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S0921-4526(17)30644-0 http://dx.doi.org/10.1016/j.physb.2017.09.058 PHYSB310284

To appear in: Physica B: Physics of Condensed Matter Received date: 10 March 2017 Revised date: 31 July 2017 Accepted date: 15 September 2017 Cite this article as: Abdenacer Assali, M. Bouslama, L. Chaabane, A. Mokadem and F. Saidi, Structural and Opto-electronic Properties of InP 1−xBix Bismide Alloys for MID−Infrared Optical Devices: A DFT + TB-mBJ Study, Physica B: Physics of Condensed Matter, http://dx.doi.org/10.1016/j.physb.2017.09.058 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Structural and Opto-electronic Properties of InP1−xBix Bismide Alloys for MID−Infrared Optical Devices: A DFT + TB-mBJ Study Abdenacer Assali a,b*, M. Bouslama b, L. Chaabane c, A. Mokadem b, F. Saidi d a

Unité de Recherche en Optique et Photonique (UROP-Sétif) − Centre de Développement des Technologies Avancées, P.O. Box 17, Baba-Hassen, 16303 Algiers, Algeria. b Laboratoire Matériaux (LABMAT), Ecole Nationale Polytechnique d'Oran (ENPO), BP 1523 Oran Mnaouar Oran 31000, Algeria. c Laboratoire de Technologie des Matériaux et de Génie des Procèdes, Faculté de Technologie, Université A/MIRA-Bejaia, Route Targa-Ouzemour 06000, Algeria. d Laboratoire de Micro-Optoélectronique et Nanostructures, Université de Monastir, Faculté des Sciences, 5019 Monastir, Tunisia.

Abstract Using full-potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT), we have studied the structural and opto-electronic properties of zinc blende InP1−xBix bismide alloys (0 x 0.5). The bowing lattice parameter exhibits a weak composition dependence on InP1−xBix alloys with b= 0.02834 Å. The band gap decreases with Bi composition by about 1.285 meV for x= 0.25 covering the middle (MID) and farwavelength infrared region [0.8810.5 m]. From DOS, the decrease of band gap can be attributed to the both upper shifts of the valence band VB and the downward shifts of the conduction band CB, due to the resonance interaction of the Bi-p orbitals at the top of the VB and hybridization of the occupied s/p orbitals of In/P/Bi atoms at the bottom of the CB, with increasing Bi composition. The dielectric functions (ε1(ω), ε2(ω)) and optical constants such as n(ω), k(ω), α(ω) and R(ω) for InP1−xBix alloys are determined for radiation up to 8 eV in excellent agreement with the measured data. The energies of the critical-point (CP) are also identified agree well with the experimental data. The InPBi material appears as a promising material to realize novel optical devices as Laser Diodes and detectors operating in the MIDInfrared spectrum region. Keywords: InP1−xBix alloys, MIDInfrared, Opto-electronic properties, DFT+TB-mBJ functional. *Corresponding author: Abdenacer Assali. E-mail address: [email protected] Tel: +213 551331490

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1. Introduction The narrow-gap IIIV bismide alloys such as GaAsBi, InAsBi, InSbBi and GaSbBi plays an important role in development optical devices operating in the infrared range, like detectors and Laser Diodes [14]. GaAsBi is one of the most extensively studied alloys among the IIIV-Bi family. It is applied in a wide range applications in opto-electronic devices and multijunction solar cells [5,6]. GaAsBi thin films was first successfully grown by Metal Organic Vapour Phase Epitaxy (MOVPE) in 1998 [7] and later by Molecular Beam Epitaxy (MBE) in 2003 [8]. The incorporation of a few percent of Bismuth (Bi) into GaAs leads a large spin-orbit (SO) splitting [9,10] allowing the decrease of band gap by about 9075 meV/% Bi [1113]. This is due to resonant interaction between the valence band maximum VBM and 6p state of Bi atom [14,15]. Indium phosphide bismide is another important new semiconductor material among the IIIV-Bi family. InPBi with unique properties including, narrow-gap varied from that of InP (1.424 eV at 300 K) [16] to semimetallic phase with increasing Bi composition and good thermal stability [17], promising it for middle (MID) and far-infrared opto-electronic devices such as super-luminescence diodes. Since InPBi alloy has received considerable attention for both experimental and theoretical investigations. Wang et al. [18] group were the first to demonstrate the growth of InPBi single crystal thin films alloys by gas source molecular beam epitaxy (MBE) technique in 2013. They found that InPBi exhibits strong photoluminescence (PL) at room temperature at 1.4–2.7 μm. Furthermore, Kopaczek et al. [19] applied Contactless Electroreflectance to study the band gap (E0) and spin-orbit splitting (SO) for InP1−xBx alloys with 0 x 0.034 in comparison with the ab-initio calculations. Polak et al. [20] reported the calculations of electronic band structure of GaSb1−xBix, InSb1−xBix, InP1−xBx and InAs1−xBix in the context of the virtual crystal approximation (VCA) and the valence band anticrossing (VBAC) model compared to the experimental data. Recently, Samajdar et al. [21] investigated the band structure of InAs1−xBix, InSb1−xBix and InP1−xBix using the Valence Band Anticrossing (VBAC) model. They found that Bi-induced strongly perturbs the valence band due to the interaction of the Bi impurity states with the HH, LH and SO bands [22]. More recently, Khan et al. [23] have studied the electronic structure, optical and thermoelectric properties of InPBi alloys using the density functional theory within EV-GGA approach. The binary compound InP is most studied than InBi, because InBi is difficult to synthesize. InP, which crystallizes in stable cubic zinc blende structure (space group F43m) [24], is of interest for numerous applications, such as fast transistors, solar cells [25], light emitting 2

diodes [26] and components for optical fiber communications [27], and it serves as the substrate for most opto-electronic devices operating at the communications wavelength of 1.55 m. InBi is a semimetallic with tetragonal (PbO) crystalline symmetry [28,29]. The Xray measurement also indicates that InBi can be crystallizes in the zinc blende with a lattice constant of 6.626 Å, as reported by Rajpalke et al. [30]. The recent advanced in electronic structure computations related to modern approaches in the density functional theory (DFT) allows predicting the properties of materials qualitatively. The novelty developed Tran–Blaha-modified Becke Johnson (TB-mBJ) is one of the most efficiently approach for describing the band gaps of semiconductors and insulators, giving results in agreement with the experimental values [31,32]. In this letter, we reports the first investigation of the structural and opto-electronic properties characteristics of InP1−xBix alloys for MID−IR optoelectronics application in the composition x range 0≤ x ≤0.5, by employing the Wu-Cohen generalized gradient approximation (WCGGA) and TB-mBJ exchange potential within FP-LAPW method in the framework of the density functional theory (DFT). The spin-orbit coupling (SOC) effects are of great significance in III−V-Bismides. Thus, the SOC effects are included in the calculations. InP1−xBix/InP is then an interesting new material for developing novel optical devices as Laser Diodes, LEDs and photodetectors in the MID−infrared range. 2. Computational details In order to compute the structural and opto-electronic properties of the ternary InP1−xBix (0 x 0.5) and binary InP and InBi compounds, we use the full potential linear augmented plane wave (FPLAPW) within the density functional theory (DFT) [33], as implemented in the WIEN2k package [34]. The exchange and correlation (XC) effect for structural properties is described using the new form of generalized gradient approximations (WC-GGA) [35], because of their high efficiency for calculating the structural parameters. The recent Tran– Blaha-modified Becke–Johnson (TB-mBJ) exchange potential approximation [36] is used to compute accurately the electronic and optical properties of binary and ternary alloys. The Muffin-Tin radius RMT values for In, P and Bi are considered to be equal to 2.3, 1.9 and 2.5 a.u., respectively. The wave functions, charge density and potential inside the Muffin-Tin spheres are expanded with an angular momentum equal to lmax=10. In the interstitial regions, the wave functions are expanded in plane wave (PWs) with a cut-off of RMTKmax= 7 in order to ensure the convergence of the calculation. The orbitals for In (4d10 5s2 5p1), P (3s2 3p3) and

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Bi (4f14 5d10 6s2 6p3) are treated as valence electrons. The Brillouin-zone integration was performed using a mesh of 72 special k-points for the binary compounds and 32 special kpoints for alloys. To model InP1−xBix alloys with the compositions x= 0.125, 0.25, 0.375 and 0.5, we adopt a 16-atom supercell In8P8−nBin which corresponds to 1×1×2 conventional cubic zinc blend cell (see Fig. 1). We have considered the zinc blend structure for all alloys in the present study. The atomic positions in alloys are relaxed and optimized at the equilibrium configurations by minimizing the forces exerted on the atoms within self-consistent FP-LAPW calculations. 3. Results and discussion 3.1 Structural properties The structural properties of the binary InP and InBi and ternary InP1−xBix compounds for the compositions x= 0.125, 0.25, 0.375 and 0.5 crystalizes in the zinc blend structure are determined. The total energies were calculated as a function of volume and were fitted to Murnaghan’s equation of state [37]. The calculated equilibrium lattice constants, bulk modulus and its derivative for zinc blend InP1−xBix alloys and their pseudobinary InP and InBi are given in Table 1 along with available experimental data and other theoretical values. The WC-GGA results for the binary compounds are in excellent agreement with the experimental values and other theoretical works. For InP compound, the calculated lattice parameter a of 5.890 Å corresponds very well to the experimental value of 5.869 Å [38]. The predicted InBi lattice parameter a equal to 6.712 Å agrees well with the theoretical value obtained by Rahim et al. [45] of 6.740 Å using the WC-GGA, but they are larger than the ones obtained experimentally. The reason for this discrepancy might be due to the uncertainty on the value of the lattice parameter of InBi hypothetic compound, given that the InBi compound is not synthetized yet. The experimental lattice parameter of 7.024 Å for InBi is obtained by extrapolated lattice parameter of InAsBi [44], while the 6.626 Å value is determined through the grown of InSbBi alloys [43]. The bulk modulus B obtained by WC-GGA calculation are in reasonable agreement with the experimental data and previous theoretical works for both binary compounds InP [40−42] and InBi [45,46]. Hence, WC-GGA gives best results for the ground state properties such as lattice constants a and bulk modulus B than other approximations like GGA and LDA [47]. It is well known the GGA usually overestimates the lattice constant while LDA is expected to underestimates them [48,49].

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The dependence lattice parameter a as a function of mole fraction x for InP1−xBix can be expressed as

xa InBi (1 x)a InP x(1 x)b

a InP

1 x Bi x

(1)

where b is the bowing parameter, aInBi and aInP are the lattice constants of InBi and InP, respectively. In Fig. 2, we show the variation of the lattice parameter a versus the Bi composition x for InP1−xBix alloys. It is clearly seen that, the lattice parameter increases lineally with increasing composition x up to 0.5. A quadratic fit of the lattice parameter a within the equation (2) gives the relation

a InP

1 x Bi x

5.88937 0.80471x 0.02834 x 2

(2)

A negligible deviation of the lattice parameter from linear Vegard’s law [50] is observed with an marginal downward bowing of 0.02834 Å. The small deviation might be mainly due to the structural relaxation effect of the In–Bi and P– Bi bond lengths. The linear dependence of the lattice parameter a on the concentration x has been observed in the most alloys of III–V group for both experimentally [51−53] and theoretically according to the structural relaxation [54,55]. In contrast, several previous theoretical works [56,57] have reported violations of Vegard’s rule for the systems with strong lattice mismatch such as III–V-N and III–V-Bi alloys. It is interesting to note here that the strong lattice mismatch between the binary compounds has a small influence on the bowing parameter when the structural relaxation is taking into account. The relaxation effect on the bowing lattice parameter alloys has been reported in our previous work quoted in Ref. [58]. We found that the bowing lattice parameter becomes very large, if we do not take into account the relaxation contribution. In Fig. 3, we show the variation of the bulk modulus as a function of Bi concentration for InP1−xBix alloys compared with the results predicted by Linear Concentration Dependence (LCD). A quadratic fit of the bulk modulus B by a second-order polynomial gives the relation

B InP

1 x Bi x

64.85571 42.20823x 8.43886 x 2

(3)

A significant deviation of the bulk modulus from the linear concentration dependence (LCD) is observed with an downward bowing equal to 8.43886 GPa. For x ≤ 0.375, the bulk modulus decreases fairly linearly by increasing Bi content with an upward bowing less than -2.656 GPa. This means that the bowing bulk modulus in InP1−xBix alloys depends on the mismatch between the bulk modulus of their binary compounds, which increases with the composition

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x. Furthermore, by increasing Bi concentration from x= 0 to x= 0.5, the InP1−xBix alloys become more compressible. 3.2 Electronic properties 3.2.1 Band structure The electronic band structure of the binary InP and InBi and ternary InP1−xBix alloys in the zinc blend structure for the compositions x= 0.125, 0.25, 0.375 and 0.5 have been calculated within TB-mBJ approach. The obtained results are summarized in Table 2, in comparison with the experimental and other theoretical values. The TB-mBJ Eg value of 1.403 eV for the binary InP compound is very consistent with the experimental value of 1.42 eV [60]. It is worth noting that this value is larger than the recent DFT reports of 0.48 eV [61], 0.564 eV [62] and 1.363 eV [23] using GGA, LDA and EV-GGA approximations, respectively. Hence, TB-mBJ approach is able to give more reliable band gap in concordance with the experimental results. Additionally, previous theoretical studies were finding that the TB-mBJ approach improves the semiconductor band gaps compared to the other exchange-correlation functionals as the standard local density approximation (LDA) and the generalized gradient approximation (GGA) as well as EV-GGA [64]. Due to that the VB maximum and CB minimum are both located at -point in the band structure, InP is found to be a direct-band gap such as the most III−V group. We found InBi exhibits a semimetallic character with a gap value equal to zero, consistent to the result obtained by Rahim et al. [45] using TB-mBJ, and larger than the one reported by Janotti et al. [63] of 1.63 eV using Virtual Crystal Approximation (VCA). In the other hand, the band gaps values obtained for the ternary InP1−xBix alloys within TB-mBJ are larger than those estimated by Khan et al. [23] using EV-GGA approach. This discrepancy is may due to the fact that the authors did not considered the structural relaxation effect within the calculations witch strongly affect the band gaps. Furthermore, Reshak et al. [65], Ziane et al. [66] and Bannow et al. [67] have been recently discussed the relaxation in influencing the band gap reduction in dilute InGaNAs and GaAsBi alloys. In Fig. 4, we display the calculated band structures and TDOS for InP1−xBix alloys for concentrations x= 0.125 and x= 0.375, as prototypes, along the various symmetry lines of the Brillouin zone. The results show that the valence band maximum (VBM) and conduction band minimum (CBM) are situated at the Γ symmetry point of the Brillouin zone (BZ) leading to the direct-band gap character for InP1−xBix alloys. 6

The calculated energy band gap versus the Bi composition x for InP1−xBix alloys using TBmBJ is presented in Fig. 5 and compared to the available experimental data. The band gap reduction with Bi-induced is very closer to the experimental data of Wang et al. [18], Kopaczek et al. [19] and Das et al. [68]. It shows a decrease of the band gap when the Bi composition x increases for x range 0 x 0.25 leading to the narrow-gap for InP1−xBix that can be cover the middle (MID) and far-wavelength infrared region [0.8810.5 m]. Then, the band gap slightly increases for x up to 0.5. A gap bowing parameter equal to 10.71 eV is obtained for InP1−xBix alloys with the composition x range up to 0.5. The main origin of gap bowing alloy is due to the size mismatch and the difference in electronegativity between the constituent elements Bi and P atoms. Additionally, the calculated band gap discontinuity (Eg= Ec+Ev) between InPBi and InP layers is about 734 meV by incorporation of 12.5% of Bi amount. InP0.875Bi0.125 alloy is expected to be lattice matched to InP substrate with a mismatch less than 1.68%, leads to high interface layers quality. Hence, the large band gap discontinuity and the lattice matching make InPBi/InP systems interesting for realized heterostructures as well as quantum wells (QWs) without including strain defects and able to confine carriers and light for advanced optical devices. 3.2.2 Density of states (DOS) In order to define the nature of electronic band structures of InP1−xBix alloys, we have employed the TB-mBJ functional to examine the total density of states (TDOS) and partial (PDOS) of these alloys for the energy range between −12 and 8 eV. The calculated total (TDOS) and partial (PDOS) density of states of the prototypes InP0.875Bi0.125 and InP0.625Bi0.375 alloys are displayed in Fig. 6. We see from Fig. 6, that the overall total DOS profiles for the two alloys are similar. We can distinguish three main energy groups two located in the valence band VB (VBlow, VBhighest) and the conduction band CB. To detail, a significant contribution of P/Bi-s states is observed in the lowest valence band (VBlow) extending from -11.55 to -9.3 eV. The region appears around -5.8 to -3.4 eV below the Fermi level is due to the In-s and P/Bi-p states. The structure near the Fermi level extends from -3.4 eV to 0 V is mainly dominated by p states of P and Bi atoms. The conduction band is formed by hybridization between In-s/p, P-p and Bi-p states. To understand how the Bi induces effect the energy band gap for InP1−xBix, we analyzed through Fig. 6 the valence band maximum (VBM) and the conduction band minimum (CBM) which are the origin of changes in band gap energy. It is observed that the VB maximum is

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mainly dominated by the 6p states of Bi atom and the resonant interaction between them leads to band gap reduces. The contribution of Bi-6p in the VBM causes narrow-gap in IIIV Bismide alloys was demonstrated by other authors [69−71]. As seen from Fig. 7, we remark that the CB minimum shifts downward with increasing Bi content due to the moves of In-5s, P-3p and Bi-6p sates to the lower energy (as shown in Fig. 6) leading to band gap decreases. This important result is in accordance to the recent study of Polak et al. [20] using the virtual crystal approximation (VCA). The authors observed a negative shift of the CB in the entire Brillouin zone with increases Bi concentration. Therefore, we can conclude that the decrease in band gap for InP1−xBix can be attributed to the both shifts of the valence band VB to upper due to Bi-p orbitals mixing at the top of the VB, and the shifts of the conduction band CB to downward due to the hybridization (anticrossing) of the occupied s/p orbitals of In/P/Bi atoms at the bottom of the CB when the Bi composition increases. 3.3 Optical properties For the design of opto-electronic devices we need accurate knowledge of some optical parameters of the based materials. The optical functions of InP1−xBix alloys with concentrations x= 0, 0.125, 0.25, 0.375 and 0.5 are computed using TB-mBJ approach for energy range 08 eV. The optical properties of materials are generally described in terms of the complex dielectric function ε(ω) given as

ε(ω) ε1 (ω) iε2 (ω)

(4)

where ε1(ω) and ε2(ω) represent the real and imaginary parts of the dielectric function, respectively. ε(ω) can be used to measure the optical properties of the medium at all photon energies E ω [72]. The imaginary part of the dielectric function ε2(ω) is calculated directly from the electronic structure through the joint density of states (DOS) and the momentum matrix elements between the occupied and the unoccupied eigenstates. The imaginary part ε2(ω) is given as follows [73]:

4 2 e 2 ε 2 (ω) 2 2 i M j m ω ij

2

f i 1 f j E f Ei ω d 3 k

(5)

where M is the dipole matrix, i and j are the initial and final states respectively, fi is the Fermi distribution for the ith state. The real part of the dielectric function ε1(ω) can be extracted from the imaginary part using the Kramers–Kroning relation [73,74].

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Other important optical constants such as refractive index n(ω), extinction coefficient k(ω), reflectivity R(ω) and absorption coefficient α(ω) can be computed from the complex dielectric function ε(ω) through the relations [75,76]. The spectral variation of the real and imaginary parts of the dielectric function for InP1−xBix alloys obtained from TB-mBJ approach are shown in Fig. 8. The imaginary part give informations about the possibility of different interband transitions related to semiconductor materials witch depend to the topology of the band structure as represent in Fig. 9 for the case of InP. The curves of the imaginary part 2() (see Fig.8-(b)) indicate that the fundamental absorption edges labeled E0 (first critical point) occur at 1.40, 0.88, 0.34, 0.06 and 0.0 eV for concentrations x= 0, 0.125, 0.25, 0.375 and 0.5, respectively. It should be notice that these critical points (CPs) are usually related to the direct optical transitions between the absolute v valence band maximum (VBM) and the conduction band minimum (CBM) at 15 – 1c

symmetry point, as shown in Fig. 4 and 6. 2() of InP exhibit main peaks labeled E1, E’0, E2 and E’1 located at 3.3, 4.78, 5.1 and 6.05 eV respectively. These peaks contain contributions v v c v c v c from interband transitions occurring between L 3 – Lc1 , 15 – 15 , X 5 – X 3 and L 3 – L 3

respectively, as shown in Fig. 9. The calculated peak energies are in very consistent with previous experiments [7781] (see table 3). For InP1−xBix, the origin of the main peaks in

2() spectra are related to the optical direct transitions from occupied In-s, P-p and Bi-p orbitals appear in the highest valence band to unoccupied In-s/p, P-p and Bi-p orbitals appear in the lowest conduction band at R, and X symmetry direction in the Brillouin Zone (BZ). The shift of the four main peaks E1, E’0, E2 and E’1 to lower energies with increasing x is clearly seen. Fig. 8-(a) shows that 1() initially increases to reach the highest value at around 3 eV. Afterwards it decreases to the lower value (negative) at 5 eV. The TB-mBJ 1() and

2() curves in InP have similarities with experimental spectra obtained by Aspnes and Studna [84] through the use of spectroscopic ellipsometry. We summarize in Table 3 the energies of the critical point (CP), static dielectric constant

1(0), refractive index n(0) and reflectivity at zero frequency R(0) for InP1−xBix alloys obtained from TB-mBJ approach along with available experimental data and other DFT calculations. Our results of the static optical constants are in reasonable good agreement with the experimental data [78,82] and previous theoretical works [23,83]. The static 1, n and R show increases with increasing Bi content from: 1= 8.4 (x= 0) to 12.3 (x= 0.5); n= 2.9 (x= 0) to 3.5 (x= 0.5); R= 29% (x= 0) to 35% (x= 0.5). 9

We show in Fig. 10 the spectral variation of the refractive index n() and extinction coefficient k(ω) for InP1−xBix alloys obtained from TB-mBJ approach. The refractive index of semiconductor materials is considered as an important physical parameter gives its transparency to the incident photons. As seen in Fig. 10, n and k for InP1−xBix reach a maximum values in 4.25 eV range, and then full down at higher energies. n and k dispersion curves in InP exhibit maxima at 4.5 eV and 4.9 eV respectively, due to the interband transition E’0. These values are very closer to the ones measured by Aspnes and Studna [84] and Cardona [85] of 4.6 eV and 4.9 eV respectively. Other critical points (CPs) are resolved at 3.1 eV and 6 eV mainly related to the E1 and E’1 transitions respectively. The overall feature of the calculated n and k using TB-mBJ are in excellent agreement with previous experimental data. Fig. 11 show the calculated absorption coefficient α(ω) and normal-incidence reflectivity R() for InP1−xBix alloys from TB-mBJ approach. InPBi show a significant absorption in 5−8 eV range corresponds to the ultraviolet region. The curves show fast rise in absorption at low photon energy above the fundamental absorption edges (E0= 1.40 eV, for InP), reaching the highest value at around 5 eV and then become stable for energy rang up to 8 eV. The dispersion curve α in InP shows several peaks due to the electronic interband transitions (VB CB). The strongest peak α at ∼ 4.9 eV is mainly due to the E’0 transition. Two other peaks occur at ∼ 3.1 eV and 6 eV are related to the E1 and E’1 transitions respectively. The obtained values of peak positions using TB-mBJ agree well with the measured ones [84]. In Fig. 11-(b) we show that the reflectivity for InP1−xBix increases to maximum value at the resonance frequency 5 eV afterwards oscillates around R value of 50%, before achieving the stability for higher energies. The reflectivity R in InP has significant values at ∼ 3 eV, 4.9 eV and 6.1 eV attributed to the E1, E’0 and E’1 transitions respectively. The calculations are very consistent to the values measured by Cardona [86] with E1 (3.15 eV) and E’0 (5 eV). It shows that with increasing Bi composition in InP1−xBix, the calculated n, k, R spectra shifts towards lower energies to the infrared rang with reduced peak heights. 4. Conclusion To summarize, the structural, electronic and optical properties of InP1−xBix bismide alloys have been investigated using FP-LAPW calculations within density functional theory with x concentration varying up to 0.5. The results of the lattice parameter a and bulk modulus B using WC-GGA are in good agreement with available experimental data and theoretical 10

calculations. The band gaps (Eg) obtained from TB-mBJ approach are very consistent to experiments. InP1−xBix alloys exhibit a linear dependence of the lattice parameter a on Bi composition x with b= 0.02834 Å. InP1−xBix with x= 0.125 can be grown lattice matched to InP with mismatch less than 1.68% leads to high interface layers quality. It has been found a no-linear decrease of the band gap with Bi content, leading to narrow-gap of InP1−xBix. The semimetallic character is expected for InP1−xBix at x 0.5. From the calculated density of states DOS, the narrow-gap for InPBi is due to the both shifts of the valence band VB to upper and the conduction band CB to downward, due to the resonance interaction of the Bi-p states at the uppermost VB and hybridization of the occupied s/p states of In/P/Bi atoms at the lowest CB with increasing Bi content. The dielectric functions ε1(ω) and ε2(ω) as well as optical constants n(ω), k(ω), R(ω) and α(ω) of InP1−xBix alloys have been discussed. The different critical points (CPs) in optical spectra related to direct electronic interband transitions are resolved along electronic band structure and excellent agreement with experimental measures is obtained. The absorption and reflectivity show maxima in 5−8 eV range corresponds to the ultraviolet region. Finally, InPBi is interesting materials for designing high-efficiency optical devices as Laser Diodes and detectors operating in the MIDwavelength infrared region.

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13

Figure captions Fig. 1. Crystal structure (zinc blende) for InP0.875Bi0.125 (a), InP0.75Bi0.25 (b) and InP0.625Bi0.375 (c) (16-atom supercell 1a×1b×2c). Fig. 2. Calculated lattice constant versus Bi composition for InP1−xBix alloys. Fig. 3. Calculated bulk modulus versus Bi composition for InP1−xBix alloys. Fig. 4. Calculated band structures and TDOS for InP0.875Bi0.125 and InP0.625Bi0.375 from TBmBJ functional. The Fermi level (Ef) is placed at energy zero. Fig. 5. Calculated energy band gap versus Bi composition for InP1−xBix from TB-mBJ compared to the available experimental data. Fig. 6. Calculated total density of states (TDOS) and partial (PDOS) for InP 0.875Bi0.125 and InP0.625Bi0.375 from TB-mBJ functional. The Fermi level (Ef) is shifted to zero. Fig. 7. Plot uppermost valence and lowest conduction bands near point (left panel) and TDOS (right panel) for InP, InP0.875Bi0.125 and InP0.625Bi0.375 compounds calculated from TBmBJ functional. The zero of energy is taken to be the valence band maximum. Fig. 8. Spectral variation of the real part ε1(ω) (a) and imaginary part ε2(ω) (b) of the dielectric function for InP1−xBix alloys calculated from TB-mBJ functional. ε1(ω) and ε2(ω) of InP are compared with experimental data [84]. Fig. 9. TB-mBJ band structure of InP with various direct interband transitions (indicated by the vertical arrows) contribute in ε2(ω) curve. Fig. 10. Spectral variation of the refractive index n() (a) and extinction coefficient k(ω) (b) for InP1−xBix alloys calculated from TB-mBJ functional. n(ω) and k(ω) of InP are compared with experimental data [84,85]. Fig. 11. Spectral variation of the absorption coefficient α(ω) (a) and reflectivity R() (b) for InP1−xBix alloys calculated from TB-mBJ functional. α(ω) and R(ω) of InP are compared with experimental data [84,86].

14

Figure 1

15

InP1-xBix

InP

Lattice parameter (Å)

6.3

Present work (WC-GGA) Exp. Adachi [38] Vegard

6.2

6.1

6.0

5.9

aInP1 x Bi x 5.88937 0.80471 x 0.02834 x 2

0.000

0.125

0.250

0.375

0.500

Composition (x) Figure 2

InP1-xBix

InP

Present work (WC-GGA) Exp. Cohen [42] Linear fit

Bulk modulus (GPa)

65

60

55

50

45

B InP1 x Bi x 64 .85571 42 .20823 x 8 .43886 x 2

0.000

0.125

0.250

Composition (x) Figure 3

16

0.375

0.500

InP0.875Bi0.125

8

TOTDOS (States/eV)

4 2

Energy (eV)

Energy (eV)

2 Ef

0 -2 -4

0

-4 -6

-8

-8

-10

-10

X

Z M

-12

0.0 0.4 0.8 1.2

R

X

Z M

Figure 4 InP1-xBix

InP 1.6

Energy band gap (eV)

R

Ef

-2

-6

-12

TDOS_Bi TDOS_P TDOS_In

4

TOTDOS (States/eV)

6

TDOS_Bi TDOS_P TDOS_In

6

InP0.625Bi0.375

8

Present work (DFT+TB-mBJ) Exp. Madelung [59] Exp. Wang et al. [18] Exp. Kopaczek et al. [19] Exp. Das [68]

1.2

0.8

0.4

0.0 0.000

0.125

0.250

Composition (x)

Figure 5

17

0.375

0.500

0.0 0.4 0.8 1.2

f

TOT-DOS

Density of States (electron/eV)

E

InP0.875Bi0.125

tot_In In_s In_p In_d

0.6 0.4 0.2 0.0 0.6

tot_P P_s P_p

0.4 0.2 0.0 0.6

tot_Bi Bi_s Bi_p Bi_d Bi_f

0.4 0.2 0.0 -12

-10

-8

-6

-4

-2

0

2

4

6

25 20 15 10 5 0

E

InP0.625Bi0.375

0.4 0.2 0.0 0.6

tot_P P_s P_p

0.4 0.2 0.0 0.6

tot_Bi Bi_s Bi_p Bi_d Bi_f

0.4 0.2 0.0 -12

8

-10

-8

-6

-4

-2

0

Energy (eV)

TOTDOS (States/eV)

4 InP 3 InP0.875Bi0.125 InP0.625Bi0.375 2 1

Ef

0 -1 -2 -3

R

Figure 7

18

TOT-DOS

tot_In In_s In_p In_d

Figure 6

-4

f

0.6

Energy (eV)

Energy (eV)

Density of States (electron/eV)

25 20 15 10 5 0

X0

5

10

15

20

2

4

6

8

25

(a) 16

Imaginary part,

InP InP0.875Bi0.125

4

InP0.75Bi0.25

0

InP0.625Bi0.375

InP0.625Bi0.375

E1

E2

InP0.5Bi0.5

15

Exp. Aspnes and Studna (InP) [84]

'

E1

10

E0

5

InP0.5Bi0.5

-4

Exp. Aspnes and Studna (InP) [84]

0

2

0

4

6

0

8

2

4

Energy (eV)

Energy (eV)

Figure 8

6 C

15

C

4

L3

C

X3

'

E1 '

E0

C

Energy (eV)

Real part,

8

(b)

E0

InP0.75Bi0.25

20 12

'

InP InP0.875Bi0.125

2

L1

C

C

1

InP

E0

E1

0

X1

E2 V

15

V

-2

V

X5

L3

V

X3

-4

-6

V

L1

L

X

Figure 9

19

Z

M

6

8

4

E1

InP InP0.875Bi0.125

(a) '

E0

3 InP InP0.875Bi0.125

'

E1

InP0.75Bi0.25

2

(b)

InP0.75Bi0.25

3

Extinction coefficient

Refractive index

4

'

E0

InP0.625Bi0.375 InP0.5Bi0.5

InP0.625Bi0.375 InP0.5Bi0.5

'

E1 E1

Exp. Aspnes and Studna (InP) [84] Exp. Cardona (InP) [85]

2

1

Exp. Aspnes and Studna (InP) [84] Exp. Cardona (InP) [85]

1

0

0

2

4

6

8

0

2

Energy (eV)

4

6

8

Energy (eV)

Figure 10

InP InP0.875Bi0.125

-1

'

'

'

(b)

E1

InP0.625Bi0.375

4

'

E0

E0

InP0.75Bi0.25

160

E1

0.6

(a)

0.5

InP0.5Bi0.5

120

Reflectivity

Absorption coefficient (10 cm )

200

Exp. Aspnes and Studna (InP) [84]

80

E1

E1 0.4

InP InP0.875Bi0.125 InP0.75Bi0.25

40

InP0.625Bi0.375

0.3

InP0.5Bi0.5

InP Exp. Cardona [86]

0 0

2

4

6

8

0

2

4

Energy (eV)

Energy (eV)

Figure 11

20

6

8

Table captions Table 1 Calculated lattice constant a(Å), bulk modulus B(GPa) and derivative of bulk modulus B’ for InP1−xBix for compositions x = 0, 0.125, 0.25, 0.375, 0.5 and 1. Lattice constant (Å)

Bulk modulus (GPa)

Bulk modulus derivative

Other calculations

Present Experiment Other calculations

Present

5.981c − 5.84d

64.76

Composition (x)

Present Experiment

(InP)

0

5.890

0.125

5.989

59.86

4.51

0.25

6.092

54.96

4.60

0.375

6.196

49.89

4.13

0.5

6.298

46.00

4.75

(InBi) 1

5.869 a,b

6.626f − 7.024g

6.712 a

b

c

6.740h − 6.867i d

e

67.0e

55.14h − 30.71i

35.34 f

59.85c − 70.79d

g

h

4.42

4.54

i

Ref. [38], Ref. [39], Ref. [40], Ref. [41], Ref. [42], Ref. [43], Ref. [44], Ref. [45], Ref. [46].

Table 2 Band gap energies for InP1−xBix for compositions x = 0, 0.125, 0.25, 0.375, 0.5 and 1. Eg (eV) Composition (x)

Present

Experiment

Other calculations

(InP)

0

1.403

1.42 a,b

1.363c − 0.480d − 0.564e

0.125

0.669

0.25

0.118

0.375

0.128

0.5

0.287

1.056c

0.000

0.00f − -1.63g

(InBi) 1 a

1.242c

Ref. [59], bRef. [60], cRef. [23], dRef. [61], eRef. [62], fRef. [45], gRef. [63].

21

Table 3 Calculated energies of the critical point (CP) in 2(), static dielectric constant 1(0), static refractive index n(0) and reflectivity at zero frequency R(0) for InP1−xBix alloys along with available experimental data and other theoretical values. Critical points (CPs)

Composition (x) (InP)

0

This work

’

’

Static dielectric constant

Static refractive index

Reflectivity (%)

E0

E1

E0

E2

E1

1

n

R

1.401 1.423a 1.350b 1.340c 1.418d

3.30 3.28a 3.17b 3.24c 3.24e

4.78 4.70a 4.70b 4.10c 4.78e

5.10 5.05a 5.10b 5.00c 5.10e

6.05

2.90 2.70f 2.93g 2.86h

23.77

6.50c 6.90c

8.42 12.5b 12.5f 8.61g 8.19h

23.2h

0.125

This work 0.882

3.02

4.76

5.02

5.95

9.14

3.02

25.30

0.25

This work

0.346

2.90

4.60

4.92

5.90

10.33 9.44g

3.21 3.07g

27.61

0.375

This work 0.061

2.70

4.44

4.84

5.65

11.56

3.40

29.76

0.5

This work

0.000

2.20

4.18

4.72

5.36

12.25 10.46g

3.50 3.23g

30.87

Expt. aRef. [77], Expt. bRef. [78], Expt. cRef. [79], Expt. dRef. [80], Expt. eRef. [81], Expt. fRef. [82], EV-GGA g

Ref. [23], mBJ-GGA hRef. [83].

22