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Solar Energy 107 (2014) 543–552

Study of wurtzite and zincblende GaN/InN based solar cells alloys:First-principles investigation within the improved modified

Becke–Johnson potential

Bakhtiar Ul Haq a, R. Ahmed a, A. Shaari a, F. El Haj Hassan b,Mohammed Benali Kanoun c, Souraya Goumri-Said c,⇑

a Department of Physics, Faculty of Science, Universiti Teknologi Malaysia, UTM Skudai, 81310 Johor, Malaysiab Universite Libanaise, Faculte des sciences (I), Laboratoire de Physique et d’electronique (LPE), Elhadath, Beirut, Lebanon

c Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia

Received 15 March 2014; received in revised form 7 May 2014; accepted 9 May 2014

Communicated by: Associate Editor Nicola Romeo

Abstract

Wurtzite GaInN alloys with flexible energy gaps are pronounced for their potential applications in optoelectronics and solar cell tech-nology. Recently the unwanted built-in fields caused by spontaneous polarization and piezoelectric effects in wurtzite (WZ) GaInN, hasturned the focus towards zinc-blende (ZB) GaInN alloys. To comprehend merits and demerits of GaInN alloys in WZ and ZB structures,we performed a comparative study of the structural, electronic and optical properties of Ga1�xInxN alloys with different In concentrationusing first-principles methodology with density function theory with generalized gradient approximations (GGA) and modified Becke–Johnson (mBJ) potential. Investigations pertaining to total energy of GaInN for the both phases, demonstrate a marginal difference,reflecting nearly equivalent stability of the ZB–GaInN to WZ–GaInN. The larger ionic radii of indium (In), result in larger values oflattice parameters of Ga1�xInxN with higher In concentration. For In deficient Ga1�xInxN, at first, the formation enthalpies increaserapidly as the In content approaches to 45% in WZ and 47% in ZB, and then decreases with the further increase in In concentration.ZB–Ga1�xInxN alloys exhibit comparatively narrower energy gaps than WZ, and get smaller with increase in In contents. The smallervalues of effective masses of free carriers, in WZ phase, than ZB phase, reflect higher carrier mobility and electrical conductivity ofWZ–Ga1�xInxN. Moreover wide energy gap of WZ–Ga1�xInxN results in large values of the absorption coefficients comparativelyand smaller static refractive indices compared to ZB–Ga1�xInxN. Comparable electronic and optical characteristics of theZB–Ga1�xInxN to WZ–Ga1�xInxN endorses it a material of choice for optoelectronics and solar cell applications besides theWZ–Ga1�xInxN.� 2014 Elsevier Ltd. All rights reserved.

Keywords: III–V alloys; Electronic structure; Thermodynamic stability; DFT; Solar cell application

http://dx.doi.org/10.1016/j.solener.2014.05.013

0038-092X/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: rashidahmed@utm.my (R. Ahmed), Souraya.Goum-

ri-Said@kaust.edu.sa (S. Goumri-Said).

1. Introduction

III-nitrides such as GaN and InN and their alloys havebeen studied intensively because of their remarkable prop-erties, including a high breakdown voltage, and high elec-tron mobility (Vurgaftman and Meyer, 2003). Morover,

544 B. Ul Haq et al. / Solar Energy 107 (2014) 543–552

with the determination of precise electronic bandgapenergy band gap value of InN (0.65–0.78 eV) Wu et al.(2002) has broadened the scope of GaInN alloys applica-tion to many areas, for example photovoltaics, long wavelength emitters and solar water splitter etcetera (Wuet al., 2002; Davydov et al., 2002; Jani et al., 2007; Dahalet al., 2009; Neufeld et al., 2008; Li et al., 2008;Nakamura et al., 2000) because of their potential in tuningdirect band gap over the entire solar spectrum.

To optimize and exploit potential of the GaN and InNfor further optoelectronics applications and solar cell tech-nology, alloying is one of the simplest ways to tailor elec-tronic and optical properties of the materials. Thesignificant difference in the fundamental energy gaps ofGaN and InN allow to engineer energy gap over a widespan (3.4 eV–0.78 eV) by their mutual alloying. Experimen-tally, band gap of Ga1�xInxN was found to vary continu-ously, as composition is increased from zero to one, from3.51 GaN to 0.78 eV InN for the wurtzite (WZ) structureof the material and from 3.30 GaN to 0.78 eV InN forthe zincblende (ZB) structure (Vurgaftman and Meyer,2003). Mutual alloying of the III-nitride compounds hasstimulated a remarkable research for the past two decadesor so (Barletta et al., 2007; Burton et al., 2006; Duqueet al., 2012; Emar et al., 2011; Ferhat and Bechstedt,2002; Haq et al., 2014; Kanoun et al., 2005; Landmannet al., 2013; Laref et al., 2013; Wei-Hua et al., 2013). It isbecause that the energy gap of blended Ga1�xInxN canbe tailored for a specific wavelength of the emitted lighti.e., from medium infrared (InN) to near ultraviolet (GaN).

GaN and InN naturally exist in the WZ phase in theground state. In WZ phase, III-nitrides and their alloys car-ries show severe spontaneous polarization and piezoelectriceffects that induce built-in fields undesirable for optoelec-tronic application. To overcome such unfavorable effects,most of the research is turned to synthesize GaInN in ZBphase using cubic substrates (Miyoshi et al., 1992; Chenget al., 1995; Tripathy et al., 2007; Hsiao et al., 2008;Yoshida, 2000) and are considered equally promising asin hexagonal phase. Even some of the physical propertiesof GaInN in ZB phase are considered to be over WZ phaselike higher carrier mobility, lower threshold current densityand larger optical gain (Duque et al., 2012; Marquardtet al., 2008; Park and Chuang, 2000). However, the un-mixing tendency of GaN and InN bring about difficultiesin the fabrication of high quality Ga1�xInxN. Conse-quently, these difficulties in the synthesis of homogenousalloys may impede their productive applications andendure gaps in their physical understanding (Burtonet al., 2006; Kuo et al., 2007, 2004).

The rapid advances in the epitaxial growth techniquesand theoretical tools have resolved several difficulties,and provoked more attention on these materials(Davydov et al., 2002; Landmann et al., 2013; Larefet al., 2013). For instance, the synthesis of high qualityInN has been shown the energy gap of InN of magnitude0.78 eV (Wu et al., 2002; Davydov et al., 2002), that was

projected to the community as from 1.8 eV to 2.1 eV(Osamura et al., 1972; Westra et al., 1988; Ikuta et al.,1998). Consequently, the energy gap of the blendedGa1�xInxN has been alleged a scattered problem (Kuoet al., 2004). The energy gap of Ga1�xInxN alloys has beenthe focus of researchers using different techniques; particu-larly DFT based first principles approach (Davydov et al.,2002; Kanoun et al., 2005; Landmann et al., 2013; Larefet al., 2013; Pugh et al., 1999; Zhang et al., 2011).

In this context, the first principles calculation based ondensity functional theory (DFT) are performed to investi-gate the fundamental properties of crystalline materials,except for its deficiency to determine accurate energy gapwith local or semi-local exchange correlation (XC) func-tional. DFT with common XC functional severely underes-timate the energy gap which is a pandect for the electronicproperties of any material. Consequently the optical proper-ties that are account of the optical transitions in the elec-tronic structure are strongly affected. Recently modifiedBecke-Johnson (mBJ) potential was proven to be highly rec-ommended for accurate electronic energy gap (Koller et al.,2011, 2012; Tran and Blaha, 2009). In fact, mBJ is anexchange potential that takes the correlation part eitherfrom LDA or GGA. Some recent studies have also provedit appropriate for nitride material (Davydov et al., 2002;Landmann et al., 2013; Laref et al., 2013). Using mBJ poten-tial, the energy gap of WZ-GaN and InN has been deter-mined as 3.09 eV (2.99 eV for ZB) and 0.76 eV (0.62 eVfor ZB) Landmann et al. (2013), that are close to experimen-tal values. Laref et al. (2013) have employed mBJ potentialto investigate Ga1�xInxN in ZB phase and have reportedresults consistent to experiments. The successful reproduc-tion of energy gap and consequently, accurate opticalparameters, at the level of mBJ calculation, warrants adetailed comparative study of Ga1�xInxN in WZ and ZBphase using mBJ potential. In addition, it is important tocheck the thermodynamic stability of Ga1�xInxN in WZand ZB phases in view of application as base material inoptoelectronic (OE) and photovoltaic (PV) devices.

In the present work, we performed a comparative inves-tigations of structural, electronic and optical properties ofGa1�xInxN for x = 0, 0.25, 0.50, 0.75 and 1 in WZ andZB. To recognize the structural geometry more suitablefor OE applications, a detailed comparison have beenmade between the two structures. The structure stability,formation enthalpy along with binodal and spinodaldecomposition temperature have been investigated at thelevel of GGA–PBE. In addition electronic energy bandgap and optical properties have also been comprehensivelyinvestigated to expose their potential for optoelectronicdevices using mBJ potential.

2. Computational details

All calculations were done using the DFT-based fullpotential (linear) augmented plane wave plus local orbitals(FP-(L)APW+lo) method as implemented in the WIEN2k

B. Ul Haq et al. / Solar Energy 107 (2014) 543–552 545

computer program (Blaha et al., 2001). The exchange andcorrelations were treated within the generalized gradientapproximation (GGA) of the Perdew, Burke and Ernzerhof(PBE) formalism Perdew et al., 1996 in addition to recentlydeveloped mBJ potential (Koller et al., 2012; Tran andBlaha, 2009). The plane wave expansion was taken Kmax

� RMT equal to 8. The muffin-tin (MT) sphere radii werechosen to be 1.77 (Ga) a.u, 1.81 (In) a.u and 1.48 (N) a.u.There are 285 k-points used in the special irreducible Brill-ouin zone (IBZ) for the well convergence of energy. Thetotal energy was converged to 10�5 Ryd/unit cell in ourpresent self-consistent computations for sound results.

3. Results and discussion

3.1. Structure and thermodynamics of Ga1�xInxN alloys

The structural properties of Ga1�xInxN have been inves-tigated to realize the effect of In substitution on Ga atomsin the blended alloy at various compositions. For this pur-pose, the unit cell of pure GaN was extended to a supercellcontaining eight atoms with 2 � 1 � 1 configuration forWZ and 1 � 1 � 1 configuration in ZB phase. To realizeGaN/InN alloying at 25%, 50% and 75% mixing concen-tration, systematic substitution of Ga atoms by In havebeen done. The volume of each alloy has been optimizedto investigate the influence of alloying on the structuralparameters of blended GaN/InN. The extracted latticeparameters from the optimized volumes in both structuresare listed in (Table 1). The calculated lattice parameters arein good agreement to the previous results. Because of largerionic radii of In than Ga, the substitution of In over Ga hasled enhanced lattice parameters of Ga1�xInxN.

The plots of lattice constants (a, c) as a function of Inconcentration have been displayed in Fig. 1; the dottedand dashed lines are drawn to show the consistency ofour results with vegard’s formalism. The increment in thelattice parameters versus In concentration follow linear fitsrepresented by Eqs. (1)–(3).

aðwzÞ ¼ 0:36xþ 3:234 ð1ÞcðwzÞ ¼ 0:54xþ 5:254 ð2ÞaðzbÞ ¼ 0:503xþ 4:564 ð3Þ

Table 1Lattice constants a and c of Ga1�xInxN for WZ and ZB phases compared to tmixing enthalpies DH(x) are also shown (kcal/mol).

Composition WZ

a c

GaN 3.22�, 3.64 (Laref et al., 2013), 3.59(Gavrilenko and Wu, 2000), 3.19(Schulz and Thiemann, 1977) exp

5.24�, 5.85 (Laref et a(Gavrilenko and Wu,(Schulz and Thiemann

Ga0.75In0.25N 3.33 5.39Ga0.50In0.50N 3.43 5.55Ga0.25In0.75N 3.51 5.66InN 3.58, 3.54 (Kim et al., 1996) exp 5.78, 5.71 (Kim et al.,

The lattice constants a and c of WZ–Ga1�xInxN areenhanced about 0.36 A and 0.54 A respectively in completealloying process. The total increment in lattice constant forZB Ga1�xInxN is 0.50 A. Although, the increment in latticeparameters is nearly linear, one can observe a weak upwardbowing in the lattice parameters for both WZ and ZBphases (Fig. 1). For stable and well-built devices basedon Ga1�xInxN, it is important to quantify the bowingobserved in the lattice parameters. To determine theexisting bowing, the Vegard’s formulation (Vegard, 1921)represented by the following Eqs. (4) and (5) for mixedalloys have been used as:

aðxÞ ¼ xaInN þ ð1� xÞaGaN � daxð1� xÞ ð4ÞcðxÞ ¼ xcInN þ ð1� xÞcGaN � dcxð1� xÞ ð5Þ

where da and dc represent the bowing of the lattice param-eters a and c. A negligible deviation from the linear behav-ior can be seen as stated by Vegard’s law; the resultsda = �0.114 A, dc = �0.126 A and da = �0.126 A areobtained for WZ and ZB phases, respectively. These resultsindicate that the value of lattice constant a has nearly linearcorrelation in between lattice and alloy composition,whereas the value of lattice constant c show larger devia-tion leading to different anisotropy. Note also that the lat-tice parameters of WZ phase have same deviation fromVegard’s law than those of ZB phase. The physical originof this deviation should be mainly due to the relaxationof the Ga–N and In–N bond lengths in Ga1�xInxN alloys.

The relative stability of the WZ and ZB structures ofGa1�xInxN compositions is determined by its formationenthalpies (DH) per cation–anion pair at 0 K given by:

DHðxÞ ¼ EðGa1�xInxNÞ � xEðInNÞ � ð1� xÞEðGaNÞ ð6Þ

This is the difference between the total energy of theblended alloy and the weighted sum of its components.In Table 1, we summarize the calculated formation enthal-pies Ga1�xInxN in WZ and ZB phases. Ga1�xInxN exhibitpositive enthalpy in both phases and is possibly due to themismatching in the lattice parameters of the parent com-pounds, as shown in Fig. 2. For In deficient Ga1�xInxNalloy, DH(x) experiences rapid increment with increase inthe In contents up to a maximum value (DHm) of0.53 kcal/mol for x = 0.45 in WZ structure and 0.47 kcal/

he experimental values and the results from the theoretical literature. The

ZB

DH a DH

l., 2013), 5.812000), 5.18, 1977) exp

4.55�, 4.48 (Landmann et al., 2013),5.50 (Logothetidis et al., 1994), 4.45(Ueno et al., 1994) exp

0.414 4.70�, 4.62 (Landmann et al., 2013) 0.3880.472 4.83�, 4.73(Landmann et al., 2013) 0.5280.385 4.95�, 4.85 (Landmann et al., 2013) 0.198

1996) exp 5.05�, 4.96 (Landmann et al., 2013),4.98 (Logothetidis et al., 1994), 4.92(Araujo et al., 2013) exp

Fig. 1. The increment in the lattice constants a, c of Wz–Ga1�xInxN hasbeen show in as a function of In concenteration, the dashed and dottedlines shows the Vegard’s formulation. The inset of figure shows thevariation of lattice constant of ZB–Ga1�xInxN. The dashed line reprsentthe variation in lattice constant according to Vegard’s law.

Fig. 2. Variation in formation enthalpies DH(x) as a function of Inconcentration. The left and right scales quantify the variation in WZ andZB phases respectively.

546 B. Ul Haq et al. / Solar Energy 107 (2014) 543–552

mol for x = 0.47 in ZB structure. For rich In alloy, itdecreases with increase in In concentration. Because of sta-bility of the hexagonal ground state, Ga1�xInxN carrieshigher mixing enthalpies than the cubic structure. Thesesmall values of formation enthalpies indicate that Ga1�xNalloys are simple to synthesis as compared to their counter-part compounds.

The interaction parameter X(x) can be extracted fromDHm using the formula: X = DHm/x(1 � x). At maximumenthalpies, X(x) is equivalent to 2.14 kcal/mol and1.88 kcal/mol for WZ and ZB phases respectively. X(x)have been used to determine the critical temperature defin-ing the limit of the Ga1�xInxN phases. In that case, thetemperature (T � x) phase diagrams are plotted in Fig. 3as a function of the In concentration as well the stableand meta stable boundaries. For alloys, T � x phasediagram indicates the stable, metastable and unstableregions. The details about T � x phase diagram are avail-able in references (Ferhat and Bechstedt, 2002; Haqet al., 2014; El Haj Hassan, 2010; Saito and Arakawa,1999). The transition temperature corresponds to the pointwhere the free energy has zero derivative (for both first andsecond derivative) (El Haj Hassan, 2010). The transition

temperature of WZ and ZB phases occur at temperatures1590 k and 1430 k respectively. These results are in goodagreement with the previous reports for cubic phase wherea Tc = 1417 k was found with DFT–LDA functional(Ferhat and Bechstedt, 2002) and 1400 k with valence-forcefield method (Saito and Arakawa, 1999).

3.2. Electronic structure and density of states

Now, we have also investigated the electronic propertiesof Ga1�xInxN in WZ and ZB phases. Fig. 4 depicts the elec-tronic band structures of WZ and ZB obtained with GGA–PBE and mBJ XC functionals. It is evident the electronicstructures of Ga1�xInxN are much alike their parent com-pounds (Davydov et al., 2002). Ga1�xInxN exhibits a directenergy band gap at high symmetry Gamma (C) point inboth phases. The calculated energy band gap values arelisted in Table 2. The underestimated energy gaps withGGA are efficiently improved with mBJ potential and clo-sely matching to experimental and other theoretical results.Fig. 4 shows that conduction band (CB) minimum is pushedto lower energies in reference to Fermi level by enhancing Inconcentration, and reflect narrower energy gap of In richGa1�xInxN alloy. The reduction in the energy gap with Inconcentration is due to the narrower energy gap of InN.The composition dependent energy gap narrowing ofGa1�xInxN alloys reveals that their band gaps can be engi-neered for OE and solar cell devices for correspondingwavelengths in the range Eg(GaN) P Eg(Ga1�xInxN) PEg(InN). Moreover, Ga1�xInxN exhibit a narrower bandgap in ZB phase than in WZ that reveal the applicationsof ZB Ga1�xInxN where comparatively narrower energygap is needed. Beside the drag down of CB minima, thepresence of the variation in In atoms influence the valenceband (VB) by reducing its width. The calculated VB widthsof electronic structures Ga1�xInxN are listed in Table 3. Weobserve a contraction in the VB widths with increase in Incontents. WZ–Ga1�xInxN carries comparatively narrowerVB than ZB–Ga1�xInxN. Note also that the bandwidth ofGa1�xInxN calculated with GGA is more shrink than mBJ.

Fig. 5 shows the non linear variation in the energy gapof WZ–Ga1�xInxN and ZB–Ga1�xInxN. The variation inthe energy gaps of Ga1�xInxN in WZ and ZB geometrieswith GGA–PBE and mBJ potential are fitted by the poly-nomial Eqs. (9)–(12) respectively.

Eg WZ–Ga1�xInxN=GGAð Þ ¼ 2:39x2 � 4:23xþ 1:88 ð9Þ

Eg WZ–Ga1�xInxN=mBJð Þ ¼ 2:21x2 � 2:21xþ 3:25 ð10Þ

Eg ZB–Ga1�xInxN=GGAð Þ ¼ 1:41x2 � 3:18þ 1:77 ð11Þ

Eg ZB–Ga1�xInxN=mBJð Þ ¼ 0:91x2 � 3:16xþ 2:99 ð12Þ

For reliable and efficient applications of Ga1�xInxN inOE devices, the deviation of energy gaps from linearvariation needs to be analyzed. In the previous studies(Ferhat and Bechstedt, 2002; Haq et al., 2014; El HajHassan, 2010) the deviation of energy gaps from linear

Fig. 3. T–x phase diagram of WZ and ZB versus the increase of In concentration. The black and red lines show the binodal and spinodal curvesrespectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. The electronic bands structures of Ga1�xInxN for x = 0.25, 0.50, and 0.75, as determined with GGA and mBJ potentials.

Table 2The energy band gaps of WZ and ZB–Ga1�xInxN x = 0, 0.25, 0.50, 0.75 and 1, as calculated using GGA and mBJ–GGA potential.

Composition Eg(WZ) Eg(ZB)

GGA mBJ GGA mBJ

GaN 1.93, 1.79 (Davydov et al.,2002)

3.33, 3.09 (Davydov et al.,2002)

1.77, 1.79 (Davydov et al.,2002)

3.0, 2.99 (Davydov et al., 2002), 3.27(Landmann et al., 2013), Exp. 3.30 (Lei et al.,1992),

Ga0.75In0.25N 0.88 2.088 1.08 2.26, 2.46 (Landmann et al., 2013)Ga0.50In0.50N 0.36 1.64 0.51 1.63 (Landmann et al., 2013)Ga0.25In0.75N 0.17 1.16 0.19 1.16, 1.32 (Landmann et al., 2013)InN 0. 0 (Davydov et al., 2002) 0.90, 0.76 (Davydov et al.,

2002)0. 0 (Davydov et al., 2002) 0.73, 0.72 (Landmann et al., 2013) 0.62

(Davydov et al., 2002), 0.78 (Lei et al., 1992)

B. Ul Haq et al. / Solar Energy 107 (2014) 543–552 547

Fig. 5. The variation in the band gap of WZ and ZB Ga1�xInxN with GGA and mBJ potential.

Table 3The valence band width and effective masses (in units of free electron mass m0) of WZ and ZB Ga1�xInxN as calculated using GGA and mBJ–GGApotential.

VB width Effective masses

WZ ZB WZ ZB

GGA mBJ GGA mBJ GGA mBj GGA mBJ

GaN 15.95 16.28 15.92 16.30 0.191 0.214 0.20 0.218Ga0.75In0.25N 15.90 16.30 15.61 15.92 0.126 0.149 0.13 0.17Ga0.50In0.50N 15.63 16.05 15.30 15.61 0.113 0.138 0.12 0.15Ga0.25In0.75N 15.30 15.66 15.02 15.46 0.104 0.117 0.11 0.14InN 14.91 15.28 14.91 15.24 0.076 0.899 0.09 0.10

548 B. Ul Haq et al. / Solar Energy 107 (2014) 543–552

variation is attributed mainly to three parameters, knownas, volume deformation (VD), charge exchange (CE), andthe structural relaxation (SR). Hence, the total bowingcan be written as b = bVD + bCE + bSR. The calculatedbowing parameters in energy gap determined with GGA–PBE and mBJ are listed in Table 4.

Another important parameter in engineering of OE andPV devices is the understanding of effective masses of elec-trons. The electronic effective masses are calculated fromthe CB parabola around high symmetry C-point in IBZ.Table 3 summarizes the values of the electronic effective

Table 4The energy gap bowing parameters of Ga1�xInxN as obtained from GGAand mBJ–GGA potentials.

Energy gap bowing WZ ZB

GGA mBJ GGA mBJ

bVD �0.12 �0.09 �0.17 �0.19bCE �1.71 �1.067 �2.43 �2.731bSR �0.33 �0.53 �0.136 �0.162b �2.16 �1.687 �2.736 �3.083

masses of Ga1�xInxN in WZ and ZB phases. The mBJ cal-culated effective masses are heavier than GGA, and is ingood agreement to the previous predictions (Davydovet al., 2002). Moreover, the calculated electronic effectivemasses for Ga1�xInxN for various compositions are in wellmatching to previous results (Kassali and Bouarissa, 2000).For instance, using empirical pseudopotential method,Kassali and Bouarissa have computed the electronic effec-tive masses for Ga0.50In0.50N of magnitude 11.2m0

(Kassali and Bouarissa, 2000). The increase in the In con-centration causes decrease in the effective masses. Thiscould be due to the lighter effective masses of electrons inInN than in GaN. The decrease in the effective masses ofelectrons reflects higher carrier mobility and electricalconductivity of In rich Ga1�xInxN. Table 3 depicts thatZB–Ga1�xInxN carries heavier effective electronic massesthan WZ structure that indicate comparatively lower car-rier mobility and electric conductivity of ZB structure thanin WZ structure.

The total and partial DOS profiles present the contribu-tion to the electronic interactions orbital and theirlocations. Since, DOS of Ga1�xInxN (for x = 0.25, 0.50

Fig. 6. The total and partial densities of states Ga0.25In0.75N of in WZ and ZB phases obtained with mBJ potential.

B. Ul Haq et al. / Solar Energy 107 (2014) 543–552 549

and 0.75) are highly symmetrical, we present the total andpartial DOS of Ga0.25In0.75N calculated with mBJ potentialas a prototype (see Fig. 6). Both WZ and ZB phases carryhighly analogous DOS profile. The major contribution toDOS in both WZ and ZB geometry is from Ga-d, In-dand N-s electrons, followed by Ga-s, p In-s, p and N-p elec-trons. Ga-d, In-d and N-s electrons are situated at lowerVB with quantitative DOS, N(e)Ga-d = 31.96 at�13.62 eV (34.98 at �13.36 for ZB), N(e)In-d = 14.47 at�13.29 eV (18.43 at �12.8 eV for ZB), N(e)N-s = 4.45(2.65 at = �15.48 for ZB), and their contribution to CBis almost negligible. The upper valence band is mainlydefined by N-p electrons followed by Ga-s, p and In-s, pelectrons. The conduction band is mostly of Ga-s, p, In-s,p and N-p character.

3.3. Optical properties

The study of optical properties of Ga1�xInxN alloys iscrucial for PV and other OE applications. We have investi-gated the optical properties using mBJ XC functional, as itdetermines highly accurate energy gap and consequentlythe optical properties. The fundamental parameter foroptical properties is the determination of dielectric functione(x), which mainly visualizes the optical transition betweenthe occupied and unoccupied states. One e2(x) is deter-mined, the other properties can be derived from it throughKramers–Kronig transformations (Kim et al., 1997). e2(x)

determined for GaN and InN in WZ and ZB structureswith mBJ potential has been depicted in Figs. 7 and 8.The peaks appear in e2(x) mainly originated from inter orintra band optical transitions. In Ga1�xInxN, the mainoptical transitions occur from mixed Ga-p, In-p, N-pappear in upper valence band to Ga-s, In-s and N-s appearin lower CB.

It is evident that e2(x) is zero for photon with energiesless than the energy gap. e2(x) appears for photon with

energies equivalent to the band gap energies at which theabsorption takes place. It can be assigned to the transitionsbetween VB maxima and CB minima. The first transitionbetween VB maxima and CB minima in WZ GaN, Ga0.25

In0.75N, Ga0.50In0.50N, Ga0.75In0.25N and InN occur at3.68 eV (3.45 eV for ZB) 2.44 eV (2.41 eV for ZB),1.83 eV (1.79 eV for ZB), 1.22 eV (1.18 eV for ZB)1.09 eV (0.75 eV for ZB) respectively. With increase inthe In concentration, the threshold energies for the firsttransition decrease because of energy gap narrowing forIn rich alloys. The slightly lower threshold energy for firsttransition in ZB geometry than WZ is due to the narrowerenergy gap in ZB geometry and is in agreement to the pre-vious studies (Laref et al., 2013). We can see that GaN inWZ phase exhibit four principle structures (Fig. 7). e2(x)

spectra for the two parent compounds is different in WZand ZB phase and reflect different optical transitions. Forinstance, e2(x) for GaN in WZ phase carries four principlestructures at energies 7.3 eV, 9.4 eV, 10.49 eV and 12.64 eVand reflect four major excitations. In ZB geometry, GaNshows three major excitations elucidated by three majorpeaks at 7.99 eV, 10.71 eV, and 12.87 eV. Similarly, WZ–InN carries three major peaks at 5.7 eV, 8.80 eV and10.85 eV. In ZB phase, the major transitions appear at3.28 eV, 6.53 eV, 9.15 eV and 11.18 eV. These spectra areclosely matching to previous reports (Laref et al., 2013;Zhang et al., 2011).

The difference in e2(x) of the parent compounds hasstrong influence on the dielectric function of the blendedGa1�xInxN. For dilute In contents, e2(x) spectra exhibitsmore identical symmetry to GaN, where In rich Ga1�xInxNalloy tends to adapt the symmetry of InN. For example, likeGaN, Ga0.75In0.25N in WZ phase shows four principle tran-sitions at 7.49 eV, 8.75 eV, 9.96 eV and 11.75 eV. Theincrease in the In contents strongly influence the e2(x)spectra, particularly the peak appearing at 8.75 eV inGa0.75In0.25N with significantly reduced intensity in

Fig. 7. The imaginary part e2(x) of dielectric function for GaN and InN in WZ and ZB phases computed using mBJ potential.

Fig. 9. The absorption spectra a(x) of Ga1�xInxN for x = 0.25, 0.50 and0.75 in WZ phase as obtained from mBJ potential. The inset of figureshows a(x) for ZB phase.

Fig. 8. The imaginary part e2(x) of dielectric function for WZ–Ga1�xInxNfor x = 0.25, 0.50 and 0.75 as calculated with mBJ potential. e2(x) forcubic phase is shown in the inset.

550 B. Ul Haq et al. / Solar Energy 107 (2014) 543–552

Ga0.50In0.50N has almost disappeared in Ga0.25In0.75N.e2(x) spectra of rich In Ga0.25In0.75N alloy is now morecomparable to parent InN with three principle peaks at6.37 eV, 9.09 eV, and 11.40 eV. Similarly, in ZB phase,e2(x) spectra of Ga0.75In0.25N reflect three major excitationsat 8.09 eV, 10.01 eV and 11.96 eV respectively. The opticaltransitions taking place in Ga1�xInxN alloys revealed by

Table 5The absorption coefficients a and refractive indices n(0) of Ga1�xInxN for WZ

a

WZ ZB

GaN 3.26 3.01�, 3.5 (Landmann et al., 2013

Ga0.75In0.25N 2.60 2.54�, 2.5 (Landmann et al., 2013Ga0.50In0.50N 1.85 1.83�, 1.8 (Landmann et al., 2013Ga0.25In0.75N 1.62 1.59�, 1.4 (Landmann et al., 2013InN 1.05 0.98�, 0.9 (Landmann et al., 2013

the principle structures in e2(x), are experiencing shift tolower energies and can be associated to the energy gap nar-rowing with increase of In concentration.

To identify the optical behavior of Ga1�xInxN, theabsorption spectra have been determined, as shown inFig. 9. Absorption coefficient, a(x), reflects the absorptionof light through a material and it is summarized in Table 5.

and ZB phases.

n(0)

WZ ZB

) 2.03 2.07�,2.07 (Landmann et al., 2013), 2.28(Reddy and Rama, 2008)

) 2.10 2.11�,2.43 (Landmann et al., 2013)) 2.14 2.15�,3.13 (Landmann et al., 2013)) 2.24 2.26�,3.61 (Landmann et al., 2013)) 2.32 2.36�,5.22 (Landmann et al., 2013)

Fig. 10. Refraction spectra R(x) for Ga1�xInxN for x = 0.25, 0.50 and0.75 in WZ phase determined with mBJ potential. The inset of figureshows R(x) for ZB phase.

B. Ul Haq et al. / Solar Energy 107 (2014) 543–552 551

In consensus to the energy gap narrowing with enhance-ment in In constituents, the absorption coefficients experi-ence decrease. Furthermore, our calculated values are ingood agreement with the available literature. The slightlylarger values of a(x) are due to comparatively larger energygap calculated with mBJ potential. It is evident that Ga0.75

In0.25N, Ga0.50In0.50N and Ga0.25In0.75N show a moderateabsorption for photon in the energy regime 2.60–7.56 eV(2.54–6.91 eV for ZB), 1.85–6 eV (1.83–6.29 eV for ZB)and 1.62–6.54 eV (1.59–5.97 eV for ZB) respectively. Theabsorption in the energy regime 1.59 to �7 eV correspond-ing to wavelength �779.77–177 nm is prominent, as it cov-ers the entire visible spectral region (Laref et al., 2013). a(x)abruptly increases for the light photon with above theseenergies. Ga0.75In0.25N, Ga0.50In0.50N and Ga0.25In0.75Nalloys show maximum absorption at energies 13.15 eV(12.54 eV for ZB), 12.38 eV (12.10 eV for ZB) and11.76 eV (11.70 eV for ZB) respectively. The intensity ofabsorption spectra diminishes with enhancement of In con-tents. Moreover, the absorption in Ga1�xInxN alloys in thecubic phase is slightly smaller than the hexagonal one and itreflects a comparatively transparency of ZB–Ga1�xInxN.

To measure the transparency of Ga1�xInxN in response ofan incident light, the refraction spectra R(x) and refractiveindex n(0) are reported in Table 5 and depicted in Fig. 10.For Ga1�xInxN, R(x) does not reveal significant variationfor energy photon in visible and near infrared showing theoptical stability of Ga1�xInxN alloys. Also, we determinedthe static refractive indices n(0) for these alloys from the refrac-tion spectra as summarized in Table 5. It is interesting to seethat the static refractive indices increase for rich In alloysand can be associated to the narrower energy gaps of thesealloys. Hence the slightly larger refractive indices ofGa1�xInxN in ZB could possibly be due to the narrowerenergy gaps. These characteristics of Ga1�xInxN alloysmake them as material of choice for OE application.

4. Conclusion

Using density functional theory with FP-L(APW+lo)method, at the level of GGA–PBE and mBJ exchange

correlation potential approaches, we investigated the phys-ical properties of cubic and hexagonal Ga1�xInxN alloys,for possible application in solar cells and optoelectronics.For calculation of electronic structure and optical proper-ties additional mBJ potential have been employed. Themarginal difference in the formation enthalpies and temper-ature phase diagrams of WZ and ZB Ga1�xInxN suggeststhe nearly equivalent stability of the two structures. Thenearly linear variation in the lattice parameters validatesthe stability of the future optoelectronic devices based onGa1�xInxN. Our results show that GaN/InN alloying giveseveral novel features favorable for optoelectronic devicesas well as for photovoltaic applications, such as the compo-sition dependence of energy gap narrowing, reducedabsorption coefficients and effective masses of free carriers.The less-stable phase, ZB–Ga1�xInxN alloys bear suffi-ciently comparable electronic and optical characteristicsand are equally favorable for OP and PV applications.

Acknowledgments

The first three authors acknowledge the financial sup-port of Ministry of Education (MOE) Universiti TeknologiMalaysia (UTM) for financial support of this researchthrough Grant Nos. Q.J130000.2526.02H89;R.J130000.7826.4F113 and Q.J130000.2526.04H14.

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