RESULTS & DISCUSSION

Chapter 3

RESULTS & DISCUSSION

3.1. Introduction

ScN is closely lattice matched to GaN, then combining the two binary semiconductors to form ScxGa1–xN alloys or pseudomorphical heterostructures could be useful in technological applications [1]. ScN is known to stabilize in the rocksalt phase. Bai [2] indicates that cubic ScN is a good lattice match for zincblende III-A nitrides. GaN crystallizes either in zincblende or in wurtzite structures.

The difference in the total energy between these two phases is very small and therefore both of them can be obtained experimentally. According to the general trends of the material properties of III–V nitrides, zincblende GaN should be better suited for controlled n- and p-type doping than wurtzite. Moreover, cubic GaN has a higher drift velocity and a somewhat lower band gap than the wurtzite structure [3].

Because of the high melting temperature of both Sc and ScN, these materials can be used as a high temperature contact for the III–A nitrides and then could replace InN in III–A–N semiconductor alloys for high temperature device design [2]. The mixed alloys might have some stability range in the zincblende structure for small semiconductor concentrations. In this chapter, a calculation of the optoelectronic band parameters for ScxGa1–xN in hypothetical zincblende structure has been performed in the framework of the empirical pseudopotential method (EPM).

3.2. Computation methodology

The calculations of the electronic structure of ScxGa1–xN are performed using the EPM under the virtual crystal approximation (VCA), disregarding the effect of compositional disorder. In the EPM, the crystal potential is represented by a linear superposition of atomic potentials, which are modified to obtain good fits to the experimental direct and indirect band gaps. Further details are presented by Cohen and Chelikowsky. [4] and in the reviews by Heine and Cohen [5,6]. In the present work, the empirical pseudopotential parameters are optimized using the non-linear least-

squares method [7]. Our non-linear least-squares method requires that the root-mean-square deviation of the calculated level spacing (LS) from the experimental ones defined by:

δ=

[ ^∑

^{

^}

]

should be minimum. In Equation (3.1), Δ E^{(i , j)}=E^{(i , j)}_exp−E^{(i , j)}_cal , where E_exp^{(i , j)} and E_cal^{(i , j)} are the observed and calculated level spacing (LSs) between the i th state at the wave vector k = k_I and the j th at k = ^kJ , respectively, in the m chosen pairs (i, j). N is the number of the empirical pseudopotential parameters. The band gap energies at Γ, X and L high-symmetry points used in the fitting procedure for ScN and GaN binary compounds are given in Table 3.1. The calculated energies given by solving the empirical pseudopotential secular equation depend non-linearly on the empirical pseudopotential parameters. The starting values of the parameters are improved step by step by iterations until δ is minimized. If we denote the parameters by p_v (v = 1,2,…, N) and write them as

p_v (n + 1) = p_v (n) + Δ p_v (3.2)

where p_v (n) is the value at the nth iteration, these corrections Δ p_v are determined simultaneously by solving a system of linear equations,

∑

N

[ ^∑

⁽

⁾⁽

⁾ ]

^∑

⁽

⁾⁽

⁾

v =1,2,.. , N¿ (3.3)

where E_cal^{(i , j)} (n) is the value at the nth iteration, Qvj is given by

Q_v^j=

∑

q , q

[

⁽

⁾ ]

(

⁽

⁾ )

C_qⁱ (k_I)(3.4)

were ^H

(

)

Ψ_kⁱ_I(r)=

∑

q

C_kⁱ

(

)

[

⁽

⁾

]

were ^kq being the reciprocal lattice vector. In the present calculations, three pairs of states ^ki

and k_j : (Γ - Γ), (Γ - X) and (Γ - L) which corresponds to three band energy level spacing are used, with k = (2π/a) (0, 0, 0) stands for Γ point, k = (2π/a) (1, 0, 0) for X point and

k = (2π/a) ( 1 2 , 1

2 , 1

2 ) for the L point (a is the lattice constant).

The pseudowavefunctions Ψ_kⁱ(r) are calculated at each iteration using all the plane wave with ^kq satisfying (ℏ/2m)

[

]

The dimension of our eigenvalue problem is a (136 × 136) matrix. However, 59 plane waves have given a good convergence.

Table 3.1. Band-gap energies for ScN and GaN used in the fits

Compound E_Γ^Γ (eV) E_Γ^X (eV) E_Γ^L (eV)

ScN 4.8 3.7 6.2

GaN 3.30 4.57 6.04

The final local adjusted symmetric ( ^VS (G)) and antisymmetric ( ^VA (G)) pseudopotential form factors for ScN and GaN are shown in Table 3.2.

Table 3.2. Pseudopotential parameters for ScN and GaN.

The alloy

potential of ScxGa1–xN is obtained as

V alloy (r) = x V VCA (r)+ (1-x) V dis(r) (3.6) where VVCA(r) is the periodic virtual crystal potential and Vdis(r) represent the non-periodic potential due to the compositional disorder.

VVCA(r) = x V ScN (r)+ (1- x) VGaN (r) (3.7)

Compound

Form factors (Ry) Lattice

constant (Å)

V_{S (3)} V_{S (8)} V_{S (11}

)

V_{A (3)} V_{A (4)} V_{A (11)}

ScN -0.43751 6 0.0 2382 4 0.025 0 . 0 2 9 5 6 3 0.320 - 0 . 2 3 8 0 4 2 4.88 GaN -0.34724 0 -0.016 0 . 2 1 2 1 7 0.15998 8 0.20 0.135 4.5

and

−p[x(1−x)]^1/2

∑

j

Δ(r−R_j)(3.8)

where j indicates that the summation over j is over the AB and AC molecular sites,

p=

[ ^∑

N_iΔ

(

)

]

∑

N_iΔ

(

)

(3.9)

where d is the nearest-neighbor distance and N the number of nearest-neighbor sites, which is 12 for the FCC structure, i indicates the i th nearest-neighbor sites and n can be extended to include the whole crystal. Although N_i becomes large and is approximately proportional to r² , the potential Δ(r) decreases more rapidly owing to screening, thus ensuring convergence of p. The pseudopotential form factors (V(G)), where G are the reciprocal lattice vectors, are then expressed as [8,9]

^Valloy (G)= (1- x) ^VGaN (G) + x ^VScN - p [x(1- x)]^1/2 ( ^VScN (G)- ^VGaN (G)) (3.10)

where p is treated as an adjustable parameter that simulates the disorder effect.

The lattice constant for ScxGa1–xN is estimated from the Vegard’s law [10] as,

aalloy(x)=¿ (1-x) a_GaN + x a_ScN (3.11)

The refractive index (n) is calculated using the Herve and Vandamme [11] empirical relation which is related directly to the fundamental energy band gap ^Eg as,

n=

√

⁽

⁾

where A and B have the values of 13.6 and 3.4 eV, respectively.

The calculation of n allowed us to estimate the optical high-frequency dielectric constant ( E_∞ ) using the expression

E_∞=n²(3.13) The static dielectric constant ( E₀ ) is calculated using the expression

E₀−1

E∞−1=1+v(3.14)

which relates ^E0 to ^E∞ through the Harrison model [12]. v in Equation (3.14) is obtained

as [13,14]

v=α_p

(

)

2α_C⁴ (3.15)

where ^αp is the polarity defined by [15]

α_p=V_A(3) V_S(3)(3.16)

and ^αc is the covalency of the material under load defined as

αc2

=1−α2p

(3.17)

V_S (3) and V_A (3) in Equation (3.16) are the symmetric and antisymmetric pseudopotential form factors at G (1 1 1), respectively.

3.3. Band gap energies

The variation of the calculated direct band gap energy E_Γ^Γ (taken as the transition Γ_V⟶Γ_C , which is the top valence band state and the lowest conduction one at the Brillouin zone center) versus the scandium content x without taking into account the compositional disorder effect for ScxGa1–xN is displayed in Figure 3.1. One may note that increasing the scandium content from 0% up to 100% increases non-linearly the value of EΓΓ showing a negative band gap

bowing parameter. A qualitatively similar behavior has been also reported by A. Benfredj et al.

[16].

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

3.0 3.5 4.0 4.5 5.0 5.5

Band gap energy (eV)

Composition x

Figure 3.1. Direct band gap energy in ScxGa1–xN as a function of Sc content.

The variation of the direct E_Γ^Γ band gap along with the indirect band gap E_Γ^X (identified as the energy of the lowest conduction state at k = (2π/a) (1.0, 0.0, 0.0), taken from the top of the valence band at the zone center) and E_Γ^L ( identified as the energy of the lowest conduction state at k = (2π/a) (0.5, 0.5, 0.5), taken from the top of the valence band at the zone center) as a function of the scandium content x has been calculated disregarding the compositional disorder effect. The results are shown in Figure 3.2. The different curves in Figure 3.2 indicate the quadratic least-squares fits to our results. Note that on going from x = 0 to 1, the direct band gap increases no-linearly whereas the indirect band gap corresponding to the L valley increases up to x

= 0.4 than it decreases non-linearly. As for the indirect band gap involving the transition in the X valley, it decreases showing a non-linear behavior. Using a full-potential linearized augmented plane waves scheme, Moreno-Armenta et al. [1] have calculated the electronic properties of wurtzite ScxGa1–xN for scandium concentrations between 0 to 1. Their results show that increasing the amount of scandium results in smaller band gaps suggesting thus a different behavior with E_Γ^Γ for zincblende ScxGa1–xN. The system transition between the direct and indirect structures occurred at the composition x 0.38 which corresponds to an estimated crossover band gap of about 4.62 eV. This transition is originated by X-conduction band. Hence, the alloy of interest becomes an indirect band gap semiconductor for scandium content exceeding 38%. This is in excellent agreement with the data reported in Ref. [16].

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 3.0

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

E_

E_X E_L

Band gap energy (eV)

Composition x

Figure 3.2. Direct ( E_Γ^Γ ) (blue curve) and indirect ( E_Γ^X ) (red curve) and ( E_Γ^L ) (green curve) band gap energies in ScxGa1–xN as a function of Sc content.

More commonly, one defines a band gap bowing parameter b by writing,

E_g(x)=E(0)+

[

]

The obtained analytical expressions for E_Γ^Γ , E_Γ^X and E_Γ^L within the expression (3.18) are as follows,

EΓΓ

=−3.26x²+4.78x+3.30 E_Γ^X=−1.59x²+0.68x+4.59

EΓL

=−5.37x²+5.53x+6.07 (3.19)

All energies are in eV. The quadratic terms correspond to the band gap optical bowing parameters. The relevant values of this parameter as calculated from the x-dependent expression Equation(3.19) are -3.26, -1.59 and -5.37 for E_Γ^Γ , E_Γ^X and E_Γ^L respectively. These values are larger than those reported in Ref. [16]. They seem to be also roughly larger than those obtained for GaxIn1-xAs [8] and InP1-xSbx [14] ternary alloys suggesting therefore that the disorder effect is more important on energy band gaps of nitrogen containing semiconductors.

In fact, the observed bowing parameters bexpt are separated into a contribution bI described by the VCA (bI = bVCA) and a contribution bII due to disorder effects [17]. Thus, we do believe that the

non-linearity of the energy band-gaps versus the composition x arises from order effects which exist already in a fictitiously periodic alloy. It is to be noted that the band-gap bowing parameters are negative, meaning that the studied band-gaps bow upwards. However, in most semiconductor alloy systems the gaps bow downwards [18, 19–21].

This is quite interesting. However, one should be careful about the results regarding the gaps of the alloy system. In fact, the calculation for the electronic structure of alloys has been made within the VCA in which the alloy potential is replaced by the concentration weighted average of the constituent potentials while neglecting compositional disorder effects. However, recent experimental and theoretical studies on several semiconductor alloys indicate that the VCA breaks down whenever the mismatch between the electronic properties of the constituent atoms exceeds a certain critical value [8,19,22]. In the present study, the lattice mismatch between GaN and ScN is estimated to be 8% which is a large mismatch. This leaves uncertainty on the accuracy of our VCA results regarding the energy band-gaps. Future experimental measurements and first-principles calculations may throw a light on this.

Table 3.3 lists some estimated E_Γ^Γ energy band gaps in ScxGa1–xN alloys for different scandium compositions. It is to be noted that all the following quantities are calculated by not including the effect of compositional disorder.

Table 3.3. Direct band gap energy ( E_Γ^Γ ) of zincblende ScxGa1–xN for various Sc concentrations x (0 ≤ x ≤ 1).

Material

Band gap energy (eV)

This work Others

GaN 3.3057 3.3 [16, 23], 3.2[18]; 3.38[24]; 3.299[25]

Sc0.1Ga0.9N 3.7567 _

Sc0.2Ga0.8N 4.126 _

Sc0.3Ga0.7N 4.431 _

Sc0.4Ga0.6N 4.678 _

Sc0.5Ga0.5N 4.8677 2.255[26]

Sc0.6Ga0.4N 4.9975 _

Sc0.7Ga0.3N 5.0623 _

Sc0.8Ga0.2N 5.0559 _

Sc0.9Ga0.1N 4.9713 _

ScN 4.8 5.8 [16, 27], 4.8 [28]

3.4. The Valence bandwidth

The dependence of the valence bandwidth (VBW) on the scandium content x in ScxGa1–xN alloys over the composition range 0 – 1 has been calculated and depicted in Figure 3.3. Our results are fitted by a quadratic least-squares procedure giving the following analytical expression:

VBW=−0.27x²−4.13x+19.78 (3.20)

As a result of an increasing scandium content x on going from 0 up to 1, the VBW is monotonically de-enhanced. Thus, the addition of more scandium atoms in the alloys of interest diminishes the VBW. This might be due to the interaction between the s and p electrons of N with d electrons of the system and the variation of binding energy of valence electrons.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0

Valence bandwidth (eV)

Composition x

Figure 3.3. Valence band width in ScxGa1–xN ternary alloys as a function of Sc content.

3.5. Antisymmetric gap and ionicity factor

The ionicity of a semiconductor is an important factor that makes a general distinction between covalent and ionic bonding in solids [29,30]. It is related to the antisymmetric gap (the gap between the first and the second valence bands at the high-symmetry point X in the Brillouin zone) [31]. Hence the knowledge of the antisymmetric gap may give information on the ionic character of the semiconductor under load [32]. Figure 3.4 depicts the dependence of the antisymmetric gap on the composition x for different amounts of Sc in ScχGa1–χN alloys. Note that the incorporation of Sc atoms in the ternary alloys under study decreases substantially the antisymmetric gap. This fact suggests that the ionicity character decreases by increasing the Sc content in the range 0 – 1 as can be seen from Figure 3.5.

The calculated iconicity factor for the material under investigation is plotted against Sc content in Figure 3.5. In accordance with the information derived from the antisymmetric gap, the iconicity factor decreases non-linearly as the scandium content increases. This can be traced back to the difference in electronegativity between Ga and Sc atoms.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

9.50 9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75

Antisymmetric gap (eV)

Composition x

Figure 3.4. Antisymmetric band gap energy in ScχGa1–χN as a function of Sc content.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Ionicity factor

Composition x

Figure 3.5. Ionicity factor in ScχGa1–χN as a function of Sc content.

3.6. The effective mass

Values of the effective mass of electrons and heavy holes are parameters which may provide

can be obtained from the band structure of the material. The simplest approximation corresponds to the parabolic E(k) dependence. Using this approximation, we have determined the effective mass in the conduction band minimum and the valence band maximum at the Γ valley from the band curvature for different Scandium contents ranging from 0 to 1. Our results regarding the behavior of the electron and heavy hole effective masses, in units of the free electron mass ^m0 , with respect to the Sc concentration for ScxGa1–xN are displayed in Figures 3.6 and 3.7. Some calculated electron and heavy hole effective masses at the Γ point of the Brillouin zone at various concentrations in the range 0 ≤ x ≤ 1 are also tabulated in Table 3.4.

Comparison of our obtained electron and heavy hole effective masses for GaN (i.e., for x

= 0) with other theoretical estimates and available experimental data [33] shows a reasonable agreement. So far, to the best of our knowledge, there are no experimental data available on effective masses of electrons and heavy holes for ScxGa1–xN in the range 0 ≤ x ≤ 1, thus our calculated values may serve as a reference. In view of Figure 3.6, one may note that both the electron and heavy hole effective masses change nonlinearly with increasing Sc content. These quantities increase with different slopes by adding some amounts of scandium, but subsequent addition of Sc appears to enhance them very rapidly. The enhancement of the electron and heavy hole effective masses may decrease the mobility in the material under investigation providing thus less opportunity on transport properties. In the same way, it has been reported that in Al1-xGaxN conventional alloys the electron effective mass at the Γ point of the Brillouin zone changes monotonically with the composition x [18].

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 0.325

Electron effective mass (mo units)

Composition x

Figure 3.6. Effective mass of the electron in ScχGa1–χN as a function of Sc content.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.85

0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25

Heavy hole effective mass (m0 units)

Composition x

Figure 3.7. Effective mass of heavy hole in ScχGa1–χN as a function of Sc content.

Table 3.4. Conduction and valence band edge electron and heavy hole effective masses (in units of the free electron mass m₀ ), at the Γ points of the Brillouin zone in zincblende ScχGa1–χN as a function of Sc content x (0 ≤ x ≤1 ).

Material

(m_e^¿)_Γ m_{h .h}^¿

This Work Others This Work Others

GaN 0.1418

0.15[25], 0.185[16], 0.127[18,34], 0.124[32], 0.13 [35], 0.19[36,37].

0.9148 1.27 [12]

Sc0.1Ga0.9N 0.156 _ 0.9223 _

Sc0.2Ga0.8N 0.1685 _ 0.9278 _

Sc0.3Ga0.7N 0.18 _ 0.9329 _

Sc0.4Ga0.6N 0.1911 _ 0.944 _

Sc0.5Ga0.5N 0.2027 _ 0.9621 _

Sc0.7Ga0.3N 0.2306 _ 1.0217 _

Sc0.8Ga0.2N 0.2491 _ 1.0675 _

Sc0.9Ga0.1N 0.2723 _ 1.1329 _

ScN 0.3013 0.281 [38] 1.216 0.93 [39]

3.7. The refractive index

Besides the band gap energy, knowledge of the refractive indices also forms an important piece of information in the design of heterostructure lasers, as well as other waveguiding devices [40]. Thus, the refractive indices and the optical dielectric constants of the scandium gallium nitride alloys of interest have to be known as a function of composition. For this purpose, the scandium concentration dependence of the refractive index (n) is plotted in Figure 3.8 Some calculated n at different compositions over the range 0-1 for ScxGa1–xN along with available known data are presented in Table 3.5. The agreement between our results and the known data reported in Ref. [27]

for GaN is better than 8% for n. Once again our results for ScxGa1–xN (0 ≤ x ≤ 1) may serve as a reference. Through Figure 3.8 one can also notice that adding some amounts of Sc in ScxGa1–xN diminishes substantially the refractive index on going from x=0 to x=0.5. Above x=0.5 the refractive index is aroused non-linearly. One may conclude then that, increasing the Sc content in ScxGa1–xN alloys enhances largely the energy band gaps and decreases substantially the refractive index for direct band gap corresponding compositions. This is against the general trend common for most of the III–V compound semiconductor alloys [41,42].

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30

Refractive index (n)

Composition x

Figure 3.8. the refractive index of the dilute nitride alloys in ScχGa1–χN as a function of Sc content.

Table 3.5. Refractive index in zincblnde ScχGa1–χN as a function of Sc content. x (0 ≤ x ≤1 ).

Material

n

This work Others

GaN 2.2364 2.5[11],

2.26[27], Sc0.1Ga0.9N 2.1486 1.88[27]

Sc0.2Ga0.8N 2.0793 _

Sc0.3Ga0.7N 2.0284 1.57[27]

Sc0.4Ga0.6N 1.9959 _

Sc0.5Ga0.5N 1.9819 2.00[27]

Sc0.6Ga0.4N 1.9862 _

Sc0.7Ga0.3N 2.009 0.95[27]

Sc0.8Ga0.2N 2.0503 _

Sc0.9Ga0.1N 2.1099 0.64[27]

ScN 2.188 1.8[27]

3.8. The dielectric constants

The variation of the static dielectric constant ( ^E0 ) and high-frequency dielectric constant ( E_∞ ) against the Sc content x is given by the analytical functions that is the quadratic least- squares fit to our data.

E_∞=−38.94x²+21.55x+2.86 (0 ≤ x ≤ 1)

^E0 =- 34.36 x² + 4.0790 x + 6.6370 (0 ≤ x ≤ 1) (3.21)

Whereas some calculated ^E0 and ^E∞ at various compositions x (0 ≤ x ≤ 1) are given in Table 3.6. For GaN the value of E₀ and E_∞ obtained by our calculation is found to be in reasonable agreement with the known one reported in Ref. [27], whereas our results regarding E₀ and ^E∞ for ScxGa1–xN (0 ≤ x ≤ 1) are predictions. In view of Equation (3.21), one can note that adding some quantities of Sc in the ScxGa1–xN alloys decreases largely E₀ and E_∞ as

depicted in Figure 3.9 showing a behavior that is qualitatively similar to that of the refractive index with larger bowing parameter.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

4.0 4.5 5.0 5.5 6.0 6.5 7.0

High-frequency Static

Dielectric constant

Composition x

Figure 3.9. The static and high-frequency dielectric constants in ScxGa1–xN as a function of Sc content.

Table 3.6. Static and high-frequency dielectric constant in zincblnde ScχGa1–χN as a function of Sc content x (0 ≤ x ≤1 ).

Material

E₀ E_∞

This work Others This work Others

GaN 6.6372 6.94[27],

9.7[43]

4.9973 5.12[27], 5.20[44]

Sc0.1Ga0.9N 5.8856 4.82[27] 4.6273 6.15[27]

Sc0.2Ga0.8N 5.2627 _ 4.3348 _

Sc0.3Ga0.7N 4.7684 4.33[27] 4.1197 5.04[27]

Sc0.4Ga0.6N 4.4029 _ 3.9819 _

Sc0.5Ga0.5N 4.166 4.31[27] 3.9217 3.93[27]

Sc0.6Ga0.4N 4.0578 _ 3.9388 _

Sc0.7Ga0.3N 4.0783 3.60[27] 4.0333 3.78[27]

Sc0.8Ga0.2N 4.2274 _ 4.2053 _

Sc0.9Ga0.1N 4.5053 3.30[27] 4.4547 3.40[27]

ScN 4.9118 3.25[27] 4.9973 3.19[27]

3.9. Transverse effective charge

The transverse effective charge e_T^¿ is a basic parameter characterizing the dielectric parameters of solid state materials. It is a dynamic quantity reflecting the covalency effects with respect to some reference ionic value [45].

The behavior of the transverse effective charge e_T^¿ when the Sc composition x increases from 0 up to 1 is depicted in Figure 3.10. It is shown that e_T^¿ is de-enhanced by increasing Sc content on going from 0 to 1. Thus higher scandium composition results in a diminution of the transverse effective charge.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75

Transverse effective charge

Composition x

Figure 3.10. Transverse effective charge in ScxGa1–xN as a function of Sc content.

3.10. Conclusion

Electronic band structures of zincblende GaN, ScN and their mixed alloys ScxGa1–xN are calculated using the empirical pseudopotential method. The composition dependence of the band gap energies has been obtained and the alloy exhibits features of both direct and indirect band gap semiconductors as a function of the composition. Other optoelectronic properties like the antisymmetric band bap, the iconicity, the effective masses of both electrons and heavy holes, the refractive index, the static and high-frequency dielectric constants as well as the transverse effective charge have all been also addressed.