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 2.2. Dissociative adsorption 329 3. Computation method 330 4. Results and discussion 330 4.1. Influence of oxygen 331 4.2. Influence of ozone 331 4.3. Simulation in presence of the two gases at operating conditions 331 4.4. Comparison between modeling and experimental sensor response 333 5. Conclusion 333 References 334 1. Introduction The performances improvement of the microsensors requires the control of technology as well as the knowledge of the mecha- nisms of reactivity and conduction. Most of them are made from a metal oxide film used as a sensitive layer. Tin oxide (SnO 2 ), ∗ Corresponding author. Tel.: +33 4 91 28 85 10; fax: +33 4 91 28 89 70. E-mail address: jacques.guerin@L2MP.fr (J. Gu ´ erin). titanium oxide (TiO 2 ), zinc oxide (ZnO) and tungsten oxide (WO 3 ), in microcrystalline state, are the most usual materials for this application [1–3]. These metallic oxides are n-type large gap under-stoichiometric semiconductors, with oxygen vacancies. Their electrical conduction is explained by oxygen vacancies 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 adsorbed oxygen is reduced by the gas and removed from the surface, the depletion layer and the resistivity are then decreased [9–12]. The numerous approaches differ by the adsorption isotherm and the way of evaluating the microcrystalline film resistiv- ity. The most useful isotherms are Langmuir and Wolkenstein isotherms. In the Langmuir model, the bonding energy between the adsorbent and the adsorbate is supposed to be independent of the covering rate. It is easy to implement in a fully analytical models and gives interesting results, particularly with metals. However the adsorption on semiconductors is more complicated because the semiconductors can exchange electrons with the adsorbate and thus create neutral and ionized species whereas that model does not take account of these two species. So it is not very realistic when it is applied to semiconductors mate- rials. Despite its disadvantages, the Langmuir model is often used with a good accuracy because for low covering rates (less than 5 ×10 −3 ) the adsorbate is almost fully ionized and the bonding energy can be compared to a constant: it is the case at high temperature, low concentration, dynamic regime [13,14]. The Wolkenstein model takes into account the electronic cou- pling between the semiconductor and the adsorbate speciesbut is rather complex to implement because it needs the simultaneous resolution with the Poisson’s equation [15–18]. The described mechanism is not the only one which is pro- posed and other models, based on slightly different adsorption 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- bent and the adsorbate seems particularly well suited to the case of the semiconductors materials. In this article one will be interested in the case of an oxidizing vapour adsorbed on a n-type semiconductor (oxygen or ozone on WO 3 sensor) but it is clear that the other schemes can be analyzed in a similar way. In the Wolkenstein model, the adsorption of an oxidizing gas species is carried out with two successive steps: ‘weak or neutral chemisorption’ and ‘strong or ionized chemisorption’ [27]. During the first step, the bond between the adsorbate and the substrate is weak and does not involve electronic trans- fer, the electrons of the atom or the molecule remain located in the vicinity of the adsorbate involving a simple deforma- tion of the orbitals. The binding energy of the adsorbate is E w and corresponds to the loss of free energy of the sys- tem during the adsorption process. This neutral chemisorption does not change the electrical properties of the material but the perturbation created by the adsorbate induces surface state E ss in the band gap. This surface state acts as a trap for the electrons. The second step (strong chemisorption) occurs when an elec- tron of the conduction band, whose energy is E c , is transferred 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 −E ss + qV s . The energy dif- ference E cs −E ss is also the difference χ ads −χ sc between the electronic affinities of the neutral adsorbate and the semicon- ductor. So, E s = χ ads −χ sc + qV s . The binding energy of the strongly adsorbed species write E w + E s = E w + 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 2 ) − for the non-dissociative kinetics (1a) 2S + O 2 → 2(S–O); (S–O) + e − → (S–O) − for the dissociative kinetics (1b) For triatomic gases as ozone O 3 one considers only one possi- bility: S + O 3 → (S–O) + O 2 ; (S–O) + e − → (S–O) − (2) 2.1. Non-dissociative adsorption In stationary conditions, the value of the covering rate θ = N ads /N * 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 lattice, θ 0 and θ − are the covering rates of the neutral and ionized species, respectively. This equation means that a strongly chemisorbed species must give again its trapped electron to the bulk and return to the neutral state before desorbing and a neutral chemisorbed species must release its bonding energy E w before desorbing. 2.2. Dissociative adsorption The presence of two free close sites is necessary so that the reaction of adsorption occurs, conversely, the reac- tion of desorption requires the presence of two close atoms. The relation of balance is thus modified in the following way: p(1 − θ) 2 N ∗ √ 2πmkT = ν exp  −E w kT  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 = 1 1 + 2exp E ss −E F kT (5) η 0 = θ 0 θ = 1 − η − (6) Eqs. (3)–(6) are related to superficial quantities, but they depend on the band bending qV s . This quantity must be calculated from the Poisson’s equation: V = q ε (n − p − N + d ) (7) In this expression, V is the intrinsic potential, n and p are the elec- 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. When two species of oxidizing adsorbates are simultaneously in the atmosphere, it is assumed that no interaction between these two species takes place in the gaseous phase and Eq. (3) is replaced by two coupled equations: k 1 p 1 (1 − θ 1 − θ 2 ) = ν 1 exp  −E w1 kT  θ 10 + θ 1− exp  −E s1 kT  (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) And the total covering rate writes: θ = θ 1 + θ 2 = k 1 A 1 (η 20 ,η 2− )p 1 + k 2 A 2 (η 10 ,η 1− )p 2 k 1 A 1 (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) With A i (η i0 ,η i− ) = ν i exp  −E wi kT  η i0 + η i− exp  −E si kT  (11) In the dissociative adsorption case Eq. (4) related to oxygen must be modified in the same way: k 1 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. In this case, the total covering rate writes: 330 J. Gu´erin et al. / Sensors and Actuators B 119 (2006) 327–334 θ = θ 1 + θ 2 = 1 k 2 p 2 + A 1 (η 20 ,η 2− ) × ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ k 2 p 2 + √ k 1 p 1 [A 1 (η 20 ,η 2− )] 2 √ k 1 p 1 A 1 (η 20 ,η 2− ) + [k 2 p 2 +A 1 (η 20 ,η 2− )]  A 1 (η 2 20 ,η 2 2− ) ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ (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 − ), the electrons and holes densities (n and p) and the intrin- sic potential V are simultaneously computed. This calculation is performed by solving the Poisson’s equation using a four points Runge Kutta method. The second step consists in solving the set of drift diffu- sion equations in the vicinity of the equilibrium solution. This solution is perturbed by a little bias current flowing between two adjacent grains which induces perturbations δV, δn and δp on V, n and p, respectively. The corresponding linear equations are then derived and the matrix inversion is performed by gaus- sian elimination. Non-equilibrium values of electric field, Fermi quasi-potentials, current densities, resistivity arethen calculated. The simulation results presented in this paper are obtained for WO 3 sensors with values usually quoted in the literature: gap width, E g = 2.7 eV and refractive index, n =2. Most of the other data areestimated from the literature related to SnO 2 : effective mass of electrons and holes, m e = m h = 0.3m 0 ; 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 and moreover the reduction in this value would lead to nano- crystalline structure not compatible with the classical statistical analysis. The superficial density of sites is 1 ×10 15 cm −2 . For a sensor application, the film resistivity is the significant physical parameter. It is also the last which can be computed because it is the result of a succession of different mechanisms. Among the various intermediate parameters, the more interest- ing are the total and ionized covering rates of the grains due to the atmosphere interaction, the electrical potential induced by the surface electric charge and the resulting electronic density. Fig. 1 shows the influence of oxygen pressure on the elec- tron density and the potential distributions in the grains under bias. The curves are drawn along an axis connecting the centers of two adjacent grains between which the current flows. When this current is null, these profiles are symmetrical but when the current increases, the balance between conduction and diffusion components involves a decrease of potential in the current direc- tion and a displacement of electrons in the reverse direction. The curves are computed for two opposite operating conditions: • under very low oxygen pressure (1 ×10 −18 bar), with a bias current equal to 1 ×10 8 A/m 2 : 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. For very high oxygen pressure, the layer resistivity reaches a limit value. This is due to the saturation of the electrons trapping process by the adsorbed species which limits the ionization rate of the adsorbed layer at 4.8 ×10 −2 . It should be noted that the increase in temperature shifts the ascending part of the curves towards the stronger pressures. The increase in resistivity is slower in the dissociative adsorp- tion case but the extreme values remain the same ones, in accor- dance with the saturation of the trapping process. 4.2. Influence of ozone Simulation was made in the presence of pure ozone, only in the non-dissociative adsorption case in accordance with the previous assumptions. The curves are drawn in Fig. 2 which summarizes the results: • the resistivity behavior is unchanged compared to oxygen, • the extreme values of the resistivity are also unchanged because of the same value of the strong chemisorption level (1 eV), • the scale of the pressures is eight decades shifted towards the lower values, what highlights the greatest reactivity of the ozone compared to the oxygen. 4.3. Simulation in presence of the two gases at operating conditions Now, the sensors response are simulated in presence of two oxidizing gases: oxygen, under a fixed partial pressure (0.2 on the reduced scale) and ozone, under variable partial pressure. The partial pressure of oxygen determines the resistivity under air ρ 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 to 1 ×10 −13 ). When this pressure increases, the desorbed atoms or ions resulting from oxygen are gradually removed and replaced by those coming from ozone, until satu- ration of the layer occurs (θ = 1). Under strong pressure, there is no more adsorbed oxygen, this is due to the greatest desorption energy of ozone (1.2 eV against 0.35 eV for non-dissociative oxygen). The results obtained in the case of the dissociative adsorption of oxygen are similar. Fig. 3b shows the covering rates resulting from oxygen and from ozone, respectively. Interpretation is more delicate since in both cases the adsorbed species is always the same: atomic oxygen, ionized or not. The ozone dissociation being easier than that of oxygen, one must think that when equilibrium is estab- lished, the atoms of oxygen resulting from the dissociation of oxygen have been replaced by other atoms of oxygen resulting from the dissociation of ozone. The oxygen adsorption on SnO 2 is generally non-dissociative for temperatures lower than 500 K and dissociative at higher temperature [17,18]. Supposing that this assumption remains true for WO 3 , the values of the total covering rate θ 0 (due to 332 J. Gu´erin et al. / Sensors and Actuators B 119 (2006) 327–334 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 − at 573 and 673 K) are given in Fig. 4a and b, respectively. We can notice that the low value of the adsorbate ionization rate saturates at a value lower than 5.4 ×10 −3 while the total covering rate reaches the unit. Fig. 5 shows the response of the layer S according to the partial ozone pressure at the same time for non-dissociative and dissociative adsorption of oxygen. It should be noted in Fig. 5 that the increase in tempera- ture which shifts the ascending part of the curves towards the strongest pressures must result in a loss of sensitivity to the low pressures. This figure shows that for the non-dissociative adsorption: • the response is always very weak at the low temperatures because of the weak desorption of the layer which is already almost saturated, • this response can become very high at high temperature with the condition of having a strong ozone concentration, which does not correspond to the normal conditions of a sensor oper- ation, Fig. 4. (a) Total covering rate of adsorption sites induced both by O 2 and O 3 in the non-dissociative (at 473 K) and dissociative (at 573 and 673 K) adsorption case. (b) Ionized covering rate of adsorption sites induced both by O 2 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 by a turbo molecular pump. The films are sputtered on SiO 2 /Si substrates with platinum electrodes in a reactive atmosphere under controlled oxygen–argon mixtures. The total pressure is stabilized at 3 ×10 −3 mbar. Both argon and oxygen flows are controlled by mass flow controllers. Oxygen content in the gas mixture, defined as the ratio of oxygen flow to the total flow, is fixed at 50%. The R.F. power applied to the target is 60 W and the temperature substrate is 300 K. The WO 3 layers are highly resistive, so interdigitated elec- trodes are used in order to reduce the sensor resistance. The distance between the electrodes is 50 ␮m. They are obtained from a sputtered Pt film, using photolithography and lift off pro- cesses. After WO 3 deposition on the Pt electrodes, the films are annealed at 425 ◦ C for 1 h 30 min in air in order to stabilize the chemical composition and the crystalline structure. To investigate the ozone sensing properties of WO 3 films, the sensors are introduced in a test chamber allowing to control the sensor temperature under variable gas concentrations. Dry air is 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 to the simulated curve. Fig. 8 gives an example of response obtained under 0.8 ppm ozone concentration with a WO 3 sensor. The curves correspond- ing to non-dissociative and dissociative chemisorption are high- lighted in their validity domain of temperature. The simulation results are in good agreement with the experimental measure- ments, especially in the non-dissociative case. 5. Conclusion The model presented in this paper is built on an approach a little different from those which are usually described in the lit- erature. It is based on the approximation of the sensitive film by a regular stacking of identical spherical grains. It can be improved using a statistics related to the grain size. The model supposes moreover that each grain is single-crystal, isotropic, and can be described by a finished number of macroscopic parameters characterizing the material. It supposes finally that the chemical mechanisms are located at the interfaces and are fully reversible 334 J. Gu´erin et al. / Sensors and Actuators B 119 (2006) 327–334 in the whole range of temperatures, what must be true in the real sensors. 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Komem, Numerical computation of chemisorption isotherms for device modeling of semiconductor gas sensors, Sens. Actu- ators B 93 (2003) 362–369. [28] V. Lantto, P.R. Romppainen, Electrical studies on the reactions of CO with different oxygen species on SnO 2 surfaces, Surf. Sci. 192 (1987) 243– 264. [29] J.F. McAleer, P.T. Moseley, J.O.W. Norris, D.E. William, Tin oxide gas sensors. Part 1. Aspects of the surface chemistry revealed by electrical conductance variations, J. Chem. Soc., Faraday Trans. I 83 (1987) 1323– 1346. 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 (L2MP–CNRS) Marseille (France) in 2002. Its principal research interests are now directed towards WO 3 gas sensors and selectivity enhancement strategies, conduction and adsorption mechanisms and modelling of sensor responses. Khalifa Aguir was bornin 1953.He is professor at Paul Cezanne, Aix-Marseille III University (France). He was awarded his Doctorat d’Etat es Sciences degree from the Paul Sabatier University Toulouse (France) in 1987. He is cur- rently head of Sensors Group at Laboratoire Materiaux & Microelectronique (L2MP–CNRS) Marseille (France). His scientific interests are thin films prepa- ration and characterization for microsystems. Since 1998, he is interested in gas microsensors and selectivity by signal treatment strategies, and electronic noses, physical and chemical properties of metal and oxides thin films, and applications in microelectronics. He currently works on WO 3 gas sensors and selectivity enhancement strategies including PCA analysis, noise spectroscopy and modelling of sensor responses. Marc Bendahan was born in 1967. He is a researcher at the Paul Cezanne, Aix-Marseille III University (France). He is also lecturer in electronics at the Institute of Technology of Marseille. He was awarded his PhD degree from the University of Aix-Marseille III in 1996 with a thesis on shape memory alloys thin films. He is specialized in thin films preparation and characterization for applications in microsystems. Since 1997, he is interested in gas microsensors and he developed a selective ammonia sensor based on CuBr mixed ionic con- ductor. He currently works at Laboratoire Materiaux & Microelectronique de Provence (L2MP–CNRS) Marseille (France), on WO 3 gas sensors and selectiv- ity enhancement strategies. . 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. 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