Cent. Eur. J. Phys. • 11(12) • 2013 • 1680-1685DOI: 10.2478/s11534-013-0314-1

Central European Journal of Physics

Structural and electronic properties of zincblendephase of TlxGa1−xAsyP1−y quaternary alloys:First-principles study

Research Article

Sinem E. Gulebaglan∗, Emel K. Dogan, Murat Aycibin, Mehmet N. Secuk, Bahattin Erdinc, HarunAkkus †

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 proper-ties of zincblende TlAs, TlP, GaAs and GaP compounds and their new semiconductor TlxGa1−xAsyP1−yquaternary alloys. Structural properties of these semiconductors are obtained with the Perdew and Wanglocal-density approximation. The lattice constants of TlxGa1−xAs, TlxGa1−xP ternary and TlxGa1−xAsyP1−yquaternary alloys were composed by Vegard’s law. Our investigation on the effect of the doping (Thalliumand Arsenic) on lattice constants and band gap shows a non-linear dependence for TlxGa1−xAsyP1−y qua-ternary alloys. The band gap of TlxGa1−xAsyP1−y, Eg(x, y) concerned by the compositions x and y. To ourawareness, there is no theoretical survey on TlxGa1−xAsyP1−y quaternary alloys and needs experimentalverification.

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 bandstructure of crystalline solids© Versita sp. z o.o.

1. Introduction

For technological advance, it is important to understandthe characteristics of semiconductors.Technological ad-vances often rely on a thorough understanding of the char-acteristics of semiconductors. Quaternary systems opennew possibilities for material engineering [1–4]. There∗E-mail: sinemerden@gmail.com (Corresponding author)†E-mail: harunakkus@yyu.edu.tr

are three parameters which have an important role inthe development of new materials. These parameters arecounted as lattice parameter, the band gap and the va-lence band offset. In scientific and technological areas,the interest on Thallium compounds have been ascendingin recent years [5–7]. Especially for optical communica-tion systems which are narrowing the band gap [8–10] andfor heterostructure field effect transistor applications [11],Thallium compounds have been recommended as benefi-cial applicant. Thallium-V compounds have been indicatedas an alternative to HgCdTe [12]. S. Singh and M. Sar-wan investigated high pressure phase transition and elas-1680

Sinem E. Gulebaglan et al.

tic behavior of TlX (X=N, P, As) semiconductors [13]. Shiet al. reported structural phase transition, electronic andelastic properties in TlX (X=N, P, As) compounds [14]. Itis recommended that these structures can be used in com-munication systems such as laser, detector and diodes.Takushima et al. [15] experimentally investigated the low-temperature epitaxial TlInAs by molecular-beam epitaxy(MBE) and showed that, by decreasing the growth tem-perature, the size and density of Tl droplets decreased.Also for some structures which contain Tl, Krishnamurthyet al. [16] calculated the near band edge absorption spec-tra and Schilfgaarde et al. [17] studied some optical andstructual properties. Koh et al. [18] experimentally inves-tigated the temperature-dependence of band gap energyon the semiconductors including Thallium in ternary andquaternary alloys such as TlInP, TlGaP and TlInGaP.During our detailed review of literature, we could not un-cover any theoretical work on the electronic and struc-tural properties of TlxGa1−xAsyP1−y quaternary alloys.Throughout this work, our calculations were based onfirst-principles and we used the local density approxima-tion (LDA) for the exchange-correlation potential. Duringour study, we analyzed the structural and electronic prop-erties of TlxGa1−xAsyP1−y with respect to different compo-sitions of Thallium and Arsenic. First we have computedthe lattice constant and band gaps for binary zincblendeTlP, GaP, TlAs and GaAs compounds and calculated thelattice constants as a function of Thallium and Arseniccompositions (x, y). Moreover, the structural and elec-tronic properties of the TlxGa1−xAsyP1−y quaternary al-loys calculated. We represented and discussed the resultsof those calculations in this paper.2. Computational details

In this paper, the structural and electronic properties ofTlxGa1−xAsyP1−y alloys are investigated with the Quan-tum Espresso program1 This programme is based on den-sity functional theory with plane waves, and pseudopten-tials. Quantum Espresso calculates ground state prop-erties and make structural optimization, molecular dy-namic... etc. In order to investigate the structural prop-erties of the semiconductor compounds, we employed theexchange-correlation potential using the LDA of Perdewand Wang [19]. The orbital for Ga ([Ar]3d104s24p1),for As ([Ar]3d104s24p3), for P([Ne]3s23p3) and for Tl([Xe]4f145d106s26p1) are treated as true valence electrons.1 S. Baroni, A. Dal Corso, S. de Gironcoli, P. Giannozzi:http://www.pwscf.org

The core states are considered assemi-relativistically (i.e.spin-orbit coupling is ignored). The crystal structure iszincblende for the TlxGa1−xAsyP1−y quaternary alloy. Weused 16-atom supercell with the 2× 2× 2 correspondingdimension. A supercell is needed to construct the quater-nary alloy TlxGa1−xAsyP1−y. Enlargement of the super-cell is not necessary for accurate computations, however,the kinetic energy cut off of wave functions and the num-ber of k-points affect the accuracy of calculations. Thus,we optimized the value of kinetic energy cut off and thenumber of k-points. Consequently, we found that 80 Ryfor the energy cut off and 12× 12× 12 k-point mesh areappropriate for the calculations. First, we composed GaPsupercell. Then, we doped Tl and As into this GaP su-percell 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 consti-tute TlxGa1−xAsyP1−y quaternary alloys.3. Results and discussion

3.1. Structural properties of TlP,TlAs, GaAs,and GaP

The quaternary compounds TlxGa1−xAsyP1−y are confinedby four binary compounds of TlP, TlAs, GaAs, and GaP.Houat at. al. [12] have investigated structural stability ofThallium-V compounds: TlN, TlP, TlAs, TlSb and TlBi.They suggested the ground state structure is zincblendephase for TlP and TlAs. It is clearly seen in Table 1 thatthe lattice constant obtained for TlP and TlAs are in rea-sonable agreement with other reported values. Similarly,a small difference is observed between calculated and ex-perimental lattice constant of GaP and GaAs which can beattributed to the general trend that LDA usually underes-timates this parameter [20]. Our calculations are carriedout using the LDA of Perdew and Wang as the exchangecorrelation potential, but Houat [12] utilized generalizedgradient approximation (GGA) and Wang [22] deal withvalence electrons and core electrons with local-densityapproximation. For this reason, there is a small differencebetween these results.The description of the our calculation model is as fol-low: we computed the structural and electronic propertiesof the binary compounds that crystalize in the two-atomunit cell zincblende lattice structure. In the course of ourinvestigation of the structural and electrical properties ofTlxGa1−xAsyP1−y quaternary compounds we have to dealwith the zincblende binary compounds of TlP, TlAs, GaAs,and GaP. The total energy values for different volumesof these binary compounds was calculated using the LDAarrangement. Then we fitted the total energies versus vol-1681

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Table 1. Itemized lattice parameter a and band gap energy Eg for theTlAs, TlP, GaAs and GaP in zinc-blende structure phase.

a (Angstrom) Band Gap Energy (eV)TlP(Present work) 5.933 ∼0.000TlP [12] 6.124 ∼0.000TlP [22] 5.747 0.158GaP(Present work) 5.346 ∼1.44GaP [24] 5.358 ∼1.360GaP [25] 5.450 2.35TlAs(Present work) 6.052 ∼0.000TlAs [12] 6.382 ∼0.000TlAs [22] 5.946 0.0000GaAs(Present work) 5.614 1.0475GaAs [22] 5.530 1.0080GaAs 5.649 [22] 1.4200 [26]ume values by using the Murnaghan equation of states inorder to get the equilibrium lattice parameters and theband gap energies.The total energy was discounted for the varying volumesand the energies were matched to the Murnaghan equa-tion [21]:

E = ET + B0VB′0

[ (V0/V )B′0B′0 − 1 + 1]

− B0V0B′0 − 1 , (1)

where V is the volume and V0 is the zero pressure equi-librium volume. B0(T ) and B′0(T ) are the Bulk modulusand the first derivation of Bulk modulus, respectively. Inthis way, we obtained the equilibrium lattice constant andband gap (Eg). In Table 1, the equilibrium lattice param-eters and band gap energies are demonstrated and ananalogy is made with the experimental results.One can see from Table 1 that the lattice parameter val-ues increase from GaP to TlAs as aGaP < aGaAs < aTlP <aTlAs. This order in the lattice parameters of these struc-tures originates in the atomic radius. The value of latticeparameter in a cubic crystal structure is proportional tothe 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 latticeparameter of structure which contains Tl atom is biggerthan the lattice parameter of structure contains Ga atom.Additionally, the lattice parameter of crystal structure in-cludes As atom is larger than the lattice parameter ofcrystal structure which includes P atom.The computed electronic band structures for TlP and TlAsand 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 forthe TlP and TlAs compounds investigated and they ex-hibit nearly semi-metalic character and GaAs and GaP

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Figure 1. The electronic band structure of zincblende phase of TlAsand TlP along high symmetry directions.

are semiconductors (see Fig. 2). The calculated band gapof TlP and TlAs is in good agreement with Ref. [12]. Someresearch groups computed the band gap and lattice pa-rameter of GaAs and GaP [22–24]. Our results are inacceptable agreement with their results.3.2. Structural properties ofTlxGa1−xAsyP1−y

According for that the Vegard’s law is acceptable, thelattice parameters of TlxGa1−xAsyP1−y quaternary alloysmostly have a linear dependence on Tl composition x andAs composition y, as can be seen in the below expressiona(x, y) = (1− x)(1− y)aTlAs + x(1− y)aGaAs+ (1− x)yaTlP + xyaGaP, (2)

where aTlAs, aGaAs, aTlP and aGaP are lattice parametersof binary compounds that are mentioned as subscripts.1682

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Figure 2. The electronic band structure of zincblende phase of GaAsand GaP along high symmetry directions.

Table 2. Calculated lattice parameter, band gap energy (Eg) and for-mation energy EForm(x, y) for the TlxGa1−xAsyP1−y quater-nary alloys.

x y a(Angstrom) Band Gap Energy (eV) Formation energy0.25 0.25 5.8253 0.0076 -0.0660.50 0.50 5.7365 -0.036 -0.1340.75 0.75 5.6658 0.00 0.319a(x, y) symbolizes the composition dependent lattice con-stant of TlxGa1−xAsyP1−y quaternary alloys. Our resultsconcerning the relation between the lattice constants ofTlxGa1−xAsyP1−y quaternary alloys and the x , y compo-sitions are illustrated in Fig. 3.We have chosen 16-atoms of 2×2×2 supercells for mod-elling the structures of TlxGa1−xAsyP1−y quaternary al-loys for different Tl and As concentrations of x and y, re-spectively (x and y = 0.25, 0.5 and 0.75). The calculatedstructural properties such as lattice parameters, band gapenergies and formation energies for different concentra-

tions of Tl and As in TlxGa1−xAsyP1−y quaternary alloysare listed in Table 2. Fig. 4., Fig. 5 and Fig. 6 showthat the electronic band structure for the TlxGa1−xAsyP1−yalloys of x= 0.25 and y=0.25; x = y=0.5; x = 0.75and y = 0.75 concentrations, respectively. We have alsostudied the electronic structures of Tl0.25Ga0.75As0.25P0.75,Tl0.5Ga0.5As0.5P0.5 and Tl0.75Ga0.25As0.75P0.25 alloys. Forthe concentration rates of x = 0.25 and y = 0.25, thequaternary alloys show semiconductor character. Theyhave an indirect band gap with the value of 0.0076 eV(see Fig. 4.). The top of valance band is located at thek-point of (-0.1, 0.0 -0.1) while the bottom of conductionband is located at (0.0, 0.1, 0.0) in the first Brillouin zone.The quaternary alloys have a semi-metallic character forthe concentration rates of x = 0.5 and y = 0.5. Thelowest unoccupied energy level appears in the k-point of(-0.1, 0.1, -0.1) while the highest occupied energy levelis located at the Gamma point of the first Brillouin zone(see Fig. 5.). It is seen from Table 2, the quaternary alloyhas a semi-metalic character for the concentration ratesof x = 0.5, y = 0.5 [see Fig. 5]. However, increasing therates of fifty percent Tl and As concentrations lead thealloy to the metalic structure [see Fig. 6]. On the otherhand, reducing the rations of fifty percent Tl and As con-centrations lead the structure to a semiconductor struc-ture [see Fig. 4]. When we analyze the obtained results,it was noticed that the values of band gaps are directlyrelated with the compositions of Thallium and Arsenic sothe doped rate of Thallium and Arsenic have an very im-portant effect on the band gaps.The formation energy, EForm(x, y) of quaternary alloys atvarious doped can be computed with the following for-mula [27]:

EForm(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 energiesof the consonant binary compounds, and ETlGaAsP is thetotal energy of the TlxGa1−xAsyP1−y quaternary alloy atrelevant concentrations.To the best of our knowledge, there are neither experi-mental nor theoretical data on the structural propertiesavailable for comparison for TlxGa1−xAsyP1−y quaternaryalloys. Our results for the zincblende structure in thepresence of TlxGa1−xAsyP1−y quaternary alloys may servefor a reference for future theoretical and experimentalworks.The requested band gaps of the alloys is very im-portant. Thus, this calculations can be very useful forengineering.1683

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Figure 3. Contour map of the computed lattice constant in Angstroms with respect to the combination x and y TlxGa1−xAsyP1−y quaternary alloys.

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Figure 4. The electronic band structure as a function compositionfor zincblende phase of Tl0.25Ga0.75As0.25P0.75.

4. Conclusion

In summary, we calculated the structural and electronicproperties of the TlAs, TlP, GaAs and GaP binary alloys.Also we analyzed the same properties of their quaternaryalloy TlxGa1−xAsyP1−y as a function of composition (x, y)using the LDA within DFT. We investigated the Thallium

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Figure 5. The electronic band structure as a function compositionfor zincblende phase of Tl0.5Ga0.5As0.5P0.5.

and Arsenic composition dependence of the lattice param-eter a(x, y), energy band gap Eg(x, y) and formation en-ergy EForm(x, y) of TlxGa1−xAsyP1−y. The structural andelectronic properties of TlAs, TlP, GaAs and GaP com-pounds are in good compatibility with the accessible gen-eral outcomes. Consequently, we found that, at nearly rateof x = y = 0.25, x = y = 0.5, and x = y = 0.75, these1684

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Figure 6. The electronic band structure as a function compositionfor zincblende phase of Tl0.75Ga0.25As0.75P0.25.

alloys are semiconductor, semi-metal and metal, respec-tively. Our calculated results are expected to be helpfulfor enhancing the performance of the optoelectronic de-vices based on cubic TlxGa1−xAsyP1−y quaternary alloys.Taking into account the lack of experimental data for thequaternary alloys, this is the first theoretical study onzincblende TlxGa1−xAsyP1−y alloys.References

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