The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure
Numerical simulation based on FPLAPW calculations is applied to study the lattice parameters, bulk modulus, band energy and optical properties of the zincblende binary solids AlN, GaN, InN under hydrostatic pressure. The results obtained are in a good agreement with experimental and theoretical valu...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1214242017-06-15T03:05:28Z The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure Berrah, S. Abid, H. Boukortt, A. Numerical simulation based on FPLAPW calculations is applied to study the lattice parameters, bulk modulus, band energy and optical properties of the zincblende binary solids AlN, GaN, InN under hydrostatic pressure. The results obtained are in a good agreement with experimental and theoretical values. 2006 Article The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure / S. Berrah, H. Abid, A. Boukortt // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 2. — С. 12-16. — Бібліогр.: 43 назв. — англ. 1560-8034 PACS 71.20.Mq, 78.40.Fy http://dspace.nbuv.gov.ua/handle/123456789/121424 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Numerical simulation based on FPLAPW calculations is applied to study the lattice parameters, bulk modulus, band energy and optical properties of the zincblende binary solids AlN, GaN, InN under hydrostatic pressure. The results obtained are in a good agreement with experimental and theoretical values. |
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Berrah, S. Abid, H. Boukortt, A. |
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Berrah, S. Abid, H. Boukortt, A. The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure Semiconductor Physics Quantum Electronics & Optoelectronics |
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Berrah, S. Abid, H. Boukortt, A. |
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Berrah, S. |
| title |
The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure |
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The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure |
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The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure |
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The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure |
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The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure |
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first principle calculation of electronic and optical properties of aln, gan and inn compounds under hydrostatic pressure |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The first principle calculation of electronic and optical properties of AlN, GaN and InN compounds under hydrostatic pressure / S. Berrah, H. Abid, A. Boukortt // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 2. — С. 12-16. — Бібліогр.: 43 назв. — англ. |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 2. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
12
PACS 71.20.Mq, 78.40.Fy
The first principle calculation of electronic and optical properties
of AlN, GaN and InN compounds under hydrostatic pressure
S. Berrah1, H. Abid2, A. Boukortt3
Applied materials laboratory, university of Sidi Bel Abbes, 22000 Algeria
1E-mail: sm_berrah@yahoo.fr
2E-mail: abid_hamza@yahoo.fr
3E-mail: boukortta@yahoo.fr
Abstract. Numerical simulation based on FPLAPW calculations is applied to study the
lattice parameters, bulk modulus, band energy and optical properties of the zincblende
binary solids AlN, GaN, InN under hydrostatic pressure. The results obtained are in a
good agreement with experimental and theoretical values.
Keywords: lattice parameter, bulk modulus, pressure coefficient, refraction index,
FPLAPW, WIEN(2k).
Manuscript received 26.12.05; accepted for publication 29.03.06.
1. Introduction
The wide energy gap III-V nitride semiconductors GaN,
AlN, InN and their quantum well structures have
received considerable attention for their device
applications in the blue and ultraviolet wavelengths [1–
7]. Recently, the successful fabrication of the blue light
III-V nitride semiconductor laser was first demonstrated
by Nakamura [1]. The vast majority of research on III-V
nitrides has been focused on the wurtzite crystal phase.
The reason is that most of III-V nitrides have been
grown on sapphire substrates which generally transfer
their hexagonal symmetry to the nitride film.
Nevertheless, interest in zincblende nitrides has been
growing recently [2–6].
The zincblende GaN has a higher saturated electron
drift velocity and a somewhat lower energy gap than
wurtzite GaN [7].
The pressure dependence of the photoluminescence
of semiconductors is very useful in understanding the
electronic energy band structure and structural
properties. The effect of pressure on the electronic
properties of III–V compounds can be investigated
experimentally in many ways [8–12]. On the other hand,
both theoretical and technical developments in density
functional theory (DFT) and pseudopotential
calculations in recent decades have provided researchers
with powerful methods for predicting electronic and
energetic properties as revealed by novel experimental
techniques. Meanwhile, the technical development of
epitaxial growth at the end of the last century has
provided the possibility for researchers to fabricate
synthetic materials with expected compositions and
structures. The situation has stimulated extensive
computational studies on high-pressure behavior of
various semiconductors [13–17].
In this work, we carry out all-electron full-potential
linearized-augmented plane waves (FPLAPW)
calculation to determine band structure and optical
properties of cubic binary AlN, GaN and InN under
pressure within the local density approximation (LDA).
2. Calculations
Total energy calculations are performed using the
FPLAPW. In this method, the unit cell is partitioned into
non-overlapping muffin-tin spheres around the atomic
sites and an interstitial region. In these two types of
regions, different basis sets are used, the Kohn-Sham
equation which is based on the DFT [18-19] is solved in
a self-consistent scheme. For the exchange-correlation
potential, we use the LDA ([20-21] in which the orbitals
of Al (3s23p1), Ga (3d104s24p1), In (4d105s25p1) and N
(2s22p3) are treated as valence electrons.
For these calculations the existing WIEN(2k) code
[22] is used and applied to large unit cells. The muffin-
tin radial adopted were 2.0 a.u (Ga), 1.60 a.u. (N),
2.1 a.u (In), and 1.8 a.u. (Al).
In the following, we use the FPLAPW method to
study the bandgap and optical properties under pressure
for the binary compounds of the zincblende type, GaN,
AlN and InN.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 2. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
13
3. Result and discussion
The theoretical lattice parameters and bulk modulus in
this section are obtained through fitting the total energy
data with the Murnaghan equation of state [23]:
0
0
0
0
0
0
0 1
)/(
)()(
0
B
VB
B
VV
B
VB
VEVE
B
′
−
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
′′
=−
′
,
where E(V) is the DFT ground-state energy with the cell
volume V, V0 is the unit-cell volume at zero pressure, B0
denotes the bulk modulus, and their first pressure
derivatives B0′ = ∂B/∂p at p = 0 GPa.
The calculated structural properties (lattice para-
meters a, bulk modulus B0 and B0′) of the binaries are
summarized in Table 1. We have an underestimation of
the lattice parameters and an overestimation of the bulk
modulus in comparison to those of experiment (Table 1),
due to the use of the LDA. Table 1 shows that B0′ ≈ 4 for
AlN, GaN and InN, which is consistent with previous
results of EOS studies [24]. By the use of our calculated
values of the bulk modulus B0, and their first pressure
derivatives B0′, the volume change with applied pressure
was calculated using the following equation [29]:
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−⎟
⎠
⎞
⎜
⎝
⎛
′
= 1
'
0
0
0
0
B
V
V
B
Bp .
The pressure dependence of Eg at the Γ, X, and L
points of the energy band for the ZB phase. From the
present energy band structure calculation are plotted in
Figs 1, 2, and 3. Since the range of cell volume variation
is ±2.0 % for all the phases in our energy band
calculations.
Table 1. The lattice parameters a, bulk modulus, and their
first pressure derivative B′0.
a (Å) 0B (GPa) 0B′
AlN Present work 4.353 207.85 4.186
PWPP[25]
Other work[26]
4.323
4.32
203.2
203
4.182
-
Experiment 4.38 [27]
4.37 [29]
202 [28] -
GaN Present work 4.475 205.38 4.80
PWPP[25]
Other work
4.335
4.446 [30]
207
201 [26]
4.136
-
Experiment 4.52[27]
4.50[2]
190 [28] -
-
InN
Present work
4.949
141.16
3.47
PWPP[25]
Other work[26]
4.801
4.92
147.6
139
4.06
-
Experiment 4.98[27] 137[28] -
Fig. 1.Variation of three bandgaps Γ, X, and L versus pressure
for GaN.
Figs 1, 2, and 3 indicate that the fundamental
bandgap stays direct for InN (Fig. 2) and indirect for
AlN (Fig. 3) under the pressure applied up to 21.5 GPa.
In contrast, for GaN (Fig. 1), the fundamental gap
becomes indirect (X) at pressure 15.53 GPa. For wurtzite
GaN Zhongqin et al. [43] with using semiempirical
tight-binding theory found that it pass from direct to
indirect bandgap under 5 % strains.
In order to calculate the pressure coefficients of the
fundamental bandgap, we have fitted )( pEg
Γ to the
following linear equation: )( pEg
Γ = )0(Γ
gE + k.p.
Where )0(Γ
gE is the energy bandgap at the Γ point when
p = 0 and is given in Table 2. k is the pressure coefficient
defined by k = pdEg /Γ different values for which are
shown in Table 2 along with some other theoretical
results.
For Γ bandgap, our calculations give
42.86 meV·GPa−1 for GaN, 19.94 meV·GPa−1 for InN,
and 44.68 meV·GPa−1 for AlN. These results are in good
agreement with the plane wave pseudopotential (PWPP)
calculations of Kim et al. [25] for GaN and AlN, which
gave 41.7 and 45.0 meV·GPa−1, respectively. For InN,
we note that it is slightly larger than ours, namely,
Fig. 2. Variation of three bandgaps Γ, X, and L versus pressure
for InN.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 2. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
14
Fig. 3. Variation of three bandgaps Γ, X, and L versus pressure
for AlN.
34.0 meV·GPa−1. Christensen and Gorczyca [15], using
LMTO calculations, have reported 42 meV·GPa−1 for
AlN, 40 meV·GPa−1 for GaN and 16 meV·GPa−1 for InN.
The pseudopotential results of Van Camp et al. [13] for
InN gave 25.4 meV·GPa−1.
Table 2. Bandgap at the Γ point and pressure coefficients
k = dpdEg /Γ for GaN, AlN, and InN.
gEΓ k (meV·GPa−1)
AlN Present work 4.24 44.68
PWPP[25] 4.503 45.0
5.94 [25] 42.0 [15]
GaN Present work 1.80 42.86
PWPP[25] 3.211 41.7
3.3 [25] 40.0 [15]
InN Present work 0.00034 19.94
PWPP[25] 0.753 34.0
Others 16 [15], 25.4 [13]
0.9 [25]
4. Optical properties
We discuss now the optical properties of GaN, AlN and
InN. Table 3 shows the dielectric constant ε1(0),
refraction index n and pressure coefficient index
d(lnn)/dp in 10−2 GPa−1 for GaN, AlN, and InN in
comparison with the data in the literature. We can state a
quite good agreement of our data with the previously
published results. Comparison of our results with
previous LMTO data presented in Table 3 shows that
LMTO data systematically underestimate experimental
and FPLAPW results.
Fig. 4 shows the variation of the imaginary part of
the electronic dielectric function ε2 under normal condi-
tions and under hydrostatic pressure for the GaN, AlN,
and InN for radiation up to 15 eV. The calculated results
are shifted rigidly upwards by 1.5 eV in GaN, 1.66 eV
for AlN and 0.69 eV for InN. There are three groups of
peaks, the first is in (3.37 – 10.58 eV) photon energy
range, they are mainly due to transitions in the vicinity
of M. This is usually associated with E1 transition.
However, the L3v-L1c transition occurs at 8.75 eV for
GaN. Similarly, the main peak in the spectra of InN and
AlN is located at 6.27 and 9.56 eV, respectively. The
second group of peaks is located in 10 – 12.75 eV for
GaN, 7.7 – 10.04 eV for InN and 9.5 – 11.95 eV for
AlN. These come from the transition L, L. The latter
group of peaks is connected mainly to transitions at Г, Γ.
The refraction index n shown in Fig. 5 was
computed as a function of real dielectric function,
1ε=n [23]. The values of the refraction index
)0(1ε=n at low frequency are depicted in Table 3, it
shown that the results occurs well with those obtained
using the Moss model [42]
25.0
95
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
gE
n , where Eg is
the direct bandgap. With looking to the pressure
coefficient index, it deduces that the refraction index
decreases under pressure, and we derived also the
refraction index.
Table 3. The calculated dielectric constant ε(0), refraction
index, and pressure coefficients of the refraction index in
10−2 GPa−1 for GaN, AlN, and InN.
ε(0) n d(lnn)/
dp(GPa−1)
GaN Present
work
5.49 2.34 −0.28
5.30 [31] 2.3 [32] −0.20 [15]
5.47 [34] 2.31[42] −0.05 [33]
GGA 5.71 [35]
LMTO 4.68 [15]
5.74 [36]
Experi-
ment
5.7[38],
4.6[37]
2.34 [37]
AlN Present
work
4.256 2.06 −0.31
4.77 [34] 1.99 [42] −0.18 [15]
GGA 4.61 [35]
LMTO 3.86 [15]
4.61 [36]
4.46 [39]
Experi-
ment
4.68 [40]
InN Present
work
8.56 2.92 −2.60
8.4 [34] 3.20 [42] −0.43 [15]
GGA 7.46 [35]
LMTO 7.16 [15]
Experi-
ment
8.40 [41]
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 2. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
15
Fig. 4. Imaginary part of the dielectric function of GaN, InN,
and AlN under normal conditions and under pressure.
Fig. 5. Refraction index of GaN, AlN, and InN.
5. Conclusions
In this work, we have reported the band structure and
optical properties of zincblende GaN, AlN and InN
under pressure with using FPLAPW method within
LDA.
It was shown that for AlN and InN, the
fundamental bandgap increases and stays direct with
pressure, while for GaN, the fundamental bandgap
becomes indirect (Γ-X) at p = 15.53 GPa. So, in the view
of fabrication of blue emitting-light devices, it is
necessary to try to decrease strains.
However, the pressure coefficient of the
fundamental gap obtained are in a good agreements with
others.
The optical properties of zincblende nitrides have
been also investigated under normal conditions and
under hydrostatic pressure. It is shown that the refraction
index decreases under pressure. Our value d(lnn)/dp =
−0.28·10−2 GPa−1 for GaN, −0.31·10−2 GPa−1 for AlN and
−2.6·10−2 GPa−1 for InN obtained from the calculated
ε1(0). They are in an excellent agreement with the
experimental value, −0.19·10−2 GPa−1 for GaN, –0.18 for
AlN and –0.43 for InN [15].
Acknowledgements
We would like to acknowledge S.Q. Wang from
Shenyang National Laboratory for Materials Science,
Institute of Metal Research, Chinese (republic of China)
and K. Louzazna from university of Béjaia (Algéria) for
their help.
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