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J Mater Sci: Mater Electron
DOI 10.1007/s10854-017-8099-4
Properties of nickel doped ­In2S3 thin films deposited by spray
pyrolysis technique
M. Kraini1 · N. Bouguila1 · N. Moutia1 · J. El Ghoul1,2 · K. Khirouni1 ·
C. Vázquez‑Vázquez3 Received: 6 July 2017 / Accepted: 19 October 2017
© Springer Science+Business Media, LLC 2017
Abstract In this work, nickel (Ni) doped indium sulfide
­(In2S3) films have been prepared by the spray pyrolysis
(CSP) technique on glass substrates at 350 °C. The Ni doping level was changed with Ni:In (0, 2 and 4% in solution).
The structural studies reveal that the deposited films are
polycrystalline in nature exhibiting cubic structure. The
crystallite size decreases from 27.5 to 23 nm and the root
mean square roughness values increase from 13 to 18 nm.
The transmission coefficient is about 70–55% in the visible
region and 85–75% in near-infrared region. The band gap
energy increases with nickel content from 2.74 to 2.82 eV
for direct transitions. The refractive index values of ­In2S3:Ni
thin films decrease from 2.43 to 2.40 and the extinction coefficient values are in the range 0.01–0.20. Besides, the AC
conductivity contribution is interpreted using the universal
Jonscher’s power law and it is found thermally activated and
it can be described by the correlated barrier-hopping models.
These studies help to form significant correlation between
temperature and activation energy. Nyquist plots show that
the electrical response is accurately fitted by the Cole–Cole
model and represented by an equivalent electrical circuit
which consists of a parallel combination of a resistance and
* M. Kraini
mabrouk.karini@gmail.com
1
Laboratory of Physics of Materials and Nanomaterials
Applied at Environment (LaPhyMNE), Faculty of Sciences
in Gabes, Gabes University, 6072 Gabès, Tunisia
2
Department of Physics, College of Sciences, Al Imam
Mohammad Ibn Saud Islamic University (IMSIU),
Riyadh 11623, Saudi Arabia
3
Laboratory of Magnetism and Nanotechnology, Institute
of Technological Research, Universidade de Santiago de
Compostela, 15782 Santiago de Compostela, Spain
a constant phase element. From this analysis, the evidence
of grain boundary conduction has been observed.
1 Introduction
Over the last decade, several semiconductors materials
including III–VI groups are used extensively for a variety
of applications. Among these semiconductors, indium sulphide ­(In2S3) is one of the potential materials for various
applications [1–6]. This becomes possible due to its stability
and wide band gap (2.0–3.7 eV) [7]. Furthermore, indium
sulphide is a potential substituent of toxic CdS as a buffer
layer in photovoltaic solar cells [8].
Various techniques have been developed to synthesize
­In2S3 such as spray pyrolysis [9, 10], ultrasonic dispersion
[11], chemical bath deposition [12], physical vapor deposition [13], vacuum thermal evaporation [14], etc. Among
these methods, spray pyrolysis is selected in this study
because it allows preparing thin films of ­In2S3 in large area
at low cost.
Indium sulfide, a typical III–VI semiconductor compound, is known to exist in three morphologies at atmospheric pressure: α, β and γ [9, 10]. β-In2S3 is the thermodynamically stable form with tetragonal or cubic crystal
structure at room temperature with a high degree of tetrahedral and octahedral vacancy sites [11, 12]. ­In2S3 is an
n-type semiconductor exhibiting excellent optoelectronic
performances because of its defected spinel structure. Due
to a large number of cation vacancies, one of the efficient
ways of improving the properties of indium sulfide films is
the addition of certain dopants, among these, the transition
metals. In addition, in recent investigations of materials, 3d
transition metal impurities have aroused a great deal of interest [15–18]. Hence, transition metal doped ­In2S3 can show
13
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J Mater Sci: Mater Electron
interesting properties by the coupling of metal d-electrons
and defect states. In this context, the effects of impurities on
physical properties due to a nickel dopant have not yet been
investigated in our knowledge. Therefore, this is the first
report on the effects of nickel incorporation on the impedance spectroscopy, structural, morphological and optical
properties of spray pyrolyzed ­In2S3 thin films.
In this work, we report the influence of Ni doping on the
structural, morphological, optical and electrical properties
of ­In2S3 films.
2 Experimental details
The ­In2S3 thin films were prepared by spraying an aqueous
solution of indium chloride ­(InCl3) and thiourea (CS(NH2)2)
in a ratio of S:In = 2.5. Nickel chloride (­ NiCl2), used as Ni
source, was added to the spray solution in a controlled way.
The nickel to indium molar ratios are Ni:In = 0 (undoped), 2
and 4% in the spray solution. Air compressed was used as a
carrier gas at a flow rate of 6 l/min. The substrate temperature was maintained at 350 °C within an accuracy of ± 5 °C.
X-ray diffraction (XRD) studies of the films were performed using monochromatic Cu-Kα radiation (1.5406 Å)
(Bruker D8 Advance diffractometer). The film surfaces were
characterized by atomic force microscope using XE-100
instrument (Park Systems Corporation) in non contact mode
(NC-AFM). Microstructures and chemical compositions of
the films were investigated by field emission scanning electron microscope (FESEM) (Zeiss Ultra PLUS) equipped
with an accessory of energy dispersive spectroscopy (EDS).
The absorption and transmission spectrum were taken from
Shimadzu UV 3101 PC spectrophotometer. Both transmittance and absorbance were recorded. A similar piece of the
substrate used for the film deposition, was employed as a
reference. For electrical measurements, we have deposited
two-electrodes of silver by vacuum evaporation technique
(Fig. 1). An Agilent 4294A impedance analyzer was used
to collect impedance measurements over a wide frequency
range (70 Hz–100 MHz) and temperature (480–620 K).
3 Results and discussion
3.1 Structural characterization
The XRD patterns of films with different values of molar
ratio Ni:In = 0, 2 and 4% are shown in Fig. 1. As it is seen,
all films are polycrystalline and all the crystallographic
peaks belong to the cubic β-In2S3 phase with diffractions
from (111), (220), (311), (222), (400), (511) and (440)
planes, according to JCPDS Card No. 32–0456. No other
phases corresponding to Ni impurity are observed which
13
Fig. 1 XRD patterns of ­In2S3:Ni films
indicates that Ni ions occupy substitutional positions and
did not change the crystalline system.
In these cases, with increasing the doping concentration the diffractogramms show a slight shift of (311) peak
from 27.617° for undoped I­ n2S3 to 27.727° for Ni:In = 4%.
Such behavior is attributed to the residual stress in the
film caused by the difference in ionic size between
­Ni2+(0.70 Å) and I­ n3+(0.80 Å). This is confirmed by lattice
parameter a, which is less than the standard value which
is a strong indication of stress in the films.
A rough estimation of the crystallite size (D) is obtained
from the principal peak (311) by using the Scherrer formula [19]:
D=
0.9
 cos 
(1)
where β is the full width at half maximum in radians, λ is the
wavelength of X-ray, θ is the Bragg angle.
J Mater Sci: Mater Electron
The calculated crystallite size D with doping concentration is given in Table 1. It can be seen that D decreases
from 27.5 to 23 nm with increasing nickel concentration.
The ionic radius of the N
­ i2+ ion is smaller than that of the
3+
­In one. So, there is a creation of compressive stress in
the films with Ni doping.
The microstrain developed in these thin films is characterized by the structural parameter (ε) which can be calculated with the following relation [20]:
=

4 tan 
(2)
where θ is the (311) diffraction angle.
This strain, which is in order of ­10−3, is caused by a
tensile stress which is due to I­ n3+ ions substitution by N
­ i2+
in the lattice.
The dislocation density (δ) for orientation (311) can be
calculated using the formula [21, 22]:
=
1
D2
(3)
The study of the variation of the dislocation density of ­In 2 S 3 :Ni (Table 1) reveals that it increases
slightly with increasing Ni:In value from 1.3 × 10 11 to
1.8 × 1011 lines cm−2. This behavior can be explained by the
change of the grain size (D) with Ni:In value [23].
3.2 Morphological characterization
Figure 2 displays the scanning electron micrographs of
the samples. As seen, the surface morphology of the films
depends on the Ni:In molar ratio. The surface of the samples
revealed continuous films with no cracks and voids and it is
Table 1 Peak position (311), full width at half maximum (β), crystallite size (D), dislocation density (δ) and microstrain (ε) as a function of
molar ratio Ni:In
Ni:In
2θ (°)
β (°)
D (nm)
a (Å)
V (Å3)
δ ­(1011 lines cm−2)
ε ­(10−3)
Undoped
2%
4%
27.617
27.694
27.727
0.3
0.33
0.35
27.5
24.8
23
10.70
10.68
10.66
1228
1218
1214
1.3
1.6
1.8
5.5
6.0
6.4
Fig. 2 FESEM images of
­In2S3 thin films for different Ni
doping
13
J Mater Sci: Mater Electron
clearly seen also from the FESEM photographs that the films
are dense without pinholes and perfectly covering the entire
substrates for all Ni:In molar ratios.
Table 2 Chemical composition of I­ n2S3:Ni films
Ni:In ratio in solution
Element
In (at.%)
S (at.%)
Ni (at.%)
Undoped
2%
4%
39.27
38.85
38.25
60.73
60.52
60.55
0
0.63
1.2
Fig. 3 NC-AFM images of ­In2S3 thin films for different Ni doping
13
Atomic percentage of the elements in the films has
reported in Table 2. The EDS analysis emphasized the
presence of In, S and Ni elements in the films. It has been
observed that upon increasing the Ni concentration, the percentage of In in the films was decreased slightly, whereas the
percentage of S was almost constant. It would be presumed
that Ni doping in the films was substitutional.
Figure 3 shows three dimensions (3D) NC-AFM images
(2 µm x 2µm) of ­In2S3:Ni thin films for different Ni:In molar
ratios. These images show that the surface morphologies of
the films are dependent on the Ni doping. The films were
well covered, homogeneous, dense and continuous. The
J Mater Sci: Mater Electron
root-mean square (RMS) roughness for samples are listed
in Table 3. The RMS roughness values increased from 13 to
18 nm with increasing Ni doping.
3.3 Optical characterization
k=
3.3.1 Transmittance and absorbance spectra
The spectra of absorbance and transmittance measured in
the wavelength range 300–2400 nm of the films of ­In2S3:Ni
for various molar ratios Ni:In are shown in Fig. 4a, b,
respectively.
One can see from the transmittance value that the UV
radiations are completely absorbed (Fig. 4a). The transmittance decreases after the doping and there is a shift of the
fundamental absorption towards shorter wavelengths. The
transmission coefficient decreased from 70 to 55% in the
visible region and from 85 to 75% in near-infrared region.
The absorption edge (Fig. 4b) of Ni doped ­In2S3 films deposited for different doping concentrations shifts to a lower
wavelength.
3.3.2 Absorption coefficient
The absorption coefficient (α) of the films can be estimated
by the Eq. [24]:
=
2.303
A
d
(4)
where d = 300 nm is the thickness of the prepared thin films,
A is the absorbance.
The variation of the absorption coefficient of ­In2S3:Ni
thin films with wavelength for different concentrations of
Ni is shown in Fig. 5a. We can perceive that α in general
decreases with increasing wavelength. It can be seen that
the value of α is in the order of ­104 cm−1. The absorption
through the ­In2S3:Ni films is relatively high at below band
gap region indicating a high concentration of free carriers.
The higher values of the absorption is attributed to that the
incoming photons have the sufficient energy to excite the
electrons from the valence band to the conduction one. The
absorption decreases in the higher wavelength region and
Table 3 RMS roughness and optical constants of ­In2S3:Ni films as
function of the molar ratio Ni:In
Ni:In
RMS roughness Eg (eV)
(nm)
Eu (eV)
n
Undoped
2%
4%
13
14
18
0.475
0.560
0.540
2.43
2.44
2.40
2.74
2.72
2.82
this decrease corresponds to the reduction in the photon’s
energy.
The extinction coefficient (k) is given by the following
expression [25]:

4
(5)
On Fig. 5b, we studied the evolution of the extinction
coefficient according to the wavelength of the ­In2S3films
doped with nickel. The values of k are high in the zone of
strong absorption and vary slightly according to the quantity
of nickel in the films. Moreover, the k values are in the range
0.01–0.20 for all wavelengths.
3.3.3 Optical energy gap and Urbach energy
The optical band gap of the films is determined by the following relation [26]:
 h = A(h − Eg )1∕2
(6)
where A is a constant, h is the Planck constant, υ is the frequency and Eg is the optical band gap.
The value of (αhν)2 is plotted as a function of the incident
photon energy (hν) in Fig. 6a. Then, the value of (hν) at
(αhν)2 = 0, obtained by extrapolation, is the optical energy
band gap.
The Urbach energy is calculated by using the following
Eq. [27]:
 = 0 exp(
EU =
[
h
)
EU
(7)
]−1
(8)
d ln 
dh
where α0 is a constant, EU is the Urbach energy, which characterizes the slope of the exponential limit (Fig. 6b). EU
values are calculated from the inverse of the slope of ln α
versus hν. The calculated values of the Eg and EU of ­In2S3:Ni
thin films as a function of Ni:In molar ratio are tabulated in
Table 3. EU values change inversely with optical band gap.
An increase of the Eg values as the nickel content increases
is evident, from 2.74 to 2.82 eV and the EU values vary from
0.475 to 0.540 eV for the films. Moreover, the reduction in
the grain size could contribute to the increase of Eg of the
films with the increase of Ni:In molar ratio. Similar remarks
were observed in other studies [7, 28–30]. Such an increase
of optical energy gap is useful for photovoltaic applications
since it increases the collection of photons in the ultraviolet
range [31].
The refractive index (n) of semiconductors typically
increases as band gap energy decreases. There are various
empirical and semi-empirical models that relate n to Eg.
13
J Mater Sci: Mater Electron
Fig. 4 Transmittance (a)
and absorbance (b) spectra of
­In2S3:Ni films
Among them, the Herve–Vandamme, this model is accurate
for most materials usually employed in the optoelectronic
device structures and high band gap materials. According
to Herve–Vandamme relationship, [32] the n and Eg can be
expressed as
13
2
n =1+
(
A
Eg + B
)2
(9)
where A and B are constants (A = 13.6 eV and B = 3.4 eV).
It is visible in Table 3 that the values of n of ­In2S3:Ni
thin films decrease from 2.43 to 2.40 with increasing Ni:In
J Mater Sci: Mater Electron
Fig. 5 Absorption coefficient
(a) and extinction coefficient (b)
of ­In2S3:Ni films
molar ratio which may be associated to the variation in
packing density of the films. These results are comparable
to that found in the literature [33–35]. Since n is strongly
connected with band gap energy. Therefore, larger band
gap energy has a smaller value of n.
3.4 Electrical studies
3.4.1 Electrical conductance analysis
Figure 7 shows the frequency dependence of the conductance G at different temperatures (480–620 K) for undoped
13
J Mater Sci: Mater Electron
Fig. 6 Variation of (αhν)2 versus photon energy for ­In2S3:Ni
films
and doped I­ n2S3 thin films with 2 and 4% in the frequency
range 70–107 Hz. The materials are characterized by a semiconductor behavior.
We observed from Fig. 7 that the profile of the total conductance can be splitted in two parts for all samples. The
first one is at low frequency, in such region; the spectrum
is characterized by the appearance of a plateau for each
13
temperature. The conductance has a small variation with
frequency and increased with temperature, this rise of conductance indicates that the conduction process is thermally
activated.
The second one is at high frequencies, the conductance
increases with frequency and can be described by the ωs
law. This increment in conductance is attributed to hopping
J Mater Sci: Mater Electron
Fig. 7 Conductance spectra
versus frequency at different
absolute temperatures
13
Fig. 8 Temperature dependence of the exponent ‘s’ for
­In2S3:Ni films
13
J Mater Sci: Mater Electron
J Mater Sci: Mater Electron
mechanism that occurs by the influence of an applied electrical field. Thus, the conductance can be described in the
studied frequency range by the Jonscher power law [36]:
(10)
where Gdc is the dc conductivity, which is calculated by
extrapolation of the curves of G to zero frequency for different temperatures, ω is angular frequency, A is a factor
depending on temperature and s is the fractional exponent.
The values of the frequency exponent s have been calculated from the slopes of the straight lines of Fig. 7 and are
plotted as a function of temperature in the Fig. 8. It is found
that 0 ≤ s ≤ 1 and ‘s’ decreases with increasing temperature.
These results prove the existence of hopping mechanism.
The exponent s is found to decrease with increasing temperature. This trend of s confirms that the correlated barrier
hopping (CBH) is the most suitable mechanism to explain
the behavior of the ac conduction mechanism of the doped
­In2S3. This behavior is in good agreement with the Mott
law [37]. This model involves a thermally assisted hopping
conduction mechanism between localized states.
In such model, the charge carriers are assumed to hop
between the sites over a potential where s can be calculated
by [38]:
G() = Gdc + GAC = Gdc + AS
s=1−
6kB T
WM
(11)
where ­WM is the binding energy, which is defined as the
energy required to remove completely an electron from one
site to one another and k­ B is Boltzmann’s constant. The
obtained values of W
­ M are summarized in Table 4. Generally, the experimental value of ­WM of the material reflects
the influence of the sample structure such as grain size and
orientation, defect distribution, phase content, Urbach tailing
phenomenon and charge density [39, 40].
Figure 9 shows the log(TGdc) versus 1000/T plot of
undoped and doped ­In2S3 films. Over a wide temperature
range, a linear variation was observed which justifies that
conductivity is dominated by thermally activated hopping
and can be expressed by Mott and Davis law [41]:
(
)
Edc
Gdc .T = A0 exp
(12)
kB T
where ­A0 is the pre-exponential factor, ­Edc is the activation
energy, T is the absolute temperature. The activation energy
can be deduced from slop of the curve. The values of ­Edc are
reported in the Table 4.
3.4.2 Electrical impedance analysis
Figure 10 shows typical complex impedance spectra
(Nyquist plots) of the undoped and doped ­In2S3 films at
different temperatures. All spectra are characterized by
the appearance of a semi circle arc with a center below
the real part axis on the Nyquist plot. This indicates that
the relaxation phenomenon of charge carriers is nonDebye [42]. As shown in Fig. 10, the maximum of the
semi-circles shifts to higher frequencies as the temperature
increases. Also, it is noticed that the radius of the semi
circles decreases when the temperature is increased. This
result indicates that the electrical conductivity is thermally
activated. As known, such material can be modeled by
an electrical equivalent circuit. According to the complex
impedance plots shown in Fig. 10, the equivalent circuit
is represented by the parallel of grain-boundary resistance
(R) and constant phase element impedance (CPE). The significant change of Nyquist plot with nickel doped permits
the correlation between the microstructure of the structure
and its electrical properties.
The CPE impedance ­(ZCPE) is defined as [43]:
ZCPE =
1
Q(j)
(13)
where Q is a constant that is independent of frequency, ω
is the angular frequency and β is an exponent of the CPE,
which is the measure of arc depression [44, 45]. When β = 1
the CPE is a capacity, for β = 0 the CPE becomes resistance
and β = -1 is an inductor.
Tables 5, 6 and 7 show the values of the parameters (R,
CPE and β) for all samples, which well fit the experimental
data. We note that R decreases when increasing temperature. The decrease of the R resistance as the temperature
increase proves the semiconductor behavior of all samples.
On the other hand, β approaches unity, then the CPE in our
case can be considered as a capacitor and we can conclude
that the samples are homogenous.
Figure 11 exhibits the variation of real part of the
impedance Z′ with frequency at different temperatures
for undoped and doped I­ n2S3 films. It is observed that Z′
have a higher values for lower temperatures and decreases
with increase in frequency. When increasing temperature,
It is clear that Z′ decreases, thus indicating an increase in
ac conductivity with rise in frequency. This result confirms the increase of conductance observed in Fig. 7. In
the high frequency region, the value of Z′ merges for all
temperatures. Such behavior proves the presence of space
polarization [46].
Table 4 Calculated values of ­Edc, ­WM and ­Ere for all samples
Ni:In
Edc (eV)
WM (meV)
Ere (eV)
Undoped
2%
4%
1.10
1.12
0.828
313
119
100
0.300
1.13
0.896
13
Fig. 9 Variation of the T.Gdc
conductance versus 1000/T for
­In2S3:Ni film
13
J Mater Sci: Mater Electron
J Mater Sci: Mater Electron
Fig. 10 Nyquist plots at different temperatures for ­In2S3:Ni
films. The inset shows the
proposed equivalent circuit for
­In2S3:Ni film
13
J Mater Sci: Mater Electron
Table 5 Values of equivalent circuit parameters for undoped film
Undoped
T (K)
R (kΩ)
CPE ­(10−11 F)
β
480
500
520
540
580
600
620
75,000
26,660
212
95
91
76
61
2.7
1.8
3.8
2.7
2.9
2.5
2.8
1
1.03
0.98
1.01
0.99
1.01
1
Table 6 Values of equivalent circuit parameters for Ni:In = 2%
Ni:In = 2%
T (K)
R (kΩ)
CPE ­(10−11 F)
β
480
500
520
540
560
580
600
620
37,783
16,509
7261
1975
570
242
128
118
1.07
1
1
1
1
1
1
1
1
1.01
1.01
1.01
1
1.01
1.01
1.01
Table 7 Values of equivalent circuit parameters for Ni:In = 4%
Ni:In = 4%
T (K)
R (kΩ)
CPE ­(10−11 F)
β
480
500
520
540
560
580
600
620
120,000
49,000
710,000
11,900
4603
3169
1513
715
3.9
4.1
1
3.5
3.82
3.76
3.65
3.7
0.98
0.99
0.98
1.01
1
1
1.01
1.01
The frequency dependence of imaginary part of impedance (Z″) at some representative temperatures is depicted
in Fig. 12. The spectra are characterized by appearance
of peaks, which shift to higher frequencies with increasing temperature. Such behavior indicates the presence of
relaxation phenomena in the system [36]. Also we noticed
that the magnitude of Z″ decreases gradually when the
temperature increases. This result possibly is related to
an accumulation of electrical charges in the material. It is
clearly visible that their different peaks have a significant
broadening. Such behavior proves the presence of temperature dependent relaxation process in the compound
13
[47]. The height of the relaxation peaks decreases with
increasing temperature, indicating the drop in the resistive properties [48]. As a result, it can be concluded that
in the films the relaxation process is well pronounced.
The impedance data of Z″ have been used to evaluate the
relaxation frequency (fr) of the electrical phenomena in
the material.
The Arrhenius plot of the relaxation frequency shown
in Fig. 13 indicates that fr satisfies the law [49]:
(
)
Ere
fr = f0 exp −
(14)
kB T
where ­f0 is the pre-exponential factor, and energy for relaxation ­(Ere) is the thermal activation energy of the carriers
charge. The values of ­Ere are reported in the Table 4. For
doped compound, the activation energy calculated from
relaxation frequency is very close to the value estimated
from conductance spectrum, this result indicating that
relaxation process and conductivity have the same origin
for doped samples [50]. Usually, the activation energy for
conduction ­(Edc) is the sum of both the creation of charge
carriers and hopping free energy of charge carriers over long
distances while the activation ­Ere is equal to the migration
free energy of charge carriers and their hopping between the
adjacent lattice sites. The difference between the conduction
and relaxation activation energies for undoped sample may
be attributed to the creation of free energy [51].
The phase angle (δ) can be expressed as follows [52]:
( �� )
Z
 = a tan
(15)
Z�
Figure 14 shows the frequency dependence of δ. The
peak position in δ shifts to the higher frequency side with
increasing temperature for all investigated samples. This
behavior confirms the presence of electric relaxation in
the material [53].
4 Conclusion
In summary, ­In2S3 thin films doped by nickel were carried
out by CSP technique with different Ni:In molar ratios. The
structural, morphological, optical and electrical properties of ­In2S3:Ni thin films have been studied in this work.
The prepared films are polycrystalline and exhibit a cubic
β-In2S3 phase. The crystallite size decreased from 27.5 to
23 nm with Ni doping. According to FESEM, the surface
morphology of the films is continuous and free of cracks.
RMS roughness increased from 12 to 18 nm. ­In2S3:Ni films
exhibit transparency over 70–55% in the visible region and
85–75% in near-infrared region. The values of Eg are found
to vary in the range 2.74–2.82 eV for direct transitions. The
J Mater Sci: Mater Electron
Fig. 11 Angular frequency
dependence of Z′ at different
temperatures
13
Fig. 12 Angular frequency
dependence of Z″ at different
temperatures
13
J Mater Sci: Mater Electron
J Mater Sci: Mater Electron
Fig. 13 Variation of relaxation
frequency ­(fr) versus 1000/T
13
Fig. 14 Phase angle versus frequency at different temperatures
for all samples
13
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J Mater Sci: Mater Electron
n values of I­ n2S3:Ni thin films decrease from 2.43 to 2.40
and the k values are in the range 0.01–0.20.
The AC conductance is a thermally activated process.
Furthermore, the AC conductance indicates that the conduction mechanism of ­In2S3:Ni is controlled by the CBH type
conduction. Impedance spectrum was characterized by the
appearance of semi-circle arc which is well fitted in terms
of electrical equivalent circuit and Cole–Cole model. Analysis of this spectrum permits to estimate the grain boundary
contribution.
Acknowledgements This work was supported by the Tunisian Ministry of Higher Education and Scientific Research, MINECO (Spain),
FEDER Funds (Projects MAT2015-67458-P and CTQ2016-79461-R)
and Fundación Ramón Areces, Spain (Project 2016-PO024).
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