Effects of heating rate on stress evolution in alkoxide-derived silica gel-coating films

Article abstract of DOI:10.1111/j.1551-2916.2006.01107.x

Silica gel films were deposited by spin coating on single-crystal Si wafers using an acid-catalyzed Si(OC₂H₅)₄ solution as a coating solution. The gel films were heated at various rates, where in situ stress measurement was conducted. In-plane tensile stress developed during the course of heating, and was found to be larger at lower heating rates at temperatures up to 350°C. The larger stress was thought to cause cracking at lower temperatures, which was previously observed at lower heating rates in in situ observation. The larger stress at lower heating rates was basically ascribed to the larger degrees of densification, which was revealed in the larger extent of reduction in thickness as well as in Si-OH/Si-O-Si and O-H/Si-O-Si infrared absorption band area ratios at lower heating rates. The difference in stress at different heating rates appeared to originate mainly in the difference observed at low temperatures below 130°C, suggesting that the heating rate particularly affects the densification that occurs via solvent evaporation. The increment in stress was reduced over 400°C when the heating rate was low, which was thought to result from the higher degree of densification already achieved below 400°C as well as the structural relaxation occurring at such high temperatures.

Full text of DOI:10.1111/j.1551-2916.2006.01107.x

J. Am. Ceram. Soc., 89 [8] 2453–2458 (2006)
DOI: 10.1111/j.1551-2916.2006.01107.x
r 2006 The American Ceramic Society
ournal
J
Effects of Heating Rate on Stress Evolution in Alkoxide-Derived Silica
Gel-Coating Films
Tadaomi Kurisu and Hiromitsu Kozukaw
Department of Materials Science and Engineering, Kansai University, Suita, Osaka 564-8680, Japan
Silica gel films were deposited by spin coating on single-crystal
Si wafers using an acid-catalyzed Si(OC2H5)4 solution as a
coating solution. The gel films were heated at various rates,
where in situ stress measurement was conducted. In-plane tensile
stress developed during the course of heating, and was found to
be larger at lower heating rates at temperatures up to 3501C.
The larger stress was thought to cause cracking at lower tem-
peratures, which was previously observed at lower heating rates
in in situ observation. The larger stress at lower heating rates
was basically ascribed to the larger degrees of densification,
which was revealed in the larger extent of reduction in thickness
as well as in Si–OH/Si–O–Si and O–H/Si–O–Si infrared ab-
sorption band area ratios at lower heating rates. The difference
in stress at different heating rates appeared to originate mainly
in the difference observed at low temperatures below 1301C,
suggesting that the heating rate particularly affects the densifi-
cation that occurs via solvent evaporation. The increment in
stress was reduced over 4001C when the heating rate was low,
which was thought to result from the higher degree of densifi-
cation already achieved below 4001C as well as the structural
relaxation occurring at such high temperatures.
present paper is macroscopic cracking occurring in gel film
densification in the heating-up stage, which cannot be avoided
even by matching the thermal expansion coefficient and is de-
tectable by the naked eye.
Processing parameters could affect the macroscopic cracking
behavior by affecting the stress generation in the heating-up
stage. Therefore, the effect of processing parameters on cracking
should be understood on the basis of in situ stress measurement
during heating. The residual stress measured after firing and
cooling is the sum of the stress generated in the heating-up stage
and of the thermal stress developing in the cooling-down stage.
Therefore, the analysis should be carried out based on in situ
stress measurement, not based on residual stress measurement,
for understanding the cracking behavior. A few papers have
been published on in situ stress measurement on gel-derived
coating films.8–10 However, the effects of processing parameters
on stress evolution have not been discussed so far.
As far as the heating rate is concerned, the authors previously
reported that higher heating rates resulted in higher cracking
onset temperatures, which qualitatively agrees with experiences
in laboratories that cracking is liable to occur when gel-coating
films are heated very slowly.3,4 This allows us to expect that a
smaller in-plane tensile stress may be generated when gel films
are heated at higher rates, and vice versa. In order to clarify how
and why the heating rate could affect the cracking behavior, the
relationship between stress and heating rate has to be investi-
gated, where stress should be measured in situ in the heating-up
stage, not at room temperature after cooling. In the present
study, silica gel films were deposited on single-crystal Si subst-
rates, and heated at various rates where in situ stress measure-
ment was conducted in order to clarify the effect of heating rate
on stress evolution.
I. Introduction
OL–GEL ceramic or glass-coating films are produced by firing
alkoxide-derived gel films. Under some conditions cracks are
S
observed in gel-derived fired films, which are detectable even by
the naked eye. For instance, thick gel films are liable to be
cracked, and high water to alkoxide ratios, high-humidity, and
low-heating rates often lead to cracking. Chelating agents1,2 and
polyvinylpyrrolidone,3,4 on the other hand, are effective in sup-
pressing crack formation as well as methyltriethoxysilane for
silica coating films.5
Gel films undergo volume shrinkage by several tens percent,
which is caused by the capillary pressure generated on solvent
vaporization and by the polycondensation reaction occurring in
films.4,6 Deposited films cannot shrink in the plane of the subst-
rate, and hence densification leads to evolution of in-plane ten-
sile stress in films. The authors recently have deposited silica and
titania gel films on single-crystal Si substrates and conducted in
situ observation during heating, finding that cracking occurs in
the heating-up stage.3,4 This clearly indicates that cracking is
truly caused by the tensile stress generated in the heating-up
stage. Cracks are also formed in fired films during cooling,
which are generated by the thermal stress, i.e., the stress due to
the difference in thermal expansion coefficient between the film
and substrate. However, such kinds of cracks are only detectable
in SEM scale in many cases, and can be avoided by matching the
thermal expansion coefficient.7 What the authors discuss in the
II. Experimental Procedure
(1) Preparation of the Gel Films
Tetraethylorthosilicate (TEOS), ethanol, and 1M nitric acid,
all purchased from Wako Pure Chemical Industries (Osaka,
Japan), and ion-exchanged water were used as the starting
materials. A starting solution of a mole ratio, TEOS:H2O:H-
NO3:C2H5OH5 1:8:0.01:4, was prepared by the following pro-
cedure. A solution of water, nitric acid, and half of the
prescribed amount of ethanol was added under magnetic stir-
ring to a solution consisting of TEOS and the other half of the
prescribed amount of ethanol. The solution thus obtained was
held at 301C for 23 h and then at 251C for 1 h in a sealed glass
container, and served as the coating solution. 0.5 mL coating
solution was dropped on a stationary single-crystal Si (100) wa-
fer 0.51–0.53 mm in thickness and 100 mm in diameter, and spin
coating was performed at a spinning rate of 5000 rpm where the
substrate was held rotated for 60 s.
M. Thouless—contributing editor
(2) In Situ Stress Measurement
Manuscript No. 21290. Received December 27, 2005; approved March 29, 2006.
This work was supported by Japan Society for the Promotion of Science (Grant-in-Aid
for Scientific Research (B)) and the High Technology Research Center of Kansai University.
wAuthor to whom correspondence should be addressed. e-mail: kozuka@ipcku.
kansai-u.ac.jp
(A) Principles of the Measurement: In situ stress meas-
urement was conducted using a thin-film stress-measurement
apparatus (FLX-2320, KLA-Tencor, San Jose, CA), which is
2453

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Journal of the American Ceramic Society—Kurisu and Kozuka
Vol. 89, No. 8
500
(c)
(b)
400
300
200
100
0
(a)
0
20
40
Time/min
60
80
100
Fig. 2. Temperature–time relationship obtained on the surface of the
substrate heated in the thin-film stress-measurement apparatus at pre-
scribed rates of (a) 51C/min, (b) 201C/min, and (c) 501C/min. The solid
lines represent the prescribed heating curves. Measurement was con-
ducted at the center of the substrate surface (J), and ca. 10 mm apart
from the edges (D and &).
Fig. 1. Deflection curves of the bare substrate measured at room tem-
perature (J) and of the coated substrate measured at 5001C (&), and
the difference in deflection (D).
equipped with a furnace and monitors the deflection of the
substrate during heating by scanning the surface with a laser
beam.
(C) Measurement of the Film Thickness: As can be seen
in Eq. (1), the film thickness tf should be obtained during the
course of heating in order to calculate the stress. Gel films were
deposited on the substrate in the way described in Section II(1).
Then, the coated substrate was divided into 10 pieces. Immedi-
ately, a part of the gel film was scrapped off with a surgical knife
in order to create a level difference for the thickness measure-
ment. The pieces of the coated substrates were kept standing
vertically and aligned parallel to each other at about 20 mm in-
tervals on an alumina boat with slits. Then, they were heated up
to 5001C at prescribed rates in an electric furnace. In the case of
the prescribed rate of 501C/min, the heating rate was controlled
so that the actual heating rate was the same as that measured in
the stress-measurement apparatus. The temperature was moni-
tored during heating with thermocouples located near each
substrate. When the temperature reached each value, the coat-
ed substrate was taken out of the furnace. The level difference
created by the surgical knife was measured using a contact probe
surface profilometer (SE-3400, Kosaka Laboratory, Tokyo, Ja-
pan) at three different points for two samples. The measured and
interpolated thickness values were used for calculating the stress.
The deflection of the bare substrate was measured at room
temperature beforehand. Immediately after deposition, the gel
films were heated in the stress measurement apparatus up to
5001C at prescribed rates of 0.51, 51, 201, and 501C/min where
the deflection was measured in situ at intervals of 251C. Figure 1
shows an example of the deflection curves of the bare substrate
measured at room temperature and of the coated substrate
measured during heating. The difference in these deflections
gives the deflection caused by the in-plane stress in the film. In-
plane stress s in films was calculated by Stoney’s equation11;
Est2s
s ¼
(1)
6ð1 ꢀ nsÞDRtf
where Es/(1ꢀns) is the biaxial elastic modulus of the substrate
(1.805ꢁ 1011 Pa),12 ts is the thickness of the substrate, tf is the
thickness of the film, and DR is defined by the following equa-
tion:
RsRf
DR ¼
(2)
Rs ꢀ Rf
(3) Other Measurements
Infrared absorption spectra and refractive index were measured
on the films heated up to various temperatures at various rates
in the same way as described in Section II(2)(C). Infrared ab-
sorption spectra were measured using a Fourier transform in-
frared (FT-IR) spectrophotometer (FT/IR-410, Jasco, Tokyo,
Japan), where a bare Si substrate was used as the reference. Re-
fractive indices nf of the films were measured using an elipso-
meter (ESM-1T, ULVAC, Chigasaki, Japan) with a He–Ne
laser at an incident angle of 701. The measurement was con-
ducted on 10 different points on the film samples. Porosity p of
the film was calculated from the refractive index nf by the fol-
lowing equation13:
where Rs and Rf are the radius of curvature of the bare and
coated substrates, respectively. The film thickness tf was meas-
ured by the procedure described in Section II(2)(C). In situ
stress measurement was conducted for three samples at each
heating rate.
(B) Measurement of the Temperature at the Surface of the
Substrate: In order to examine the actual heating rate in the
stress-measurement apparatus, the temperature–time relation-
ship was studied by the following procedure. Using an inorganic
adhesive (Aron Ceramic E, Toagosei, Tokyo, Japan), three
chromel–alumel thermocouples (0.19 mm in cross-section
diameter were attached on the bare substrate surface: one at
the center and the others at ca. 10 mm apart from the edges.
The temperature at the substrate surface was monitored in situ
during heating up to 5001C at prescribed rates of 51, 201, and
501C/min.
ðn2f ꢀ 1Þðn2c þ 2Þ
1 ꢀ p ¼
(3)
ðn2f þ 2Þðn2c ꢀ 1Þ
Figure 2 shows the relationship between temperature and time
monitored during heating. In the case of the prescribed rates of
51 and 201C/min, the actual heating rates were 4.81 and 181C/
min, respectively, both of which are close to the prescribed heat-
ing rates. However, when the prescribed rate was 501C/min, the
actual rate was 501C/min close to room temperature, decreasing
down to 201C/min at 5001C because of the limited heating ability
of the apparatus. In Section III, ‘‘Results,’’ the prescribed heat-
ing rates are used in description although the differences are
found between the prescribed and actual heating rates.
where nc is the refractive index of the fully dense material and is
assumed to be 1.46, the refractive index of silica glass.
III. Results
(1) Stress Evolution in Films
Figure 3(a) shows the variation in thickness observed on films
heated at various rates. The error bars denote the standard de-
viation. The initial thickness of the gel films was about 0.3 mm,

August 2006
Effects of the Heating Rate on Stress Evolution in Silica Gel-Coating Films
2455
0.35
14
12
−1
50°C min
10
8
0.30
0.25
−1
20°C min
6
−1
0.5°C min
4
−1
5°C min
2
−1
−1
5°C min
20°C min
50°C min
−1
0
0.5°C min
−1
0.20
0
−2
100
200
300
400
500
0
100
200
300
400
500
Temperature/°C
Temperature/°C
(a)
Fig. 4. Variation in D bow of the coated substrates measured during the
course of heating at various rates.
5
0
shows the evolution of the in-plane stress during the course of
heating. The error bars denote the maximum and minimum
values calculated, respectively, i.e., the stress calculated from the
maximum deflection and minimum thickness, and that from the
minimum deflection and maximum thickness, respectively. In-
plane tensile stress was generated, and increased with tempera-
ture, reaching about 500 MPa at 5001C. It should be noted that
lower stress was observed at higher heating rates; the difference
in stress was ca. 150 MPa at 2501C. Namely, the evolution of
stress tended to be restrained at higher heating rates.
In Fig. 6 a significant difference was observed between dif-
ferent heating rates in the slope at low temperatures up to
1301C; the slope was larger at lower heating rates. On the oth-
er hand, the slope was nearly the same at 1301–3501C between
different heating rates. However, the slope became smaller at
lower heating rates at temperatures over 4001C, leading to a
decrease in the difference in stress between different heating
rates.
−1
50°C min
−1
−5
20°C min
−10
−15
−20
−25
−1
5°C min
−1
0.5°C min
−30
0
100
200
300
400
500
Temperature/°C
(b)
−1
14
12
10
8
0.5°C min
Fig. 3. Variation in film thickness during the course of heating at var-
ious rates. (a) Thickness values and (b) thickness change in percent.
−1
5°C min
−1
−1
20°C min
and the films decreased in thickness to 0.22–0.25 mm, by 17%–
27%, when heated up to 5001C. It should be noted that lower
heating rates resulted in a larger extent of reduction in thickness,
which can be seen more clearly in Fig. 3(b), where the change in
thickness is described in percent.
50°C min
The maximum difference in deflection between the bare and
coated substrates is called D bow (Fig. 1). Figure 4 shows the
variation in D bow measured during the course of heating. The
error bars denote the maximum and minimum values obtained
on three samples. As can be seen in the figure, the D bow of the
substrate increased with increasing temperature, i.e., the subst-
rate was warped due to the in-plane stress in the film. In order to
confirm that the deflection of the substrate observed (Fig. 4) is
truly due to the stress generated in films, the deflection of bare
substrates was also measured at various heating rates. The var-
iation of D bow measured on bare substrates is shown in Fig. 5.
Negligible deflection was observed irrespective of the heating
rate.
6
4
2
0
−2
0
100
200
300
400
500
Temperature/°C
The stress in films was calculated from the film thickness
(Fig. 3(a)) and the deflection of the substrates (Fig. 4). Figure 6
Fig. 5. Variation in D bow of the bare substrates measured during the
course of heating at various rates.

2456
Journal of the American Ceramic Society—Kurisu and Kozuka
Vol. 89, No. 8
0.25
600
500
400
300
200
100
0
0.20
0.15
0.10
−1
20°C min
−1
0.5°C min
−1
5°C min
−1
5°C min
0.05
−1
20°C min
−1
0.5°C min
−1
50°C min
0
−100
0
100
200
300
400
500
0
100
200
300
400
500
Temperature/°C
Temperature/°C
(a)
Fig. 6. Variation in stress in films during the course of heating at var-
ious rates.
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
(2) Thermal Decomposition Behavior
Figure 7 shows the infrared absorption spectra of the films heat-
ed up to 5001C at various rates. The films had absorption bands
assigned to Si–OH (950 cmꢀ1) and O–H (3400 cmꢀ1) vibrations,
which were smaller at lower heating rates. The ratios of the ab-
sorption peak area, Si–OH (950 cmꢀ1)/Si–O–Si (1100 cmꢀ1) and
O–H (3400 cmꢀ1)/Si–O–Si (1100 cmꢀ1), are plotted against tem-
perature in Fig. 8. The Si–OH/Si–O–Si and O–H/Si–O–Si ratios
decreased with increasing temperature, and were smaller at low-
er heating rates. Lower heating rates led to a more significant
reduction in the peak area ratio at 251–1001C.
−1
20°C min
−1
5°C min
(3) Refractive Index and Porosity
−1
0.5°C min
Figures 9(a) and (b) show the dependence of refractive index and
porosity, respectively, on the heating rate for the films heated up
to 4001 and 5001C. The films heated up to 5001C exhibited no
0
100
200
300
400
500
Temperature/°C
(b)
Fig. 8. Variation in absorption band area ratio during the course of
heating at various rates. (a) Si–OH/Si–O–Si and (b) O–H/Si–O–Si.
−1
100°C min
apparent difference in refractive index and porosity between
different heating rates, while those heated up to 4001C tended to
have lower refractive indices and higher porosities at higher
heating rates.
−1
50°C min
−1
20°C min
IV. Discussion
As is experienced in laboratories, gel coatings are liable to crack
or delaminate when heated up slowly. Cracking is avoidable
rather by rapid heating, for instance, by inserting gel films di-
rectly into a furnace of a prescribed firing temperature. The au-
thors previously conducted in situ observation of cracking
during the course of heating on silica and titania gel films de-
posited on single-crystal Si substrates. Cracking was found to
occur in the heating-up stage, and lower heating rates resulted in
cracking at lower temperatures.3,4 The present study demon-
strated that the in-plane tensile stress generated in the heating-
up stage is larger at lower heating rates (Fig. 6). It can now be
concluded that lower heating rates induce larger in-plane tensile
stress, which causes cracking at lower temperatures.
−1
5°C min
−1
0.5°C min
4000 3500 3000
2500 2000 1500 1000
500
−1
Wavenumber/cm
Fig. 7. Infrared absorption spectra of the films heated up to 5001C at
various rates.

August 2006
Effects of the Heating Rate on Stress Evolution in Silica Gel-Coating Films
2457
they decreased more significantly at lower heating rates at tem-
peratures below 1301C while at temperatures over 1301C the
slopes were similar. These observations suggest that densificat-
ion is promoted to a larger extent at lower heating rates, espe-
cially at temperatures below 1301C, which leads to larger slopes
in stress–temperature curves. The solvent evaporates from the
gel films at these temperatures (o1301C), accompanied by ev-
olution of capillary pressure. Capillary pressure itself contrib-
utes to in-plane tensile stress and also promotes pore shrinkage,
which leads to promotion of condensation reaction and densifi-
cation. Solvent evaporation, pore shrinkage, or condensation
reaction is a kinetic process and hence needs time for progress.
Lower heating rates provide enough time for these processes to
proceed, leading to a more significant densification particularly
at these low temperatures.
On the other hand, the difference in stress over 4001C is also
interesting. The increment in stress is reduced at such high tem-
peratures when the gel films are heated at lower rates (Fig. 6);
the stress even appears to cease increasing over 4001C at a heat-
ing rate of 0.51C/min. One of the reasons for the decreased slope
is the larger extent of densification achieved at temperatures
around 4001C at lower heating rates; smaller porosities have al-
ready been achieved at 4001C at lower heating rates as revealed
in Fig. 9(b). Another cause of the decreased slope in stress–tem-
perature curves is structural relaxation occurring under large
stress at such high temperatures. Structural relaxation is also a
kinetic process, requiring time for its progress. Lower heating
rates provide enough time for structural relaxation, giving rise to
decreased slopes in stress–temperature curves.
1.5
500°C
1.4
1.3
1.2
1.1
400°C
1.0
0
20
40
60
80
100
−1
Heating rate/°C min
(a)
100
80
60
40
20
As discussed above, lower heating rates give rise to larger in-
plane tensile stress in the heating-up stage, leading to cracking at
lower temperatures. It is the temperature range where solvent
evaporates that significantly affects the degree of the increment
in stress; lower heating rates promote condensation and dens-
ification, especially at such low temperatures, as revealed in Figs.
3 and 8. At high temperatures close to 5001C, on the other hand,
the stress is not necessarily larger at lower heating rates, because
of the high degrees of densification already achieved at lower
temperatures and the structural relaxation occurring at such
high temperatures.
400°C
500°C
V. Conclusions
Silica gel films were deposited on single-crystal Si wafers using
an acid-catalyzed TEOS solution as the coating solution. The gel
films were heated at various rates, where in situ stress measure-
ment was conducted.
0
0
20
40
60
80
100
(1) In-plane tensile stress was larger at lower heating rates at
temperatures up to 3501C. The larger stress was thought to
cause cracking at lower temperatures observed previously at
lower heating rates. The larger stress at lower heating rates was
basically ascribed to larger degrees of densification, which was
revealed in the larger extent of reduction in thickness as well as
in Si–OH/Si–O–Si and O–H/Si–O–Si absorption band area ra-
tios.
(2) The difference in stress at different heating rates ap-
peared to originate mainly in the difference occurring at low
temperatures below 1301C, where solvent evaporates. At these
low temperatures, larger degrees of densification were also ob-
served at lower heating rates.
−1
Heating rate/°C min
(b)
Fig. 9. Dependence of (a) refractive index and (b) porosity on heating
rate for the films heated up to 4001 and 5001C.
The evolution of in-plane tensile stress originates in the dens-
ification of films constrained on the substrate during heating as
well as the capillary pressure generated on solvent evaporation.
Lower heating rates resulted in a larger reduction in thickness
(Fig. 3(b)) as well as in Si–OH/Si–O–Si and O–H/Si–O–Si band
area ratios (Fig. 8) during the course of heating. These suggest
that lower heating rates promote densification via condensation
reaction in films. This is also revealed in the porosity data
(Fig. 9(b)), where the films heated up to 4001C tended to have
smaller porosities when heated at lower rates.
(3) The increment in stress was reduced over 4001C when the
heating rates were low. This was thought to result from the higher
degree of densification already achieved below 4001C as well as
the structural relaxation occurring at such high temperatures.
More detailed observation of Fig. 6, however, allows us to
notice that lower heating rates provide larger slopes in stress–
temperature curves at temperatures below 1301C while at 1301–
3501C the slopes are similar between different heating rates. The
difference in stress at higher temperatures seems to originate in
these different slopes observed at temperatures below 1301C.
The film thickness (Fig. 3(b)) and the Si–OH/Si–O–Si and O–H/
Si–O–Si band area ratios (Fig. 8) exhibited a similar tendency;
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