S Smiy

M Bejar
email: bejar_moez@yahoo.fr

E Dhahri

T Fiorido

K Aguir

V Martini-Laithier

M Bendahan

Film-thickness influence on ozone detection of perovskite La0.8Pb0.1Ca0.1Fe1-xCoxO3 based sensors

Keywords: Perovskite, Sensors, Thin films, Films thickness, Ozone sensor

In this study, La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) thin films with respective thicknesses of 300 and 600 nm have been prepared by the drop coating technique onto 𝑆𝑆𝑆𝑆/𝑆𝑆𝑆𝑆𝑆𝑆 2 substrate with platinum interdigitated electrodes. The effect of cobalt-content and films thickness on the ozone sensing properties have been studied. The sensors responses have been determined in an operating temperature range between 160 and 280°C. Sensors have been exposed to different concentrations between 50 and 400 ppb of ozone gas at a constant flow rate of 500 ml/min dry air.

The studied La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) compounds could be a promising sensitive film for ozone detection, especially for the thinnest sensitive layer, 300 nm in our case.

still the main drawback of these materials. These materials are currently studied in forms of nanostructured such as nanowires, nanotubes and nanorods thanks to their large surface area and nano-size effect [START_REF] Aguir | Trends in metal oxide thin films: Synthesis and applications of tin oxide[END_REF][START_REF] Avansi | One-dimensional V2O5/TiO2 heterostructures for chemiresistive ozone sensors[END_REF]. But these materials are characterized by a very high operating temperature for example in the case of WO3 and Au-ZnO prepared by the hydrothermal method, the operating temperature is found to be equal to 200°C and 206°C, respectively, in presence of 1000 ppb of BTEX [START_REF] Silva | BTEX gas sensor based on hematite microrhombuses[END_REF]. Added to that, many works are interested on the study of materials which are nonporous, mesoporous and other materials characterized by nanometric size used for gas sensing application [START_REF] Silva | BTEX gas sensor based on hematite microrhombuses[END_REF][START_REF] Shahmoradi | Noninvasive Detection of Ammonia in the Breath of Hemodialysis Patients Using a Highly Sensitive Ammonia Sensor Based on a Polypyrrole/Sulfonated Graphene Nanocomposite[END_REF][START_REF] Souissi | Highly sensitive nitrogen dioxide gas sensors based on sprayed β-In2S3 film[END_REF].

Perovskite materials are promising candidates for the detection of ozone-gas [START_REF] Silva | Ozone and nitrogen dioxide gas sensor based on a nanostructured[END_REF][START_REF] Mori | Ozone detection in air using 𝑆𝑆𝑚𝑚𝐹𝐹𝐹𝐹𝑆𝑆 3 gas sensor for air quality classification[END_REF][START_REF] Mastelaro | Ozone gas sensor based on nanocrystalline SrTi 1-𝑥𝑥 Fe 𝑥𝑥 O 3 thin films[END_REF][START_REF] Kang | Rapid detection of ozone in the parts per billion range using a novel Ni-Al layered double hydroxide[END_REF][START_REF] Itagaki | 𝑆𝑆 3 and 𝑁𝑁𝑆𝑆 2 sensing properties of SmFe 1-𝑥𝑥 Co 𝑥𝑥 O 3 perovskite oxides[END_REF].

For instance, 𝑆𝑆𝑆𝑆𝑇𝑇𝑆𝑆 0.85 𝐹𝐹𝐹𝐹 0.15 𝑆𝑆 3 sensor was used in the detection of 800 𝑝𝑝𝑝𝑝𝑝𝑝 of ozone gas at the operating temperature of 250 °𝐶𝐶 [START_REF] Kang | Rapid detection of ozone in the parts per billion range using a novel Ni-Al layered double hydroxide[END_REF]. M. Mori et al. found that introducing Co [START_REF] Belkacem | Cobalt nanograins effect on the ozone detection by WO3 sensors[END_REF] in place of Fe was accompanied by a decrease in the operating temperature of this sensor [START_REF] Itagaki | 𝑆𝑆 3 and 𝑁𝑁𝑆𝑆 2 sensing properties of SmFe 1-𝑥𝑥 Co 𝑥𝑥 O 3 perovskite oxides[END_REF]. 𝐿𝐿𝐿𝐿𝐹𝐹𝐹𝐹𝑆𝑆 3 is a multifunctional perovskite material, which was used in the detection of many dangerous oxidizing gases such us 𝑁𝑁𝑆𝑆 2 [START_REF] Thirumalairajan | Surface morphologydependent room-temperature LaFeO 3 nanostructure thin films as selective 𝑁𝑁𝑆𝑆 2 gas sensor prepared by radio frequency magnetronsputtering[END_REF] and 𝑆𝑆𝑆𝑆 2 [START_REF] Palimar | Investigation of Ca substitution on the gas sensing potentiel of 𝐿𝐿𝐿𝐿𝐹𝐹𝐹𝐹𝑆𝑆 3 nanoparticles towards low concentration 𝑁𝑁𝑆𝑆 2 gas[END_REF].

However, LaFeO 3 is characterized by a high resistance [START_REF] Zhang | Fabrication of electrospun LaFeO3 nanotubes via annealing technique for fast ethanol detection[END_REF], which is a disadvantage in the field of gas sensors. For this reason, it is necessary to replace the lanthanum in LaFeO 3 with lower-valence cations, such as Sr, Ca and Pb [START_REF] Mizusaki | Non stoichiometry and defect Structure of the perovskite-type oxides 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝑆𝑆𝑆𝑆 𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3-𝛿𝛿[END_REF][START_REF] Smiy | Correlation between structural, magnetic and gas sensor properties of La 0.885 Pb 0.005 Ca 0.11 Fe 1-x Co x O 3 compounds[END_REF][START_REF] Mizusaki | Thermodynamic quantities and defect equilibrium in the perovskite-type oxide solid solution 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3-𝛿𝛿[END_REF]. The gas-sensing properties of La 1-𝑥𝑥 Ca 𝑥𝑥 FeO 3 and La 1-𝑥𝑥 Pb 𝑥𝑥 FeO 3 have been studied respectively by L.B. Kong et al. [START_REF] Kong | Gas-sensing property and mechanism of 𝐶𝐶𝐿𝐿 𝑥𝑥 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3 ceramics[END_REF] and P. Song et al. [START_REF] Song | The structure, electrical and ethanol-sensing properties of 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝑃𝑃𝑝𝑝 𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3 perovskite ceramics with 𝑥𝑥 ≤ 0.3[END_REF]. It has been confirmed that these perovskites, with a composition where 𝑥𝑥 = 0.2, show a higher response and greater selectivity to CO and ethanol gases, respectively. Usually, the perovskite materials used in the field of gas sensing are used in pellets forms, therefore and in order to increase the sensitivity of these sensors it is necessary to deposit these materials using chemical method which is sol gel by drop coating because the response increases in case of the use of chemical preparation method

[33].
In our previous published work related to this framework, we have demonstrated that introducing cobalt instead of Iron in 𝐿𝐿𝐿𝐿 0.885 𝑃𝑃𝑝𝑝 0.005 𝐶𝐶𝐿𝐿 0.11 𝐹𝐹𝐹𝐹 1-𝑥𝑥 𝐶𝐶𝐶𝐶 𝑥𝑥 𝑆𝑆 2.95 (𝑥𝑥 = 0.00, 0.05, 0.10 𝐿𝐿𝑍𝑍𝑎𝑎 0.15) compounds leads to the decrease of the operating temperature from 270 °𝐶𝐶 to 250 °𝐶𝐶 when Co-content increase from 0 % to 5 % in presence of the 𝑁𝑁𝑊𝑊 3 reducing gas [START_REF] Smiy | Correlation between structural, magnetic and gas sensor properties of La 0.885 Pb 0.005 Ca 0.11 Fe 1-x Co x O 3 compounds[END_REF]. Moreover, the responses of 𝐿𝐿𝐿𝐿 0.8 𝑃𝑃𝑝𝑝 0.1 𝐶𝐶𝐿𝐿 0.1 𝐹𝐹𝐹𝐹 1-𝑥𝑥 𝐶𝐶𝐶𝐶 𝑥𝑥 𝑆𝑆 3 (0.00 ≤ 𝑥𝑥 ≤ 0.20) sensors found in this study were higher than those of 𝐿𝐿𝐿𝐿 0.885 𝑃𝑃𝑝𝑝 0.005 𝐶𝐶𝐿𝐿 0.11 𝐹𝐹𝐹𝐹 1-𝑥𝑥 𝐶𝐶𝐶𝐶 𝑥𝑥 𝑆𝑆 2.95 (0.00 ≤ 𝑥𝑥 ≤ 0.15) sensors found in our previously study [START_REF] Smiy | Correlation between structural, magnetic and gas sensor properties of La 0.885 Pb 0.005 Ca 0.11 Fe 1-x Co x O 3 compounds[END_REF]. But in these works, perovskite materials are used in pellets forms. In this context, in our recent article, the substitution of Fe by Co and substitute La by Ca and Pb in 𝐿𝐿𝐿𝐿𝐹𝐹𝐹𝐹𝑆𝑆 3 sensor can lead to an increase of the response 𝑆𝑆 and a decrease of the operating temperature for these materials [START_REF] Mizusaki | Non stoichiometry and defect Structure of the perovskite-type oxides 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝑆𝑆𝑆𝑆 𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3-𝛿𝛿[END_REF][START_REF] Smiy | Correlation between structural, magnetic and gas sensor properties of La 0.885 Pb 0.005 Ca 0.11 Fe 1-x Co x O 3 compounds[END_REF][START_REF] Mizusaki | Thermodynamic quantities and defect equilibrium in the perovskite-type oxide solid solution 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3-𝛿𝛿[END_REF][START_REF] Kong | Gas-sensing property and mechanism of 𝐶𝐶𝐿𝐿 𝑥𝑥 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3 ceramics[END_REF][START_REF] Song | The structure, electrical and ethanol-sensing properties of 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝑃𝑃𝑝𝑝 𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3 perovskite ceramics with 𝑥𝑥 ≤ 0.3[END_REF][START_REF] Li | Flexible Room-Temperature NH3 Sensor for Ultrasensitive, Selective, and Humidity-Independent Gas Detection[END_REF][START_REF] Mizusaki | Thermodynamic quantities and defect equilibrium in the perovskite-type oxide solid solution 𝐿𝐿𝐿𝐿 1-𝑥𝑥 𝐹𝐹𝐹𝐹𝑆𝑆 3-𝛿𝛿[END_REF]. The aim of the present work was to develop 𝐿𝐿𝐿𝐿 0.8 𝑃𝑃𝑝𝑝 0.1 𝐶𝐶𝐿𝐿 0.1 𝐹𝐹𝐹𝐹 1-𝑥𝑥 𝐶𝐶𝐶𝐶 𝑥𝑥 𝑆𝑆 3 films (𝑥𝑥 = 0.10 and 𝑥𝑥 = 0.20) by drop-coating method based on the use of nano-powders synthesized by the sol-gel technic. Also, in this work, the 𝑆𝑆 3 sensing properties of our sensors as a function of films thickness are investigated.

II-EXPERIMENTAL DETAILS

II-1) Elaboration of nano-powders and thin films deposition

A series of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) samples have been prepared using the sol-gel technic with La(NO

3 ) 3 6H 2 O, Pb(NO 3 ) 2 2H 2 O, Ca(NO 3 ) 2 6H 2 O, Fe(NO 3 )9H 2 O and Co(NO 3 ) 2 6H 2 O
as precursors (all chemicals were of 99.99% purity and purchased from Sigma-Aldrich). Firstly, precursors have been dissolved in distilled water to obtain a mixed solution. Citric acid 𝐶𝐶 6 𝑊𝑊 8 𝑆𝑆 7 and few drops of ethylene glycol have been added when these nitrates are completely dissolved in order to ensure homogenization and gel formation (the ratio amount of citric acid/ethylene glycol was 1:4). The obtained powders are sintered respectively at 300 °C (24 h), 600 °C (24 h) and 900 °C (24 h) to obtain the corresponding phase. Finally, the structure of the prepared compounds has been characterized by X-ray diffraction using 𝐶𝐶𝐶𝐶𝐶𝐶 𝛼𝛼 radiation �𝜆𝜆 = 1.5406 Å�. The thin films deposition of the prepared compounds has been performed on 𝑆𝑆𝑆𝑆/𝑆𝑆𝑆𝑆𝑆𝑆 2 substrate by the drop-coating technique. A mixture of 20 mg and 20 ml of 2-propanol has been prepared for each compound. The suspensions have been ultrasonicated for 10 𝑚𝑚𝑆𝑆𝑍𝑍 at 40 °𝐶𝐶 in order to ensure homogenization for the mixture. The coating of 𝑆𝑆𝑆𝑆/𝑆𝑆𝑆𝑆𝑆𝑆 2 substrate with inter-digitated 𝑃𝑃𝑃𝑃-electrodes, has been carried out drop by drop using a micropipette. Two thin films have been obtained after the deposition of 8 and 16 drops which correspond to 20 µl and 40 µl, respectively. The deposition of thin films was followed by an annealing for 1 h at 500 °C.

II-2) Gas sensitivity measurements

We investigated the 𝑆𝑆 3 sensing properties of our La0.8Pb0.1Ca0.1Fe1-xCoxO3 material for two film thicknesses 300 nm (8 drops) and 600 nm (16 drops) for x = 0.00 and x = 0.20. Sensors have been placed in a test chamber which allowed the control of the temperature under variable 𝑆𝑆 3 concentrations (𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲 𝟏𝟏). The volume of the chamber is about 2 liters. Dry air has been used as a reference gas.

Ozone gas has been generated by oxidizing a part of oxygen in the dry air using a pen-ray UV lamp (Stable Ozone Generator UVP/185 𝑍𝑍𝑚𝑚). The different ozone concentrations have been obtained by partially masking the UV lamp whose range is between 30 𝑝𝑝𝑝𝑝𝑝𝑝 and 800 𝑝𝑝𝑝𝑝𝑝𝑝 with a dry air flow rate maintained at 0.5 ℓ / 𝑚𝑚𝑆𝑆𝑍𝑍. An ozone analyzer (reference Seres 2000G), has been used to calibrate and verify the correct ozone concentrations during the tests. The operating temperature of La0.8Pb0.1Ca0.1Fe1-xCoxO3 based sensors has been adjusted between 160 °C and 280 °C in order to optimize the sensor response. The sensor bias voltage has been fixed to 1 V and the current is measured using a keithley 4250 sourcemeter. The response 𝑆𝑆 is defined as:

𝑆𝑆 = 𝑅𝑅 𝑎𝑎 𝑅𝑅 𝑔𝑔 (𝑬𝑬𝑬𝑬. 𝟏𝟏)
Where 𝑅𝑅 𝑎𝑎 is the sensor resistance under dry air and 𝑅𝑅 𝑔𝑔 the sensor resistance under ozone with dry air. sensors.

III-RESULTS AND DISCUSSION

III-1) 𝑿𝑿𝑿𝑿𝑿𝑿and EDX studies

The grain size was determined by using the Scherrer method [35]:

𝑋𝑋 𝑆𝑆𝑆𝑆 = 𝑘𝑘 × λ β cos θ (𝑬𝑬𝑬𝑬. 𝟐𝟐)
Where k is the grain form factor (𝑘𝑘 = 0.9), 𝜆𝜆 = 1.5406 Å represents the wavelength, 𝜃𝜃 defines the Bragg angle for the most intense peak and β is the full width at half maximum of the most intense peak.

The calculated value of the crystallite size (𝑋𝑋 𝑆𝑆𝑆𝑆 ) was found equal to 43. Film's thickness has been measured after annealing using a DEKTAK 6M mechanical profilometer. The average film thickness was found to be equal to 300 nm and 600nm for coating process with 8 and 16 drops, respectively (𝑻𝑻𝒂𝒂𝒃𝒃𝑻𝑻𝑲𝑲 𝟏𝟏). As it is known, each sensor can be characterized by its optimal operating temperature (𝑇𝑇 𝑂𝑂 ) because the temperature has a significant effect on the gas response. The response and recovery times have been investigated, and the results have been illustrated in 𝑻𝑻𝒂𝒂𝒃𝒃𝑻𝑻𝑲𝑲 𝟒𝟒. The response time is the time needed to reach 90% of the final steady state signal and the recovery time (return time) was defined as the time needed to reach 10% of the final

Figure 1 :

 1 Figure 1: General diagram of measurements setup used to characterize ozone microsensors.

  In order to check the crystallinity of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) nanopowders, a Bragg (θ-2θ) X-ray diffraction (𝑋𝑋𝑅𝑅𝑋𝑋) has been applied, CuKα radiation (𝜆𝜆 = 1.5406 Å) and 0.02 angle step have been used for the 𝑋𝑋𝑅𝑅𝑋𝑋 analysis. The analysis of 𝑋𝑋𝑅𝑅𝑋𝑋 patterns (𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲 𝟐𝟐) proves that the prepared samples crystalize in the orthorhombic system with Pnma group [19].

Figure 2 :

 2 Figure 2: X-ray diffraction patterns of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) compounds, all peaks are indexed in the orthorhombic 𝑃𝑃𝑍𝑍𝑚𝑚𝐿𝐿 symmetry.

Figure 3 (Figure 3 (

 33 Figure 3(𝒂𝒂, 𝒃𝒃): Energy dispersive spectra (𝐸𝐸𝑋𝑋𝑋𝑋) of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 (a) and x = 0.20 (b)) sensors.

4 III- 2 )d

 42 𝑍𝑍𝑚𝑚 and 43.2 𝑍𝑍𝑚𝑚 for 𝑥𝑥 = 0.10 and 𝑥𝑥 = 0.20, respectively. The obtained values are comparable to those found for other compounds considered as nanometric materials for gas-sensing application [36, 37]. Moreover, it is reported that nanometric materials present significant activity and consequently, facilitate the chemisorption of oxygen of these compounds [38]. Finally, it is worth to mention that the incorporation of the Co ion in place of Iron leads to the decrease of the crystallite size value. Dependence between film thickness and ozone sensing properties of 𝐋𝐋𝐁𝐁 𝟎𝟎.𝟖𝟖 𝐏𝐏𝐏𝐏 𝟎𝟎.𝟏𝟏 𝐂𝐂𝐁𝐁 𝟎𝟎.𝟏𝟏 𝐅𝐅𝐁𝐁 𝟏𝟏-𝒙𝒙 𝐂𝐂𝐂𝐂 𝒙𝒙 𝐎𝐎 𝟑𝟑 (𝒙𝒙 = 𝟎𝟎. 𝟏𝟏𝟎𝟎, 𝒙𝒙 = 𝟎𝟎. 𝟐𝟐𝟎𝟎) sensors c The deposition of 𝐿𝐿𝐿𝐿 0.8 𝑃𝑃𝑝𝑝 0.1 𝐶𝐶𝐿𝐿 0.1 𝐹𝐹𝐹𝐹 1-𝑥𝑥 𝐶𝐶𝐶𝐶 𝑥𝑥 𝑆𝑆 3 (𝑥𝑥 = 0.10 and 𝑥𝑥 = 0.20) nano powders over the Si/SiO2 substrate has been checked by optical microscope analysis. The results depicted in 𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲. 𝟒𝟒, show the optical views of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) compounds after deposition of 8 and 16 drops.

Figure 4 :

 4 Figure 4: Optical view of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) sensors after deposit of 8 and 16 drops.

Figure 5 :

 5 Figure 5: Ozone gas response of La 0.8 Pb 0.1 Ca 0.1 Fe 0.9 Co 0.1 O 3 ( 𝑥𝑥 = 0.10) sensor as a function of time at several temperatures (190, 210, 230 and 260 °𝐶𝐶) for a thickness film equal to 300 𝑍𝑍𝑚𝑚 (8 drops) and 600 𝑍𝑍𝑚𝑚 (16 drops) for an exposure time equal to 1 𝑚𝑚𝑆𝑆𝑍𝑍 (𝑪𝑪 = 𝟏𝟏𝟎𝟎𝟎𝟎 𝒑𝒑𝒑𝒑𝒃𝒃).

Figure 6 :

 6 Figure 6: Ozone gas response of La 0.8 Pb 0.1 Ca 0.1 Fe 0.8 Co 0.2 O 3 ( 𝑥𝑥 = 0.20) sensor as a function of time at several temperatures (170, 210, 230 and 260 °𝐶𝐶) for a thickness film equal to 300 𝑍𝑍𝑚𝑚 (8 drops) and 600 𝑍𝑍𝑚𝑚 (16 drops) for an exposure time equal to 1 𝑚𝑚𝑆𝑆𝑍𝑍 (𝐶𝐶 = 100 𝑝𝑝𝑝𝑝𝑝𝑝).

Furthermore, the

  response (𝑆𝑆) of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) sensors for thickness films equal to 300 𝑍𝑍𝑚𝑚 and 600 𝑍𝑍𝑚𝑚 for an exposure time equal to 1𝑚𝑚𝑆𝑆𝑍𝑍 has been performed. The decrease of the resistance when sensors are exposed to 𝑆𝑆 3 gas, which is an oxidizing gas, indicates the p-type semiconductor behaviour of the studied sensors[START_REF] Bejaoui | Theoretical and experimental study of the response of CuO gas sensor under ozone[END_REF]. The responses obtained with the thickness 300 𝑍𝑍𝑚𝑚 are higher than those found with a thickness of 600 𝑍𝑍𝑚𝑚. In fact, when the thickness of the film increases, the electrodes are buried[START_REF] Li | Flexible Room-Temperature NH3 Sensor for Ultrasensitive, Selective, and Humidity-Independent Gas Detection[END_REF]. Then, the oxygen species are trapped at the top of the La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) film, which reduces the diffusion in the part between the electrodes, inducing the response decrease. On the other hand, the result show that for 𝑥𝑥 = 0.10 and at 𝑇𝑇 = 210, 230 and 260 °𝐶𝐶, the 𝑅𝑅(𝑃𝑃) curve does not return to the baseline. This variation depends on the amount of oxygen adsorbed on the surface because the electron trapped by the oxygen at the surface from the semiconductor decreases the resistance by increasing the major charge carrier (ℎ𝐶𝐶𝑘𝑘𝐹𝐹) concentration[START_REF] Bejaoui | Theoretical and experimental study of the response of CuO gas sensor under ozone[END_REF]. However, for a temperature equal to 190 °𝐶𝐶, we observe the presence of some stability of 𝑅𝑅(𝑃𝑃) curve. So, we can predict that the operating temperature is expected to be equal to 190 °𝐶𝐶 for 𝑥𝑥 = 0.10 sensor and this temperature decreases to 170 °𝐶𝐶 for 𝐿𝐿𝐿𝐿 0.8 𝑃𝑃𝑝𝑝 0.1 𝐶𝐶𝐿𝐿 0.1 𝐹𝐹𝐹𝐹 0.8 𝐶𝐶𝐶𝐶 0.2 𝑆𝑆 3 sensor.

Figure. 7

 7 Figure. 7 summarizes the ozone response (𝑆𝑆) values of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) with a thickness film equal to 300 𝑍𝑍𝑚𝑚 and 600 𝑍𝑍𝑚𝑚 per each sensor in presence of 𝑆𝑆 3 gas when concentration is equal to 100 𝑝𝑝𝑝𝑝𝑝𝑝 at different working temperatures. As it is known, each sensor can be characterized by its optimal operating

Figure 7 :[ 41 ]

 741 Figure 7: The relationship between response �𝑆𝑆 = 𝑅𝑅 𝑎𝑎 𝑅𝑅 𝑔𝑔 ⁄ � and temperature (𝑇𝑇) of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) based sensor during ozone exposing time of 1 𝑚𝑚𝑆𝑆𝑍𝑍 at 100 𝑝𝑝𝑝𝑝𝑝𝑝 concentration as a function of film thickness. 𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲. 𝟕𝟕 reveals that the optimum operating temperatures (𝑇𝑇 𝑂𝑂 ) for our sensors was found to be equal to 190 °𝐶𝐶 and 170 °𝐶𝐶 for 𝑥𝑥 = 0.10 and 0.20, respectively. Lee and reedy [41] have revealed that many factors, as oxygen species, the rates of adsorption and desorption, and the charge carrier concentration, contribute to the sensor response. The activities of the electrons and oxygen species in the sensing reactions depend on the operating temperatures [42]. From 𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲 𝟓𝟓, we can note that the 𝑆𝑆 values increase not only by decreasing filmthickness, but also by increasing cobalt rate [43]. To further investigate the attitude of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) sensors to detect various ozone concentrations levels, the sensitivity of the prepared sensors in presence of different concentration of ozone gas for an exposure time equal to 4 min were investigated and the results are shown in 𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲 𝟖𝟖 ( 𝑥𝑥 = 0.10 ) and 𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲 𝟗𝟗 ( 𝑥𝑥 = 0.20). The results show that curves present partial reversibility to the base line of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) sensors towards 50, 100, 200, 300, and 400 𝑝𝑝𝑝𝑝𝑝𝑝 at the operating temperature.

Figure 8 :

 8 Figure 8: La 0.8 Pb 0.1 Ca 0.1 Fe 0.9 Co 0.1 O 3 ( 𝑥𝑥 = 0.10) sensor response (𝑆𝑆) to different oxidizing gas (𝑆𝑆 3 ) concentrations (50, 100, 200, 300 𝐿𝐿𝑍𝑍𝑎𝑎 400 𝑝𝑝𝑝𝑝𝑝𝑝) for a film thickness equal to 300 𝑍𝑍𝑚𝑚 (8 drops) and 600 𝑍𝑍𝑚𝑚 (16 drops) at 𝑇𝑇 𝑂𝑂 = 190 °𝐶𝐶 and for an exposure time equal to 4 𝑚𝑚𝑆𝑆𝑍𝑍.

Figure 9 :

 9 Figure 9: La 0.8 Pb 0.1 Ca 0.1 Fe 0.8 Co 0.2 O 3 ( 𝑥𝑥 = 0.20 ) sensor response (𝑆𝑆) to different oxidizing gas (𝑆𝑆 3 ) concentrations (50, 100, 200, 300 and 400 𝑝𝑝𝑝𝑝𝑝𝑝) for a film thickness equal to 300 𝑍𝑍𝑚𝑚 (8 drops) and 600 𝑍𝑍𝑚𝑚 (16 drops) at 𝑇𝑇 𝑂𝑂 = 170 °𝐶𝐶 and for an exposure time equal to 4 𝑚𝑚𝑆𝑆𝑍𝑍.All characteristics of gas sensors, such as signal, response, and recovery times, depend on the gas diffusion effects and the rate of reaction. This phenomenon is demonstrated theoretically, using the model of 𝑆𝑆𝑍𝑍𝑆𝑆 2[START_REF] Smiy | New perovskite compound La 0.885 Pb 0.005 Ca 0.11 FeO 2.95 for gas sensing application[END_REF]. When oxygen species are adsorbed, a depletion layer is formed on the surface of the sensing films.

Figure 10 :

 10 Figure 10: Response (𝑆𝑆 = 𝑅𝑅 𝑎𝑎 /𝑅𝑅 𝑔𝑔 ) vs. 𝑆𝑆 3 concentrations (50, 100, 200, 300 and 400 𝑝𝑝𝑝𝑝𝑝𝑝) at the working temperature (𝑇𝑇 = 190 °𝐶𝐶) for 𝑥𝑥 = 0.10 and (𝑇𝑇 = 170 °𝐶𝐶) for 𝑥𝑥 = 0.20 sensors.

Table 1 :

 1 Mean

				Thickness (𝒏𝒏𝒏𝒏)			Mean	Standard	Error repeatability (%)
								thickness	deviation	= (Standard
		test 1 test 2 test 3 test 4 test 5 test 6	(𝒏𝒏𝒏𝒏)	(𝒏𝒏𝒏𝒏)	deviation/Mean thickness)
	8 drops	288	316	321	302	287	286	300	15,5	5
	16 drops	589	604	609	612	599	588	600	10	1,7

thickness, standard deviation, and repeatability error of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) sensors. After the deposit of our material, measurements of the sensor resistance as a function of time have been carried out at different temperatures and with different La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) film thicknesses (𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑲𝑲𝑲𝑲𝑲𝑲 𝟓𝟓 and 6).

.20, 8 drops x = 0.10, 8 drops x = 0.10, 16 drops x = 0.20, 16 drops

Table 2 :

 2 Response �𝑆𝑆 = 𝑅𝑅 𝑎𝑎 𝑅𝑅 𝑔𝑔 Moreover, the response of the prepared sensors was found higher than the response reported for other metal oxide semiconductor (𝑻𝑻𝒂𝒂𝒃𝒃𝑻𝑻𝑲𝑲. 𝟑𝟑) [45-47], and than other perovskite materials cited as potentials 𝑆𝑆 3 sensing [48].

	𝑪𝑪 (𝒑𝒑𝒑𝒑𝒏𝒏)	𝑺𝑺 (𝟎𝟎. 𝟏𝟏𝟎𝟎) 𝟑𝟑𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏	𝑺𝑺 (𝟎𝟎. 𝟏𝟏𝟎𝟎) 𝟔𝟔𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏	𝑺𝑺 (𝟎𝟎. 𝟐𝟐𝟎𝟎) 𝟑𝟑𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏	𝑺𝑺 (𝟎𝟎. 𝟐𝟐𝟎𝟎) 𝟔𝟔𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏
	𝟎𝟎. 𝟎𝟎𝟓𝟓	1.586	1.264	1.753	1.420
	𝟎𝟎. 𝟏𝟏	2.020	1.407	2.111	1.642
	𝟎𝟎. 𝟐𝟐	2.475	1.523	3.264	1.793
	𝟎𝟎. 𝟑𝟑	2.926	1.690	4.273	2.001
	𝟎𝟎. 𝟒𝟒	3.391	1.716	6.563	2.091

⁄ � of La 0.8 Pb 0.1 Ca 0.1 Fe 1-𝑥𝑥 Co 𝑥𝑥 O 3 (𝑥𝑥 = 0.10 𝐿𝐿𝑍𝑍𝑎𝑎 𝑥𝑥 = 0.20) sensors during an ozone exposing time of 4 𝑚𝑚𝑆𝑆𝑍𝑍 at different gas concentrations as a function of film thickness (300 𝑍𝑍𝑚𝑚 and 600 𝑍𝑍𝑚𝑚).

Table 3 :

 3 Comparison of sensing performances of different sensors for the detection of 𝑆𝑆 3 .

	Sensors	𝑻𝑻 𝑶𝑶 (°𝑪𝑪)	𝑪𝑪(𝒑𝒑𝒑𝒑𝒏𝒏)	𝑿𝑿𝑲𝑲𝑲𝑲𝒑𝒑𝑲𝑲𝒏𝒏𝑲𝑲𝑲𝑲 (𝑺𝑺)	𝑿𝑿𝑲𝑲𝑹𝑹
	𝑺𝑺𝒏𝒏𝑶𝑶 𝟐𝟐	20	0.217	1.6	[45]
	𝑪𝑪𝑭𝑭𝑶𝑶	250	0.6	2.5	[46]
	𝒁𝒁𝒏𝒏 -𝑴𝑴𝑲𝑲𝑺𝑺 𝟐𝟐	25	5	1.8	[47]
	𝑺𝑺𝒏𝒏𝑭𝑭𝑲𝑲 𝟎𝟎.𝟖𝟖 𝑪𝑪𝑲𝑲 𝟎𝟎.𝟐𝟐 𝑶𝑶 𝟑𝟑	200	400	3	[48]

Table 4 :

 4 Response �𝜏𝜏 𝑟𝑟𝑟𝑟𝑔𝑔𝑟𝑟 � and recovery (𝜏𝜏 𝑟𝑟𝑟𝑟𝑟𝑟 ) times of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) sensors for a thicknesses film equal to 300 𝑍𝑍𝑚𝑚 and 600 𝑍𝑍𝑚𝑚 at different concentrations (𝐶𝐶) at the operating temperature for each sensor.

	Sensors	𝑻𝑻 (°𝑪𝑪)	𝑪𝑪 (𝒑𝒑𝒑𝒑𝒃𝒃)	𝝉𝝉 𝑲𝑲𝑲𝑲𝑲𝑲𝒑𝒑 (𝒏𝒏𝑭𝑭𝒏𝒏)	𝝉𝝉 𝑲𝑲𝑲𝑲𝒄𝒄 (𝒏𝒏𝑭𝑭𝒏𝒏)
	𝒙𝒙 = 𝟎𝟎. 𝟏𝟏𝟎𝟎 ∶ 𝟑𝟑𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏	190	50 200 400	3.3 2.2 1.9	10.2 21.2 30.1
	𝒙𝒙 = 𝟎𝟎. 𝟏𝟏𝟎𝟎 ∶ 𝟔𝟔𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏	190	50 200 400	3.5 3.3 3.1	26.1 49.9 58.3
			50	3.5	8.3
	𝒙𝒙 = 𝟎𝟎. 𝟐𝟐𝟎𝟎 ∶ 𝟑𝟑𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏	170	200	2.5	14.1
			400	2.1	41.3
	𝒙𝒙 = 𝟎𝟎. 𝟐𝟐𝟎𝟎 ∶ 𝟔𝟔𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏	170	50 200 400	2.8 2.6 2.3	28.2 44.6 52.4

steady state signal [START_REF] Waser | Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices[END_REF]. In the case of our sensors, the response time �τ 𝑟𝑟𝑟𝑟𝑔𝑔𝑟𝑟 � increases from 1.95 𝑚𝑚𝑆𝑆𝑍𝑍 to 3.12 𝑚𝑚𝑆𝑆𝑍𝑍 for 𝑥𝑥 = 0.10 when concentration is equal to 400 𝑝𝑝𝑝𝑝𝑝𝑝 and when thickness film increases from 300 𝑍𝑍𝑚𝑚 to 600 𝑍𝑍𝑚𝑚.

IV-CONCLUSION

The present work demonstrates the feasibility of the use of La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) films deposited by drop coating, as ozone sensors. La0.8Pb0.1Ca0.1Fe1-xCoxO3 (x = 0.10 and x = 0.20) structural properties revealed the presence of an orthorhombic structure with nanometric grain size. The study of the response �𝑆𝑆 = 𝑅𝑅 𝑔𝑔 /𝑅𝑅 𝑎𝑎 � of our compounds proves the ability of our samples to detect low concentration equal to 50 𝑝𝑝𝑝𝑝𝑝𝑝 (𝑠𝑠𝐶𝐶𝑝𝑝 -𝑝𝑝𝑝𝑝𝑚𝑚) of ozone gas. Responses are more important in case of a thickness film equal to 300 𝑍𝑍𝑚𝑚 compared to those found in case of film thickness of 600 𝑍𝑍𝑚𝑚. The optimal working temperature was found to be equal to 190 ℃ with 𝑥𝑥 = 0.10 and decreases to 170 ℃ for the sample doped with 20% of cobalt.


F Poggiolesi

Grounding and propositional identity: a solution to Wilhelm's inconsistencies

, it can easily be shown that standard conditions for immediate partial grounding and relevant identity conditions for propositions are inconsistent with one another. This is an unfortunate situation for all grounding enthusiasts; however, by adopting the approach presented by Poggiolesi (2016a,b) which displays a more-fined grained use of negations, it can also be shown that consistency can be restored back.

In the paper Grounding and propositional identity, [START_REF] Wilhelm | Grounding and propositional identity[END_REF] has shown that standard conditions for immediate partial grounding and relevant identity conditions for propositions are inconsistent with one another. This is of course an unfortunate situation for all grounding enthusiasts. In this paper we first diagnose the source of the inconsistencies and then, by adopting the more recent grounding approach proposed by [START_REF] Poggiolesi | On defining the notion of complete and immediate formal grounding[END_REF][START_REF] Poggiolesi | On constructing a logic for the notion of complete and immediate formal grounding[END_REF], we show how to eliminate them.

We focus on a formal language L that contains parentheses (, ), atoms p, q ... and the classical connectives ¬, ∧, ∨, → and ↔. L contains a binary sentence operator ≈ for regimenting claims about ground-propositional identity: intuitively, A ≈ B says that A and B are the same proposition from a grounding perspective. And L contains the sentence operator for regimenting claims about grounding: intuitively, A B stands for A immediately partially grounds B. For the purposes of this paper, we do not allow and ≈ to be in the scope of themselves or each other. As is standard, we assume that ¬, ∧, ∨, →, ↔ obey the usual principles of classical logic, and that A ≈ B obeys the usual principles of identity: in particular, it is reflexive and conforms to a version of Leibniz's law.

We first list the grounding conditions and ground-identity conditions for propositions that [START_REF] Wilhelm | Grounding and propositional identity[END_REF] In addition, we assume that for some atom p (6) p ∧ ¬(p p).

And finally we have, for any propositional formula A, B,

(7) A ∧ B ≈ ¬(¬A ∨ ¬B), (8) A ∨ B ≈ ¬(¬A ∧ ¬B).
Let us illustrate informally how to generate one of the inconsistencies identified by Wilhelm. At the centre is a tension concerning what (4) and ( 5) imply about the relationship between p and ¬¬p. It follows from (4) that ¬¬p is a ground of ¬(¬p∨¬p) and from (1) that p is a ground of p∧p. However, since, by (7), p ∧ p ≈ ¬(¬p ∨ ¬p), it follows from ( 4) or (1) that p ≈ ¬¬p. By contrast, (5) states that p is a ground of ¬¬p. By Leibniz's law, these two conclusions enter into contradiction with the assumption that p does not ground itself, (6). So the inconsistency highlights an equivocation about which 'grounding level' ¬¬p is on, in comparison with p. And any route out of it will have to clearly take a position on this question: is ¬¬p on a level higher than p, as implied by ( 5), or on the same level, as implied by ( 1), ( 4) and ( 7)? The account of grounding developed by [START_REF] Poggiolesi | On defining the notion of complete and immediate formal grounding[END_REF][START_REF] Poggiolesi | On constructing a logic for the notion of complete and immediate formal grounding[END_REF] comes down unequivocally in favor of the former, motivated by the counterintuitive consequences that conditions such as (4) generate. For instance, conditions (4) and ( 7) imply that ¬¬p is a ground of p ∧ p, which is implausible.

Hence, Poggiolesi proposes to replace (4) by the following condition. For any propositional formula A, B, C,

(4 ) A ¬(B ∨ C) if, and only if, ¬(B ∨ C) and A ≈ B * or A ≈ C * ,
where the symbol * is defined in the following way:

Definition 1. For any propositional formula A, A * , is defined as follows:

A * = ¬ n-1 E, if A = ¬ n E and n is odd ¬ n+1 E, if A = ¬ n E and n is even
where the main connective in E is not a negation, n 0 and 0 is taken to be an even number.

Condition (4 ) coincides with (4) in cases such as ¬(p ∨ q), identifying the partial grounds as ¬p or ¬q. However it diverges precisely on cases such as ¬(¬p ∨ ¬q): whereas (4) identifies the partial grounds as ¬¬p or ¬¬q, according to (4 ) the partial grounds are p or q. The grounds identified by (4 ) thus do not enter in conflict with condition (5).

Analogous considerations apply to condition (2), which Poggiolesi replaces by (2 ). For any propositional formula A, B, C

(2 ) A ¬(B ∧ C) if, and only if, A and A ≈ B * or A ≈ C * , (2 ) and ( 4) have shown to be part of a solid logical grounding system1 and to be philosophically well-founded.2 As we shall show, they are necessary conditions for the consistency result.

Note that ( 7) and ( 8) suffer from similar issues to (2) and ( 4). In a grounding framework, what counts for two propositions to be identical is not just that they have the same truth values, but also that they have the same grounds. However, A ∧ B and ¬(¬A ∨ ¬B) do not necessarily have the same grounds, and similarly for A ∨ B and ¬(¬A ∧ ¬B). For instance, taking A = ¬p and B = ¬q (for atoms p and q), A ∧ B = ¬p ∧ ¬q has grounds ¬p or ¬q (by ( 1)), but ¬(¬A ∨ ¬B) = ¬(¬¬p ∨ ¬¬q) has grounds ¬¬¬p or ¬¬¬q (according to both (4) and ( 4) ). The following conditions provide an adequate alternative. For any propositional formula A, B,

(7 ) A ∧ B ≈ (A * ∨ B * ) * , (8 ) A ∨ B ≈ (A * ∧ B * ) * .
Finally, under Poggiolesi's approach, the number of consecutive negations occurring before a formula plays an important role, as is clear from the use of * in the place of negation in conditions ( 2), ( 4), ( 7), ( 8). For this reason, Leibniz's law should be applied to formulas written in terms of * rather than straightforwardly in terms of negations. For an occurrence of a formula A in the formula C, let C[(¬) m A] denote that it occurs in the immediate scope of precisely m negations (with m ≥ 0).3 Note that, by Definition 1, (¬) m A is either identical to (¬) 2n A for some n, or it is identical to (¬) 2n A * for some n. However, for any B such that A ≈ B, substituting B for A in C[(¬) m A] does not always yield the same proposition (up to ≈) as substituting B for A in the corresponding

C[(¬) 2n A] or C[(¬) 2n A * ].
For instance, with A = p ∧ q for propositional atoms p and q, and C = ¬A = ¬(p ∧ q), substituting ¬(¬p ∨ ¬q) = B ≈ A for A in ¬A yields ¬¬(¬p∨¬q). By contrast, C = ¬A = ¬(p∧q) = A * , so substituting B for A here yields B * = ¬p ∨ ¬q. Since ¬p and ¬q are immediate partial grounds for both C = ¬(p∧q) and ¬p∨¬q (by ( 2) and (3)), but not of ¬¬(¬p∨¬q) (by ( 5)), it is clear that the latter substitution, but not the former, is the relevant one for Leibniz's law in a grounding context. Here we thus understand Leibniz's law to apply to the reformulation of formulas in terms of pairs of negations (¬) 2n and * . With these elements in place, we now show that Poggiolesi's approach supports a consistent account of grounding and propositional identity.

Theorem 2. Conditions (1), ( 2), (3), (4 ), ( 5), ( 6), ( 7), (8 ) are jointly consistent.

Proof. In order to show that conditions (1), ( 2), ( 3), ( 4), ( 5), ( 6), ( 7), ( 8) are jointly consistent, we will construct a classical interpretation4 mapping the formulas of L to the truth values T and F under which every condition is satisfied.

To this end, we first define several relations between propositional formulas (i.e. formulas not containing or ≈). The relation ∼ = is defined as follows. For any propositional formula A and B, A ∼ = B if, and only if, B is the formula A itself or it is A * . The relation .

= is defined to be the closure of ∼ = under conditions ( 7) and ( 8), according to the reformulation of formulas in terms of pairs of negations (¬) 2n and * discussed above. For any propositional formula A and B, we say that A is an immediate g-subformula of B if, and only if, one of the following holds: It is easy to check that conditions (1), ( 2), (3), (4 ), ( 5), ( 7) and ( 8) are satisfied by this interpretation. Moreover, ( 6) is satisfied for the atom p, and the relevant form of Leibniz's law holds. Since an inconsistency would contradict the classical interpretation of negation, it follows that (1), ( 2), (3), ( 4), ( 5), ( 6), ( 7) and ( 8) are jointly consistent.

  • D) and A . = C or A . = D.We use S(A) to denote the set of all immediate g-subformulas of the propositional formula A. Finally, we use |= to denote the classical consequence relation (over propositional formulas).Let us now define an interpretation I. We begin with an arbitrary assignment of truth values to atoms such that there is some atom p with I(p) = T . The propositional connectives are interpreted classically, with I(¬A) = T iff I(A) = F and so on. The partial grounding and propositional identity connectives and ≈ are treated by I as follows. For any propositional formula A, B,I(A B) = T if, and only if the following three conditions are satisfied: (i) A ∈ S(B); (ii) I(B) = T if B = C ∧ D or B = ¬(C ∨ D), I(A) = T otherwise; (iii) it holds that: -|= A → B, or -|= ¬A → ¬B. I(A ≈ B) = T , if, and only if, the following two conditions are satisfied: (iv) |= A ↔ B, and (v) S(A) = S(B).

See Poggiolesi (2018).

See Poggiolesi (2016a,b).

So the next connective applied to (¬) m A in C, if there is one, is not a negation.

We follow[START_REF] Poggiolesi | A proof-theoretical framework for several types of grounding[END_REF] for constructing such interpretation.