ab-initio computationalstudy Structural,electronicandopticalpropertiesforchalcopyritesemiconductingmaterials: Optik

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Optik

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Short note

Structural, electronic and optical properties for chalcopyrite semiconducting materials: ab-initio computational study

Moufdi Hadjab

^a,b,⁎

, Miloud Ibrir

^c

, Smail Berrah

^d

, Hamza Abid

^b

, Mohammad Alam Saeed

^e,f

aThin Films Development and Applications Unit UDCMA, Setif–Research Center in Industrial Technologies CRTI, B. O. Box 64, Cheraga, 16014, Algiers, Algeria

bApplied Materials Laboratory, Djillali Liabes University of Sidi Bel Abbes, 22000, Sidi Bel Abbes, Algeria

cLaboratory of Physics of Materials and its Applications, Mohamed Boudiaf University, Msila, 28000, Algeria

dMastery Renewable Energies Laboratory LMER, University of A. Mira, Bejaia, 6000, Algeria

eDepartment of Physics, Faculty of Science, Universiti Teknologi Malaysia, Skudai, 81310, Johor Bahru, Malaysia

fDivision of Science and Technology, University of Education, Lahore, Pakistan

A R T I C L E I N F O

Keywords:

Chalcopyrite FP-LAPW Optical properties Thin-ﬁlms solar cells Wien2k

A B S T R A C T

Investigation of the physical properties of chalcopyrite materials usingab-initiomethods have been carried out to simulate a new structure of thin-films photovoltaic cells with high conversion efficiency. The Density Functional Theory calculations have been performed using Wien2k computational package by employing the full-potential linearized augmented plane wave method. Structural and electronic properties of chalcopyrite semiconducting material Copper–Indium–Gallium–Seleniumi.e.CuIn_1-xGa_xSe₂have been investigated using local density approximation for the exchange-correlation potential. The electronic structures and linear optical properties have been studied using both the semi-local Becke-Johnson potential and its modified formi.e.mBJ and TB-mBJ. Computational results are in good agreement with those acquired experimentally. The viability of alloys in realization of ultra-thin-film based (CIGS) solar cells with high performance has been proposed after simulation and analysis study using one of solar cell simulation tools. The studied material exhibits capability to become a promising candidate for fabrication of optoelectronic and photovoltaic devices.

1. Introduction

Chalcopyrite semiconducting materials specifically based on copper indium selenium (CIS) and copper gallium selenium (CGS) have become promising materials for fabrication of thinfilm solar cells owing to their interesting structural and optical properties [1,2]. CIS and CGS are direct band gap and have a strong optical absorption coefficient and high term stability against photo degradation [3,4]. Solar modules based on CIGS offer an excellent optical properties, high conversion efficiency, low production cost and long-term durability and are considered to be competitive with current silicon technology [5]. Best record efficiencies of 19.9 [6]

and 20.3% [7] have been achieved at the National Renewable Energy Laboratory (NREL), USA, and the Centre of Solar Energy &

Hydrogen Research (ZSW), Germany, respectively. There is a great interest on fabrication technology of the chalcopyrite CuIn1- xGaxSe2solar cells. CIGS thinﬁlms have been elaborated using diﬀerent techniques including, selenization of sequentially stacked precursors [8], physical evaporation [9] and rapid thermal process [10]. On the other hand, some theoretical performances are found

https://doi.org/10.1016/j.ijleo.2018.05.044 Received 24 March 2018; Accepted 10 May 2018

⁎Corresponding author at: Applied Materials Laboratory, Djillali Liabes University of Sidi Bel Abbes, 22000, Sidi Bel Abbes, Algeria.

E-mail address:moufdi84@yahoo.fr(M. Hadjab).

Optik - International Journal for Light and Electron Optics 169 (2018) 69–76

T

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by Heriche et al. [11], Arbouz et al. [12], Benmir [13], Parisi et al. [14], Bhuiyan et al. [15] and Chen et al. [16]. The authors have reported eﬃciencies of 16.4–22.3%, for the heterojunction based on CIGS thin solar cells using the numerical simulation tools [11–16].

The current research work is an attempt to investigate the structural, electronic and optical properties of CuIn1-xGaxSe2in the chalcopyrite phase withx= 0 and 1 keeping in view the application of these materials in advanced optoelectronic devices.

2. Computational details

The structural, electronic and optical properties of the CuInSe2and CuGaSe2compound semiconductors in chalcopyrite phase have been investigated by employing full potential linearized augmented plane wave (FP-LAPW) method [17] to solve the Kohn- Sham equations within framework of Density Functional Theory (DFT) [18,19] using Wien2k tool. The atomic configuration of both cell structures in 2D/3D is presented inFig. 1. The local density approximation (LDA) has been applied for exchange and correlation potential [20,21] to compute the structural and electronic properties; {lattice constants, internal cell parameter, bulk modulus,first derivative pressure, gap energy values, band structures and total density of stats} for both materials. Semi-local Becke-Johnson potentiali.e.mBJ [22] was used to investigate the electronic and optical properties; {optical dielectric function, refractive index, reflectivity, absorption coefficient} of ternary compounds.

The product of smallest radii of the muffin-tin (MT) sphere and maximum K-vector in the Brillouin Zone (BZ)i.e.RMT×KMAXwas taken as 8 for plane wave expansion. The cut-offfor the Fourier-expanded charge density (GMAX) was truncated at 14. The expansion in spherical harmonic functions inside non-overlapping muffin-tin spheres (lMAX) was expanded to 6 in order to keep the same degree of convergence. The RMTvalues were taken to be 2.0, 2.2, 2.05 and 2.1 atomic units for Cu, In, Ga and Se, respectively. For the irreducible wedge of the BZ, a grid of 10 × 10 × 10 meshes (1000 k-points) was used. However, for optical calculations, denser meshes with 2000 k-points were used. Self-consistent convergence was obtained for energy≤10⁻⁴Ryd.

Fig. 1.Graphical presentations in 2D/3D of chalcopyrites: a) CuInSe₂and b) CuGaSe₂.

M. Hadjab et al. Optik - International Journal for Light and Electron Optics 169 (2018) 69–76

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3. Results and discussion

The structural properties such as equilibrium lattice constants; a and c, bulk modulus B, and itsﬁrst pressure derivative B have been investigated byﬁtting the Murnaghan’s equation of state (EOS’s) [23] to obtain the total energies versus volume curves within LDA approximation.

All considered compounds have the chalcopyrite structure and space group I-42d.Figs. 2 and 3represent the energy-volume curves and c/a ratio. The energy was calculated by changing systematically the volume V0and c0/a0. The energy-volume curves are obtained byﬁtting Murnaghan’s equation of state to the computed total energies and 4th degree polynomial equation for each material, separately. The bulk modulus Bₒ, equilibrium lattice constants (a, c and a/c) and the internal cell parameter (u) are determined fromFigs. 2 and 3. The results of optimized structures parameters for CIS and CGS compounds are summarized inTable 1.

Consequently, optimization was carried out by considering experimental values reported earlier. Firstly, the internal parameter‘u’

is obtained using relaxation (minimization) of the initial crystal structures of both materials using experimental values of‘a’and‘c’.

Secondly, total energy was plotted as a function of volume and afterfitting EOS values are obtained. Thirdly, total energy was plotted as a function of c/a ratio and calculated values werefitted to the 4th degree polynomial equation to obtain c/a ratio. Finally, volume expression was utilized to obtain thefinal structural parameters of the compounds.

The viability of these chalcopyrite materials in various optoelectronic devices requires a profound understanding of their electronic properties such as band structure, energy gap (Eg) and the density of states (DOS). The band gap values assessed using LDA and mBJ approximations along the high symmetry direction in BZ are shown inFig. 4. The maxima of valence band and minima of the conduction band are located at same k-value conﬁrming the direct band gap nature of these chalcopyrite crystals.Table 2presents a comparison of band gap values with already reported experimental and theoretical studies. The use of mBJ scheme enhances the value of band gap energy.

The optical properties such as dielectric function, optical conductivity, refractive index, reflectivity and absorption coefficient of both materials in chalcopyrite structure were calculated according to the mBJ approximation because of the optimized band-gap values. A dense mesh of 2000 k-points with half-width broadening of 0.2 eV is taken to be was used to investigate the precise optical properties [31]. The complex dielectric functionε(ω) of semiconducting materials given by:ε(ω) =εreal(ω) + iεimaginary(ω) can help to calculate other optical parameters such as the absorption coefficientα(ω), refractive index n(ω) and reflectivity R(ω). Imaginary part of the dielectric function is given as:

∫

∑

= −

ε ω e

πm ω M k δ ω k ω d k

( ) [| ( )| [ ( ) ]]

imaginary c v c v

2ℏ

2 2 , 2

, 3

(1) Fig. 2.Calculated total energy as a function of unit cell volume for chalcopyrites; a) CuInSe2and b) CuGaSe2.

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The integral is over the BZ, where Mc,v (k) is the dipole moment presenting the direct transitions between valence and conduction bands.ωc,v(k) = Eck-Evkis the transition energy, the real partεreal(ω) can be obtained from the expression ofεimaginary(ω) by using Kramer–Kroning equation [32,33]:

∫

= + ′ ′

′ −

∞

ε ω

πp ε ω dω

ω ω

( ) 1 2 ( )

real

imaginary 0

2 2

(2) The optical properties such asα(ω), n(ω) and R(ω) can be extracted by using the following relations [34] :

= + −

α ω( ) 2 [ [ω εreal( )ω2 εimaginary( )ω2 εreal( )] ]ω 1

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= + +

n ω( ) [[εreal( )ω2 εimaginary( ) ]ω2 1/2 εreal( )]/2ω

(4) Fig. 3.Calculated total energy as a function of c/a ratio for chalcopyrites; a) CuInSe2and b) CuGaSe2.

Table 1

Calculated structural properties according to LDA approximation for both CIS and CGS chalcopyrite structures, compared with experimental and other theoretical works.

Structural parameters a(Å) c/a c(Å) u B(GPa) B’

Materials

CuInSe2(Present work with LDA) Expt. Ref. [24]

Expt. Ref. [25]

Theo. Ref. [26]

Theo. Ref. [27]

Theo. Ref. [28]

5.71 5.78 5.873 5.862 5.91 5.733

2.011 1.998 1.972 2.012 1.96 1.988

11.484 11.55 11.583 11.792 11.583 11.40

0.215 – – 0.22 0.244 0.25

70.562 – – 64.01[29]

– 53.22

4.978

CuGaSe2(Present work with LDA) Expt. Ref. [24]

Expt. Ref. [25]

Theo. Ref. [26]

Theo. Ref. [27]

Theo. Ref. [28]

5.5 5.61 5.604 5.665 5.709 5.542

1.99 1.961 1.978 1.983 1.946 1.957

10.946 11.00 11.089 10.60 11.112 10.84

0.241 – – 0.247 0.244 0.25

76.754 – – 69.31[29]

– 57.84

4.941

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= + − + + R ω( ) [ εreal( )ω2 jεimaginary( )ω 1 / εreal( )ω2 jεimaginary( )ω 1 ]2

(5) The optical properties have been investigated under two type of polarizationsi.e.ordinary alongx, ydirection (E⊥c) and extraordinary alongzdirection (E//c).

Fig. 5shows the plots of real part dielectric function and photon energy for both chalcopyrite compounds ranging from 0–15 eV.

The zero frequency limitε1(0) is a signiﬁcant quantity actually governed by the band gap of the material. The computed values of ε1(0) using mBJ approximation are listed inTable 3which are in good agreement with theoretical and experimental results obtained under ordinary and extraordinary polarization for both chalcopyrite compounds. The imaginary part of dielectric functionε2(ω)

Fig. 4.Band structure and TDOS for both chalcopyrites; a) CuInSe2and b) CuGaSe2within mBJ approximation.

Table 2

Calculated Band gap (Eg) within LDA and mBJ approximations for CIS and CGS chalcopyrite structures, compared with experimental and other theoretical works.

Materials Eg [eV]

Present work Expt. / theo. data

LDA mBJ Expt. Theo.

CuInSe2 0.00 0.55 0.98 [30] 0.31 [26]

0.41 [26]

0.26 [28]

CuGaSe2 0.20 1.27 1.68 [30] 0.82 [26]

2.58 [26]

0.83 [28]

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depicts various inter-band transitions between valence and conduction band (Fig. 6). The transparency of semiconducting materials cab be evaluated by refractive index n(ω) which an important optical parameter to access the viability of the material in fabrication of thinﬁlm solar cells [35].Fig. 7displays n(ω) curves for both ternary compounds for photon energy up to 16 eV. These values are obtained within mBJ approximation and are listed inTable 3. Refractive index has peak value for photon energies within the visible region.Fig. 8shows that absorption coeﬃcient when plotted against photon energy ranging from 0–15 eV, depicts enhanced optical absorption for wide range of energiesi.e.from 1–11 eV. The appearance of few absorption peaks resulted from inter-band transitions suggests that semiconducting chalcopyrite materials are good when absorption in the visible region is required.

Fig. 5.Real part of dielectric function for the chalcopyrites; CuInSe₂and CuGaSe₂.

Table 3

Calculated optical dielectric constant, static reﬂectivity and static refractive index for the chalcopyrite’s CuInSe₂and CuGaSe₂within mBJ approximation compared with published works.

Static parameters ε1(0) R(0) n(0)

Materials E⊥c E//c E⊥c E//c E⊥c E//c

CuInSe2(Present work with LDA) Theo. Ref. [26]

Theo. Ref. [27]

Theo. Ref. [28]

8.95 – 10.55 8.15

8.44 – – –

0.25 0.26 – –

2.90 – – –

2.99 – 3.25 4.04

0.24 – – – CuGaSe2(Present work with LDA)

Theo. Ref. [27]

Theo. Ref. [28]

7.90 9.72 7.64

7.82 – –

0.22 – –

2.8 – –

2.81 3.12 3.91

0.22 – –

Fig. 6.Imaginary part of dielectric function for the chalcopyrites; CuInSe₂and CuGaSe₂.

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Fig. 7.Refractive index for the chalcopyrites; CuInSe₂and CuGaSe₂.

Fig. 8.Absorption coeﬃcient for the chalcopyrites; CuInSe₂and CuGaSe₂.

Fig. 9.Reﬂectivity for the chalcopyrites; CuInSe₂and CuGaSe₂.

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The reflectivity of light R(ω) is also an important optical parameters when studying semiconducting materials for solar cell applications. The low values of reflectivity (Fig. 9) from the surface for proposed semiconducting chalcopyrite materials would make them good candidate for optoelectronic applications. The values of reflectivity obtained using mBJ functional for photon energy up to 15 eV are listed inTable 3.

4. Conclusion

In summary, density functional theory based calculations have been carried out to investigate the structural, electronic and optical properties of CIS and CGS chalcopyrite materials. The implementation of FP-LAPW method with LDA approximation and modiﬁed semi-local mBJ functional seems an appropriate methodology to optimize structural and optical parameters.

The observed values of energy gaps are close enough to those obtained experimentally and much better than theoretically reported results. The values of optical dielectric function, refractive index, reﬂectivity and absorption coeﬃcient obtained via mBJ revealed that these CIS and CGS chalcopyrite materials have potential to become an attractive material for solar cell applications and advanced optoelectronic devices.

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