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InN based solar cells alloys: First-principles investigation within the improved modified Becke–Johnson potential
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ScienceDirect Solar Energy 107 (2014) 543–552 www.elsevier.com/locate/solener
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, Malaysia Universite´ Libanaise, Faculte des sciences (I), Laboratoire de Physique et d’e´lectronique (LPE), Elhadath, Beirut, Lebanon c Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia b
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 technology. Recently the unwanted built-in fields caused by spontaneous polarization and piezoelectric effects in wurtzite (WZ) GaInN, has turned 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 Ga1xInxN alloys with different In concentration using 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 of lattice parameters of Ga1xInxN with higher In concentration. For In deficient Ga1xInxN, at first, the formation enthalpies increase rapidly as the In content approaches to 45% in WZ and 47% in ZB, and then decreases with the further increase in In concentration. ZB–Ga1xInxN alloys exhibit comparatively narrower energy gaps than WZ, and get smaller with increase in In contents. The smaller values of effective masses of free carriers, in WZ phase, than ZB phase, reflect higher carrier mobility and electrical conductivity of WZ–Ga1xInxN. Moreover wide energy gap of WZ–Ga1xInxN results in large values of the absorption coefficients comparatively and smaller static refractive indices compared to ZB–Ga1xInxN. Comparable electronic and optical characteristics of the ZB–Ga1xInxN to WZ–Ga1xInxN endorses it a material of choice for optoelectronics and solar cell applications besides the WZ–Ga1xInxN. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: III–V alloys; Electronic structure; Thermodynamic stability; DFT; Solar cell application
1. Introduction
⇑ Corresponding author.
E-mail addresses: [email protected] (R. Ahmed), [email protected] (S. Goumri-Said). http://dx.doi.org/10.1016/j.solener.2014.05.013 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
III-nitrides such as GaN and InN and their alloys have been studied intensively because of their remarkable properties, including a high breakdown voltage, and high electron mobility (Vurgaftman and Meyer, 2003). Morover,
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with the determination of precise electronic bandgap energy band gap value of InN (0.65–0.78 eV) Wu et al. (2002) has broadened the scope of GaInN alloys application to many areas, for example photovoltaics, long wave length emitters and solar water splitter etcetera (Wu et al., 2002; Davydov et al., 2002; Jani et al., 2007; Dahal et al., 2009; Neufeld et al., 2008; Li et al., 2008; Nakamura et al., 2000) because of their potential in tuning direct band gap over the entire solar spectrum. To optimize and exploit potential of the GaN and InN for further optoelectronics applications and solar cell technology, alloying is one of the simplest ways to tailor electronic and optical properties of the materials. The significant difference in the fundamental energy gaps of GaN and InN allow to engineer energy gap over a wide span (3.4 eV–0.78 eV) by their mutual alloying. Experimentally, band gap of Ga1xInxN was found to vary continuously, as composition is increased from zero to one, from 3.51 GaN to 0.78 eV InN for the wurtzite (WZ) structure of the material and from 3.30 GaN to 0.78 eV InN for the zincblende (ZB) structure (Vurgaftman and Meyer, 2003). Mutual alloying of the III-nitride compounds has stimulated a remarkable research for the past two decades or so (Barletta et al., 2007; Burton et al., 2006; Duque et al., 2012; Emar et al., 2011; Ferhat and Bechstedt, 2002; Haq et al., 2014; Kanoun et al., 2005; Landmann et al., 2013; Laref et al., 2013; Wei-Hua et al., 2013). It is because that the energy gap of blended Ga1xInxN can be tailored for a specific wavelength of the emitted light i.e., from medium infrared (InN) to near ultraviolet (GaN). GaN and InN naturally exist in the WZ phase in the ground state. In WZ phase, III-nitrides and their alloys carries show severe spontaneous polarization and piezoelectric effects that induce built-in fields undesirable for optoelectronic application. To overcome such unfavorable effects, most of the research is turned to synthesize GaInN in ZB phase using cubic substrates (Miyoshi et al., 1992; Cheng et al., 1995; Tripathy et al., 2007; Hsiao et al., 2008; Yoshida, 2000) and are considered equally promising as in hexagonal phase. Even some of the physical properties of GaInN in ZB phase are considered to be over WZ phase like higher carrier mobility, lower threshold current density and larger optical gain (Duque et al., 2012; Marquardt et al., 2008; Park and Chuang, 2000). However, the unmixing tendency of GaN and InN bring about difficulties in the fabrication of high quality Ga1xInxN. Consequently, these difficulties in the synthesis of homogenous alloys may impede their productive applications and endure gaps in their physical understanding (Burton et al., 2006; Kuo et al., 2007, 2004). The rapid advances in the epitaxial growth techniques and theoretical tools have resolved several difficulties, and provoked more attention on these materials (Davydov et al., 2002; Landmann et al., 2013; Laref et al., 2013). For instance, the synthesis of high quality InN has been shown the energy gap of InN of magnitude 0.78 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 blended Ga1xInxN has been alleged a scattered problem (Kuo et al., 2004). The energy gap of Ga1xInxN alloys has been the focus of researchers using different techniques; particularly DFT based first principles approach (Davydov et al., 2002; Kanoun et al., 2005; Landmann et al., 2013; Laref et al., 2013; Pugh et al., 1999; Zhang et al., 2011). In this context, the first principles calculation based on density functional theory (DFT) are performed to investigate the fundamental properties of crystalline materials, except for its deficiency to determine accurate energy gap with local or semi-local exchange correlation (XC) functional. DFT with common XC functional severely underestimate the energy gap which is a pandect for the electronic properties of any material. Consequently the optical properties that are account of the optical transitions in the electronic structure are strongly affected. Recently modified Becke-Johnson (mBJ) potential was proven to be highly recommended for accurate electronic energy gap (Koller et al., 2011, 2012; Tran and Blaha, 2009). In fact, mBJ is an exchange potential that takes the correlation part either from LDA or GGA. Some recent studies have also proved it appropriate for nitride material (Davydov et al., 2002; Landmann et al., 2013; Laref et al., 2013). Using mBJ potential, the energy gap of WZ-GaN and InN has been determined as 3.09 eV (2.99 eV for ZB) and 0.76 eV (0.62 eV for ZB) Landmann et al. (2013), that are close to experimental values. Laref et al. (2013) have employed mBJ potential to investigate Ga1xInxN in ZB phase and have reported results consistent to experiments. The successful reproduction of energy gap and consequently, accurate optical parameters, at the level of mBJ calculation, warrants a detailed comparative study of Ga1xInxN in WZ and ZB phase using mBJ potential. In addition, it is important to check the thermodynamic stability of Ga1xInxN in WZ and ZB phases in view of application as base material in optoelectronic (OE) and photovoltaic (PV) devices. In the present work, we performed a comparative investigations of structural, electronic and optical properties of Ga1xInxN for x = 0, 0.25, 0.50, 0.75 and 1 in WZ and ZB. To recognize the structural geometry more suitable for OE applications, a detailed comparison have been made between the two structures. The structure stability, formation enthalpy along with binodal and spinodal decomposition temperature have been investigated at the level of GGA–PBE. In addition electronic energy band gap and optical properties have also been comprehensively investigated to expose their potential for optoelectronic devices using mBJ potential. 2. Computational details All calculations were done using the DFT-based full potential (linear) augmented plane wave plus local orbitals (FP-(L)APW+lo) method as implemented in the WIEN2k
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computer program (Blaha et al., 2001). The exchange and correlations were treated within the generalized gradient approximation (GGA) of the Perdew, Burke and Ernzerhof (PBE) formalism Perdew et al., 1996 in addition to recently developed mBJ potential (Koller et al., 2012; Tran and Blaha, 2009). The plane wave expansion was taken Kmax RMT equal to 8. The muffin-tin (MT) sphere radii were chosen 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 Brillouin zone (IBZ) for the well convergence of energy. The total energy was converged to 105 Ryd/unit cell in our present self-consistent computations for sound results. 3. Results and discussion 3.1. Structure and thermodynamics of Ga1xInxN alloys The structural properties of Ga1xInxN have been investigated to realize the effect of In substitution on Ga atoms in the blended alloy at various compositions. For this purpose, the unit cell of pure GaN was extended to a supercell containing eight atoms with 2 1 1 configuration for WZ and 1 1 1 configuration in ZB phase. To realize GaN/InN alloying at 25%, 50% and 75% mixing concentration, systematic substitution of Ga atoms by In have been done. The volume of each alloy has been optimized to investigate the influence of alloying on the structural parameters of blended GaN/InN. The extracted lattice parameters from the optimized volumes in both structures are listed in (Table 1). The calculated lattice parameters are in good agreement to the previous results. Because of larger ionic radii of In than Ga, the substitution of In over Ga has led enhanced lattice parameters of Ga1xInxN. The plots of lattice constants (a, c) as a function of In concentration have been displayed in Fig. 1; the dotted and dashed lines are drawn to show the consistency of our results with vegard’s formalism. The increment in the lattice parameters versus In concentration follow linear fits represented by Eqs. (1)–(3). aðwzÞ ¼ 0:36x þ 3:234
ð1Þ
cðwzÞ ¼ 0:54x þ 5:254
ð2Þ
aðzbÞ ¼ 0:503x þ 4:564
ð3Þ
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The lattice constants a and c of WZ–Ga1xInxN are ˚ and 0.54 A ˚ respectively in complete enhanced about 0.36 A alloying process. The total increment in lattice constant for ˚ . Although, the increment in lattice ZB Ga1xInxN is 0.50 A parameters is nearly linear, one can observe a weak upward bowing in the lattice parameters for both WZ and ZB phases (Fig. 1). For stable and well-built devices based on Ga1xInxN, it is important to quantify the bowing observed in the lattice parameters. To determine the existing bowing, the Vegard’s formulation (Vegard, 1921) represented by the following Eqs. (4) and (5) for mixed alloys have been used as: aðxÞ ¼ xaInN þ ð1 xÞaGaN daxð1 xÞ
ð4Þ
cðxÞ ¼ xcInN þ ð1 xÞcGaN dcxð1 xÞ
ð5Þ
where da and dc represent the bowing of the lattice parameters a and c. A negligible deviation from the linear behavior can be seen as stated by Vegard’s law; the results ˚ , dc = 0.126 A ˚ and da = 0.126 A ˚ are da = 0.114 A obtained for WZ and ZB phases, respectively. These results indicate that the value of lattice constant a has nearly linear correlation in between lattice and alloy composition, whereas the value of lattice constant c show larger deviation leading to different anisotropy. Note also that the lattice parameters of WZ phase have same deviation from Vegard’s law than those of ZB phase. The physical origin of this deviation should be mainly due to the relaxation of the Ga–N and In–N bond lengths in Ga1xInxN alloys. The relative stability of the WZ and ZB structures of Ga1xInxN compositions is determined by its formation enthalpies (DH) per cation–anion pair at 0 K given by: DH ðxÞ ¼ EðGa1x Inx NÞ xEðInNÞ ð1 xÞEðGaNÞ
ð6Þ
This is the difference between the total energy of the blended alloy and the weighted sum of its components. In Table 1, we summarize the calculated formation enthalpies Ga1xInxN in WZ and ZB phases. Ga1xInxN exhibit positive enthalpy in both phases and is possibly due to the mismatching in the lattice parameters of the parent compounds, as shown in Fig. 2. For In deficient Ga1xInxN alloy, DH(x) experiences rapid increment with increase in the In contents up to a maximum value (DHm) of 0.53 kcal/mol for x = 0.45 in WZ structure and 0.47 kcal/
Table 1 Lattice constants a and c of Ga1xInxN for WZ and ZB phases compared to the experimental values and the results from the theoretical literature. The mixing enthalpies DH(x) are also shown (kcal/mol). Composition
WZ
ZB
a GaN
Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
c
3.22 , 3.64 (Laref et al., 2013), 3.59 (Gavrilenko and Wu, 2000), 3.19 (Schulz and Thiemann, 1977) exp 3.33 3.43 3.51 3.58, 3.54 (Kim et al., 1996) exp
DH
5.24 , 5.85 (Laref et al., 2013), 5.81 (Gavrilenko and Wu, 2000), 5.18 (Schulz and Thiemann, 1977) exp 5.39 5.55 5.66 5.78, 5.71 (Kim et al., 1996) exp
a
DH
0.414 0.472 0.385
4.55 , 4.48 (Landmann et al., 2013), 5.50 (Logothetidis et al., 1994), 4.45 (Ueno et al., 1994) exp 4.70, 4.62 (Landmann et al., 2013) 4.83, 4.73(Landmann et al., 2013) 4.95, 4.85 (Landmann et al., 2013) 5.05, 4.96 (Landmann et al., 2013), 4.98 (Logothetidis et al., 1994), 4.92 (Araujo et al., 2013) exp
0.388 0.528 0.198
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temperature of WZ and ZB phases occur at temperatures 1590 k and 1430 k respectively. These results are in good agreement with the previous reports for cubic phase where a Tc = 1417 k was found with DFT–LDA functional (Ferhat and Bechstedt, 2002) and 1400 k with valence-force field method (Saito and Arakawa, 1999). 3.2. Electronic structure and density of states
Fig. 1. The increment in the lattice constants a, c of Wz–Ga1xInxN has been show in as a function of In concenteration, the dashed and dotted lines shows the Vegard’s formulation. The inset of figure shows the variation of lattice constant of ZB–Ga1xInxN. The dashed line reprsent the variation in lattice constant according to Vegard’s law.
Fig. 2. Variation in formation enthalpies DH(x) as a function of In concentration. The left and right scales quantify the variation in WZ and ZB phases respectively.
mol for x = 0.47 in ZB structure. For rich In alloy, it decreases with increase in In concentration. Because of stability of the hexagonal ground state, Ga1xInxN carries higher mixing enthalpies than the cubic structure. These small values of formation enthalpies indicate that Ga1xN alloys are simple to synthesis as compared to their counterpart compounds. The interaction parameter X(x) can be extracted from DHm using the formula: X = DHm/x(1 x). At maximum enthalpies, X(x) is equivalent to 2.14 kcal/mol and 1.88 kcal/mol for WZ and ZB phases respectively. X(x) have been used to determine the critical temperature defining the limit of the Ga1xInxN phases. In that case, the temperature (T x) phase diagrams are plotted in Fig. 3 as a function of the In concentration as well the stable and meta stable boundaries. For alloys, T x phase diagram indicates the stable, metastable and unstable regions. The details about T x phase diagram are available in references (Ferhat and Bechstedt, 2002; Haq et al., 2014; El Haj Hassan, 2010; Saito and Arakawa, 1999). The transition temperature corresponds to the point where the free energy has zero derivative (for both first and second derivative) (El Haj Hassan, 2010). The transition
Now, we have also investigated the electronic properties of Ga1xInxN in WZ and ZB phases. Fig. 4 depicts the electronic band structures of WZ and ZB obtained with GGA– PBE and mBJ XC functionals. It is evident the electronic structures of Ga1xInxN are much alike their parent compounds (Davydov et al., 2002). Ga1xInxN exhibits a direct energy band gap at high symmetry Gamma (C) point in both phases. The calculated energy band gap values are listed in Table 2. The underestimated energy gaps with GGA are efficiently improved with mBJ potential and closely matching to experimental and other theoretical results. Fig. 4 shows that conduction band (CB) minimum is pushed to lower energies in reference to Fermi level by enhancing In concentration, and reflect narrower energy gap of In rich Ga1xInxN alloy. The reduction in the energy gap with In concentration is due to the narrower energy gap of InN. The composition dependent energy gap narrowing of Ga1xInxN alloys reveals that their band gaps can be engineered for OE and solar cell devices for corresponding wavelengths in the range Eg(GaN) P Eg(Ga1xInxN) P Eg(InN). Moreover, Ga1xInxN exhibit a narrower band gap in ZB phase than in WZ that reveal the applications of ZB Ga1xInxN where comparatively narrower energy gap is needed. Beside the drag down of CB minima, the presence of the variation in In atoms influence the valence band (VB) by reducing its width. The calculated VB widths of electronic structures Ga1xInxN are listed in Table 3. We observe a contraction in the VB widths with increase in In contents. WZ–Ga1xInxN carries comparatively narrower VB than ZB–Ga1xInxN. Note also that the bandwidth of Ga1xInxN calculated with GGA is more shrink than mBJ. Fig. 5 shows the non linear variation in the energy gap of WZ–Ga1xInxN and ZB–Ga1xInxN. The variation in the energy gaps of Ga1xInxN in WZ and ZB geometries with GGA–PBE and mBJ potential are fitted by the polynomial Eqs. (9)–(12) respectively. EgðWZ–Ga1xInxN=GGAÞ ¼ 2:39x2 4:23x þ 1:88
ð9Þ
EgðWZ–Ga1xInxN=mBJÞ ¼ 2:21x2 2:21x þ 3:25
ð10Þ
2
EgðZB–Ga1xInxN=GGAÞ ¼ 1:41x 3:18 þ 1:77
ð11Þ
EgðZB–Ga1xInxN=mBJÞ ¼ 0:91x2 3:16x þ 2:99
ð12Þ
For reliable and efficient applications of Ga1xInxN in OE devices, the deviation of energy gaps from linear variation needs to be analyzed. In the previous studies (Ferhat and Bechstedt, 2002; Haq et al., 2014; El Haj Hassan, 2010) the deviation of energy gaps from linear
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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 curves respectively. (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 Ga1xInxN for x = 0.25, 0.50, and 0.75, as determined with GGA and mBJ potentials.
Table 2 The energy band gaps of WZ and ZB–Ga1xInxN 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)
Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
0.88 0.36 0.17 0. 0 (Davydov et al., 2002)
2.088 1.64 1.16 0.90, 0.76 (Davydov et al., 2002)
1.08 0.51 0.19 0. 0 (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), 2.26, 2.46 (Landmann et al., 2013) 1.63 (Landmann et al., 2013) 1.16, 1.32 (Landmann et al., 2013) 0.73, 0.72 (Landmann et al., 2013) 0.62 (Davydov et al., 2002), 0.78 (Lei et al., 1992)
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Table 3 The valence band width and effective masses (in units of free electron mass m0) of WZ and ZB Ga1xInxN as calculated using GGA and mBJ–GGA potential. VB width
Effective masses
WZ
GaN Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
ZB
WZ
ZB
GGA
mBJ
GGA
mBJ
GGA
mBj
GGA
mBJ
15.95 15.90 15.63 15.30 14.91
16.28 16.30 16.05 15.66 15.28
15.92 15.61 15.30 15.02 14.91
16.30 15.92 15.61 15.46 15.24
0.191 0.126 0.113 0.104 0.076
0.214 0.149 0.138 0.117 0.899
0.20 0.13 0.12 0.11 0.09
0.218 0.17 0.15 0.14 0.10
Fig. 5. The variation in the band gap of WZ and ZB Ga1xInxN with GGA and mBJ potential.
variation is attributed mainly to three parameters, known as, volume deformation (VD), charge exchange (CE), and the structural relaxation (SR). Hence, the total bowing can be written as b = bVD + bCE + bSR. The calculated bowing parameters in energy gap determined with GGA– PBE and mBJ are listed in Table 4. Another important parameter in engineering of OE and PV devices is the understanding of effective masses of electrons. The electronic effective masses are calculated from the CB parabola around high symmetry C-point in IBZ. Table 3 summarizes the values of the electronic effective
Table 4 The energy gap bowing parameters of Ga1xInxN as obtained from GGA and mBJ–GGA potentials. Energy gap bowing
bVD bCE bSR b
WZ
ZB
GGA
mBJ
GGA
mBJ
0.12 1.71 0.33 2.16
0.09 1.067 0.53 1.687
0.17 2.43 0.136 2.736
0.19 2.731 0.162 3.083
masses of Ga1xInxN in WZ and ZB phases. The mBJ calculated effective masses are heavier than GGA, and is in good agreement to the previous predictions (Davydov et al., 2002). Moreover, the calculated electronic effective masses for Ga1xInxN for various compositions are in well matching to previous results (Kassali and Bouarissa, 2000). For instance, using empirical pseudopotential method, Kassali and Bouarissa have computed the electronic effective masses for Ga0.50In0.50N of magnitude 11.2m0 (Kassali and Bouarissa, 2000). The increase in the In concentration causes decrease in the effective masses. This could be due to the lighter effective masses of electrons in InN than in GaN. The decrease in the effective masses of electrons reflects higher carrier mobility and electrical conductivity of In rich Ga1xInxN. Table 3 depicts that ZB–Ga1xInxN carries heavier effective electronic masses than WZ structure that indicate comparatively lower carrier mobility and electric conductivity of ZB structure than in WZ structure. The total and partial DOS profiles present the contribution to the electronic interactions orbital and their locations. Since, DOS of Ga1xInxN (for x = 0.25, 0.50
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Fig. 6. The total and partial densities of states Ga0.25In0.75N of in WZ and ZB phases obtained with mBJ potential.
and 0.75) are highly symmetrical, we present the total and partial DOS of Ga0.25In0.75N calculated with mBJ potential as a prototype (see Fig. 6). Both WZ and ZB phases carry highly analogous DOS profile. The major contribution to DOS in both WZ and ZB geometry is from Ga-d, In-d and N-s electrons, followed by Ga-s, p In-s, p and N-p electrons. Ga-d, In-d and N-s electrons are situated at lower VB 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 CB is almost negligible. The upper valence band is mainly defined by N-p electrons followed by Ga-s, p and In-s, p electrons. 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 Ga1xInxN alloys is crucial for PV and other OE applications. We have investigated the optical properties using mBJ XC functional, as it determines highly accurate energy gap and consequently the optical properties. The fundamental parameter for optical properties is the determination of dielectric function e(x), which mainly visualizes the optical transition between the occupied and unoccupied states. One e2(x) is determined, the other properties can be derived from it through Kramers–Kronig transformations (Kim et al., 1997). e2(x) determined for GaN and InN in WZ and ZB structures with mBJ potential has been depicted in Figs. 7 and 8. The peaks appear in e2(x) mainly originated from inter or intra band optical transitions. In Ga1xInxN, the main optical transitions occur from mixed Ga-p, In-p, N-p appear in upper valence band to Ga-s, In-s and N-s appear in lower CB. It is evident that e2(x) is zero for photon with energies less than the energy gap. e2(x) appears for photon with
energies equivalent to the band gap energies at which the absorption takes place. It can be assigned to the transitions between VB maxima and CB minima. The first transition between VB maxima and CB minima in WZ GaN, Ga0.25 In0.75N, Ga0.50In0.50N, Ga0.75In0.25N and InN occur at 3.68 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 in the In concentration, the threshold energies for the first transition decrease because of energy gap narrowing for In rich alloys. The slightly lower threshold energy for first transition in ZB geometry than WZ is due to the narrower energy gap in ZB geometry and is in agreement to the previous studies (Laref et al., 2013). We can see that GaN in WZ phase exhibit four principle structures (Fig. 7). e2(x) spectra for the two parent compounds is different in WZ and ZB phase and reflect different optical transitions. For instance, e2(x) for GaN in WZ phase carries four principle structures at energies 7.3 eV, 9.4 eV, 10.49 eV and 12.64 eV and reflect four major excitations. In ZB geometry, GaN shows three major excitations elucidated by three major peaks 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 and 10.85 eV. In ZB phase, the major transitions appear at 3.28 eV, 6.53 eV, 9.15 eV and 11.18 eV. These spectra are closely matching to previous reports (Laref et al., 2013; Zhang et al., 2011). The difference in e2(x) of the parent compounds has strong influence on the dielectric function of the blended Ga1xInxN. For dilute In contents, e2(x) spectra exhibits more identical symmetry to GaN, where In rich Ga1xInxN alloy tends to adapt the symmetry of InN. For example, like GaN, Ga0.75In0.25N in WZ phase shows four principle transitions at 7.49 eV, 8.75 eV, 9.96 eV and 11.75 eV. The increase in the In contents strongly influence the e2(x) spectra, particularly the peak appearing at 8.75 eV in Ga0.75In0.25N with significantly reduced intensity in
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Fig. 7. The imaginary part e2(x) of dielectric function for GaN and InN in WZ and ZB phases computed using mBJ potential.
Fig. 8. The imaginary part e2(x) of dielectric function for WZ–Ga1xInxN for x = 0.25, 0.50 and 0.75 as calculated with mBJ potential. e2(x) for cubic phase is shown in the inset.
Fig. 9. The absorption spectra a(x) of Ga1xInxN for x = 0.25, 0.50 and 0.75 in WZ phase as obtained from mBJ potential. The inset of figure shows a(x) for ZB phase.
Ga0.50In0.50N has almost disappeared in Ga0.25In0.75N. e2(x) spectra of rich In Ga0.25In0.75N alloy is now more comparable to parent InN with three principle peaks at 6.37 eV, 9.09 eV, and 11.40 eV. Similarly, in ZB phase, e2(x) spectra of Ga0.75In0.25N reflect three major excitations at 8.09 eV, 10.01 eV and 11.96 eV respectively. The optical transitions taking place in Ga1xInxN alloys revealed by
the principle structures in e2(x), are experiencing shift to lower energies and can be associated to the energy gap narrowing with increase of In concentration. To identify the optical behavior of Ga1xInxN, the absorption spectra have been determined, as shown in Fig. 9. Absorption coefficient, a(x), reflects the absorption of light through a material and it is summarized in Table 5.
Table 5 The absorption coefficients a and refractive indices n(0) of Ga1xInxN for WZ and ZB phases. n(0)
a WZ
ZB
WZ
ZB 2.07,2.07 (Landmann et al., (Reddy and Rama, 2008) 2.11,2.43 (Landmann et al., 2.15,3.13 (Landmann et al., 2.26,3.61 (Landmann et al., 2.36,5.22 (Landmann et al.,
GaN
3.26
3.01 , 3.5 (Landmann et al., 2013)
2.03
Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
2.60 1.85 1.62 1.05
2.54, 1.83, 1.59, 0.98,
2.10 2.14 2.24 2.32
2.5 1.8 1.4 0.9
(Landmann (Landmann (Landmann (Landmann
et et et et
al., al., al., al.,
2013) 2013) 2013) 2013)
2013), 2.28 2013) 2013) 2013) 2013)
B. Ul Haq et al. / Solar Energy 107 (2014) 543–552
Fig. 10. Refraction spectra R(x) for Ga1xInxN for x = 0.25, 0.50 and 0.75 in WZ phase determined with mBJ potential. The inset of figure shows R(x) for ZB phase.
In consensus to the energy gap narrowing with enhancement in In constituents, the absorption coefficients experience decrease. Furthermore, our calculated values are in good agreement with the available literature. The slightly larger values of a(x) are due to comparatively larger energy gap calculated with mBJ potential. It is evident that Ga0.75 In0.25N, Ga0.50In0.50N and Ga0.25In0.75N show a moderate absorption 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. The absorption in the energy regime 1.59 to 7 eV corresponding to wavelength 779.77–177 nm is prominent, as it covers the entire visible spectral region (Laref et al., 2013). a(x) abruptly increases for the light photon with above these energies. Ga0.75In0.25N, Ga0.50In0.50N and Ga0.25In0.75N alloys show maximum absorption at energies 13.15 eV (12.54 eV for ZB), 12.38 eV (12.10 eV for ZB) and 11.76 eV (11.70 eV for ZB) respectively. The intensity of absorption spectra diminishes with enhancement of In contents. Moreover, the absorption in Ga1xInxN alloys in the cubic phase is slightly smaller than the hexagonal one and it reflects a comparatively transparency of ZB–Ga1xInxN. To measure the transparency of Ga1xInxN in response of an incident light, the refraction spectra R(x) and refractive index n(0) are reported in Table 5 and depicted in Fig. 10. For Ga1xInxN, R(x) does not reveal significant variation for energy photon in visible and near infrared showing the optical stability of Ga1xInxN alloys. Also, we determined the static refractive indices n(0) for these alloys from the refraction spectra as summarized in Table 5. It is interesting to see that the static refractive indices increase for rich In alloys and can be associated to the narrower energy gaps of these alloys. Hence the slightly larger refractive indices of Ga1xInxN in ZB could possibly be due to the narrower energy gaps. These characteristics of Ga1xInxN alloys make 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
551
correlation potential approaches, we investigated the physical properties of cubic and hexagonal Ga1xInxN alloys, for possible application in solar cells and optoelectronics. For calculation of electronic structure and optical properties additional mBJ potential have been employed. The marginal difference in the formation enthalpies and temperature phase diagrams of WZ and ZB Ga1xInxN suggests the nearly equivalent stability of the two structures. The nearly linear variation in the lattice parameters validates the stability of the future optoelectronic devices based on Ga1xInxN. Our results show that GaN/InN alloying give several novel features favorable for optoelectronic devices as well as for photovoltaic applications, such as the composition dependence of energy gap narrowing, reduced absorption coefficients and effective masses of free carriers. The less-stable phase, ZB–Ga1xInxN alloys bear sufficiently comparable electronic and optical characteristics and are equally favorable for OP and PV applications. Acknowledgments The first three authors acknowledge the financial support of Ministry of Education (MOE) Universiti Teknologi Malaysia (UTM) for financial support of this research through Grant Nos. Q.J130000.2526.02H89; R.J130000.7826.4F113 and Q.J130000.2526.04H14. References Araujo, R.B., de Almeida, J., da Silva, A.F., 2013. J. Appl. Phys. 114 (18), 183702. Barletta, P.T., Acar Berkman, E., Moody, B.F., El-Masry, N.A., Emara, A.M., Reed, M.J., Bedair, S., 2007. Appl. Phys. Lett. 90 (15), 151109151109-3. Blaha, P., Schwarz, K., Madsen, G., Kvasnicka, D., Luitz, J., 2001. An Augmented Plane Wave Plus Local Orbitals Program For Calculating Crystal Properties. Vienna University of Technology, Austria. Burton, B., Van de Walle, A., Kattner, U., 2006. J. Appl. Phys. 100 (11), 113528–113528-6. Cheng, T., Jenkins, L., Hooper, S., Foxon, C., Orton, J., Lacklison, D., 1995. Appl. Phys. Lett. 66 (12), 1509–1511. Dahal, R., Pantha, B., Li, J., Lin, J., Jiang, H., 2009. Appl. Phys. Lett. 94 (6), 063505. Davydov, V.Y., Klochikhin, A., Seisyan, R., Emtsev, V., Ivanov, S., Bechstedt, F., Furthmu¨ller, J., Harima, H., Mudryi, A., Aderhold, J., 2002. Phys. Status Solidi B 229 (3), r1–r3. Duque, C.M., Mora-Ramos, M.E., Duque, C.A., 2012. Nanoscale Res. Lett. 7 (1), 1–8. El Haj Hassan, F., Breidi, A., Ghemid, S., Amrani, B., Meradji, H., Page`s, O., 2010. J. Alloys Compd. 499 (1), 80–89. Emar, A.M., Berkman, E.A., Zavada, J., El-Masry, N.A., Bedair, S., 2011. Phys. Status Solidi C 8 (7–8), 2034–2037. Ferhat, M., Bechstedt, F., 2002. Phys. Rev. B 65 (7), 075213. Gavrilenko, V., Wu, R., 2000. Phys. Rev. B 61 (4), 2632. Haq, B.U., Ahmed, R., El Haj Hassan, F., Khenata, R., Kasmin, M.K., Goumri-Said, S., 2014. Sol. Energy 100, 1–8. Hsiao, C.-L., Liu, T.-W., Wu, C.-T., Hsu, H.-C., Hsu, G.-M., Chen, L.-C., Shiao, W.-Y., Yang, C., Gallstrom, A., Holtz, P.-O., 2008. Appl. Phys. Lett. 92 (11), 111914-111914-3. Ikuta, K., Inoue, Y., Takai, O., 1998. Thin Solid Films 334 (1), 49–53. Jani, O., Ferguson, I., Honsberg, C., Kurtz, S., 2007. Appl. Phys. Lett. 91 (13), 132117-132117-3.
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Kanoun, M., Goumri-Said, S., Merad, A., Mariette, H., 2005. J. Appl. Phys. 98, 063710. Kassali, K., Bouarissa, N., 2000. Solid-State Electron. 44 (3), 501–507. Kim, K., Lambrecht, W.R., Segall, B., 1996. Phys. Rev. B 53 (24), 16310. Kim, K., Lambrecht, W.R., Segall, B., 1997. Phys. Rev. B 56 (11), 7018. Koller, D., Tran, F., Blaha, P., 2011. Phys. Rev. B 83 (19), 195134. Koller, D., Tran, F., Blaha, P., 2012. Phys. Rev. B 85 (15), 155109. Kuo, Y.-K., Liou, B.-T., Yen, S.-H., Chu, H.-Y., 2004. Opt. Commun. 237 (4), 363–369. Kuo, Y.-K., Chu, H.-Y., Yen, S.-H., Liou, B.-T., Chen, M.-L., 2007. Opt. Commun. 280 (1), 153–156. Landmann, M., Rauls, E., Schmidt, W., Ro¨ppischer, M., Cobet, C., Esser, N., Schupp, T., As, D.J., Feneberg, M., Goldhahn, R., 2013. Phys. Rev. B 87 (19), 195210. Laref, A., Altujar, A., Luo, S., 2013. Eur. Phys. J. B 86 (11), 1–11. Lei, T., Moustakas, T., Graham, R., He, Y., Berkowitz, S., 1992. J. Appl. Phys. 71 (10), 4933–4943. Li, J., Lin, J., Jiang, H., 2008. Appl. Phys. Lett. 93 (16), 162107. Logothetidis, S., Petalas, J., Cardona, M., Moustakas, T., 1994. Phys. Rev. B 50 (24), 18017. Marquardt, O., Mourad, D., Schulz, S., Hickel, T., Czycholl, G., Neugebauer, J., 2008. Phys. Rev. B 78 (23), 235302. Miyoshi, S., Onabe, K., Ohkouchi, N., Yaguchi, H., Ito, R., Fukatsu, S., Shiraki, Y., 1992. J. Cryst. Growth 124 (1), 439–442. Nakamura, S., Pearton, S., Fasol, G., 2000. The Blue Laser Diode: The Complete Story. Springer. Neufeld, C.J., Toledo, N.G., Cruz, S.C., Iza, M., DenBaars, S.P., Mishra, U.K., 2008. Appl. Phys. Lett. 93 (14), 143502-143502-3.
Osamura, K., Nakajima, K., Murakami, Y., Shingu, P.H., Ohtsuki, A., 1972. Solid State Commun. 11 (5), 617–621. Park, S.-H., Chuang, S.-L., 2000. J. Appl. Phys. 87 (1), 353–364. Perdew, J.P., Burke, K., Ernzerhof, M., 1996. Phys. Rev. Lett. 77 (18), 3865. Pugh, S., Dugdale, D., Brand, S., Abram, R., 1999. J. Appl. Phys. 86 (7), 3768–3772. Reddy, R., Rama Gopal, K., Narasimhulu, K., Reddy, L., Kumar, K.R., Reddy, C., Ahmed, S.N., 2008. Opt. Mater. 31 (2), 209–212. Saito, T., Arakawa, Y., 1999. Phys. Rev. B 60 (3), 1701. Schulz, H., Thiemann, K., 1977. Solid State Commun. 23 (11), 815–819. Tran, F., Blaha, P., 2009. Phys. Rev. Lett. 102 (22), 226401. Tripathy, S., Lin, V., Teo, S., Dadgar, A., Diez, A., Bla¨sing, J., Krost, A., 2007. Appl. Phys. Lett. 91, 231109. Ueno, M., Yoshida, M., Onodera, A., Shimomura, O., Takemura, K., 1994. Phys. Rev. B 49 (1), 14. Vegard, L., 1921. Z. Phys. A: Hadrons Nucl. 5 (1), 17–26. Vurgaftman, I., Meyer, J., 2003. J. Appl. Phys. 94 (6), 3675–3696. Wei-Hua, W., Guo-Zhong, Z., Xi-Xia, L., 2013. Chin. Phys. B 22 (12), 120205. Westra, K., Lawson, R., Brett, M., 1988. J. Vac. Sci. Technol., A 6 (3), 1730–1732. Wu, J., Walukiewicz, W., Yu, K., Ager Iii, J., Haller, E., Lu, H., Schaff, W.J., Saito, Y., Nanishi, Y., 2002. Appl. Phys. Lett. 80 (21), 3967– 3969. Yoshida, S., 2000. Physica E 7 (3), 907–914. Zhang, S., Shi, J.-J., Zhang, M., Yang, M., Li, J., 2011. J. Phys. D Appl. Phys. 44 (49), 495304.
ScienceDirect Solar Energy 107 (2014) 543–552 www.elsevier.com/locate/solener
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, Malaysia Universite´ Libanaise, Faculte des sciences (I), Laboratoire de Physique et d’e´lectronique (LPE), Elhadath, Beirut, Lebanon c Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia b
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 technology. Recently the unwanted built-in fields caused by spontaneous polarization and piezoelectric effects in wurtzite (WZ) GaInN, has turned 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 Ga1xInxN alloys with different In concentration using 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 of lattice parameters of Ga1xInxN with higher In concentration. For In deficient Ga1xInxN, at first, the formation enthalpies increase rapidly as the In content approaches to 45% in WZ and 47% in ZB, and then decreases with the further increase in In concentration. ZB–Ga1xInxN alloys exhibit comparatively narrower energy gaps than WZ, and get smaller with increase in In contents. The smaller values of effective masses of free carriers, in WZ phase, than ZB phase, reflect higher carrier mobility and electrical conductivity of WZ–Ga1xInxN. Moreover wide energy gap of WZ–Ga1xInxN results in large values of the absorption coefficients comparatively and smaller static refractive indices compared to ZB–Ga1xInxN. Comparable electronic and optical characteristics of the ZB–Ga1xInxN to WZ–Ga1xInxN endorses it a material of choice for optoelectronics and solar cell applications besides the WZ–Ga1xInxN. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: III–V alloys; Electronic structure; Thermodynamic stability; DFT; Solar cell application
1. Introduction
⇑ Corresponding author.
E-mail addresses: [email protected] (R. Ahmed), [email protected] (S. Goumri-Said). http://dx.doi.org/10.1016/j.solener.2014.05.013 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
III-nitrides such as GaN and InN and their alloys have been studied intensively because of their remarkable properties, including a high breakdown voltage, and high electron mobility (Vurgaftman and Meyer, 2003). Morover,
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with the determination of precise electronic bandgap energy band gap value of InN (0.65–0.78 eV) Wu et al. (2002) has broadened the scope of GaInN alloys application to many areas, for example photovoltaics, long wave length emitters and solar water splitter etcetera (Wu et al., 2002; Davydov et al., 2002; Jani et al., 2007; Dahal et al., 2009; Neufeld et al., 2008; Li et al., 2008; Nakamura et al., 2000) because of their potential in tuning direct band gap over the entire solar spectrum. To optimize and exploit potential of the GaN and InN for further optoelectronics applications and solar cell technology, alloying is one of the simplest ways to tailor electronic and optical properties of the materials. The significant difference in the fundamental energy gaps of GaN and InN allow to engineer energy gap over a wide span (3.4 eV–0.78 eV) by their mutual alloying. Experimentally, band gap of Ga1xInxN was found to vary continuously, as composition is increased from zero to one, from 3.51 GaN to 0.78 eV InN for the wurtzite (WZ) structure of the material and from 3.30 GaN to 0.78 eV InN for the zincblende (ZB) structure (Vurgaftman and Meyer, 2003). Mutual alloying of the III-nitride compounds has stimulated a remarkable research for the past two decades or so (Barletta et al., 2007; Burton et al., 2006; Duque et al., 2012; Emar et al., 2011; Ferhat and Bechstedt, 2002; Haq et al., 2014; Kanoun et al., 2005; Landmann et al., 2013; Laref et al., 2013; Wei-Hua et al., 2013). It is because that the energy gap of blended Ga1xInxN can be tailored for a specific wavelength of the emitted light i.e., from medium infrared (InN) to near ultraviolet (GaN). GaN and InN naturally exist in the WZ phase in the ground state. In WZ phase, III-nitrides and their alloys carries show severe spontaneous polarization and piezoelectric effects that induce built-in fields undesirable for optoelectronic application. To overcome such unfavorable effects, most of the research is turned to synthesize GaInN in ZB phase using cubic substrates (Miyoshi et al., 1992; Cheng et al., 1995; Tripathy et al., 2007; Hsiao et al., 2008; Yoshida, 2000) and are considered equally promising as in hexagonal phase. Even some of the physical properties of GaInN in ZB phase are considered to be over WZ phase like higher carrier mobility, lower threshold current density and larger optical gain (Duque et al., 2012; Marquardt et al., 2008; Park and Chuang, 2000). However, the unmixing tendency of GaN and InN bring about difficulties in the fabrication of high quality Ga1xInxN. Consequently, these difficulties in the synthesis of homogenous alloys may impede their productive applications and endure gaps in their physical understanding (Burton et al., 2006; Kuo et al., 2007, 2004). The rapid advances in the epitaxial growth techniques and theoretical tools have resolved several difficulties, and provoked more attention on these materials (Davydov et al., 2002; Landmann et al., 2013; Laref et al., 2013). For instance, the synthesis of high quality InN has been shown the energy gap of InN of magnitude 0.78 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 blended Ga1xInxN has been alleged a scattered problem (Kuo et al., 2004). The energy gap of Ga1xInxN alloys has been the focus of researchers using different techniques; particularly DFT based first principles approach (Davydov et al., 2002; Kanoun et al., 2005; Landmann et al., 2013; Laref et al., 2013; Pugh et al., 1999; Zhang et al., 2011). In this context, the first principles calculation based on density functional theory (DFT) are performed to investigate the fundamental properties of crystalline materials, except for its deficiency to determine accurate energy gap with local or semi-local exchange correlation (XC) functional. DFT with common XC functional severely underestimate the energy gap which is a pandect for the electronic properties of any material. Consequently the optical properties that are account of the optical transitions in the electronic structure are strongly affected. Recently modified Becke-Johnson (mBJ) potential was proven to be highly recommended for accurate electronic energy gap (Koller et al., 2011, 2012; Tran and Blaha, 2009). In fact, mBJ is an exchange potential that takes the correlation part either from LDA or GGA. Some recent studies have also proved it appropriate for nitride material (Davydov et al., 2002; Landmann et al., 2013; Laref et al., 2013). Using mBJ potential, the energy gap of WZ-GaN and InN has been determined as 3.09 eV (2.99 eV for ZB) and 0.76 eV (0.62 eV for ZB) Landmann et al. (2013), that are close to experimental values. Laref et al. (2013) have employed mBJ potential to investigate Ga1xInxN in ZB phase and have reported results consistent to experiments. The successful reproduction of energy gap and consequently, accurate optical parameters, at the level of mBJ calculation, warrants a detailed comparative study of Ga1xInxN in WZ and ZB phase using mBJ potential. In addition, it is important to check the thermodynamic stability of Ga1xInxN in WZ and ZB phases in view of application as base material in optoelectronic (OE) and photovoltaic (PV) devices. In the present work, we performed a comparative investigations of structural, electronic and optical properties of Ga1xInxN for x = 0, 0.25, 0.50, 0.75 and 1 in WZ and ZB. To recognize the structural geometry more suitable for OE applications, a detailed comparison have been made between the two structures. The structure stability, formation enthalpy along with binodal and spinodal decomposition temperature have been investigated at the level of GGA–PBE. In addition electronic energy band gap and optical properties have also been comprehensively investigated to expose their potential for optoelectronic devices using mBJ potential. 2. Computational details All calculations were done using the DFT-based full potential (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
computer program (Blaha et al., 2001). The exchange and correlations were treated within the generalized gradient approximation (GGA) of the Perdew, Burke and Ernzerhof (PBE) formalism Perdew et al., 1996 in addition to recently developed mBJ potential (Koller et al., 2012; Tran and Blaha, 2009). The plane wave expansion was taken Kmax RMT equal to 8. The muffin-tin (MT) sphere radii were chosen 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 Brillouin zone (IBZ) for the well convergence of energy. The total energy was converged to 105 Ryd/unit cell in our present self-consistent computations for sound results. 3. Results and discussion 3.1. Structure and thermodynamics of Ga1xInxN alloys The structural properties of Ga1xInxN have been investigated to realize the effect of In substitution on Ga atoms in the blended alloy at various compositions. For this purpose, the unit cell of pure GaN was extended to a supercell containing eight atoms with 2 1 1 configuration for WZ and 1 1 1 configuration in ZB phase. To realize GaN/InN alloying at 25%, 50% and 75% mixing concentration, systematic substitution of Ga atoms by In have been done. The volume of each alloy has been optimized to investigate the influence of alloying on the structural parameters of blended GaN/InN. The extracted lattice parameters from the optimized volumes in both structures are listed in (Table 1). The calculated lattice parameters are in good agreement to the previous results. Because of larger ionic radii of In than Ga, the substitution of In over Ga has led enhanced lattice parameters of Ga1xInxN. The plots of lattice constants (a, c) as a function of In concentration have been displayed in Fig. 1; the dotted and dashed lines are drawn to show the consistency of our results with vegard’s formalism. The increment in the lattice parameters versus In concentration follow linear fits represented by Eqs. (1)–(3). aðwzÞ ¼ 0:36x þ 3:234
ð1Þ
cðwzÞ ¼ 0:54x þ 5:254
ð2Þ
aðzbÞ ¼ 0:503x þ 4:564
ð3Þ
545
The lattice constants a and c of WZ–Ga1xInxN are ˚ and 0.54 A ˚ respectively in complete enhanced about 0.36 A alloying process. The total increment in lattice constant for ˚ . Although, the increment in lattice ZB Ga1xInxN is 0.50 A parameters is nearly linear, one can observe a weak upward bowing in the lattice parameters for both WZ and ZB phases (Fig. 1). For stable and well-built devices based on Ga1xInxN, it is important to quantify the bowing observed in the lattice parameters. To determine the existing bowing, the Vegard’s formulation (Vegard, 1921) represented by the following Eqs. (4) and (5) for mixed alloys have been used as: aðxÞ ¼ xaInN þ ð1 xÞaGaN daxð1 xÞ
ð4Þ
cðxÞ ¼ xcInN þ ð1 xÞcGaN dcxð1 xÞ
ð5Þ
where da and dc represent the bowing of the lattice parameters a and c. A negligible deviation from the linear behavior can be seen as stated by Vegard’s law; the results ˚ , dc = 0.126 A ˚ and da = 0.126 A ˚ are da = 0.114 A obtained for WZ and ZB phases, respectively. These results indicate that the value of lattice constant a has nearly linear correlation in between lattice and alloy composition, whereas the value of lattice constant c show larger deviation leading to different anisotropy. Note also that the lattice parameters of WZ phase have same deviation from Vegard’s law than those of ZB phase. The physical origin of this deviation should be mainly due to the relaxation of the Ga–N and In–N bond lengths in Ga1xInxN alloys. The relative stability of the WZ and ZB structures of Ga1xInxN compositions is determined by its formation enthalpies (DH) per cation–anion pair at 0 K given by: DH ðxÞ ¼ EðGa1x Inx NÞ xEðInNÞ ð1 xÞEðGaNÞ
ð6Þ
This is the difference between the total energy of the blended alloy and the weighted sum of its components. In Table 1, we summarize the calculated formation enthalpies Ga1xInxN in WZ and ZB phases. Ga1xInxN exhibit positive enthalpy in both phases and is possibly due to the mismatching in the lattice parameters of the parent compounds, as shown in Fig. 2. For In deficient Ga1xInxN alloy, DH(x) experiences rapid increment with increase in the In contents up to a maximum value (DHm) of 0.53 kcal/mol for x = 0.45 in WZ structure and 0.47 kcal/
Table 1 Lattice constants a and c of Ga1xInxN for WZ and ZB phases compared to the experimental values and the results from the theoretical literature. The mixing enthalpies DH(x) are also shown (kcal/mol). Composition
WZ
ZB
a GaN
Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
c
3.22 , 3.64 (Laref et al., 2013), 3.59 (Gavrilenko and Wu, 2000), 3.19 (Schulz and Thiemann, 1977) exp 3.33 3.43 3.51 3.58, 3.54 (Kim et al., 1996) exp
DH
5.24 , 5.85 (Laref et al., 2013), 5.81 (Gavrilenko and Wu, 2000), 5.18 (Schulz and Thiemann, 1977) exp 5.39 5.55 5.66 5.78, 5.71 (Kim et al., 1996) exp
a
DH
0.414 0.472 0.385
4.55 , 4.48 (Landmann et al., 2013), 5.50 (Logothetidis et al., 1994), 4.45 (Ueno et al., 1994) exp 4.70, 4.62 (Landmann et al., 2013) 4.83, 4.73(Landmann et al., 2013) 4.95, 4.85 (Landmann et al., 2013) 5.05, 4.96 (Landmann et al., 2013), 4.98 (Logothetidis et al., 1994), 4.92 (Araujo et al., 2013) exp
0.388 0.528 0.198
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temperature of WZ and ZB phases occur at temperatures 1590 k and 1430 k respectively. These results are in good agreement with the previous reports for cubic phase where a Tc = 1417 k was found with DFT–LDA functional (Ferhat and Bechstedt, 2002) and 1400 k with valence-force field method (Saito and Arakawa, 1999). 3.2. Electronic structure and density of states
Fig. 1. The increment in the lattice constants a, c of Wz–Ga1xInxN has been show in as a function of In concenteration, the dashed and dotted lines shows the Vegard’s formulation. The inset of figure shows the variation of lattice constant of ZB–Ga1xInxN. The dashed line reprsent the variation in lattice constant according to Vegard’s law.
Fig. 2. Variation in formation enthalpies DH(x) as a function of In concentration. The left and right scales quantify the variation in WZ and ZB phases respectively.
mol for x = 0.47 in ZB structure. For rich In alloy, it decreases with increase in In concentration. Because of stability of the hexagonal ground state, Ga1xInxN carries higher mixing enthalpies than the cubic structure. These small values of formation enthalpies indicate that Ga1xN alloys are simple to synthesis as compared to their counterpart compounds. The interaction parameter X(x) can be extracted from DHm using the formula: X = DHm/x(1 x). At maximum enthalpies, X(x) is equivalent to 2.14 kcal/mol and 1.88 kcal/mol for WZ and ZB phases respectively. X(x) have been used to determine the critical temperature defining the limit of the Ga1xInxN phases. In that case, the temperature (T x) phase diagrams are plotted in Fig. 3 as a function of the In concentration as well the stable and meta stable boundaries. For alloys, T x phase diagram indicates the stable, metastable and unstable regions. The details about T x phase diagram are available in references (Ferhat and Bechstedt, 2002; Haq et al., 2014; El Haj Hassan, 2010; Saito and Arakawa, 1999). The transition temperature corresponds to the point where the free energy has zero derivative (for both first and second derivative) (El Haj Hassan, 2010). The transition
Now, we have also investigated the electronic properties of Ga1xInxN in WZ and ZB phases. Fig. 4 depicts the electronic band structures of WZ and ZB obtained with GGA– PBE and mBJ XC functionals. It is evident the electronic structures of Ga1xInxN are much alike their parent compounds (Davydov et al., 2002). Ga1xInxN exhibits a direct energy band gap at high symmetry Gamma (C) point in both phases. The calculated energy band gap values are listed in Table 2. The underestimated energy gaps with GGA are efficiently improved with mBJ potential and closely matching to experimental and other theoretical results. Fig. 4 shows that conduction band (CB) minimum is pushed to lower energies in reference to Fermi level by enhancing In concentration, and reflect narrower energy gap of In rich Ga1xInxN alloy. The reduction in the energy gap with In concentration is due to the narrower energy gap of InN. The composition dependent energy gap narrowing of Ga1xInxN alloys reveals that their band gaps can be engineered for OE and solar cell devices for corresponding wavelengths in the range Eg(GaN) P Eg(Ga1xInxN) P Eg(InN). Moreover, Ga1xInxN exhibit a narrower band gap in ZB phase than in WZ that reveal the applications of ZB Ga1xInxN where comparatively narrower energy gap is needed. Beside the drag down of CB minima, the presence of the variation in In atoms influence the valence band (VB) by reducing its width. The calculated VB widths of electronic structures Ga1xInxN are listed in Table 3. We observe a contraction in the VB widths with increase in In contents. WZ–Ga1xInxN carries comparatively narrower VB than ZB–Ga1xInxN. Note also that the bandwidth of Ga1xInxN calculated with GGA is more shrink than mBJ. Fig. 5 shows the non linear variation in the energy gap of WZ–Ga1xInxN and ZB–Ga1xInxN. The variation in the energy gaps of Ga1xInxN in WZ and ZB geometries with GGA–PBE and mBJ potential are fitted by the polynomial Eqs. (9)–(12) respectively. EgðWZ–Ga1xInxN=GGAÞ ¼ 2:39x2 4:23x þ 1:88
ð9Þ
EgðWZ–Ga1xInxN=mBJÞ ¼ 2:21x2 2:21x þ 3:25
ð10Þ
2
EgðZB–Ga1xInxN=GGAÞ ¼ 1:41x 3:18 þ 1:77
ð11Þ
EgðZB–Ga1xInxN=mBJÞ ¼ 0:91x2 3:16x þ 2:99
ð12Þ
For reliable and efficient applications of Ga1xInxN in OE devices, the deviation of energy gaps from linear variation needs to be analyzed. In the previous studies (Ferhat and Bechstedt, 2002; Haq et al., 2014; El Haj Hassan, 2010) the deviation of energy gaps from linear
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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 curves respectively. (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 Ga1xInxN for x = 0.25, 0.50, and 0.75, as determined with GGA and mBJ potentials.
Table 2 The energy band gaps of WZ and ZB–Ga1xInxN 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)
Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
0.88 0.36 0.17 0. 0 (Davydov et al., 2002)
2.088 1.64 1.16 0.90, 0.76 (Davydov et al., 2002)
1.08 0.51 0.19 0. 0 (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), 2.26, 2.46 (Landmann et al., 2013) 1.63 (Landmann et al., 2013) 1.16, 1.32 (Landmann et al., 2013) 0.73, 0.72 (Landmann et al., 2013) 0.62 (Davydov et al., 2002), 0.78 (Lei et al., 1992)
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Table 3 The valence band width and effective masses (in units of free electron mass m0) of WZ and ZB Ga1xInxN as calculated using GGA and mBJ–GGA potential. VB width
Effective masses
WZ
GaN Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
ZB
WZ
ZB
GGA
mBJ
GGA
mBJ
GGA
mBj
GGA
mBJ
15.95 15.90 15.63 15.30 14.91
16.28 16.30 16.05 15.66 15.28
15.92 15.61 15.30 15.02 14.91
16.30 15.92 15.61 15.46 15.24
0.191 0.126 0.113 0.104 0.076
0.214 0.149 0.138 0.117 0.899
0.20 0.13 0.12 0.11 0.09
0.218 0.17 0.15 0.14 0.10
Fig. 5. The variation in the band gap of WZ and ZB Ga1xInxN with GGA and mBJ potential.
variation is attributed mainly to three parameters, known as, volume deformation (VD), charge exchange (CE), and the structural relaxation (SR). Hence, the total bowing can be written as b = bVD + bCE + bSR. The calculated bowing parameters in energy gap determined with GGA– PBE and mBJ are listed in Table 4. Another important parameter in engineering of OE and PV devices is the understanding of effective masses of electrons. The electronic effective masses are calculated from the CB parabola around high symmetry C-point in IBZ. Table 3 summarizes the values of the electronic effective
Table 4 The energy gap bowing parameters of Ga1xInxN as obtained from GGA and mBJ–GGA potentials. Energy gap bowing
bVD bCE bSR b
WZ
ZB
GGA
mBJ
GGA
mBJ
0.12 1.71 0.33 2.16
0.09 1.067 0.53 1.687
0.17 2.43 0.136 2.736
0.19 2.731 0.162 3.083
masses of Ga1xInxN in WZ and ZB phases. The mBJ calculated effective masses are heavier than GGA, and is in good agreement to the previous predictions (Davydov et al., 2002). Moreover, the calculated electronic effective masses for Ga1xInxN for various compositions are in well matching to previous results (Kassali and Bouarissa, 2000). For instance, using empirical pseudopotential method, Kassali and Bouarissa have computed the electronic effective masses for Ga0.50In0.50N of magnitude 11.2m0 (Kassali and Bouarissa, 2000). The increase in the In concentration causes decrease in the effective masses. This could be due to the lighter effective masses of electrons in InN than in GaN. The decrease in the effective masses of electrons reflects higher carrier mobility and electrical conductivity of In rich Ga1xInxN. Table 3 depicts that ZB–Ga1xInxN carries heavier effective electronic masses than WZ structure that indicate comparatively lower carrier mobility and electric conductivity of ZB structure than in WZ structure. The total and partial DOS profiles present the contribution to the electronic interactions orbital and their locations. Since, DOS of Ga1xInxN (for x = 0.25, 0.50
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Fig. 6. The total and partial densities of states Ga0.25In0.75N of in WZ and ZB phases obtained with mBJ potential.
and 0.75) are highly symmetrical, we present the total and partial DOS of Ga0.25In0.75N calculated with mBJ potential as a prototype (see Fig. 6). Both WZ and ZB phases carry highly analogous DOS profile. The major contribution to DOS in both WZ and ZB geometry is from Ga-d, In-d and N-s electrons, followed by Ga-s, p In-s, p and N-p electrons. Ga-d, In-d and N-s electrons are situated at lower VB 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 CB is almost negligible. The upper valence band is mainly defined by N-p electrons followed by Ga-s, p and In-s, p electrons. 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 Ga1xInxN alloys is crucial for PV and other OE applications. We have investigated the optical properties using mBJ XC functional, as it determines highly accurate energy gap and consequently the optical properties. The fundamental parameter for optical properties is the determination of dielectric function e(x), which mainly visualizes the optical transition between the occupied and unoccupied states. One e2(x) is determined, the other properties can be derived from it through Kramers–Kronig transformations (Kim et al., 1997). e2(x) determined for GaN and InN in WZ and ZB structures with mBJ potential has been depicted in Figs. 7 and 8. The peaks appear in e2(x) mainly originated from inter or intra band optical transitions. In Ga1xInxN, the main optical transitions occur from mixed Ga-p, In-p, N-p appear in upper valence band to Ga-s, In-s and N-s appear in lower CB. It is evident that e2(x) is zero for photon with energies less than the energy gap. e2(x) appears for photon with
energies equivalent to the band gap energies at which the absorption takes place. It can be assigned to the transitions between VB maxima and CB minima. The first transition between VB maxima and CB minima in WZ GaN, Ga0.25 In0.75N, Ga0.50In0.50N, Ga0.75In0.25N and InN occur at 3.68 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 in the In concentration, the threshold energies for the first transition decrease because of energy gap narrowing for In rich alloys. The slightly lower threshold energy for first transition in ZB geometry than WZ is due to the narrower energy gap in ZB geometry and is in agreement to the previous studies (Laref et al., 2013). We can see that GaN in WZ phase exhibit four principle structures (Fig. 7). e2(x) spectra for the two parent compounds is different in WZ and ZB phase and reflect different optical transitions. For instance, e2(x) for GaN in WZ phase carries four principle structures at energies 7.3 eV, 9.4 eV, 10.49 eV and 12.64 eV and reflect four major excitations. In ZB geometry, GaN shows three major excitations elucidated by three major peaks 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 and 10.85 eV. In ZB phase, the major transitions appear at 3.28 eV, 6.53 eV, 9.15 eV and 11.18 eV. These spectra are closely matching to previous reports (Laref et al., 2013; Zhang et al., 2011). The difference in e2(x) of the parent compounds has strong influence on the dielectric function of the blended Ga1xInxN. For dilute In contents, e2(x) spectra exhibits more identical symmetry to GaN, where In rich Ga1xInxN alloy tends to adapt the symmetry of InN. For example, like GaN, Ga0.75In0.25N in WZ phase shows four principle transitions at 7.49 eV, 8.75 eV, 9.96 eV and 11.75 eV. The increase in the In contents strongly influence the e2(x) spectra, particularly the peak appearing at 8.75 eV in Ga0.75In0.25N with significantly reduced intensity in
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Fig. 7. The imaginary part e2(x) of dielectric function for GaN and InN in WZ and ZB phases computed using mBJ potential.
Fig. 8. The imaginary part e2(x) of dielectric function for WZ–Ga1xInxN for x = 0.25, 0.50 and 0.75 as calculated with mBJ potential. e2(x) for cubic phase is shown in the inset.
Fig. 9. The absorption spectra a(x) of Ga1xInxN for x = 0.25, 0.50 and 0.75 in WZ phase as obtained from mBJ potential. The inset of figure shows a(x) for ZB phase.
Ga0.50In0.50N has almost disappeared in Ga0.25In0.75N. e2(x) spectra of rich In Ga0.25In0.75N alloy is now more comparable to parent InN with three principle peaks at 6.37 eV, 9.09 eV, and 11.40 eV. Similarly, in ZB phase, e2(x) spectra of Ga0.75In0.25N reflect three major excitations at 8.09 eV, 10.01 eV and 11.96 eV respectively. The optical transitions taking place in Ga1xInxN alloys revealed by
the principle structures in e2(x), are experiencing shift to lower energies and can be associated to the energy gap narrowing with increase of In concentration. To identify the optical behavior of Ga1xInxN, the absorption spectra have been determined, as shown in Fig. 9. Absorption coefficient, a(x), reflects the absorption of light through a material and it is summarized in Table 5.
Table 5 The absorption coefficients a and refractive indices n(0) of Ga1xInxN for WZ and ZB phases. n(0)
a WZ
ZB
WZ
ZB 2.07,2.07 (Landmann et al., (Reddy and Rama, 2008) 2.11,2.43 (Landmann et al., 2.15,3.13 (Landmann et al., 2.26,3.61 (Landmann et al., 2.36,5.22 (Landmann et al.,
GaN
3.26
3.01 , 3.5 (Landmann et al., 2013)
2.03
Ga0.75In0.25N Ga0.50In0.50N Ga0.25In0.75N InN
2.60 1.85 1.62 1.05
2.54, 1.83, 1.59, 0.98,
2.10 2.14 2.24 2.32
2.5 1.8 1.4 0.9
(Landmann (Landmann (Landmann (Landmann
et et et et
al., al., al., al.,
2013) 2013) 2013) 2013)
2013), 2.28 2013) 2013) 2013) 2013)
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Fig. 10. Refraction spectra R(x) for Ga1xInxN for x = 0.25, 0.50 and 0.75 in WZ phase determined with mBJ potential. The inset of figure shows R(x) for ZB phase.
In consensus to the energy gap narrowing with enhancement in In constituents, the absorption coefficients experience decrease. Furthermore, our calculated values are in good agreement with the available literature. The slightly larger values of a(x) are due to comparatively larger energy gap calculated with mBJ potential. It is evident that Ga0.75 In0.25N, Ga0.50In0.50N and Ga0.25In0.75N show a moderate absorption 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. The absorption in the energy regime 1.59 to 7 eV corresponding to wavelength 779.77–177 nm is prominent, as it covers the entire visible spectral region (Laref et al., 2013). a(x) abruptly increases for the light photon with above these energies. Ga0.75In0.25N, Ga0.50In0.50N and Ga0.25In0.75N alloys show maximum absorption at energies 13.15 eV (12.54 eV for ZB), 12.38 eV (12.10 eV for ZB) and 11.76 eV (11.70 eV for ZB) respectively. The intensity of absorption spectra diminishes with enhancement of In contents. Moreover, the absorption in Ga1xInxN alloys in the cubic phase is slightly smaller than the hexagonal one and it reflects a comparatively transparency of ZB–Ga1xInxN. To measure the transparency of Ga1xInxN in response of an incident light, the refraction spectra R(x) and refractive index n(0) are reported in Table 5 and depicted in Fig. 10. For Ga1xInxN, R(x) does not reveal significant variation for energy photon in visible and near infrared showing the optical stability of Ga1xInxN alloys. Also, we determined the static refractive indices n(0) for these alloys from the refraction spectra as summarized in Table 5. It is interesting to see that the static refractive indices increase for rich In alloys and can be associated to the narrower energy gaps of these alloys. Hence the slightly larger refractive indices of Ga1xInxN in ZB could possibly be due to the narrower energy gaps. These characteristics of Ga1xInxN alloys make 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
551
correlation potential approaches, we investigated the physical properties of cubic and hexagonal Ga1xInxN alloys, for possible application in solar cells and optoelectronics. For calculation of electronic structure and optical properties additional mBJ potential have been employed. The marginal difference in the formation enthalpies and temperature phase diagrams of WZ and ZB Ga1xInxN suggests the nearly equivalent stability of the two structures. The nearly linear variation in the lattice parameters validates the stability of the future optoelectronic devices based on Ga1xInxN. Our results show that GaN/InN alloying give several novel features favorable for optoelectronic devices as well as for photovoltaic applications, such as the composition dependence of energy gap narrowing, reduced absorption coefficients and effective masses of free carriers. The less-stable phase, ZB–Ga1xInxN alloys bear sufficiently comparable electronic and optical characteristics and are equally favorable for OP and PV applications. Acknowledgments The first three authors acknowledge the financial support of Ministry of Education (MOE) Universiti Teknologi Malaysia (UTM) for financial support of this research through Grant Nos. Q.J130000.2526.02H89; R.J130000.7826.4F113 and Q.J130000.2526.04H14. References Araujo, R.B., de Almeida, J., da Silva, A.F., 2013. J. Appl. Phys. 114 (18), 183702. Barletta, P.T., Acar Berkman, E., Moody, B.F., El-Masry, N.A., Emara, A.M., Reed, M.J., Bedair, S., 2007. Appl. Phys. Lett. 90 (15), 151109151109-3. Blaha, P., Schwarz, K., Madsen, G., Kvasnicka, D., Luitz, J., 2001. An Augmented Plane Wave Plus Local Orbitals Program For Calculating Crystal Properties. Vienna University of Technology, Austria. Burton, B., Van de Walle, A., Kattner, U., 2006. J. Appl. Phys. 100 (11), 113528–113528-6. Cheng, T., Jenkins, L., Hooper, S., Foxon, C., Orton, J., Lacklison, D., 1995. Appl. Phys. Lett. 66 (12), 1509–1511. Dahal, R., Pantha, B., Li, J., Lin, J., Jiang, H., 2009. Appl. Phys. Lett. 94 (6), 063505. Davydov, V.Y., Klochikhin, A., Seisyan, R., Emtsev, V., Ivanov, S., Bechstedt, F., Furthmu¨ller, J., Harima, H., Mudryi, A., Aderhold, J., 2002. Phys. Status Solidi B 229 (3), r1–r3. Duque, C.M., Mora-Ramos, M.E., Duque, C.A., 2012. Nanoscale Res. Lett. 7 (1), 1–8. El Haj Hassan, F., Breidi, A., Ghemid, S., Amrani, B., Meradji, H., Page`s, O., 2010. J. Alloys Compd. 499 (1), 80–89. Emar, A.M., Berkman, E.A., Zavada, J., El-Masry, N.A., Bedair, S., 2011. Phys. Status Solidi C 8 (7–8), 2034–2037. Ferhat, M., Bechstedt, F., 2002. Phys. Rev. B 65 (7), 075213. Gavrilenko, V., Wu, R., 2000. Phys. Rev. B 61 (4), 2632. Haq, B.U., Ahmed, R., El Haj Hassan, F., Khenata, R., Kasmin, M.K., Goumri-Said, S., 2014. Sol. Energy 100, 1–8. Hsiao, C.-L., Liu, T.-W., Wu, C.-T., Hsu, H.-C., Hsu, G.-M., Chen, L.-C., Shiao, W.-Y., Yang, C., Gallstrom, A., Holtz, P.-O., 2008. Appl. Phys. Lett. 92 (11), 111914-111914-3. Ikuta, K., Inoue, Y., Takai, O., 1998. Thin Solid Films 334 (1), 49–53. Jani, O., Ferguson, I., Honsberg, C., Kurtz, S., 2007. Appl. Phys. Lett. 91 (13), 132117-132117-3.
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