Novel BTlGaN semiconducting materials for infrared opto-electronic devices

Accepted Manuscript Regular article Novel BTlGaN Semiconducting Materials for Infrared Opto-Electronic Devices Abdenacer Assali, M'hamed Bouslama PII: DOI: Reference:

S1350-4495(16)30673-9 http://dx.doi.org/10.1016/j.infrared.2017.01.006 INFPHY 2211

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Infrared Physics & Technology

Received Date: Revised Date: Accepted Date:

27 November 2016 6 January 2017 7 January 2017

Please cite this article as: A. Assali, M. Bouslama, Novel BTlGaN Semiconducting Materials for Infrared OptoElectronic Devices, Infrared Physics & Technology (2017), doi: http://dx.doi.org/10.1016/j.infrared.2017.01.006

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Novel BTlGaN Semiconducting Materials for Infrared OptoElectronic Devices Abdenacer Assali a,b,* and M’hamed Bouslama b a

Unité de Recherche en Optique et Photonique (UROP-Sétif), Centre de Développement des Technologies Avancées (CDTA), Cité 20 Aout 1956 Baba Hassen, Alger, Algeria.

b

Laboratoire Matériaux (LABMAT), Ecole Nationale Polytechnique d'Oran (ENPO), BP 1523 Oran Mnaouar Oran 31000, Algeria.

Abstract BTlGaN quaternary alloys are proposed as new semiconductor materials for infrared optoelectronic applications. The structural and opto-electronic properties of zinc blende BxTlyGa1−x−yN alloys lattice matched to GaN with (0 ≤ x and y ≤ 0.187) are studied using density functional theory (DFT) within full-potential linearized augmented plane wave (FPLAPW) method. The calculated structural parameters such as lattice constant a0 and bulk modulus B0 are found to be in good agreement with experimental data using the new form of generalized gradient approximation (GGA-WC). The band gaps of the compounds are also found very close to the experimental results using the recently developed Tran–Blahamodified Becke–Johnson (TB-mBJ) exchange potential. A quaternary BxTlyGa1−x−yN is expected to be lattice matched to the GaN substrate with concentrations x= 0.125 and y= 0.187 allows to produce high interface layers quality. It has been found that B incorporation into BTlGaN does not significantly affect the band gap, while the addition of dilute Tl content leads to induce a strong reduction of the band gap, which in turn increases the emission wavelengths to the infrared region. The refractivity, reflectivity and absorption coefficient of these alloys were investigated. BTlGaN/GaN is an interesting new material to be used as active layer/barriers in quantum wells suitable for realizing advanced Laser Diodes and LightEmitting Diodes as new sources of light emitting in the infrared spectrum region. Keywords: BTlGaN quaternary alloy, Laser Diodes, Lattice-matching, TB-mBJ functional, Opto-Electronic properties. *Corresponding author: Abdenacer Assali. E-mail address: [email protected]. Tel: +213 551331490

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1. Introduction The emergence of III-nitrides materials in the last decades received significant attention due to their wide direct-band gaps and high temperature stability promising for opto-electronic applications like fabrication of Laser Diodes and Light-Emitting Diodes (LED’s) operating throughout green, blue and ultraviolet spectral regions [1−4], for their use to develop new optical devices such as high-resolution laser printing and high-density optical storage data [5,6]. Recently, thallium containing III−V semiconductors have been proposed as promising materials for various potential applications in the infrared range such as Laser Diodes and detectors [7−10]. Among thallium-III−V, TlGaAs was proposed as a new semiconductor alloy promising for fabricated Laser Diodes operating at a wavelength of 1.3 m on a GaAs substrate [11]. Beneyton et al. [12] have been successfully synthetized TlGaAs alloys by molecular beam epitaxy (MBE) technique. TlGaAs/GaAs multiple-quantum-well (MQW) structures were grown on GaAs substrates by Kajikawa et al. [13] using MBE. Bilgeς Akyüz et al. [14] used the plane wave pseudopotential method within the local density approximation to determine the electronic structures of TlGaAs alloys with Tl concentration x range (0 < x < 1). Dantas et al. [15] reported the structural, electronic, and optical properties of the new predicted Al1−xTlxN alloys using the First-principles calculations. Saidi-Houat et al. [16] proposed Ga1−xTlxN as new semiconducting materials for opto-electronic applications. Winiarski [17] investigated the band structures of zinc blende TlxGa1−xN alloys with the MBJLDA potential. It is found that high Tl-doped III−V materials decreases significantly the band gap which in turn increases the emission wavelengths and reduces their temperature dependence [18,19]. However, Ga1−xTlxN/GaN heterostructures have the disadvantage of lattice mismatch for high Tl-content, due to the deference between lattice parameters, causes high misfit dislocation at the interface layers leading to degrade the performance of optical devices and reduces the efficiency in solar cells [20]. One possible way to reduce lattice mismatch is by incorporation of small amounts of boron into Ga1−xTlxN, allows reducing tensile strain could be obtained for higher Tl-content. In this letter, we propose BxTlyGa1−x−yN as new semiconducting alloys for opto-electronic applications. The purpose is to predict a new single quantum well Laser by using a BxTlyGa1−x−yN layer as an active layer with a specific oscillation wavelength and lattice matching to a GaN substrate. 2

BTlGaN system could be an alternative to the quinary TlInGaAsN-based double quantum well (DQW) structures with TlGaAsN barriers used to fabricate Light emitting diodes (LEDs) [21]. We use accurate DFT First-principle calculations to investigate structural, electronic and optical properties of BxTlyGa1−x−yN alloys lattice matched to GaN containing lower Boron (B) and Thulium (Tl) concentrations up to (x, y) = 0.187. First, we compute the structural parameters of zinc blende BxTlyGa1−x−yN alloys including lattice parameter and bulk modulus. Second, we have calculated the electronic band structure and the density of states of BxTlyGa1−x−yN alloys. Finally, we investigate the optical properties of quaternary alloys under boron composition effect. By varying the B and Tl compositions, we found BxTlyGa1−x−yN is capable of lattice matching with a GaN substrate and the band gaps tuning in the infrared spectral range, which is useful for the design of high-efficiency quantum well structures without including any strain. 2. Computational details We have computed the structural and opto-electronic properties of the predicted BxTlyGa1−x−yN alloy. The calculations were carried out using the full-potential linearized augmented plane wave (FP-LAPW) method as embedded in the WIEN2k code [22] within the density functional theory (DFT) [23]. The exchange and correlation potential for structural properties was treated using the new form of generalized gradient approximations (GGAWC). For electronic properties, we used the recently proposed Tran–Blaha-modified Becke– Johnson (TB-mBJ) correction of the exchange potential [24] which gives very accurate band gaps of semiconductors and insulators, and the exchange–correlation potential of GGA-PBE [25]. Furthermore, the optical properties of these semiconductors are also calculated using the TB-mBJ approach. We expand the basis function up to RMTKmax=7, where RMT is the smallest muffin-tin radius and Kmax gives the magnitude of the k vector in the plane wave’s expansion. The maximum value for partial waves inside the atomic sphere is l=10. The orbital for B (s2 2p1), for Tl (4f14 4d10 6s2 6p1), for Ga (3d10 4s2 4p1) and for N (2s2 2p3) are treated as valence electrons. The muffin-tin radii used in the calculations are 1.4, 2.05, 1.9 and 1.42 a.u. for B, Tl, Ga and N, respectively. For the irreducible wedge of the Brillouin zone, a Monkorst-Pack mesh [26] of 72 special k-points for the binary compounds and 30 special k-points were used for the supercell alloys. The number of k-points and the plane wave cut-off were chosen to ensure convergence of total-energy differences. 3

For modelling random zinc blende BxTlyGa1−x−yN alloys we use 32-atom supercell which corresponds to 2×2×1 repetition of the conventional cubic unit cell. We have considered the zinc blende structure for all concerned materials used in this study, assuming that the alloys will be stable in the structure of the parent compound GaN. We have relaxed the atomic positions and optimized at the equilibrium state. 3. Results and discussion 3.1. Structural properties A. Binary compounds First, the GGA-WC approximation as implanted by the full-potential linearized augmented plane wave (FP-LAPW) method is performed to compute the structural properties of the binary BN, TlN and GaN compounds in the zinc blende phase. The equilibrium structural parameters such as the lattice constant a0 and bulk modulus B0 are derived from the total energy calculations as a function of unit cell volume. The obtained energy values are fitted by Murnaghan’s equation of states [27]. The numerical results of ground state are summarized in Table 1 along with the available theoretical and experimental results and other theoretical works. Our results of lattice constant obtained from the GGA-WC scheme are very close to the experimental values for the binary cases, GaN and BN. In the case of TlN, the results are also found to be in good agreement with the previous theoretical values, and no experimental data have been found in the literature to compared, because it has been not synthesized yet. B. Quaternary BxTlyGa1−x−yN alloys In Fig. 1, we show the variation of the lattice constant as a function of x and y concentrations for zinc blende BxTlyGa1−x−yN alloys. It is clearly seen that the lattice constant of ZB BxTlyGa1−x−yN alloys varied linearly with concentration x and y. We find that TlyGa1−yN alloys have the same behavior of lattice constant to other III-nitride semiconductor alloys such as TlyAl1−yN [15] and TlxIn1−xN [28]. Other ab-initio studies for Tl-doped GaN, AlN and InN also reported a linear behavior of a0 as a function of Tl content [15,17,28]. While Saidi-Houat et al. [16] are obtained a large deviation from Vegard’s law for TlyGa1−yN alloys for the composition range 0 ≤ y ≤ 1, using GGA-PBE approximation without including the structural relaxation. The origin of lattice parameter bowings in these alloys has been attributed to the relaxation effect of the Ga–N and Tl–N bond lengths, and the mismatch between GaN and TlN compounds. 4

Furthermore, high Tl-doped into GaN substrate leads to an increase of lattice mismatch to produce tensile strain and high misfit dislocations in TlyGa1−yN/GaN epitaxial layers, which in turn stimulate nonradiative recombinations that responsible to limited luminescence efficiency in semiconductors [29]. But, the incorporation of small amounts of B into TlyGa1−yN alloys minimized lattice mismatch with a GaN substrate from ∆a/a= 2.74% (for Tl0.187Ga0.812N) to ∆a/a= 0.15% (for B0.125Ga0.187Ga0.688N), and thus reduced strain effect at the

interface layers of

BxTlyGa1−x−yN/GaN heterostructures. This makes B0.125Tl0.187Ga0.688N/GaN a promising material for design of single quantum wells (SQWs) without including strain. 3.2. Electronic structure A. Binary compounds A self-consistent scalar relativistic FP-LAPW is used to compute the electronic band structure of binary BN, TlN and GaN in the zinc blende structure, in which the exchange and correlation were treated in both TB-mBJ and GGA-PBE approaches. In Table 2 gives the results of band gaps compared with available experimental and theoretical data. The zinc blend GaN shows a wide direct-band gap of 3.12 eV, while the BN compound has an indirect-band gap of 5.838 eV according to the TB-mBJ approximation. The case of the ZB TlN, the band gap energy is direct and equal to zero that indicates a semi-metallic character. The values of the band gap obtained from TB-mBJ approximation are found to be in excellent agreement with available experimental values and other theoretical results. Therefore, this numerical calculation approach can be considered as a good tool to reproduce band gaps of semiconductor materials close to the experiment. While, the band gaps extracted from the conventional GGA-PBE approximation are understated to the experimental values. This is due to the limitation of GGA-PBE through the DFT theory [30]. B. Quaternary BxTlyGa1−x−yN alloys In Fig. 2, we show the band structures of BxTlyGa1−x−yN alloys for concentrations x = y = 0.062 and x = y = 0.187 along the various symmetry lines of Brillouin zone. Our calculations show that the maximum of the valence band and the minimum of the conduction band are both at the symmetry point Γ in the Brillouin zone, and this character is shown for all alloys. We deduce that the zinc blende BxTlyGa1−x−yN alloys have a direct-band gap, which is most appropriate for optical devices. 5

The variation of direct-band gaps Γ-Γ as a function of x and y concentrations for BxTlyGa1−x−yN alloys are displayed in Fig. 3. It is clearly seen that the band gap increases slightly with the increases of boron concentration, consistent with previous reports [43,44]. While it decreases strongly by increasing the amount of thallium, because of the semi-metallic character of TlN. Alloys show a strong band gap bowing with respect to the thallium composition y, due to significant differences in atomic size and electronegativity between Tl and N atoms. The strong band gap bowings are also reported in other thallium-doped III-nitrides such as TlyAl1−yN [15] and TlyIn1−yN [28]. Additionally, the results are used to predict a new separate confinement heterostructure (SCH) Laser with a single quantum well based on B0.125Tl0.187Ga0.688N QW, Tl0.062Ga0.937N as waveguides (barrier layers) and GaN as cladding layers, as can be seen in Fig. 4. By using B0.125Tl0.187Ga0.688N to form the active layer, it is capable to obtain the active layer which lattice match with Tl0.062Ga0.937N barrier layers (∆a/a~ 0.75%), with a band gap of 1.639 eV corresponds to a wavelength of 756 nm (in the infrared region). The step in the band gap energy between B0.125Tl0.187Ga0.688N active layer and Tl0.062Ga0.937N barrier layers is of about 1484 meV, sufficient to confine carriers in the QW. The cladding layer is made by GaN, the discontinuity in the conduction band between cladding layers and the waveguide layers (Tl0.062Ga0.937N) as large as 753 meV, and the lattice mismatch between them is achieved (∆a/a~ 0.9%). To understand the nature of the electronic band structure, we have computed the total density of states (TDOS) and partial (PDOS) for zinc blend B0.187Tl0.187Ga0.626N using TB-mBJ approximation, as shown in Fig. 5. We can distinguish three regions, two regions in the valence band (VBmin) and (VBmax) below the Fermi level (Ef, considered as energy reference), and conduction band (CB) above Fermi level. The VBmin located in the energy range [-11, -10 eV] is mainly dominated by the Tl-4d state. The VBmax region extends from -7.5 to 0.0 eV is divided into two under regions. The first one is due to the B-s and Tl-6s states, while the second region is formed essentially by N2p state. The conduction band (CB) region is dominated by Tl-6s state with a small contribution of B-2p and Ga-4s states. We also interest to knowledge the orbital atoms that contribute in the lowest conduction band which is the origin of change in the band gap. As it can be seen in Fig. 5, the conduction band minimum (CBM) is mainly contributed by 6s state of Tl-doped. Thus, the large reduction in

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band gap of BxTlyGa1−x−yN alloy is due to the resonance interaction between 6s state of Tlinduced and the conduction band minimum CBM. 3.3 Optical constants The recent advancement in the calculation based on the DFT theory and TB-mBJ approach as implanted by the FP-LAPW method allows better prediction of the optical properties. In this part, we have calculated the optical properties for zinc blend BxTlyGa1−x−yN alloys for compositions x = 0, 0.062, 0.125, 0.187, and y = 0.187, using TB-mBJ functional. The optical constants can be obtained from the complex dielectric function ε(ω):

 ()  1 ()  i 2 ()

(1)

where: ε1(ω) and ε2(ω) are the real and imaginary parts of the dielectric function, respectively. The dispersion of the imaginary part of the dielectric function ε2(ω) can be calculated from the momentum matrix elements between the occupied and the unoccupied wavefunctions. The real part of the dielectric function ε1(ω) can be obtained from the imaginary part ε2(ω) by the Kramers-Kronig relationship [53]: ε1(ω)  1 

2  ω' ε2 (ω' ) dω'  0 ω'2 ω2

(2)

The other optical functions such as refractive index n(ω), reflectivity R(ω) and absorption coefficient α(ω) can be derived from ε1(ω) and ε2(ω) [54]. Fig. 6 shows the real and imaginary parts of the dielectric function for zinc blend BxTlyGa1−x−yN for photon energy range up to 30 eV. As shown in Fig. 6-(b), the spectra of ε2(ω) indicate that the fundamental absorption edges labeled E0 (first critical point) occur at 1.76, 1.82, 1.95 and 2.05 eV for concentrations x= 0, 0.062, 0.125 and 0.187, respectively, and y= 0.187. These critical points (CPs) are mainly related to the direct optical transitions between the valence band maximum (VBM) and the v conduction band minimum (CBM) at 15 – 1c point (see Fig. 2). Also, ε2(ω) exhibit three

intense peaks labeled E1, E2 and E3 for all alloys. The origin of these peaks is mainly attributed to the interband transitions form the occupied B-2p/s, Tl-4d/6s, Ga-4s and N-2p states appear in the highest valence band to the unoccupied B-2p, Tl-6s, Ga-4s and N-2p states appear in the lowest conduction band along R,  and X symmetry direction in the Brillouin Zone (BZ). We observe that the curves of ε2(ω) shifted towards lower energies with increases in their amplitude namely at (E2, E3) energy positions when the concentration of B increases. As seen in Fig. 6-(a), ε1(ω) firstly increases to reach a maximum value at around 2 7

eV, and then decreases to the lower value (negative) at 15 eV. The smallest values (ε1 1) show the reflectiveness of materials for the incident electromagnetic waves [55]. Thus, the alloys exhibit a metallic character in this energy rang. We found that the static dielectric constant increases with increasing B composition, from 5.2 (for x = 0) to 5.47 (for x = 0.125). The calculated refractive index n( ) and reflectivity R( ) for BxTlyGa1−x−yN alloys are shown in Fig. 7. As shown in Fig. 7-(a), B-induces increases the static refractive index by 10%, from 2.25 (for x = 0) to 2.35 (for x = 0.125). This difference in refractive index confines the light in the BTlGaN layer, interesting to be used it as an active layer for high-efficiency QW Lasers. According to Fig. 7-(b), the calculated reflectivity reaches the maximum value of roughly 48% (for x = 0) at the energy around 14.5 eV, which decreases to 40% when B composition vary up to 0.187. The calculated absorption coefficient α(ω) for BxTlyGa1−x−yN alloys are showed in Fig. 8. The absorption coefficient is zero below the absorption edges, and then the curves show a fast increasing absorption to reach a maximum values at energy around 14 eV. At higher energy, the absorption decreases quickly. The alloys show a strong absorption in the energy range between 8.5 and 20 eV corresponds to the ultraviolet spectrum region. 4. Conclusion In summary, FP-LAPW calculations based on DFT theory have been performed to investigate the structural, electronic and optical properties of zinc blend quaternary BxTlyGa1−x−yN alloys lattice matched to GaN. Our calculations show that the structural parameters are in good agreement with experimental results using GGA-WC approximation. The electronic band structure and density of states are also found to be in excellent agreement with experimental values using the recent TB-mBJ exchange potential. BxTlyGa1−x−yN alloy is expected to be lattice matched with a GaN substrate for concentrations x = 0.125 and y = 0.187 leads to high interface quality. The alloys exhibit a strong reduction in the band gap with incorporation of Tl and B that can be tuned in the infrared spectrum region. The results show a strong absorption in the energy range [8.5, 20 eV] corresponds to the ultraviolet region. The optical constants such as refractive index and reflectivity are improved with addition of B concentration. This makes the predicted BxTlyGa1−x−yN interesting materials to be used as active layers for design of single quantum wells (SQWs) under the lattice matching condition and without any strain suitable for developing advanced opto-electronic devices as Laser Diodes and LEDs emitting in the infrared spectrum region. 8

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Figure captions Fig. 1. Calculated lattice parameter as a function of x and y compositions for zinc blend BxTlyGa1−x−yN alloys. Fig. 2. Calculated band structures for zinc blend B0.062Tl0.062Ga0.876N and B0.187Tl0.187Ga0.626N alloys from TB-mBJ functional. The Fermi level is set to zero. Fig. 3. Calculated direct-band gap Γ-Γ as a function of x and y compositions for zinc blend BxTlyGa1−x−yN alloys from TB-mBJ functional. Fig. 4. Schematic of a predicted quantum well structure BTlGaN/TlGaN/GaN. Fig. 5. Total (TDOS) and partial (PDOS) density for zinc blend B0.187Tl0.187Ga0.626N as prototype, calculated from TB-mBJ functional. Fig. 6. The calculated imaginary part (a) and real part (b) of the dielectric function for BxTlyGa1−x−yN alloys, from TB-mBJ functional. Fig. 7. The calculated refractive index n( ) (a) and reflectivity R( ) (b) for zinc blend BxTlyGa1−x−yN alloys, from TB-mBJ functional. Fig. 8. The calculated absorption coefficient α(ω) for zinc blend BxTlyGa1−x−yN alloys, from TB-mBJ functional.

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4.64

y (Tl)= 0 y (Tl)= 0.062 y (Tl)= 0.125 y (Tl)= 0.187

Lattice parameter (Å)

4.60 4.56

GaN lattice parameter

4.52 4.48 4.44 4.40 4.36

(a) 0.00

0.03

0.06

0.09

0.12

0.15

0.18

B Concentration (x)

x (B)= 0 x (B)= 0.062 x (B)= 0.125 x (B)= 0.187

4.64

Lattice parameter (Å)

4.60 4.56

GaN lattice parameter

4.52 4.48 4.44 4.40 4.36

(b) 0.00

0.03

0.06

0.09

0.12

Tl Concentration (y)

Figure 1

13

0.15

0.18

B0.062Tl0.062Ga0.876N

10

10

8

8

6

6

4

4

2

2

0

EF

-2 -4

0

-4 -6

-8

-8

-10

-10

-12

-12

R



  X Z M





Figure 2

14

EF

-2

-6

-14

B0.187Tl0.817Ga0.626N

12

Energy (eV)

Energy (eV)

12

-14

R



  X Z M





y Tl)= 0 y (Tl)= 0.062 y (Tl)= 0.125 y (Tl)= 0.187

Band gap energy (eV)

3.6

3.2

2.8

2.4

2.0

(a)

1.6 0.00

0.03

0.06

0.09

0.12

0.15

0.18

B concentration (x)

3.4

x (B)= 0 x (B)= 0.062 x (B)= 0.125 x (B)= 0.187

Band gap energy (eV)

3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6

(b) 0.00

0.03

0.06

0.09

0.12

Tl concentration (y)

Figure 3

15

0.15

0.18

Density of States (electron/eV)

Figure 4

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.8 0.6 0.4 0.2 0.0 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.8 0.6 0.4 0.2 0.0

Dos tot_B Dos tot_Tl Dos tot_Ga Dos tot_N

EF

B0.187Tl0.817Ga0.626N

B_s B_p

Tl_s Tl_p Tl_d Tl_f Ga_s Ga_p Ga_d

N_s N_p

VBhigher

CB

VBlow

-12 -10

-8

-6

-4

-2

0

2

Energy (eV) Figure 5

16

4

6

8

10

12

8

(a)

Tl0.187Ga0.812N B- 6.25% B- 12.5% B- 18.75%

6



4 2 0 -2 0

5

10

15 20 Energy (eV)

25

30

7

(b) 6

Tl0.187Ga0.812N

E2 E1

B- 6.25% B- 12.5% B- 18.75%

E3

5 

6

4 4

E0

3 2

2 0 1

1

2

3

4

0 0

5

10

15 20 Energy (eV)

Figure 6

17

25

30

3.0

(a)

Tl0.187Ga0.812N B- 6.25% B- 12.5% B- 18.75%

Refractive index (in a.u.)

2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25

30

Reflectivity (in a.u.)

Energy (eV)

0.5 (b)

Tl0.187Ga0.812N

0.4

B- 6.25% B- 12.5% B- 18.75%

0.3 0.2 0.1 0.0 0

5

10

15 20 Energy (eV)

Figure 7

18

25

30

250

B- 6.25% B- 12.5% B- 18.75%

200

4

-1

Absorption (in 10 cm )

Tl0.187Ga0.812N

150

100

50

0 0

5

10

15 20 Energy (eV)

Figure 8

19

25

30

Table captions

Table 1 Lattice constant a(Å) and bulk modulus B(GPa) for zinc blende GaN, TlN and BN along with other experimental and theoretical values. Lattice constant (Å)

Bulk modulus (GPa)

Binary compounds

This work

Experiment data

Theoretical work

This work

Experiment data

Theoretical work

GaN

4.521

4.52a - 4.52b

4.46c- 4.48d - 4.47e

185.15

190f

202c - 206.3d

TlN

5.224

-

5.129g - 4.882h

170.14

-

114.9g – 141.1h

BN

3.617

3.615b

3.58 i - 3.62j

388.73

382k

406 i - 408.89l

a

Ref. [31] bRef. [32] cRef. [33] dRef. [34] eRef. [35] fRef. [36] gRef. [37] hRef. [38] iRef. [39] jRef. [40] kRef. [41] l Ref. [42].

Table 2 Direct Γ-Γ and indirect Γ-X band gaps (in eV) for zinc blende GaN, TlN and BN, using GGAPBE and TB-mBJ. This work Binary compounds GaN TlN BN a

GGA-PBE EΓ_Γ EΓ_X EΓ_Γ EΓ_X EΓ_Γ EΓ_X

1.669 3.357 0.000 3.081 8.823 4.470

TB-mBJ 3.123 4.862 0.000 4.096 10.39 5.838

Experiment data a

b

3.42 - 3.27 6h

Theoretical work 2.95c 0.0d - 0.11e 8.78f - 9.09g 4.45f - 4.39i

Ref. [45] bRef. [46] cRef. [47] dRef. [48] eRef. [28] fRef. [49] gRef. [50] hRef. [51] iRef. [52].

20

Highlights  The structural and optoelectronic properties of new quaternary BxTlyGa1−x−yN alloys lattice matched to GaN have been investigated using FP-LAPW method within DFT theory.  The band structure and density of states are well predicted by modified Becke–Johnson (mBJ) exchange potential.  The optical responses of considered alloys are presented.  A quaternary BxTlyGa1−x−yN alloy is expected to be lattice matched to a GaN substrate and

the band gaps tuning in the infrared spectral range.

21