Comparative study of optical properties of In0.25

Comparative study of optical properties of

In _0.25 Ga _0.75 As and In _0.75 Ga _0.25 As in zinc-blende phase by first-principles calculations

Moufdi Hadjab^{1, 2*}, Hassene Nezzari¹, Smail Berrah³, Hamza Abid²

1Research Center in Industrial Technologies CRTI, P. O. Box 64, Cheraga 16014, Algiers / Thin Films Development and Applications Unit (UDCMA), Setif- Algeria

2 Applied Materials Laboratory (AML), Research Center, University Djillali Liabes, 22000 Sidi Bel Abbes, Algeria

3 Mastery Renewable Energies Laboratory (LMER), University of A. Mira, Bejaia, Algeria

*m.hadjab@crti.dz

Abstract—The full-potential linearized augmented plane wave method (FP-LAPW) within Density Functional Theory (DFT) framework as implemented in the WIEN2K computational code is used in order to study the structural, electronic and optical properties of In_0.25Ga_0.75As and In_0.75Ga_0.25As ternaries alloys.

The structural parameters such as lattice parameters, bulk modulus, and its pressure derivative were extracted using the Local Density Approximation (LDA), and the one of Wu and Cohen (GGA-WC) for the exchange-correlation (XC) functional.

In addition, the electronic and the optical properties of our compounds were obtained by using the new semi-local modified Becke–Johnson potential (TB-mBJ) developed by Tran and Blaha. The performed results were compared with experimental data and other computational works. Consequently, our computations of the equilibrium lattice parameter and bulk modulus generally give a good agreement with the experimental measurements. For electronic and optical properties, we deduced that the TB-mBJ approach is relatively more suitable for the properties of our both ternaries alloys.

Keywords— DFT; FP-LAPW; InGaAs, Optical parameters.

I. INTRODUCTION

Presently, the III–V Semiconductors materials based on GaAs, InAs and their ternary alloys InxGa1-xAs are attractive materials in vast scientific and technological usefulness because of their potential use in photonic, electronic and optoelectronic devices, such as, Metal Insulator Semiconductor Photo-detectors, Blue and Green Light- Emitting Diode, thin-films solar cells, Electro-optic Waveguide Modulators, High-Electron-Mobility-Transistor (HEMT), diode lasers and metal–oxide–semiconductor capacitor (MOSCAP) [1-10]. In recent years, some experimental and theoretical works have been published about the physical properties of these compounds. Kumar et al. [11]

have studied some of these properties such as the equilibrium lattice constants, dielectric function and critical points energies of InGaAs alloys within the FP–LAPW method using the PBE-GGA approximation. Ghidoni et al. [12] have

computed the Density of States (DOS) and energy bands of InxGa1-xAs alloys for x=0.5, within the Full Potential Linear Muffin-Tin Orbital (FP-LMTO) method using the DFT-LDA.

Hussien et al., [13] also, have calculated electronic structures of InGaAs nanocrystals alloy using ab-initio DFT calculation coupled with Large Unit Cell (LUC) method. Othman et al., [14] have studied also the structural and optoelectronic properties of InGaAs alloys, only for x=0 and 0.5, using Cambridge Serial Total Energy Package (CASTEP) code, with LDA. To the best of our knowledge, there is no other theoretical calculation on the structural, electronic and optical properties of the cubic In0.25Ga0.75As and In0.75Ga0.25As ternaries alloys using FP-LAPW method, within the modified semi–local Becke–Johnson functional (TB-mBJ)

In the present work, we performed an ab-initio calculation within the DFT framework to predict the impact of the In- concentrations (x) on the physical properties of InxGa1-xAs alloys.

II. CALCULATION METHOD

The structural, electronic and optical properties of cubic In0.25Ga0.75As et In0.75Ga0.25As random alloys presented in this work are performed using the FP-LAPW method implemented in the WIEN2K code package [15] under the framework of DFT [16]. We apply a 16-atom super-cell, which correspond to 1×1×2 (Fig. 1) that is twice size of the primitive cubic unit cell in basic plane direction.

For the XC potential, the (LDA) [17] and the GGA-WC functional [18] were applied in calculating structural properties for x=0.0, 0.25, 0.75 and 1.0. In addition to these approaches, the alternative GGA-EV [19] and the TB-mBJ potential [20] were used for better reproduction of the electronic and optical properties of binary and ternary alloys.

Both last approximations were used only for obtaining the optoelectronic properties and not for the structural parameters.

These calculations involve a plane wave expansion with an RMT×KMAX=8, where RMT is the smallest radii of the muffin- tin (MT) sphere and KMAX respresents the maximum K-vector

in the Brillouin Zone (BZ). The RMT (Muffin-Tin Radii) values were taken to be 2.0 atomic unit (a.u) for In and 1.8 for Ga and As for the ternaries under consideration. The expansion in spherical harmonic functions inside non- overlapping Muffin-Tin spheres is expanded up to lmax=10.

The cut-off for the Fourier-expanded charge density was truncated at Gmax=12 (a.u)^-1. For the irreducible wedge of the BZ, a denser mesh, between 252 and 436 special k-points is used for our alloys, in our calculations. Self-consistent calculations are considered to have converged when the total energy of the system is stable within ≤ 0.0001 Ryd.

Fig. 1. Crystal structures for In0.25Ga0.75As and In0.75Ga0.25As (1×1×2 supercell).

III. RESULTS AND DISCUSSIONS

A. Structural properties

By the fitting of the Murnaghan’s equation of state (EOS) (eq. 1) [21] to the total energies versus volume for yields the equilibrium lattice parameter (a), bulk modulus B, and the first pressure derivative of the bulk modulus B’ of InxGa1-xAs ternary alloys, for x=0.0, 0.25, 0.75 and 1.0. These parameters were computed using the LDA and WC-GGA schemes. The volume optimization is obtained by the use of the experimetal values of the binary compounds as entred parameters.

For GaAs, In0.25Ga0.75As, In0.75Ga0.25As and InAs, the total energy volume curves has been exploited in order to provide the structural parameters (a, B and B’) according to LDA and WC-GGA approximations as shown in Table 1. We noticed a good agreement from a simple comparaison between our achieved results and theoretical experimental values. Hence, The LDA approach underestimate the lattice parameters by around 0.5% to 0.9% while the WC-GGA scheme overestimate it by around 0.1% to 0.5%. Moreover, we remarked as well from our calculated B and B’, that the obtained LDA and WC-GGA results are also shown to be in good agreement along with the reported experimental and other available theoretical works. To the best of our

knowledge, there are no experimental data for the a, B and B’

structural constants of In0.25Ga0.75As and In0.75Ga0.25As alloys.

For this the lattice parameters for the ternary alloys under study were defined from predicted values within Vegard's law that were used as entred parameters.

B. Electronic properties

The purposeful application of materials in diverse electronic devices requires a deep understanding of the electronic properties such as the band structure and total density of states (TDOS). For the cubic phase, the energy band-gaps values of InxGa1-xAs alloys for all studied compositions (x=0.0, 0.25, 0.5, 0.75 and 1.0) were calculated using LDA, WC-GGA, EV-GGA and mBJ approach. Only the results of mBJ are presented in this work, since the similarity patterns were remarked for the used approximations to investigate the electronic properties.

We have investigated the band structure for InxGa1-xAs (x=

0.25 and 0.75) subsequent TDOS from the computed equilibrium lattice parameter. The calculated electronic band structures and TDOS are in correspondence with each other (see Fig. 2 a and b). The predicted band gap (Eg) values estimated by LDA, WC-GGA, EV-GGA and mBJ approximations, along the high symmetry direction in the first Brillouin Zone for GaAs, InAs and InxGa1−xAs alloys are listed in Table 2, compared with experimental data and other available theoretical values. We can deduce that all our cubic mixed crystals have a direct band-gaps because the top valence is located at Γv point and the bottom conduction at Γc. Also, it becomes clear from the Table 2. that the band gap values are superior in the case of mBJ than those achieved by using the LDA, WC-GGA and EV-GGA indicating the improvement of calculated electronic band structure as compared to the under-estimations generally remarked for LDA and WC-GGA and EV-GGA calculations. Fig. 3 shows plots of the band-gap as a function of indium composition x for InxGa1-xAs alloys compared to experimental data. It is obvious that the band-gap curves decrease with increasing of indium content. Also, our results obtained within mBJ approach are in reasonable agreement with the model achieved experimently by Goetz et al. [37] for different x concentrations.

The curves in Fig. 3 show that for all four schemes, the variation in band gap energy as a function of indium content in InxGa1-xAs presents a negative deviation from Vegard's law.

This deviation is described by the total bowing constant b which is computed by fitting the non-linear variation of the computed band gaps versus concentration x within this quadratic function:

b x x E x xE

x

E_{gInGa As gGaAs gInAs}

x

x ₎( ) _{( )} (1 ) _{( )} (1 )

( ₁ = + − − −

− (1)

TABLEI.CALCULATED LATTICE CONSTANT (A), BULK MODULUS (B) AND ITS FIRST PRESSURE DERIVATIVE (B’) ACCORDING TO LDA AND WC-GGA FOR GAAS, INAS AND INXGA1-XAS ALLOYS, COMPARED WITH EXPERIMENTAL AND OTHER THEORETICAL CALCULATIONS.

Our calculated band gap values for InxGa1-xAs ternary alloy shown in Fig. 3 are fitted by the expression (1) following the variations quadratic equation:















+

−

=

+

−

=

+

−

=

+

−

=

−

−

−

−

−

−

2 )

(

2 )

(

2 )

(

2 )

(

575 . 1 927 . 1 974 . 0

971 . 0 69 . 1 965 . 0

32 . 0 114 . 1 825 . 0

447 . 0 433 . 1 016 . 1

1 1 1 1

x x E

x x E

x x E

x x E

mBJ As Ga In g

GGA EV

As Ga In g

GGA WC

As Ga In g LDA

As Ga In g

x x

x x

x x

x x

(2)

The equations (2) gives a bowing parameters b = 0.447, 0.32, 0.971 and 1.575 according to the LDA, WC-GGA, EV- GGA and mBJ respectively. It has to be evident from the above equations that the direct band gaps versus x concentrations have a nonlinear behavior.

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

Energy (eV)

0 10 20

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 a) In_0.25Ga_0.75As

TDOS

E_F TDOS (states/eV)

Γ M Σ Z X

∆

R Λ Γ

Fig. 2 (a). Band structure and total density of states (TDOS) calculated for InxGa1-xAs alloys, for x=0.25 using mBJ functional.

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

0 10 20

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10

Energy (eV) TDOS

b) In_0.75Ga_0.25As

EF TDOS (states/eV)

Γ M Σ Z X

∆

R Λ Γ

Fig. 2 (b). Band structure and total density of states (TDOS) calculated for InxGa1-xAs alloys, for x=0.75 using mBJ functional.

Compounds a(Å) B(GPa) B’

LDA WC-GGA Experiment Other work LDA WC-GGA Experiment Other work LDA WC-GGA

GaAs 5,6028 5,6589 5.653 [23, 24, 25]

5.614[26], 5.530[27], 5.664[28], 5.666[29], 5.507[30], 5.536[31]

75.0325 70.7173 77 [23], 75.5 [24]

68.977[28], 81 [31], 74.043[32], 69.674[32]

4.269 4.224

In0.25Ga0.75As 5,7297 5,7899 - 5.871[11] 68,0018 62,868 - - 4.950 4.569

In0.5Ga0.5As 5,8416 5,9026 5.855[10] 5.791[36],

6.003[11] 65,0221 60,3818 - 68.30 [36] 4.673 4.472

In0.75Ga0.25As 5,9399 6,0035 - 6.105[11] 61,8755 57,5749 - - 4.558 3.6

InAs 6,0261 6,0911 6.058 [23, 24]

5.921[27], 6.6063 [33], 6.15 [34], 5.856[30], 6.03[35], 6.195 [35],

5.956[36]

60,1633 54.9921 58 [33, 35]

61.7[27], 64 [34], 48.1 [35], 60.9 [35], 65.7[36]

4.985 4.7876

0,00 0,25 0,50 0,75 1,00 0,0

0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2

Energy gap (eV)

Composition x

Present work (WC-GGA) Present work (LDA) Present work (EV-GGA) Present work (mBJ) Model of Goetz et al.

Experimental

In_xGa_1-xAs

Fig. 3. Band gap as a function of indium composition x for InxGa1-xAs alloys according to LDA, WC-GGA, EV-GGA and mBJ methods compared to the model of Goetz et al.[37] and experimental data [20,38,39].

TABLE 2.CALCULATED BAND GAP (EG) WITHIN LDA,WC-GGA,EV-GGA AND MBJ APPROXIMATIONS FOR GAAS,INAS AND INXGA_1-XAS COMPARED

WITH EXPERIMENTAL DATA AND OTHER THEORETICAL VALUES.

C. Optical properties

In this section, we have investigated the optical results of InxGa1-xAs alloys (x=0.25 and 0.75) in zinc-blende structure with the three selected approximations; WC-GGA, EV-GGA and mBJ. But we show only the calculations according to the mBJ approximation because of the enhanced band-gap values. For this, we used a mesh of 436 special k-points over the irreducible BZ (grid of 12×12×6 meshes). The half-width broadening [41] is taken to be 0.2 eV.

With the help of the complex dielectric function of the semiconductor that can be given by:

ε(ω)=εreal(ω)+iεimaginary(ω) (3) The other optical quantities such as the absorption coefficient α(ω), the refractive index n(ω), the extinction coefficient k(ω) and the reflectivity R(ω) were determined.

The imaginary part εimaginary(ω) of the dielectric function is obtained directly from the different interband transitions between the valence and conduction bands, using the joint DOS and the optical matrix elements in long-wavelength limit [42]. The imaginary part εimaginary(ω) is given by:

[ ]

[

^{M k k}

]

^{d k}

m e

v c v c imaginary

3 ,

2 2 ,

2 2

) ( ) ( )

(^{ω =}_{π ω}

∑∫

^{δω −ω}

ε ^h (4)

The integral is over the first BZ, where M_c,v(k) is the moment dipole elements intending the direct transitions of electron between VB and CB states, and ωc,v(k)= Eck-Evk is the transition energy. The real part εreal(ω) can be calculated from the feature of ε_imaginary(ω) through the use of the Kramer–

Kroning relation [22,43]:

( )

' '

'2 2

0

2 ( )

1 ^imaginary

real

p ε ω dω

ε ω

π ω ω

= + ∞

∫

− (5) From these two parts of the dielectric function we can easy extract the rest of the optical properties such as α(ω), n(ω), k(ω) and R(ω) [29,44,45]:

[

^{[ ( )2 ( )2 ( )]}

]

^1/2

2 )

(ω ω ε ω ε ω ε ω

α = _real + _imaginary − _real (6)

2 / )]

( ] ) ( )

( [[

)

(ω ε_real ω ² ε_imaginary ω ^21/2 ε_real ω

n = + + (7)

2 / )]

( ]

) ( )

( [[

)

(ω ε_real ω ² ε_imaginary ω ^{2 1/2} ε_real ω

k = + − (8)

[

( )² ( ) 1/ ( )² ( ) 1

]

²

)

(ω = ε_realω +jε_imaginaryω − ε_realω +jε_imaginaryω +

R (9)

The calculated mBJ results of the real part of the optical dielectric function as a function of photon energy for InxGa1- xAs are displayed in Fig. 4 in the range of 0–10 eV. We report in this graph (Fig. 4), the experimental results found by Kim [46]. The εreal(ω) has a positive values up to 4.694 and 4.638 and for x=0.25 and 0.75 respectively. After that, εreal(ω) becomes negative. The main peaks of the real part for InxGa1- xAs occur at 16.08 and 14.586 eV for the compounds In0.25Ga0.75As and In0.75Ga0.25As respectively. For the considered concentrations, the computed values of static dielectric constant εreal(0) using WC-GGA, EV-GGA and mBJ approximations are listed in Table 3. It is clear that the calculated values of static εreal (0) increases with increasing of indium composition.

0 1 2 3 4 5 6 7 8 9 10

-10 -5 0 5 10 15 20 25

Photon energy (eV) εreal

In_0,25Ga_0,75As In_0,75Ga_0,25As

Exp. (In_0,49Ga_0,51As) of T. J. Kim et al.

Fig. 4. The real part of dielectric function for In0.25Ga0.75As and In0.75Ga0.25As alloys within mBJ approach.

Fig.5 shows the imaginary part of the dielectric function within mBJ approach for InxGa1-xAs alloys as a function of photon energy range up to 10 eV. From the feature of

Materials Eg (eV)

LDA WC-

GGA EV-

GGA mBJ Exp. Theoretical results

GaAs 0.483 0.361 0.979 1.586 1.52 [20]

1.56 [32], 1.047[26], 1.008[27], 1.379[36]

In0.25Ga0.75As 0.077 0.0 0.593 1.131 - - In0.5Ga0.5As 0.0 0.0 0.371 0.863 0.846

[38] 0.34[12], 0.596[36]

In0.75Ga0.25As 0.0 0.0 0.260 0.692 - -

InAs 0.0 0.0 0.241 0.615

0.42 [39], 0.417 [24]

0.593[32], 0.34[40], 0.192[27], 0.41 [36]

occur at 1.131 and 0.692 eV for In0.25Ga0.75As and In0.75Ga0.25As, respectively. These points are Γ_15v→Γ_1c splitting, which gives generally the threshold for direct optical transitions between the absolute VBmax and the CBmin

(see Fig. 3). Also, the curves of Fig. 5 display three groups of peaks in the energy ranges between the absorption threshold and 6.5 eV of photon energy. For the InxGa1-xAs system (x=0.25 and 0.75), the corresponding numeric values of the critical points of the imaginary dielectric function vary in accordance with the direct energy band gap values. The calculated critical points are summarized in Table 3. The major origin of the peaks is attributed to the electronic inter- band transition from the occupied states localized in VBmax to unoccupied states localized in CBmin along R, Γ and X symmetry direction in the BZ.

0 1 2 3 4 5 6 7 8 9 10

0 5 10 15 20 25 30

In_0,25Ga_0,75As In_0,75Ga_0,25As

Exp. (In_0,49Ga_0,51As) of T. J. Kim et al.

Photon energy (eV) εimaginary

Fig. 5. The imaginary part of dielectric function for In0.25Ga0.75As and In0.75Ga0.25As alloys within mBJ approach.

The refractive index n(ω) is an important optical parameter related to the microscopic atomic interaction [47]. This parameter has an indispensable impact in optoelectronic properties for the devices such as, detectors, solar cells and wave guides [48]. In fact, this parameter can measures the transparency of semiconductor materials versus spectral radiations. The Fig. 6 indicates the spectral plots of the refractive index for our both ternary alloys within mBJ approach for x=0.25 and 0.75, over a range of photon energies up to 10 eV. The Table 3 presents the computed zero refractive indices n(0) within WC-GGA, EV-GGA and mBJ. The curves of the refractive index (displayed in Fig. 6) indicates two main peaks, The first peak occurs at 2.62 and 2.353 for In0.25Ga0.75As and In0.75Ga0.25As, respectively. The second peaks were found at 4.285 and 4.367 of photon energy for (x=0.25 and 0.75) respectively. Here, the n(ω) reaches a maximum value in the visible light region.

The computed extinction coefficients k(ω) for InxGa1-xAs ternary alloys within mBJ scheme are given in Fig. 7. We remark three peaks coming from the shift of electrons from valence band to conduction band. The maximum values of k(ω) are 3.125 and 3.045 at 4.721 and 4.693 eV for both compounds of compositions (x= 0.25 and 0.75), respectively.

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6

n

Photon energy (eV) In_0,25Ga_0,75As

In_0,75Ga_0,25As

Exp. (GaAs) of Aspnes and Studna Exp. (InAs) of Aspnes and Studna

Fig. 6. Refractive index for In0.25Ga0.75As and In0.75Ga0.25As alloys within mBJ approach.

0 1 2 3 4 5 6 7 8 9 10

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5

Photon energy (eV)

k

In_0,25Ga_0,75As In_0,75Ga_0,25As

Exp. (GaAs) of Aspnes and Studna.

Exp. (InAs) of Aspnes and Studna.

Fig. 7. Extinction coefficient for In0.25Ga0.75As and In0.75Ga0.25As alloys within mBJ approach.

Reflectivity of light R(ω) is one of the most indispensable parameters in linear optical calculations. Additionally, reflectivity is so sensitive to a complicated combination of the two parts of the dielectric function. This is essentially due to the reflection light energy part at the surface of semiconductor materials. Fig. 8 shows the reflectivity spectra of InxGa1-xAs for (x= 0.25 and 0.75) versus photon energy by using mBJ functional. The values of zero frequency reflectivities R(0) within WC-GGA, EV-GGA and mBJ approaches are listed in Table 3. The maximum values (shown in Fig. 8) are positioned at 6.9 and 6.57 eV for our compositions x respectively. The wavelength of the maximum R(ω) is given around 0.179 µm (179.74 nm).

0 1 2 3 4 5 6 7 8 9 10 0,0

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

R

Photon Energy (eV) In_0,25Ga_0,75As In_0,75Ga_0,25As

Exp. (GaAs) of Aspnes and Studna.

Exp. (InAs) of Aspnes and Studna.

Fig. 8. Reflectivity for In0.25Ga0.75As and In0.75Ga0.25As alloys within mBJ approach.

0 1 2 3 4 5 6 7 8

0 20 40 60 80 100 120 140 160 180 200 220

α(ω).104 (cm-1)

Photon energy (eV) In_0,25Ga_0,75As

In_0,75Ga_0,25As

Exp (GaAs) of Aspnes and Studna Exp (InAs) of Aspnes and Studna

Fig. 9. Absorption function for In0.25Ga0.75As and In0.75Ga0.25As alloys within mBJ approach.

The absorption phenomenon is produced when the photon energy of the incident beam is higher than the energy band gap. The form of the spectral components of the absorption coefficient α(ω) by using mBJ approach is plotted in Fig. 9 in the energy range from zero to 8eV. From the feature of the curves, there is a considerable quantity of absorption occurring between 4.5 and 15 eV corresponding to the Ultraviolet (UV) area. The absorption starts at about 1.1 and 0.7 eV for each composition x, respectively, which consequent to the fundamental absorption edge. The zero absorption coefficient for both alloys is observed for photons possessing energies below the energy band gap in the infrared region (along the wavelengths ~1500 nm). The spectra of α(ω) show three main peaks corresponding to the energies 3.3 eV (~E1 transitions), 5.0 eV (~E2 transitions) and 6.2 eV (~E3 transitions). However, the maximum absorption decreases considerably when Ga is replaced by In amount increases from 166.78×10⁴ cm^-1 to 159.94×10⁴ cm^-1 at photon energy of 6.16 and 6.46 eV for In Ga As and

absorption threshold decreases with increasing x concentration, this decrease is due to the variation of band gap energies. Our results are in quite agreement with the experimental data reported from [49] for GaAs and InAs were added for comparison with our achieved results.

TABLE 3.CALCULATED OPTICAL DIELECTRIC CONSTANT, STATIC REFLECTIVITY, STATIC REFRACTIVE INDEX AND CRITICAL POINTS OF

εimaginary(ω) ^OF IN0.25GA0.75AS AND IN0.75GA0.25AS ALLOYS, WITHIN WC- GGA,EV-GGA AND MBJ APPROXIMATIONS.

IV. CONCLUSION

In this paper, we have used the ab-initio calculations, applying the FP-LAPW method of DFT within LDA, WC- GGA, EV-GGA and mBJ schemes to estimate the structural, electronic and optical properties of the cubic InxGa1-xAs alloys for x=0.25 and 0.75. Initially, we have predicted the structural properties of the binary materials GaAs and InAs. Our results are very close to the available experimental data and other theoretical values. Also, we optimized the equilibrium volumes and the bulk modulus of InxGa1-xAs alloys for x vary between 0.0 and 1.0 by step of 0.25. The achieved results fitted to a quadratic equation. The computed lattice parameters increase with indium concentration, viewing a slight deviation from Vegard’s law. While, the band gap energy has been obtained within the three exchange approximations. By increasing the x concentration, we remarked a decrease of the band gap in the ternary alloys, this is due to the incorporation of In into GaAs. Our results of Eg showing within mBJ scheme a good agreement with the model of Goetz et al.. The InxGa1-xAs alloy is of direct band gap, proportionate with optical transitions. The In incorporation has an effect on the optical parametres of studied ternary alloys for x=0.25 and 0.75. There is a small increase of optical dielectric constant, static reflectivity and static refractive index when the In amount increases for intermediate concentrations x. Finally, It is expected that this alloys has a particular interest in the optoelectronic devices as solar cells.

Approximation In0.25Ga0.75As In0.75Ga0.25As

WC-GGA 15.141 16.55

EV-GGA 11.252 11.885

ε1(0)

mBJ 10.03 10.3

WC-GGA 0.349 0.366

EV-GGA 0.292 0.302

R(0)

mBJ 0.27 0.275

WC-GGA 3.891 4.068

EV-GGA 3.354 3.447

n(0)

mBJ 3.167 3.209

E0 (Γ15c- Γ1v) 1.131 0.692 E1 (L3c- L1v) 2.98 2.952 E2 (X5c- X3v) 4.557 4.53 CP’s of

εimaginary(ω)

E3 (L3c- L3v) 5.918 5.782

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