Single-oscillator model and determination of optical constants of some optical thin film materials

Article abstract of DOI:10.1016/j.physb.2004.09.097

The optical properties of some optical thin film materials have been investigated by means of the optical transmittance and reflectance spectra. The dispersion of the refractive index is discussed in terms of the Wemple-DiDomenico single oscillator model.

Full text of DOI:10.1016/j.physb.2004.09.097

ARTICLE IN PRESS
Physica B 353 (2004) 210–216
www.elsevier.com/locate/physb
Single-oscillator model and determination of optical constants
of some optical thin film materials
a,
F. Yakuphanoglu , A. Cukurovali , I. Yilmaz
Ã
b
b
˙
aDepartment of Physics, Faculty of Arts and Sciences, Firat University, 23169 Elazig, Turkey
bDepartment of Chemistry, Faculty of Arts and Sciences, Firat University, 23169 Elazig, Turkey
Received 10 May 2004; received in revised form 2 August 2004; accepted 28 September 2004
Abstract
The optical properties of some optical thin film materials have been investigated by means of the optical
transmittance and reflectance spectra. The dispersion of the refractive index is discussed in terms of the
Wemple–DiDomenico single oscillator model. The optical band gap values were calculated for Taue model and
Wemple–Didomenico model. The optical band gaps which turned out to depend significantly on the metal coordination
were calculated in terms of Taue method and Wemple–Didomenico model. The E
WD
opt
values obtained from
Wemple–Didomenico model are in agreement with those determined from the Taue model. The type of optical
transition responsible for optical absorption is indirect transition with an energy gap of 2.12–2.39 eV. The dispersion
energies Ed of the thin films are in the range of 29.69–14.32 eV. The real and imaginary parts of the dielectric constant of
the films were determined. The real and imaginary parts follow the same pattern and it is seen that the values of real
part are higher than imaginary parts.
r 2004 Elsevier B.V. All rights reserved.
Keywords: Optical materials; Dispersion of refractive index; Optical band gap
1. Introduction
coordinates as deprotonated or neutral forms. The
ortho-hydroxy Schiff bases form the intra-mole-
cular hydrogen bonds and they are interesting
ligands. Several adducts of non-transition, early
transition and f-metals with such bases acting as
neutral ligands [2] have been studied. Thiazoles
represent a very interesting class of thin films
because of their wide applications in pharmaceu-
tical, phytosanitary, analytical, and industrial
aspects, e.g. as fungicides, anthelmintics and
As is known, Schiff bases from the condensation
of salicylaldehyde with alkyl and arylamines are
known as N-alkyl or N-aryl salicylaldimines and
widely used in coordination chemistry [1] which
Ã
Corresponding author. Tel.: +90424 23700006591; fax:
+90424 2330062.
E-mail address: fyhan@hotmail.com (F. Yakuphanoglu).
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2004.09.097

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F. Yakuphanoglu et al. / Physica B 353 (2004) 210–216
211
herbicides [3]. On the other hand, cyclobutane
2. Experimental
carboxylic acids in different forms were described
as highly potent l-Glutamate, N-methyl-D-aspar-
tate (NMDA) agonist, NMDA antagonists and
anticonvulsive drugs [4,5]. However, the syntheses
and complexation properties of 1,1,3-trisubstituted
cyclobutane-substituted thiazoles and their Schiff
base derivatives containing the mesityl group have
not been reported so far. Recently, there has been
considerable interest in the chemistry of Schiff
base compounds containing thiosemicarbazones
and their metal complexes due to their biological
activities [6] and nonlinear optical properties [7].
These compounds, containing cyclobutane,
thiazole and Schiff base functions in their mole-
cules, seem to be suitable candidates for further
chemical modifications and may be optical
communication and optical devices. Therefore,
the optical absorption spectra have proved to be
very useful for elucidation of the electronic
structure and optical constant of these materials.
Transition metal complexes have a number of
electrical properties in the dark which similar to
those of classic crystalline and amorphous semi-
conductors and these compounds can behave
like intrinsic semiconductors. Optical and electri-
cal properties of the metal complexes have
become an increasingly interesting area of semi-
conducting and optical materials because these
materials possess great potential for device
applications such as Schottky diode, solid state
devices and optical sensor. The study of optical
absorption of transition metal complexes, particu-
larly the absorption edge has proved to be very
useful for elucidation of the electronic structure of
these materials [8]. It is possible to determine
indirect and direct transition occurring in the band
gap of the metal complexes by optical absorption
spectra [8]. The optical constants such as refractive
index, absorption index and dielectric constant can
be analyzed by transmittance and reflectance
spectra.
2.1. Synthesis of the compounds
The ligand LH (0.2028g, 0.50mmol) was dis-
solved in absolute ethanol (15–20mL). A solution
of 0.25mmol of the metal salt [Co(AcO)2 ꢀ 4H2O
(0.0623g), Cu(AcO)2 ꢀ H2O (0.0499 g), Ni(AcO)2 ꢀ
4H2O (0.0623 g) Zn(AcO)2 ꢀ 2H2O (0.0549 g)] in
ethanol (10 mL) was added dropwise with contin-
uous stirring. In the case of Co(II) complexes, a
slow stream of nitrogen was passed through the
solution. Every mixture was refluxed for 1 h and
then left to stand overnight at room temperature.
The complexes, precipitated as microcrystal, were
filtered, washed with cold ethanol and water several
times and dried in vacuum at 60 1C (over P4O10)
and stored in a desiccator over CaCl2. The
synthesized complexes were characterized and
described elsewhere [9]. The chemical structure of
the complexes is given in Fig. 1. The solution of the
films was homogenized for 5 h and was rotated for
homogeneous mixing. Then, the thin films depos-
ited on quartz substrates were prepared by evapor-
ating the solvent from a solution of the compounds.
The sum of transmittance and reflectance spectra in
the transparent region was found as 100% within
experimental error for the films. Thus, the homo-
geneity of the films was confirmed by these results
[10]. The crystal structure of the films was studied
In the present work, we are to investigate optical
properties of some optical thin materials-based
metal complexes so that this information would be
helping the researchers toward applying these
materials in optical communication and optical
devices.
Fig. 1. The chemical structure of the compounds.

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by X-ray diffraction study. But, any peak is not
observed in the X-ray pattern. This confirmed that
the films have amorphous structure. From the
measured spectral curves, the average thicknesses of
the films were determined using optical spectral
curves of the films [11]. The values of film thickness
of the Co(II), Ni(II), Cu(II) and Zn(II) films were
approximately found as 588, 586, 584 and 582 nm,
respectively. UV–Vis spectra of the thin films
having different thicknesses were recorded at room
temperature using a CECIL CE-5502 UV–Vis
instrument.
3. Results and discussion
3.1. Optical absorption at the fundamental edge
Figs. 2(a, b) show the transmittance and
reflectance spectra of the thin films as a function
of wavelength. The absorption coefficient a was
calculated using the well-known formula, a=ꢁ1/
dln[T/(1ꢁR)2]. The experimental results show that
the dominant transition is the indirect one by the
proposed Taue [12]. Thus, the plots of (ahn)1/2 vs.
hn were plotted to obtain optical band gaps of the
thin films, as shown in Fig. 3. As a result of
indirect transition, Eq. (1) is determined as,
Fig. 2. (a) The transmittance and (b) reflectance spectra of the
thin films.
The absorption edge can be determined from the
exponential dependence of the absorption coeffi-
cient and it is determined as [13],
1=2
ðahnÞ ¼ Aðhn ꢁ EoptÞ:
(1)
Indirect gap was determined from the linear
portions as shown in figures and the values are
given in Table 1. When the optical band gaps
were compared with each other, their order follows
ZnðIIÞE oNiðIIÞE oCoðIIÞE oCuðIIÞE : It is
aðhnÞ ¼ ao expðhn=EuÞ;
(2)
where ao is a constant and Eu is the Urbach
energy. Plotting the dependence of ln a vs. hn as
shown in Fig. 4 should give a straight line. The Eu
values were calculated from the following relation-
ship,
opt
opt
opt
opt
observed that Eopt values follow a certain trend
except for Cu(II) sample and they decrease with
increasing atomic number of the metal ion in the
compounds, in which the atomic number follows
the order of Co(II)oNi(II)oCu(II)oZn(II). This
suggests that the atomic number of metal ion
dominates on the optical band gaps of the films, if
the materials studied have the same coordination
geometry. It is evaluated that the materials studied
except for Cu(II) sample have tetrahedral geome-
try. Thus, we suggest that the metal coordination
is dominant on the optical band gaps.
ꢀ
ꢁꢁ1
d ln a
d hn
Eu ¼
:
(3)
The steepness parameter, s ¼ kT=Eu; characteriz-
ing the broadening of the optical absorption edge
due to electron phonon or exciton–phonon inter-
actions [14] was also determined taking T=300 K
and given in Table 1. The s values of the samples
except for Cu(II) sample change inversely with
optical band gaps. The atomic number of the

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213
metal ion causes a shift in the optical absorption
3.2. Dispersion behavior of refractive index
edge therefore change in the band structure of the
films. It is found that the optical absorption edge
of the films except for Cu(II) decreases with
increasing atomic number of the metal ion. The
atomic number is responsible for the width of
localized states in the optical band of the films and
it decreases the width of localized states in the
optical band gap. That is why, the s values change
inversely with optical band gaps of the films.
We determined values of n and k from the
transmittance and reflectance spectra of the thin
films. The reflectance spectra of the thin films
exhibit a peak at energies to the interband
transitions. The reflectance and refractive index
of any solid certain constant wavelength are
expressed as [15],
al
k ¼
;
(4)
(5)
4p
2
ðn ꢁ 1Þ þ k2
R ¼
:
2
ðn þ 1Þ þ k2
The spectral curves of n values determined using
above relationships are shown in Fig. 5. As seen, n
values increase with increasing photon energy and
Fig. 3. The (ahn)1/2 vs. hn plots of the thin films.
Fig. 4. The Urbach plots of the thin films.
Table 1
The optical parameters of the thin films
Film
EoptT(eV)
EWopDt (eV)
Eu (meV)
s
Eo (eV)
Ed (eV)
n
1
lo (nm)
So (mꢁ2
)
Co(II)
Ni(II)
Cu(II)
Zn(II)
2.30
2.25
2.39
2.12
2.15
2.41
2.46
2.24
347.7
287.4
322.6
253.6
0.071
0.086
0.077
0.098
4.30
4.82
4.94
4.48
18.52
14.32
29.69
23.6
4.99
2.35
2.73
6.35
288.3
270.7
281.1
276.7
5.06 1013
1.69 1013
2.15 1013
7.43 1013
T
Eopt (eV) optical band gap obtained from the Taue model, E
WD
opt
(eV) optical band gap obtained from the Wemple–Didomenico
model, Eu (meV) width of the localized states obtained from the Urbach plot, s steepness parameter, Eo (eV), the oscillator energy, Ed
(eV), the dispersion energy, n the long wavelength refractive index, lo(nm) average interband oscillator wavelength and So (mꢁ2) the
average oscillator strength.
1

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Fig. 6. The 1/(n2ꢁ1) vs. (hn)2 plots of the thin films.
the optical band gap, Eopt, can be obtained from
the Wemple–Didomenico model. The optical band
gap values, Eopt, were also calculated from the
Wemple–DiDomenico dispersion parameter, Eo,
using Eopt ꢂ Eo=2 relationship [18,19]. The EoWpDt
values obtained from Wemple–Didomenico model
are in agreement with those determined from the
Taue model (see Table 1).
Fig. 5. The refractive index plots of the thin films.
the refractive index values of the thin films shows
significant differences. This is due to the major
contribution of virtual electronic transitions in the
thin films. This leads to a significant change in the
optical parameters. In the interband region there is
appreciable modification of the photon energy
dependence of the refractive index. A peak is
observed in the refractive index spectra of the
compound and shifts toward higher photon
energies. The refractive index dispersion of the
compounds studied can be fitted by the Wemple–-
DiDomenico relationship. The dispersion plays an
important role in the research for optical materi-
als, because it is a significant factor in optical
communication and in designing devices for
spectral dispersion. The result of refractive index
dispersion below the interband absorption edge
corresponds to the fundamental electronic excita-
tion spectrum. Thus, the refractive index is related
to photon energy through the relationship [16,17],
The long wavelength refractive index (n ),
1
average interband oscillator wavelength (lo) and
the average oscillator strength (So) for the thin
films were determined using the following relation-
ship [20],
ꢀ
ꢁ
2
ðn21 ꢁ 1Þ
lo
l
¼ 1 ꢁ
;
(7)
ðn2 ꢁ 1Þ
where (n ) and (lo) values were calculated from
1
the plots of (n2ꢁ1) vs. lꢁ2 and are given in Table 1.
Eq. (7) can also be written as,
ðSol2oÞ
n2 ꢁ 1 ¼
;
(8)
ð1 ꢁ l2o=l2Þ
where So ¼ ðn21 ꢁ 1Þ=lo2: The Eo and So values
were obtained using above equation and are given
in Table 1. These values are of the same order as
those obtained by DiDomenico and Wemple [20]
for a number of materials.
EoEd
E2o ꢁ ðhnÞ
n2 ¼ 1 þ
;
(6)
2
where Eo and Ed are single-oscillator constants.
We calculated the values of the parameters Eo and
Ed by plotting (n2ꢁ1)ꢁ1 vs. (hn)2 (Fig. 6) and they
are given in Table 1. The parameter Ed is the
oscillator strength or dispersion energy which is a
measure of the strength of interband optical
transitions. The oscillator energy Eo is an average
energy gap. Furthermore, an approximate value of
3.3. Complex dielectric constant
The real and imaginary parts of the dielectric
constant can be given in the following form [21];
ꢀ1 ¼ n2 ꢁ k2 and ꢀ2 ¼ 2nk:
(9)

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The dependences of e1 and ꢀ2 on photon energy
4. Conclusions
are shown in Figs. 7(a, b). The real and imaginary
parts follow the same pattern and it is seen that the
values of real part are higher than imaginary parts.
The variation of the dielectric constant with
photon energy indicates that some interactions
between photons and electrons in the films are
produced in this energy range. These interactions
are observed on the shapes of the real and
imaginary parts of the dielectric constant and they
cause formation of peaks in dielectric spectra. This
formation depends on the type of the compound.
The maximum peak height of these peaks corre-
sponds to plasma frequency.
On the basis of the optical investigations of the
films, the following results were obtained. The
optical band gaps which turned out to depend
significantly on the metal coordination were
calculated in terms of Taue method and Wem-
WD
ple–Didomenico model. The E
opt
values obtained
from Wemple–Didomenico model are in agree-
ment with those determined from the Taue model.
The type of optical transition responsible for
optical absorption was indirect transitions. The
optical constants (refractive index n, extinction
coefficient k and dielectric constant) were analyzed
from the transmittance and reflectance spectra.
The spectral dependence of the optical curves
indicates that the optical parameters change with
metal coordination in the films.
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