Effect of crystal structure on optical properties of sol-gel derived zirconia thin films

Article abstract of DOI:10.1016/j.jallcom.2012.12.115

The optical properties of sol-gel derived zirconia thin films and their relation to the crystal structure are studied in this paper. ZrO₂ films were deposited on quartz glass and silicon wafer substrates by sol-gel method with conventional furn

Full text of DOI:10.1016/j.jallcom.2012.12.115

Journal of Alloys and Compounds 556 (2013) 182–187
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Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Effect of crystal structure on optical properties of sol–gel derived zirconia thin films
⇑
⇑
Xiaodong Wang , Guangming Wu, Bin Zhou, Jun Shen
Pohl Institute of Solid State Physics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, Tongji University, Shanghai 200092, PR China
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 11 July 2012
Received in revised form 8 November 2012
Accepted 23 December 2012
Available online 29 December 2012
The optical properties of sol–gel derived zirconia thin films and their relation to the crystal structure are
studied in this paper. ZrO films were deposited on quartz glass and silicon wafer substrates by sol–gel
2
method with conventional furnace annealing (CFA) and rapid thermal annealing (RTA). Crystal structures
of the films were analyzed by X-ray diffraction (XRD) and Raman spectroscopy, while refractive indices of
the films were determined from the reflectance and transmittance spectra. The refractive indices vary
with the function of crystal structure and density of the films, which depends on annealing temperature
and annealing technique. Lattice-mismatch between monoclinic phase and tetragonal phase was found
Keywords:
Zirconia
Sol–gel processes
Refractive index
CFA
2
to reduce the refractive index of ZrO films.
Ó 2012 Elsevier B.V. All rights reserved.
RTA
1
. Introduction
2. Experimental
.1. Preparation of ZrO
The ZrO2 sol was prepared using zirconium butoxide (Zr(OC H ) (TBOZ), 80% in
2
2
sol
Sol–gel derived thin films have been widely studied and devel-
oped because of their high laser-induced damage thresholds (LIDTs)
1,2], which is the bottleneck in scaling up high power laser systems
for future laser fusion technology [3]. In addition to the high LIDT,
sol–gel ZrO thin film also has wide optical bandgap, wide spectral
4
9 4
[
butanol (Sigma–Aldrich)) as precursor, with anhydrous ethanol (EtOH) as solvent,
deionized water for hydrolysis, acetylacetone (CH COCH COCH , AcAc) as chelating
agent and acetic acid (CH COOH, HAc) as catalyst. To control the fast hydrolysis of
3
2
3
3
2
TBOZ, the addition sequence of reagents is important to prepare a transparent and
stable sol. During synthesis, two different but equal parts of ethanol solutions were
prepared. In the first part, TBOZ was dissolved into anhydrous ethanol containing
AcAc. After being mixed with HAc, the solution was then sealed and kept stirring
for 30 min to achieve a complete chelation between the alkoxide and AcAc. The sec-
ond part of the solution was then prepared by mixing the deionized water with
anhydrous ethanol. These two solutions were then mixed and stirred for 2 h to
region of transparency from visible to near infrared (NIR), as well as
the high chemical and thermal stabilities [4–8]. Therefore, it has
been used as a common high refractive index film material in depos-
iting optical coatings [9], especially the highly-reflective (HR) coat-
ings [10–12] for application in high-power lasers.
As is known to all, zirconia exhibits amorphous and three
crystalline phases: monoclinic, tetragonal and cubic structures
achieve hydrolysis and condensation. The molar ratio was TBOZ:EtOH:H
HAc:AcAc = 1:15:3:1.6:0.2. The mixture was finally aged in a stable environment
with humidity lower than 30% and temperature of 20–25 °C) for 120 h.
2
O:
(
[
2
13–17]. For sol–gel derived ZrO thin films, the crystal structure
depends greatly on thermal annealing, which has a strong influ-
ence on the optical properties of the films. A large number of stud-
ies have been done to investigate the annealing effect on the
2
.2. Preparation of ZrO
2
thin films
The silicon wafer and quartz glass substrates were firstly cleaned thoroughly,
structural and optical properties of ZrO
none of them studied the detailed relationship between the crystal
structure and optical properties of the ZrO films systematically.
2
films [4,18–20]. However,
heated at 200 °C for 20 min, and then cooled down to room temperature. A dip-
coating apparatus (Chemat Dip Master-200) was used for the deposition, and the
film thickness could be adjusted by the withdrawal rate (0–30 cm/min). After each
coating, the films were firstly pretreated at 100 °C for 1 h, and then heat-treated in
muffle furnace for 2 h at different temperatures ranging from 100 to 800 °C. For
RTA, the samples were heated in a rapid thermal processor (AG Associates Heat-
pulse 610) for only 60 s, at temperatures ranging from 200 to 800 °C.
2
Therefore, we devote this work to understand the effect of the crys-
tal structure on the optical properties of zirconia films. Conven-
tional furnace annealing and rapid thermal annealing at various
2
temperatures were used to obtain ZrO films with different struc-
tures. The correlation between the structure evolution and optical
properties were then studied and analyzed.
2.3. Characterization
Raman spectra were recorded at room temperature with a Jobin–Yvon micro-
Raman apparatus (HR-800) equipped with a 30 mW He-Cd laser (Kimmon Koha,
IK3301R-G) emitting at 325 nm and a microscope (Olympus BX41). An edge filter
was used in the Raman setup to block the Rayleigh scattering light and stray laser
bands. The laser beam irradiating the sample was attenuated to below 0.1 mW in
⇑
Corresponding authors. Tel.: +86 21 6598 2762; fax: +86 21 6598 6071.
E-mail addresses: xiaodong_wang@tongji.edu.cn (X. Wang), shenjun67@
tongji.edu.cn (J. Shen).
0
925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jallcom.2012.12.115

X. Wang et al. / Journal of Alloys and Compounds 556 (2013) 182–187
183
order to avoid laser-induced heating. Before each measurement, a silicon wafer was
used for the wavenumber calibration of the spectrometer. The spectral resolution
by the emerging t-ZrO
2
Raman vibration modes at 271, 466,
ꢀ1
6
43 cm [22]. For temperature up to 500 °C, these Raman peaks
ꢀ
1
was estimated to be 1.6 cm . XRD patterns were collected by a diffractometer
Dandong Fangyuan, DX-2700) with Cu K of wavelength of 1.54 Å. Fourier trans-
form infrared (FTIR) spectroscopy measurements were performed in the range of
get sharper and shift towards lower frequencies. Meanwhile, the
(
a
Raman modes at 179, 190, 222, 333, 347, 381, 476, 556,
ꢀ
1
ꢀ1
4
00–4000 cm using Bruker Tensor 27 FTIR spectrometer. The transmittance and
616 cm that come from the m-ZrO are also observed [22], which
2
reflectance spectra of the films were measured in the 400–1000 nm region using
a Jasco-V570 UV–VIS-NIR double beam spectrometer. The surface morphology of
the films was investigated by atomic force microscope (AFM, PSIA XE-100) in non-
contact mode.
means that the conventional furnace annealed films were crystal-
lized into a mixed phase of tetragonal and monoclinic structures
at this temperature. With the increase of the annealing tempera-
ture, the Raman peaks of the monoclinic phase further get stronger
and sharper while that of tetragonal phase get weaker, which indi-
cates the transformation of tetragonal to monoclinic. However, the
3
. Results and discussion
ZrO
2
film still co-exists with two phases until 800 °C. Due to the
XRD characterizations have been conducted to confirm the ZrO
phase composition occurring after thermal annealing at different
temperatures by CFA and RTA, as shown in Fig. 1. The ‘‘t’’ and
‘m’’ in the figure denote the tetragonal and monoclinic phase,
respectively. The sharp peaks at 33.16° and 61.84° are due to the
2
high penetration depth of the laser line, the very strong peak at
ꢀ1
5
20.7 cm from the LO phonon of silicon is also visible in the
ꢀ1
Raman spectra. The peak at around 320 cm is ascribed to the
overtone of 2TA(X) of the silicon wafer [23].
Fig. 2b presents the Raman spectra of ZrO thin films obtained
2
by RTA. It can be recognized from the Raman spectra that crystal-
‘
diffractions from silicon substrates. For the samples annealed at
4
(
00 °C by CFA, four peaks from tetragonal (011), (110), (112),
121) planes appear, indicating the formation of a dominantly
tetragonal phase. At 500 °C, the XRD pattern shows both of the
monoclinic ZrO (m-ZrO ) and tetragonal ZrO (t-ZrO ) characteris-
tic peaks, which is a result of a mixture of tetragonal and mono-
clinic phases in the ZrO thin film. As the annealing temperature
is increased to 800 °C, the ZrO tetragonal peaks are reduced
lization does not start until the temperature reaches to 500 °C. The
ꢀ1
appeared Raman modes at 274, 461, 647 cm
t-ZrO . The peak sharpening after increasing the annealing temper-
atures reveals the improvement in the crystallinity of the annealed
films. At 800 °C, still no Raman mode of m-ZrO is detected, which
2
is consistent with the XRD results.
The average crystallite size in our films can be calculated from
the XRD line broadening (Fig. 1) using the Scherrer’s formula as
follow [24]:
are related to
2
2
2
2
2
2
2
remarkably, while the monoclinic peaks become stronger, which
shows a dominantly monoclinic phase.
As shown in Fig. 1b, the 400 °C RTA annealed film displays no
peak originating from crystalline ZrO
phous nature of the film. Four peaks from t-ZrO
2
, which indicates the amor-
0:89k
C ¼
2
appear in pattern
b cos h
of 500 °C annealed film. By further increasing the annealing tem-
perature, these peaks get sharper and shift towards lower degrees.
However, only the tetragonal phase exists even if the temperature
reaches 800 °C. These results indicate that RTA has a propensity to
where C is the crystallite size, k is the wavelength of the Cu K
radiation (k = 1.54 Å), b is the full width at half maximum (FWHM,
in radians) of crystal plane (t(011) for t-ZrO and m(111) for
m-ZrO ) and h is the diffraction angle. The calculated crystallite size
of the tetragonal phase and monoclinic phase of the samples an-
nealed at different temperatures is summarized in Table 1. It can
be observed that as the temperature increases, there is a slight in-
crease in the crystallite size for both CFA and RTA annealed samples.
a
2
generate t-ZrO
Raman spectroscopy is a sensitive tool for detecting the corre-
sponding bonding changes in ZrO upon annealing, whose results
are shown in Fig. 2. Due to the XRD peak overlap, it may be difficult
to distinguish the ZrO tetragonal phase from the cubic phase so-
lely by XRD [21]. Therefore, the Raman spectroscopy results are
combined with XRD to further identify t-ZrO . In the 100 and
00 °C CFA annealed zirconia films, the Raman spectra do not con-
2
compared with CFA.
2
2
2
For CFA, the t-ZrO
23.1 nm and m-ZrO
the RTA annealed t-ZrO
7.8 nm to 10.4 nm. Also, the CFA obtained t-ZrO
crystallite size than RTA obtained t-ZrO . These results show that
2
crystallite size increases from 11.0 nm to
2
2
increases from 9.3 nm to 23.6 nm. Similarly,
3
2
crystallite size only slightly increases from
has a larger
tain characteristic peaks from crystalline ZrO
2
, confirming that the
2
sample is dominated by amorphous phase. As the zirconia film is
2
heated to 400 °C, tetragonal phase becomes dominant as indicated
the tetragonal phase is stabilized below 11 nm. This also agrees
(a)
(b)
2
Fig. 1. XRD patterns of ZrO films annealed at different temperatures (a) CFA (b) RTA.

1
84
X. Wang et al. / Journal of Alloys and Compounds 556 (2013) 182–187
2
Fig. 2. Raman spectra of ZrO films annealed at different temperatures (a) CFA (b) RTA.
Table 1
Crystallite size of t-ZrO
2
and m-ZrO
2
annealed at different temperatures.
removed. The IR absorption bands related to t-ZrO
2
appear at
is ob-
5
00 °C and no absorption band corresponding to m-ZrO
2
Sample
t-ZrO
h/°
2
m-ZrO
2h/°
–
31.534
31.681
31.711
31.715
–
–
–
–
2
served in the whole rapid annealing process. As noticed from the
figure, the CAH and C@O vibrations at 1445 and 1556 cm still
present at the highest rapid annealing temperature so that the
zirconia films have impurity defect. This impurity defect plays an
important role in defining the phase stability of zirconia hence it
2
b/°
C
t
/nm
b/°
C
m
/nm
ꢀ1
CFA400
CFA500
CFA600
CFA700
CFA800
RTA500
RTA600
RTA700
RTA800
30.505
30.472
30.461
30.474
30.476
30.623
30.487
30.651
30.533
0.742
0.676
0.637
0.548
0.353
1.047
0.928
0.799
0.782
11.0
12.0
12.8
14.9
23.1
7.8
–
–
0.875
0.492
0.424
0.346
–
9.3
16.6
19.3
23.6
–
–
–
–
2 2
inhibits the transition from t-ZrO to m-ZrO .
On the basis of the combination of the results of XRD, Raman
and FTIR spectroscopy, we know that apart from crystallite size,
the presence of water molecules and impurities also influence
phase structure. Therefore, RTA annealed films are more stabilized
8.8
–
10.2
10.4
–
–
2
in t-ZrO .
The AFM imaging was performed to study the surface morphol-
ogy changes induced by thermal annealing. Fig. 4a shows the sur-
face topography of the films annealed by CFA at 300, 400, 500 and
800 °C, respectively. The 300 °C annealed film shows structureless
reasonably with that reported by Garvie, who attributed the forma-
tion of metastable tetragonal phase to the critical crystallite size ef-
fect [25]. As the particle size approaches nano-scale, surface
energies become significant in stabilizing the tetragonal phase.
q
smooth surface with a root mean square surface roughness (R ) of
Therefore, the RTA annealed films are stabilized in t-ZrO
such films have the smaller crystallite sizes.
2
because
0.489 nm. When the film is treated at 400 °C, there is a preferred
orientation of the regularly shaped grains, which suggests the
In order to investigate the organic components influence on the
structure of the films, the vibrational properties of ZrO films have
growth of the nano-crystalline ZrO
crease of the annealing temperature, the grains get larger and more
ordered. After annealing at 800 °C, the roughness R increases to
1.214 nm. For RTA annealed samples (Fig. 4b), it also shows an
increasing grain size and ordering degree with the increase of the
annealing temperature. However, the RTA annealed samples have
a comparatively smaller grain size and smooth surface roughness
(Table 2). The morphology changes are due to the different crystal-
2
grains. With the further in-
2
been studied by FTIR spectroscopy. Fig. 3a presents the FTIR spec-
tra of the films treated by CFA. It can be seen that organic groups
such as the ethyl, acetyl, and the ethoxide groups still present in
q
ꢀ
1
the low temperature annealed films.
t
OH at 3431 cm
, tC–O–C at
ꢀ1
1
ꢀ1
1
028 cm
,
t
CH2
,
t
CH3 at 2945, 2874 cm , dCH2, dCH3 at 1344,
448 cm , dC@O at 1562 cm , dH2O at 1642 cm , as well as
ZrAOH and ZrAOAZr stretching vibrations at 617 and 464 cm
ꢀ
ꢀ1
ꢀ1
1
ꢀ1
2
lization of ZrO and densification of the films.
are all visible in the spectrum of 100 °C annealed ZrO
2
film. After
Determination of the optical constants, e.g., refractive index,
thickness is a topic of fundamental and technological importance
in optical films. In general, the film thickness and optical constants
can be extracted from physical and optical model by comparing to
experimental data. Here, characterization technique based on
least-square fitting to the measured reflectance and transmittance
ꢀ1
annealing at 400 °C, the absorption band at 3431 cm disappears,
implying that annealing at 400 °C results in a nearly complete re-
moval of the hydroxyl group. Meanwhile, the appearance of a
ꢀ
1
new band at 437 cm is assigned to the t-ZrO
the observed absorption bands at 409, 487, 570, 742 cm are cor-
responding to m-ZrO [22,26], and get intense with the tempera-
ture increase. The band around 1070 cm
2
[22]. At 500 °C,
ꢀ1
2
spectra is used [27]. The optical parameters of the ZrO layer were
2
ꢀ1
can be assigned to
determined from the measured transmittance and reflectance
spectra for each film by fitting simultaneously the results obtained
with calculations and measurements over the 400–1000 nm re-
gion. In this study, both sides of the glass substrate were coated
through dip-coating method. Therefore, we built a five layer model
SiAO bonds. The most probable explanation is that a reaction at
the oxide/Si interface occurs as the band intensity increases with
annealing temperatures.
The FTIR spectra of ZrO
2
films obtained by RTA are also mea-
sured as shown in Fig. 3b. It can be found from the figure that
the absorption band around 3400 cm disappears after rapid ther-
mal annealed at 500 °C, indicating the hydroxyl group of the film is
2
to simulate the ZrO films (Fig. 5a). For simplicity, the Cauchy for-
mula [28], which was a optical model for insulators and dielectric
films, was used to describe the dispersion relationship of the film
ꢀ1

X. Wang et al. / Journal of Alloys and Compounds 556 (2013) 182–187
185
(
a)
(b)
2
Fig. 3. FTIR spectra of ZrO films annealed at different temperatures (a) CFA (b) RTA.
Fig. 4. AFM images of films annealed at 300, 400, 500 and 800 °C by different annealing methods (a) CFA (b) RTA.
Table 2
2
of ZrO films annealed at different temperatures.
measured and fitted transmittance and reflectance spectra are
plotted in Fig. 5b. The fitted curves (solid line) agree well with the
experimental dada (circles), which indicates the Cauchy formula
R
q
Temperature/(°C)
300
400
500
800
R
R
q
_CFA/nm
_RTA/nm
0.489
0.367
0.366
0.202
0.687
0.284
1.214
0.644
can well describe the dispersion relationship of the ZrO
400–1000 nm. The thickness and refractive indices of the film at
00–1000 nm are then determined and shown in Fig. 5c. The same
analysis procedure was repeated for all the ZrO films annealed by
2
films in
q
4
2
different methods. The calculated RMSE parameters of all the films
are listed in Table 3. All the obtained RMSE values are less than 1,
which ensure the reliability of the determined optical constants.
The determined refractive indices at He–Ne laser wavelength of
633 nm and thickness of the films are chosen and plotted in Fig. 6
to study the variation during the annealing. In CFA, as can be
known from XRD and Raman analysis, the films annealed from
100 to 300 °C are amorphous. It can be seen that the amorphous
zirconia films have low refractive indices compared with those of
the crystallized films. The refractive index of the pretreated
(100 °C) film is 1.559, which is approximately the same as that
reported by Guo et al. [30] and Cueto et al. [31]. As a result of
layer. To judge the quality of the fitting, the root mean squared er-
ror (RMSE) was defined by:
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
h
i X
n
2
j
n
2
j
2
RMSE ¼
ðYexp ꢀ Ycalc Þ ꢁ weight
=
weight ;
j¼1
j
j
j¼1
where n is the number of selected experimental data, Yexp is the
value of the experimental data, Ycalc is the calculated value and
weight is the weight of each experimental point. The lower the RMSE
j
value, the better is the agreement between fitted and experimental
data. It is generally considered a good agreement between the fitted
and experimental data when RMSE is between 0 and 1 [29]. A typical

1
86
X. Wang et al. / Journal of Alloys and Compounds 556 (2013) 182–187
Fig. 5. (a) Schematic representation of the proposed five layer physical model for the calculation (b) ezxperimental and calculated transmittance and reflectance curves for
film annealed by CFA at 200 °C (c) refractive index dispersion of ZrO film annealed by CFA at 200 °C.
2
Table 3
2
RMSE results of all the ZrO films annealed at different temperatures.
Temperature/(°C)
200
300
400
500
600
700
800
RMSE_CFA
RMSE_RTA
0.1938
0.1832
0.2973
0.1765
0.3041
0.2074
0.2682
0.2292
0.3540
0.4959
0.3240
0.7709
0.3145
0.4352
Fig. 6. Variation of refractive index at 633 nm and thickness of ZrO
2
films (a) CFA (b) RTA.
decomposition and evaporation of the organic groups with the in-
crease of the annealing temperature, the porous structure of the
amorphous films is destroyed and hence the packing density be-
comes larger which then increases the refractive index distinctly.
After annealing at 400 °C, the film is crystallized to tetragonal
phase and shows a refractive index of 1.870. In addition, with the
increase of the annealing temperature, the refractive index first de-
here is different from that reported by Liu et al. [18] and Liang et al.
[19]. This anomalous evolution can be explained by the phase trans-
formation of zirconia. After annealed at 500 °C, the film is composed
2 2
of t-ZrO and m-ZrO mixed phases. The lattice-mismatch between
the new monoclinic phase and parent tetragonal phase increases
the porosity of the film. This porosity increase is larger than the de-
crease induced by thermal densification, which in turn then reduces
its refractive index. Increasing annealing temperature (600–800 °C)
promotes the densification of the film and further transformation
creases and then increases with the watershed temperature of
1
5
00 °C (as shown in red circle part of Fig. 6a). The result presented
2 2
of t-ZrO to m-ZrO , which then results in the increase of the
1
refractive index continuously again. The thickness of the coatings
decreases from 198.3 nm (annealed at 200 °C) to 91.0 nm (annealed
For interpretation of color in Fig. 6, the reader is referred to the web version of
this article.

X. Wang et al. / Journal of Alloys and Compounds 556 (2013) 182–187
187
at 800 °C). And it is found the decrease between 200 °C and 400 °C is
larger than that between 400 °C and 900 °C, indicating the densifica-
tion of amorphous ZrO is larger than that of crystallized ZrO films.
Acknowledgement
2
2
We thank Jiandong Wu for the AFM measurement. This
work was financially supported by National Natural Science
Foundation of China (Grant Nos. 11074189, U1230113), National
Key Technology Research and Development Program of China
(Grant No. 2013BAJ01B01), Shanghai Committee of Science and
Technology, China (Grant Nos. 11nm0501600, 11nm0501300),
Fundamental Research Funds for the Central Universities (Grant
No. 2012KJ014) and China Postdoctoral Science Foundation (Grant
No. 2012M520925).
This is consistent with the refractive index change during annealing.
Additionally, it can be found from Fig. 6b that different anneal-
ing procedure caused a significant change in refractive index vari-
ation of the samples during the annealing. From 200 to 400 °C (by
RTA), the organic groups and absorbed water still exist. The resid-
ual organic segments have a low refractive index and also preserve
the film with a high porosity, hence make the film a low refractive
index. Thermally induced densification of the film only results in a
slight increase of refractive index from 1.575 to 1.594. After an-
nealed at 500 °C, the pores left by the removal of organic segments
decrease the refractive index while crystallization increases it.
Therefore, the refractive index of the film only increases to 1.606.
Upon annealing at higher temperatures, the densification and in-
creased crystallinity of the films give rise to a rapid increase of
the refractive index, from 1.606 to 1.929 between 500 and
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[
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(n = 1.898). Considering that in RTA process, the film annealed at
(
8
00 °C is tetragonal phase, which would not have the lattice-mis-
[
match induced porosity change that happened in CFA treated films.
Therefore, the refractive index in RTA is larger than that of CFA.
This result proves the refractive index variance occurred on the
CFA treated films from another point of view.
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066–1074.
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(
[
1
[
21] F. Lu, J. Zhang, M. Huang, F. Namavar, R.C. Ewing, J. Lian, J. Phys. Chem. C 115
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(
4
. Conclusion
[
[
[
[
[
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23] X. Wang, J. Shen, Q. Pan, J. Raman Spectrosc. 42 (2011) 1578–1582.
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The effect of crystal structures on the optical properties of ZrO
2
thin films prepared by sol–gel technique has been studied. XRD,
Raman, FTIR and UV–VIS–NIR spectrometers were used to study
the crystal structures, organic components and optical properties,
respectively. Crystal structures of the films were tuned through
controlling the thermal annealing methods and temperatures.
The refractive indices, which determine the optical properties of
the films, vary with the crystal structure of the films. It is also
found that the lattice-mismatch between monoclinic phase and
tetragonal phase increases the porosity of the film, which in turn
reduces the refractive index of the film.
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28] F.A. Jenkins, H.E. White, Fundamentals of Optics, Fourth ed., McGraw-Hill Inc.,
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1
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(