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# Optical constants of MOCVD-grown Aurivillius phases in the Bi4Ti3O12–Na0.5Bi0.5TiO3 system measured by spectroscopic ellipsometry

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## Abstract and Figures

Thin films of bismuth titanate Bi4Ti3O12 and different sodium–bismuth–titanate phases Na0.5Bi8.5Ti7O27, Na0.5Bi4.5Ti4O15, and Na0.5Bi0.5TiO3 with different numbers of perovskite units (m) between two Bi2O2 intermediate layers were epitaxially grown on (001) SrTiO3 substrates by metal-organic chemical vapor deposition. The optical properties of these ferroelectric thin films were investigated by spectroscopic ellipsometry (SE) at room temperature in the 0.73–6.48eV spectral range. In the analysis of the SE measured spectra Cauchy transparent, Tauc–Lorentz and Gaussian dispersion relations were used to characterize the optical properties of the films. Our analysis clearly shows that the refractive index of the Aurivillius phases decreases with increasing m, while the optical band gap increases with increasing m. The obtained dielectric function spectra revealed a shoulder and a broad absorption band at about 3.7 and 4.5 eV, respectively, for Bi4Ti3O12 and a broad absorption band around 4.5 eV for the perovskite phase Na0.5Bi0.5TiO3. A shift in the resonance energies to lower energy with increasing m is observed.
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Appl Phys A (2011) 105:81–88
DOI 10.1007/s00339-011-6581-z
Optical constants of MOCVD-grown Aurivillius phases
in the Bi4Ti3O12–Na0.5Bi0.5TiO3system measured
by spectroscopic ellipsometry
S. Bin Anooz ·J. Schwarzkopf ·P. Pe tr i k ·
M. Schmidbauer ·A. Duk ·E. Agocs ·R. Fornari
Received: 1 April 2011 / Accepted: 23 August 2011 / Published online: 14 September 2011
Abstract Thin ﬁlms of bismuth titanate Bi4Ti3O12 and dif-
ferent sodium–bismuth–titanate phases Na0.5Bi8.5Ti7O27,
Na0.5Bi4.5Ti4O15, and Na0.5Bi0.5TiO3with different num-
bers of perovskite units (m) between two Bi2O2interme-
diate layers were epitaxially grown on (001) SrTiO3sub-
strates by metal-organic chemical vapor deposition. The op-
tical properties of these ferroelectric thin ﬁlms were inves-
tigated by spectroscopic ellipsometry (SE) at room temper-
ature in the 0.73–6.48 eV spectral range. In the analysis of
the SE measured spectra Cauchy transparent, Tauc–Lorentz
and Gaussian dispersion relations were used to character-
ize the optical properties of the ﬁlms. Our analysis clearly
shows that the refractive index of the Aurivillius phases de-
creases with increasing m, while the optical band gap in-
creases with increasing m. The obtained dielectric function
spectra revealed a shoulder and a broad absorption band
at about 3.7 and 4.5 eV, respectively, for Bi4Ti3O12 and
a broad absorption band around 4.5 eV for the perovskite
phase Na0.5Bi0.5TiO3. A shift in the resonance energies to
lower energy with increasing mis observed.
S. Bin Anooz ()·J. Schwarzkopf ·M. Schmidbauer ·A. Duk ·
R. Fornari
Leibniz Institute for Crystal Growth (IKZ), Max-Born-Str. 2,
12489 Berlin, Germany
e-mail: binanooz@ikz-berlin.de
S. Bin Anooz
Physics Department, Faculty of Science, Hadhramout University
of Science and Technology, Mukalla 50511, Republic of Yemen
P. Petrik ·E. Agocs
Research Institute for Technical Physics and Materials Science,
P.O. Box 49, 1525 Budapest, Hungary
E. Agocs
University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary
1 Introduction
Ferroelectric materials have been considered as one of the
These materials have been used for integrated device ap-
plications such as tunable microwave devices, integrated
optical modulators, infrared sensors, and nonvolatile fer-
roelectric random access memories [13]. In recent years,
growing attention has been given to the research of high-
performance lead-free piezoelectric materials in order to
replace the widely used lead-based piezoelectric ceramics
with environmental friendly materials [4,5]. Layered per-
ovskites of the Aurivillius family have been regarded as
promising alternatives. They were discovered by Aurivillius
[6] and Subbarao [7] who described them by the general
formula (Am1BmO3m+1)2(Bi2O2)2+, where A =Bi3+,
Ba2+,Sr
2+,Ca
2+,Pb
2+,K
+,Na
+, and B =Ti4+,Fe
3+,
Nb5+,Ta
5+,Mo
6+,W
6+,mis the number of perovskite-
like layers interleaved by layers having a ﬂuorite struc-
ture. While Bi4Ti3O12 with m=3(BTO),Na
0.5Bi8.5Ti7O27
with m=3.5 (NBT3.5), and Na0.5Bi4.5Ti4O15 with m=4
(NBT4) are Aurivillius phases, Na0.5Bi0.5TiO3exhibits a
perovskite structure, but can nevertheless be regarded as a
layered structure with m=∞(NBT)[811]. All of them
are lead-free compounds. The Na containing compounds
were so far exclusively investigated as bulk crystals and ce-
ramics [1214], only few reports exist for thin ﬁlms. Since
they offer excellent ferroelectric properties [1517], suc-
cessfully deposition of these phases in thin ﬁlm form is of
great interest, because most application of the ferroelectric
materials is expected in their thin ﬁlms forms.
The optical properties of BTO bulk crystals and thin
ﬁlms grown by different techniques have been extensively
discussed in the literature [1820], while only few authors
have reported optical properties of NBTpolycrystalline
82 S. Bin Anooz et al.
and single crystals [17,21,22]. However, optical proper-
tiesofNBTthin ﬁlms grown by metal-organic chemi-
cal vapor deposition (MOCVD) have not been reported so
far. Furthermore, there are no literature data about NBT3.5
and NBT4, neither for bulk crystals nor for thin ﬁlms. Since
most ferroelectric materials exhibit excellent optical prop-
erties, it is interesting to investigate the optical properties
of sodium–bismuth–titanate thin ﬁlms, which have been
marginally reported up to date, and to provide some use-
ful references for their potential applications in integrated
optics devices. Optical characterization of thin ﬁlms gives
information about physical properties, like band gap energy
and band structure, optically active defects etc. Considerable
differences between optical constants of bulk material and
of thin ﬁlms prepared under varying growth characteristics
are often reported. Therefore determination of optical con-
stants for each individual ﬁlm by a non-destructive method
like spectroscopic ellipsometry (SE) [2325] is highly rec-
ommended.
Aim of this paper is to present the results of the in-
vestigation on optical properties of Aurivillius phases in
the Bi4Ti3O12 –Na0.5Bi0.5TiO3thin ﬁlms system grown by
MOCVD technique and to discuss them with respect to
those of Bi4Ti3O12 and with respect to their number of per-
ovskite units m.
2 Experimental
The Aurivillius phases Bi4Ti3O12,Na
0.5Bi8.5Ti7O27 , and
Na0.5Bi4.5Ti4O15 as well as the perovskite Na0.5Bi0.5TiO3
were epitaxially deposited on SrTiO3(STO) (001) substrates
in thin ﬁlm form by the liquid-delivery spin MOCVD tech-
nique. Our vertical system includes two peristaltic pumps
for the transport of the liquid precursor solutions to two in-
dependent and separated ﬂash evaporators: one for the Bi/Ti
precursor solution and the other for the Na precursor solu-
tion. The temperatures of both ﬂash evaporators were ad-
justed to 230°C. Bi(thd)3((thd) =2,2,6,6-tetramethyl-3,5-
heptanedione), Ti(OiPr)2(thd)2(OiPr =iso-propoxide), and
Na(thd), dissolved in toluene, were used as source materi-
als for Bi, Ti, and Na, respectively. All ﬁlms were deposited
at a substrate temperature of 750°C. The different sodium–
bismuth–titanate phases were achieved by varying the Na to
Bi concentration ratio from 0 to 3. The preparation of the
ﬁlms has been described in detail elsewhere [26].
The ﬁlms were structurally characterized by high resolu-
tion x-ray diffraction (HRXRD). Behind a pre-collimating
parabolic Göbel mirror a Ge 220 double crystal monochro-
mator was utilized to select the Cu Kα1line at λ=
1.54056 Å and to collimate the incident x-ray beam to about
20 arcsecs. Primary and detector slits of 0.3 mm were used
to effectively suppress the scattering background.
Ellipsometric data were collected using a Woollam M-
2000DI rotating compensator ellipsometer in the spectral
range of 0.73–6.48 eV with an incidence angle of 70°. In
ellipsometry, one deals with the measurements of the rel-
ative changes in the amplitude and the phase of a polar-
ized monochromatic incident light upon an oblique reﬂec-
tion from the sample surface. Experimentally, the measured
ellipsometric angles are and, that are related to the optical
and structural properties of the sample deﬁned by [27]
ρ=Rp
Rs=tanψ·ei(1)
where Rpand Rsare the complex reﬂection coefﬁcients
of the light polarized parallel (p) and perpendicular (s)to
the plane of incidence, respectively. The reﬂectance (R) was
measured using a Lambda19 by Perkin-Elmer.
3 Results and discussion
HRXRD patterns of thin ﬁlms of BTO, NBT3.5, NBT4 and
NBTare presented in Fig. 1. The diffraction patterns were
assigned according to the diffraction data of Bi4Ti3O12,
Na0.5Bi8.5Ti7O27 ,Na
0.5Bi4.5Ti4O15 and Na0.5Bi0.5TiO3
structure (powder diffraction ﬁle (PDF) 35-795, 32-1044,
74-1316, 89-3109, respectively, from the standard powder
diffraction data). The ﬁlms with m=3, 3.5 and are
single-phase, whereas the ﬁlm with m=4 contains a small
amount of the NBTphase, implied by the peak which
is indicated by (001)in the NBT4 diffractogram. The in-
set of Fig. 1shows the HRXRD rocking curve of NBT
around the (002) Bragg reﬂection, where the peak becomes
more pronounce compared to the (001) Bragg peak. From
the x-ray data, the out-of-plane lattice parameters cfor
BTO, NBT3.5, NBT4 and NBTare derived and listed
in Table 1. It is obviously that the out-of-plane lattice pa-
rameter of NBT3.5 and NBT4 increased compared to the
BTO ﬁlm, since the number of perovskite-like units in the
elementary cell also increased. The NBTﬁlm exhibits
a remarkably smaller lattice parameter due to its pure per-
ovskite structure. All cparameters of the ﬁlms are smaller
than the corresponding bulk values, which indicate that the
ﬁlms are tensiley strained. The details of the structure are
reported elsewhere [26].
3.1 Optical properties
In order to extract the dielectric function, ε(E) =εr(E) +
i(E), of the ﬁlms, the optical spectrum of bare STO a sub-
strate was measured independently. The results agree well
with those of Dejneka et al. [28]. The recorded data for the
sodium–bismuth–titanate ﬁlms on the STO substrate were
then evaluated by different models.
Optical constants of MOCVD-grown Aurivillius phases in the Bi4Ti3O12–Na0.5Bi0.5TiO3system measured 83
Fig. 1 HRXRD rocking curves
(θ–2θscans) of BTO, NBT3.5,
NBT4 and NBTphases. The
inset displays the HRXRD
rocking curve of NBTaround
the (002) Bragg reﬂection
Table 1 Out-of-plane lattice
parameters cof the four possible
compounds in the
Bi4Ti3O12 –Na0.5Bi0.5TiO3
system as determined by
HRXRD. The corresponding c
lattice parameter of the bulk
for comparison
Phase mLattice parameters, c(Å)
Film Bulk
Bi4Ti3O12 [7] BTO 3.0 32.64 32.83
Na0.5Bi8.5Ti7O27 [8] NBT3.5 3.5 36.66 36.80
Na0.5Bi4.5Ti4O15 [9] NBT4.0 4.0 40.66 40.75
Na0.5Bi0.5TiO3[10]NBT3.53.870 3.890
(pseudocubic notation)
3.1.1 Cauchy dispersion
To determine accurately thickness and refractive index (n)
of a ﬁlm it is desirable to ﬁnd a region of the measured spec-
tral range where the ﬁlm is transparent (or nearly transpar-
ent). This allows simpler models with fewer parameters to
be used in ﬁtting the data. A four-component stack com-
posed of substrate/ﬁlm/roughness layer/ambient was em-
ployed and the optical properties of the surface roughness
layer are represented by a Bruggeman effective medium ap-
proximation [29] consisting of a 50% bulk ﬁlm/50% void
mixture. The measured values for ψand Δin the energy re-
gion of 0.73–2.75 eV under an incident angle of 70° are plot-
tedinFigs.2(a) and (b). The ﬁt was optimized by minimiz-
ing the mean-square error (MSE). From the experimental
data for ψand Δ, the refractive index and the ﬁlms thickness
were obtained through a ﬁtting of ψand Δby the Cauchy
Transparent (CT) dispersion relation, described by
n(λ) =A+B
λ2+C
λ4(2)
and the extinction coefﬁcient k=0 for all measured wave-
lengths, where A,B, and Care free ﬁt parameters and λis the
wavelength. The ﬁtted data for ψand Δare also shown in
Fig. 2. On the basis of the CT dispersion the refractive index
of Aurivillius phases and perovskite in the transparent re-
84 S. Bin Anooz et al.
Fig. 2 Experimental (dots) and CT-modeled (solid lines)(a)ψ(E)
and (b)Δ(E) spectra of BTO, NBT3.5, NBT4 and NBTphases
Fig. 3 Refractive index (n) obtained using CT-model from spectro-
scopic ellipsometry analysis of BTO, NBT3.5, NBT4 and NBT
phases
gion were determined and presented in Fig. 3, which shows
that the refractive index increases with increasing photon
energy as expected. However, it is also striking that nde-
creases with increasing m. For instance, at E=1.5eV,n
changes from 2.61 for m=3to2.42form=∞. These val-
ues are in good agreement with literature values of n=2.7
[22] and n=2.5[17,21]forBi
4Ti3O12 and Na0.5Bi0.5TiO3
single crystals, respectively. No optical constants have been
Table 2 The best-ﬁt parameters from the SE analysis with CT and
3TL dispersions evaluated for the sodium–bismuth–titanate phases in
the Bi4Ti3O12 –Na0.5Bi0.5TiO3system
Phase m=3.0m=3.5m=4.0m=∞
tf(nm) 63.2±0.13a75.1±0.13a45.6±1.30a35.2±0.33a
ts(nm) 3.97 ±0.06a4.41 ±0.02a6.68 ±0.27a7.85 ±0.15a
ATL1 (eV) 64.4 ±3.9 74.5 ±3.6 27.2 ±9.2 1.38 ±0.93
Γ(eV) 0.65 ±0.02 0.67 ±0.02 0.19 ±0.04 2.01 ±0.01
E01 (eV) 3.83 ±0.01 3.84 ±0.01 3.67 ±0.01 4.12 ±0.02
Eg(eV) 3.18 ±0.01 3.32 ±0.01 3.41 ±0.02 3.22 ±0.01
ATL2 (eV) 147.9 ±1.8 174.8 ±1.5 288.2 ±8.0 228.2 ±2.5
Γ2(eV) 1.49 ±0.01 1.46 ±0.01 1.52 ±0.02 1.35±0.01
E02 (eV) 4.73 ±0.01 4.72 ±0.01 4.39 ±0.01 4.34 ±0.01
ATL3 (eV) 36.6 ±0.63 36.2 ±0.36 17.9 ±0.66 39.2±3.35
Γ3(eV) 2.22 ±0.06 1.86 ±0.03 0.96 ±0.06 2.72±0.33
E03 (eV) 7.29 ±0.01 7.22 ±0.01 7.02 ±0.02 7.40 ±0.12
MSE 1.31a0.87a1.88a1.82a
2.41b1.35b3.11b4.39b
2.62c2.17c4.66c5.03c
aCauchy transparent
bTriple Tauc–Lorentz
cGaussian
reported up to date for the other two Aurivillius phases. The
ﬁlm thicknesses (tf) and the surface roughness (ts)forBTO,
NBT3.5, NBT4 and NBTthin ﬁlms, evaluated using the
CT dispersion, are listed in Table 2.
3.1.2 Tauc–Lorentz dispersion
The Tauc–Lorentz dispersion formula has been success-
fully applied to many amorphous and crystalline materials
[23,30,31]. In the Tauc–Lorentz model [32], the imaginary
part of the dielectric function, εiTL(E ), is given as the prod-
uct of the Tauc function [33]: εiT=AT(E Eg)2/E2and
the Lorentz oscillator function L(E):
L(E) =ALE0ΓE
(E2E2
0)2+Γ2E2(3)
Hence
εiTL(E) =ATLE0Γ(EEg)2
(E2E2
0)2+Γ2E2·1
EE>E
g
=0EEg(4)
where ATL is the amplitude factor, proportional to the den-
sity of the material and to the momentum matrix element. E0
is the peak transition energy and Egis the band gap energy.
Γis the broadening parameter, inversely related to crystal-
lite size, and εis the high frequency dielectric constant.
Optical constants of MOCVD-grown Aurivillius phases in the Bi4Ti3O12–Na0.5Bi0.5TiO3system measured 85
Fig. 4 Experimental (dots) and 3TL-modeled (solid lines)(a)ψ(E)
and (b)Δ(E) spectra of BTO, NBT3.5, NBT4 and NBTphases
The real part of the dielectric function, εrTL, can be then
obtained by using the Kramers–Kronig relation
εrTL(E) =ε+2
πP+
Eg
ξεiTL )
ξE2(5)
Using a simple layers model described in the Cauchy dis-
persion we ﬁtted the data to obtain a TL dispersion for each
ﬁlm. We found that a triple TL-oscillator (3TL), sharing a
common Tauc gap, is necessary to describe the optical dis-
persion with sufﬁcient accuracy. In order to reduce the num-
ber of free ﬁt parameters and make a reliable comparison
between the different ﬁlms, the ﬁlms thickness and the sur-
face roughness obtained using the CT dispersion were ﬁxed,
and the high frequency dielectric constant εwas assumed
to be 1.5 for all ﬁlms. Figures 4(a) and (b) show the exper-
imental ψand Δspectra in a larger energy range of 0.73–
6.48 eV (transparent and absorbent region) for the Auriv-
illius phases BTO, NBT3.5, and NBT4 and the perovskite
structure NBTalong with the corresponding spectral sim-
ulation by the 3TL model. The results of these best-ﬁt oper-
ations are also shown in Table 2. It is obvious that the values
of the band gap energy increase with increasing mfor the
Aurivillius phases (m=3, 3.5 and 4).
Fig. 5 Experimental (dots) and Gaussian-modeled (solid lines)
(a)ψ(E) and (b)Δ(E) spectra of BTO, NBT3.5, NBT4 and NBT
phases
3.1.3 Gaussian dispersion
We repeated the ﬁtting procedure with a sum of Gaussian
peaks, describing the photon energy dependence of εiG,to
conﬁrm the results obtained using Tauc–Lorentz dispersion.
This allows us to compare the increase of the band gap en-
ergy with increasing mfor the Aurivillius phases obtained
using the TL dispersion with the shift in the absorption edge
of εiGevaluated from the Gaussian dispersion. The Gaus-
sian oscillator type [34] produces a Gaussian line shape in
εiG:
εiG(E) =AGexp (E EG/BG)2(6)
where AGis the oscillator amplitude, EGis the center en-
ergy, and BGis a broadening term. The real part of the
dielectric function εrGis calculated using the Kramers–
Kronig relation (5).
The ψand Δspectra of the BTO, NBT3.5, NBT4 and
NBTﬁlms together with the corresponding Gaussian dis-
persions are shown in Figs. 5(a) and (b). It is found that the
calculated from the Gaussian dispersion agree well with the
experimental data. Thus, it appears that also this dispersion
is suitable to describe the spectra of these ﬁlms. The MSE
values of the ﬁtting with the CT, 3TL and Gaussian dis-
persions are listed in Table 2. It is clear that the MSE for
86 S. Bin Anooz et al.
Fig. 6 Dielectric function spectra (a)εrGand (b)εiGobtained us-
ing Gaussian-model from spectroscopic ellipsometry analysis of BTO,
NBT3.5, NBT4 and NBTphases. Insert εiGof the same phases over
a spectral range from 3.3 to 4.1 eV
the Gaussian dispersion are slightly higher than that of the
3TL dispersion for the Aurivillius phases and the perovskite
phase. This conﬁrms that the Tauc–Lorentz dispersion is the
most suitable for describing the dielectric function of poly-
crystalline oxide ﬁlms [35].
Using the Gaussian dispersion the calculated real and
imaginary parts of the dielectric function for the BTO,
NBT3.5, NBT4 and NBTthin ﬁlms are shown in Figs.
6(a) and (b). From this ﬁgure three conclusions can be
drawn. (i) For all Aurivillius phases a shoulder at the low
energy side of the resonance peak in εiGcan be observed.
The intensity of the shoulder decreases with increasing m
and disappears in the case of NBT. (ii) A shift in the res-
onance energies to lower energies with increasing mis ob-
served. (iii) The absorption edge shifted to higher energies
with increasing mfor the Aurivillius phases (in good agree-
ment with the band gap energy behavior).
For comparison between the Tauc–Lorentz and Gaussian
dispersions for the BTO and NBTthin ﬁlms the corre-
sponding dielectric functions εrTL,εrGand εiTL ,εiGare
presented in Figs. 7(a) and (b) (for clarity and since the val-
ues of εiTL in the low energy range must be zero, different
energy scales were used). There is a good agreement be-
tween real and imaginary dielectric function evaluated by
Fig. 7 Dielectric function spectra obtained using (a)3TLand
(b) Gaussian models from spectroscopic ellipsometry analysis.
(c) Measured reﬂectivity, of the BTO and NBTphases
3TL and Gaussian dispersions. For BTO the shoulder be-
tween 3.7 and 4.1 eV and the mean absorption band at about
4.5 eV coincides with the optical conductivity and dielec-
Singh et al. [36]. For the NBTthin ﬁlm the mean absorp-
tion band has been revealed at 4.5 eV, and attributed to the
transition from the O 2pvalence band (VB) to the Ti 3dor
Bi 6plower-energy conduction band (CB) [21]. This corre-
sponds well to the broad absorption band at 4.2–4.5 eV for
Na0.5Bi0.5TiO3single crystals reported by Andriyevsky et
al. [17]. The main characteristics of the reﬂectivity of both
ﬁlms (Fig. 7c) are consistent with the imaginary dielectric
function in the absorption region.
In the inset of Fig. 6(b) the energy position, at which the
imaginary part of the dielectric function reaches the value 2
(E(εiG=2)) is given. It represents the shift of the absorp-
tion edge evaluated from the Gaussian dispersion versus m.
The dependence of E(εiG=2) and of the band gap energy
(Eg) obtained from the 3TL dispersion on the number of
perovskite units min the Aurivillius phases are shown in
Fig. 8. It is apparent that the increase of the band gap energy
with increasing m(obtained by 3TL dispersion Table 2)for
the Aurivillius phases agrees well with the shift in the ab-
sorption edge of εiGevaluated by Gaussian dispersion.
Moreover, it was found that the band gap energies for
BTO (3.18 eV) and NBT(3.22 eV) thin ﬁlms are slightly
Optical constants of MOCVD-grown Aurivillius phases in the Bi4Ti3O12–Na0.5Bi0.5TiO3system measured 87
Fig. 8 The band gap energy and the energy at εiG=2 as functions of
the number of perovskite-like layers, mof BTO, NBT3.5, NBT4 and
NBTphases
greater than that of Bi4Ti3O12 ﬁlm and Na0.5Bi0.5TiO3sin-
gle crystal, which are reported to be 3.1 eV [36] and 3.03 eV
[21], respectively. Beside the substitution of Bi by Na ions
connected with the formation of four perovskite units be-
tween two (Bi2O2)2+intermediate layers or a pure per-
ovskite structure, for the discussion of the optical proper-
ties of the ﬁlms it has to be considered that all ﬁlms were
grown under tensile lattice strain (Table 1). From the litera-
ture it is known that an in-plane biaxial strain induced by a
lattice mismatch between ﬁlm and substrate material, inﬂu-
ences the electrical and optical material properties depend-
ing on the sign of the strain [37,38]. Tensile strain leading
to a blue shift in the band gap energy of oxide ﬁlms has
been also reported [39,40]. Since all ﬁlms were grown un-
der tensile strain and no publication concerning strain effect
in the Bi4Ti3O12 +Na0.5Bi0.5TiO3system is available we
can only “speculate” about the effect of the lattice strain on
the optical properties. Recently, Dejneka et al. [28] studied
the effect of biaxial tensile strains on optical function and
band edge transitions of SrTiO3ﬁlms deposited on KTaO3
(100) substrates. They observed that tensile strains result
in a shift of the low energy band gap optical transitions to
higher energies, and they explained that blue shift by the
increasing of the in-plane lattice constant immediately and
onset of polar phase inherent in tensile strain-induced ul-
tra thin SrTiO3ﬁlms. The band structure of SrTiO3in the
used energy region is mainly determined by the Ti 3dstates
of the lowest conduction band (CB) and O 2pstates of the
upper valence band (VB)). Likewise the ﬁrst transition in
Na0.5Bi0.5TiO3is essentially deﬁned by the O 2pVB and
the Ti 3dor Bi 6plower-energy CB [21].Basedonthese
similarities we expect an analogue behavior of the optical
band gap of NBTﬁlms, if the in-plane parameter is in-
creased due to tensile ﬁlm growth. We assume that the strain
effect in the ﬁlms contribute to the higher values of the band
gap energy of the BTO and NBTthin ﬁlms in comparison
to the values of the corresponding single crystals. Since the
total tensile strain in the ﬁlms, ε=(dfd0)/d0, decreases
with increasing number m, this effect should have a dimin-
ishing inﬂuence for the phases with higher m. Consequently,
the dependency of Egon min (Fig. 8) is mainly determined
on the formation of different crystallographic phases.
For NBT3.5 and NBT4 thin ﬁlms no optical data have
been published up to date. Only Cheng et al. [41] reported
a band gap energy of about 3.6 eV for K0.5Bi4.5Ti4O15 thin
ﬁlms. They explained this higher value in comparison with
that of BTO (3.1 eV [36]) on the basis of the lower elec-
tronegativity of the potassium ion (0.82) compared to the
bismuth ion (1.90). Since the electronegativity of Na (0.93)
is marginally larger than that of K, we conclude that the
band gap energy for Na0.5Bi4.5Ti4O15 is remarkably higher
than that of Bi4Ti3O12 , but slightly smaller than that of
K0.5Bi4.5Ti4O15 , which well agrees with our data (Fig. 8).
On the other hand, the dependence of Egon the number of
perovskite-like layers for the Aurivillius phases, was seen
to follow a linear trend. The deviation of NBTfrom this
trend can be explain by the fact that phase has different
structure (perovskite). Based on these observations the in-
crease of Egwith enhanced incorporation of Na in the Au-
rivillius phases can be explained as follows: The electronic
energy level of an element is opposite to its electronegativity
[42]. In the case of BTO, the band structure is generally de-
ﬁned by Ti 3dstates in addition to the Bi 6plevels (CB) and
O2plevel (VB) [36]. The incorporation of Na, with lower
electronegativity and higher energy level than Bi 6p, thus
leads to up shift of the conduction band and a broadening of
the band gap. The increase of the band gap energy with in-
creasing number mindicates that NBT3.5 and NBT4 might
have higher intrinsic resistance, which is favorable in terms
of higher breakdown voltage and reduced electric leakage.
4 Conclusions
In summary, lead-free thin ﬁlms of Bi4Ti3O12,Na
0.5Bi8.5
Ti7O27,Na
0.5Bi4.5Ti4O15 and Na0.5Bi0.5TiO3, which can
be regarded as Aurivillius phases, with m=3, 3.5, 4 and ,
respectively, were grown by metal-organic chemical vapor
deposition. The optical properties of these ﬁlms have been
investigated in the 0.73–6.48 eV energy region by spectro-
scopic ellipsometry. Cauchy transparent, Tauc–Lorentz and
Gaussian dispersions were found to be suitable for modeling
the optical properties of these phases. Our analysis clearly
shows that the refractive index decreases, while the band gap
energy of the Aurivillius phases increases with increasing m.
The obtained dielectric function spectra revealed the effect
of Na substituting Bi on the band structure, where a shoulder
and a broad absorption band for Bi4Ti3O12 is transferred to
only one broad absorption band for Na0.5Bi0.5TiO3.
88 S. Bin Anooz et al.
Acknowledgements S. Bin Anooz gratefully acknowledges the
“Alexander von Humboldt Foundation” (AvH) for the scholarship
which makes possible his stay at the Leibniz Institute for Crystal
Growth (IKZ). The authors wish to thank Dr. G. Wagner for fruitful
discussions and A. Kwasniewski for HRXRD measurements. This re-
search activity at IKZ was ﬁnancially supported by German Federal
Government and Land Berlin within the Scheme “Pakt für Forschung
und Innovation”. The Hungarian authors wish to acknowledge the sup-
port from EU FP6-Program No. 026134 RII3 ANNA.
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