Original
Paper
phys. stat. sol. (a) 205, No. 4 (2008)
827
As evident from Fig. 3, the inclusion of an anisotropy
model for n(λ) did not work for all of the films studied in
this work. While the samples annealed at low temperatures
are best represented by a uniaxial anisotropic model, the
samples annealed at higher temperatures do not need an
anisotropy model. In order to uncover the composition of
amorphous-titania, anatase and void in each sample, we
further analyzed the ellipsometry data using a Bruggerman
effective medium approximation. We find that while the
void density stays close to 40% for h-mesoTiO and 45%
2
for c-meso-TiO , the volume fraction of anatase within the
2
titinia framework steadily increased as a function of the
annealing temperature. In the case of h-meso-TiO , the vol-
2
ume fraction of anatase was 0% at 300 °C and reached
100% at 600 °C. On the other hand, in the case of c-meso-
TiO the volume fraction of anatase was already 35% at
2,
300 °C and reached 100% at 550 °C. These results corre-
spond well with the crystallinity profile as a function of
temperature obtained from X-ray diffraction experiments
[4].
Figure 4 Ordinary (n = n ) and extraordinary (n ) indices of re-
x y z
fraction for 2D hexagonal meso-TiO film annealed at 300 °C.
2
The interesting result that arises from the ellipsometry
analysis, namely, the transition from optically anisotropic
mesoporous structure, it probably enables the oxygen
to diffuse efficiently into the whole lattice, creating
stoichiometric anatase, and resulting in a lower n(λ).
In order to further reduce the error between the ex-
perimental and the modeled data (i.e., mean square error,
to isotropic medium in meso-TiO thin films can be ex-
2
plained in terms of the thermal reconstruction process in
meso-TiO . With increasing annealing temperature meso-
2
TiO thin films display a unidirectional contraction of the
2
MSE), we had to represent the meso-TiO films as an ani-
2
framework along the z-axis as well as a transformation of
sotropy medium. As shown in Fig. 3, the inclusion of ani-
sotropy reduces the MSE by nearly half for the films an- the framework from amorphous-titania to anatase. As
mentioned earlier, the anisotropy of meso-TiO films an-
2
nealed at lower temperatures. The films were best repre-
sented by a uniaxial-anisotropic model for n(λ), which de-
mands that the two in-plane n (n and n ) be equal but the
nealed at low temperature (<500 °C for h-meso-TiO and
2
<400 °C for c-meso-TiO ) is most likely the result of the
2
x
y
unidirectional lattice contraction as demonstrated for
out-of-plane n (n ) to be different [9]. In other words, the
z
films are negatively birefringent; higher n for light propa- meso-SiO [11]. It is, however, surprising that the aniso-
2
tropy of meso-TiO thin film disappears above a certain
2
gating with its electric field vector oscillating along the
plane of the film, compared to light propagating with its
electric field perpendicular to the plane of the film.
temperature in spite of the continuous lattice contraction
with increasing temperature as determined by X-ray meas-
urements [4]. This is probably due to the nucleation and
growth of anatase nanocrystallites within the channel walls
where the existing thinner walls in mesostructure disappear
while crystallites within thicker walls grow [3–5]. In
In Fig. 4, we have shown the three indices of refraction
for a representative sample from this study. It is worth not-
ing the introduction of a biaxial anisotropic model (i.e.,
n ≠ n ≠ n ) to represent the n(λ) for the films did not im-
x
y
z
meso-TiO therefore, as the structure is annealed, the well-
2
prove the fits, a point which was confirmed by the fact that
both Ψ and ∆ spectra remain similar when the experiment
was performed for different azimuthal angles (i.e., keeping
the same angle of incidence but rotating the sample in an
axis perpendicular to the surface of the sample) [10]. The
fact that n = n for this system suggests that the channel
defined pore architecture is replaced with coarsened crys-
tallite assemblies, resulting in the disappearance of optical
anisotropy caused mainly by anisotropic pores.
4 Conclusion We have determined the dispersion of
the index of refraction [n(λ)] and the ratio between amor-
phous and anatase forms of titania in a series of 2D-
hexagonal and 3D-cubic mesoporous titania samples that
x
y
axes are randomly organized in the x,y-plane, a result cor-
roborated by X-ray and scanning electron microscopy re-
sults. As we have found in silica-based periodic mesopor-
ous films, this anisotropy is triggered by the fact that the were annealed at different annealing temperatures. The in-
crease in n(λ) with annealing temperature, for both types of
mosoporos titania, is due to the transformation of the
original amorphous-titania to anatase, a result verified by
determining the composition (i.e., amorphous, anatase and
film undergoes a uniaxial contraction during the annealing
process [11]. The observation that the degree of birefrin-
gence in the meso-TiO films is higher in comparison to the
2
silica-based periodic mesoporous films gives further cre-
dence to this explanation, as the titania films undergo a void) of each sample using a Bruggerman effective me-
dium approximation. In addition, ellipsometry also showed
that the samples annealed at low-temperatures were aniso-
higher uniaxial contraction than the silica films, as indi-
cated by X-ray and ellipsometry results.
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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