Densification and porosity evaluation of ZrO –3 mol.% Y O sol–gel 2 2 3 thin films

Abstract

Densification of ZrO –3 mol.% Y O sol–gel thin films after heating in air at 100 8CFTF1100 8C is investigated, with 2 23 particular emphasis on porosity evaluation. For this purpose, the refractive index and thickness of the films are determined from transmission spectrometry. Three densification regimes were clearly identified: T-300 8C, 300 8C FTF 800 8C and T)800 8C. For porosity evaluation, a simple strategy based only on film thickness measurements is used. These porosity values are compared with those obtained from refractive index measurements, applying commonly used analytical expressions. Our results clearly show that the porosity of thin films is underestimated when the Lorentz–Lorenz expression is used. Implications for preparation of ZrO sol–gel thin films are also discussed. 2 2003 Elsevier B.V. All rights reserved.

Full text

Thin Solid Films 458 (2004)92–97
0040-6090/04/$ - see front matter 䊚2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2003.11.311
Densification and porosity evaluation of ZrO –3 mol.% Y O sol–gel
223
thin films
A. Dıaz-Parralejo , R. Caruso , A.L. Ortiz , F. Guiberteau *
ab a a,
´
Departamento de Electronica e Ingenierıa Electromecanica, Escuela de Ingenierıas Industriales, Universidad de Extremadura, 06071 Badajoz,
a
´´´ ´
Spain
Instituto de Fısica Rosario (CONICET-UNR). Av. 27 de Febrero 210 Bis. 2000 Rosario, Argentina
b
´
Received 19 May 2003; received in revised form 28 November 2003; accepted 28 November 2003
Abstract
Densification of ZrO –3 mol.% Y O sol–gel thin films after heating in air at 100 8CFTF1100 8C is investigated, with
223
particular emphasis on porosity evaluation. For this purpose, the refractive index and thickness of the films are determined from
transmission spectrometry. Three densification regimes were clearly identified: T-300 8C, 300 8CFTF800 8C and T)800 8C.
For porosity evaluation, a simple strategy based only on film thickness measurements is used. These porosity values are compared
with those obtained from refractive index measurements, applying commonly used analytical expressions. Our results clearly show
that the porosity of thin films is underestimated when the Lorentz–Lorenz expression is used. Implications for preparation of
ZrO sol–gel thin films are also discussed.
2
䊚2003 Elsevier B.V. All rights reserved.
Keywords: Zirconia-films; Porosity; Sol–gel; Densification
1. Introduction
There are different techniques to obtain thin films
(physical vapour deposition, sputtering, electron beam
evaporation, sol–gel, etc.)w1x. Among them the sol–
gel route w2,3xoffers certain advantages such as sim-
plicity and low cost, capability of coating large surface
areas, low processing temperatures, high optical quality
of films, etc. In addition, this method is suitable to
obtain almost any single- or multi-component oxide
coating (ZrO , Al O , SiO , TiO , etc.).
223 2 2
In particular, zirconia (ZrO )based thin films have
2
promising applications in optics and, especially, as
protective barriers. For example, these coatings can be
used to provide specific optical properties in glasses
(anti-reflection, selective reflection, photochromism,
etc.)w4x, to prevent chemical corrosion and gas oxida-
tion in metals w5,6x, and even in functional applications
such as oxygen sensors w7xor buffer layers in micro-
*Corresponding author. Tel.: q34-924-289530; fax: q34-924-
289601.
E-mail address: guiberto@materiales.unex.es (F. Guiberteau).
electronic devices w8x. All of these applications are
based on the interesting combination of mechanical,
chemical, and physical properties exhibited by these
ceramics. Indeed, zirconia has a large thermal expansion
coefficient (;10=10 8C)but its thermal conduc-
y6y1
tivity (;2.09 W m s K)is approximately two orders
y1
of magnitude lower than those of metals, enabling its
use as a thermal barrier coating. Also, yttria (YO)
23
doped zirconia can exhibit good mechanical properties,
combining a high wear resistance with a moderate
toughness, frequently associated with the activation of a
transformation toughening mechanism w9x. In addition,
zirconia has a high refractive index (2.21 at a wave-
length of
l
s630 nm), low absorption, and large optical
band gap (;3.8–3.2 eV), and therefore its correspond-
ing films have proven very useful for many optical
applications. However, the structure and properties of
thin films can differ significantly from those of the bulk
material. In particular, thin film properties depend on
porosity (P)and thickness (t), rendering control of both
characteristics during the densification process a critical
issue in thin film preparation. Consequently, accurate

93A. Dıaz-Parralejo et al. / Thin Solid Films 458 (2004) 92–97
´
Fig. 1. Schematic diagram showing light transmission through a thin
film (refractive index, n)of thickness (t), deposited on a thick trans-
parent substrate (refractive index, s). The incident and transmitted
intensities are denoted as Iand I, respectively.
0t
Fig. 2. Transmittance spectrum of a ZrO –3 mol.% Y O sol–gel thin
223
film (two layers)deposited on a quartz-fused silica substrate.
measurements of film porosity and thickness are essen-
tial to select the optimum fabrication strategy.
Unfortunately, the porosity evaluation of thin films is
not as straightforward as the measurement of thickness.
Although the porosity of powders can be measured by
conventional gas adsorption techniques, these methods
can not be applied directly to thin films. Not even the
new sophisticated methods developed for measuring
porosity in as-deposited films w10xare completely sat-
isfactory, because the results are only related to surface
accessible pores. For these reasons, porosity evaluation
of thin films is usually made from refractive index (n)
measurements, using different expressions proposed in
the literature w10–12x.
The present study was designed with two objectives
in mind. The first is to investigate the densification
upon heating of 3 mol.% yttria-doped zirconia thin films
obtained by the sol–gel route. For this purpose, we used
exclusively data obtained from transmittance spectra in
order to determine the refractive index and thickness of
zirconia films heated at temperatures (T)between 100
and 1100 8C. The second objective is to study the
adequacy of the different expressions proposed in the
literature to evaluate film porosity, from refractive index
measurements. To achieve this objective we compared
these porosity values with those obtained using a quasi-
direct method based only on film thickness
measurements.
2. Thin film characterization from transmittance
spectra
2.1. Refractive index and thickness
The refractive index and thickness of a thin film can
be calculated from a simple transmittance spectrum
using the Swanepoel method w13x. This method can
only be applied to thin films deposited on transparent
substrates several orders of magnitude thicker than the
film (see Fig. 1). When film thickness is uniform,
interference effects give rise to the typical transmittance
spectrum with successive maxima and minima (see Fig.
2). Practical application of this method entails, as a first
step, the calculation of the maximum and minimum
transmittance envelope functions, T(
l
)and T(
l
),
Mm
respectively (see Fig. 2). From these functions the
refractive index n(
l
)can be obtained as:
1
1y2y
22
wz
2
x|
nsNqNys(1)
Ž.
y~
where
2
TyTsq1
Mm
Ns2sq(2)
TT 2
Mm
sbeing the refractive index of the substrate.
Then, the film thickness can be obtained from the
refractive index corresponding to adjacent extreme val-
ues, nsn(
l
)and nsn(
l
)through the following
11 22
expression:
ll
12
tsM(3)
2lnyln
Ž.
12 21
with Ms1 for two adjacent maxima (or minima)and
Ms1y2 for two adjacent unlike extremes.
The accuracy of the Swanepoel method for measuring
nand tis better than 1% and, consequently, when
applicable it is undoubtedly an excellent option. To
ensure the presence of interference effects in the spec-
trum a minimum film thickness is required. In this work
we used two-layer films to obviate this problem.
2.2. Porosity
As already mentioned, direct evaluation of thin film
porosity is not easy. To the best of our knowledge there

94 A. Dıaz-Parralejo et al. / Thin Solid Films 458 (2004) 92–97
´
Fig. 3. Calculated pore volume fraction (P)vs. refractive index (n)
of porous films according to Eqs. (4)–(6)(assuming ns2.17).
d
are three expressions in the literature for evaluating
porosity in terms of the refractive index (usually at
l
s
500–600 nm)of the film. The simplest is:
nyn
d
Ps(4)
1yn
d
where Pis the pore volume fraction, nthe refractive
index of the porous film, and nthe refractive index of
d
the film after full densification w10x. A modification of
Eq. (4)has been proposed by Yoldas w11x, in the form:
2
nynnqnny1
dd
Pss1y(5)
2
1yn1qnny1
dd d
which is frequently reported in the literature. Finally,
another widely accepted expression for Pis:
22
ny1nq2
d
Ps1y(6)
22
ny1nq2
d
which is derived from the Lorentz–Lorenz expression
w12x.
It is worth noting that these three equations can be
obtained from a simple mixture rule according to the
following general equation:
wx
Fns1yPFn qPF n (7)
Ž. Ž . Ž .
dp
where 1yPis the volume fraction of the dense film
(refractive index, n)and Pthe volume fraction of the
d
pores (refractive index of the substance within the pores,
n). Indeed, Eqs. (4)–(6)can be directly obtained from
p
Eq. (7), by considering that ns1(i.e. air filled pores)
p
and substituting into Eq. (7)the refractive index func-
tions F(n)sn,F(n)sny1, and ,
2
ny1
i
2
Fn s
Ž.
ii ii i2
nq2
i
respectively.
Fig. 3 shows the porosity values obtained from Eqs.
(4)–(6)for ZrO –3 mol.% Y O porous films, assum-
223
ing that ns2.17 for this specific material w14x. As one
d
can see, porosity values vary considerably from one
expression to another. It should be mentioned that
refractive indices of zirconia sol–gel coatings usually
lie within the interval 1.6–1.9 in which the differences
are especially pronounced (see Fig. 3). Therefore ques-
tions arise concerning the validity of these expressions.
3. Experimental method
3.1. Preparation of the films
The starting solution for the sol–gel process was
prepared by mixing and stirring zirconium (IV)n-
propoxide (ZNP)with propanol (PrOH)in an anhydrous
nitrogen atmosphere to avoid hydroxide precipitation,
using nitric acid (HNO )as catalyst. This solution was
3
then mixed with a second solution of yttrium (III)
acetate (YAcØ4H O)in PrOH and HNO to obtain the
23
precursor solution for the ZrO –3 mol.% Y O coatings.
223
After 1 h mixing and stirring, distilled water was added
without stopping the stirring process that was continued
for 4 additional hours. The ZNPyPrOHyHOyHNO
23
molar ratios in the final solution were 1:15:6:1.
Quartz fused (99.9% SiO )2.5=7.6 cm sheets (sup-
2
plied by Goodfellow Ltd.)were used as substrates in
this work. This selection allows us to heat the films at
temperatures TF1100 8C without substrate degradation.
The sheets were previously immersed in acetic acid for
24 h, then cleaned in distilled water and finally in
ethanol in an ultrasonic bath for 15 min.
Deposition of ZrO –3 mol.% Y O films was per-
223
formed in air by dip-coating. According to the Gugliel-
mi–Zenezini equation w15xa specific liquid film
thickness can be obtained from a solution by fixing the
g
Ø
n
product,
g
being the solution viscosity and
n
the
substrate withdrawal rate. In the present work we used
g
Ø
n
s48 cP cm min , with
g
in the range 4.6–4.9 cP.
y1
Obviously, the final thickness of the films will depend
on the particular heat treatment conditions. With the
aim of investigating the influence of temperature on
film thickness and porosity, a set of samples were heat
treated in air at temperatures in the range of 100
8CFTF1100 8C for 2 h. The dipping process and
thermal treatment were repeated once in order to obtain
two-layer coatings. The influence of the time was also
checked by again treating the films obtained at 100,
200, 300, 500 and 900 8C for 1 to 46 more hours at the
same temperature.
3.2. Characterization of the films
An ultraviolet-visible spectrophotometer (Helios a,
Thermo Spectronic)was used to obtain the transmission

95A. Dıaz-Parralejo et al. / Thin Solid Films 458 (2004) 92–97
´
Fig. 4. Refractive index (n)vs. heating temperature (T)for ZrO –3
2
mol.% Y O porous films, calculated from transmittance spectra and
23
using the Swanepoel method. Three regimes (indicated)are clearly
identified.
Fig. 5. Thickness (t)vs. heating temperature (T)for ZrO –3 mol.%
2
Y O porous films, calculated from transmission spectra and using the
23
Swanepoel method. The value at 1100 8C corresponds to a fully dense
film (ts220 nm). Three regimes (indicated)can be clearly
d
identified.
spectra of the samples. The thickness and the refractive
index of the films (at
l
s600 nm)were obtained from
these transmission spectra using the Swanepoel method
w13xalready described in Section 2. An atomic force
microscope (Park Scientific Instrument, Geneva, Swit-
zerland)was used to obtain topographical images of
selected coatings. Imaging was performed in contact
mode at 22 nN, using a cantilever with spring constant
of 0.4 N m and Si N pyramidal tip with curvature
y134
radius of 10 nm.
In this work we have used a quasi-direct method to
evaluate porosity based exclusively on film thickness
measurements from the transmittance spectra. Based on
the definition of porosity one may write:
t
d
Ps1y(8)
t
where tis the thickness of the porous film, and tthe
d
film thickness after full densification. Obviously, appli-
cation of this method entails the selection of an adequate
heat treatment schedule to achieve full densification of
the film. Here we consider that full densification is
achieved when the refractive index of the film reaches
the value corresponding to dense ZrO –3 mol.% Y O ,
223
i.e. 2.17 w14x.
4. Results and discussion
Fig. 4 shows the refractive index values (at
l
s600
nm)of two layer films heated at different temperatures
(100 8CFTF1100 8C)for 2 h. As expected, these
values increase when the temperature increases due to
densification of the film. Note that the refractive index
value corresponding to a fully dense ZrO –3 mol.%
2
Y O sample (ns2.17)is approached at 1100 8C(see
23 d
Fig. 4). The corresponding thickness values of these
films, obtained also from the Swanepoel method, are
shown in Fig. 5. According to Figs. 4 and 5, the
thickness value at 1100 8C corresponds to a completely
dense film, i.e. ts220 nm. The heat treatments were
d
limited to a maximum temperature of 1100 8C to avoid
substrate degradation. Nevertheless, the same films
deposited on sapphire substrates were heat treated at
1100 8C, 1200 8C and 1250 8C. Within experiment
error, no differences in the refractive indexes were
detected (ns2.17), reinforcing that at 1100 8C a fully
d
dense film is obtained.
Figs. 4 and 5 also suggest the existence of three
densification regimes. The most pronounced film thick-
ness reduction occurs between 100 8C and 300 8C(zone
I). In this first regime residuals of the sol–gel synthesis
(liquids, organic groups, etc.)are removed from the film
which, at this stage, has an amorphous and highly
porous structure w3,16x. Obviously, when the heating
temperature increases, elimination of these residuals is
favoured (evaporation, burning, etc.)and thereby den-
sification of the vitreous structure is clearly improved.
However, between 300 8C and 800 8C(zone II), due to
crystallisation of the film, there is hardly any reduction
of film thickness. Indeed, once crystallisation initiates,
at approximately 300–400 8Cw17x, atomic mobility is
drastically reduced and, therefore, temperature has less
influence on film densification. Finally, a more pro-
nounced reduction in thickness is observed at tempera-
tures beyond 800 8C(zone III), where diffusion occurs
through the crystalline structure and subsequent grain
growth becomes an efficient densification mechanism.
Evidence of grain growth in regime III is shown in the
AFM images of Fig. 6 corresponding to coatings heat
treated at 800 8C and 1100 8C for 2 h. A detailed
inspection of these images reveals that the structures
resolved at 800 8C are in fact groups of four to five
individual grains (average size 30–40 nm), as previous-
ly observed in similar coatings deposited on AISI 310

96 A. Dıaz-Parralejo et al. / Thin Solid Films 458 (2004) 92–97
´
Fig. 6. AFM images of films heated at 800 8C(a)and 1100 8C(b).
These temperatures correspond to the limits of regime III (see Fig.
5). Differences in grain size are apparent, suggesting the activation of
diffusion mechanisms in this range.
Fig. 7. Thickness (t)vs. heating time for ZrO –3 mol.% Y O porous
223
films heat treated at temperatures (indicated)in regimes I, II and III.
The dashed line represents the thickness corresponding to a complete-
ly dense film (i.e. ts220 nm).
d
Fig. 8. Comparative plot of porosity values (P)obtained from refrac-
tive index measurements, using Eqs. (4)–(6)(open symbols), and
from direct thickness measurements using Eq. (8)(solid symbols).
w18x. However, at 1100 8C the individual grains (average
size 100–200 nm)are clearly visible.
These results have interesting implications concerning
the efficacy of increasing temperature on improvements
in density of the films. Indeed, according to these results
once crystallisation of the film is achieved and sol–gel
residuals have been eliminated (approx. 300–400 8C),
increasing temperature further does not seem very prac-
tical to improve film densification. Although further
densification can be achieved at T)800 8C(zone III),
heat treatments in this regime are not practical due to
the degradation that most widely used substrates (silica-
based glasses or metals)suffer at these temperatures.
Only when the residual stresses need to be increased
can treatments at T)400 8C be justified.
We now consider the influence of heating time on
film thickness. As illustrated in Fig. 7, at 100 8C and
200 8C(regime I)time has a noticeable effect on film
thickness, which tends asymptotically towards a constant
value after a certain heating time. On the contrary, at
300 8C and 500 8C(regime II)time has little or no
influence. Finally, at 900 8C(regime III)film thickness
declines progressively to the full dense value after long
heating time (48 h). These results are consistent with
our analysis of the three densification regimes mentioned
above. Effectively, in zone I densification increases with
time as sol–gel residual elimination occurs, until a
certain constant thickness value is achieved when all
residuals which can be eliminated at that temperature
are removed. Obviously, these constant thickness values
decrease with increasing temperature. On the contrary,
in regime II time has no influence because almost all
the residuals have already been eliminated and the
temperature is too low for diffusion processes to be
activated. Finally, in zone III, diffusion becomes an
effective transport mechanism and, therefore, time
improves film densification.
Next, we focus on the thin film porosity evaluation.
Fig. 8 shows the porosity values obtained from direct
thickness measurements wEq. (8)xvs. the heating tem-
perature. Also, porosity values obtained from refractive
index wEqs. (4)–(6)xare plotted in the same figure for
comparison. Several implications are immediately
deduced. First, these results suggest the adequacy of the
Yoldas expression wEq. (5)xat TG300 8C, which also
gives the closest values at T-300 8C. However, the
Lorentz–Lorenz expression wEq. (6)xw
7,14,19–21x
noticeably underestimates the porosity (by approx. 50%
at T-800 8C). Questions therefore arise concerning the
porosity data reported in the literature obtained by
applying that equation. Finally, it is remarkable that the
results obtained from Eq. (4), associated with the sim-
plest mixture rule wF(n)sn, into Eq. (7)x, are even
ii
better than those obtained from the Lorentz–Lorenz
expression.
Although our results show the Yoldas expression to
be adequate for evaluating Pat TG300 8C, its values
are underestimated at T-300 8C(by approx. 10–25%).
This is due to the assumption that film pores contain air
(ns1), which is not exactly true at T-300 8C where
p

97A. Dıaz-Parralejo et al. / Thin Solid Films 458 (2004) 92–97
´
residuals from the sol–gel synthesis remain within the
pores. In this context, the application of Eq. (5)at T-
300 8C implies an underestimate of the porosity, in
agreement with our results. Besides, it is also assumed
that the nvalue corresponding to the crystalline struc-
d
ture (T)300–400 8C)is also valid for the vitreous
structure (T-300 8C), which is not exactly true. Of
course, such low temperatures are of little practical
interest.
5. Concluding remarks
In the present work we have studied the densification
process of zirconia sol–gel thin films, identifying three
densification regimes. In the first (T-300 8C), increas-
ing temperature has a noticeable effect on the vitreous
film density, which increases rapidly due to removal of
residuals from the sol–gel synthesis. On the contrary, in
the second regime (300 8CFTF800 8C), the crystalline
film density is hardly affected by temperature. Conse-
quently, once most residuals have been eliminated
(approx. 300-400 8C)and a crystalline structure is
achieved, it does not seem practical to increase the
heating temperature further, especially if substrate deg-
radation can occur. Finally, at T)800 8C, diffusion
processes are activated through the crystalline structure
and significant grain growth occurs (from 30–40 nm at
800 8C to 100–200 nm at 1100 8C). In this last regime,
full densification of the film can be achieved by increas-
ing either the heating temperature or time.
With respect to the porosity evaluation from trans-
mittance spectra analysis, the present study reveals the
adequacy of the Yoldas expression, whereas the Lor-
entz–Lorenz expression gives the worst results. Indeed,
this expression significantly underestimates the porosity
of thin films (approx. 50% at 300 8CFTF800 8Cin
our case). These results are especially relevant for
applications where film porosity evaluation is a key
issue—i.e. chemical protection of substrates (oxidation,
corrosion, etc.).
Acknowledgments
The authors thank Dr P. Miranda for fruitful discus-
sions. A grateful acknowledgement is also due to Con-
icet (Argentina)and the Ministerio de Educacion,
´
Cultura y Deporte (Spain)under Grant SB2000-0087
for supporting the stay of Dr Caruso in Spain. This
study was supported by funds from Consejerıa de
´
Educacion, Ciencia y Tecnologıa, Junta de Extremadura
´´
(Spain)-Fondo Social Europeo under Grant IPR00A084
and from Ministerio de Ciencia y Tecnologıa (Spain)-
´
FEDER under Grant MAT2001-3644.
References
w1xM. Ohring, The Materials Science of Thin Films, Academic
Press, London, 1992.
w2xC.J. Brinker, G.W. Scherer, Sol–Gel Science: The Physics and
Chemistry of Sol–Gel Processing, Academic Press, San Diego,
1989.
w3xJ.D. Wright, N.A.J.M. Sommerdijk, Sol–Gel Materials Chem-
istry and Applications, Taylor and Francis, London, 2001.
w4xD.R. Uhlmann, T. Suratwala, K. Davidson, J.M. Boulton, G.
Teowee, J. Non-Cryst. Solids 218 (1997)113.
w5xM. Atik, C.R. Kha, P. Delimaneto, L.A. Avaca, M.A. Aegerter,
J. Zarzycki, J. Mater. Sci. 25 (1995)178.
w6xW. Boysen, A. Frattini, N. Pellegri, O. de Sanctis, Surf. Coat.
Technol. 122 (1999)14.
w7xC. McDonagh, P. Bowe, K. Mongey, B.D. MacCraith, J. Non-
Cryst. Solids 306 (2002)138.
w8xY. Yu, X. Wang, Y. Cao, X. Hu, Appl. Surf. Sci. 172 (2001)
260.
w9xD.J. Green, R.H.J. Hannink, M.V. Swain, Transformation
Toughening of Ceramics, CRC Press, Boca Raton, FL, 1989.
w10xD.J. Taylor, P.F. Fleig, S.L. Hietala, Thin Solid Films 332
(1998)257.
w11xB.E. Yoldas, Applied Optics 19 (1980)1425.
w12xM. Born, E. Wolf, Principles of Optics, Pergamon Press,
Oxford, 1987.
w13xR.J. Swanepoel, J. Phys. E: Sci. Instrum. 16 (1983)1214.
w14xM. Boulouz, L. Martin, A. Boulouz, A. Boyer, Mater. Sci.
Eng. B 67 (1999)122.
w15xM. Guglielmi, S. Zenezini, J. Non-Cryst. Solids 121 (1990)
303.
w16xK. Tsukuma, Y. Kubota, T. Tsukidate, in: A.H. Heuer, L.W.
Hobbs (Eds.), Science and Technology of Zirconia, Advances
in Ceramics, 12, The American Ceramic Society Inc, Colum-
bus, OH, 1984, p. 382.
w17xM.J. Paterson, D.G. McCulloch, P.J.K. Paterson, B. Ben-
Nissan, Thin Solid Films 311 (1997)196.
w18xR. Caruso, A. Dıaz-Parralejo, P. Miranda, F. Guiberteau, J.
´
Mater. Res. 16 (2001)2391.
w19xK. Miyazawa, R. Maeda, K. Ito, Solid State Ionics 108 (1998)
85.
w20xM. Boulouz, A. Boulouz, A. Giani, A. Boyer, Thin Solid Films
323 (1998)85.
w21xA. Maia Seco, M. Clara Goncalves, R.M. Almeida, Mater. Sci.
¸
Eng. B 76 (2000)193.