The Effect of Annealing Temperature on Statistical Properties of WO3 Surface
G. R. Jafari a,b, A. A. Saberi c, R. Azimirad c, A. Z. Moshfegh c, and S. Rouhani c
Department of Physics, Shahid Beheshti University, Evin, Tehran 19839, Iran
Department of Nano-Science, IPM, P. O. Box 19395-5531, Tehran, Iran
Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran
We have studied the effect of annealing temperature on the statistical properties of WO3 surface
using atomic force microscopy techniques (AFM). We have applied both level crossing and structure
function methods. Level crossing analysis indicates an optimum annealing temperature of around
400oC at which the effective area of the WO3 thin film is maximum, whereas composition of the
surface remains stoichiometric. The complexity of the height fluctuation of surfaces was charac-
terized by roughness, roughness exponent and lateral size of surface features. We have found that
there is a phase transition at around 400oC from one set to two sets of roughness parameters. This
happens due to microstructural changes from amorphous to crystalline structure in the samples that
has been already found experimentally.
I. INTRODUCTION
Transition metal oxides represent a large family of
materials possessing various interesting properties, such
as superconductivity, colossal magneto-resistance and
piezoelectricity. Among them, tungsten oxide is of in-
tense interest and has been investigated extensively for its
distinctive properties. With outstanding electrochromic
[1, 2, 3, 4, 5, 6], photochromic [7], gaschromic [8], gas
sensor [9, 10, 11], photo-catalyst [12], and photolumines-
cence properties [13], tungsten oxide has been used to
construct ”smart-window”, anti-glare rear view mirrors
of automobile, non-emissive displays, optical recording
devices, solid-state gas sensors, humidity and tempera-
ture sensors, biosensors, photonic crystals, and so forth.
WO3 thin films can be prepared by various deposition
techniques such as thermal evaporation [3, 8], spray py-
rolysis [14], sputtering [6], pulsed laser ablation [10, 11],
sol-gel coating [2, 5, 15], and chemical vapor deposition
[16].
The gas sensitivity of WO3 heavily depends upon film
parameters such as composition, morphology (e.g. grain
size), nanostructure and microstructure (e.g. porosity,
surface-to-volume ratio). Film parameters are related to
the deposition technique used, the deposition conditions
and the subsequent annealing process. Annealing,
which is an essential process to obtain stable films with
well-defined microstructure, causes stoichiometry and
microstructural changes that have a high influence on the
sensing characteristics of the films [17]. Moreover, the
surface structure and surface morphology of the metal
oxides are also important for different applications. In
fact, the electrochromic devices are made of amorphous
oxides [1], while crystalline phase plays a major role in
catalysts and sensors [17]. This is because, the minor
change in their chemical composition and crystalline
structure could modify different properties of the metal
oxides.
In practice, one of the effective ways to modify the
surface morphology is annealing process at various
temperatures. So far, most of morphological analysis
related to the WO3 surface were accessible through
the experimental methods. Usually these analysis
are rigorous and time consuming. Moreover, lack of
the suitable analysis for AFM data to find the nano
and microstructural properties of surfaces was feeling
perfectly.
In this article, we introduce the methods: roughness
analysis and level crossing as suitable candidates and
show that we can get easily the structure and morpho-
logical properties of a surface in a fast manner, only
using the AFM observation as an initial data.
The roughness of a surface has been studied as a
simple growth model using analytical and numerical
methods [18, 19, 20, 21, 22, 23, 24, 25, 26]. These
studies quite generally proposed that the height fluc-
tuations have a self-similar character and their average
correlations exhibit a dynamic scaling form. Also some
authors recently use the average frequency of positive
slope level crossing to provide further complete analysis
on roughness of a surface [27]. This stochastic approach
has turned out to be a promising tool also for other
systems with scale dependent complexity, such as in
surface growth where one would like to measure the
roughness [28]. Some authors have applied this method
to study the fluctuations of velocity fields in Burgers
turbulence [29] and the Kardar-Parisi-Zhang equation in
(d+1)-dimensions [30] and analyzing the stock market
[31].
In this work, we have used the scaling analysis to
determine the roughness, roughness exponent and the
lateral size of surface features. Moreover, level crossing
analysis has been utilized to estimate the effective area
of a surface.
This paper is organized as follows: In section II, we
have discussed about the film preparation and experi-
http://arxiv.org/abs/0704.1023v1
mental results obtained from AFM, XPS and UV-visible
spectrophotometer for the annealed samples at the vari-
ous temperatures. In section III, we have introduced the
analytical methods briefly. Data description and data
analysis based on the statistical parameters of WO3 sur-
face as a function of annealing temperatures are given in
section IV.Finally, section V concludes presented results.
II. EXPERIMENTALS
Thin films of WO3 were deposited on microscope slide
glass using thermal evaporation method. The deposition
system was evacuated to a base pressure of ∼ 4×10−3Pa.
Thickness of the deposited films was considered about
200 nm measured by the stylus and optical techniques.
More details about the other deposition parameters of
the films are recently reported elsewhere [32].
To study the effect of annealing temperature on sur-
face structure and optical properties of the samples, they
were annealed at 200, 300, 350, 400, 450, and 500oC in
air for a period of 60 min. Optical transmission and
reflection measurements of the deposited films were per-
formed in a range of 300-1100 nm wavelength using a
Jascow V530 ultraviolet (UV)-visible spectrophotometer
with resolution of 1 nm.
X-ray photoelectron spectroscopy (XPS) using a Specs
EA 10 Plus concentric hemispherical analyzer (CHA)
with Al Kα anode at energy of 1486.6 eV was employed
to study the atomic composition and chemical state of
the tungsten oxide thin films. The pressure in the ultra
high vacuum surface analysis chamber was less than
1.0×10−7Pa. All binding energy values were determined
by calibration and fixing the C(1s) line to 285.0 eV . The
XPS data analysis and deconvolution were performed
by SDP (version 4.0) software. The nanoscale Surface
topography of the deposited films was investigated by
Thermo Microscope Autoprobe CP-Research atomic
force microscopy (AFM) in air with a silicon tip of 10
nm radius in contact method. The AFM images were
recorded with resolution of about 20 nm in a scale of
5× 5 µm.
A. XPS Characterization
The elemental and chemical characterizations of the
films were performed by XPS. Figure 1a shows theW (4f)
core level spectra recorded on the ”as deposited” WO3
sample, and the results of its fitting analysis. To repro-
duce the experimental data, one doublet function was
used for the W (4f) component. This contains W (4f7/2)
at 35.6 eV and W (4f5/2) at 37.8 eV with a full-width
at half-maximum (FWHM) of 1.75± 0.04 eV . The area
ratio of these two peaks is 0.75 which is supported by
the spin-orbit splitting theory of 4f levels. Moreover,
the structure was shifted by 5 eV toward higher energy
FIG. 1: W (4f) core level spectra of WO3 thin films: a) ”as
deposited” and b) annealed at 500oC.
relative to the metal state.
It is thus clear that the main peaks in our XPS spectrum
attributed to the W 6+ state on the surface [1, 2, 33]. In
stoichiometricWO3, the six valence electrons of the tung-
sten atom are transferred into the oxygen p-like bands,
which are thus completely filled. In this case, the tung-
sten 5d valence electrons have no part of their wave func-
tion near the tungsten atom and the remaining electrons
in the tungsten atom experience a stronger Coulomb in-
teraction with the nucleus than in the case of tungsten
atom in a metal, in which the screening of the nucleus
has a component due to the 5d valence electrons. There-
fore, the binding energy of the W (4f) level is larger in
WO3 than in metallic tungsten. If an oxygen vacancy
exists, the electronic density near its adjacent W atom
increases, the screening of its nucleus is higher and, thus,
the 4f level energy is expected to be at lower binding
energy [1].
By increasing the annealing temperature it was ob-
served that the position of W (4f) peak did not obviously
change. But for WO3 thin film annealed at 500
oC (Fig.
1b), the W (4f) peak moved to a lower binding energy so
that W (4f7/2) position was observed at 35.0 eV . This
can be related to oxygen vacancy at this high annealing
temperature and formation of W 5+.
B. Optical Characterization
The transmittance and reflectance spectra in the
visible and infrared range recorded for the WO3 thin
films before and after annealing at different temperatures
(Fig. 2a). It is seen that, the transmittance of the ”as
deposited” films in the visible range varies from about
80 up to nearly 100% (without considering the substrate
contribution). Correspondingly, maximum value of the
reflectance for both the film and the substrate is about
20% (the reflectance from the bare glass substrate was
measured about 10%). The sharp reduction in the
transmittance spectrum at the wavelength of ∼ 350nm
is due to the fundamental absorption edge that was also
reported previously [1, 2, 3].
The oscillations in the transmission and reflection
spectra are caused by optical interference. The optical
transmittance of WO3 films strongly depends on the
oxygen content of the films. In fact, non-stoichiometric
films with composition of WO3−x show a blue tinge for
x > 0.03 [34].
The ”as deposited” pure tungsten oxide films were
highly transparent with no observable blue coloration,
under our experimental conditions. As can be seen
from Fig. 2a after annealing process at 200 to 400oC,
the transmittance and reflectance of the WO3 films
have not changed significantly. Only, the position of
the oscillations altered due to thickness reduction and
film condensation after the heat-treatment process
[1]. At 500oC transmittance and reflectance of the
annealed WO3 film is reduced about 10%, therefore at
this temperature, the film turn into non-stoichiometric
composition, so that it could be seen from changing
color of the film.
The optical gap (Eg) was evaluated from the ab-
sorption coefficient (α) using the standard relation:
(αhν)1/η = A(hν − Eg), in which η depends on the
kind of optical transition in semiconductors, and α was
determined near the absorption edge using the simple
relation: α = ln[(1 − R)2/T ]/d ,where d is thickness
of the film. More useful explanation about the optical
band gap calculation reported in [32]. The relationship
between the optical band gap energy and annealing
temperature for WO3 thin films has been shown in Fig.
2b. As can be seen from it, the optical band gap for
the ”as deposited” WO3 evaluated 3.4 eV . Amorphous
structure of the ”as deposited” WO3 causes to Eg is
bigger than 2.7 eV . After annealing samples at 200 and
300oC, the optical band gap decreased slightly about 0.1
eV which can be related to condensation of the films.
But the optical band gap of the WO3 annealed at 400
reduced to 3.1 eV due to crystallization of the film. This
reduction continues to 2.5 eV for the sample annealed
at 500oC. Reason of the Eg becomes smaller than 2.7
eV is oxygen vacancy at this temperature as was seen in
Fig 1b. It is to note that for evaporated WO3 films one
has found 2.7 < Eg < 3.5 eV [1].
λ ( )
400 600 800 1000
27 oC
200 oC
300 oC
400 oC
500 oC
100 200 300 400 500
FIG. 2: a) Optical transmittance (T) and reflectance (R) and
b) Optical band gap energy of the WO3 thin films annealed
at different temperatures.
C. AFM Analysis
To study the effect of the annealing process on the sur-
face morphology of the films, we have shown AFM images
of the WO3 surfaces annealed at the different tempera-
tures : 200, 300, 350, 400, 450, 500oC in Figure 1. As
can be seen from Fig. 1, for the annealed film at 200oC,
it seems that the surface morphology of the film is rela-
tively the same with a smooth surface, amorphous struc-
ture and nanometric grain size, as also reported by other
investigators for WO3 films [35, 36]. We have also ob-
served similar image for the ”as deposited” WO3 which
is not shown here. For WO3 thin films, increasing an-
nealing temperature to 350oC did not significantly ef-
fect on surface parameters because it is low temperature
for crystallization of WO3 [1]. But at higher annealing
temperatures 400, 450 and 500oC, surface grain size and
FIG. 3: AFM images of WO3 thin films annealed at various
temperatures a) 200, b) 300, c) 350, d) 400, e) 450 and f)
500oC, respectively.
roughness begin to increase. The more precise analysis
of these surfaces are given in the next section.
III. STATISTICAL QUANTITIES
A. Roughness Analysis
It is also known that to derive the quantitative infor-
mation of the surface morphology one may consider a
sample of size L and define the mean height of growing
film h and its roughness σ by:
σ(L, t) = (〈(h − h)2〉)1/2 (1)
where t is growing time and 〈· · ·〉 denotes an averaging
over different samples, respectively. Moreover, growing
time is a factor which can be applied to control the sur-
face roughness of thin films.
Let us now calculate the roughness exponent of the
growing surface. Starting from a flat interface (one of
the possible initial conditions), it is conjectured that a
scaling of lenght by factor b and of time by factor bz (z is
the dynamical scaling exponent), rescales the roughness
σ by factor bχ as follows [18]:
σ(bL, bzt) = bασ(L, t) (2)
which implies that
σ(L, t) = Lαf(t/Lz). (3)
For large t and fixed L (i.e.x = t/Lz → ∞) σ saturate.
However, for fixed and large L and t ≪ Lz, one expects
that correlations of the height fluctuations are set up only
within a distance t1/z and thus must be independent of
L. This implies that for x ≪ 1, f(x) ∼ xβg′(λ) with
β = α/z. Thus, dynamic scaling postulates that
σ(L, t) =
tβ, t≪ Lz;
Lα, t≫ Lz.
The roughness exponent α and the dynamic exponent β
characterize the self-affine geometry of the surface and its
dynamics, respectively. In the present work, we see the
surfaces at the limit t → ∞ and so we will only obtain
the α exponent.
The common procedure to measure the roughness ex-
ponent of a rough surface is use of the surface structure
function depending on the length scale l which is defined
S2(l) = 〈|h(x+ l)− h(x)|2〉. (5)
It is equivalent to the statistics of height-height corre-
lation function C(l) for stationary surfaces, i.e. S2(l) =
2σ2(1−C(l)). The second order structure function S2(l),
scales with l as l2α.
B. Level Crossing Analysis
Let ν+α denotes the number of positive slope crossing
of h(x) − h̄ = α for interval L.
Since the process is homogeneous, if we take a second
time interval of L immediately following the first we shall
obtain the same result, and for two intervals together we
shall therefore obtain [28]:
N+α (2L) = 2N
α (L), (6)
from which it follows that, for a homogeneous process,
the average number of crossing is proportional to the in-
terval L. Hence
N+α (L) ∝ L, (7)
N+α (L) = ν
αL, (8)
where ν+α is the average frequency of positive slope cross-
ing of the level h(x) − h̄ = α. We now consider how the
frequency parameter ν+α can be deduced from the under-
lying probability distributions for h(x)− h̄.
Consider a small length scale δx of a typical sample func-
tion. Since we are assuming that the process h(x)− h̄ is a
smooth function of x, with no sudden ups and downs, if
δx is small enough, the sample can only cross h(x)−h̄ = α
with positive slope if h(x) − h̄ < α at the beginning of
the interval L. Furthermore, there is a minimum slope
at x if the level h(x) − h̄ = α is to be crossed in interval
∆x depending on the value of h(x)− h̄ at position x. So
there will be a positive crossing of h(x) − h̄ = α in the
next interval ∆x if, at x,
h(x)− h̄ < α and
h(x) − h̄
h(x) − h̄
As shown in [28], the frequency ν+α can be written in
terms of joint PDF (probability distribution function ) of
p(α, y′) as follows:
ν+α =
p(α, y′)y′dy′. (10)
and then the quantity N+tot which is defined as:
N+tot =
ν+α |α− ᾱ|dα. (11)
will measure the total number of crossing the surface with
positive slope. So, the N+tot and square area of growing
surface are in the same order. Concerning this, it can be
utilized as another quantity to study further the rough-
ness of a surface [27].
l ( m)
0.5 1 1.5 2
FIG. 4: Log-Log plot of the selection structure function of
various annealed temperature: a) 27, b) 200, c) 300, d) 350,
e) 400, f) 450, g) 500oC.
IV. RESULTS AND DISCUSSION
Thin films of WO3 were deposited by using thermal
evaporation method and then surface micrographs of
WO3 samples were obtained by AFM technique after
annealed at different temperatures (Fig.3).
These micrographs were then analyzed using methods
from stochastic data analysis have introduced in the
last section. Figure 3 shows AFM images of WO3 thin
films annealed at 200 ,300 ,350 ,400 ,450, and 500oC.
The ”as deposited” and annealed sample at 200oC
(Fig. 3a) have columnar structure, indicating that up
to 200oC no significant changes in the microstructure
occurs. However, at higher temperatures (figs. 3b-3f) we
have observed increased grain size and rougher surface.
Specifically at 500oC (Fig. 3f) we observe stark changes
in the micrograph which is accompanied by composition
changes in the surface. This can be related to the phase
transition to Magneli phase e.g. WO3−x in the annealing
process [36]. This is also confirmed by our XPS and
UV-visible spectrophotometry analysis (Sec. II). These
are shown the significant formation of W 5+ state in the
surface at 500oC.
Also our analysis shows that below 400oC the surfaces
are in amorphous phase with the same behavior for all
scales, but as soon as the crystalline phase appears the
system behaves differently which diagnostics at small and
large scale for temperatures above 400oC. By using pa-
rameters of the analytical method given here, these tran-
sitions can be quantified.
h ( m)
-0.02 -0.01 0 0.01 0.02
10000
200 oC
300 oC
400 oC
500 oC
FIG. 5: The average frequency ν+α as a function of height h
Now, we will use the statistical parameters introduced
in the last section and will obtain some quantitative
information about the effect of annealing temperature
on the surface topography of the WO3 samples.
The structure function S2(l) as defined in Eq.(5) can
be used to quantify the topology of a rough surface. The
structure function S2(l) is plotted against the length
scale of the sample in Fig.4 . The saturated S2(l) is an
indication of the surface roughness, as 2σ2. The most
obvious observation indicates that roughness is raised
with increasing annealing temperature. Roughness has
a minimum of 0.91nm at 27 and 200oC and a maximum
of 48nm at 500oC. This is because higher temperatures
create higher peaks (i.e. peaks with more deviations
from the average) . All exponents which is derivable
from S2(l) have been summarized and given in Table I.
As depicted in Fig.4 , the structure function S2(l),
has a different behavior in the various temperatures. So
that, in the annealing temperature range 27-350oC it
has a typical behavior in all scales, but in the higher
temperature range 400-500oC its behavior is different
in the small and large scales. In the other words, the
phase transition is occurred at 400oC, because for higher
temperatures, there are two sets of roughness parameters
needed to simulate the surface morphology. It can be
related to the phase transition in the structure of the
surface from amorphous to crystalline phase has been
yielded from the band gap energy (see the section II.B).
The slope of each S2(l) curves at the small and
large scales yields the roughness exponents α and α′ of
100 200 300 400 500
FIG. 6: The normalized N+
behavior as a function of an-
nealing temperature. The solid line is plotted according to
Eq.(12) around 400oC .
the corresponding surface. Hence, it is seen that the
mono roughness exponent increases with the addition of
annealing temperature up to 400oC. In the higher tem-
peratures, we have obtained two roughness exponents(
α-α′) equal to the 0.40-0.14, 0.71-0.20, and 0.69-0.24
for temperatures 400, 450 and 500oC, respectively.
Difference in the α values, in these temperatures, are in
agreement with changes of correlation length. Where the
correlation length, is the distance at which the structure
function behaves differently.
The range of the scaling upon correlation length listed
in the forth column in table I. The value of C∗s denotes
the correlation length at small scales and C∗l for large
scales. The higher C∗ value represents a smoother
surface (as we expected from Fig.3). The correlation
length obtained from the structure function is also a
measure of minimum lateral size of surface features at
each annealing temperature.
The another important WO3 film parameter is the ef-
fective area of the sample which has an important role
in the gas sensitivity of WO3 surfaces. To obtain a mea-
sure for this, we utilize the level crossing analysis. As
shown in Fig.5, the average frequency ν+α as a function
of height h, is plotted for the various annealing tempera-
tures. The broad curves indicate the higher magnitude of
height fluctuations around the average, and sharp curves
show that the most of fluctuations are around the height
average. This conclusion is in the correspondence with
the results obtained from Fig.3.
According to the Eq.(11) N+α i.e. The total number of
the crossing surface with positive slope is proportional to
the square of area of the growing surface. To obtain the
optimum value of the effective area, we have calculated
the ratio of effective areas with respect to the area of
the ”as deposited” surface (27oC). The values are given
TABLE I: The Roughness exponent, roughness, correlation
length and effective area relative to the ”as deposited” sample
area (27oC).
T [oC] α− α′ σ[nm] C∗s -C
[nm] N+/N+(27oC)
27 0.15− none 0.91 60− none 1.00
200 0.15− none 0.98 60− none 1.08± 0.02
300 0.61− none 2.20 100− none 1.17± 0.02
350 0.62− none 11.50 100− none 1.67± 0.02
400 0.40 − 0.15 17.00 100 − 300 2.00± 0.02
450 0.71 − 0.20 30.00 400− 1000 1.72± 0.02
500 0.69 − 0.24 48.00 200− 1400 1.41± 0.02
in the last column in Table I. It means, although the
roughness increases by the annealing temperature but
the effective square area of the rough surface has a
maximum value of N+tot [27].
For more clarity, we have calculated the temperature
dependence of normalized N+α numerically (Fig.6)
around 400oC, and we have obtained the three following
functions for this quantity :
N+tot(T ) = (5.0718− 0.0223× T + 2.72× 10
−5 × T 2)−1(12)
ln(N+tot(T )) = −6.3632+ 0.0344× T − 4.20× 10
−5 × T 2(13)
N+tot(T ) = −8.7057+ 0.0520× T − 6.37× 10
−5 × T 2(14)
According to this figure, the maximum value of the
effective area is at 400oC (with respect to its value
at 27oC) with the relative value equal to 2.00. Thus,
applying this analysis easily shows that if one follows
the condition which the effective area as an important
parameter in the gas sensitivity of WO3 surfaces is
optimum and furthermore, the film composition has not
been changed (e.g. The Magneli phase transition has
not been occurred), should choose the annealed surface
at 400oC for better performance.
V. CONCLUSIONS
We have investigated the role of annealing tempera-
ture, as an external parameter, to control the statisti-
cal properties of a rough WO3 surface. The AFM mi-
crostructure of the surfaces is just needed to apply in our
analysis. We have computed the statistical quantities
such as roughness exponent, roughness and lateral size
of surface features of the ”as deposited” and annealed
surfaces at 200, 300, 350, 400, 450, and 500oC, using the
structure function. We have seen a phase transition at
400oC, because for higher temperatures there are two sets
of roughness parameters, due to structural changes from
amorphous to the crystalline phase. Moreover, using the
level crossing analysis we have obtained an optimum an-
nealing temperature, 400oC in which the surface of the
WO3 has maximum value about twice relative to the ”as
deposited” film without any changes in the film composi-
tion that may increase surface reaction of the WO3 film
as the gas sensor or photo-catalyst.
VI. ACKNOWLEDGMENT
GRJ and AAS would like to thank S.M.Fazeli for his
useful comments and especially M.R.Rahimitabar for his
useful lectures on ”stochastic data analysis”. AZM would
like to acknowledge research council of Sharif University
of Technology for financial support of the work.
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http://arxiv.org/abs/cond-mat/0509077
http://arxiv.org/abs/cond-mat/0508180

  We have studied the effect of annealing temperature on the statistical
properties of $WO_3$ surface using atomic force microscopy techniques (AFM). We
have applied both level crossing and structure function methods. Level crossing
analysis indicates an optimum annealing temperature of around 400$^oC$ at which
the effective area of the $WO_3$ thin film is maximum, whereas composition of
the surface remains stoichiometric. The complexity of the height fluctuation of
surfaces was characterized by roughness, roughness exponent and lateral size of
surface features. We have found that there is a phase transition at around
400$^oC$ from one set to two sets of roughness parameters. This happens due to
microstructural changes from amorphous to crystalline structure in the samples
that has been already found experimentally.

The Effect of Annealing Temperature on Statistical Properties of WO3 Surface
G. R. Jafari a,b, A. A. Saberi c, R. Azimirad c, A. Z. Moshfegh c, and S. Rouhani c
Department of Physics, Shahid Beheshti University, Evin, Tehran 19839, Iran
Department of Nano-Science, IPM, P. O. Box 19395-5531, Tehran, Iran
Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran
We have studied the effect of annealing temperature on the statistical properties of WO3 surface
using atomic force microscopy techniques (AFM). We have applied both level crossing and structure
function methods. Level crossing analysis indicates an optimum annealing temperature of around
400oC at which the effective area of the WO3 thin film is maximum, whereas composition of the
surface remains stoichiometric. The complexity of the height fluctuation of surfaces was charac-
terized by roughness, roughness exponent and lateral size of surface features. We have found that
there is a phase transition at around 400oC from one set to two sets of roughness parameters. This
happens due to microstructural changes from amorphous to crystalline structure in the samples that
has been already found experimentally.
I. INTRODUCTION
Transition metal oxides represent a large family of
materials possessing various interesting properties, such
as superconductivity, colossal magneto-resistance and
piezoelectricity. Among them, tungsten oxide is of in-
tense interest and has been investigated extensively for its
distinctive properties. With outstanding electrochromic
[1, 2, 3, 4, 5, 6], photochromic [7], gaschromic [8], gas
sensor [9, 10, 11], photo-catalyst [12], and photolumines-
cence properties [13], tungsten oxide has been used to
construct ”smart-window”, anti-glare rear view mirrors
of automobile, non-emissive displays, optical recording
devices, solid-state gas sensors, humidity and tempera-
ture sensors, biosensors, photonic crystals, and so forth.
WO3 thin films can be prepared by various deposition
techniques such as thermal evaporation [3, 8], spray py-
rolysis [14], sputtering [6], pulsed laser ablation [10, 11],
sol-gel coating [2, 5, 15], and chemical vapor deposition
[16].
The gas sensitivity of WO3 heavily depends upon film
parameters such as composition, morphology (e.g. grain
size), nanostructure and microstructure (e.g. porosity,
surface-to-volume ratio). Film parameters are related to
the deposition technique used, the deposition conditions
and the subsequent annealing process. Annealing,
which is an essential process to obtain stable films with
well-defined microstructure, causes stoichiometry and
microstructural changes that have a high influence on the
sensing characteristics of the films [17]. Moreover, the
surface structure and surface morphology of the metal
oxides are also important for different applications. In
fact, the electrochromic devices are made of amorphous
oxides [1], while crystalline phase plays a major role in
catalysts and sensors [17]. This is because, the minor
change in their chemical composition and crystalline
structure could modify different properties of the metal
oxides.
In practice, one of the effective ways to modify the
surface morphology is annealing process at various
temperatures. So far, most of morphological analysis
related to the WO3 surface were accessible through
the experimental methods. Usually these analysis
are rigorous and time consuming. Moreover, lack of
the suitable analysis for AFM data to find the nano
and microstructural properties of surfaces was feeling
perfectly.
In this article, we introduce the methods: roughness
analysis and level crossing as suitable candidates and
show that we can get easily the structure and morpho-
logical properties of a surface in a fast manner, only
using the AFM observation as an initial data.
The roughness of a surface has been studied as a
simple growth model using analytical and numerical
methods [18, 19, 20, 21, 22, 23, 24, 25, 26]. These
studies quite generally proposed that the height fluc-
tuations have a self-similar character and their average
correlations exhibit a dynamic scaling form. Also some
authors recently use the average frequency of positive
slope level crossing to provide further complete analysis
on roughness of a surface [27]. This stochastic approach
has turned out to be a promising tool also for other
systems with scale dependent complexity, such as in
surface growth where one would like to measure the
roughness [28]. Some authors have applied this method
to study the fluctuations of velocity fields in Burgers
turbulence [29] and the Kardar-Parisi-Zhang equation in
(d+1)-dimensions [30] and analyzing the stock market
[31].
In this work, we have used the scaling analysis to
determine the roughness, roughness exponent and the
lateral size of surface features. Moreover, level crossing
analysis has been utilized to estimate the effective area
of a surface.
This paper is organized as follows: In section II, we
have discussed about the film preparation and experi-
http://arxiv.org/abs/0704.1023v1
mental results obtained from AFM, XPS and UV-visible
spectrophotometer for the annealed samples at the vari-
ous temperatures. In section III, we have introduced the
analytical methods briefly. Data description and data
analysis based on the statistical parameters of WO3 sur-
face as a function of annealing temperatures are given in
section IV.Finally, section V concludes presented results.
II. EXPERIMENTALS
Thin films of WO3 were deposited on microscope slide
glass using thermal evaporation method. The deposition
system was evacuated to a base pressure of ∼ 4×10−3Pa.
Thickness of the deposited films was considered about
200 nm measured by the stylus and optical techniques.
More details about the other deposition parameters of
the films are recently reported elsewhere [32].
To study the effect of annealing temperature on sur-
face structure and optical properties of the samples, they
were annealed at 200, 300, 350, 400, 450, and 500oC in
air for a period of 60 min. Optical transmission and
reflection measurements of the deposited films were per-
formed in a range of 300-1100 nm wavelength using a
Jascow V530 ultraviolet (UV)-visible spectrophotometer
with resolution of 1 nm.
X-ray photoelectron spectroscopy (XPS) using a Specs
EA 10 Plus concentric hemispherical analyzer (CHA)
with Al Kα anode at energy of 1486.6 eV was employed
to study the atomic composition and chemical state of
the tungsten oxide thin films. The pressure in the ultra
high vacuum surface analysis chamber was less than
1.0×10−7Pa. All binding energy values were determined
by calibration and fixing the C(1s) line to 285.0 eV . The
XPS data analysis and deconvolution were performed
by SDP (version 4.0) software. The nanoscale Surface
topography of the deposited films was investigated by
Thermo Microscope Autoprobe CP-Research atomic
force microscopy (AFM) in air with a silicon tip of 10
nm radius in contact method. The AFM images were
recorded with resolution of about 20 nm in a scale of
5× 5 µm.
A. XPS Characterization
The elemental and chemical characterizations of the
films were performed by XPS. Figure 1a shows theW (4f)
core level spectra recorded on the ”as deposited” WO3
sample, and the results of its fitting analysis. To repro-
duce the experimental data, one doublet function was
used for the W (4f) component. This contains W (4f7/2)
at 35.6 eV and W (4f5/2) at 37.8 eV with a full-width
at half-maximum (FWHM) of 1.75± 0.04 eV . The area
ratio of these two peaks is 0.75 which is supported by
the spin-orbit splitting theory of 4f levels. Moreover,
the structure was shifted by 5 eV toward higher energy
FIG. 1: W (4f) core level spectra of WO3 thin films: a) ”as
deposited” and b) annealed at 500oC.
relative to the metal state.
It is thus clear that the main peaks in our XPS spectrum
attributed to the W 6+ state on the surface [1, 2, 33]. In
stoichiometricWO3, the six valence electrons of the tung-
sten atom are transferred into the oxygen p-like bands,
which are thus completely filled. In this case, the tung-
sten 5d valence electrons have no part of their wave func-
tion near the tungsten atom and the remaining electrons
in the tungsten atom experience a stronger Coulomb in-
teraction with the nucleus than in the case of tungsten
atom in a metal, in which the screening of the nucleus
has a component due to the 5d valence electrons. There-
fore, the binding energy of the W (4f) level is larger in
WO3 than in metallic tungsten. If an oxygen vacancy
exists, the electronic density near its adjacent W atom
increases, the screening of its nucleus is higher and, thus,
the 4f level energy is expected to be at lower binding
energy [1].
By increasing the annealing temperature it was ob-
served that the position of W (4f) peak did not obviously
change. But for WO3 thin film annealed at 500
oC (Fig.
1b), the W (4f) peak moved to a lower binding energy so
that W (4f7/2) position was observed at 35.0 eV . This
can be related to oxygen vacancy at this high annealing
temperature and formation of W 5+.
B. Optical Characterization
The transmittance and reflectance spectra in the
visible and infrared range recorded for the WO3 thin
films before and after annealing at different temperatures
(Fig. 2a). It is seen that, the transmittance of the ”as
deposited” films in the visible range varies from about
80 up to nearly 100% (without considering the substrate
contribution). Correspondingly, maximum value of the
reflectance for both the film and the substrate is about
20% (the reflectance from the bare glass substrate was
measured about 10%). The sharp reduction in the
transmittance spectrum at the wavelength of ∼ 350nm
is due to the fundamental absorption edge that was also
reported previously [1, 2, 3].
The oscillations in the transmission and reflection
spectra are caused by optical interference. The optical
transmittance of WO3 films strongly depends on the
oxygen content of the films. In fact, non-stoichiometric
films with composition of WO3−x show a blue tinge for
x > 0.03 [34].
The ”as deposited” pure tungsten oxide films were
highly transparent with no observable blue coloration,
under our experimental conditions. As can be seen
from Fig. 2a after annealing process at 200 to 400oC,
the transmittance and reflectance of the WO3 films
have not changed significantly. Only, the position of
the oscillations altered due to thickness reduction and
film condensation after the heat-treatment process
[1]. At 500oC transmittance and reflectance of the
annealed WO3 film is reduced about 10%, therefore at
this temperature, the film turn into non-stoichiometric
composition, so that it could be seen from changing
color of the film.
The optical gap (Eg) was evaluated from the ab-
sorption coefficient (α) using the standard relation:
(αhν)1/η = A(hν − Eg), in which η depends on the
kind of optical transition in semiconductors, and α was
determined near the absorption edge using the simple
relation: α = ln[(1 − R)2/T ]/d ,where d is thickness
of the film. More useful explanation about the optical
band gap calculation reported in [32]. The relationship
between the optical band gap energy and annealing
temperature for WO3 thin films has been shown in Fig.
2b. As can be seen from it, the optical band gap for
the ”as deposited” WO3 evaluated 3.4 eV . Amorphous
structure of the ”as deposited” WO3 causes to Eg is
bigger than 2.7 eV . After annealing samples at 200 and
300oC, the optical band gap decreased slightly about 0.1
eV which can be related to condensation of the films.
But the optical band gap of the WO3 annealed at 400
reduced to 3.1 eV due to crystallization of the film. This
reduction continues to 2.5 eV for the sample annealed
at 500oC. Reason of the Eg becomes smaller than 2.7
eV is oxygen vacancy at this temperature as was seen in
Fig 1b. It is to note that for evaporated WO3 films one
has found 2.7 < Eg < 3.5 eV [1].
λ ( )
400 600 800 1000
27 oC
200 oC
300 oC
400 oC
500 oC
100 200 300 400 500
FIG. 2: a) Optical transmittance (T) and reflectance (R) and
b) Optical band gap energy of the WO3 thin films annealed
at different temperatures.
C. AFM Analysis
To study the effect of the annealing process on the sur-
face morphology of the films, we have shown AFM images
of the WO3 surfaces annealed at the different tempera-
tures : 200, 300, 350, 400, 450, 500oC in Figure 1. As
can be seen from Fig. 1, for the annealed film at 200oC,
it seems that the surface morphology of the film is rela-
tively the same with a smooth surface, amorphous struc-
ture and nanometric grain size, as also reported by other
investigators for WO3 films [35, 36]. We have also ob-
served similar image for the ”as deposited” WO3 which
is not shown here. For WO3 thin films, increasing an-
nealing temperature to 350oC did not significantly ef-
fect on surface parameters because it is low temperature
for crystallization of WO3 [1]. But at higher annealing
temperatures 400, 450 and 500oC, surface grain size and
FIG. 3: AFM images of WO3 thin films annealed at various
temperatures a) 200, b) 300, c) 350, d) 400, e) 450 and f)
500oC, respectively.
roughness begin to increase. The more precise analysis
of these surfaces are given in the next section.
III. STATISTICAL QUANTITIES
A. Roughness Analysis
It is also known that to derive the quantitative infor-
mation of the surface morphology one may consider a
sample of size L and define the mean height of growing
film h and its roughness σ by:
σ(L, t) = (〈(h − h)2〉)1/2 (1)
where t is growing time and 〈· · ·〉 denotes an averaging
over different samples, respectively. Moreover, growing
time is a factor which can be applied to control the sur-
face roughness of thin films.
Let us now calculate the roughness exponent of the
growing surface. Starting from a flat interface (one of
the possible initial conditions), it is conjectured that a
scaling of lenght by factor b and of time by factor bz (z is
the dynamical scaling exponent), rescales the roughness
σ by factor bχ as follows [18]:
σ(bL, bzt) = bασ(L, t) (2)
which implies that
σ(L, t) = Lαf(t/Lz). (3)
For large t and fixed L (i.e.x = t/Lz → ∞) σ saturate.
However, for fixed and large L and t ≪ Lz, one expects
that correlations of the height fluctuations are set up only
within a distance t1/z and thus must be independent of
L. This implies that for x ≪ 1, f(x) ∼ xβg′(λ) with
β = α/z. Thus, dynamic scaling postulates that
σ(L, t) =
tβ, t≪ Lz;
Lα, t≫ Lz.
The roughness exponent α and the dynamic exponent β
characterize the self-affine geometry of the surface and its
dynamics, respectively. In the present work, we see the
surfaces at the limit t → ∞ and so we will only obtain
the α exponent.
The common procedure to measure the roughness ex-
ponent of a rough surface is use of the surface structure
function depending on the length scale l which is defined
S2(l) = 〈|h(x+ l)− h(x)|2〉. (5)
It is equivalent to the statistics of height-height corre-
lation function C(l) for stationary surfaces, i.e. S2(l) =
2σ2(1−C(l)). The second order structure function S2(l),
scales with l as l2α.
B. Level Crossing Analysis
Let ν+α denotes the number of positive slope crossing
of h(x) − h̄ = α for interval L.
Since the process is homogeneous, if we take a second
time interval of L immediately following the first we shall
obtain the same result, and for two intervals together we
shall therefore obtain [28]:
N+α (2L) = 2N
α (L), (6)
from which it follows that, for a homogeneous process,
the average number of crossing is proportional to the in-
terval L. Hence
N+α (L) ∝ L, (7)
N+α (L) = ν
αL, (8)
where ν+α is the average frequency of positive slope cross-
ing of the level h(x) − h̄ = α. We now consider how the
frequency parameter ν+α can be deduced from the under-
lying probability distributions for h(x)− h̄.
Consider a small length scale δx of a typical sample func-
tion. Since we are assuming that the process h(x)− h̄ is a
smooth function of x, with no sudden ups and downs, if
δx is small enough, the sample can only cross h(x)−h̄ = α
with positive slope if h(x) − h̄ < α at the beginning of
the interval L. Furthermore, there is a minimum slope
at x if the level h(x) − h̄ = α is to be crossed in interval
∆x depending on the value of h(x)− h̄ at position x. So
there will be a positive crossing of h(x) − h̄ = α in the
next interval ∆x if, at x,
h(x)− h̄ < α and
h(x) − h̄
h(x) − h̄
As shown in [28], the frequency ν+α can be written in
terms of joint PDF (probability distribution function ) of
p(α, y′) as follows:
ν+α =
p(α, y′)y′dy′. (10)
and then the quantity N+tot which is defined as:
N+tot =
ν+α |α− ᾱ|dα. (11)
will measure the total number of crossing the surface with
positive slope. So, the N+tot and square area of growing
surface are in the same order. Concerning this, it can be
utilized as another quantity to study further the rough-
ness of a surface [27].
l ( m)
0.5 1 1.5 2
FIG. 4: Log-Log plot of the selection structure function of
various annealed temperature: a) 27, b) 200, c) 300, d) 350,
e) 400, f) 450, g) 500oC.
IV. RESULTS AND DISCUSSION
Thin films of WO3 were deposited by using thermal
evaporation method and then surface micrographs of
WO3 samples were obtained by AFM technique after
annealed at different temperatures (Fig.3).
These micrographs were then analyzed using methods
from stochastic data analysis have introduced in the
last section. Figure 3 shows AFM images of WO3 thin
films annealed at 200 ,300 ,350 ,400 ,450, and 500oC.
The ”as deposited” and annealed sample at 200oC
(Fig. 3a) have columnar structure, indicating that up
to 200oC no significant changes in the microstructure
occurs. However, at higher temperatures (figs. 3b-3f) we
have observed increased grain size and rougher surface.
Specifically at 500oC (Fig. 3f) we observe stark changes
in the micrograph which is accompanied by composition
changes in the surface. This can be related to the phase
transition to Magneli phase e.g. WO3−x in the annealing
process [36]. This is also confirmed by our XPS and
UV-visible spectrophotometry analysis (Sec. II). These
are shown the significant formation of W 5+ state in the
surface at 500oC.
Also our analysis shows that below 400oC the surfaces
are in amorphous phase with the same behavior for all
scales, but as soon as the crystalline phase appears the
system behaves differently which diagnostics at small and
large scale for temperatures above 400oC. By using pa-
rameters of the analytical method given here, these tran-
sitions can be quantified.
h ( m)
-0.02 -0.01 0 0.01 0.02
10000
200 oC
300 oC
400 oC
500 oC
FIG. 5: The average frequency ν+α as a function of height h
Now, we will use the statistical parameters introduced
in the last section and will obtain some quantitative
information about the effect of annealing temperature
on the surface topography of the WO3 samples.
The structure function S2(l) as defined in Eq.(5) can
be used to quantify the topology of a rough surface. The
structure function S2(l) is plotted against the length
scale of the sample in Fig.4 . The saturated S2(l) is an
indication of the surface roughness, as 2σ2. The most
obvious observation indicates that roughness is raised
with increasing annealing temperature. Roughness has
a minimum of 0.91nm at 27 and 200oC and a maximum
of 48nm at 500oC. This is because higher temperatures
create higher peaks (i.e. peaks with more deviations
from the average) . All exponents which is derivable
from S2(l) have been summarized and given in Table I.
As depicted in Fig.4 , the structure function S2(l),
has a different behavior in the various temperatures. So
that, in the annealing temperature range 27-350oC it
has a typical behavior in all scales, but in the higher
temperature range 400-500oC its behavior is different
in the small and large scales. In the other words, the
phase transition is occurred at 400oC, because for higher
temperatures, there are two sets of roughness parameters
needed to simulate the surface morphology. It can be
related to the phase transition in the structure of the
surface from amorphous to crystalline phase has been
yielded from the band gap energy (see the section II.B).
The slope of each S2(l) curves at the small and
large scales yields the roughness exponents α and α′ of
100 200 300 400 500
FIG. 6: The normalized N+
behavior as a function of an-
nealing temperature. The solid line is plotted according to
Eq.(12) around 400oC .
the corresponding surface. Hence, it is seen that the
mono roughness exponent increases with the addition of
annealing temperature up to 400oC. In the higher tem-
peratures, we have obtained two roughness exponents(
α-α′) equal to the 0.40-0.14, 0.71-0.20, and 0.69-0.24
for temperatures 400, 450 and 500oC, respectively.
Difference in the α values, in these temperatures, are in
agreement with changes of correlation length. Where the
correlation length, is the distance at which the structure
function behaves differently.
The range of the scaling upon correlation length listed
in the forth column in table I. The value of C∗s denotes
the correlation length at small scales and C∗l for large
scales. The higher C∗ value represents a smoother
surface (as we expected from Fig.3). The correlation
length obtained from the structure function is also a
measure of minimum lateral size of surface features at
each annealing temperature.
The another important WO3 film parameter is the ef-
fective area of the sample which has an important role
in the gas sensitivity of WO3 surfaces. To obtain a mea-
sure for this, we utilize the level crossing analysis. As
shown in Fig.5, the average frequency ν+α as a function
of height h, is plotted for the various annealing tempera-
tures. The broad curves indicate the higher magnitude of
height fluctuations around the average, and sharp curves
show that the most of fluctuations are around the height
average. This conclusion is in the correspondence with
the results obtained from Fig.3.
According to the Eq.(11) N+α i.e. The total number of
the crossing surface with positive slope is proportional to
the square of area of the growing surface. To obtain the
optimum value of the effective area, we have calculated
the ratio of effective areas with respect to the area of
the ”as deposited” surface (27oC). The values are given
TABLE I: The Roughness exponent, roughness, correlation
length and effective area relative to the ”as deposited” sample
area (27oC).
T [oC] α− α′ σ[nm] C∗s -C
[nm] N+/N+(27oC)
27 0.15− none 0.91 60− none 1.00
200 0.15− none 0.98 60− none 1.08± 0.02
300 0.61− none 2.20 100− none 1.17± 0.02
350 0.62− none 11.50 100− none 1.67± 0.02
400 0.40 − 0.15 17.00 100 − 300 2.00± 0.02
450 0.71 − 0.20 30.00 400− 1000 1.72± 0.02
500 0.69 − 0.24 48.00 200− 1400 1.41± 0.02
in the last column in Table I. It means, although the
roughness increases by the annealing temperature but
the effective square area of the rough surface has a
maximum value of N+tot [27].
For more clarity, we have calculated the temperature
dependence of normalized N+α numerically (Fig.6)
around 400oC, and we have obtained the three following
functions for this quantity :
N+tot(T ) = (5.0718− 0.0223× T + 2.72× 10
−5 × T 2)−1(12)
ln(N+tot(T )) = −6.3632+ 0.0344× T − 4.20× 10
−5 × T 2(13)
N+tot(T ) = −8.7057+ 0.0520× T − 6.37× 10
−5 × T 2(14)
According to this figure, the maximum value of the
effective area is at 400oC (with respect to its value
at 27oC) with the relative value equal to 2.00. Thus,
applying this analysis easily shows that if one follows
the condition which the effective area as an important
parameter in the gas sensitivity of WO3 surfaces is
optimum and furthermore, the film composition has not
been changed (e.g. The Magneli phase transition has
not been occurred), should choose the annealed surface
at 400oC for better performance.
V. CONCLUSIONS
We have investigated the role of annealing tempera-
ture, as an external parameter, to control the statisti-
cal properties of a rough WO3 surface. The AFM mi-
crostructure of the surfaces is just needed to apply in our
analysis. We have computed the statistical quantities
such as roughness exponent, roughness and lateral size
of surface features of the ”as deposited” and annealed
surfaces at 200, 300, 350, 400, 450, and 500oC, using the
structure function. We have seen a phase transition at
400oC, because for higher temperatures there are two sets
of roughness parameters, due to structural changes from
amorphous to the crystalline phase. Moreover, using the
level crossing analysis we have obtained an optimum an-
nealing temperature, 400oC in which the surface of the
WO3 has maximum value about twice relative to the ”as
deposited” film without any changes in the film composi-
tion that may increase surface reaction of the WO3 film
as the gas sensor or photo-catalyst.
VI. ACKNOWLEDGMENT
GRJ and AAS would like to thank S.M.Fazeli for his
useful comments and especially M.R.Rahimitabar for his
useful lectures on ”stochastic data analysis”. AZM would
like to acknowledge research council of Sharif University
of Technology for financial support of the work.
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http://arxiv.org/abs/cond-mat/0509077
http://arxiv.org/abs/cond-mat/0508180
