Far-infrared spectra of amorphous titanium dioxide ﬁlms
G. Scarel a,*, C.R. Aita a
, H. Tanaka b
, K. Hisano b
a
Department of Materials Engineering, University of Wisconsin–Milwaukee, P.O. Box 784, Milwaukee, WI 53201, USA
b
Department of Applied Physics, The National Defense Academy, Yokosuka 239, Japan
Abstract
The amorphous TiO2 ﬁlm structure on an aluminum substrate was studied by far infrared reﬂection–absorption
spectroscopic (IRAS) analysis. The transverse (TO) and longitudinal (LO) optical modes of the amorphous oxide ﬁlms
were studied experimentally and through simulation. These optical modes were compared to those of the corresponding
crystal. While TO modes of the ﬁlms correspond to those of the crystal, the LO modes do not. The best agreement
between the experimental and the simulated IRAS spectra is obtained when an appropriate dielectric function efilmðmÞ is
chosen. efilmðmÞ must be related to the amorphous character of the ﬁlms e.g. by averaging the anisotropic crystal
properties. As a consequence of our ﬁndings, the Berreman eﬀect does apply in amorphous ﬁlms to absorption bands at
frequencies of the peaks of the loss function Im[À1=efilmðmÞ], which does not correspond to frequencies of the LO modes
of the crystal. Ó 2002 Elsevier Science Ltd. All rights reserved.
PACS: 77.55; 73.80
1. Introduction
Due to its high dielectric constant [1,2], amorphous
TiO2 is a candidate to replace amorphous
SiO2 and SiN as the dielectric layer in ultra-thin
ﬁlm capacitors. For this reason, it is necessary to
analyze and precisely characterize the thin TiO2
ﬁlms. We observe transverse (TO) and longitudinal
(LO) modes to study the eﬀects of the amorphous
character of anatase TiO2 ﬁlms grown on
aluminum substrate. The amorphous character of
thin ﬁlms consists of topological [3] and orientational
disorder. Due to topological disorder, bond
length and bond angles are diﬀerent from those of
the crystal. Moreover, due to orientational disorder,
the TiO6 units, typical of anatase, are all
randomly oriented. In amorphous ﬁlms however,
even though topological disorder is present, a
TO–LO splitting is present which is similar to
the one of crystals [4,5]. This information is very
important because it allows us to use, for amorphous
TiO2 ﬁlms, frequencies of corresponding
TO and LO modes equal to those in a crystal and
reported in Table 1 [6].
The eﬀects of orientational disorder are investigated
in this paper using infrared reﬂection–
absorption spectroscopic (IRAS) and the Berreman
eﬀect. The latter predicts that the frequency of TO
and LO modes of a thin ﬁlm can be measured
Journal of Non-Crystalline Solids 303 (2002) 50–53
www.elsevier.com/locate/jnoncrysol
*
Corresponding author. Present address: Laboratorio MDMINFM,
Via Olivetti 2, 20041 Agrate Brianza, MI, Italy.
E-mail address: gscarel@mdmlab.mi.infm.it (G. Scarel).
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved.
PII: S0022-3093(02)00963-8
directly using an oblique polarized infrared beam
[7].
2. Experimental procedure
Amorphous TiO2 ﬁlms, 0.25 lm thick, were
grown at room temperature by reactive sputter
deposition technique in a 100% O2 gas atmosphere
[8]. The structure of the ﬁlms was determined using
X-ray diﬀraction [8] analysis of ﬁlms grown on
fused silica. The presence of an anatase shortrange
order was established using Raman spectroscopy
[9] analysis of ﬁlms grown on silicon.
Far-IRAS spectra (between 100 and 600 cmÀ1
)
of ﬁlms on aluminum were measured using a
Fourier transform infrared spectrometer by Bruker
(Model IFS 113v). The instrument is equipped with
a 3.5 lm mylar beam-splitter which selects radiation,
produced by a glowbar source, in the 50–700
cmÀ1
frequency range. The instrument is equipped
also with a polyethylene polarizer to linearly s- and
p-polarize the incoming infrared beam. A TGS
pyroelectric detector collects the infrared beam
reﬂected by the sample. For each spectrum, 100
scans were taken with a 4 cmÀ1
resolution at a ﬁxed
angle of incidence / ¼ 45°. Measurements were
made at a pressure of 1 Â 10À3
Torr and room
temperature. An aluminum-coated glass substrate
was used as reference. IRAS spectra were calculated
using MATHEMATICA from the Fresnel reﬂection
coeﬃcients [10] for a three-layer system.
3. Results and discussion
Experimental and calculated far IRAS spectra
measured using a s- and a p-polarized beam at
/ ¼ 45° for the 0.25 lm anatase TiO2 ﬁlm on
aluminum are shown in Figs. 1 and 2.
The frequencies of the relevant absorption
bands measured using a s-polarized beam are reported
both in Fig. 1 and in Table 2. The frequencies
of the absorption bands measured using a
p-polarized beam are reported both in Fig. 2 and
in Table 2.
Fig. 1. Experimental and calculated (inset) far IRAS spectra
measured with s-polarized beam.
Fig. 2. Experimental and calculated (inset) far IRAS spectra
measured with p-polarized beam.
Table 1
Frequencies, damping factors, and high frequency dielectric
constants for optical modes in anatase TiO2 at room temperature
[6]
Optical mode Frequency, m
(cmÀ1
)
Damping factor,
c (cmÀ1
)
For optical modes with A2u symmetry in anatase TiO2
(e1 ¼ 5:41)
mTO1 367 68
mLO1 755 79
For optical modes with Eu symmetry in anatase TiO2
(e1 ¼ 5:82)
mTO2 262 36
mLO2 366 4.1
mTO3 435 32
mLO3 876 33
G. Scarel et al. / Journal of Non-Crystalline Solids 303 (2002) 50–53 51
For the calculation of the reﬂection coeﬃcient
and, consequently, of the IRAS spectra, an expression
for efilmðmÞ is used that is an average of its
value in the anisotropic crystal [11]. This expression,
shown in Eq. (1), has been successfully applied
in amorphous [11] and polycrystalline ﬁlms
[12]:
efilmðmÞ ¼ ½ekðmÞ þ 2e?ðmÞ=3: ð1Þ
In Eq. (1), ekðmÞ and e?ðmÞ are the dielectric functions
of anatase TiO2 in the A2u and the Eu symmetries
respectively. These functions are expressed
according to the factorized form [13]. Absorption
is expected at the frequencies of the peaks of loss
functions Im[efilmðmÞ] and Im[À1=efilmðmÞ]. These
functions are calculated and plotted versus frequency
in Fig. 3. The frequencies where peaks
occur in the loss functions are reported both in
Fig. 3 and in Table 2.
Table 2 shows that there are absorption bands
measured using a p-polarized beam at frequencies
higher than 800 cmÀ1
, which are not shown in the
spectra of Figs. 1 and 2. Table 2 shows that all the
absorption bands detected using a s-polarized
beam, both in the experimental and in the calculated
spectra, appear at frequencies of the peaks of
Im[efilmðmÞ] and of TO modes (Table 1). Two absorption
bands detected using a p-polarized beam,
both in the experimental and in the calculated
spectra, do also appear at frequencies of peaks
of Im[efilmðmÞ] and of TO modes. The other absorption
bands, also detected using a p-polarized
beam, do appear at frequencies of peaks of
Im[À1=efilmðmÞ] and these absorption bands obey
the Berreman eﬀect, because they are absent in
spectra measured using a s-polarized beam [7].
None of the detected absorption bands, however,
appears at frequencies of LO modes. This fact is
interesting, given that originally the Berreman effect
is expected to aﬀect absorption bands appearing
at frequencies of LO modes.
4. Conclusions
We conclude that, from the microscopic point
of view, the TO and the LO modes keep their
identity in the anatase TiO6 unit. Macroscopically
however, the random orientation of the anatase
TiO6 units has a dominant eﬀect in IRAS spectra.
As a clear consequence, we see from Table 2 that
in IRAS spectra of amorphous ﬁlms, only the
frequencies of the TO modes can be measured directly
but the frequencies of LO modes can not be
Table 2
Comparison of experimental and calculated frequencies of absorption bands in IRAS spectra (/ ¼ 45°) of the 0.25 lm thick TiO2 ﬁlm
on aluminum with those of peaks of loss functions and those of optical modes for anatase TiO2 in Table 1
Beam polariz. Exp. freq. (cmÀ1
) Calc. freq.
(cmÀ1
)
Im[eðmÞ] (cmÀ1
) Im[À1=eðmÞ]
(cmÀ1
)
mTO (cmÀ1
) mLO (cmÀ1
)
s 260 261 262 – 262-mTO2 –
355 372 366 – 367-mTO1 –
442 437 436 – 435-mTO3 –
p 260 262 262 – 262-mTO2 –
335a
328 – 326 – –
398 395 – 396 – –
443 437 436 – 435-mTO3 –
853 839 – 838 – –
a
Weak.
Fig. 3. The loss functions as a function of frequency for anatase
TiO2.
52 G. Scarel et al. / Journal of Non-Crystalline Solids 303 (2002) 50–53
measured at all. This is very diﬀerent than the case
of crystalline ﬁlms for whom both the frequencies
of TO and LO modes can be directly measured
[14].
Acknowledgements
The authors would like to acknowledge
C.J. Hirschmugl (Physics, UWM), R.S. Sorbello
(Physics, UWM) and A.S. Sklyarov (Advanced
Analysis Facility, UWM) for assistance and fruitful
discussions.
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