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A Study of Electronic and Optical Properties of CuInSe Nanowires Payman Nayebia, Mohsen Emami-Razavi, and Esmaeil Zaminpayma J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10749 • Publication Date (Web): 08 Feb 2016 Downloaded from http://pubs.acs.org on February 17, 2016

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The Journal of Physical Chemistry

A Study of Electronic and Optical Properties of CuInSe2 Nanowires Payman Nayebia, Mohsen Emami-Razavib , and Esmaeil Zaminpayma c a

Physics Department, Saveh Branch, Islamic Azad University, Save, Iran

b

Plasma Physics Research Center, Science and Research Branch, Islamic Azad

University, P.O. Box 14665-678, Tehran, Iran c

Physics Group, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Abstract: The electronic and optical properties of the CuInSe2 nanowires have been investigated via density functional theory (DFT). We have used numerical atomic orbital bases set with local-density approximation. The norm-conserving pseudopotentials of Troullier and Martins have been used. In our calculation we used nanowires in two shapes of hexagonal and triangular with their diameters ranging from 8 to 15 Å in 1 − 10 growth direction. The geometrical parameters are in good agreement compared to other experimental or theoretical results. We show that for the nanowires there is a significant contraction of the Cu-Se and In-Se bond lengths at the edge of the wires (4.7%), as for the wires at the center, it is 2.6%. Moreover, we have investigated the band structures and atom-projected density of states of the nanowires. These studies confirm that CuInSe2 nanowires are semiconductors with a direct band gap. These studies also show the existence of hybridization between Cu-d with Se-p states in the middle valance sub-bands of the CuInSe2 nanowires. We demonstrate that for the nanowires, as the diameter of the CuInSe2 nanowire augments, its relative band gap reduces. From the projected density of states of atoms, the peaks are decreasing from edge to center of nanowires. Also, the highest valence bands involve atoms located at the surface. Finally, it is found that the values of real and imaginary part of dielectric function, absorption and refractive index of the CuInSe2 nanowires are smaller compared to the bulk ones. 1 ACS Paragon Plus Environment


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Keywords: Density Functional Theory, Semiconductor Nanowires, CuInSe2, Electronic Properties, Optical Properties.

1. INTRODUCTION Due to the particular shape and dimension of nanowires, they have very interesting properties in fundamental and applied science. The diameters of nanowire are smaller than the wavelength of light in the optical domain. Therefore, the interaction of nanowires with light may cause some new phenomena which find applications in solar cells technology, lasers, computers, and new generation of optoeleronic devices (see, for examples 1-3, and refs therein). Semiconductor nanowires have the advantages that their electronic structure can be band gap engineered by varying the size, growth direction, composition, and cross section due to the quantum confinement effects1, and the nanowires may become metallic, semiconductor or insulator by saturating with hydrogen.4,5 The quantum confinement is realized by reducing the size of a system. The effects of the confinement on the various physical properties of the nanowires have been studied by different researchers and have applications in different areas6-7, such as chemistry and physics. Some calculations have been reported by different authors about the structural, electronic, and optical properties of very small nanowires using ab initio methods such as density-functional theory (DFT).8-12 For example, Agrawal et al.8 have investigated the structural, electronic and optical properties of ultrathin bismuth nanowires. As pointed out in their ab initio study8, they have obtained 14 stable Bin (n = 1, 6) wire configurations. They8 also observed that all the wire configurations display noncrystalline bulk atomic structures, and concluded that

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the inclusion of spin–orbit coupling in their computations greatly influences all the physical properties of the wires. Moreover, Dai et al13 investigated electronic structures, magnetic properties, and spin-dependent electron transport characteristics of C-doped ZnO nanowires by using first-principle methods based on DFT with Perdew-Burke-Ernzerhof (PBE) generalized gradient approximations (GGA) and nonequilibrium techniques of Green’s functions. Durgun et al.14 reported a DFT calculation using the projector augmented wave (PAW) potentials. They14 have investigated the atomic, electronic, and magnetic properties of hydrogen-saturated silicon nanowires that are considerably doped by transition metal (TM) atoms placed at different interstitial and substitutional sites. Iacomino et al.15 have carried out first-principles computations on anatase TiO2 nanowires to examine the dependence of their structural and electronic properties on the size, the surface coverage, and the morphology. In Ref.16, the authors reported a simple colloidal synthesis of two types of Sb2S3 nanowires with small band gap, and they investigated the nanowires’ electronic and optical properties. Because of their natural compatibility of I-III-VI2 chalcopyrite semiconductors thin film like CuInSe2 compounds (CIS) in solar cell technologies, their nanowires have significant potential for use in technologies related to photovoltaic devices. In spite of such promising applications in new instruments, relatively few ab initio calculations have been performed for the CIS nanostructures. CIS nanowires have been fabricated successfully. CuInSe2 nanowire arrays were constructed by electrode position from aqueous solutions of copper sulfate, indium sulfate, selenium dioxide, and citric acid. For this purpose the anodic alumina membranes have been used as 3 ACS Paragon Plus Environment


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templates.17 Also, Phok et al.18 reported the electrodeposition of CuInSe2 nanowires by a pulse electrodeposition method. Peng et al.19 reported CIS 1 − 10 nanowires by the synthesis of CIS single crystalline nanowires via an Au-catalyzed vapor-liquid-solid (VLS) growth. The aim of the present work is to study the dependence of the structural, electronic and optical properties of CuInSe2 nanowires as functions of the diameter size within the framework of first-principles density functional theory. To the best of our knowledge there was no paper available in the literature that studies the “optical” properties of CuInSe2 nanowires. In this manuscript, numerical atomic orbital (NAO) pseudopotential methods have been applied (as a localized basis set). The technique of calculations is as follows. First, we have computed lattice parameters, band gap, and density of states of bulk CIS. Second, we have generated CuInSe2 nanowires in the 1 − 10 growth direction for both hexagonal and triangular cross sections. Then, we have worked out structural properties, band structure and atomprojected (partial) density of states (PDOS) of nanowires. Also, optical constants of the nanowires, including the dielectric function, reflectivity, refractive index and absorption values are analyzed. 2. Materials and Methods DFT calculations have been performed with the LDA, by the Perdew and Wang (PW) exchange-correlation functional.20 The SIESTA code21 has been used in the calculations. The norm-conserving pseudopotential of Troullier and Martins22 is employed, with the valence electron configurations of H:1s1, Cu:[Ar] 4s1 3d10, Se: [Ar] 4s2 4p1 and In:[Kr] 4d10 5s2 5p1. Double zeta basis set has been applied for all atoms. 4 ACS Paragon Plus Environment

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We have achieved to obtain the structural optimization of the nanowires by shifting atoms and unit cell vectors to locate the minimal forces and stresses on them. The conditions of minimal forces and stresses are as follows: mesh cutoff energy is at 200Ry, maximum force tolerance is smaller than 0.04 eV/Å, and density matrix mixing weight is at 0.05. Also, the total energy tolerance of the subject under study is 1×10−4 eV/atom. For bulk of CuInSe2 the Monkhorst-Pack (MP) k-grid has been employed at 8 × 8 × 8 that generated 296 K points in the Brillion zone. In addition, for all nanowires a 1 × 1 × 4 k grid has been applied, causing 3 k points for both hexagonal and triangular cross-section nanowires in the Brillion zone. As it is shown in Fig. 1, nanowires are generated in the direction 1 − 10 with hexagonal and triangular cross-section with their diameters ranging from 8 to19A°.

Fig.1. Nanowires in the [1-10] direction with hexagonal and triangular cross-section



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3. Results and discussions The structural properties of the bulk CuInSe2 have been first calculated so that we examine the accuracy of our calculations. In this work the related Wyckoff locations of atoms in the unit cell, Cu (0, 0, 0), In (0, 0, 1/2) and Se (u, 1/4, 1/8) have been employed. For the standard zinc-blend lattice with the existence of two distinct cations (Cu, In), an inner distortion in the body-centered tetragonal unit cells is observed. The anion displacement parameter u measures the corresponding distortion, namely: u – 1/4 = (R2Cu-Se – R2In-Se) /a2

(1)

Where RCu-Se and RIn-Se are the bond lengths. Before relaxation, the crystal parameter is set to a=5.78 A° and after relaxation the values of crystal lattice parameters such as a, c, bond lengths, angels and u have been computed. Table 1 shows the experimental and theoretical values. Table1. The calculated and experimental structural parameters of Bulk CuInSe2 Structural properties a(A) c(A) c/a u(A) RCu-Se RIn-Se Cu-In-Se angle

Present work

Experiment

Calculation

5.7599 11.602 2.01 0.216 2.393 2.618 109.52

5.782a 11.62a 2.00a 0.232a -

5.832b 11.622b 1.99b 0.22b 2.424c 2.598c -

a.Ref 23 , b. Ref.24, c. Ref.25

As it can be seen from Table 1, our results and other calculations are in good agreement. The lattice parameters of a, c and bond lengths with our calculation are 6 ACS Paragon Plus Environment

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about 0.3% smaller than the experimental values, whereas for c/a and u parameters the corresponding numbers are quite the same. When a crystal size reduces to a nanoscale range, the surface to bulk ratio will start to dominate the electronic and mechanical properties of the material. Hence, they can be modified. For nanowires, because of surface dangling bond formation or breaking of lattice symmetry, some changes in bond length and bond angle at the edge of the nanowires will happen. For the surface atoms in the nanowires, there are only few nearest neighbors. Hence, coordination numbers will be lowered compared to the bulk material where the atoms are very much coordinated. Therefore, the bond lengths at the edge of nanowire will be smaller than those of the bulk. Equal results for constructions of bond lengths can be found in many other works.26-32 The average calculated bond lengths at the center and edge parts for nanowires in unsaturated state are shown in Table 2. One can see that the average bond lengths at the edge of the nanowires for all the ranges, and the contractions compared to the bulk values are about 4.70%. However, at the center of the nanowires it is found that the contraction is smaller than 2.6%. Similar results for constructions of bond lengths can be found in many calculations.26-32 Moreover, the contraction in the bonds at the edge of the nanowires gives rise to an analogous change in Cu-SIn bond angles, with the Cu-S-In angles of nanowires being 108.70° prior to relaxation, changing to the average amount of 110.2° following the relaxation for the edge of nanowires, and the average amount of 109.1° for the center of nanowires.



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Table2. The calculated bond lengths at the center and edge parts for the nanowires Shape and Size Triangular 26atom 44atoms Hexagonal 32 atoms 48 atoms

RCu-Se

At the center RIn-Se

RCu-Se

At the edge RIn-Se

contraction

contraction

2.419 2.384

2.654 2.637

0.55-0.1% 0.6-0.67%

2.337 2.3358

2.528 2.558

2.5-4.7% 2.6-3.9%

2.412 2.384

2.594 2.585

0.5-2.2% 2.0-2.6%

2.277 2.335

2.583 2.576

4.5-4.7% 2.18-2.9%

The values of the energy band structure along the symmetry directions and the partial density of states for the nanowires has been presented here. We found that the theoretical gap results are around 0.01eV for bulk CuInSe2 crystal in which it has a direct band gap. We have good agreement between the value of our energy gap and other theoretical results.24,33,34 However, it is obviously an underestimation of the actual band gap. This is not uncommon consequence after all since there are the usual shortcoming issues in the density functional theory.24,33,34

Fig. 2 shows the band structures near the Fermi levels of the nanowires. The energy zero is put at the highest occupied state (HOS). For the nanowires, the valence band consists of three sub-bands.


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Fig.2. Calculated band structures near the Fermi levels of the nanowires with hexagonal and triangular cross-section.

For example, for Hexa2*2 (48atoms) nanowire the topmost valance sub-bands are between the HOS (0eV) and −8 eV. The middle one is located somewhere between −11 eV and −14 eV. The lowest valance sub-bands are placed between −15 eV and −16.6eV. The top valance sub-bands are greatly dominated by the hybridization of Cu-d states with the Se-p states. Moreover, in the middle sub-band we have found a small admixture of In-d with Se-p states. Finally, the In-d states provide the major contribution to the deeply located band, which is placed around −20 eV. The hybridization of atom’s states is the same for other hexagonal and triangular nanowires.



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The band gaps have been obtained as a function of diameter and shape of the nanowire by SIESTA codes.21 The results are presented in Fig. 3. The band gap for all nanowires is larger than the bulk band gap.

Fig.3. Relative band gap (∆E ) as a function of diameter and shape of nanowires.

As the size of the nanowires augment, the band gaps reduce, reflecting the impact of quantum confinement.

In Fig. 4, the partial density of states (PDOS) for the nanowire is shown. The energy zero is placed at the highest occupied state (HOS). We have considered Copper, Indium and Selenium atoms at the edge of the nanowires and within their center for comparison purpose. In addition, we study how the PDOS varies with the nanowires’ diameters. 10 ACS Paragon Plus Environment

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Fig.4. The nanowires’ partial density of states (PDOS) plots for atoms located at the edge and center of them with hexagonal and triangular cross-section. The energy zero is set at the highest occupied state.



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As it can be seen from Fig. 4, for the Copper atoms at the edge of a nanowire, there are distinct peaks around −1.88 eV (contributed from Cu-3d) and at near -15 eV for Indium PDOS (contributed from In-4d). Also, we have two peaks which are located between -3.5 eV and -12.3 eV for Sulfur PDOS (contributed from Se-4p and Se-4s). These peaks have been decreased for the PDOS of all atoms in the nanowires’ center. These results can be observed through various ranges of nanowire diameters, both for hexagonal and triangular shaped nanowires. This means that the highest valence bands include atoms that are located at the surface. Moreover, as seen for all the atoms, the peaks are increased when the size of nanowires increases.

We compute the imaginary part of the dielectric function. Thereupon, we evaluate the matrix elements between the occupied and unoccupied wave functions (using SIESTA21):

ω =

.

-$& − ω

ћ

∑ ! < ψ%$& |( |ψ)$& > < ψ)$& +( +ψ%$& > ,-$%& −

(2),

where p is the momentum matrix element between α and β band with same crystal %

)

momentum k, ψ$& and ψ$& are the occupied and unoccupied wave functions with %

.

relevant energy of -$& and -$& . ћ is the Planck constant, e is the charge of electron, m is the electron mass, and ω is the angular frequency. It is known that the dielectric function is primarily connected with the electronic response. The imaginary part of the dielectric function depends on the band gap. 12 ACS Paragon Plus Environment

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Therefore, a scissor operator has been employed in order to fit the obtained theoretical gap values with the available experimental data. We have used the convenience of energy shift for CuInSe2 compounds. Thereupon, we have computed the real part of dielectric function using Kramers–Kronig relations. The calculated dielectric function for the CuInSe2 nanowires is presented in Fig. 5. The imaginary part spectrum have four peaks located at around 2.5 -7.5 eV for all shapes and size of the nanowires. The first peak is located at 2.53 eV, the second one at 4.16 eV, the third one at 5.38eV and the last one at 6.83eV. Compared to the CuInSe2 bulk, the energy position of almost all corresponding peaks of the dielectric function spectrum (ε (ω)) for the nanowires is blue-shifted. This can be explained because of presence of larger band-gaps in the nanowires compared to the bulk of CuInSe2.

Fig.5. The imaginary and real parts of the dielectric function for the nanowires with hexagonal and triangular cross-section. “Tri” and “Hexa” represent and “triangular” and “hexagonal ”, respectively.

In Fig. 6, we have shown the calculated value of the dispersion of the refractive index for CuInSe2 nanowires. The estimate value of n(0) for the nanowires are 13 ACS Paragon Plus Environment


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1.39, 1.82, 1.20 and 1.55 for the Hexa.2*2, Hexa.2*3, Tri.2 and Tri.3, respectively. Our calculated refractive index for the nanowires is less than the bulk value of 3.10.35 Moreover, as the nanowire’s size increases, the refractive index also increases.

Fig.6. Dispersion of the refractive index for the nanowires. “Tri” and “Hexa” represent “triangular” and “hexagonal ” , respectively.

We present the graph of optical reflectivity of the CuInSe2 nanowires with respect to different energies in Fig.7. As it can be seen in the graph, the main peaks for the nanowires have been shifted to higher energy values compared to the bulk value of


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CuInSe2. Moreover, one can see that by increasing the size of the nanowires, the reflectivity increases.

Fig.7. Reflectivity spectra for the nanowires. “Hexa” and “Tri” represent “hexagonal” and “triangular”, respectively.

The absorption spectrum and the imaginary part of the dielectric function can be related to each other. This is because of electronic transitions between the valence and conduction bands. We present the absorption coefficient spectra for the nanowires in Fig. 8. As it can be seen, the peaks corresponding to the nanowires become lower compared to their bulk value35 and they move to the higher energy locations. For example, for the first peak of bulk of CuInSe2 the corresponding 15 ACS Paragon Plus Environment


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value is around 2.20 eV35, while for the CuInSe2 nanowires, the peaks locations are as follows: 2.42 eV (Hexa.2*2), 2.39 eV (Hexa.2*3), 2.33 eV (Tri.2), and 2.23 eV (Tri.3).

Fig. 8. Absorption coefficients for the bulk and the nanowires. “Hexa” and “Tri” represent “hexagonal ” and “triangular”, respectively.

When the scissor operator is applied the absorption spectrum displays the absorption threshold which is related to its band gap result. For the nanowires, the absorption threshold is calculated at 1.20, 1.22, 1.32 and 1.24 eV for Hexa2*2, Hexa2*3, Tri3 and Tri2, respectively, while for bulk this value is about 3.21 eV.


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4. Conclusion

In this manuscript, we were particularly interested in analyzing the electronic and optical properties of CuInSe2 semiconductor nanowires using density functional theory. This material can be used for photovoltaic and nonlinear optical devices. First-principle calculations have been used in order to study the various properties CuInSe2 nanowires in the 1 − 10 growth direction using the NAO bases set with LDA approximation by SIESTA code. For bulk CuInSe2 crystal, the results obtained for the geometrical parameters such as anion displacement and lattice parameters reasonably agree with other experimental or theoretical work.

With the change in atomic positions of the nanowires by relaxation, the average bond lengths of the atoms in center of nanowires and bond angle change across the range of nanowire diameters and shapes. We have also found a considerable contraction of the Cu-S and In-S bond lengths at the edge of the wires (4.7%), while for the wires which are located in the middle, it is 2.6%.

From the band structure of the nanowire, it is found that the band gap decreases as the nanowire’s diameter increases. Moreover, from PDOS we can see that in the nanowires, the peaks are decreasing from the edge to the center of nanowires, and they increase while the nanowire’s diameter increases. Also, the highest valence bands involve atoms which are located at the surface.

With respect to optical properties of CuInSe2 nanowires, the dielectric function, reflectivity, refractive index, and absorption spectrums have been calculated. It is found that the imaginary part of dielectric functions of the nanowires have main peaks which are located at different energy locations of those bulk. Moreover, the 17 ACS Paragon Plus Environment


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effect of the nanowire’s diameter on the optical properties of CuInSe2 has been studied. The results show that the optical parameter increases while the size of nanowires increases.

Finally, one should note that the ab initio study of the structural, electronic and optical properties of the semiconductor nanowires is of fundamental interest and it will pave the way for the use of nanowires in the future optoelectronic devices.

References:

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Study of Electronic and Optical Properties of CuInSe2 Nanowires - The

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