First-principles investigation of structural and electronic properties of Tl x Al1− x P ternary alloys

In this study, the structural and electronic properties of semiconductor Tl x Al1−x P alloys were derived from minimum total energy by using Density Functional Theory with Local Density Approximation. A 16 atom supercell was used to model the ternary Tl x Al1−x P alloys. The lattice constant, electronic band gap energies and bowing parameters was examined. The lattice constant of the Tl x Al1−x P alloys comply well with Vegard's law. Also, the polynomial equation of concentration dependent electronic band gap energy of the Tl x Al1−x P is Eg (x) = 2.02693x 3 − 2.17819x 2 − 1.15118x + 1.29644 (eV). Electronic band gap bowing parameters vary depending on the Thallium concentration value. It was concluded that the average bowing parameter of Tl x Al1−x P alloys was b = 1.1649 eV.


Introduction
Although naive Thallium is toxicological [1], Thalliumcontaining alloys have been committed as encouraging materials for implementations in the optical communication system [2]. Thallium-containing alloys status for nano technological applications were investigated with experimental and theoretical studies [3][4][5][6][7]. There are many studies in the literature on the suitability of Tl-containing alloys as photo detectors [8][9][10][11]. Alloys composed of III-V compounds containing thallium are alternative materials for photodetectors operating in the infrared region [7,12,13]. Thallium is used in bearing shafts as it has good wear resistance. Thalliumcontaining alloys are important materials in the electronics industry for soldering materials, rectifiers and bearing [14]. Schilfgaarde et al. [7] and Krishnamurthy et al. [15] conducted studies on TlInP, TlInAs and TlInSb. Yamamoto et al. [12] produced TlGaAs and TlInAs by the molecular beam epitaxy method. Said-Houat et al. [2] and Dantas et al. [3] revealed theoretical studies on AlTlN and GaTlN. TlP, TlN, TlAs, TlSb and TlBi studies were carried out using density functional theory [16][17][18][19]. Mankefors and Svensson [13] investigated abinitio calculations of Ga 1−x Tl x As alloys. They examined the dependence of lattice constant, electronic band gap and bowing parameter on Thallium concentration. Koh et al. [5] studied photoconductivity measurement and temperature changes of band gap energies for TlInP, TlGaP and TlInGaP. Gulebaglan et al. [20] calculated the structural and electronic properties of zincblende new semiconductor Tl x Ga 1−x As y P 1−y quaternary alloys. Bil-gec Akyuz et al. [21] investigated bowing parameter of Tl x Ga 1−x As ternary alloys. Yildiz Tunali et al. [22] reported the structural and electronic properties of zincblende Ga x Tl 1−x P alloys. Meynoian et al. experimentally investigated the electro-optical properties of "Thallium aluminium-codoped zinc oxide" materials [23]. Salem and Abdulwahed prepared single crystals thallium bismuth diselenide and declared electrical properties of TlBiSe 2 [24]. Khon et al. experimentally investigated and reported the electronic, thermal and transport properties of the TlPbSbTe alloy [25].
Investigations using density functional theory can be used to support experimental studies. Apart from this, even if a compound or alloy has not been synthesized yet, it can be a source for experimental or engineering studies by determining many properties. For this reason, some properties of Tl x Al 1−x P alloys, which have not been synthesized yet, have been investigated.
Density functional theory is a method used to determine the properties of atoms, molecules, and crystal structures. The discovery of new materials or in the design of materials knowledge of the properties of the material that provide the calculation time and budget savings. So it is important to have knowledge about crystal structures before working in the laboratory. The approximations used to define the exchange and correlation term in calculations using density functional theory are local density approximation (LDA) [26] and generalized gradient approximation (GGA) [27]. The structural and electronic properties of many crystals have been investigated using these approximations [28][29][30][31]. However, the approximations used in the studies made with the density functional theory have been tried to be developed by the researchers. For example, local density approximation plus the multi-orbital mean-field Hubbard model (LDA+U) and Fermi-Löwdin orbital self-interaction correction (FLO-SIC) approach. There are studies in which studies are conducted using the approximations developed in the literature [32][33][34]. With these developed approximations, studies examining the electronic properties of crystal structures have been brought to the literature [35][36][37].
In this present work, the structural and electronic properties of the Tl x Al 1−x P have been studied using density functional theory. The plan of the current study is as follows: A description of the computational method is given in Section 2. Then, the lattice constant and energy band structures and bowing parameters of Tl x Al 1−x P alloys are examined in Section 3. Finally, a short result of this study is given in Section 4.

Computational method
In preparing this study, structural and electronic properties of Tl x Al 1−x P alloys in Zincblende structure were investigated by using Local Density Approximation [26] with Quantum Espresso program [38]. Electron-ion interactions were identified by ultrasoft pseudopotentials and the cut-off energy was tested with these pseudopotentials. The wave functions were selected as a cut off 60 Ry on a plane wave basis. This cut-off energy value was used in the Tl x Al 1−x P alloys performed using the standard special k-points technique of Monkhorst and Pack [39]. This a 12 × 12 × 12 lattice was used during the investigations. The selected plane-wave cut-off energy and k-point number were carefully checked to ensure the minimum of total energy. Supercell containing 16 atoms were used for Tl x Al 1−x P alloys. 2 × 2 × 2 classical Zincblende cubic cells corresponding to the 16 atom supercell were applied. There are different atomic configurations which need to be structurally optimized. Similar results were obtained by calculating the electronic band gap energy for entire configuration. In this way, the average effect of the doped was examined. Starting with the maximum AlP clustered configuration, the Aluminium atoms were removed from the clusters one at a time and Thallium atoms were added one by one to produce a clustered alloy. Atomic coordinates for each Thallium percentage were relaxed. In addition, Tl (4f 14 5d 10 6s 2 6p 1 ), Al (3s 2 3p 1 ) and P (3s 2 3p 3 ) orbitals as valance electrons, it was discussed. Spin-orbital interactions were not insert account in the calculations. The mean error value of the energy obtained during the calculations process is lower than 10. 10 −8 Ry. This ensures high accuracy results.

Results and discussion
First, the structural and electronic properties of the compounds of TlP and AlP were examined. The ground states of the binary compounds TlP and AlP are the structure in Zincblende (B3) and the space group is F43m (216). The total energies of TlP and AlP were calculated as a function of volume in the Zincblende phase using plane wave pseudopotentials. The energy volume curve is fit to the Vinet [40] equation. Then the lattice constants and bulk modulus are obtained for TlP and AlP. All investigated values are in good agreement with the previous calculations. These values are given in Table 1.
The calculated lattice constant value of TlP and AlP are 5.933 and 5.41 Å, respectively. According to these results, it was seen that there is a difference of 0.11% and 0.7% between lattice parameters calculated with other theoretical results [41,43] for TlP and AlP compounds, respectively. This difference is acceptable. The value of the lattice parameter calculated for AlP compound is very close to the experimental value [43]. Since TlP has not yet been synthesized, it has not been experimentally compared. The electronic properties calculations give an electronic band gap of 1.42 eV for AlP and 0.0 eV for TlP. The result of AlP is in agreement other theoretical and experimental results and the result of another compound, TlP, is agreement other theoretical results. The experimentally obtained electronic band gap of the TlP compound is not yet available. These values are given in Table 2. The investigated electronic band structures are plotted in Figures 1 and 2 for TlP and AlP, respectively.
The atomic coordinates of AlP compound in the Zincblende phase are Al (0.0 0.0 0.0) and P (0.25 0.25 0.25). If the AlP compound is grown to 2×2×2, a super cell of 16 atoms is obtained. This structure continues to preserve the Zincblende structure. The crystal structure of the Tl x Al 1−x P alloys formed, when Thallium is   added to the material, the addition is made at the ratio of the number of Thallium atoms placed. In this case, starting from Vegard's law [47], the lattice constants of Tl x Al 1−x P alloys can be expressed in relation to the Thallium doped ratio (x). For this reason, calculations were made based on Vegard's law for Tl x Al 1−x P alloys in the ground state. The lattice constant of the Tl x Al 1−x P alloys can be calculated by Vegard's law as follows: where a(x) is the lattice constant of Tl x Al 1−x P, a TlP is the lattice constant of TlP and a AlP is the lattice constant of AlP.
The lattice constants of Zincblende Tl x Al 1−x P alloys have been found to be almost directly proportional to the additive ratio (x) to the alloy are shown in Figure 3. For different concentration percentages, bond lengths between T1 and P atoms and bond lengths between Al  and P atoms were calculated using the XCRYSDEN computer program [48]. These calculated values are listed in Table 3. The electronic band gap energy of Tl x Al 1−x P: can be expressed.
Here, E g,TlP is the electronic band gap energy of TlP, E g,AlP is the electronic band gap energy of AlP E g (x) is the electronic band gap energy depending on the doped ratio of Tl x Al 1−x P, and b is the electronic band gap bowing parameter of Tl x Al 1−x P alloys. Table 4 shows that a large reduction in the electronic band gap of the AlP is observed, depending on the concentration of Thallium. In addition, electronic energy band gap diagram of Tl x Al 1−x P is shown in Figures 4-9.
First of all, it should be noted that the electronic properties of the AlP compound will be affected by the Tl doping. In this case, the electronic band gap will change. One of the aims of this study is to examine this change.
The electronic bowing parameter values obtained from each concentration are shown in Figure 10 and an average band gap bowing parameter of 1.1649 eV calculated from Equation (3) to 0 < x < 100. The result of the study showed that the Thallium concentration decreases, the electronic band gap of Tl x Al 1−x P    decreases. If the density of Thallium is high, the electron concentration in the alloy is higher, which further reduces the edge of the conduction band. The electronic band gap energy of the AlP binary structure is 1.415 eV, while 50% Thallium is added, which reduces the electronic band gap of the Tl 0.5 Al 0.5 P alloy to 0.5076 eV. As the doped percentage increased, the electronic band gap was calculated as 0.0 eV.   The electronic band gap value of the Tl x Al 1−x P alloys' structure decreases with the addition of Thallium as in the structure of Tl x Al 1−x As. That is, the AlAs and AlP crystal structures react similar to Thallium doped [49]. These alloy materials are thought to be very useful in the construction of infrared optical devices. Furthermore, it is recognized that the ternary alloys have a parabolic composition structure for the electronic band gap. The size of the parabolic factor is known as the bowing parameter. It is possible to define the linear bowing function from these results. This curve has the minimum value and the maximum value. Figure 10 shows the variation of the bowing parameter depending on the concentration ratio. As seen in Figure 10, the bowing parameter suddenly increases at x = 0.25 Thallium concentration. Shi et al. [50] were investigated the variation of the concentrationdependent bowing parameter of the Tl x Al 1−x N ternary alloys in the Wurtzite crystal structure. According to these results, if the value of the bowing parameter in the x = 0.25 Thallium contribution is compared with the value in the x = 0.375 Thallium contribution, an increase in the bowing parameter value is observed. However, when the bowing parameter value of x = 0.375 Thallium contribution and the value of the bowing parameter are compared with the x = 0.5 Thallium contribution, a decrease is observed in the value of the bowing parameter. This decrease continues as the Thallium doping value increases. In the Tl x Al 1−x P alloys whose properties are predicted, it is thought that this shot and decrease in the bowing parameter is due to the electron concentration, as in the Tl x Al 1−x N ternary alloys [42]. It is thought that Tl x Al 1−x P alloy can be used in the design of optoelectronic devices.
Bowing parameter function b(x), can be expressed.
In order to understand the physical origins of the band gap and the bowing parameter depending on the doped quantity, it is necessary to physically divide b into three parts. The bowing parameter is defined as the sum of these three parts; The bowing parameter and its components (b VD , b CE , b SR ) are listed in Table 5.

Conclusion
Using the numerical simulation programme with firstprinciples calculations, lattice constants of TlP and AlP binary compounds and Tl x Al 1−x P alloys in Zincblende structure were calculated. The results for TlP and AlP are consistent with other results in the literature. The electronic band structure of Tl x Al 1−x P alloys at different concentrations was calculated. The lattice constant of the alloy was found to be compatible with Vegard's law. According to the simulation results, the electronic energy band gap of the Tl x Al 1−x P alloys is calculated by the third-order polynomial equation, such as E g (x) = 2.02693x 3 − 2.17819x 2 − 1.15118x + 1.29644 (eV). The bowing parameter of the energy band gap was found to be strongly dependent on the doped ratio. The average bowing parameter of Tl x Al 1−x P alloys was calculated as 1.1649 eV. It is anticipated that the TlAlP alloy may be suitable for use in the design of optoelectronic devices. It is believed that these results will direct experimental and theoretical studies.

Disclosure statement
No potential conflict of interest was reported by the author(s).