Article
pubs.acs.org/JPCC
Study of Electronic and Optical Properties of CuInSe2 Nanowires
Payman Nayebi,† Mohsen Emami-Razavi,*,‡ and Esmaeil Zaminpayma§
†
Department of Physics, College of Technical and Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran
Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, P.O. Box 14665-678, Tehran, Iran
§
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. 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 the (1−10) growth direction. The geometrical parameters are in
good agreement compared with 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 valence 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 with the bulk ones.
1. INTRODUCTION
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 densityfunctional 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
study,8 they have obtained 14 stable Bin (n = 1, 6) wire
configurations. They8 also observed that all of the wire
configurations display noncrystalline bulk atomic structures
and concluded that the inclusion of spin−orbit coupling in their
computations greatly influences all physical properties of the
wires.
Moreover, Dai et al.13 investigated electronic structures,
magnetic properties, and spin-dependent electron-transport
characteristics of C-doped ZnO nanowires by using firstprinciple methods based on DFT with Perdew−Burke−
Because of 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 that find applications in solar cell technology,
lasers, computers, and a new generation of optoeleronic devices
(see, for example, refs 1−3 and references therein).
Semiconductor nanowires have the advantage that their
electronic structure can be band gap engineered by varying the
size, growth direction, composition, and cross section due to
the quantum-confinement effects,1 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
areas,6,7 such as chemistry and physics.
© 2016 American Chemical Society
Received: November 3, 2015
Revised: February 6, 2016
Published: February 8, 2016
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DOI: 10.1021/acs.jpcc.5b10749
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The Journal of Physical Chemistry C
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 crosssection nanowires in the Brillion zone. As it is shown in Figure
1, nanowires are generated in the direction (1−10) with
hexagonal and triangular cross-section with their diameters
ranging from 8 to 19 Å.
Ernzerhof (PBE) generalized gradient approximations (GGAs)
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 transitionmetal (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 the natural compatibility of I−III−VI2 chalcopyrite semiconductor thin films like CuInSe2 compounds (CIS) in
solar cell technologies, their nanowires have significant
potential for use in technologies related to photovoltaic
devices. Despite 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
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.
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 atom-projected (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.
Figure 1. Nanowires in the [1−10] direction with hexagonal and
triangular cross-section.
3. RESULTS AND DISCUSSION
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 bodycentered tetragonal unit cells is observed. The anion displacement parameter u measures the corresponding distortion,
namely
u − 1/4 = (R2Cu − Se − R2 In − Se)/a 2
(1)
where RCu−Se and RIn−Se are the bond lengths. Before relaxation,
the crystal parameter is set to a = 5.78 Å and after relaxation the
values of crystal lattice parameters such as a, c, bond lengths,
angles, and u have been computed. Table 1 shows the
experimental and theoretical values.
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.
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 200 Ry, maximum force tolerance is <0.04 eV/Å, and density
matrix mixing weight is at 0.05. Also, the total energy tolerance
Table 1. Calculated and Experimental Structural Parameters
of Bulk CuInSe2
a
4590
structural properties
present work
experiment
calculation
a (Å)
c (Å)
c/a
u (Å)
RCu−Se
RIn−Se
Cu−In−Se angle
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
Ref 23. bRef 24. cRef 25.
DOI: 10.1021/acs.jpcc.5b10749
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Table 2. Calculated Bond Lengths at the Center and Edge Parts for the Nanowires
at the center
triangular
26
44
hexagonal
32
48
at the edge
RCu−Se
RIn−Se
contraction
RCu−Se
RIn−Se
contraction
atoms
atoms
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%
atoms
atoms
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%
shape and size
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 ∼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 surfaceto-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 with 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 ranges and the contractions compared with
the bulk values are ∼4.70%; however, at the center of the
nanowires it is found that the contraction is <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−
S−In 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.
The values of the energy band structure along the symmetry
directions and the partial density of states for the nanowires
have been presented here. We found that the theoretical gap
results are ∼0.01 eV 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 because there are the
usual shortcoming issues in the density functional theory.24,33,34
Figure 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.
For example, for Hexa2*2 (48atoms) nanowire the topmost
valence sub-bands are between the HOS (0 eV) and −8 eV.
The middle one is located somewhere between −11 and −14
eV. The lowest valence sub-bands are placed between −15 and
−16.6 eV. The top valence 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
Figure 2. Calculated band structures near the Fermi levels of the
nanowires with hexagonal and triangular cross-section.
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.
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 Figure 3. The band gap for all nanowires is larger
than the bulk band gap.
As the size of the nanowires augment, the band gaps reduce,
reflecting the impact of quantum confinement.
In Figure 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
Figure 3. Relative band gap (ΔEg) as a function of diameter and shape
of nanowires.
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Figure 4. Nanowires’ partial density of states (PDOS) plots for atoms located at the edge and center of them with hexagonal and triangular crosssection. The energy zero is set at the highest occupied state.
their center for comparison purpose. In addition, we study how
the PDOS varies with the nanowires’ diameters.
As it can be seen from Figure 4, for the copper atoms at the
edge of a nanowire, there are distinct peaks around −1.88 eV
(contributed from Cu-3d) and near −15 eV for indium PDOS
(contributed from In-4d). Also, we have two peaks that are
located between −3.5 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 for both 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
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)
{inter}
Imεαβ
(ω) =
ℏ2e 2
πm 2 ω 2
δ(Ekc n
∑ ∫ dk ⟨ψkc |pα |ψkν ⟩⟨ψkν |p β |ψkc ⟩
n
n
n
n
n
− Ekvn − ω)
(2,)
where p is the momentum matrix element between α and β
bands with the same crystal momentum k and ψckn and ψνkn are
the occupied and unoccupied wave functions with relevant
c
v
energy of Ekn and Ekn. ℏ 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. Therefore, a
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Figure 5. 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.
scissor operator has been employed 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 Figure 5. The imaginary part spectrum has 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 5.38 eV, and the last one at 6.83
eV. Compared with the CuInSe2 bulk, the energy position of
almost all corresponding peaks of the dielectric function
spectrum (ε(ω)) for the nanowires are blue-shifted. This can
be explained because of presence of larger band gaps in the
nanowires compared with the bulk of CuInSe2.
In Figure 6, we have shown the calculated value of the
dispersion of the refractive index for CuInSe2 nanowires. The
Figure 7. Reflectivity spectra for the nanowires. “Hexa” and “Tri”
represent “hexagonal” and “triangular”, respectively.
been shifted to higher energy values compared with the bulk
value of CuInSe2. Moreover, one can see that by increasing the
size of the nanowires the reflectivity increases.
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 Figure 8. As it can be seen, the peaks
corresponding to the nanowires become lower compared
with their bulk value35 and they move to the higher energy
locations. For example, for the first peak of bulk of CuInSe2 the
corresponding value is ∼2.20 eV,35 while for the CuInSe2
nanowires, the peaks locations are as follows: 2.42 (Hexa.2*2),
2.39 (Hexa.2*3), 2.33 (Tri.2), and 2.23 eV (Tri.3).
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 ∼3.21 eV.
Figure 6. Dispersion of the refractive index for the nanowires. “Tri”
and “Hexa” represent “triangular” and “hexagonal ”, respectively.
estimate value of n(0) for the nanowires are 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.
We present the graph of optical reflectivity of the CuInSe2
nanowires with respect to different energies in Figure 7. As it
can be seen in the graph, the main peaks for the nanowires have
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
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Figure 8. Absorption coefficients for the bulk and the nanowires.
“Hexa” and “Tri” represent “hexagonal ” and “triangular”, respectively.
used for photovoltaic and nonlinear optical devices. Firstprinciple calculations have been used to study the various
properties of CuInSe2 nanowires in the (1−10) growth
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With respect to optical properties of CuInSe2 nanowires, the
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Moreover, the 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.
■
Article
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
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