ion bombardment effect on the band gap of anatase TiO2 ultrathin films M.-B. Bouzourâa1*, Y. Battie1, A. En Naciri1*, F. Araiedh1, F. Ducos1, N. Chaoui1 1LCP-A2MC,
*
Institut Jean Barriol, Metz, Université de Lorraine, France
Corresponding authors:
[email protected],
[email protected]
ABSTRACT We report a study of the effect of nitrogen ion bombardment on the optical properties of anatase TiO2 ultrathin films, particularly the band gap energy. The TiO2 films were prepared by a sol-gel method and dip-coating process. The as-prepared TiO2 films were then exposed to a
low-energy ion beam from a microwave electron cyclotron resonance (ESR) ion source.
Raman and spectroscopic ellipsometry (SE) analysis were performed on TiO2 films prepared at different
exposure times. The Raman measurements reveal the conservation of the
anatase TiO2 crystalline structure after the ion beam exposure. From a detailed ellipsometric study, the thickness of layers, the dielectric function, the band gap and the Urbach energies were determined. The obtained results show an increase of the TiO2 band gap with the decrease of thickness of films during
exposure time. The band gap energy was blue
shifted from 20 meV to 140 meV as the exposure time was increased from 5 min to 20 min when the thickness was decreased from 30 nm to 21 nm. This increasing of band gap energy could be explained by the thickness effect. From the band tail, the Urbach energy was also affected by
ion beam. These results are in good agreement with the observed broadening
of the Raman band the O-Ti-O bending vibration mode, as the exposure time increases.
Keywords TiO2;
ion bombardment; Ellipsometry; Raman; Band gap energy; Urbach energy 1
1.
Introduction
Titanium dioxide (TiO2) semiconductor has attracted great interest from researcher due to its optical, chemical and electronic properties [1]. These characteristics are fueled and fanned by its prospects for several applications in photocatalysis [2], dye-sensitized solar cells [3], blue lighting [4] and self-cleaning surfaces [5]. However, the anatase phase of TiO2 has large band gap (3.2 eV) traducing limit efficiency in ultra violet range. A More efficient TiO2 material can be achieved by TiO2 to absorb light in the visible region. Thereby, the incorporation of nitrogen (N) in TiO2 matrix is suitable for enhancing TiO2 photo-activity under the sunlight [6]. Despite the absorption in visible range, there are several optical studies relating to the effect of N atoms on the band gap of anatase TiO2 [5-13]. For example, some authors [7-9] have founded a band gap narrowing due to the modification of the valence band by the hybridization of the two levels O 2p and N 2p, while other researchers [10, 11] have shown that the band gap is unchanged and the N 2p states are localized just above the O 2p valence band maximum. Whereas in recent publications [12, 13], the authors have founded a decrease in the band gap for relatively high N concentration using transmission measurements [12, 13], while for low N concentration, the band gap is conserved [12, 13] and a localized N 2p states are created [13]. In these previous works, the band gap was estimated by transmission measurements and by theoretical calculations of the density of states. However, spectroscopic ellipsometry (SE) technique is a powerful tool to determine the optical properties of materials such as the optical band gap [14]. Recently, SE was used to study the optical constants and band gap evolution with phase transition in sub-20-nm-thick TiO2 films prepared by atomic layer deposition [15]. Deducing from band gap evolution, the authors have found that the anatase TiO2 transforms to rutile TiO2 at high annealing temperature around 800 °C [15]. Consequently, SE can deduce the crystalline structure of deposited and annealed films. For this, in this paper, we propose to study by SE the
ion bombardment effect on the band gap energy of TiO2 ultrathin films
with thickness varying between 21 nm and 30 nm. The Raman spectroscopy was used to study the effect of
ion bombardment on the crystalline structure of the TiO2 films. SE was
also used to extract the dielectric function, the band gap and the Urbach energies of the films from the numerical analysis using constrained cubic splines method, Tauc-Lorentz and Urbach models. These results will be helpful to understand the thickness effect of ultrathin films on the optical responses. 2
2.
Experimental
2.1
Preparation of the TiO2 ultrathin films
The sol-gel method was used to elaborate the TiO2 films. The preparation procedure of the sol is detailed elsewhere [16]. Briefly, titanium tetraisopropoxide (Aldrich, 99%) was used as a precursor to synthesize the titania sol via an acid catalyzed sol-gel process at room temperature and under argon atmosphere. Propan-2-ol (Aldrich, 99.8%) and hydrochloric acid (ARCOS Organics) were used as solvent and catalyst, respectively. The sol was deposited onto quartz microscope slides. Prior to use, the quartz substrates were successively cleaned with acetone and ethanol for 10 min and dried with a stream of nitrogen gas. The quartz substrates were then coated with the sol by dip-coating at a withdrawal speed of 100 mm/min under a relative humidity of 55% and then dried at 70°C for 5 min. This operation was repeated several times in order to obtain a thickness of several tens of nm. The obtained coatings were further dried in an oven at 80 °C for 12 h and then calcinated at 450 °C in air during 2 h. In order to limit cracks of the films, the temperature of the furnace was raised at 5 °C/min and the sample was gradually cooled down to room temperature.
2.2
exposure
The as-obtained TiO2 ultrathin films were exposed to a low-energy
ions beam during 5, 10
and 20 min. These experiments were performed in a stainless steel high-vacuum chamber with a base pressure of 8.10-8 mbar. The
ions beam comes from a microwave electron
cyclotron resonance (ECR) ion source (Gen II-Tectra). During the operation, the nitrogen pressure was kept at 5.10-4 mbar. The ions energy and the current were 500 eV and 10 mA, respectively. The distance between the nitrogen source and the films surface was 100 mm and the fluence was then of about 1015 ions/cm2. During the exposition, the temperature of the films was maintained at 580 °C in order to promote nitrogen diffusion. The films were also rotated during the whole process in order to ensure a homogenous exposure.
The Raman spectra were recorded using a LabRAM HR 800 spectrometer with a resolution of 0.3 cm−1. The source used for Raman measurements was the HeNe laser (633 nm) fixed at a power of 10 mW. The ellipsometric data were obtained by a phase modulated UVISEL
3
Horiba ellipsometer. Ellipsometry measures the changes of the polarization state between the incident and the reflected light on the samples. The measured values are the ellipsometric angles and . They are related to the ratio between the reflection coefficients of the sample for p-polarized light (rp) and s-polarized light (rs) by the following relationship [17]:
,
Eq. (1)
The UVISEL ellipsometer measures the I S and IC parameters that are related to the ellipsometric angles by [18]:
and
.
Eq. (2)
The optical responses of all TiO2 ultrathin films were investigated in the 0.6-4.6 eV spectral range at angle of incidence of 50°.
3.
Results and discussion
3.1
Raman analysis
Fig. 1 presents the Raman spectra of the TiO2 after 0, 5, 10 and 20 min exposure time to the ion beam. The observed vibration modes at 142 cm-1,197 cm-1, 395 cm-1, 514 cm-1 and 637 cm-1 are attributed to the anatase phase [19]. These modes are also observed in the spectra of irradiated samples traducing the conservation of the anatase crystalline structure. Other authors have found that the anatase TiO2 transforms to rutile TiO2 at high annealing temperature around 800 °C [15]. The low frequency modes at 142 cm-1 and at 197 cm-1 and that at 637 cm-1 are attributed to the O-Ti-O bending vibration [19]. Their corresponding peaks decrease in intensity as the
exposure time increases traducing the decrease of the O-
Ti-O vibration concentration. The insert of Fig. 1 shows no significant Raman shift of low frequency mode at 142 cm-1 involving no stress in TiO2 ultrathin films with the
exposure
time. More details about the
exposure time dependence of the full width half maximum of the
-1
142 cm mode are discussed in section concerning the SE measurements. Two modes at 208 cm-1 and 260 cm-1 are observed in the spectra of the samples exposed to the
beam. These
modes are attributed to titanium oxinitride TiO2-xNx [20, 21] and titanium nitride TiNx, respectively [22]. It is interesting to note that the intensities of these bands increase with 4
ion exposure time. The bands located at 310 cm-1 and at 560 cm-1 are attributed to the Ti-N vibration suggesting that nitrogen substitutes oxygen atoms in the anatase lattice [21]. Four bands are shown in TiO2-xNx Raman spectra and centered at 123 cm-1, 160 cm-1, 425 cm-1 and 490 cm-1. Their amplitudes are higher for TiO2-xNx_20 sample. They are attributed to the quartz substrate contribution (see Fig. 1). The intensity of bands increases with bombarding time at the expense of the Raman peak at 142 cm-1 . This suggests a thinning of the TiO2 films with the increase of
ion exposure time. SE confirmed this statement about the thinning of
TiO2 layers.
Intensity (a. u.)
Intensity (a. u.)
*
(a) TiO2 (b) TiO2-xNx _5 (c) TiO2-xNx _10 (d) TiO2-xNx _20 (e) Quartz
(a) (b) (c) (d)
120
130
140
150
160
-1
* : Anatase phase
170
Raman shift (cm )
*
*
*
*
*
(a)
*
*
* (b) TiNx
TiN (c)
TiO2-xNx
TiN (d) (e)
x7
100
200
300
400
500
600
700
-1
Raman shift (cm ) Fig. 1.
3.2
ion exposure time dependence on Raman TiO2 spectra.
Spectroscopic ellipsometric measurements
As the ellipsometry is an indirect characterization tool, the combination of a dispersion law and a physical model is required to exploit SE data. Several dispersion laws such as TaucLorentz [23] and Forouhi-Bloomer [24] were used to extract the optical constants of TiO2 by modeling data. Recently, Likhachev et al. [25] demonstrated that the constrained cubic spline (CCS) is an efficient tool to improve the fitting quality of experimental data. This technique is consistent with Kramers-Kronig relations [26]. In addition, this approach is adapted to describe the dielectric function of different materials such as Si, InP and Al [27], Au 5
nanoparticles [28] and ZnO [29, 30]. Here, the CCS technique was used to determine the dielectric function of the TiO2 samples exposed to the
beam.
Fig. 2 presents the ellipsometric measurements (IC, IS) of TiO2 at different
ion exposure
time fitted by minimizing the following mean-square error () using the LevenbergMarquardt [17]:
where
,
and
,
Eq. (3)
are the theoretical and experimental values of IC and
IS, respectively. N is the number of collected data.
and
are the standard deviation of
ellipsometric measurements. The physical model used for SE data analysis is shown in Fig. 3. This model is composed of two sub-layers located on a semi-infinite quartz substrate. The upper one is a dense TiO2 or TiO2-xNx layer and the other is a rough layer described by an effective dielectric function according to the Bruggeman effective medium theory [31]. In the modeling, the known parameter is the dielectric function of quartz substrate [32]. The unknown parameters are the thickness of each sub-layer and the dielectric function of TiO2 and TiO2-xNx which were determined by the CCS technique. The principle of the CCS method is based on the determination of the imaginary part of dielectric function by a collection of connected splines. Each spline is given by a third order polynomial that links successive energy nodes [29]. The imaginary dielectric function of TiO2 was divided into a set of splines using 17 nodes located between 0.6 eV and 6 eV. The real part of the complex dielectric function is then calculated by using the Kramers Kronig relations. Through these splines, the calculated and compared with experimental measurements
and
and
are
by minimizing
the mean square error Good agreement was found between measured and calculated SE spectra (IC, IS) for all the samples as shown in Fig. 2.
6
0.3
(a) TiO2
(b) TiO2-xNx _5 0.3
(1) Is_exp Is _ mod (2) Ic_exp Ic _ mod
0.0
0.0
(1)
(1)
(Is, Ic)
(Is, Ic)
(1) Is_exp Is _ mod (2) Ic_exp Ic _ mod
-0.3
(2)
-0.3
(2) -0.6
-0.6
-0.9
-0.9
1
2
3
4
1
5
2
Energy (eV) 0.3
3
4
5
Energy (eV) 0.3
(c) TiO2-xNx _10
(d) TiO2-xNx _20 (1) Is_exp Is _ mod (2) Ic_exp Ic _ mod
(1) Is_exp Is _ mod (2) Ic_exp Ic _ mod
0.0
0.0
(1)
(Is, Ic)
(Is, Ic)
(1)
-0.3
-0.3
(2)
(2) -0.6
-0.6
-0.9
-0.9
1
2
3
4
1
5
Energy (eV)
2
3
4
5
Energy (eV)
Fig. 2. Measured and calculated (IC, IS) ellipsometric parameters of (a) TiO2 and TiO2 exposed to the ion beam during (b) 5 min, (c) 10 min and (d) 20 min. The calculations are based on the model given in Fig. 3 and CCS numerical method.
7
L2 L1
TiO2 or TiO2-xNx
Substrate: Quartz Fig. 3. Physical model used to extract the optical properties of TiO2 and TiO2-xNx.
The physical model shown in Fig. 3 for all samples is summarized in the Table 1. The layer is thinner with increasing exposure time. This sputtering of the TiO2 films is in agreement with the observed decrease of the anatase modes in the Raman spectra as the exposure time to the ion beam increases. Sample
TiO2
TiO2-xNx _5
TiO2-xNx _10
TiO2-xNx _20
L1(nm)
30
30
26.5
21.3
L2(nm)
6
7.4
6.7
1.2
Table 1: L1 thickness values of TiO2 and TiO2-xNx layers. L2 the corresponding roughness values.
The TiO2 dielectric functions obtained by CCS are shown in Fig. 4. The bombarding of TiO2 by
ion induces an absorption tail in the visible range from 2 eV to around 3.5 eV. This
absorption is likely to be due to the contribution of N atoms which occupy both interstitial (Ni) and substitutional (N s) sites in the TiO2 anatase lattice [6, 7, 33]. Ns atoms substitute the oxygen vacancy (Ov) sites in the TiO2 films and its energy level is localized just above the TiO2 valence band [33]. The energy level of Ni is deeper than that of N s [33]. The electronic transitions of absorption tail through Ni and Ns energetic levels increases with the exposure time as shown in Fig. 4(b). Furthermore, as shown in Fig. 4(b) the intensity of the absorption band at around 4 eV decreases and broadens as the exposure time increases. This broadening can be ascribed to the defect states generated by the
ion beam. 8
12 (a) TiO2 TiO2-xNx _5 TiO2-xNx _10 TiO2-xNx _20
r
9
6
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
3.5
4.0
4.5
Energy (eV) (b)
TiO2 TiO2-xNx _5 TiO2-xNx _10 TiO2-xNx _20
i
6
3
Ns Ni 0 1.0
1.5
2.0
2.5
3.0
Energy (eV) Fig. 4. (a) Real and (b) imaginary parts of TiO2 dielectric function with
exposure time.
Even if the CCS calculation is an appropriate method for determining the variation of the TiO2 dielectric function of the films, it does not provide other physical parameters such as their band gap energy or their Urbach energy. For this reason, the obtained spectra by CCS
9
method (
) were fitted by combining the Tauc-Lorentz (TL) and Urbach models [34].
The imaginary part of the dielectric function shown in Fig. 5 is obtained using this equation:
,
where
and
Eq. (4)
correspond to imaginary part of the dielectric function described by TL and
Urbach, respectively [34]:
Eq. (5)
Six free parameters in the Tauc-Lorentz dispersion model are fitted: the band gap energy ( the amplitude (
), the energy of the absorption band (
), the amplitude factor (
),
), the
broadening parameter (
) associated with the absorption band and the maximum energy of
transitions
). The Urbach energy
(
>E1>
and the intensity coefficient
free parameters to be considered in the Urbach model.
is an energy given by:
.
According to Fig. 5, it clearly shows that
and
are the only
Eq. (6)
are affected by the
ion bombarding
time. Furthermore, the Urbach part shown in Fig. 5 is composed of two ranges: the exponential tail and the polynomial part. These two ranges change with the exposure time. Equation 4 reproduces accurately the imaginary part of the dielectric function as shown in Fig. 5. In function of bombarding time, the TL contribution is also affected. The unknown parameters determined by the models are summarized in Table 2. The band gap energy of TiO2 (3.39 eV) is higher than the value of the bulk anatase TiO2 (3.20 eV) [35]. This difference can be explained by the dependence of the band gap energy on the thickness. It increases from 3.16 eV to ~3.35 eV when the thickness of the films decreases from 300 nm to ~100 nm [36, 37]. The band gap value can also be affected by sol-gel synthesis conditions of TiO2 [38, 39].
10
9
(b) TiO2-xNx _5
(a) TiO2 i _ ccs i _ sim TL U
i _ ccs i _ sim TL U
6
i
i
6
I: Urbach exponential tail II: Urbach polynomial part
3
3
I
II
I
II
0
0 1
2
3
1
4
3
4
(d) TiO2-xNx _20
(c) TiO2-xNx _10 i _ ccs i _ sim TL U
i _ ccs i _ sim TL U
6
i
i
6
2
Energy (eV)
Energy (eV)
3
3
I
I
II
II
0
0 1
2
3
1
4
2
3
4
Energy (eV)
Energy (eV)
Fig. 5. Imaginary part of dielectric function of (a) TiO2 and TiO2 exposed to the ion beam during (b) 5 min, (c) 10 min and (d) 20 min obtained by TL and Urbach models.
11
Eg_TU (eV)
E1 (eV)
TiO2
0.003
3.39±0.01
4±0.01
TiO2-xNx _5
0.007
3.41±0.02
TiO2-xNx _10 0.006 TiO2-xNx _20 0.008
B1 (eV)
Eu (eV)
Iu
0.35±0.02 0.13±0.03
0.95±0.2
3.94±0.01
0.3±0.02
8.67±0.5
3.46±0.02
3.9±0.01
0.31±0.02 0.31±0.01 12.37±0.5
3.53±0.02
3.85±0.08 0.51±0.02 0.39±0.01
0.31±0.01
17±0.5
Table 2: Selected parameters of TL and Urbach models.
Furthermore, the TiO2 band gap can be deduced by Tauc’s plot extrapolation technique. For crystalline semi-conductor with an indirect band gap, such as anatase TiO2, the dependence of the absorption coefficient
on the energy E can be approximated by [40]:
,
where C is a constant. The Eg of TiO2 as a function of linearly extrapolating the
Eq. (7)
ion exposure time is estimated by
data on the rising slope to zero by a linear fit line with
Equation (7) (see Fig. 6). The Eg values determined by Tauc plot (Eg-T) decrease with the exposure time contrary to their estimated by TL and Urbach models (Eg-TU) (see Fig. 7). In addition, the Eg-T values are lower than the Eg-TU when TiO2 films exposed to
ion beam.
We conclude that the Tauc plot method does not yield the right energy gap values for TiO2xNx
films owing to the presence of the absorption tail caused by the defect levels Ni and Ns
(see Fig. 4). As a consequence, these extracted Eg-T values are more underestimated as a function of defects concentration.
12
1600
1600
1200
800
400
TiO2 TiO2-xNx _5
1/2
( E) (m eV )
1200
-1/2
0
1200
800
1/2
800
400
TiO2-xNx _10 TiO2-xNx _20
0
400
3.2
3.4
3.6
3.8
4.0
TiO2 TiO2-xNx _5 TiO2-xNx _10 TiO2-xNx _20
Energy (eV)
0
2.5
3.0
3.5
4.0
Energy (eV) Fig. 6. Tauc’s plots for TiO2 and TiO2 exposed to the
ion beam.
The Eg-TU energy increases with exposure time. From the Table 2, the band gap energy value (3.39 eV) of TiO2 is blue shifted in the case of TiO2-xNx by 20 meV, 70 meV and 140 meV corresponding to the exposure time of 5 min, 10 min and 20 min, respectively. This strong change of band gap energy with the exposure time is attributed to both effects of the film thickness and
ion bombardment. Indeed, it is well known that the thickness effect of
ultrathin films leads to the modification of the optical responses [15, 36, 37]. For example, the band gap of TiO2 increases from 3.41 eV to 3.71 eV when the thickness of the films decreases from 20 nm to 2.5 nm [15]. In our case, the optical gap changes from 3.39 eV to 3.53 eV when the thickness decreases from 30 nm to 21 nm.
13
3.56
Eg-TU Eg-T
3.52
3.48
Eg(eV)
3.44
3.40
3.36
3.32
3.28
3.24 0
5
10
15
20
2+
N ion exposure time (min) Fig. 7. Band gap energy dependence with
ion exposure time.
For the optical direct transition E 1 at the Г-Z direction of the first Brillouin zone [41], the energy value is found to be less affected by
ion exposure. The average value is 3.9 eV
close to that of TiO2 traducing the conservation of the crystalline structure of TiO 2 after ion exposure, which is also in agreement with Raman analysis. Concerning the B1 parameter of optical transition, it is strongly correlated with crystalline quality and defects concentration in the crystal. The B1 value change only after an exposure time of 20 min suggesting the formation of more defects in TiO2 which is corroborated by the increase of the FWHM of the 142 cm-1 peak in the Raman spectra. The Urbach energy Eu value of 0.130 eV, obtained for TiO2, is in agreement with literature for crystalline TiO2 films [42]. Fig. 8 shows the Eu energy value and Raman FWHM at 142 cm-1 as a function of
ion exposure time. The Raman FWHM mode at 142 cm-1 changes with
the defects concentration in TiO2 films. For Eu energy, the value increases between 0 and 5 min, due to the formation of both deep and shallow defects Ni and Ns, respectively. Between 5 min and 10 min, the Eu energy value is almost unchanged because only the shallow level Ns increases with the exposure time as shown in Fig. 4(b). Beyond 10 min, the Eu energy value increases with the increase of deep level Ni (see Fig. 4(b)). Consequently, the Eu energy is
14
more affected by Ni defect level. On the other hand, the
values are also affected by defects
concentration as can be seen in Table 2.
Urbach energy -1
18
0.30
16
0.25 14 0.20
-1
12
Raman FWHM (cm )
Eu(eV)
FWHM of mode at 142 cm 0.35
0.15 10 0.10
0
5
10
15
20
2+
N ion exposure time (min)
Fig. 8. Urbach energy of TiO2 and FWHM of Raman mode at 142 cm-1 with time.
4.
ion exposure
Conclusion
In summary, the optical properties of TiO2 ultrathin films were investigated by using ellipsometry over the
ion exposure time during 5 min, 10 min and 20 min. The
conservation of the anatase TiO2 crystalline structure after bombarding by
ion beam and
the presence of N bounded to Ti was established by Raman measurements. This study highlights both the effects of the thickness of ultrathin films and the nitrogen ion bombardment on the optical responses, particularly on the band gap energy. Urbach energy (Eu) of anatase TiO2 was founded to be affected by
ion beam. We have determined the
ion exposure time dependence of the dielectric function of TiO2 by combining the TaucLorentz and the Urbach models. Imaginary part of TiO2-xNx dielectric function exhibits an absorption tail band in the visible range of 2 eV and 3.5 eV attributed to the electronic transitions through substitutional (Ns) and interstitial (Ni) states above the valence band, respectively. We have found the widening of the band gap of TiO2 with 15
ion exposure time
which is consistent with the thickness effect. The band gap energy of 3.39 eV measured by ellipsometry from TiO2 was blue shifted in the case of TiO2-xNx by 20 meV, 70 meV and 140 meV corresponding to the exposure time of 5 min, 10 min and 20 min, respectively. The Urbach energy and the Raman FWHM of the O-Ti-O bending vibration have allowed confirming the increase of defects in TiO2 films with
ion bombarding time, particularly
after 20 min.
Acknowledgment The authors would like to acknowledge Pascal Franchetti (LCP-A2MC) for technical assistance in Raman spectroscopy measurements.
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