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Synthetic Metals 223 (2017) 80–86

Contents lists available at ScienceDirect

Synthetic Metals

jo ur nal homep age: www.elsev ier .com/ locate /synmet

ilm thickness by interference pattern and optical characterization ofolyaniline by spectroscopic ellipsometry

oaquim Brasil de Lima Filho ∗, Ángel Alberto Hidalgoniversidade Federal do Piauí, Ininga, 64049-550, Teresina, PI, Brazil

r t i c l e i n f o

rticle history:eceived 26 November 2015eceived in revised form8 November 2016ccepted 22 November 2016

a b s t r a c t

Although Polyaniline (PAni) has been largely studied during several decades, many of its features are stillnot completely understood. Its optical properties have been widely characterized by simple techniquessuch as absorbance, transmittance, or reflectance in UV–vis–NIR spectral range, but mathematical modeldescribing its optical properties is still scarce. In this study, spectroscopic ellipsometry was utilized toprovide spectral data of PAni thin films. We develop a method for film thickness estimation by analysis of

eywords:olyanilineotating polarizer spectroscopicllipsometryauc–Lorentz modelnterference pattern

interference pattern and we show a very good-quality fitting to measured data with Tauc–Lorentz modelin the spectral range 200–1600 nm.

© 2016 Elsevier B.V. All rights reserved.

. Introduction

Polyaniline (PAni) is one of the most analysed organic semi-onductor materials due to its perspectives of applications inreas ranging from biotechnology, with the investigation of bio-ompatibility of materials [1] and bio-sensors [2–6], to the industryf electronic devices [7–9]. One of the advantages of PAni is itsasy synthesis and processing, having several different routes,mong which the main ones are the chemical [10–12] and thelectrochemical [13,14]. In any case, the obtained PAni has elec-rical properties similar to conductor materials (highly dopedemiconductors), but it is possible to turn it into an insulator byreatment in a basic environment. This switch behaviour rendershis material as an important candidate to applications on sensorso monitor acid/base environment [15–18].

These characteristics of PAni make it become target of exten-

ive study and seek for the comprehension of its film conformation,ptical properties and mechanism of electrical conduction [19].urthermore, its versatility, low cost, and ease on obtainmentakes it become an important material for the investigation and

∗ Corresponding author. Present address: Grupo de Polímeros Bernhard Gross –FSC/USP, Rua Miguel Petroni, 168, 13.566-590, São Carlos, SP, Brazil.

E-mail addresses: joaquimbrasil@ifsc.usp.br (J.B. de Lima Filho),ngel@ufpi.edu.br (Á.A. Hidalgo).

ttp://dx.doi.org/10.1016/j.synthmet.2016.11.025379-6779/© 2016 Elsevier B.V. All rights reserved.

understanding of the basic properties of more complex, less versa-tile, more expensive polymers.

Among other several techniques, the optical properties of PAnican be accomplished by using spectroscopic ellipsometry, whichhas the advantages of being a very versatile, precise and nondestructive technique. In this study, an accurate mathematical dis-persion model for PAni under the grounds of Sellmeier model isprovided. To do this, ellipsometry characterization is performedin the range 200–1600 nm and the interference pattern is used inorder to infer PAni film thickness.

2. Survey on ellipsometry theory

Ellipsometry is an optical characterization technique developedby P.A. Drude in the 19th century [20]. It consists on the analysisof how the polarization state of light changes after reflection by asurface. The name of the technique comes from the fact that a lin-early polarized incoming light is generally reflected off by surfacesas an elliptically polarized light [20,21], as sketched in Fig. 1.

The state of polarization of an electromagnetic wave can bedefined by two parameters, � and �, where the parameter � isrelated to the relative intensity between p- and s-components of

the electric field, and � is related to phase difference between p-and s-components of the electric field [22] (see Fig. 1). Since thechange on the polarization state of light due to reflection dependson the properties of the reflecting surface, the parameters � and

J.B. de Lima Filho, Á.A. Hidalgo / Synth

Fig. 1. Experimental setup of an ellipsometer. In this figure, the optical path con-taining the directions of incidence and reflection (plane of incidence) is in the planeof the page. It is parallel to the direction p and perpendicular to the direction s.The directions p, s, and k (direction of propagation of the light beam), in this order,are defined to obey the corkscrew-rule. Therefore, because of the limitations of 2D-dpb

�p

wg

r

a

r

n

w

n

coofloF

fibt

Fiao

rawing, the insets illustrating the state of polarization of light at each part of itsath are presented with its actual plane rotated +90◦ about the p-axis to provideetter view and understanding.

are related to its optical properties. Therefore, the ellipsometricarameters are defined in terms of complex quantities by [22,21]

rp

rs≡ � ≡ tan �ei�, (1)

here rp and rs are the Fresnel coefficients of reflection, which areiven by

p = nT cos �I − nI cos �T

nT cos �I + nI cos �T(2)

nd

s = nI cos �I − nT cos �T

nI cos �I + nT cos �T(3)

Combining Eqs. (1)–(3), it can be shown that

˜2T = n2

I sin2�I

[1 + tan2�I

(1 − �

1 + �

)2]

= n2I sin2�I

[1 + tan2�I

(1 − tan2� − i2 tan � sin �

1 + tan2� + 2 tan � cos �

)2]

, (4)

here nT is the pseudo refractive index of the surface given by

˜T = nT + i�T. (5)

In Eq. (5), nT is termed pseudo refractive index because the cal-ulation of the material’s optical properties by means of Eq. (4)nly gives the actual refractive index and extinction coefficientf the material when measurement of � and � is performed onat, homogeneous, and isotropic material, and when there is noverlapping of topside and backside reflected lights, as sketched inig. 2.

Fig. 2(a) shows a typical case in which, no matter how thin thelm is, it will be treated as a substrate if it is opaque and absorbsackside reflected light. Fig. 2(b) shows the case in which althoughhe material is transparent, it is thick enough such that it is possible

ig. 2. Three different situations concerning incident/reflected light: depending onts thickness and transparency, a layer can be classified as a substrate or a filmccording to whether the backside reflected light superposes the topside reflectedne or not.

etic Metals 223 (2017) 80–86 81

to separate the topside reflected light beam from the backside one.In contrast, in Fig. 2(c) it is impossible to separate both reflections.

The device utilized in this work was the GES5-Ellipsometer,provided by SOPRA. It is a Variable Angle Spectroscopic Ellipsome-ter (VASE) with rotating polarizer. As its intrinsic characteristic, itmeasures light intensity with respect to the angular position of therotating polarizer. If Ipol is the intensity of polarized light that leavesthe rotating polarizer, then the light intensity Idet that reaches thedetector is given by

Idet = I0(1 + cos 2P + sin 2P), (6)

where P is the angular position of the rotating polarizer, A is theangular position of the stationary analyzer, and⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

I0 ≡ Ipol|rs|2(tan2�cos2A + sin2A)2

≡ tan2� − tan2A

tan2� + tan2A

ˇ ≡ 2 tan � tan A cos �

tan2� + tan2A.

(7)

Light intensity-based measurements have the advantage toassure the better alignment of the system and the maximization ofthe ratio signal/noise, by setting up the system in order to minimizethe residue and the symmetry [23].

After data acquisition, the device performs a Fourier analysis ofthe measured intensity over the polarizer angular position P andcalculates the coefficients ˛(A = 45◦) and ˇ(A = 45◦) as functions ofwavelength or photon energy. From now on, in order to economizenotation in equations, these two parameters will be stated as ˛45and ˇ45. Then, in terms of these parameters, Eq. (4) becomes

n2T = n2

I sin2�I

⎡⎣1 − tan2�I

(˛45 + i

√1 − ˛2

45 − ˇ245

1 + ˇ45

)2⎤⎦ , (8)

which allows one to obtain the complex pseudo refractive index ofthe surface.

3. Experimental: PAni synthesis and processing

Doped PAni was obtained through chemical synthesis in thermalenvironment with temperature below 10 ◦C, in which 500 mL of analcoholic solution of sulphuric acid (13.8 mL of acid to 486.2 mLof alcohol) was gently mixed to 20.0 mL of doubly distilled anilineunder constant stirring while 20.0 mL of an aqueous solution ofammonium persulphate (0.576 g/mL) was slowly added in dropletsat an approximate rate of 10 s per each dropped droplet. After 4-hof reaction, the resultant content was filtered, the liquid part beingdiscarded. The solid content retained in the filter was washed withacetone in abundance in order to remove oligomers.

After this process, in order to get undoped PAni, the resultantsolid material was mixed to a solution 30 mL NH4OH:990 mL H2Oand left under constant stirring for 12 h. Then the system wasfiltered and the solid residue was washed with Milli-Q water inabundance. The material was then dried under 60 ◦C and ambientpressure. The dried PAni was then pulverized and stored. The PAniobtained with this process is known as emeraldine blue.

One solution of 498.9 mg of PAni in 25.0 mL of N-methyl-2-pyrrolidone (NMP) was prepared. In order to obtain a film with athickness of about 2870 nm (previously calculated), a number of 15

droplets, each with mean value of 11.5 �L, was deposited on glasssurface of 3.08 cm2. The surface of the glass substrate was treatedin acidic solution of 1 HCl:1 MeOH for thirty minutes, followed byrinse of Milli-Q water in abundance and gently dried under air jet.

82 J.B. de Lima Filho, Á.A. Hidalgo / Synthetic Metals 223 (2017) 80–86

45 for a film of PAni coated on glass substrate.

Ta

4

getoio

pocrat

ftm

i

Table 1Values for the best simulation of refractive index in the infrared region along withthe thickness of the film.

ε∞ S �0 (nm) d (nm)

Value 1.75 1.5 500 3000

Fi

Fig. 3. Spectral data in terms of ˛45 and ˇ

he film was then formed by casting in vacuum under the temper-ture of 60 ◦C.

. Results and discussion

Ellipsometric spectral data measured on a film of PAni coated onlass substrate gave the plotted graph shown in Fig. 3. The interfer-nce pattern in the range from ∼0.75 to ∼1.75 eV is an evidence thathe film is transparent in that spectral region. This occurs because ofverlapping between topside and backside reflection, as sketchedn Fig. 2(c). This information is useful in order to infer the thicknessf the film.

Considering that the state of polarization of the light exiting theolarizer is given by the azimuth P and that the state of polarizationf the reflected beam is given by the Fresnel amplitudes rp and rs, itan be shown, by combining Eqs. (1) and (7), that the intensity of theeflected light upon a system constituted of a thin layer coated on

substrate is related to the ellipsometric parameter ˛45 accordingo

I(A, P, �)∣∣A=45

◦ ∝ sin2P

1 − ˛45(�), (9)

rom which, by taking the first and second derivatives with respect

o �, it can be shown that the intensity maxima coincide with ˛45

axima.Fig. 4 shows the measured ˛45 in the spectral region where

nterference pattern is seen.

ig. 4. Measurement data of ˛45 parameter in the spectral region between 0.75 and 1.75ndicated along with the successive interference order m, m + 1,. . ..

Uncertainty 2% 2% 2% <3%

If the wavelengths �m corresponding to constructive interfer-ence of order m is known along with the refractive index n(�m),then it is possible to determine the film thickness d by applyingequation [21]

m = 2d

�m

√n2(�m) − sin2i +

2, (10)

where i is the angle of incidence of the beam with respect tothe normal to the surface and is a parameter that accounts thephase change due to the reflection of the wave leaving the inter-face film/substrate: it is zero if the refractive index of the substrateis larger than the refractive index of the film, otherwise it is unit.

However, neither the value of m nor n(�m) were known at themoment of the data acquisition. Thus, in order to estimate thefilm thickness, it was inferred that its refractive index was larger

than that of the substrate (nglass ≈ 1.5), according to references[24,25], and then Eq. (10) was plotted along with a simulationunder the grounds of Sellmeier model (Eq. (11)) for an estimate of

eV. The arrows point at maxima values of ˛45 and its corresponding wavelength is

J.B. de Lima Filho, Á.A. Hidalgo / Synth

Fig. 5. Interference order (black diamonds) is plotted according to Eq. (10) by assum-ing that refractive index in the infrared region is governed by Sellmeier model undera small uncertainty (grey error bars). The grey triangles give a redundant test bydetermining n(�m) from inversion of Eq. (9), assuming the lowest possible values ofmio

tt

n

sioooivvtcatfitdap

wc

covered by the black error bars. In this model, film thickness is a parameter thats step-by-step increased until the black error bars cover successive integer valuesf m.

he refractive index n(�) of PAni in the infrared region. Fig. 5 showshe best simulation acquired for the values presented in Table 1.

2 = ε∞ +∑

i

Si�2

�2 − �2i

. (11)

In a self-consistent procedure, the strategy behind Fig. 5 con-ists in specifying a small initial value of film thickness along withnitial values of Sellmeier parameters with large uncertainties inrder to generate the curves that constrain the refractive indexf the thin film (grey error bars). With this, there will be a rangef refractive index adopted for each wavelength. This refractivendex range and the film thickness lead to an uncertainty in thealue of m given by Eq. (10) (black error bars). In a next step, thealue of film thickness is continuously increased in order to leado a situation in which the uncertainty bars for interference orderover successive integer values of m. Then, the found values of mre inserted back in Eq. (10) in order to obtain values of refrac-ive index (grey triangles). If the generated refractive indexes aretted in the uncertainty region given by Sellmeier model, thenhe film thickness is accepted to be close to the real value. Theetermination of thickness will lead to more confidence as longs the fitting occurs for smaller uncertainties of the Sellmeier

arameters.

After inferring the film thickness, the next task became to decidehich mathematical model should be used in order to fit the opti-

al properties measured for the system PAni film/glass substrate.

Fig. 6. Measurement data (dotted line) and fitting function (continuous curve) to ˛

etic Metals 223 (2017) 80–86 83

Guided by the discussion established by Al-Attar et al. [26], the firsttrials for mathematical fittings were performed under the basis ofthe Lorentz model (Eq. (12)) for the polyaniline film along with theSellmeier (Eq. (11)) model for the substrate. Several trials were car-ried out with no success, what led to disposing the Lorentz modeland assuming the Tauc–Lorentz model [27], whose imaginary partof the dielectric function is given by Eq. (14) and its real part isobtained through Kramers–Kroning relations.

In many situations, the Lorentz model shows to be adequateto fit data because it is complex-valued and, therefore, accuratelyreproduce the real and imaginary parts of the refractive index forseveral materials. Lorentz model is given by

ε = ε∞ +∑

j

AjE2j

(E2j

− E2) + iE,jE, (12)

where Aj is the strength of the resonance, Ej is the energy of theresonance and E ,j is the damping term. It is related to the material’srefractive index by

n = ε2. (13)

Although Lorentz model has been successfully utilized to fitdata of many materials, Tauc–Lorentz model has shown to bemore appropriate to fit data of amorphous materials [28–31].Tauc–Lorentz model considers the contribution of the gap energyEg,j introducing a cutoff in the imaginary part of the material’sdielectric function, such that εI,j = 0 for E < Eg,j, and

εI,j = AjEjE,j(E − Eg,j)2

(E2 − E2j)2 + E2

,jE2

1E

, E > Eg,j. (14)

Therefore, since polymers are generally amorphous, data fit-ting gives better results when performed with Tauc–Lorentz modelthan with Lorentz model. The model consists of four Tauc–Lorentzoscillators, which are justified by the asymmetric band transitions.Fig. 6 shows a good fitting in the spectral range from 200 nm to1600 nm with R2 = 0.9912 and RMSE = 0.00874 accomplished by theparameters given in Table 2.

Table 2 is drawn in such a way that it also describes the mod-elled structure, which consists of a substrate in the bottom, thePAni film in the middle, and a thin roughness layer. The surround-ing environment is the air and it was omitted from the structureof Table 2. Observe that the influence of the substrate occurs only

in the NIR region ranging from ∼0.75 eV to ∼1.5 eV, since the over-layed PAni film is opaque in the remaining measured spectral range.Then, in order to account the influence of the substrate in the datafitting, Sellmeier model was applied with the parameters reported

45 and ˇ45 for PAni film coated on glass. The goodness of fitting is R2 > 0.99.

84 J.B. de Lima Filho, Á.A. Hidalgo / Synthetic Metals 223 (2017) 80–86

Table 2Structure, models and values of parameters that result in the best fitting to measured data for PAni coated on glass. The structure consists of a glass substrate below a PAnifilm and a roughness (RGNSS) layer between PAni and air, and the range interval is 200–1600 nm. The values between parentheses are the amplitude of uncertainty relatedto the last significant figures. The uncertainty is due to the fitting process.

RGNSS tknss = 0.4940 (2) nm; dep. coeff. = 0.333; conc. = 0.5

ε∞ = 1.74(3) thickness = 3020.805 (1)

j Aj (eV) Ej (eV) E ,j (eV) Eg,j (eV)

PANI Tauc–Lorentz

1 12.8 (2) 1.748 (2) 0.432 (3) 1.275 (4)2 0.655 (5) 2.103 (3) 0.568 (4) 0.00 (2)3 35 (1) 3.51 (1) 1.02 (1) 2.80 (1)4 133 (15) 5.70 (5) 1.61 (5) 5.06 (3)

ε∞ = 1

j Sj �j

GLASS Sellmeier1 0.6961663 0.06840432 0.4079426 0.11624143 0.8974794 9.896161

F btaino rs giv

btppfi

tm

TCo

ig. 7. Comparison of the real and imaginary parts of the complex refractive index of the complex refractive index generated from Tauc–Lorentz model with paramete

y Kitamura et al. [32]. In addition, the PAni films were consideredo be flat, uniform, isotropic and homogeneous in this modellingrocedure. Table 3 shows the cross correlation coefficients of thearameters of the mathematical model calculated after the datatting.

A comparison of the refractive index calculated by Eq. (8) andhe one calculated by this model can give a clue of how good this

odel is. Such a comparison is shown in Fig. 7. Since the PAni

able 3ross correlation coefficients of the mathematical model parameters of the fitting procether parameters are defined in Table 2.

tR tF A1 E1 E ,1 Eg,1 A2 E2 E ,2

Eg,4 −0.0137 0.0082 −0.0178 −0.0154 −0.0455 0.0142 −0.0005 −0.0031 0.0E ,4 0.1116 −0.0531 0.0448 0.4229 0.3273 −0.1368 0.1248 −0.0676 −0E4 0.2075 −0.0855 −0.5651 0.6001 −0.4811 −0.5343 −0.0793 0.0905 0.1A4 0.094 −0.2384 −0.4067 −0.0006 −0.6431 −0.1876 −0.1503 0.1197 0.1Eg,3 0.316 −0.0948 0.0343 0.0852 0.0268 0.0548 0.0482 0.0043 −0E ,3 0.4315 −0.0392 0.1236 0.0896 0.0673 0.1347 −0.159 0.248 0.0E3 −0.3036 0.0303 −0.074 −0.0652 −0.0279 −0.0917 0.0572 −0.1051 0.0A3 0.4141 −0.0786 0.0828 0.0977 0.0482 0.1028 −0.0219 0.0964 −0Eg,2 0.0645 −0.0408 0.1988 −0.0882 0.2388 0.1456 0.941 −0.7705 −0E ,2 0.1228 0.046 −0.0708 0.0963 −0.1311 −0.0379 −0.5333 0.3809E2 0.1175 −0.108 −0.1357 0.1019 −0.1049 −0.0976 −0.8923A2 0.1184 0.0081 0.2 −0.0569 0.1993 0.1547Eg,1 0.1147 0.1527 0.9522 −0.7429 0.1681E ,1 0.1605 −0.0102 0.3927 −0.0592E1 0.2922 −0.169 −0.7084A1 0.0868 0.1597tF −0.4017

ed directly from the measured parameters ˛45 and ˇ45 by Eq. (8) (dotted curve) anden by the values displayed in Table 2.

film shows to be opaque in the spectral region below 800 nm, thepseudo refractive index calculated by Eq. (8) is very close to theactual refractive index of the film. Tauc–Lorentz model generatesvery close values to the pseudo refractive index in such a spec-tral region, which evinces that the model is good. In the remaining

region, the pseudo refractive index is no longer close to the actualrefractive index of the film because it accounts both topside andbackside reflected light information, and therefore only the model

ss. In this table, tR and tF are the roughness and film thicknesses, respectively. The

Eg,2 A3 E3 E ,3 Eg,3 A4 E4 E ,4

018 −0.0023 −0.0048 0.0033 −0.0039 −0.0045 0.36 −0.034 0.0541.0484 0.1275 0.0338 −0.0202 0.0537 0.0152 −0.4427 0.33015 −0.1416 0.0799 −0.0582 0.0892 0.0597 0.3428545 −0.2028 0.0486 −0.0404 0.0411 0.0435.0682 0.0765 0.9611 −0.9252 0.0463565 −0.1567 0.2735 −0.2738458 0.0248 −0.9807.029 −0.0004.7336

/ Synthetic Metals 223 (2017) 80–86 85

ct

toToamitiFaiiots

rotubtzo

Fig. 8. Multiple points measurements were performed by sliding the sample inequal distances in both directions east–west and north–south with the aid of thestep motor controlled sample stage. The dark grey area represents the matrix formed

J.B. de Lima Filho, Á.A. Hidalgo

an specify the actual optical behaviour of the material in that spec-ral range.

The mathematical model required four Tauc–Lorentz oscilla-ors, each one having four free parameters, what leads to a totalf 16 parameters for data fittings (apart from thickness and ε∞).he number of fitting parameters is large, but this is consequencef the oversimplification in the samples structure, which weressumed to be isotropic, homogeneous, uniform, and flat. Severaleasurements were performed for different points on the sample,

n a matrix covering a region of area more than ten times largerhan the area defined by the ellipsometer beam spot, as sketchedn Fig. 8. Comparisons between these measurements, plotted inig. 9, shows that the optical properties is practically the same forll analyzed points, what leads to the conclusion that the samples in fact homogeneous, uniform, and flat. A more detailed analysiss required in order to have any conclusion about the anisotropyf the sample. Such analysis would require rotation of the samplehrough an axis that coincides with the position of the beam on theample.

It is known that polyaniline shows different optical absorptionelated to its different oxidation states. For instance, in any of itsxidation states, polyaniline absorption peak around 3.8 eV relatedo �–�* transitions, but a second peak in 2 eV is assigned to molec-lar excitons in the emeraldine base, while in the pernigraniline

ase the second absorption peak is located at 2.3 eV and is assignedo Peierls dimerization gap [33]. In addition, UV–vis characteri-ation has been suggested as a method to determine the state ofxidation of polyaniline samples with good accuracy according to

Fig. 9. Ellipsometric characterization of d

by the spots, represented by the light grey circles.

the relative spectral peak intensity [34]. The energies Ej (j = 0, 1, 2,and 3) in Table 2 are in agreement with the polyaniline absorptionpeaks if it is assumed that the samples consist of a mixture of dif-ferent oxidation states of polyaniline. The strengths Aj is relatedto the concentration of such different oxidation states. ThereforeA1 > A2 implies that emeraldine base has larger concentration thanpernigraniline base in the analyzed samples. The energy E4 can be

assigned to the work function of polyaniline, as already suggestedby Park et al. [35] as well as by Choi et al. [36].

ifferent points on the same sample.

8 / Synth

5

Vdpaafiibpmiebn

bcttttotrg

A

dPC(

R

[

[

[

[

[

[

[

[

[

[

[

[

[[

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[Won Min Yun, Oh Kwan Kwon, Chan Eon Park, Kwan-Do Kim, Hoon-Kyu Shin,

6 J.B. de Lima Filho, Á.A. Hidalgo

. Conclusions

Besides of being a very powerful technique, Rotating Polarizerariable Angle Spectroscopic Ellipsometry (RP-VASE) measuredata are very difficult to be analysed, due to the various fittingarameters it requires, depending on model, properties of char-cterized material, film thickness, spectral range, etc. RP-VASEpplied to the optical characterization of polyaniline (PAni) thinlms obtained by chemical synthesis and coated on glass by cast-

ng showed that Tauc–Lorentz model with four oscillators led to theest fitting of measured data. This result is different to the three-eak Lorentz model proposed by Al-Attar et al. [26]. The differencesay come from different synthesis and deposition processes, since

n their sample were produced by electrochemical synthesis, gen-rating conducting PAni, while in this study, the PAni was obtainedy chemical synthesis and undoped in basic solution, leading to aon conducting material.

Before the fitting procedure, the film thickness was determinedy the analysis of the interference pattern by a self-consistent pro-edure that links the order of interference to the transparency ofhe material described by the Sellmeier model using the construc-ive interference peaks. Comparison between Figs. 5 and 7 showshat the refractive index of PAni obtained by the self-consistenthickness determination procedure agrees with the refractive indexbtained by the Tauc–Lorentz model for the infrared region. In addi-ion, the refractive index calculated from Eq. (8) agrees with theefractive index calculated by Tauc–Lorentz model with parametersiven in Table 2 in the remaining region, as shown in Fig. 7.

cknowledgement

Authors acknowledge the support provided by: Universi-ade Federal do Piauí (UFPI), Fundo de Amparo á Pesquisa doiauí (FAPEPI), Instituto Nacional de Eletrônica Orgânica (INEO),oordenac ão de Aperfeic oamento de Pessoal de Nível SuperiorCAPES), Conselho Nacional de Pesquisa (CNPq).

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