Sensors and Actuators B 119 (2006) 327–334
Review
Modeling of the conduction in a WO
3
thin film as ozone sensor
J. Gu
´
erin
∗
, K. Aguir, M. Bendahan
L2MP UMR-CNRS, F.S.T. St. J´erˆome, Service 152, Universit´e Paul C´ezanne, 13397 Marseille Cedex 20, France
Received 22 July 2005; received in revised form 21 November 2005; accepted 1 December 2005
Available online 20 January 2006
Abstract
In this paper we propose a model for ozone detection in atmospheric conditions. The sensitive layer material used in this study is tungsten oxide.
The interaction between the semiconductor surface and the gases is approached by means of the adsorption theory described by Wolkenstein
in order to determine the equilibrium state of the grains. The layer conductivity is then determined by computing the current flowing between
the grains (in the spherical assumption) across the depletion layer induced by the adsorbed molecules and the semiconductor interaction. This
calculation is performed using the “drift diffusion” equation set.
We have first analyzed the oxygen adsorption effect, then the ozone adsorption one and finally, the combined action of the two mixed gases on
the sensor layer.
This model takes into account the fundamental mechanisms implied in the gas detection and the results obtained are in good agreement with the
experimental results.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Adsorption; Electrical conductivity; WO
3
; Gas sensors; Ozone; Modeling; Thin films
Contents
1. Introduction 327
2. Wolkenstein adsorption theory 328
2.1. Non-dissociative adsorption 329

which induce defect states in the band gap and act as electron
donors [4,5].
Electrical measurements based on the impedance spec-
troscopy allow to understand the mechanisms involved in the
0925-4005/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.snb.2005.12.005
328 J. Gu´erin et al. / Sensors and Actuators B 119 (2006) 327–334
change of the sensitive layer resistivity in presence of oxidizing
or reducing gas. This method shows that the Schottky barrier
which is spread out between adjacent grains is increased by oxi-
dizing vapours and decreased in the opposite case [6–8], that
implies a variation of resistivity in the same way.
Since 1980, many authors have developed models in order
to describe the functionality of gas sensors. Most of them
are based on the same principle. In a first time, the surface
of the grains adsorbs molecules or atoms (O
2
or O) from
air which, because of their oxidizing properties, can ionize
negatively (O
2
−
or O
−
) and act as electron acceptors [3].A
depletion layer is then created in each grain and the electri-
cal conductivity of the sensitive film is decreased. In a second
time, if an oxidizing gas is present in the atmosphere, this
new species is also adsorbed and the mechanism is ampli-
fied. Conversely, if a reducing gas is present, a part of the

isotherms [19–21] oroxidation of the surface vacancies by ozone
[22] are described in the literature.
In a previous paper [23], a model of gas sensor based on the
conductivity decrease of a polycrystalline film of metal oxide
(WO
3
), in an oxidizing atmosphere, was already described. The
interaction between the gas and the surface was modeled by
Langmuir isotherm and the electrical resistivity was evaluated
by solving the transport equations.
This paper deals with ozone detection in the atmosphere,
the influence of another gas is not studied. The action of oxy-
gen is first analyzed, then the ozone one. The combined action
of the two mixed gases is finally studied at the end of this
article.
In each case, the interaction between the semiconduc-
tor material and the gases is approached by means of the
adsorption theory of Wolkenstein in order to determine the
equilibrium state of the grains. The film conductivity is
then determined by computing the current flowing between
the grains (supposed spherical) across the depletion layer.
This is performed using the Shockley Read Hall generation
recombination model and the “drift diffusion” equations set,
largely used for the calculation of the semiconductor devices
[24].
The simulation results are in good agreement with the exper-
imental measurements.
2. Wolkenstein adsorption theory
The Wolkenstein adsorption model [25,26] which introduces
in a natural way the reciprocal interactions between the adsor-

from the semiconductor to the adsorbed species. The binding
energy of the adsorbate is increased by E
s
= E
c
−E
ss
, that is
the loss of free energy of the system during the ionization pro-
cess. This process involves the creation of a negative superficial
charge and a chemisorption induced surface potential barrier V
s
(V
s
< 0).
Let us nameE
cs
= E
c
−qV
s
the surface conduction bandlevel,
one can write E
s
= E
c
−E
ss
= E
cs

+ χ
ads
−χ
sc
+ qV
s
.
This expression shows that the binding energy of the strongly
adsorbed species decreases when the covering rate increases
what facilitates the desorption.
The neutral chemisorption mechanism is only limited by the
number of adsorption sites at the surface of the material, while
the strong one is limited by the upper band bending.
J. Gu´erin et al. / Sensors and Actuators B 119 (2006) 327–334 329
For the diatomic gases as oxygen, the adsorption may be
non-dissociative (generally at low temperature) or dissociative
(at higher temperature). The corresponding chemical reactions
between a diatomic molecule O
2
and one or two free adsorption
sites S are:
S + O
2
→ (S–O
2
); (S–O
2
) + e
−
→ (S–O

is determined by the adsorption and desorption bal-
ance:
p(1 − θ)
N
∗
√
2πmkT
= ν exp

−E
w
kT

θ
0
+ θ
−
exp

−E
s
kT

(3)
In the firstterm, p is thegas partial pressure andm is its molecular
mass, N
*
is the total density of adsorption sites, k the Boltzman
constant and T is the thermodynamic temperature.
In the second term, ν is the typical phonon frequency of the


θ
2
0
+ θ
2
−
exp

−E
s
kT

(4)
It is to be noticed that the adsorption kinetics of a triatomic gas
(expression 2), which utilizes only one adsorption site has the
same behavior than a non-dissociative kinetics.
In any case, θ
−
and θ
0
are related to the total covering rate θ
by the Fermi–Dirac statistics:
η
−
=
θ
−
θ
=

tron and hole densities, respectively, N
+
d
the density of ionized
oxygen vacancies and ε is the permittivity.
n, p and N
+
d
are calculatedby the setof classicaldrift diffusion
equations using Fermi–Dirac statistics.
Thus, the computation of the solution of Eqs. (3), (5) and (6)
or (4)–(6) must be performed simultaneously with that of the
Poisson’s equation. The boundary condition is given by Gauss
law at the surface of each grain:
E
n
=
σ
ε
=
−qN
∗
θ
−
ε
(8)
E
n
is the normal electric field and σ is the superficial density of
charge.


(9a)
k
2
p
2
(1 − θ
1
− θ
2
)
= ν
2
exp

−E
w2
kT

θ
20
+ θ
2−
exp

−E
s2
kT

(9b)

(η
20
,η
2−
)p
1
+ k
2
A
2
(η
10
,η
1−
)p
2
+A
1
(η
20
,η
2−
)A
2
(η
10
,η
1−
)
(10)

p
1
(1 − θ
1
− θ
2
)
2
= ν
1
exp

−E
w1
kT

θ
2
10
+ θ
2
1−
exp

−E
s1
kT

(12)
whereas Eq. (9b) remains valid for ozone.

⎪
⎪
⎩
k
2
p
2
+
√
k
1
p
1
[A
1
(η
20
,η
2−
)]
2
√
k
1
p
1
A
1
(η
20

⎪
⎪
⎪
⎪
⎪
⎭
(13)
The previous set of Eqs. (5)–(7) and (10) or (5)–(7) and (13)
cannot be analytically solved, but a numerical resolution is pos-
sible if one chooses grains of simple geometrical form [15].No
shape of grain is fully satisfactory to model a thin polycrystalline
layer made up of grains which have a great disparity of shape and
size. In this work, the grains are supposed to be quasi-spherical,
identical in size, andsingle-crystal. They are jointed, coupled the
ones with the others by a small contact surface allowing a great
porosity. Each grain is bathed by theatmosphere to becontrolled.
This simplified model allows at the same time to easily deter-
mine the electrical features of a grain and to take into account the
various mechanisms taking part in electric conduction. Indeed,
by supposing that the film consists of an homogeneous stacking
of identical spherical grains of known properties, the resistivity
of the layer results from the properties of only one grain.
3. Computation method
Computation is carried out in two steps.
The first step consists in determining the thermodynamic
equilibrium state (no bias) of the grains surrounded by their
environment. The neutral and ionized covering rates (θ
0
and
θ

typical phonon frequency, ν =10
13
Hz [26,10]; strong oxygen
and ozone chemisorption level depth, χ
ads
−χ
sc
= 1 eV (S–O
or S–O
2
occupied sites) [28,29]. The desorption energy E
w
is equal to 0.1 eV and 0.35 eV for oxygen dissociative and
non-dissociative chemisorption, respectively and 1.2 eV for
ozone.
4. Results and discussion
The stoichiometry, the grain size and the superficial density
of the adsorption sites are the only adjustable parameters of
simulations. The other parameters are related to the sensitive
layer material.
The oxygen vacancy density is assumed to be 1 ×10
19
cm
−3
(corresponding to a chemical composition WO
2.99959
) with a
donor level located on the conduction band (quasi-total ion-
ization). The grains are 20 nm radius, this size is comparable
with the granularity of the layers carried out in the laboratory

: the depletion zone is narrow
and the resistivity is weak,
• under high oxygen pressure (1 bar), with a bias current equal
to 1 A/m
2
; the depletion zone isspread out until in the medium
of the grain and the resistivity is much higher.
The operating conditions of the sensor are driven by atmo-
spheric oxygen which determines its baseline. It is thus useful to
analyze separately the influences of the oxygen and ozone partial
pressures before to take into account the ozone detection.
Fig. 1. Influence of oxygen pressure on electron density and potential at 473 K.
J. Gu´erin et al. / Sensors and Actuators B 119 (2006) 327–334 331
Fig. 2. Layer resistivity vs. oxygen or ozone pressure.
4.1. Influence of oxygen
The simulations are carried out in pure oxygen atmosphere
at different temperatures in the range of 473–673 K and variable
pressure.
Fig. 2 shows the behavior of the film resistivity accord-
ing to the oxygen pressure in the cases of non-dissociative
and dissociative adsorption. On this figure and on the fol-
lowing ones, the unit of pressure is the atmospheric pressure:
1013 mb. For very low oxygen pressure, the value of the resis-
tivity, approximately 2 ×10
−2
 cm is almost independent on
the temperature. This is due for a part to the choice of the
null donor level of oxygen vacancies and to the weak varia-
tion of mobility (like 1/T) in the temperature range for the other
part.

0
whereas the mixture determines the resistivity under
gas ρ
gas
.
The response S is defined by the ratio S = ρ
gas
/ρ
0
.
Fig. 3a shows the variation of the covering rates of the adsorp-
tion sites by oxygen (molecular O
2
or ionized O
2
−
) and by the
ozone (atomic O or ionized O
−
) according to the partial pres-
sure of ozone in the non-dissociative chemisorption case. For
very low ozone pressure (1 ×10
−18
), the covering rate is prin-
cipally due to atmospheric oxygen pressure (1 ×10
−2
) since
the covering rate due to ozone is more than seven decades
lower (1 ×10
−10

Fig. 3. (a) Total covering rate of adsorption sites induced separately by O
2
and
O
3
in the non-dissociative adsorption case. (b) Total covering rate of adsorption
sites induced separately by O
2
and O
3
in the dissociative adsorption case.
species O
2
,O
2
−
, O or O
−
at 473 K and O or O
−
at 573 and
673 K) and ionized covering rate θ
−
(due to species O
2
−
or O
−
at 473 K and O
−

and O
3
in
the non-dissociative (at 473 K) and dissociative (at 573 and 673 K) adsorption
case.
• for an operation as sensor or detector, there exists for each
pressure to be detected, an optimal temperature which pro-
vides the highest sensitivity Σ =dS/dp.
The behavior of S in the case of dissociative adsorption is
slightly different: the response is significant at low temperature:
140 at 473 K against 50 for non-dissociative adsorption.
Fig. 6 represents the computed response of a sensor placed
in normal operating conditions. Two curves are calculated in
Fig. 5. Response of the layer vs. ozone partial pressure in the two adsorption
cases.
J. Gu´erin et al. / Sensors and Actuators B 119 (2006) 327–334 333
Fig. 6. Response of the layer vs. ozone partial pressure.
non-dissociative adsorption mode at 423 and 473 K and four
curves are calculated in dissociative adsorption mode for the
higher temperature values. In the considered range of partial
pressure, the optimum response is obtained around 523 K.
4.4. Comparison between modeling and experimental
sensor response
WO
3
sensors are prepared by reactive radio frequency
(13.56 MHz) magnetron sputtering, using a 99.9% pure tung-
sten target. The vacuum chamber is evacuated to 5 ×10
−7
mbar

used as a reference gas. Ozone is generated by oxidizing oxygen
molecules of a dry air flow exposed to a calibrated pen-ray UV
lamp.
The resistance measurement is carried out by a picoammeter
HP 4140B.
These sensors have a high sensitivity at ozone, the response is
typically 100–300 at 0.8 ppm. However they are very dependent
on the variations of process, so the dispersion of characteristics
among the different manufacturing batches requires an adjust-
ment of the simulation parameters.
Fig. 7 gives an example of response (experimental and simu-
lated) versus ozone pressure at 523 K. The experimental curve is
Fig. 7. Simulation of the response of the layervs. ozone partial pressure at 523 K
in the two adsorption cases and comparison with an experimental sensor.
Fig. 8. Simulation of the response of the layer vs. ozone temperature at 0.8 ppm
ozone in the two adsorption cases and comparison with an experimental sensor.
obtained with aWO
3
sensor while thesimulated one is computed
in the dissociative chemisorption case with desorption energies
E
w
= 0.05 and 1.195 eV for O
2
and O
3
, respectively and a phonon
frequency ν =3×10
13
Hz. The experimental dots are very close

adsorption at temperature lower than 550 K and a dissociative
behavior at higher temperature.
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Biographies
Jacques Guerin was born in France in 1947. He received his engineer-
ing diploma in electronics and radio-communication at the Institut National
Polytechnique of Grenoble (INPG) in 1972 and his PhD from the Univer-
sity of Aix-Marseille III (Paul Cezanne) with a thesis on spatial silicon solar
cells for observation satellites. After various research and engineering devel-
opments (thermionic conversion, electronic power devices ), he joined the
Sensors Group of the Laboratoire Materiaux & Microelectronique de Provence