, A. Das, E. Sarigiannidou, and E. Monroy, Strain relaxation in GaN/
N
Ga
Al
x
1
x
-
superlattices grown by plasma molecular-beam epitaxy // J. Appl. Phys. 110, 033501 (2011).
26.
A.V. Kuchuk, V.P. Kladko, T.L. Petrenko, V.P. Bryksa, A.E. Belyaev, Yu.I. Mazur, M.E. Ware, E.A. DeCuir Jr, and G.J. Salamo, Mechanism of strain-influenced quantum well thickness reduction in GaN/AlN short-period superlattices // Nanotechnology, 25, 245602 (2014).
� �
Fig. 4. SNMS depth profiles of Al and Ga elements in � EMBED Equation.3 ��� SL: а) S1, b) S2. Upper (red) curves – Ga distribution, lower (black) curves – Al distribution.
Table 1. Technological (nominal) and experimental parameters of AlхGa1–хN/GaN.
Sample�
Layers of SL�
Tnomin,
nm�
tXRD,
nm�
tSIMS,
nm�
Тnomin/TXRD/Тrefl, nm�
xSIMS/xXRD, %�
Ns, � EMBED Equation.3 ����
Rcurv, m�
�
S1�
GaN�
9�
10�
10�
15.6/17/17.2�
9/10�
8.37�
6.8�
�
�
AlGaN�
6.6�
7�
8�
�
�
�
�
�
S2�
GaN�
6�
5.5�
6.5�
16/18.7/18�
10/10�
6.00�
6.6�
�
�
AlGaN�
10�
13.2�
12.66�
�
�
�
�
�
Table 2. Lattice parameters of the buffer layer and SL: ideal and calculated values.
Sample�
� EMBED Equation.3 ���, nm�
� EMBED Equation.3 ���, nm�
� EMBED Equation.3 ���, nm�
� EMBED Equation.3 ���, nm�
(aSL(, nm�
(cSL(, nm�
� EMBED Equation.3 ���, nm�
� EMBED Equation.3 ���, nm�
�
S1�
0.318598�
0.51767�
0.31892�
0.51850�
0.316422�
0.520625�
0.316314�
0.521985�
�
S2�
0.318368�
0.51708�
0.31892�
0.51850�
0.315526�
0.521079�
0.315417�
0.522979�
�
� �
Fig. 2. RSM � EMBED Equation.3 ��� for SL AlGaN/GaN: S1 (a), S2 (b). Qу and Qx are reciprocal space coordinates perpendicular and parallel to the surface, respectively. � EMBED Equation.3 ��� is the diffraction vector, � EMBED Equation.3 ��� – surface normal vector, SL0 – position of SL0 satellite.
� �
Fig. 3. ω–2θ-scans for symmetrical reflex 0002 from SL AlGaN/GaN: а) S1, b) S2. Experiment – lower (red) curve, fitting– upper (black) curve. SLn – satellites of SL.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
317
2
7
cm
10
-
´
id
SL
a
id
SL
c
id
a
GaN
id
c
GaN
buf
a
GaN
buf
c
GaN
(
)
4
2
11
H
r
n
r
_1472802285.unknown
_1477903335.unknown
_1477903381.unknown
_1477903556.unknown
_1477903599.unknown
_1477904360.unknown
_1477904685.unknown
_1477904019.unknown
_1477903588.unknown
_1477903385.unknown
_1477903350.unknown
_1477903354.unknown
_1477903347.unknown
_1472926383.unknown
_1472926682.unknown
_1473236819.unknown
_1473238159.unknown
_1473238557.unknown
_1473236825.unknown
_1472929946.unknown
_1472930695.unknown
_1472929865.unknown
_1472926643.unknown
_1472802470.unknown
_1472802550.unknown
_1472924653.unknown
_1472924816.unknown
_1472924225.unknown
_1472924252.unknown
_1472802680.unknown
_1472802509.unknown
_1472802435.unknown
_1472802448.unknown
_1472802342.unknown
_1472753389.unknown
_1472754516.unknown
_1472754793.unknown
_1472758126.unknown
_1472758277.unknown
_1472800819.unknown
_1472800896.unknown
_1472801784.unknown
_1472800862.unknown
_1472800807.unknown
_1472758233.unknown
_1472756149.unknown
_1472757095.unknown
_1472755034.unknown
_1472754581.unknown
_1472754764.unknown
_1472754537.unknown
_1472754196.unknown
_1472754410.unknown
_1472754471.unknown
_1472754207.unknown
_1472753567.unknown
_1472754172.unknown
_1472753417.unknown
_1472753109.unknown
_1472753171.unknown
_1472753205.unknown
_1472753131.unknown
_1472752949.unknown
_1472753096.unknown
_1472752945.unknown
_1462195047.doc
aAlGaN
aav
aGaN
compressive
buffer
(a1
(a2
tensile
AlGaN
GaN
Рис. 4 . Схематическое распределение параметра решетки a по глубине сверхрешетки AlGaN/GaN на буферном слое GaN. Пунктирные линии соответствуют параметру a для ненапряженных слоев и среднему значению по периоду сверхрешетки.в сверхрешетке.
|