First-Principles Predictions on Structural Stability, Electronic, Optical, and Thermal Properties of Semiconductors GaNxAs1-x: Materials for Futuristic Optoelectronic Energy Devices


 The knowledge of the physical properties of a material is crucial to realize its practical technological applications.Here, a study related to phase stability, transition pressure, electronic, optical,and thermal propertiesof GaAs, GaN, as well as their mixed ternary alloys GaN0.25As0.75, GaN0.5As0.5, andGaN0.75As0.25 is presented. The study is performed by employing "full-potential linearized augmented-plane-wave plus local-orbital, (FP-L(APW+lo))approach framed within density functional theory (DFT)" and recognized within WIEN2k computational code. The results of the phase stability show that the GaNxAs1-x alloys are stable for all compositions in the zinc blendephase (B3),except for x=1,, whereas the structure corresponding to x=1 composition is found to be more stable inthe wurtzite (B4) phase. The physicalproperties of the more stable phases corresponding to each composition are explored. The pressure-induced phase transition is also investigatedcorresponding to each composition. The electronic and optical properties are investigated using the Tran-Blahamodified Becke-Johnson (mBJ) potential approach. To explore the thermal properties, the "quasi-harmonic Debye model" approach is employed. Our calculated results of the absorption coefficients and optical band gap show that these alloys could be appropriate candidates for applications in solar cell and optoelectronic devices.


Introduction
III-V nitrides binary compounds have shown their potential candidatures for optoelectronics such as light-emitting diodes operating at high temperatures and high-power electronics working for visible to ultraviolet wavelengths [1]. Their alloying has further widened the scope of their applications. More recently, alloys of diluted nitrides have gripped large considerations of material scientists because of showing uncommon physical properties and aspiring device applications as base materials [2], in particular, GaNAs alloys have revealed their great potential for the optoelectronic devices developed on the GaAs substrate [3,4].
They have shown their substantial potential for long-wavelength laser diodes with high-level stability at higher temperatures as well [5].
The mutual alloying of GaAs and GaN is considered to be the panorama of many futuristic optoelectronic applications as well [6]. It has been noticed in several studies that an addition of a very small quantity of nitrogen (N) into GaAs shows an unexpected change in the bandgap energy and an alteration in the electronic band structure resulting in the promising applications of these materials for long-wavelength telecommunications [7,8]. Moreover, GaAs-based structuring systems are more preferred over the InP-based systems as a distributed Bragg reflector (DBR) mirroring because of their superiority in epitaxial lattice matching for the state-of-the-art short-haul networks components [9]. Investigations in III-V nitrides alloys particularly in GaNxAs1-x have been increased many times owing to the fact of their electronic band structure's sensitivity with the addition of the nitrogen content and resulting in their several applications including high-efficiency solar cells and optoelectronic devices [10,11].
However, GaNAs alloys are found to be inclined to show phase separation, because of the large miscibility gap [12,13], with increasing concentration of the N resulting in the development of extreme inhomogeneous material alongside the inclusion of the phases of GaAs, GaNAs, and GaN. It means that the growth of good quality diluted nitrides GaNAs alloys are too difficult due to the big miscibility gap between GaAs and GaN. Somehow this problem has been addressed by fabricating GaNAs alloys by molecular beam epitaxial (MBE) growth technique using nonequilibrium conditions [6,12,14]. Although investigations (theoretical and experimental) are found in the literature to deal with the large miscibility gap between GaN (wurtzite) and GaAs (zincblende), most are related to GaNAs alloying with a low concentration of N [15] because of big issues of phase separation and aligned large miscibility gap at a large concentration of N. To date not too many studies are found in the literature related to resolve big miscibility gap for the entire range of x for GaNAs Alloys because of the structural stability issues of the structure of GaN (wurtzite) and GaAs (zincblende). This has created a lot of interest for investigations at both (experimental and theoretical) levels in GaNAs [16].
For the fabricated GaNAs alloys, some fundamental studies to investigate compositional variations and surface morphology by MBE technique [17], photoluminescence mechanism at low-temperature GaNAs/GaAs system  passivation of the isovalent atoms of N and electrically active group IV of the GaNAs Alloys and more recently in another study also it was shown that when Si is doped in GaNAs, the interaction between Si and N initiated the mutual passivation resulting in the purging the Si electrical activity and increase in the bandgap energy [29][30][31][32].
Similarly, some theoretical studies also found concerning structural and electronic properties Although diverse studies are found in the literature to be reported in the literature, as shown above, rare investigations are found in the literature regarding structural stability corresponding to the entire concentration range of x for GaNxAs1-x alloys by first-principles DFT approach because of the complexity of the structural stability between wurtzite and zincblende of GaN and GaAs respectively.
In this study, we present a comprehensive study related to structural stability, transition pressure, electronic, optical, and thermal properties of the GaNAs alloys over the entire alloying range of GaN and GaAs by employing first principles-based computational code WIEN2k which is based on the methodology FP-L(APW+lo) framed within DFT.

Method of Computations
In order to do our computational work concerning phase stability, transition pressure, electronic, optical, and thermal properties of the GaNxAs1-x alloys for 0 ≤ x ≤ 1, WIEN2k computational code based FP-L(APW+lo) approach designed within DFT was employed [45][46][47]. To obtain the structural parameters, structural stability, and transition pressure, the Wu-Cohen approach for generalized gradient approximation (WC-GGA) was implemented for incorporating exchange-correlation functional part of the total energy calculations (WC-GGA) [48], whereas for determining the electronic and optical properties, modified -Becke-Johnson (mBJ) was used. To do the calculations of electronic band structures and optical properties, the modified Becke-Johnson approach (mBJ) [49] was used being more simple, fast, and robust as well as more accurate to reproduce results for bandgap energy closer to experimental data, particularly for insulators and semiconductors. In this method of computations, at first, for each concentration, a unit cell was simulated. The obtained units were then divided into two regions: interstitial and Muffin tin spheres. Different basis sets are used in both regions to expand crystal potential, wave function as well as charge density. In the Muffin tin spheres, assumed by considering their centres at atomic nuclei, atomic-like wave functions are used for defining their basis set but for the interstitial region, the basis set is termed in plane waves. To expand the wave functions, charge density, and potential defined inside muffin tin spheres, the maximum value of 'l' was restricted to 10 but for the expansion of plane basis set in the interstitial region, the cut off value of RMT×Kmax was taken equal to 8 which determines the size of the basis set, where RMT represents radii muffin tin (MT) spheres and Kmax denotes the maximum value of the wave vector. The charge density and potential in the interstitial region were expanded as a Fourier series by taking the maximum value of lattice vector Gmax=12 (Ryd) 1

Structural phase stability
To recognize the structural stability of GaNxAs1-x alloys, in this section we present our computed results of structural parameters which are obtained at the level of WC-GGA approximation. The obtained results of the ground state energy as a function of the unit cell volume for the four phases (rock-salt (B1), CsCl (B2), zinc-blende (B3), and wurtzite (B4)) of GaAs, GaN0.25As0.75, GaN0.5As0.5, GaN0.75As0.25, and GaN are plotted and shown in Fig.1.
From Fig.1, we see that the lowest energy value corresponds to the more stable phase. By following these lines, we see that for the concentrations of x = 0; 0.25; 0.5; 0.75, zinc-blende (B3) is found to be more stable but for the concentration, x=1, wurtzite (B4) phase is found more stable.
To calculate the transition pressure, the relation for the Gibbs free energy relation (G) as given below is used.
As the calculations within DFT are carried out at absolute zero (T=0K), therefore, the abovesaid relation (1) reduces to G = E + PV, which is also equivalent to the enthalpy of formation  there is also no study available for comparison to our knowledge.
We also calculated ∆E 0 (E0B3 -E0B4) for each concentration of x. The concentration at which the phase transition occurs is shown in Fig. 3. From Fig. 3, it can be seen that the transition occurs from phase B3 to B4 at x =0. 98 Table 2. Hence Our results for (a) concerning the GaN0.25As0.75, GaN0.5As0.5, and GaN0.75As0.25 alloys in their B3 phase are found in nice agreement with the theoretical data, but for B our values are slightly higher than the theoretical results, for their other three phases, no results neither experimental nor theoretical are available to make the comparison for alloys and the binary compound GaN, our results for the three phases (B1, B3, and B4) are found to be a good one.

Band structures
It is very important to investigate the electronic properties of any semiconductor, in particular, its energy band gap, theoretically as well as experimentally before it using as a base material in an electronic device, to investigate its relevance in such a manufacturing treat. We, therefore, determined the band structures of the stable phases of the GaNxAs1-x alloys using the mBJ scheme, as we already have been predicted that B3 is the most stable for the compositions GaAs, GaN0.25As0.75, GaN0.5As0.5, and GaN0.75As0.25 and B4 for the composition x=1, that is, for GaN as represented in for concentration x = 0, 0.25, and 0.5 for B3 phase, whereas its variation as a function of the nitrogen concentration can be seen from the Fig. 6. As can be seen from  Table 3. The results of previously reported calculations and experimental data are also tabulated in Table 3 for comparison. We x From our calculations, we found the value of the bowing parameter equal to 4.787eV at the level of the mBJ scheme.

Density of states
The total and partial density of states are calculated for GaNxAs1-x with x=0, 0.25, 0.5 and x=0.75 in the zinc-blende phase whereas for x=1 in the wurtzite phase using mBJ approximation as shown in Fig. 7. From Fig. 7, the plotted data of the partial density of states for GaAs displays the divergence of the valence band into two parts. The first part from -11.348 eV to -9.879 eV is dominated by the main contributions of the s-As orbitals, where the second region from -6.325 eV to Fermi level (EF) of the valence band is shaped from the main contributions of s-Ga and p-As orbitals. The formation of the conduction band is predominantly contributed by the s-Ga, p-Ga, and p-As. we see that the total and partial density of states are the same, that is, the valence band from -11.779 eV to -10.059 eV is found to be made mainly from the contributions of the s-Ga, s-As, and s-N states. The part of the valence band from -6.592eV to Fermi level is dominantly shaped by s and p states of the atoms of Ga, As, and N present in the alloy's composition.
Similarly, the conduction band is mainly formed by s and p states of the atoms (Ga, As, and N) present in the composition of the alloys.

Optical properties
To investigate the optical behavior of the investigated alloys, both the real (ɛ1(ω)) & imaginary ( 2 ( )) parts of the dielectric function ɛ(ω) are computed by employing the Kramer-Krong approach as given in the literature [112] and reported in the following relations: Where ħ relation describes the photon energy, p is used to denote the momentum operator which is described as p=(ħ/ )( / ), | >, corresponds to eigenfunction and f(kn) denotes Fermi distribution function. However, microscopic optical parameters for example reflectivity R(ω), refractive index n(ω), and absorption coefficient α (ω) are derived from 1 ( ) and 2 ( ) by using relations given in the follows: At frequency zero, the static refractive index value is appraised by the following relation: To confirm the accuracy of our results, the following additional models have also been employed to calculate optical properties: a) Herve and Vandamme's relation [113] is as given below: In the relation above, Eg and k denote the bandgap energy and constant=108 eV respectively.  Table 4 with the results obtained from other models ( Herve., Ravindra, Moss.) as well. Our results obtained of static dielectric constant ε1(0) for GaAs are lower than the theoretical models (Herve., and Moss.) and are closer to (Ravindra) and slightly less than the reported experimental [116] and theoretical values in the literature    Moreover, the variation of n(ω) of GaAs is also similar as reported already in references [57,58]. However, for the GaN and mixed alloys GaNxAs1-x, no report is found in the literature.
Our computed results for static refractive indices n(0) are shown in Table 4 By applying the Debye Using the "quasi-harmonic Debye model" and retrieved data from the E-V curve, different thermodynamic parameters at different pressures as well as temperatures have been calculated for investigated alloys. In these investigations, thermodynamics parameters for the above-said alloys have been evaluated for a wide range of temperatures i.e. from 0-1100K at P = 0 GPa as shown in Figs.

15-20. The variation in volumes with the variation in temperature at
P=0GPa is shown in Fig. 15. From Fig. 15 it is can be seen that the value of the volumes increases with the increase in temperature for each concentration of x it because crystal volume increases with increasing temperature. From Fig. 15 Investigation of the heat capacity and entropy is necessary for many applications, for example, at constant volume, their knowledge of the vibratory properties of a crystalline material is necessary. Fig. 18 shows our calculated results of the heat capacity as a function of temperature and fixed pressure (0 GPa) for all the investigated concentrations of the GaNxAs1x alloys. From Fig. 18 Our obtained results for entropy S with respect to varying temperature and at fixed pressure P = 0 GPa are displayed in Fig. 19. From Fig. 19,