Non-local exchange correlation functionals impact on the structural, electronic and optical

properties of III–V arsenides

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Semicond. Sci. Technol. 28 (2013) 105015 (13pp) doi:10.1088/0268-1242/28/10/105015

Non-local exchange correlation functionalsimpact on the structural, electronic andoptical properties of III–V arsenidesN Najwa Anua1, R Ahmed1,3, A Shaari1, M A Saeed1, Bakhtiar Ul Haq1

and Souraya Goumri-Said2

1 Department of Physics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor,Malaysia2 Physical Sciences and Engineering Division, King Abdullah University of Science and Technology(KAUST), Thuwal 23955, Saudi Arabia

E-mail: rashidahmed@utm.my, rasofi@hotmail.com and Souraya.Goumri-Said@kaust.edu.sa

Received 1 April 2013, in final form 11 June 2013Published 19 August 2013Online at stacks.iop.org/SST/28/105015

AbstractExchange correlation (XC) energy functionals play a vital role in the efficiency of densityfunctional theory (DFT) calculations, more soundly in the calculation of fundamentalelectronic energy bandgap. In the present DFT study of III-arsenides, we investigate theimplications of XC-energy functional and corresponding potential on the structural, electronicand optical properties of XAs (X = B, Al, Ga, In). Firstly we report and discuss the optimizedstructural lattice parameters and the band gap calculations performed within differentnon-local XC functionals as implemented in the DFT-packages: WIEN2k, CASTEP andSIESTA. These packages are representative of the available code in ab initio studies.We employed the LDA, GGA-PBE, GGA-WC and mBJ-LDA using WIEN2k. In CASTEP, weemployed the hybrid functional, sX-LDA. Furthermore LDA, GGA-PBE and meta-GGA wereemployed using SIESTA code. Our results point to GGA-WC as a more appropriateapproximation for the calculations of structural parameters. However our electronicbandstructure calculations at the level of mBJ-LDA potential show considerable improvementsover the other XC functionals, even the sX-LDA hybrid functional. We report also the opticalproperties within mBJ potential, which show a nice agreement with the experimentalmeasurements in addition to other theoretical results.

(Some figures may appear in colour only in the online journal)

1. Introduction

III–V semiconductors are essential for their unfailingapplications as base materials in electronic and optoelectronicdevices. Among these, XAs such as BAs, AlAs, InAs andGaAs are of particular interest for their unique physicalproperties such as wide band gaps, low density, highthermal conductivities, and dielectric constants [1]. Thesematerials almost cover the whole visible spectrum from redto violet light. These properties have made XAs materialspotential candidates for many advanced technologies, and are

3 Author to whom any correspondence should be addressed.

extensively in use as base materials in integrated circuits,filters, lasers, photo detectors, modulators, light-emittingdiodes etc. At ambient temperature and pressure, XAs havebeen recognized to be stable in zinc-blende (ZB) structureand reported, in available experimental and theoretical studies,indirect band gap structure for BAs and AlAs and directfor GaAs and InAs. On account of their peculiar nature ofphysical properties and substantial applications in commercialtechnologies, in particular, electronic and optoelectronicdevices, XAs are widely explored.

Overall, all members of XAs demonstrate uniqueelectronic structure and corresponding physical properties:BAs exhibits strong covalent nature [2], and has analogous

0268-1242/13/105015+13$33.00 1 © 2013 IOP Publishing Ltd Printed in the UK & the USA

Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

electronic nature to silicon that makes it unique amongthe other III–V compounds [3]. Being a wide band gapsemiconductor, BAs is considered a suitable partner foralloying with GaAs and AlAs [4]. In a recent experimentalstudy [5], it has been used as a p-type electrode andreported as a suitable candidate for photo-electrochemical andphotovoltaic applications. However, difficult synthesis of BAsmeans its properties are still under debate [6]. Similarly GaAs,owing to direct wide bandgap and having small electroniceffective mass, besides many other applications, is exploitedin ultra fast transistors especially where reliability is the mainconcern. Like AlAs and InAs, it plays a fundamental roleas a part of many optoelectronic heterojunction devices andsystems.

Operating characteristics of the electronic andoptoelectronic devices not only depends on materialengineering at a practical level; it also demands clearunderstanding of the electronic and optical propertiesof these materials. To exploit their optimized potential,further investigations are therefore crucial at both levels(experimental and theoretical). As promising optoelectronicmaterials, beside the experimental investigations, reportson theoretical/computational studies are also available inliterature: Chimot et al [7] studied structural and electronicproperties of BAs, GaAs, InAs and their alloys within thedensity functional theory (DFT) framework of virtual crystalapproximation. They recommended XAs materials and theiralloys as an alternative to the InP substrate, for the epitaxialgrowth of nanostructures to fabricate field-effect transistors,lasers and storable absorbers in the field of optoelectronics.Zaoui et al [8] and Boudjemline et al [9] reported theelectronic and optical properties of BAs using LDA andGGA-PBE within DFT. Using an FP-LAPW method Arabiet al [10] studied structural and electronic properties ofGaAs in four different phases. Ahmed et al [11] have alsoinvestigated structural and electronic properties of XAs usingLDA, GGA and GGA-EV. Amrani et al [12] studied thestructural parameters, electronic and optical properties atnormal and high pressure using FP-LAPW method at the levelof LDA. Ground state and high-pressure structural parameterswere also investigated by Wang et al [13] using full potentiallinearized muffin-tin orbital (FP-LMTO) scheme at the levelof GGA. Similarly Hart et al [4] investigated ground stateas well as electronic properties of BAs, AlAs, InAs andGaAs within DFT using LDA approximation. Most recentlyGuemou et al [14] studied the structural, electronic and opticalproperties of BAs, GaAs and their alloys using LDA andGGA. Though a sizeable number of DFT investigations havebeen reported in literature previously using different forms ofexchange correlation (XC) functional, mostly they reproduceunderestimated values of fundamental bandgap values,especially in the case of semiconductors and insulators, andcorresponding optical properties.

Correct knowledge of fundamental and optical bandgap,both theoretically and experimentally, is crucial because thisplays a decisive role for their applications as a base materialin electronics and optoelectronics devices, and to exploittheir potential for further applications such as solar cell

technology. Though DFT-based computer simulations havemade it possible now to investigate electronic bandstructure atatomic scale and the corresponding fundamental propertiesof materials in an amazingly short time and at low cost,and have predicted the properties of materials not yetsynthesized, reproduction of accurate electronic bandgapwithin conventional DFT is not straightforward. This isbecause standard DFT XC functionals (LDA, GGA-PBE)are basically designed to cope with ground state properties.However, to overcome this difficulty a proper choice ofXC potential functional is crucial to reproduce electronicband gap and optical properties comparable to experimentalmeasurements. One of them is the Tran–Blaha modified BeckeJohnson (TB-mBJ) XC potential, which has been reported inseveral studies of semiconductors and insulators to calculatethe energy gap with high accuracy near to experimental value.Highly accurate results at effectively low cost have proclaimedmBJ as superior to other approaches. Similarly, the role ofhybrid functionals is also appreciated on a large scale.

Motivated by fascinating features of DFT computersimulations, applications of XAs in cutting edge technologiesand the balanced role of mBJ-LDA exchange and correlationpotential to reproduce bandgap for semiconductors andinsulators, we investigate some of the fundamental propertiesof XAs (X = B, Al, Ga, In) using FP-L(APW+lo) framedwithin DFT [15, 16]. However, to investigate the response ofXC-potential to band gap calculation we also employ LDA,GGA-PBE, WC-GGA, meta-GGA and sX-LDA in addition tomBJ-LDA.

2. Theoretical approaches, methods andcomputational details

As introduced, we opted for three robust packages: CASTEP,SIESTA and WIEN2k. CASTEP and SIESTA codes use thepseudo-potential descriptions for the crystal potential, wherethe inner core electrons are ‘folded in’ with the nuclearpotential, which reduces the number of particles which mustbe calculated explicitly and allows the use of plane-wavebasis sets. WIEN2k is based on the all-electrons approachfor calculations (called full potential method).

To carry out calculation of structural properties, weapplied GGA-WC [17]; GGA-PBE [18] and LDA [19]as implemented in WIEN2k, where to investigate therole of exchange and correlation potential on the DFTresults of electronic and optical properties, we use mBJ[20] potential additionally. To perform our computations,valence electrons of B(2s22p1), Al(3s23p1), Ga(3d104s24p1),In(4d105s25p1) and As(3d104s24p3) are differentiated from thecore electrons of B(1s2), Al (1s22s22p6), Ga (1s22s22p63s23p6),In (1s22s22p63s23p63d104s24p6), and As (1s22s22p63s23p6). Tomodel and simulate an FCC unit cell of XAs compoundsin ZB phase with space group F-43m, atomic positions areconsidered inside a unit cell as: X at (0, 0, 0) and As at (1/4,1/4, 1/4). Then the unit cell is divided into interstitial andnon-overlapping atomic spheres. Inside atomic spheres (radiusR muffin-tin spheres) denoted by RMT around each atom,spherical harmonic expansion is used to treat Kohn–Sham

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

(KS) wave functions, charge density as well as potential. Plane-wave basis set, in the interstitial space, is used. RMT valuesof 1.7 a.u and 2.1 a.u are used for B and As to simulate BAsstructure, and for GaAs 2.09 a.u and 2.1 a.u are used, whereasin the case of AlAs and InAs, 2.0, 2.1 and 2.4 a.u for Al,As and In atoms, respectively. Inside MT sphere, sphericallysymmetric potential is assumed and outside it is taken constant.To get good energy convergence in the irreducible wedge ofthe Brillouin zone, we used 35 k-points, RMT × Kmax = 8, andGmax = 14.

To perform CASTEP computations [21], we employed thehybrid functional (sX-LDA) because sX-LDA is also reportedin literature to reproduce acceptable values of bandgap energyespecially for III–V semiconductor materials with comparablecomputational cost of standard LDA. In the screenedexchange (sX) local density approximation (sX-LDA), toovercome the LDA shortcoming of self-interaction, non-localexchange potential of electron interaction is included byadding statically screened exact Hartree–Fock exchange tosome extent into LDA formulism without compromising theadvantages of LDA. In fact, sX-LDA scheme was ‘developedin the context of the generalized KS procedure’ [22]. In ourCASTEP calculations the same basis sets for valence electronare used as in WIEN2k calculations, but the core electronsare described by employing an ultrasoft pseudo-potential(UPP). The pseudo-atomic calculations performed for ourelements are: As 4s24p3, In 5s25p1, Ga 3d10 4s2 4p1, B 2s2 2p1,Al 3s2 3p1. The following plane-wave basis set cut-off energywas considered: 250 eV for AlAs and InAs, 440 eV forBAs and 590 eV for GaAs. For geometry optimization,Broyden–Fletcher–Goldfarb–Shanno (BFGS) scheme wasused for k-point sampling.

Siesta code [23, 24] also solves the standard KS equationsself-consistently. To perform our calculations with this code,we employed LDA, GGA-PBE and meta-GGA [25] functionalapproximations to incorporate the XC term. Meta-GGAhas the upper hand over standard GGA-PBE because itinvolves an additional second-order derivative term of kineticenergy density that results in marginal improvement incomparison with experiments. In this approach of calculations,valence electrons were described using ‘norm-conservingTroullier–Martins pseudo-potentials scheme’ [26]. Non-localcomponents and atomic core were expressed using Kleimanand Bylander fully factorized form [27, 28]. Sankey andNiklewsky proposed ‘finite-range pseudo-atomic orbitals’[29], which are exploited as the ‘split-valence double zeta basisset with polarization’ (DZP) for valence electrons. Similarvalues of energy cut-off were used as mentioned in CASTEPcode. Brillouin zone integration was also sampled using asimilar approach to that adopted for WIEN2k and CASTEPruns.

3. Results and discussions

3.1. Structural properties

At ambient conditions of temperature and pressure XAscompounds exist in stable ZB structure with space group

F-43 m (No-216). In our present DFT study, optimizationof each structure over a range ±10% around equilibriumvolume is performed and obtained data is fitted to Murnaghan’sequation of state [30] to find out equilibrium lattice constants,bulk modulus and its pressure derivative, and total energyfor each compound of XAs. These calculations of structuralproperties were performed at the level of LDA (WIEN2k,SIESTA), GGA-PBE (WIEN2k, SIESTA) and GGA-WC(WIEN2k), sX-LDA (CASTEP) and meta-GGA (SIESTA).Our calculated lattice constants, bulk modulus and its pressurederivative, and total energy of unit cell with different exchangeand correlation energy functionals are listed in table 1. Forthe sake of comparison, the experimental measurements aswell as the data from previously theoretical works are alsoshown. Although the results of all XC-potentials are in goodagreement with the experimental and other theoretical data,the calculated value of lattice constant ‘a’ with GGA-WC issignificantly closer to experimental value, indicating it as amore suitable approach for calculating structural properties.The calculated value of ‘a’ with GGA-PBE is slightly higher(for all the three codes) while with LDA is slightly smaller incomparison with experiment. The observed discrepancy in thevalue of ‘a’ with LDA and GGA-PBE in our work to that ofexperimental values is a well established fact [31]. For bulkmodulus, even though the calculated value is not as accurateas the experimental value, it is in good agreement with othercomputational data. However, our calculated results at thelevel of LDA are closer to reported experimental values thanGGA-PBE and GGA-WC.

3.2. Electronic structure and the bandgap calculations

For the investigations of electronic properties of XAs wecalculated the electronic band structure and density of states(DOS). Calculations of electronic band structure have beenperformed using some important (local and non-local) XCfunctional to investigate their impact comprehensively. Forefficient and reliable results we used the experimental latticeparameters in our calculations. The calculated electronicband structures with different XC-potentials are shown infigures 1–3 for WIEN2k, CASTEP and SIESTA codes,respectively. Moreover, we report the band gap values asextracted from these calculations in table 2. To checkauthenticity of our work, we compared the obtained resultswith the former theoretical calculation and the experimentalresults extracted from the literature.

From the electronic band structures of GaAs and InAsit can be seen clearly that the conduction band minimaand valence band maxima are lying at the same highsymmetry �-point in Brillouin zone, thus endorsing directband gap semiconductors. On the other hand, BAs, andAlAs band structures reveal their indirect band gap naturebecause their V.B maxima and C.B minima are lying atdifferent symmetry points in Brillion zone. From WIEN2kcalculation, it is evident that mBJ functional calculatesthe band gap value wider and close to experimental valuefollowed by GGA-PBE, GGA-WC and LDA. For thecase of GaAs, from SIESTA code calculation, we see

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

Table 1. The calculated data is compared to the experimental and other theoretical data available in the literature.

Lattice Volume Bulk Modulus B0 PressureCompounds Method parameter a(A0) V0 (a.u)3 (GPa) derivative B′ Total energy (eV)

BAsOur work GGA-PBE 4.815 188.518 131.9 4.199 −62 203.8613WIEN2k GGA-WC 4.778 184.095 140.8 4.278 −62 115.4178

LDA 4.741 179.788 148.8 4.741 −62 188.9545CASTEP sX-LDA 4.776 179.768 140.7 4.277 −62 115.3980SIESTA GGA-PBE 4.823 186.768 143.5 4.125 −63 125.3760

Meta-GGA 4.775 178.965 143.8 4.237 −62 188.3459LDA 4.739 178.685 151.2 4.098 −62 289.4622

Experiment 4.777 [37] 3.984 [42]

Others calculations FP-LDA 4.741 [11] 79.795 [11] 147.5 [11] 4.216 [11]FP-GGA 4.817 [11] 188.563 [11] 131.2 [11] 4.179 [11]FP-LDA 4.743 [38] 152 [38] 3.65 [38]FP-GGA 4.812 [38] 153 [38] 3.75 [38]FP-GGA 4.784 [39] 137 [39] 3.49 [38]HF 4.828 [40] 162 [40]HF 4.83 [41] 149 [41]

AlAsOur work GGA-PBE 5.725 317.525 66.63 4.331 −68 136.1056WIEN2k GGA-WC 5.673 308.623 72.08 4.162 −68 117.3111

LDA 5.630 301.312 75.06 4.309 −68 029.1549

CASTEP sX-LDA 5.645 324.124 79.9 4.277 −68 112.3050SIESTA GGA-PBE 5.739 307.117 76.3 4.125 −67 928.3580

Meta-GGA 5.679 301.678 66.1 4.237 −67 985.2969LDA 5.633 301.243 79.2 4.098 −68 286.5012

Experiment 5.620 [37] 82.0 [42] 4.182 [42]

5.661 [43] 77.3 [48]Others calculations FP-LDA 5.633 [11] 301.526 [11] 75.1 [11] 4.512 [11]

FP-GGA 5.734 [11] 317.988 [11] 66.5 [11] 4.184 [11]PP-LDA 5.614 [44] 74.7 [44] 4.182 [45]PP-GGA 5.690 [45] 71.0 [45]FP-LDA 5.664 [46] 71.0 [46]FP-LDA 5.644 [47] 75.4 [47] 4.4 [47]HF 5.741 [40] 90.0 [40]HF 5.76 [41] 79.0 [41]

GaAsOur work GGA-PBE 5.749 320.652 60.84 4.256 −114 430.5449

GGA-WC 5.665 306.749 68.10 4.394 −114 404.7767WIEN2k LDA 5.607 297.380 72.40 4.539 −14 272.1906

sX-LDA 5.645 318.120 57.39 4.469 −114 427.2342CASTEP GGA-PBE 5.748 322.513 66.12 4.241 −112 336.7767SIESTA Meta-GGA 5.679 288.260 69.91 4.298 −113 211.2736

LDA 5.601 289.432 86.95 4.621 −116 598.3451

5.654 [37] 77.0 [42] 4.487 [42]Experiment 5.65 [44] 76.0 [51]

FP-LDA 5.608 [11] 297.606 [11] 75.2 [11] 4.814 [11]Other calculations FP-GGA 5.748 [11] 320.309 [11] 60.8 [11] 4.800 [11]

PP-GGA 5.530 [44] 75.7 [44] 4.487 [44]PP-GGA 5.700 [45] 65.0 [45]FP-LDA 5.651 [46] 63.0 [46]FP-LDA 5.508 [49] 77.1 [49]FP-LDA 5.649 [47] 74.2 [47]FP-LDA 5.592 [50] 81.1 [50] 4.800 [50]FP-GGA 5.726 [50] 68.0 [50] 4.460 [40]HF 5.755 [40] 87.0 [40] 4.450 [40]HF 5.760 [41] 77.0 [41]

InAsOur work GGA-PBE 6.192 400.659 50.10 4.191 −221 620.9974WIEN2k GGA-WC 6.096 382.4398 56.20 4.525 −221 588.1455

LDA 6.035 370.858 56.93 4.58 −221 397.9506CASTEP sX-LDA 6.089 388.234 49.23 4.178 −221 910.3345SIESTA GGA-PBE 6.096 400.1245 62.18 4.439 −221 898.2390

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Table 1. (Continued.)

Lattice Volume Bulk Modulus B0 PressureCompounds Method parameter a(A0) V0 (a.u)3 (GPa) derivative B′ Total energy (eV)

Meta-GGA 6.289 359.772 46.94 4.67 −221 403.1245LDA 5.956 388.353 53.32 4.68 −221 603.2373

Experiment 6.036 [37] 58.0 [42] 4.79 [53]Other calculations FP-LDA 6.030 [11] 60.9 [11] 4.691 [11]

FP-GGA 6.195 [11] 48.1 [11] 4.683 [11]PP-LDA 5.921 [44] 61.7 [44] 4.545 [44]PP-LDA 5.902 [52] 370.879 [11] 61.9 [52] 4.488 [52]FP-LDA 6.015 [47] 401.104 [11] 60.3 [47] 4.9 [47]HF 6.152 [40] 74.0 [40]HF 6.150 [41] 64.0 [41]

that GGA-PBE and LDA are underestimating the bandgap compared to the meta-GGA value. On the otherhand, for InAs, we can observe that both LDA andmeta-GGA are failing compared to GGA-PBE, whereasGGA-PBE results are somewhat closer to the experiment.For the hybrid functional, as calculations performed usingCASTEP code, though sX is approaching the experimentalband gap, results with mBJ approach are more systematic andclosest to experiments.

From the calculated electronic structures of XAs, wecalculated the valence band width by considering all the statesin the valence band as a single group. The mBJ calculates aslightly narrower valence band width compared to the LDA andGGA-PBE (table 3). This shows that although, mBJ improvedthe energy gap value compare to LDA and GGA-PBE, itsresponse to the band width is not very significant. On theother hand, sX significantly overestimates the bandwidthas calculated with common LDA and GGA-PBE. However,following the recent work on band widths and gaps calculationfrom the Tran–Blaha functional and with a comparison withmany-body perturbation theory, performed on some oxidesand semiconductors [32], Martin Schlipf, et al [33] haveimplemented HSE hybrid functional within the FLAPWmethod. It was revealed that Tran–Blaha functional leadsto band gaps in much better agreement with experimentsthan LDA but it globally underestimates, often strongly, thevalence (and conduction) band widths (more than LDA). If wecompare the InAs band gap as found with HSE03 approach[34], we notice that for InAs, they found a zero band gap,consequently our approach mBJ-LDA is leading to correctionof the calculation from LDA.

More recently Lucero et al [35] have reported animproved middle-range screened hybrid exchange functionalin order to determine the lattice parameters and band gap forsemiconductors. In this work, a comparison between HSE06and functional hybrid, developed a few years ago, called Tao,Perdew, Staroverov and Scuseria [25] have been presented.The presented approach developed by Henderson, Izmaylov,Scuseria and Savin (HISS) was able to perform extremelywell for elemental and binary semiconductors with narrow orvisible spectrum band gaps as well as some wider gap or moreionic systems used in devices. HISS was proven to be moreefficient than HSE06 for some III–V compounds such as BAs,but they proved that HISS may be a useful adjunct to HSE inthe modelling of geometry-sensitive semiconductors.

In order to complete our description of the electronicstructure with mBJ approach, we calculate the DOS of XAswith mBJ-XC-potential as displayed in figure 4. The DOSprofiles of all the four compounds are highly analogous inarrangement of electronic states. There are three significantstructures in DOS of each compound separated by a gap. Thefirst structure that appears below −10 eV is mainly attributedto the s orbital of As. The comparatively dispersed secondstructure in DOS is mainly composed of highly hybridized sand p states of X and p states of As. This structure appears inenergy regime ∼−8 to 0 eV in BAs, ∼−6 to 0 eV in AlAs,∼−6.7 to 0 eV in InAs, and ∼−5.6 to 0 in GaAs. The bottomof the conduction band is mainly originated from the mixtureof s and p states of X and As elements.

3.3. Optical properties

In the presence of an external electromagnetic field,the linear response of a system is usually describedby the frequency dependent dielectric function ε(ω) =ε1 (ω) + iε2 (ω) , which is directly associated with electronicstructure. ε1 (ω) and ε2 (ω) are real (dispersive) andimaginary(absorptive) parts of the complex dielectric function.The structures appearing in spectra of ε(ω) mainly describethe transitions of electrons, which may be either inter bandor intra band. However in semiconductors, where there areno intra band transitions, structures in ε(ω) are thus causedby transitions of electrons between the occupied states in V.Band unoccupied C.B states along high symmetry points inBZ. Moreover a single peak in ε2 (ω) may not correspondto a single transition as there might occur many transitionssimultaneously at an energy corresponding to a single peak.ε2 (ω) is evaluated from momentum matrix elements and isgiven by the relation

ε2 = 2e2π

�ε0

∑

k,V,C

∣∣�CK |u.r|�C

k

∣∣2δ(EC

k − EVk − E

).

The real part of the dielectric function can be derived fromε2 (ω) using Kramers–Kronig transformations. Once thevalues of ε1 (ω) and ε2 (ω) are evaluated, the other energy-dependent optical parameters can be determined using theseobtained values of ε1 (ω) and ε2 (ω).

Our evaluated optical parameters in the present workwith mBJ are shown in figures 5–7. These parameters areinvestigated in the energy range 0–30 eV. XAs’ real and

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

Figure 1. The electronic structure of III–V arsenides with various XC potential have been shown calculated with LDA, PBE-GGA,WC-GGA, and LDA-mBJ (obtained from WIEN2k code).

Figure 2. The electronic structure of III–V arsenides with sX-LDA (obtained from CASTEP code).

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

Figure 3. The electronic structure of III–V arsenides with SIESTA code (LDA, GGA-PBE and meta-GGA).

imaginary components of ε(ω) have been shown in figure 5and corresponding calculated static dielectric function valueshave been listed in table 4.

Table 4, shows a good agreement in our calculated staticdielectric function values to the experimental measurementsand other theoretical results. Figure 5 shows that a major peakin imaginary part spectra arises at 6.05 eV and 6.02 eV forBas and AlAs, respectively. In the case of InAs and GaAs themajor curve appears between two humps. In InAs and GaAscurves, the major structures are located at energies 4.55 eV

and 4.17 eV, which are in good agreement with those reportedin [12, 14].

The absorption spectra α(ω) of XAs, calculated in thepresent study, have been shown in figure 6. The figure showsa very small absorption at lower energies (below the band gapenergy) for all XAs compounds. This absorption is mainly dueto free carrier absorption, and is said to be Urbach’s absorption.Dominant absorption starts at 3.41 eV, 1.01 eV, 2.52 eV and0.57 eV for BAs, AlAs, InAs and GaAs, respectively. Theabsorption spectra for all compounds show a fast increase at

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Table 2. The energy bandgap (Eg) properties of Bas, AlAs, GaAs and InAs.

Compounds Methods XC Eg(eV) Type of band gap

BAsPresent work FP-LAPW (WIEN2k) GGA-PBE 1.235 Indirect(�-min)

GGA-WC 1.142 Indirect(�-min)LDA 1.176 Indirect(�-min)LDA-mBJ 1.730 Indirect(�-min)

UPP (CASTEP) LDA-sX 1.933 Indirect(�-min)NCP (SIESTA) GGA-PBE 2.52 318 Indirect(�-min)

LDA 1.48 901 Indirect(�-min)Meta-GGA 1.4347 Indirect(�-min)

Experiment 0.67 [54, 55]1.46 ± 0.025

Other Calculations LDA 1.13 [11] Indirect(�-min)GGA 1.18 [11] Indirect(�-min)GGA-EV 1.79 [11] Indirect(�-min)LDA 1.12 [38] Indirect(�-min)GGA 1.21 [38] Indirect(�-min)GGA 1.23 [39] Indirect(�-min)GGA 1.25 [56] Indirect(�-min)

AlAs FP-LAPW GGA-PBE 1.478 Indirect(�-min)Our work GGA-WC 1.365 Indirect(�-min)

LDA 1.385 Indirect(�-min)LDA-mBJ 2.21 Indirect(�-min)

UPP (CASTEP) LDA-sX 1.944 Indirect(�-min)GGA-PBE 1.35 496 Indirect(�-min)LDA 1.4279 Indirect(�-min)

NCP (SIESTA) Meta-GGA 2.5433 Indirect(�-min)

Experiment 2.24 [48]

Other calculations LDA 1.31 [11] Indirect(�-min)GGA 1.40 [11] Indirect(�-min)GG-EV 2.25 [11] Indirect(�-min)LDA 1.37 [46] Indirect(�-min)LDA 1.25 [47] Indirect(�-min)LDA 1.32 [45] Indirect(�-min)GGA 1.39 [45] Indirect(�-min)LDA 1.35 [57] Indirect(�-min)LDA 1.31 [58] Indirect(�-min)

GaAsOur work FP-LAPW GGA-PBE 0.329 Direct (�-�)

UPP (CASTEP) GGA-WC 0.206 Direct (�-�)LDA 1.613 Direct (�-�)LDA-mBJ 1.46 Direct (�-�)LDA-sX 1.639 Direct (�-�)GGA-PBE 0.52 317 Direct (�-�)

NCP (SIESTA) LDA 0.54 755 Direct (�-�)Meta-GGA 1.27 637 Direct (�-�)

Experiment 1.42 [59]

Other Calculations PP-PW LDA 0.28 [11] Direct (�-�)GGA 0.51 [11] Direct (�-�)GGA-EV 1.03 [11] Direct (�-�)LDA 0.23 [42, 46] Direct (�-�)LDA 0.18 [56, 60] Direct (�-�)LDA 0.09 [43, 47] Direct (�GGA-EV 0.97 [57, 61] Direct (�LDA 0.32 [41, 45] Direct (�GGA 0.49 [41, 45] Direct (�-�)

InAsOur work FP-LAPW GGA-PBE 0.118 Direct (�-�)

GGA-WC 0.024 Direct (�-�)LDA 0 Direct (�-�)LDA-mBJ 0.760 Direct (�-�)

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

Table 2. (Continued.)

Compounds Methods XC Eg(eV) Type of band gap

UPP (CASTEP) LDA-sX 1.598 Direct (�-�)NCP (SIESTA) GGA-PBE 0.523 Direct (�-�)

LDA 0.0 Direct (�-�)Meta-GGA 0.0 Direct (�-�)

Experiment 0.42 [54]Other Calculations FP-LAPW LDA 0.00 [11] Direct (�-�)

PP-LAPW GGA 0.00 [11] Direct (�-�)GGA-EV 0.40 [11] Direct (�-�)LDA −0.64 [47] Direct (�-�)LDA 0.00 [58] Direct (�-�)

(a) (b)

(c) (d )

Figure 4. Density of states of XAs (a) BAs, (b) AlAs, (c) GaAs, (d) InAs) calculated with mBJ potential.

energies close to their band gap values. This is because of thefact that photons of energies higher than the band gap valuescause transition from V.B to C.B. All compounds show a broadspectrum of absorption for higher energies. We analyzed fromour calculations that all the materials have highly absorptivenature in UV region mainly corresponding to the region3.43–24 eV for BAs, 1.04–20.50 for AlAs, 2.53–27.83for GaAs and for InAs 0.59–21.97eV. The maximumabsorption takes place at 7.93, 6.65, 6.51 and 5.78 eVcorresponding to BAs, AlAs, GaAs and InAs. However α(ω)experiences a gradual decrease for energies higher than theseenergies.

The energy lost by an electron while it is traversingthrough a medium is described by the energy loss functionL(ω) and mathematically can be written as 1/ε(ω). XAs spectraof L(ω) against photon energy have been schematically shownin figure 6. The structures appearing in L(ω) spectrum areassociated with plasma frequency. The structures appearingbelow 10 eV are assigned to π -electrons, whereas thoseoccurring at higher energies are attributed to π + σ plasmons[36]. Moreover, these structures appear at that energy wherethe dispersive component of dielectric function transformsfrom metallic to dielectric nature, that is, from negative valueto positive value. From figure 5, it is evident that all the

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

Figure 5. The calculated real and imaginary parts of dielectric functions of XAs calculated with mBJ potential.

Figure 6. The calculated absorption coefficient α (ω), energy loss function L(ω) and reflectivity spectra of XAs calculated with mB potential.

four compounds exhibit a single metallic region in ε1 (ω).In accordance, L(ω) of XAs shows a single peak at energies21.91, 17.34, 14.46 and 16.09 eV, a remarkably negative ε1 (ω)

transforms to positive at about the same energies.

XAs reflectivity spectra R(ω), calculated in the presentwork, have been shown in figure 6. R(ω) is generally describedas the ratio between incident and reflected beam of lightthrough a medium. Our investigations show that the reflectivity

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

Figure 7. The calculated refractive index n(ω) and extinction coefficient k(ω) spectra of XAs calculated with XAs.

Table 3. The valence band width of XAs calculated with differentXC functionals.

V.B Bandwidth BAs AlAs GaAs InAs

WIEN2kLDA 15.40 12.04 12.60 12.00GGA-PBE 15.44 11.99 12.56 11.97GGA-WC 15.43 12.08 12.67 11.96mBJ 15.17 11.60 12.41 11.59SIESTALDA 15.26 11.97 12.65 11.85GGA-PBE 15.30 11.96 12.69 10.97Meta-GGA 15.34 11.97 12.71 11.79CASTEPsX 17.81 13.67 14.80 13.50

index is less than 24% for BAs in energy range 0–1.31 eVand above 31.11eV, less than 22% for AlAs in energy range0–1.18 eV and above 17.53 eV, less than 26% for InAs inenergy range 0–0.72 eV and above 14.51 eV and less than33% for energy 0–0.17 eV and above 15 eV for GaAs. Thisshows the transparent nature of XAs materials for UV lightat these energies. All XAs show a broader structure in energyregime 3.9–21.7, 3.74–15.57, 1.10–14.95, 2.6259–12.66 eVfor BAs, AlAs, GaAs and InAs, respectively.

Table 4. The static dielectric function of XAs calculated with mBJpotential in WIEN2k package.

ε1(0) Experimental Other theoretical

BAs 8.17 790 9.9 [7], 9.38 [14], 9.9 [9]AlAs 7.32 084 8.20 [62] 9.775 [12]InAs 9.48 144 14.5 [63] 16.8 [7]GaAs 14.3007 12.9 [64] 14.8 [65], 15.2 [7]

Table 5. Refractive index for XAs calculated with mBJ potential inWIEN2k package.

n(0)

BAs 2.85 972AlAs 2.70 573 2.864 [62] 3.126 [12]InAs 3.07 925GaAs 3.78 179

The spectra of refractive index n(ω) and extinctioncoefficient k(ω) have been shown in figure 7. Both parameters,n(ω) and k(ω) have their origin in ε2 (ω). The static refractiveindex n(0) values for XAs have been listed in table 5. Ourcalculated values successfully satisfy the condition n(0)2 =ε1(0), indicating the high level reliability of our calculations

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Semicond. Sci. Technol. 28 (2013) 105015 N N Anua et al

with mBJ potential. Refraction spectra show that n(ω)increases with increase in photon energy in the lower energyregime for ultra violet region. For BAs, AlAs, GaAs andInAs, n(ω) attain maximum values of 4.31, 4.71, 4.05 and3.69 at energies 5.07, 4.53, 3.95 and 4.39 eV, respectively.Extinction coefficients reveal the absorption of light. k(ω)have distinct peaks at maximum intensity 3.34, 3.26, 3.41 and3.78 corresponding to energies 6.24 eV, 4.99 eV, 4.36 eV and2.70 eV, respectively.

4. Conclusion

We employed three different computational approaches, basedon density functional theory, in order to observe the mostreliable approach, able to extract the correct electronic bandgap. We presented at first a discussion of the geometryoptimization and extracted the relaxed lattice parameters aswell as the bulk modulus, its derivative and total energyfor all the employed functionals. It was found that almostall employed approaches and functionals have succeededin determining lattice parameters closer to experimentalmeasurements. The main goal was to see the dependence ofthe band gap on the employed approximations, especially non-local exchange-correlation functionals. It is observed, in thisstudy, that some approaches were successful in one compoundbut were found to have failed in another. However, calculatedband structure and obtained results of bandgap, at the level ofmBJ-LDA approximation of Vxc incorporated in FP-LAPWscheme of calculation, were systematic and reliable. It isalso found that mBJ-LDA is not only suitable for electronicproperties; it gives reliable results for optical parameters. Thus,our study endorses mBJ-LDA approach as one of the best Vxc

approximations for DFT investigations related to electronicand optical properties.

Acknowledgments

Authors would like to thank the Ministry of HigherEducation (MOHE) Malaysia/Universiti Teknologi Malaysia(UTM) for financial support for this research work throughgrant nos R.J130000.7726.4D034; Q.J130000.2526.02H89;R.J130000.7826.4F113. Moreover, SGS wish to thank theresearch computing service (KAUST-IT) for access toCASTEP code.

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