J. Nig. Soc. Phys. Sci. 3 (2021) 334–339

Journal of the
Nigerian Society

of Physical
Sciences

Effect of Substitutional Point Defect of Gold (Au) in Indium (In)
Site of Double Halide Perovskite (Cs2InSbCl6)

I. Magajia,∗, A. Shuaibua, M. S. Abubakara, M. Isaha, A. Hussainia

aDepartment of Physics, Faculty of Science, Kaduna State University, P.M.B, 2339, Kaduna, Nigeria

Abstract

Lead (Pb) free (non-toxic) perovskite solar cells materials have attracted great interest in the commercialization of the photovoltaic devices. In
this work, density functional theory (DFT) and linear response time-dependent within density functional theory (TDDFT) are used to simulate
and investigate the effect of gold (Au) doped Pb-free double halide perovskite A2BB′X6(A = Cs; B = In, Au; B′ = Sb; X = Cl) on the structural,
electronic, and optical properties for perovskite solar cell application. On the structural properties, bond length and bulk modulus calculations
show that the doped compound is more likely to resist deformation than the undoped compound. The calculated band structure for both materials
(doped and undoped) reveals the presence of the Valence Band Maximum (VBM) and the Conduction Band Minimum (CBM) at around the same
symmetry point which indicates a direct band gap nature (at Γ− point). The band gap value for the initial compound (Eg= 0.99 eV) agrees with
published theoretical values. For the gold doped compound, the value of the band gap increased to a value of 1.25 eV. The result of the optical
properties shows that the Au-doped material has higher absorption coefficient, lower reflectivity and higher optical conductivity when compared
with the initial, as such demonstrates better properties as a candidate for solar cell applications and in other optoelectronic devices.

DOI:10.46481/jnsps.2021.352

Keywords: Perovskite, Photovoltaic solar cell, Optical, Structural

Article History :
Received: 17 August 2021
Received in revised form: 05 October 2021
Accepted for publication: 07 October 2021
Published: 29 November 2021

©2021 Journal of the Nigerian Society of Physical Sciences. All rights reserved.
Communicated by: E. Etim

1. Introduction

Traditionally, silicon has been the most widely used ma-
terials in most successful photovoltaic solar cells. However,
high processing or manufacturing cost, unavailability of effec-
tive mass production technique, reflection, and recombination
and absorption losses limit the use of silicon photovoltaic so-
lar cells. Perovskite materials which are generally photonic
materials have shown great promising qualities to replace sil-
icon as solar cell materials. The Lead-based halide perovskite

∗Corresponding author tel. no:
Email address: imagaji05@gmail.com (I. Magaji )

are considered to be most promising material for solar cell ab-
sorbers [1]. However the environmental hazard and the toxicity
nature associated with the lead-based halide perovskite still re-
main a major concern. Recently, there has been tremendous ef-
forts in developing new halide perovskite which will potentially
turnaround the instability and toxicity problems associated with
emerging lead-based perovskite solar cell devices. Indium
(In)-based double perovskite; Cs2InBiCl6 and Cs2InSbCl6 were
proposed to be good return photovoltaic solar cell material, ev-
idently due to the suitable direct band gaps foretold by Spin-
Orbit Coupling with Hybrid Functional (SOC+HSE) calcula-
tion, minimal effective masses for electron-hole, and thermal
stability towards decomposition [5]. The large dielectric con-

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stant [2], low cost fabrication [3], high optical absorption coef-
ficient [4], low exciton binding energy, [5], efficient solar ab-
sorption when used as light absorbing layer [6], long carrier
diffusion length [7], and swift increase in power conversion effi-
ciency (PCE) [8], are among the properties that makes the dou-
ble halide and other similar perovskite solar cells very promis-
ing for commercialization. The major concern of the proposed
indium (In) based double perovskite is the stability of indium
(In) state specifically against oxidizing to In (III) [1]. Point
defect is a promising way to control such instability particu-
larly against reduction oxidation reaction (REDOX). In semi-
conductors, point defects play a fundamental role in enhancing
material properties. Substitutional point defect was employed
by total substitution of indium with gold elements in the com-
pound. Generally, transition metals when used as dopant im-
proves material conductivity. The surface plasmon resonance
(SPR) property of gold influences the used of it as the substitute
in the compound. In this work, first principle DFT and linear
response TDDFT calculations were used to study the effect of
Substitutional point defect of transitional metal (gold) alloyed
along Indium (In) region of Cs2InSbCl6 for potential solar cell
application.

2. Computational Details

The first principle calculations were carried out within the
frame work of DFT and TDDFT by the use of plane-wave
(Pw) pseudopotential technique as implemented in quantum
ESPRESSO suite. Generalized gradient approximation (GGA)
was used as exchange-correlation functional formulated by
Perdew Burke Ernzerhof (PBE). The lead-free halide perovskite
compound (Cs2InSbCl6) is a face-centered-cubic (FCC) which
is a member of the cubic lattice structure in the space group
Fm-3m. It simple primitive cell contains 10 atoms. However,
a super cell of 40 atoms was used throughout the course of this
work. The structural parameters (lattice parameters and inter-
nal atomic coordinate) were optimized and fully relaxed using
Broyden-Flectcher-Goldfarb-Shanno (BFGS) quasi-Newton al-
gorithm. 60 and 240 Ry were set for the convergence test of the
kinetic energy cut-off for wave function and charge densities re-
spectively. The Monkhorst-packk-point mesh sampling of Bril-
louin zone integration was set as 6 x 6 x 6 and a denser k-point
mesh of 12 x 12 x 12 for density of state (DOS). 10−7 was set
as the convergence threshold for self-consistent-field (SCF) it-
eration. The output of the SCF calculation provides the value
of pressure P in equation 1 which was used to calculate the bulk
modulus of the materials.

B0 = −V
d p
dv = B1 + B2, B1 = −V 1

(p1− p2 )
(v1− v2 )

, B2 = −V 1
(p1− p3 )
(v1− v3 )

Where B0 is the bulk modulus, V is the volume of the structure,
and P is the pressure

3. Result and Discussion

3.1. Structural properties
The optimized crystal lattice parameters obtained are a =

b = c = 11.342 Å and α = β = γ = 900. The value obtained

is in consistent with the experimental value 11.32 Å [9]. The
cesium Cs atom site (1) in Figure 1(a) was observed to have a
bond with at least an atom site of each of the element existing
in the material. It has ten (10) neighboring atoms sites with
three (3) Indium (In), 3 Chlorine (Cl), two (2) Antimony (Sb),
and 2 cesium (Cs) atoms. A total bond length of 30.594 Å ex-
ists between the Cs atom site (1) and the neighboring atoms.
The alloying of Au element in the In site of the compound
reduces the total bond length to 30.588 Å. The alloyed com-
pound Cs2AuSbCl6 figure 1(b) having lesser total bond length
when compared to the initial compound Cs2InSbCl6 is likely to
be more stable. This is because the lesser the bond length the
stronger the bond [10].
The strength, hardness, compressibility or flexibility of materi-
als is often determined by the bulk modulus of the material.
The bulk modulus (which is a function of pressure and vol-
ume) of the material was calculated (using equation 1). The
result obtained shows that the bulk modulus of the material
Cs2InSbCl6 calculated is 28.44 Gpa. The substitution of In with
Au raises this property to 30.93 Gpa. The ability of a material
to resist deformation under applied stress is often defined by its
bulk modulus [11]. Greater value of the bulk modulus implies
strong resistance to deformation and it indicates high compres-
sive strength [12]. This means that the material (Cs2AuSbCl6)
will offer more durability and resistance to deformation and as
such it is suitable for solar cell application [11].

3.2. Electronic Properties

The band structure of the compounds Cs2InSbCl6 and
Cs2AuSbCl6 were calculated using the projected augmented
wave (PAW) within DFT-GGA functionals. The band was cal-
culated in the high symmetry directions of the Brillion zone (X
- Γ - W - Γ - L) for both compounds. It is observed that both
materials demonstrate semiconducting behavior. The structures
clearly reveals that both the valence band maximum (VBM) and
the conduction band minimum (CBM) exist at Γ-point symme-
try. This indicates that the parent compound (Cs2InSbCl6) and
the alloyed (Cs2AuSbCl6) are direct band gap materials. The
band gap of the material (Figure 2(b)) increased to 1.25 eV after
substitution of In with Au element (Cs2AuSbCl6) in the parent
compound (Figure 2(a) ) which has a band gap value of 0.99
eV that is in excellent agreement with the value of 0.98 eV ob-
tained by [1] and most recently 1.02 eV obtained by [9]. The
density of state (DOS) shows the number of available states in
the system, the number of the allowed electron (hole) states per
volume at given energy. Thus, it’s a tool for determining the
energy distributions and carrier concentrations within semicon-
ductor [13].
The plotted DOS (Figure 3(a) and 3(b)) clearly reveals the semi-
conducting behavior of the materials. It clearly shows the ex-
istence of energy range below and above the Fermi level (0
eV). It shows that the higher peaks are situated at the valence
band for Cs2InSbCl6 (Figure 3(a)) and at conduction band for
Cs2AuSbCl6 (Figure 3(b)). This indicates the presence of many
electrons at the particular energy state.

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Figure 1. Crystal Structure

Figure 2. Band structure

Figure 3. Density of State (DOS)

3.3. Optical properties
The study of optical properties involves the determining ma-
terial response to an applied electromagnetic field particularly
to visible light [14].The knowledge is essential in determina-

tion of the efficiency of photovoltaic materials. Theoretically,
an important function used in solid state physics to determine
the linear response is the complex dielectric function [15]. The
dielectric function ε (ω) = ε1 (ω) + iε2 (ω) (where ε1 (ω) is

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Figure 4. Dielectric Functions

the real part and iε2 (ω) is the imaginary part) of the materials
were calculated within the linear response TDDFT. The opti-
cal transition mechanism is illustrated by the imaginary part of
the dielectric function. A greater value for dielectric constant
of material indicates that the material has comparatively low
charge carrier recombination rate and as such the entire per-
formance of the optoelectronics material will be improved [13].
The result obtained for Cs2InSbCl6 (Figure 4(a)) shows that the
value of the imaginary part (ε2) becomes zero at about 23.5 eV.
This means that the material becomes transparent above 23.5
eV [14]. Generally, the value of ε2 becomes nonzero immedi-
ately absorption starts. It can be seen that for ε2 the main peaks
are located at 2 eV, 3 eV, 4 eV, and 5 eV (Figure 4(a)). An im-
portant remark to make from the real part (ε1) plot is that ε1 de-
creases to negative values. The negative values of (ε1) indicates
that at the particular energy level, there is mostly rejection of the
incidence electromagnetic waves from the medium, as such the
material exhibit metallic behavior [14]. As such it serves as pro-
tective means from the radiations in the energy region. Compar-
ing the result with the alloyed compound (Cs2AuSbCl6) Figure
4(b) shows that the alloyed material will absorb radiations up to
about 24 eV which is higher than the initial compound (13 eV).
This is in line with the difference in the electronic band gap ob-
tained from the band structure (Figure 2(a) and (b)). Also, it is
observed that here’s a difference in the high positive peak value
of ε1 with about 100 eV that exists between the initial (about
50 eV) and the alloyed compound (about 150 eV). This means
that the alloyed compound is a good absorber of radiations. As
such it is considered as potential good photovoltaic material for
optoelectronics application.
The absorption coefficient spectrum provides knowledge on the
extent at which material absorbs photons. It indicates how far
the light of a specific energy can penetrate into a material before

being absorbed [14]. Figure 5(a) shows the absorption coeffi-
cient graph which provides information about optimum solar
energy conversion efficiency. It reveals the absorption spec-
tra for Cs2InSbCl6and Cs2AuSbCl6. The absorption abruptly
rises for energies higher than 0.5 eV which is in line with the
band gap energy value. The absorption values are in the or-
der of 10 4cm −1 from the infrared to visible and down to the
ultraviolet range (1.24 eV to 1.7 eV to above 3.3 eV). Several
peaks were noticed to exist with Cs2InSbCl6 having its highest
peak located just within the infrared energy region while the
compound Cs2AuSbCl6 was noticed to have its utmost peaks
located within the ultraviolet region (above 3.3 eV). This af-
firms the result obtained by the DFT calculation of the elec-
tronic band structure (Figure 2(a) & (b)) which reveals that the
compound Cs2AuSbCl6 has a wider band gap than Cs2InSbCl6.
This is evidently the reason for the difference in the energy
range of the highest peaks. An important remark to make is that
the material with higher peak in the high energy region will be
a good absorber material and as such it is considered as a better
candidate for photovoltaic applications.
The electron energy loss function EELS is a vital optical param-
eter used in explaining the energy loss of a fast electron travers-
ing a material which is large at plasma frequency [14]. Figure
5(b) represent the corresponding EELS in function of photon
energy of the materials. The prominent peaks were found to
be at 28.02 eV for Cs2InSbCl6, 29.5 eV for Cs2AuSbCl6. The
sharp maxima peak for EELS indicates the existence of plasma
resonance which appears at a specific incident light frequency
which corresponds to the trailing edges in the reflection spectra
often called plasma frequency (ωρ). The imaginary part of the
dielectric function is zero at this point of energy which indicates
rapid reduction in reflectance [15].
Reflectivity is an important optical parameter used to describe

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Figure 5. (a) Absorption Coefficient, (b) Electron Energy Loss Spectra, (c) Reflectivity, (d) Conductivity, (e) Refractive Index

the ratio of reflected photon energy from material surface to the
photon energy incident on the surface. Figure 5(c) shows the
reflectivity of the materials (Cs2InSbCl6 and Cs2AuSbCl6) as

function of photon energy. The first edges were found to be at
90%, and 80% for Cs2InSbCl6, and Cs2AuSbCl6 respectively.
These edges were noticed to be within the low energy level.

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The reflectivity begins to decrease as the energy increases from
infrared region. It then increases to other peaks of 75, and 70
percent for Cs2AuSbCl6 and Cs2InSbCl6 respectively. These
peaks were found to be located from visible to ultraviolet en-
ergy range. The decrease in the reflectivity in the high energy
region means that the material is transmitting in the ultraviolet
wavelength as a result of lower reflectance within the energy
range. An important remark to make is that, the material with
high reflectivity in the high energy region can be used as a good
coating material to avoid solar heating [14].
Conductivity is an important optical property that provides in-
formation on the electrical conductivity of material. The mea-
sure of ease at which heat or electric charge pass through
a material is termed conductivity. Figure 5(d) below shows
the conductivity of the materials. It is observed that the
material Cs2InSbCl6 has its own highest optical conductivity
value of 400 Ω−1cm−1. The conductivity rises to about 500
Ω−1cm−1 for Cs2AuSbCl6. The increase in the photoconductiv-
ity of Cs2AuSbCl6 is due to high absorption of photons [14].
The material Cs2AuSbCl6 will consequently be a better candi-
date for photovoltaic applications.
The refractive index of a material is a dimensionless quantity
which describes how much light travels or refracted after enter-
ing a material [15]. Figure 5(e) shows the refractive index n (ω)
as a function of photon energy for the materials. The static re-
fractive index n (0) was found to be 2.5 and 3.4 for Cs2AuSbCl6
and Cs2InSbCl6 respectively. From the graph, the materials
possess a high refractive index at infrared region around (1.24
eV-1.7 eV) to visible region (1.7 eV-3.3 eV) and drastically de-
crease at higher energy from the visible to ultraviolet region
(above 3.3 eV). Furthermore, after 2.5 eV, and 6.0 eV the ve-
locity of light is greater than the light celerity because n (ω)
is less than one for Cs2InSbCl6, and Cs2AuSbCl6 respectively.
The n (0) attain by Cs2AuSbCl6 (2.5) which is lower than the
initial Cs2InSbCl6 (3.4) will be less dense as such, the light rays
will bend more away from the normal line. The result obtained
for Cs2AuSbCl6 (2.5) is in consistent with the result obtained
for other lead-free halide Cs2TiI6 double perovskite of n (0) =
2.6 [18]. As such, Cs2AuSbCl6 can be considered as a good
photovoltaic material.

4. Conclusion

In this research work, investigation was carried out on the effect
of substitutional point defect in the structural, electronic and
optical properties of a lead-free halide perovskites Cs2InSbCl6
for photovoltaic application within the framework of DFT-GGA
(for the structural and electronic properties) and TDDFT (for
optical properties) as implemented in quantum ESPRESSO
(q.e-6.5).
A substitutional point defect was performed in the indium site
of the compound with substitution of indium with a gold ele-
ment. The effect was investigated on both the structural, elec-
tronic and optical properties. The result of the structural inves-
tigation shows that the alloyed compound (Cs2AuSbCl6) has

less total bond length when compared with the initial compound
(Cs2InSbCl6) and such it makes more stable. The higher magni-
tude of bulk modulus attained by the alloyed compound means
that it will offer more durability and resistance to deformation
which makes it suitable for solar cell application. The elec-
tronic band structure (Figure 2) shows the substitution widened
the band gap from 0.99 eV to 1.25 eV. This increase in the band
gap value of the defect compound indicates higher absorption of
photons energy. The result of the optical properties shows that
the defect material has higher absorption coefficient, lower re-
flectivity and higher optical conductivity when compared with
the initial, this means that the defect compound is a good pho-
tovoltaic material and potentially better candidate for solar cell
application.

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