Electronic, optical and thermoelectric properties of bulk and surface ...

Accepted Manuscript Electronic, optical and thermoelectric properties of bulk and surface (001) CuInTe2: A first principles study D.P. Rai, Sandeep, A. Shankar, Anup Pradhan Sakhya, T.P. Sinha, P. GrimaGallardo, H. Cabrera, R. Khenata, M.P. Ghimire, R.K. Thapa PII:

S0925-8388(16)34372-9

DOI:

10.1016/j.jallcom.2016.12.443

Reference:

JALCOM 40366

To appear in:

Journal of Alloys and Compounds

Received Date: 24 September 2016 Revised Date:

14 December 2016

Accepted Date: 31 December 2016

Please cite this article as: D.P. Rai, Sandeep, A. Shankar, A.P. Sakhya, T.P. Sinha, P. Grima-Gallardo, H. Cabrera, R. Khenata, M.P. Ghimire, R.K. Thapa, Electronic, optical and thermoelectric properties of bulk and surface (001) CuInTe2: A first principles study, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2016.12.443. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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ACCEPTED MANUSCRIPT Electronic, optical and thermoelectric properties of bulk and surface (001) CuInTe2 : A first principles study D. P. Rai,1, ∗ Sandeep,2 A. Shankar,3 Anup Pradhan Sakhya,4 T. P. Sinha,4 P. Grima-Gallardo,5 H. Cabrera,6, 7 R. Khenata,8 M. P. Ghimire,9 and R. K. Thapa2 1

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Department of Physics, Pachhunga University College, Aizawl, India-796001 2 Department of Physics, Mizoram University, Aizawl, India-796009 3 Department of Physics, University of North Bengal, Darjeeling, India-734013 4 Department of Physics, Bose Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata, India-700009 5 Centro de Estudios en Semiconductores (C.E.S.), Departamento de Fsica, Facultad de Ciencias, Universidad de Los Andes, Mrida 5101, Venezuela 6 Centro Multidisciplinario de Ciencias, Instituto Venezolano de Investigaciones Cientficas, Mrida 5101, Venezuela 7 SPIE-ICTP Anchor Research in Optics Program Laboratory, International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste 34151, Italy 8 Laboratoire de Physique Quantique de la matire et de Modlisation Mathmatique (LPQ3M), Universit de Mascara, Mascara, Algeria-29000 9 Condensed Matter Physics Research Centre, Butwal-13, Rupandehi, Lumbini, Nepal (Dated:)

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The electronic, optical and thermoelectric properties of bulk and surface of CuInTe2 were investigated by first-principles calculation based on full potential linearized augmented plane wave (FP-LAPW) method. The electron-exchange correlation is taken as generalized gradient approximation (GGA). To improve the energy band gap a modified version of semi-local orbital independent potential called modified Becke Johnson (mBJ) potential is used. The calculated energy band gap of CuInTe2 is in good agreement with available experimental and theoretical results. Both the bulk and surface of CuInTe2 is a direct band gap semiconductor, shows a transition along (Γ − Γ) symmetry point. The calculated band gap of surface and bulk within GGA/mBJ are 0.38/0.63 eV and 0.75/1.13 eV, respectively. This shows an optical interaction of materials at UV range, which can exploited as a heterojunction absorptive layer for solar cell materials. The thermoelectric properties were also calculated based on the Boltzmann semi-local transport theory. The sharp and flat bands along (Γ − Γ) in bulk and surface is responsible for high value of Seebeck coefficient and electrical conductivity, respectively. The higher value of Seebeck coefficient and electrical conductivity is a key to enhance the thermoelectric efficiency.

I.

INTRODUCTION

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The current research in material science is mainly focused in the search and designing of multi-functional materials. In last decades varieties of materials have been studied by various experimental and theoretical methods. Like Heusler compounds for spintronic[1], Spinel for energy storage electrochemical cell[2], Skutterudite for thermoelectric[3], Perovskite for solar cell[4], ferroelectric[5], etc. Among all CuInTe2 is the prospective ternary semiconductor material with chalcopyrite structure. The chalcopyrite compounds CuInX2 where X stands for S, Se, Te, As, Sb etc which shows specific tetrahedral environment [6]. The bulk and thin film chalcopyrites have been extensively studied in recent years due to their unique thermal, optical and electronic properties which can be exploited in the electronic and optoelectronic devices. Also there are several reports on experimental work of CuInTe2 films as a photo-voltaic devices, due to high energy conversion efficiency [7]. The CuInTe2 films are fabricated through many methods such as microwave irradiation, polyol synthesis, silicate matrix method, etc. [8–10]. A semiconductor chalcopyrites (Cu-III-VI2 ) is a key material in multi-junction thin-film solar cells [11–13]. The thin-film

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Corresponding author, E-mail: [email protected]

multi-junction such as ZnO/CdS/CuInSe2 showed high solar energy conversion efficiency up to 14% [14]. Some Cu-based chalcopyrites such as CuInX2 (X = Te, Se, S) and CuAlTe2 have both p and n-type conductive [15–17] and can be altered from one type to another by doping [18]. In many studies CuInTe2 was found to have a very high absorption coefficient (α = 104 -105 cm−1 ) and an energy gap in the range (0.93-1.06)eV, being very close to the optimum for solar energy conversion [19–21]. Thus CuInTe2 can be a potential absorber layer in hetero-junction devices with other semiconductors [22]. Termsaithong et al. found decreased in band gaps from 0.73 to 0.64 eV in Boron doped CuInTe2 thin film, using the successive ionic layer adsorption (7-9 nm) reaction (SILAR) technique on the TiO2 electrode and reported the photo-voltaic performance of 0.18% as compared to undoped system 0.02% [23]. Despite of numerous experimental work on the thin films, very few theoretical studies have been conducted on the surface and ultra-thin film structures of CuInTe2 . Other than its effective response to light energy for potential application in optoelectronic, it has also been stimulated well to the heat energy. The generation of electric potential with applied heat (thermoelectric) is an innovative way to dealt the ever-growing depletion of traditional fossil fuels. However, commercial application of thermoelectric material is limited due to low conversion efficiency [24], which is usually determined by the dimensionless figure of

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also be considered as ultra-thin film. The surfaces of CuInTe2 surfaces at different faces (001, 010, 101, 111, 110) are presented in Fig.1(b). We performed a scf calculation to check the minimum energy at 0 K for [010], [101], [111], [001], [110] faces. The calculated total energy of different surfaces are represented in order as, [001] < [010] < [101] < [111] < [110]. The surface [001] is found to be the most stable structure with the minimum energy [Fig.1(b)]. The ground state relaxed structure was performed by volume optimization method based on the Murnaghan0 s equation of states [56]. The volume versus energy plot is shown in Fig.1(a). The calculated lattice parameters are a=0.6311(nm) and c=1.263(nm), in good agreement with the previous report a=0.6195(nm) and c=1.242(nm)[23]. For the surface the optimized lattice constants are a=0.606 (nm) and c=2.516 (nm). The electronic structures are calculated by FP-LAPW method based on KSDFT, as implemented in the WIEN2K package [54]. The electron-exchange and correlation are described within GGA. To improve the electronic band gap of CuInTe2 , a modified Becke and Johnson exchange potential (TB-mBJ) is implemented. The non-spherical contributions to the charge density and potential within the muffin tin (MT) spheres are considered up to lmax = 10 (the highest value of angular momentum functions). The cut-off parameter is RM T x Kmax =7 where Kmax is the maximum value of the reciprocal lattice vector in the plane wave expansion and RM T is the smallest atomic sphere radii of all atomic spheres. In the interstitial region the charge density and potential are expanded as a Fourier series with wave vectors up to Gmax =12 a.u−1 . The kmesh of dimensions 10×10×10 was generated for bulk from Monhkorst-Pack scheme [55] for Brillouin-zone integrations by using 1000 k-points. For the slabs, geometry (6×6×1), (8×6×1), (4×6×1), (6×4×1) and (6×6×1) k-meshes were generated for (001), (010), (101), (110) and (111) surfaces, respectively. The criteria for the convergence of the selfconsistent DFT calculation is 0.001 eV in total energy. The formation energy (∆ Ef ) is also calculated to examine the ground state alloying stability of CuInTe2 . The negative value of ∆ Ef indicates stronger bonding and more alloying stability of the crystal [57]. The energy of formation (∆ Ef ) of a compound CuInTe2 is calculated by subtracting the sum of the energies (ECu +EIn +2ET e ) of pure constituent elements in their stable crystal structures from the total energy (Ef ) of the compound. Therefore, the ∆ Ef of the compound CuInTe2 is calculated using the following expression [32, 58]:

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merit, ZT = S 2 σT /κ where S is the Seebeck coefficient; σ is the electrical conductivity; T is the absolute temperature and κ is the electronic thermal conductivity[25–27]. Several researchers have studied a diverse variety of thermoelectric (TE) materials, such as Bi2 T e3 , PbTe, Cu2 S, Cu2 Se, skutterudites, Heusler compounds and clathrates [28–33]. Moreover, the search for novel, highly efficient and cost effective material is always an open challenge. More recently, the semiconductor chalcopyrites (Cu-III-VI2 ) show a remarkable thermoelectric (TE) efficiency. The ZT values of CuGaTe2 are 1.4 and 1.69 calculated from experiment [34] and theory [35, 36] at 950K, respectively. These values are well above the bench mark value ∼ 1 and in comparison with the conventional thermoelectric materials like Bi2 T e3 [37] and PbTe-based compounds [38]. The band energy modification near Fermi energy (EF ) through super-lattice, thin film and doping of heavy elements has been successful in improving the thermoelectric performance of the Cu(Al,In,Ga)Se/Te2 [39, 40]. While, to optimize the figure of merit in relation to pivotal material’s property, electronic band structure is to be considered. The materials’ structure should be rigid with high melting point within the working temperature as far as waste heat recovery is concerned. This motivates the present study of evaluating the insight of a material’s properties for their technological application. Therefore, we have performed the full potential linearized augmented plane wave (FP-LAPW) method based on density functional (DFT) calculations to analyze the influence of the energy band near EF . The electronic structures especially the energy band gap are poorly defined within traditional DFT (LDA/GGA) [41] which is due to the lack of their mix bonding, as it fails to account the electrons residing in the interstitial region. Therefore, we have implemented a most widely recommended and an orbital independent exchange semi-local potential which is obtained by modifying Becke and Johnson exchange potential called TB-mBJ [42– 44] to obtained an accurate electronic structure and energy band gap. There are many current reports where TB-mBJ has accurately determined the electronic band structures, undertaken in semiconductor BeX (X = S,Se, Te)[45], double perovskites Ba/Sr2 FeReO6 [46], full-Heusler alloy Co2 VSb [47], X-Phosphides/Nitrides (X = B,Al, Ga, In) [48, 49] zinc blend transition metal [50, 51], topological half-Heusler (THH) [52] etc.

II.

COMPUTATIONAL DETAILS

The primitive cell of CuInTe2 is of tetragonal structure (space group I-42d) with Cu-In8 and Cu-Te4 octahedral. The unit cell structure of CuInTe2 generated from a 3D visualization program package (VESTA)[53] is presented in Fig.1(a). On the other hand, the model different surfaces (slabs) are formed by 3x3x3 supercell. A vacuum of 1.5 nm is considered to avoid the repetition of unit cell and break the crystal symmetry along the z-plane, as a result the interaction of atomic wave function is discontinued. The repetition of the unit cell allows only in x-y plane. Thus the 2D CuInTe2 surface terminated with Cu-In. The 2D CuInTe2 surface can

∆Ef =

Ef − (ECu + EIn + 2ET e ) (1 + 1 + 2)

(1)

The calculated volume, bulk modulus, lattice constant, individual energies of element (Cu, In, Te), formation energy and ∆Hf = ∆Ef /Vol (eV/a.u.3 ) of CuInTe2 (bulk and surface) are presented in Table I. III.

RESULT AND DISCUSSION

Here, we intend to study the comparative effect of bulk and surface (001) on the physical properties of CuInTe2 . The

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FIG. 1. (a) Crystal structure and Volume Vs Energy curve (b) Orientation of Surfaces with at different total energies.

c/a System Bulk Surface *Ref[23]

Vol.(a.u.3 ) 1697.179 7070.542

B (GPa) 46.012 47.379

Present

Expt.

1.263 0.631 2.516 0.606

1.242 * 0.619 2.531 0.610

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TABLE I. Volume of unit cell, Bulk modulus, c/a, Individual energies (Cu, In, Te), ∆Ef (eV), ∆Hf = ∆Ef /Vol (eV/a.u.3 )

Cu -14844.362 -59232.665

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optimized lattice parameters are used to calculate the electronic, optical and thermoelectric properties of CuInTe2 . As we know the GGA gives poor interpretation of electronic band structures. Thus the partial density of states (PDOS) calculated form TB-mBJ for both bulk and surface is presented in Fig.2(a-d).

Bond length 3.084 1.542 1.763

∆X 0.04 0.45 0.41

If 0.10 4.90 4.10

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Bond Cu-In Cu-Te In-Te

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˚ ∆X (eV), Ionic fraction (If ) in % TABLE II. Bond length (A),

A.

Character Covalent Ionic Ionic

Electronic properties

In this section we have discussed the electronic structure of bulk and surface of CuInTe2 . The atoms participating in the formation of crystal structure forms a 3D cage with Cu sitting at the corner with In and Te atoms residing along side in the tetrahedral voids. CuInTe2 is a direct band gap semiconductor with Eg =1.02 eV [59, 61, 62] which is smaller than that of CuInS2 [63] and CuInSe2 [64]. The reason for low band gap

In -43914.155 -2130453.382

Energy (Ry) Te -49225.246 -197019.120

∆Ef (Ry) -247211.688 -145365.055

∆Hf 145.656 -20.5632

is due to the longer Cu-Te bond, presumably result in weaker p−d hybridization and low electro-negativity of Te atom gives stronger chemical bond as well [65]. However CuInTe2 exhibit a mixture of ionic and covalent bonds. The ionic or covalent character of a bond can be determined from the difference in electro-negativities of the two atoms as shown by Eq. 2 [67] If = 1 − exp−

∆X 2 4

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where ∆X=XA -XB , XA and XB are the electronegativities of two atoms. The ionic character of Cu-In, CuTe and In-Te are calculated in terms of % and presented in Table II. Cu-In bond gives the lowest ionic character due to their low value of difference in electro-negativities. Also evident from the electron density plot which shows a covalent bonding between Cu-In as presented in Fig 3. In all cases the Cu-d10 occupies the valence band between -2.5 eV to 0.00 eV [Fig.2(a,b)]. The maximum contributions are found in the range of -1.0 eV to -2.5 eV due to Cu (d-eg + d-t2g ). While In-p and Te-p shows significant contribution, mostly below -3.0 eV. The presence of sharp bands in the conduction region are due to the In-p and Te-p states [Fig.2(a)]. The localized Cu-d hybridizes with Te-p/In-p states just below the EF , to form a bonding, which shifts the energy band below EF in the valence region, while a corresponding anti-bonding is formed in the conduction band giving rise to a band gap

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TABLE III. Energy band gap and Static dielectric constant ε1 (0) of CuInTe2 (bulk & surface)

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FIG. 3. Electron density plot of bulk CuInTe2 in 100-plane

[60]. Thus the direct band gap is formed due to the hybridization between Cu d-t2g and Te-p states along Γ − Γ symmetry [Fig.4(a)]. The calculated band gap of a bulk material is 0.75 eV within GGA, underestimated as compared to experimental value 1.02-1.12 eV [19, 61]. While, implementing an orbital independent semi-local exchange potential called modified Becke Johnson (TB-mBJ) potential a band gap has been improved to 1.13 eV, in better agreement with the experimental data [Fig.2(b)]. The earlier report confirmed a strong quantum confinement effect in CuInTe2 due to large Bohr atomic radius than CuInS2 and CuInSe2 [10]. The concept of quan-

Static dielectric constant [ε1 (0)]

Expt. 0.94c 0.83d

Bulk-xx/zz Surface-xx/zz 14.5/13.0 11.0/10.0 10.5/8.5 6.4/5.8

tum confinement is considered as the minimization of material’s dimension up to the wavelengths of the electrons in the sample. The quantum confinement obviously alter the electronic structure which changes the optical properties from the bulk material. For a higher dimension material (bulk) whose size is lot more larger than the electron’s wavelength gives continuous spectrum of energy band. The minimization of material’s structure to a nano-scale will change the continuous energy spectrum to discrete energy levels, which will facilitated the charge transfer due to trapping of optimum incident energy. The calculated electronic structure of surface shows the flat and dense bands with decreased in magnitude of energy band gap along Γ − M symmetry [Fig.4(b)]. The calculated band gap of surface within GGA and TB-mBJ are ∼ 0.3 eV and ∼ 0.63 eV, respectively. The surface’s band gaps are compared with the experimental band gap of thin film (7-9)nm 0.83 eV[23]. Though the surface thickness is not justified as it is an ultra thin film. The calculated band gaps of bulk and surface are tabulated in TableIII

B.

Optical properties properties

Optical properties of a solid state material indicates the interaction of the incident photon with the atoms, considered as

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where (¯ hω) is the plasma energy. Figs. 5(a-d) displays the calculated real-imaginary dielectric function and EEL-Abs as a function of photon energy of bulk and surface respectively. The static dielectric function ε1 (0) is inversely related with the square of the energy gap (Eg ) so the higher value of ε1 (0) gives low band gap [68]. The static dielectric function ε1 (0) of a bulk material is maximum within GGA as compared to mBJ, also εxx (0) > εzz (0) [Fig.5(a)]. The calculated value of ε1 (0) is tabulated in TableIII. The smaller magnitude of ε1 (0) in surface (001) as compared to the bulk gives smaller value of energy band gap [Fig.5(c)]. The slow rise of ε1 (ω) at an energy range 0.0−2.0 eV indicates the interaction of material with the photons. In bulk, the sharp peaks of ε1 (ω) occurs at 0.80 eV and 1.3 eV within GGA and mBJ, respectively, but for the surface the mean peak shift towards lower energies with lower magnitudes, Fig. 5(c). A group of three smaller peaks appear in the range from (2.0-5.0) eV. After that ε1 (ω) decreases sharply and becomes negative in the short energy range from 4.5-5.5 eV, where the phonon is damped, reaches a minimum and then slowly increases at high energy. The imaginary part is related to the band structure and describes the absorptive behavior. Fig.5(a, c) shows the imaginary part of dielectric function of bulk and surface, the optical response occurs at approximately 0.5-6.5 eV, representing the threshold value for direct optical transition from VB Cu (d-t2g ) to CB (Te-p) which may be considered along Γ − Γ point. The presence of numerous sharp peaks denoted by 1,2,3,4,5,6 of ε2 (ω) spectral lines indicates the abrupt increase in number of transitions. The first peak occurs at ∼ 1.5 eV, originated from the direct transition along Γ − Γ point, the second peak occurs at ∼ 2.5 eV form L-L and the third highest peak at ∼ 4.0 is possibly from direct transitions along X-X point. After calculating the imaginary and real parts of the dielectric function, the optical absorption coefficient α(ω) and energy loss function (EEL) were calculated. Fig.5(b,d) represents the graph of electron energy loss (EEL) as a function of photon energy. The EEL is an important parameter to define the nonscattering and elastically scattering of electrons (zero energy

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an optical response of a material which can be described by dielectric function, ε(ω). The optical properties are in close relation with the band structures of a semiconductor and the inter band transitions are considered. In the present work, all the spectra are plotted against the incident energy perpendicular (xx) and parallel (zz) to the tetragonal c-axis of the crystal. The dielectric function ε(ω) of a material depending on the frequency has some important role in determining the physical properties of solids. It has two parts real (ε1 ) and imaginary (ε2 ) [68]. The real part and imaginary part of the dielectric function are calculated using the Kramers-Kronig relations [45, 69–71].

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where P denotes the principal part of the integral, ωnn0 is the energy difference between the two states, dSk is an energy surface with constant value and Pnn0 is the dipole matrix element between the initial and final states. The real part of the absorption coefficient (Abs.) is given by √ α(ω) = 2ωk(ω) = 2ω[(ε1 (ω)2 + ε2 (ω)2 )1/2 − ε1 (ω)]1/2 (6) Similarly the absorption coefficient can be calculated from Beer’s law is α = 2kω = 4πk c c . While the electron energy loss function (EEL) [72] is given by 1 ε2 lm( ) = − 2 ε ε1 + ε22

(7)

The static dielectric function ε1 (0) and low ε1 (ω) are strongly depend on the semiconductor0 s band gap. Penn model relating the inverse relation with band gap Eg [73] 2 ε1 (0) ∼ = 1 + (¯hωp /Eg )

(8)

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loss). At energy range (8.00-14.00 eV) the energy losses are mainly due to the mixture of single electron excitations and collective excitations (plasmons). The prominent peak appears at high energy 12 eV. We have observed that the peak in the EEL corresponds to a low flat spectral line in the absorption coefficient which indicates the electron scattering at that energy range Fig.5 (b,d). In Fig. 5(b), the optical absorption peaks shows the strong absorption of the photon energy in the range (2.0-8.0) eV which is in consistent with the ε2 (ω). This shows that the compound CuInTe2 is optically active. Also the surface absorb all the UV-range between 1.5 eV and 8.0 eV. Thus the surface/ultra-thin film of CuInTe2 can be a potential absorptive layer in the photo-voltaic solar cell devices.

C.

Thermoelectric properties

The temperature dependent Seebeck coefficient S, thermal conductivity (κ), electrical conductivity (σ) divided by the scattering time (τ ) are calculated from Boltzmann semiclassical transport equation as implemented in computational code called BoltzTrap [74]. Eq.9 interprets electrical conductivity tensors [75]:   ∂f0 (T, ε, µ) σα,β = e2 Σi,k − vα vβ τk ∂ε

(9)

where α, β are the tensor indices, vα and vβ are the group velocities, e is the electron charge and τk is the relaxation time. The electrons contribution remain near the chemical potential (µ) in a narrow range of µ − kB T < ε < µ + kB T , where kB is the Boltzmann constant [76]. The transport distribution

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FIG. 6. (a) Seebeck coefficient (S) (b) Electrical conductivity (σ/τ ) (c) Electronic thermal conductivity (κ/τ ) & (d) Figure of merit (ZT).

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(10)

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which is the kernel of all transport coefficients. From the rigid band approach, the electrical conductivity, thermal conductivity and Seebeck coefficient can be written as a function of temperature (T ) and chemical potential (µ) by integrating the transport distribution [78] as presented in Eq. 11,12,13   Z ∂f0 (T, ε, µ) 2 dε (11) σ=e Ξi,k − ∂ε

κ=

2 kB T

ekB S= σ



Z Ξi,k

ε−µ kB T



Z Ξi,k

2   ∂f0 (T, ε, µ) − dε ∂ε

(12)

  ∂f0 (T, ε, µ) − dε ∂ε

(13)

ε−µ kB T

Here f0 is a Fermi-Dirac distribution function. The thermoelectric efficiency of a material is in close relation with the

electronic band structure and the thermal conductivity. The code BoltzTraP include only the electronic thermal conductivity (κ) whereas the phonon contribution is neglected. The Seebeck coefficient and electrical conductivity can be gauze from the the energy bands at the vicinity of the EF . The presence of sharp band in the conduction band of a bulk mate¯2 1 rial is a signature of an effective mass ( m∗ = h¯12 ddE2 k¯ ) [18], which enhances the Seebeck effect (see Fig.4). As one can see the top of the valence band is a hybrid of both sharp and flat bands, which is favorable for thermoelectric performance[75]. Whereas, in case of the surface (001) the band energies near EF are composed of only dense and flat bands, facilitated the charge mobilities as a result a higher value of electrical conductivity [75]. The charge transfer are also initiated by the narrow bands along Γ symmetry near EF between Cu-dt2g and In-p states. The thermoelectric efficiency denoted as ZT (figure of merit) has been calculated from equation (14). ZT =

S 2 σT κ

(14)

ACCEPTED MANUSCRIPT 8 TABLE IV. calculated Seebeck coefficient S (µV /K), electrical conductivity σ/τ (Ωms)−1 , thermal conductivity k/τ (W/mKs) and figure of merit ZT of CuInTe2 with the experimental data Bulk σ/τ 5.95x1017 5.71x1017 6.68x1017 7.77x1017 8.98x1017 1.04x1018 1.21x1018 1.30x1018

κ/τ 1.59x1012 5.50x1012 1.02x1013 1.70x1013 2.72x1013 4.24x1013 6.51x1013 8.00x1013

ZT(Present/Expt.) 0.107 0.320 0.530/0.10* 0.704/0.15* 0.742/0.18* 0.762/0.28* 0.772/0.58* 0.775/0.82*

S 60 163 210 220 217 209 201 196

σ/τ 2.18x1017 3.35x1017 5.42x1017 7.81x1017 1.03x1018 1.30x1018 1.56x1018 1.68x1018

κ/τ 1.19x1012 5.29x1012 1.21x1013 2.16x1013 3.35x1013 4.48x1013 6.50x1013 7.56x1013

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S 7.670 99.730 178/257*/204** 180/275*/242** 195/278*/270** 211/300*/280** 235/260* 244/270*

ZT 0.09 0.42 0.69 0.79 0.80 0.76 0.72 0.68

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Temp (K) 100 200 300 400 500 600 700 800 *Ref:[80], **Ref:[81]

Surface

maximum calculated ZT value of surface is 0.82 at 500K. The Seebeck coefficient (S) and ZT values at temperatures (100800)K are compared with the experimental results[80, 81] and shown in Table III.

[1] J. Zhou, B. Sa, Z. Sun, C. Si and R. Ahuja, RSC Adv. 5, 7381473919 (2015).

[2] N. Garg, M. Mishra, Govind and A. K. Ganguli, RSC Adv. 5,

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The high value of ZT is related with high value of S, σ/τ and low value of κ/τ . The ZT ∼ 1 is considered to be a benchmark value for the practical application of TE-materials [79]. The calculated S, σ/τ , κ/τ and ZT are presented in Fig. 6. The presence of flat dense bands near EF of surface as compared to the bulk predicts higher values of charge carriers shown in Fig.4(a-c). In Fig. 6(a), we have observed the increasing magnitudes of S with increasing temperature, indicating more transfer of charge carrier concentrations. Our calculated results of thermoelectric parameters are compared with experimental results obtained from ZEM3/ULVAC-RIKO[80, 81] and plot of S shows the similar behavior as that of experimental plot (see Fig. 4a)[80, 81]. The absolute value of S for the bulk system at 300 K are 154 µV /K and 178 µV /K within GGA and mBJ respectively(see Table III). The calculated S values of bulk system is in good agreement with the previous experimental results 204 µV /K[81] and 257 µV /K (annealed sample for 7 days) [80]. In Fig. 6b, the electrical conductivity(σ/τ ) shows the decreasing trend up to 100 K and increases linearly with increase in temperature, showing semiconductor like behavior. The calculated σ/τ of bulk and surface at 300 K are 5.10x1017 (Ωms)−1 and 2.65x1017 (Ωms)−1 . The σ/τ cannot be compared directly with the previous experimental result of σ unless and until τ is known. The calculated electronic thermal conductivity κ/τ is plotted in Fig. 6(c). It shows that κ/τ and and σ/τ are linearly dependent so its a great challenge to decouple and control them independently. The dimensionless figure of merit ZT is calculated from the measured physical properties by using the equation 14 and is presented in Fig. 6(d). The room temperature (300K) value of ZT are 0.40(GGA), 0.48(mBJ) for bulk and 0.55 for the surface (001) in good agreement with the experimental results[80, 81]. At higher temperatures the ZT value slightly decreases for the surface, due to a decrease in S and sharp increase in κ/τ . The

IV.

CONCLUSION

In this present work, the structural, electronic, optical and transport properties of CuInTe2 is studied using Density Functional theory (DFT) within GGA and mBJ. Structural parameters are found to compare well with the available data in the previous reports. The use of GGA poorly defined band gap of ∼ 0.75 eV and ∼ 0.38 eV for bulk and surface, respectively. The GGA band gaps are wide opened up to 1.13 eV and 0.63 eV for bulk and surface respectively with the application of mBJ potential and in good agreement with the experimental values. The calculation of transport properties using Boltzmann transport equation within the constant relaxation time approximation predicts the dominant activities of p-type carrier concentrations. For p-type carrier concentration the temperature dependent thermoelectric properties of CuInbTe2 are derived. The calculated value of figure of merit (ZT) at 300K for bulk and surface are ∼ 0.53 and ∼ 0.69 respectively, in qualitative agreement with the experimental result. We have analyzed the important application of the chalcopyrite-type compounds as a potential energy converters. The presence of flat-dense band in the surface and a direct band gap matching with the near edge IR-UV range, may serve as a heterojunction absorptive layer in photo-voltaic devices. While the combination of heavy and light bands in the bulk material gives sufficient credential to increase its efficiency as a thermoelectric energy converters. Acknowledgments: DPR acknowledges UGC Start-UpGrant No.F.30-52/2014/BSR (New Delhi, India). RKT a grant from SERB-DST,New Delhi, India. APS a research fellowship from DST-INSPIRE, India.

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Highlights:

We have calculated the minimum energy of different surfaces. 001 face is found to be most stable with minimum energy. It is found that TB-mBJ enhanced the electronic band gap. The band gap matching with IR-UV gives an optical transition.

•

The thermoelectric properties are calculated from BoltzTraP.

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