The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys
Numerical simulation based on FP-LAPW calculations is applied to study direct and indirect band gap energy of the cubic AlxGa₁₋xN, InxGa₁₋xN and InxAl₁₋xN alloys.The direct and indirect band-gap bowing parameter is also calculated, and the values obtained are very important, as we find a stron...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2008
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| Цитувати: | The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys / S. Berrah, A. Boukortt, H. Abid // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 59-62. — Бібліогр.: 34 назв. — англ. |
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irk-123456789-1186702017-05-31T03:06:44Z The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys Berrah, S. Boukortt, A. Abid, A. Numerical simulation based on FP-LAPW calculations is applied to study direct and indirect band gap energy of the cubic AlxGa₁₋xN, InxGa₁₋xN and InxAl₁₋xN alloys.The direct and indirect band-gap bowing parameter is also calculated, and the values obtained are very important, as we find a strong dependence of the bowing parameter on the composition. 2008 Article The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys / S. Berrah, A. Boukortt, H. Abid // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 59-62. — Бібліогр.: 34 назв. — англ. 1560-8034 PACS 71.20.-b, 71.55.Eq http://dspace.nbuv.gov.ua/handle/123456789/118670 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
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Numerical simulation based on FP-LAPW calculations is applied to study
direct and indirect band gap energy of the cubic AlxGa₁₋xN, InxGa₁₋xN and InxAl₁₋xN
alloys.The direct and indirect band-gap bowing parameter is also calculated, and the
values obtained are very important, as we find a strong dependence of the bowing
parameter on the composition. |
| format |
Article |
| author |
Berrah, S. Boukortt, A. Abid, A. |
| spellingShingle |
Berrah, S. Boukortt, A. Abid, A. The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Berrah, S. Boukortt, A. Abid, A. |
| author_sort |
Berrah, S. |
| title |
The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys |
| title_short |
The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys |
| title_full |
The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys |
| title_fullStr |
The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys |
| title_full_unstemmed |
The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys |
| title_sort |
composition effect on the bowing parameter in the cubic ingan, algan and alinn alloys |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118670 |
| citation_txt |
The composition effect on the bowing parameter in the cubic InGaN, AlGaN and AlInN alloys / S. Berrah, A. Boukortt, H. Abid // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 59-62. — Бібліогр.: 34 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 59-62.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
59
PACS 71.20.-b, 71.55.Eq
The composition effect on the bowing parameter
in the cubic InGaN, AlGaN and AlInN alloys
S. Berrah, A. Boukortt, and H. Abid
Applied materials laboratory, university of Sidi Bel Abbes, 22000 Algeria
E-mail: sm_berrah@yahoo.fr.
Abstract. Numerical simulation based on FP-LAPW calculations is applied to study
direct and indirect band gap energy of the cubic AlxGa1-xN, InxGa1-xN and InxAl1-xN
alloys.The direct and indirect band-gap bowing parameter is also calculated, and the
values obtained are very important, as we find a strong dependence of the bowing
parameter on the composition.
Keywords: III-V ternary alloys, band-gap bowing parameter, WIEN(2k).
Manuscript received 17.12.07; accepted for publication 07.02.08; published online 31.03.08.
1. Introduction
III-V nitrides and their alloys are becoming increasingly
important for the development of optical and high
temperature electronic devices due to their wide band
gap. These materials and their quaternary alloys cover
the energy band-gap range of 0.7-6.2 eV and high
saturation velocity [1-3]. For their potentials in opto-
electronics (emitters and detectors) [4-6] and high power
electronic devices as have been treated in length and
received recently countless weight.
The recent progress in this field led to fabrication
of efficient light emitting diodes and laser diodes
operating in the green-blue-UV spectral region [7-8]. In
contrast to the ternary InGaN and AlGaN alloys [9-11],
slight attention has been paid to InAlN, due to the
difficulty in growing it [12-14]. The InAlN alloy
exhibits a large band-gap variation, and it is expected
that the alloy lattice matched to GaN [15] would have a
sufficiently large energy.
In this work, we study the influence of the band
gap bowing on the structural and electronic properties of
the cubic ternary alloys InGaN, AlGaN, and AlInN.
2. Calculation
Total energy calculations are performed using the full
potential linearized augmented plane wave (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 kinds of regions,
different basis sets are used. Inside the atomic sphere, a
linear combination of radial functions multiplied by
spherical harmonics is used, furthermore, the plane
waves are used in the interstitial region.
The Kohn-Sham equation that is based on the
density functional theory (DFT) is solved in a self-
consistent scheme. For the exchange-correlation
potential, we use the local density approximation (LDA)
[16-19]. The orbital of Al (3s23p1), Ga (3d104s24p1), In
(4d105s25p1) and N (2s22p3) are treated as valence
electrons.
In these calculations, the existing WIEN2k code
[20] is used. The required precision in the total energy
was achieved by using a large plane wave (PW) cut-off.
In the linear APW (LAPW) method the relevant
convergence parameter is RMT: Kmax = 8.
The ordered cubic alloys were modelled using the
Landau-Lifshitz structures [21, 22] in which the binary
compounds AlN, GaN, and InN possess a zinc-blende
structure, the ternary alloys for the composition x = 0.5
(InGaN)2, (AlGaN)2, and (InAlN)2 are modelled using
the chalcopyrite structure, which could be considered as
a (2,2) zinc-blende superlattice along the 〈201〉 direction.
For the composition x = 0.75 or x = 0.25 (In3GaN4
or InGa3N4), (Al3GaN4 or AlGa3N4), and (In3AlN4 or
InAl3N4) we have adopted the luzonite structure.
3. Results and discussion
3.1. Electronic properties
The different values of the band gap at Γ and X point of
the binary compound GaN, AlN, and InN are
summarized in Table 1, as seen in this table, the
FPLAPW method underrates the gap, it is owing to two
facts, the first is using LDA and the second is the
presence of the states d known by their effect on the gap
in the GaN and InN compounds.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 59-62.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
60
Table 1. The direct and indirect band gaps of AlN, GaN,
and InN by our calculation and those by other researchers.
The both compounds GaN and InN present a direct
band gap, whilst AlN has an indirect band gap.
In the ternary alloys, InGaN, AlGaN and InAlN,
the direct band gap (Γ) and indirect (X) one are existing
in Figs. 1, 2, and 3, respectively. Although the gap is
underestimated, its variation is well described by the
LDA.
In InxGa1-xN the gap stays direct in the range
composition from x = 0 corresponding to GaN to
x = 1 (InN).
In AlxGa1-xN, the direct and indirect band gaps are
prearranged in Fig. 2. We witness a rapid variation of
the direct band gap with the Al composition; it
conforms to the linear change. In contrast, the indirect
band gap varies gradually. Nevertheless, there is a
direct-indirect switch near x = 0.573, when the band
gap of AlN dominates. This result is in accord with the
values obtained by Albanesi et al. [26] and Wen-Wei
Lin et al. [27], as they found 0.57 and 0.571 with using
the ideal structure and CASTEP calculations,
correspondingly.
0 , 0 0 , 2 0 , 4 0 , 6 0 , 8 1 , 0
0 , 0
0 , 5
1 , 0
1 , 5
2 , 0
2 , 5
3 , 0
3 , 5
4 , 0
4 , 5
5 , 0
I n G a N
I n d i r e c t
D i r e c t
B
a
n
d
-G
a
p
E
n
e
rg
y
(
e
V
)
I n d i u m C o m p o s i t i o n x
Fig. 1. Band-gap energy of InxGa1-xN as a function of indium
composition x, the open circles are the experimental values of
the direct band gap obtained by R. Goldhahn et al. [25].
0 , 0 0 , 2 0 , 4 0 , 6 0 , 8 1 , 0
1 , 0
1 , 5
2 , 0
2 , 5
3 , 0
3 , 5
4 , 0
4 , 5
5 , 0
5 , 5
A l G a N ( D i r e c t )
( I n d i r e c t )
B
a
n
d
-g
a
p
e
n
e
rg
y
(
e
V
)
A l u m i n i u m c o m p o s i t i o n x
Fig. 2. Band-gap energy of AlxGa1-xN as a function of indium
composition x, the open circles are the experimental values of
the direct band gap of Takanobu Suzuki et al. [28].
For AlxIn1-xN, the direct and indirect band gaps are
offered in Fig. 3. There is a swift growth of the indirect
band gap through the composition, hence there is a
transition from direct (Γ) to indirect (X) band gap for
x = 0.23, this result agrees well with the calculation of
Wen-Wei Lin et al. [27], who obtained the transition for
x = 0.244 with using the CASTEP.
4. Discussions
To be aware on the origin of the direct band gap bowing
in III-nitrides alloys AlGaN, InGaN, and InAlN, we
have proceed to the calculation of this parameter
according to the rule of Zunger [29]. In this law, the
bowing parameter is decomposed to three terms, ahead
of developing those terms, we consider in the first pace,
the beneath reaction:
xAC(aAC) + (1 – x)BC(aBC) →AxB1-xC(aeq). (1)
Where aAC and aBC are the equilibrium lattice constants
of the binary compounds AC and BC, respectively, and
aeq is the equilibrium lattice constant of the AxB1-xC
alloy with the average composition x.
0 , 0 0 , 2 0 , 4 0 , 6 0 , 8 1 , 0
0
1
2
3
4
5
A l I n N D i r e c t
I n d i r e c t
B
a
n
d
-g
a
p
e
n
e
rg
y
(
e
V
)
A l u m i n i u m c o m p o s i t i o n x
Fig. 3. Band-gap energy of AlxIn1-xN as a function of
aluminum composition x.
)eV(Γ
gE ( )eVΧ
gE
AlN Present work 4.25 3.16
PWPP [23] 4.503
Exp. [24]
5.94
GaN Present work 1.58 3.2
PWPP [23] 3.211
Exp. [24]
3.3
InN Present work 0.0 1.56
PWPP [23] 0.753
Exp. [24] 0.9
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 59-62.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
61
The second step is to divide the reaction 1 to three
parts:
AC(aAC) + BC(aBC) → AC(a) + BC(a), (2)
xAC(a) + (1–x)BC(a) → AxB1-xC(a), (3)
AxB1-xC(a) → AxB1-xC(aeq). (4)
The first equation (2), dealings the volume
deformation effect on the gap bowing, the corresponding
involvement to the bowing is bVD, it is caused by the
effect of the volume deformation. The second reaction
(3) is due to charge-exchange (CE) contribution bCE, it
reflects a charge transfer effect, it is due to the different
averaged bonding behaviour at the lattice constant a.
The last part (4), measures amend due to the structural
relaxation (SR) in passing from the unrelaxed to the
relaxed alloy, it notes bSR, thus, the total gap bowing
parameter becomes:
b= bVD + bCE + bSR.
Table 2. Direct band-gap bowing parameters of AlGaN (a),
InGaN (b), and InAlN (c) for different composition, all
values are in eV.
a) AlGaN
x composition range 0.25 0.5 0.75
bVD –0.092 –0.08 –0.08
bCE 0.412 0.73 1.20
bSR 0.56 0.10 0.197
b 0.88 0.75 1.317
Other works: 0.068 [31], 0.05 [32], 0.755 [27],
0.632 [24], 0.068 [34].
b) InGaN
x composition range 0.25 0.5 0.75
bVD 1.04 0.90 0.67
bCE 0.49 0.94 0.49
bSR 0.14 0.84 0.10
b 1.67 2.68 1.26
Other works: 1.379 [27], 1.89 [30], 1.37 [24],
1.4 [33], 1.36 [34].
c) AlInN
x composition range 0.25 0.5 0.75
bVD 1.02 1.11 1.21
bCE 2.74 2.32 2.35
bSR 0.42 0.81 0.90
b 4.18 4.24 4.46
Other works: 2.729 [27], 2.914 [24], 1.41 [34].
The results obtained are depicted in Table 2 (a, b,
and c), the value of the bowing linked to the volume
deformation bVD depends on the differences between the
lattice constants of the binary compounds AlN, GaN,
and InN. We imply that bVD is more important in AlInN
and InGaN than AlGaN, this is related to lattice
mismatching between binary compounds, which is 2.5 %
for GaN/AlN, 10 % for GaN/InN and 13 % for AlN/InN.
The bowing due to a charge transfer effect bCE is more
important in AlInN than AlGaN and InGaN, this is
owing to the unlike electronegativities of In and Al
atoms. Finally, the contribution due to the structural
relaxation is tiny for AlGaN, InGaN, and AlInN, in
which the main displacement is due to the anion.
5. Conclusion
Numerical simulation based on first-principle
calculations is developed to investigate the band gap of
the cubic zincblende AlxGa1-xN, InxGa1-xN, and AlxIn1-xN
alloys. From the simulation results, we found that the
band gap sustains an important departure in the AlGaN
and InAlN, in which a transition from direct to indirect
band gap is ruling. The bowing parameter of band gap is
found to be subjugated by the volume deformation and
the charge exchange in AlInN. In this case, there is a
strong dependence of the bowing on the composition
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