quaternary alloys

Cent. Eur. J. Phys. • 11(12) • 2013 • 1680-1685
DOI: 10.2478/s11534-013-0314-1
Central European Journal of Physics
Structural and electronic properties of zincblende
phase of Tlx Ga1−x AsyP1−y quaternary alloys:
First-principles study
Research Article
Sinem E. Gulebaglan∗ , Emel K. Dogan, Murat Aycibin, Mehmet N. Secuk, Bahattin Erdinc, Harun
Akkus †
Physics Department, Faculty of Sciences, Yüzüncü Yıl University,
65080 Van, Turkey
Received 03 July 2013; accepted 10 October 2013
Abstract:
Using the first-principles band-structure method, we have calculated the structural and electronic properties of zincblende TlAs, TlP, GaAs and GaP compounds and their new semiconductor Tlx Ga1−x Asy P1−y
quaternary alloys. Structural properties of these semiconductors are obtained with the Perdew and Wang
local-density approximation. The lattice constants of Tlx Ga1−x As, Tlx Ga1−x P ternary and Tlx Ga1−x Asy P1−y
quaternary alloys were composed by Vegard’s law. Our investigation on the effect of the doping (Thallium
and Arsenic) on lattice constants and band gap shows a non-linear dependence for Tlx Ga1−x Asy P1−y quaternary alloys. The band gap of Tlx Ga1−x Asy P1−y , Eg (x, y) concerned by the compositions x and y. To our
awareness, there is no theoretical survey on Tlx Ga1−x Asy P1−y quaternary alloys and needs experimental
verification.
PACS (2008): 71.15.Mb, 71.20.-b , 71.23.-k
Keywords:
density functional theory • electronic structure of disordered solids • electron density of states and band
structure of crystalline solids
© Versita sp. z o.o.
1.
Introduction
For technological advance, it is important to understand
the characteristics of semiconductors.Technological advances often rely on a thorough understanding of the characteristics of semiconductors. Quaternary systems open
new possibilities for material engineering [1–4]. There
∗
†
E-mail: [email protected] (Corresponding author)
E-mail: [email protected]
are three parameters which have an important role in
the development of new materials. These parameters are
counted as lattice parameter, the band gap and the valence band offset. In scientific and technological areas,
the interest on Thallium compounds have been ascending
in recent years [5–7]. Especially for optical communication systems which are narrowing the band gap [8–10] and
for heterostructure field effect transistor applications [11],
Thallium compounds have been recommended as beneficial applicant. Thallium-V compounds have been indicated
as an alternative to HgCdTe [12]. S. Singh and M. Sarwan investigated high pressure phase transition and elas-
1680
Unauthenticated
Download Date | 10/13/16 7:35 AM
Sinem E. Gulebaglan et al.
tic behavior of TlX (X=N, P, As) semiconductors [13]. Shi
et al. reported structural phase transition, electronic and
elastic properties in TlX (X=N, P, As) compounds [14]. It
is recommended that these structures can be used in communication systems such as laser, detector and diodes.
Takushima et al. [15] experimentally investigated the lowtemperature epitaxial TlInAs by molecular-beam epitaxy
(MBE) and showed that, by decreasing the growth temperature, the size and density of Tl droplets decreased.
Also for some structures which contain Tl, Krishnamurthy
et al. [16] calculated the near band edge absorption spectra and Schilfgaarde et al. [17] studied some optical and
structual properties. Koh et al. [18] experimentally investigated the temperature-dependence of band gap energy
on the semiconductors including Thallium in ternary and
quaternary alloys such as TlInP, TlGaP and TlInGaP.
During our detailed review of literature, we could not uncover any theoretical work on the electronic and structural properties of Tlx Ga1−x Asy P1−y quaternary alloys.
Throughout this work, our calculations were based on
first-principles and we used the local density approximation (LDA) for the exchange-correlation potential. During
our study, we analyzed the structural and electronic properties of Tlx Ga1−x Asy P1−y with respect to different compositions of Thallium and Arsenic. First we have computed
the lattice constant and band gaps for binary zincblende
TlP, GaP, TlAs and GaAs compounds and calculated the
lattice constants as a function of Thallium and Arsenic
compositions (x, y). Moreover, the structural and electronic properties of the Tlx Ga1−x Asy P1−y quaternary alloys calculated. We represented and discussed the results
of those calculations in this paper.
2.
Computational details
In this paper, the structural and electronic properties of
Tlx Ga1−x Asy P1−y alloys are investigated with the Quantum Espresso program1 This programme is based on density functional theory with plane waves, and pseudoptentials. Quantum Espresso calculates ground state properties and make structural optimization, molecular dynamic... etc. In order to investigate the structural properties of the semiconductor compounds, we employed the
exchange-correlation potential using the LDA of Perdew
and Wang [19]. The orbital for Ga ([Ar]3d10 4s2 4p1 ),
for As ([Ar]3d10 4s2 4p3 ), for P([Ne]3s2 3p3 ) and for Tl
([Xe]4f 14 5d10 6s2 6p1 ) are treated as true valence electrons.
S. Baroni, A. Dal Corso, S. de Gironcoli, P. Giannozzi:
http://www.pwscf.org
1
The core states are considered assemi-relativistically (i.e.
spin-orbit coupling is ignored). The crystal structure is
zincblende for the Tlx Ga1−x Asy P1−y quaternary alloy. We
used 16-atom supercell with the 2 × 2 × 2 corresponding
dimension. A supercell is needed to construct the quaternary alloy Tlx Ga1−x Asy P1−y . Enlargement of the supercell is not necessary for accurate computations, however,
the kinetic energy cut off of wave functions and the number of k-points affect the accuracy of calculations. Thus,
we optimized the value of kinetic energy cut off and the
number of k-points. Consequently, we found that 80 Ry
for the energy cut off and 12 × 12 × 12 k-point mesh are
appropriate for the calculations. First, we composed GaP
supercell. Then, we doped Tl and As into this GaP supercell with the determined concentrations of Tl (x=0.25,
0.50, 0.75) and As (y=0.25, 0.50, 0.75) in order to constitute Tlx Ga1−x Asy P1−y quaternary alloys.
3.
Results and discussion
3.1. Structural properties of TlP,TlAs, GaAs,
and GaP
The quaternary compounds Tlx Ga1−x Asy P1−y are confined
by four binary compounds of TlP, TlAs, GaAs, and GaP.
Houat at. al. [12] have investigated structural stability of
Thallium-V compounds: TlN, TlP, TlAs, TlSb and TlBi.
They suggested the ground state structure is zincblende
phase for TlP and TlAs. It is clearly seen in Table 1 that
the lattice constant obtained for TlP and TlAs are in reasonable agreement with other reported values. Similarly,
a small difference is observed between calculated and experimental lattice constant of GaP and GaAs which can be
attributed to the general trend that LDA usually underestimates this parameter [20]. Our calculations are carried
out using the LDA of Perdew and Wang as the exchange
correlation potential, but Houat [12] utilized generalized
gradient approximation (GGA) and Wang [22] deal with
valence electrons and core electrons with local-density
approximation. For this reason, there is a small difference
between these results.
The description of the our calculation model is as follow: we computed the structural and electronic properties
of the binary compounds that crystalize in the two-atom
unit cell zincblende lattice structure. In the course of our
investigation of the structural and electrical properties of
Tlx Ga1−x Asy P1−y quaternary compounds we have to deal
with the zincblende binary compounds of TlP, TlAs, GaAs,
and GaP. The total energy values for different volumes
of these binary compounds was calculated using the LDA
arrangement. Then we fitted the total energies versus vol1681
Unauthenticated
Download Date | 10/13/16 7:35 AM
Structural and electronic properties of zincblende phase of Tlx Ga1−x Asy P1−y quaternary alloys: First-principles study
Table 1.
TlAs (Zincblende)
Itemized lattice parameter a and band gap energy Eg for the
TlAs, TlP, GaAs and GaP in zinc-blende structure phase.
15
10
a (Angstrom) Band Gap Energy (eV)
5.933
∼0.000
TlP [12]
6.124
∼0.000
TlP [22]
5.747
0.158
GaP(Present work)
5.346
∼1.44
GaP [24]
5.358
∼1.360
GaP [25]
5.450
2.35
TlAs(Present work)
6.052
∼0.000
TlAs [12]
6.382
∼0.000
TlAs [22]
5.946
0.0000
GaAs(Present work)
5.614
1.0475
GaAs [22]
5.530
1.0080
5.649 [22]
1.4200 [26]
GaAs
5
Energy (eV)
TlP(Present work)
0
-5
-10
-15
Γ
X
W
L
Γ
K
W
U
K
W
U
TlP (Zincblende)
15
10
E = ET +
B0 V
0
B0
"
0
B0
#
B0 V 0
(V0 /V )
+1 − 0
,
0
B0 − 1
B0 − 1
5
Energy (eV)
ume values by using the Murnaghan equation of states in
order to get the equilibrium lattice parameters and the
band gap energies.
The total energy was discounted for the varying volumes
and the energies were matched to the Murnaghan equation [21]:
0
-5
-10
-15
(1)
where V is the volume and V0 is the zero pressure equi0
librium volume. B0 (T ) and B0 (T ) are the Bulk modulus
and the first derivation of Bulk modulus, respectively. In
this way, we obtained the equilibrium lattice constant and
band gap (Eg ). In Table 1, the equilibrium lattice parameters and band gap energies are demonstrated and an
analogy is made with the experimental results.
One can see from Table 1 that the lattice parameter values increase from GaP to TlAs as aGaP < aGaAs < aTlP <
aTlAs . This order in the lattice parameters of these structures originates in the atomic radius. The value of lattice
parameter in a cubic crystal structure is proportional to
the radius of atoms contained in the crystal structures.
The atomic radius of Ga, Tl, P, and As are 122, 145, 107,
and 119 picometers, respectively. Therefore, the lattice
parameter of structure which contains Tl atom is bigger
than the lattice parameter of structure contains Ga atom.
Additionally, the lattice parameter of crystal structure includes As atom is larger than the lattice parameter of
crystal structure which includes P atom.
The computed electronic band structures for TlP and TlAs
and for GaAs and GaP are plotted in Fig. 1 and Fig. 2.
It can be seen from Fig. 1 that there is no band gap for
the TlP and TlAs compounds investigated and they exhibit nearly semi-metalic character and GaAs and GaP
Figure 1.
Γ
X
W
L
Γ
The electronic band structure of zincblende phase of TlAs
and TlP along high symmetry directions.
are semiconductors (see Fig. 2). The calculated band gap
of TlP and TlAs is in good agreement with Ref. [12]. Some
research groups computed the band gap and lattice parameter of GaAs and GaP [22–24]. Our results are in
acceptable agreement with their results.
3.2. Structural
Tlx Ga1−x Asy P1−y
properties
of
According for that the Vegard’s law is acceptable, the
lattice parameters of Tlx Ga1−x Asy P1−y quaternary alloys
mostly have a linear dependence on Tl composition x and
As composition y, as can be seen in the below expression
a(x, y) = (1 − x)(1 − y)aTlAs + x(1 − y)aGaAs
+ (1 − x)yaTlP + xyaGaP ,
(2)
where aTlAs , aGaAs , aTlP and aGaP are lattice parameters
of binary compounds that are mentioned as subscripts.
1682
Unauthenticated
Download Date | 10/13/16 7:35 AM
Sinem E. Gulebaglan et al.
GaAs (Zincblende)
15
10
Energy (eV)
5
0
-5
-10
-15
Γ
X
W
Γ
L
K
W
U
GaP(zincblende)
15
Energy (eV)
10
5
0
-5
-10
-15
Γ
Figure 2.
X
W
Γ
L
K
W
U
The electronic band structure of zincblende phase of GaAs
and GaP along high symmetry directions.
Table 2.
Calculated lattice parameter, band gap energy (Eg ) and formation energy EF orm (x, y) for the Tlx Ga1−x Asy P1−y quaternary alloys.
x
a(Angstrom) Band Gap Energy (eV) Formation energy
y
0.25 0.25
5.8253
0.0076
-0.066
0.50 0.50
5.7365
-0.036
-0.134
0.75 0.75
5.6658
0.00
0.319
a(x, y) symbolizes the composition dependent lattice constant of Tlx Ga1−x Asy P1−y quaternary alloys. Our results
concerning the relation between the lattice constants of
Tlx Ga1−x Asy P1−y quaternary alloys and the x, y compositions are illustrated in Fig. 3.
We have chosen 16-atoms of 2 × 2 × 2 supercells for modelling the structures of Tlx Ga1−x Asy P1−y quaternary alloys for different Tl and As concentrations of x and y, respectively (x and y = 0.25, 0.5 and 0.75). The calculated
structural properties such as lattice parameters, band gap
energies and formation energies for different concentra-
tions of Tl and As in Tlx Ga1−x Asy P1−y quaternary alloys
are listed in Table 2. Fig. 4., Fig. 5 and Fig. 6 show
that the electronic band structure for the Tlx Ga1−x Asy P1−y
alloys of x= 0.25 and y=0.25; x = y=0.5; x = 0.75
and y = 0.75 concentrations, respectively. We have also
studied the electronic structures of Tl0.25 Ga0.75 As0.25 P0.75 ,
Tl0.5 Ga0.5 As0.5 P0.5 and Tl0.75 Ga0.25 As0.75 P0.25 alloys. For
the concentration rates of x = 0.25 and y = 0.25, the
quaternary alloys show semiconductor character. They
have an indirect band gap with the value of 0.0076 eV
(see Fig. 4.). The top of valance band is located at the
k-point of (-0.1, 0.0 -0.1) while the bottom of conduction
band is located at (0.0, 0.1, 0.0) in the first Brillouin zone.
The quaternary alloys have a semi-metallic character for
the concentration rates of x = 0.5 and y = 0.5. The
lowest unoccupied energy level appears in the k-point of
(-0.1, 0.1, -0.1) while the highest occupied energy level
is located at the Gamma point of the first Brillouin zone
(see Fig. 5.). It is seen from Table 2, the quaternary alloy
has a semi-metalic character for the concentration rates
of x = 0.5, y = 0.5 [see Fig. 5]. However, increasing the
rates of fifty percent Tl and As concentrations lead the
alloy to the metalic structure [see Fig. 6]. On the other
hand, reducing the rations of fifty percent Tl and As concentrations lead the structure to a semiconductor structure [see Fig. 4]. When we analyze the obtained results,
it was noticed that the values of band gaps are directly
related with the compositions of Thallium and Arsenic so
the doped rate of Thallium and Arsenic have an very important effect on the band gaps.
The formation energy, EF orm (x, y) of quaternary alloys at
various doped can be computed with the following formula [27]:
EF orm (x, y) = ETlGaAsP (x, y) − xyEGaP + (1 − x)yETlAs
+ x(1 − y)EGaAs + (1 − x)(1 − y)ETlP ,
(3)
where ETlAs , ETlP , EGaAs , and EGaP are the total energies
of the consonant binary compounds, and ETlGaAsP is the
total energy of the Tlx Ga1−x Asy P1−y quaternary alloy at
relevant concentrations.
To the best of our knowledge, there are neither experimental nor theoretical data on the structural properties
available for comparison for Tlx Ga1−x Asy P1−y quaternary
alloys. Our results for the zincblende structure in the
presence of Tlx Ga1−x Asy P1−y quaternary alloys may serve
for a reference for future theoretical and experimental
works.The requested band gaps of the alloys is very important. Thus, this calculations can be very useful for
engineering.
1683
Unauthenticated
Download Date | 10/13/16 7:35 AM
Structural and electronic properties of zincblende phase of Tlx Ga1−x Asy P1−y quaternary alloys: First-principles study
GaP
TlP
1.0
Arsenic composition (y)
6.0
5.6
5.7
5.5
0.5
5.8
5.9
5.5
5.9
0.0
0.0
0.5
TlAs
Contour map of the computed lattice constant in Angstroms with respect to the combination x and y Tlx Ga1−x Asy P1−y quaternary alloys.
6
6
4
4
2
2
0
0
-2
-4
-2
-4
-6
-6
-8
-8
-10
Γ
Figure 4.
4.
Thallium composition (x)
Energy (eV)
Energy (eV)
Figure 3.
1.0
GaAs
X
W
L
Γ
K
W
U
The electronic band structure as a function composition
for zincblende phase of Tl0.25 Ga0.75 As0.25 P0.75 .
Conclusion
In summary, we calculated the structural and electronic
properties of the TlAs, TlP, GaAs and GaP binary alloys.
Also we analyzed the same properties of their quaternary
alloy Tlx Ga1−x Asy P1−y as a function of composition (x, y)
using the LDA within DFT. We investigated the Thallium
-10
Γ
Figure 5.
X
W
L
Γ
K
W
U
The electronic band structure as a function composition
for zincblende phase of Tl0.5 Ga0.5 As0.5 P0.5 .
and Arsenic composition dependence of the lattice parameter a(x, y), energy band gap Eg(x, y) and formation energy EF orm (x, y) of Tlx Ga1−x Asy P1−y . The structural and
electronic properties of TlAs, TlP, GaAs and GaP compounds are in good compatibility with the accessible general outcomes. Consequently, we found that, at nearly rate
of x = y = 0.25, x = y = 0.5, and x = y = 0.75, these
1684
Unauthenticated
Download Date | 10/13/16 7:35 AM
Sinem E. Gulebaglan et al.
6
4
Energy (eV)
2
0
-2
-4
-6
-8
-10
Γ
Figure 6.
X
W
L
Γ
K
W
U
The electronic band structure as a function composition
for zincblende phase of Tl0.75 Ga0.25 As0.75 P0.25 .
alloys are semiconductor, semi-metal and metal, respectively. Our calculated results are expected to be helpful
for enhancing the performance of the optoelectronic devices based on cubic Tlx Ga1−x Asy P1−y quaternary alloys.
Taking into account the lack of experimental data for the
quaternary alloys, this is the first theoretical study on
zincblende Tlx Ga1−x Asy P1−y alloys.
References
[1] H. X. Jiang, J. Y. Lin, Opto-Electron. Rev. 10, 271
(2002)
[2] S. S. Ng, Z. Hassan, H. Abu Hassan, World Academy
of Science, Engineering and Technology 31, 185
(2009)
[3] H. H. Amer, S. Ebraheem, K. E. Ghareeb, F. A. Eissa,
S. Eid, N. M. Abdel-kader, Chem. Mater. Res. 3, 30
(2013)
[4] S. Adachi, J. Appl. Phys. 61, 4896 (1987)
[5] H. M. A. Mazouza, A. Belabbesa, A. Zaouib, M. Ferhat, Superlattice. Microst. 48, 560 (2010)
[6] Y. O. Ciftci, K. Colakoglu, E. Deligoz, Cent. Eur. J.
Phys. 6, 802 (2008)
[7] S. E. Gulebaglan, Modern Phys. Lett. B 26, 1250199
(2012)
[8] Y. Kajikawa, S. Asahina, N. Kanayama, Jpn. J. App.
Phys. 140, 28 (2001)
[9] Y. Kajikawa, H. Kuboto, S. Asahina, N. Kanayama, J.
Cryst. Growth. 237, 1495 (2002)
[10] Y. Kajikawa, N. Kobayoshi, N. Nishimoto, J. App.
Phys. 93, 2752 (2003)
[11] S. P. Svensson, F. J. Crowne, J. App. Phys. 83, 2599
(1998)
[12] N. Saidi–Houat, A. Zaoui, M. Ferhat, J.
Phys.:Condens. Matter 19, 106221 (2007)
[13] S. Singh, M. Sarwan, J. Phys. Chem. Solid. 74, 487
(2013)
[14] L. Shi, Y. Duan, L.Qin, Comput. Mater. Sci. 50, 203
(2010)
[15] M. Takushima et al., J. Cryst. Growth 301, 117 (2007)
[16] S. Krishnamurthy, A. B. Chen, A. Sher, App. Phys.
Lett. 80, 4045 (1996)
[17] M. V. Schilfgaarde, A. B. Chen, S. Krishnamurthy, A.
Sher, App. Phys. Lett. 65, 2714 (1994)
[18] H. Koh et al., J. Cryst. Growth 188, 107 (1998)
[19] J. P. Perdew, A. Zunger, Phys. Rev. B 23, 5048 (1981)
[20] A. Yildiz, U. Akinci, O. Gulseren, I. Sokmen, J.Phys.:
Condens. Matter 21, 485403 (2009)
[21] F. D. Murnaghan, Am. J. Math. 49, 235 (1937)
[22] S. Q. Wang, H. Q. Ye, Phys. Rev. B 66, 235111 (2002)
[23] R. Ahmed, S. J. Hashmifar, H. Akbarzadeh, M. Ahmed,
F. Aleem, Comput. Mater. Sci. 39, 580 (2007)
[24] R. M. Wentzcovitch, K. J. Chang, M. L. Cohen, Phys.
Rev. B 34, 1071 (1986)
[25] R. W. G. Wyckoff (Ed.), Crystal Structures, 2nd edition
(Krieger, Malabar, 1986)
[26] P. D. Ye, J. Vac, Sci. Technol. A. 26, 696 (2008)
[27] K. Hacini, H. Meradji, S. Ghemid, F. El Haj Hassan,
Chin. Phys. B 21, 036102 (2012)
1685
Unauthenticated
Download Date | 10/13/16 7:35 AM