A deep analysis of conductance in nanostructured SnO2 thick films has been performed. A model for field-assisted thermionic barrier crossing is being proposed to explain the film conductivity. Themodel has been applied to explain the behavior of resistance in vacuum of two sets of nanostructured thick-films with grains having two well-distinct characteristic radii (R = 25nm and R = 125 nm). In the first case the grain radius is shorter than the depletion region width, a limit at which overlapping of barriers takes place, and in the second case it is longer. The behavior of resistance in the presence of dry air has been explained through the mechanism of barrier modulation through gas chemisorption.Fil: Malagú, C.. Universita Di Ferrara; ItaliaFil: Carotta, M. Cristina. Universita Di Ferrara; ItaliaFil: Martinelli, Giuliano. Universita Di Ferrara; ItaliaFil: Ponce, Miguel Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; ArgentinaFil: Castro, Miriam Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; ArgentinaFil: Aldao, Celso Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; Argentin

Aldao, Celso Manuel

Carotta, M. Cristina

Castro, Miriam Susana

Malagú, C.

Martinelli, Giuliano

Ponce, Miguel Adolfo

Journal of Sensors

English

LAReferencia - Red Federada de Repositorios Institucionales de Publicaciones Científicas Latinoamericanas

Hindawi Publishing CorporationJournal of SensorsVolume 2009, Article ID 402527, 5 pagesdoi:10.1155/2009/402527Research ArticleField-Assisted and Thermionic Contributions toConductance in SnO2 Thick-FilmsC. Malagù,1 M. C. Carotta,1 G. Martinelli,1 M. A. Ponce,2 M. S. Castro,2 and C. M. Aldao21 Department of Physics, University of Ferrara, Via Saragat 1/C, 44100 Ferrara, Italy2 Institute of Materials Science and Technology (INTEMA), National University of Mar del Plata, CONICET, Juan B. Justo 4302,B7608FDQ Mar del Plata, ArgentinaCorrespondence should be addressed to C. Malagù, malagu@fe.infn.itReceived 27 January 2009; Revised 27 May 2009; Accepted 23 June 2009Recommended by Giorgio SberveglieriA deep analysis of conductance in nanostructured SnO2 thick films has been performed. A model for field-assisted thermionicbarrier crossing is being proposed to explain the film conductivity. The model has been applied to explain the behavior of resistancein vacuum of two sets of nanostructured thick-films with grains having two well-distinct characteristic radii (R = 25 nm andR = 125 nm). In the first case the grain radius is shorter than the depletion region width, a limit at which overlapping of barrierstakes place, and in the second case it is longer. The behavior of resistance in the presence of dry air has been explained through themechanism of barrier modulation through gas chemisorption.Copyright © 2009 C. Malagù et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.1. IntroductionIn the last two decades, gas sensors based on SnO2 thick filmsbecame the dominant solid state devices for the gas detectionin domestic, commercial, and industrial alarms [1, 2]. Itis widely accepted that, when oxygen chemisorbs, electronstransfer from the bulk to the surface of the grain modifyingthe barriers at the grain boundaries [3]. In particular,after oxygen chemisorption, the barrier height, Vs, and thedepletion width, Λ, become larger and, as a consequence,the sample resistance increases. Different factors (such astype of defects, morphology, and additives) contribute to theelectrical response of the gas sensor [4, 5].The film resistivity (or conductivity) is broadly usedto characterize a sensor, and the widely acknowledgedphenomenological equation [2, 6, 7] isρ = ρoExp(eVskT), (1)where ρo is the bulk resistivity, k the Boltzmann constant, andT the absolute temperature.In this work, the resistance of undoped SnO2 thick-film gas sensors is analyzed as a function of temperaturein vacuum and in dry air atmosphere. In order to explainthe results, thermionic and tunneling contributions to theelectrical conduction have been considered.2. ExperimentalCommercial high-purity SnO2 (Aldrich, medium particlesize 0.4 μm) was ground until a medium particle size of0.1 μm (labeled powders P1). A calcination process carriedout at 1100◦C for 2 hours led to powders with larger particlesize (labeled powders P2). Then, a paste was prepared withan organic binder (glycerol) and the powders P1 and P2. Theused solid/organic binder ratio was 1/2. No dopants wereadded.Thick, porous film samples were made by painting ontoinsulating alumina substrate on which electrodes with aninterdigit shape have been deposited by sputtering. Finally,samples were thermally treated for 2 hours in air at 500◦C.Samples were labeled S1 (small particle size) and S2 (largeparticle size). The thickness of the films was measured with aSurtronic 3+ (Taylor Hobson) profilometer with a diamondstylus (radius: 1 μm). To image the tin oxide surfaces aJEOL JSM 6700F SEM was employed. The X-ray data werecollected with a Siemens D-500 difractometer using CuKαradiation.2 Journal of SensorsDynamical resistance curves were measured while chang-ing the vacuum into air flux and, after having reachedquasisaturation, changing the dry air flux back into vacuum(10−4 mmHg). In temperature cycling experiments, resis-tance was measured while raising and then decreasing thetemperature from room temperature up to 420◦C at a rateof ∼2◦C/min with the sample kept in air (40 mmHg).3. ModellingTo model the resistance of the two sets of sensors, a field-assisted mechanism for barrier crossing is proposed (see [8]).We applied the WKB approximation to a double parabolicbarrier of the following form:V(r) =⎧⎪⎪⎨⎪⎪⎩VsΛ2(r +Λ)2, −Λ ≤ r ≤ 0,VsΛ2(r −Λ)2, 0 ≤ r ≤ Λ.(2)The tunnelling and thermionic contributions to the currentdensity, with respect to the flat band case, were calculatedfollowing the classical work of Crowell and Rideout for asingle parabolic barrier [9]. The whole calculation resultedin a factor two in the exponent of the tunneling partof [9, equation (13)]. Thus, we found for the tunnelingcontribution, here called I1, and for the thermionic one, herecalled I2, respectively,I1 = eVskT∫ 10Exp{−eVskT[α +2kTy(α)E00]}dα,I2 = Exp(−eVskT),(3)wherey(α) = (1− α)0.5 − αLn[1 + (1− α)0.5α0.5],α = EeVs,E00 = eh4π(Ndm∗ ε)1/2,(4)with E being the energy of an electron in the conductionband. From numerical solutions of (3) it turns out that therelative tunneling emission with respect to the thermionicone (I1/I2) is an increasing function of E00/kT ratio. For agiven material, E00 is fixed; thus the tunneling contribution ismore effective at lower temperatures. Moreover the solutionof (3) at a fixed temperature shows, as discussed in [8] (ourfactor two does not alter the trend), that the lower the barrierthe more important the relative thermionic contributionwith respect to the field assisted one. This phenomenongives an explanation to the experimental evidence presentedbelow.4. Results and DiscussionIn Figures 1(a) and 1(b), SEM micrographs of the samplesS1 and S2 are shown. Both samples present homogeneous200 nm Mag = 150 kX EHT = 3 kV WD = 1mm Signal = 1 Signal B = InLens Signal A = InLens(a)200 nm Mag = 80 kX EHT = 4.99 kV WD = 3mm Signal = 1 Signal B = InLens Signal A = InLens(b)Figure 1: (a) SEM micrograph for a sample labeled S1 (R < Λ). (b)SEM micrograph for a sample labeled S2 (R > Λ).microstructures. From SEM micrographs a significant differ-ence in the microstructures of S1 and S2 is observed. Thesamples showed the presence of agglomerates, but samplesmade with larger particle size (S2) showed a highly porousmicrostructure with the presence of some cracks (not shownin this figure). The average particle radius of samples labeledS1 was determined to be 25 nm, while for samples labeled S2it was determined to be 125 nm. The mean thickness of thefilms determined by the profilometer was 100 μm for samplesS1 and 440 μm for samples S2.Since SEM imager for sample S1 is not clear enough toprovide reliable grain size determination, we have performedX-Ray Diffraction (XRD) on this sample for comparison.From XRD, the film is found to be composed of SnO2with a high degree of crystalline. In Figure 2, the peakcorresponding to the (211) plane is showed. The grain sizesof the samples were calculated following Scherrer’s law [10]:t = 0, 9 · λB · cos(θB), (5)where t is the SnO2 particle size; λ is the wavelength (Co =1.788 Å); B is the angular width (in terms of 2θB) measured inradians that corresponds to the full width at half-maximum;θB is the value of the angle of the peak of the highestintensity. Through this equation, a particle size, t, of 41 nmJournal of Sensors 30200400600800100012001400160018002000Intensity30 30.2 30.4 30.6 30.8 31 31.2 31.4 31.6 31.8 322θSample 130.97B = 0.264.01× 10−3Figure 2: XRD of sample 1 to compare with SEM measurement.was calculated for sample S1. This result is in agreement withthat found using SEM.Figure 3 shows the electrical response (resistance versustime) of the sample with smaller particle size after changingthe vacuum (10−2 mmHg) into air flux (t = 0) and backinto vacuum. In Figure 3, curve A—experiment carried outat 280◦C—after a quick increasing due to air exposure,the electrical resistance is almost constant over a lapse of700 seconds. On the other hand, at the temperature of420◦C (Figure 3, curve B) a diminution in the resistanceafter a quick increase is observed. Figure 4 shows electricalresponses (resistance versus time) of the sample S2 afterchanging the vacuum into air flux (t = 0) and back intovacuum. Curve A shows an electrical response similar tothose observed in sample S1 at the low temperature (Figure 3,curve A). When the temperature is increased at values closeto 420◦C, a slow decreasing in the resistance with exposuretime was registered (Figure 4, curve B). This behavior issimilar to that observed at the high temperature in sample S1for the longest exposition times. However, due to the greaterthickness in sample S2, a slower electrical response withrespect to S1 in the studied temperature range is detected.Resistance versus time curves can be understood byconsidering that intergranular potential barriers are respon-sible for the observed electrical response [11]. The rapidincrease of the resistance, when samples are exposed to air,indicates that equilibrium at the surface is quickly reached.The interaction of oxygen with grain surfaces produces thetransfer of electrons from the bulk to the surface. From thisprocess, Vs and Λ become larger and, as a consequence,the sample resistance increases. The long term changes inthe resistance observed after a quick initial change in theatmosphere can be explained in terms of oxygen in- and out-diffusion [12] that reflects in a slow change of the dopinglevel, Nd.Samples with larger particle size (S2) showed a relativelyslower response than samples with smaller particle size (S1).This result could be explained by considering that samples02468Resistance(KΩ)0 200 400 600 800 1000 1200Time (s)280 ◦C420 ◦CVacuumABAirFigure 3: Dynamical response (resistance versus time) of S1 afterchanging the vacuum into air flux (t = 0) and back into vacuum.(a) T = 280◦C. (b) T = 420◦C.0123×103Resistance(Ω)0 5000 10000Time (s)280 ◦C420 ◦CVacuumABAirFigure 4: Dynamical response (resistance versus time) of S2 afterchanging the vacuum into air flux (t = 0) and back into vacuum.(a) T = 280◦C. (b) T = 420◦C.S2 are thicker than S1. It has long been suggested that theresponse time of a semiconductor gas sensor could be relatedto the reactivity and diffusion of gas molecules inside gassensing layers [13, 14].Regarding the behaviour of resistance in vacuum a moresubtle analysis is required. The values of resistance in vacuumfor the samples S1 and S2 are reported in Table 1 at thetemperatures of 280 and 420◦C, respectively.Samples S2 show a lower resistance than samples S1 atboth temperatures due to the lower number of grains. But itis worth noticing that, whereas at the high temperature thevalue of the resistance is comparable to that of the smaller4 Journal of Sensors−25 250V′sΔEr(nm)R < ΛBarrier(V)Figure 5: R < Λ, the potential is not zero at the centre of the grain.The potential barrier that electrons have to cross is ΔE < eV ′s . V′s isthe distance between the conduction band at surface and the Fermilevel; it holds V ′s < Vs [13].Table 1: Average resistance values in vacuum of samples S1 and S2at the two operating temperatures.S1 (R = 25 nm) S2 (R = 125 nm)280◦C R = 0.565 kΩ R = 0.105 kΩ420◦C R = 0.110 kΩ R = 0.085 kΩgrained sample, at the low temperature the resistance of S1 isfive times larger than that of S2. The case of grains with R < Λ(S1) is sketched in Figure 5. In a previous work [15] we havedemonstrated that the barrier height in vacuum, which wewill call here V ′s , of SnO2 grains with R < Λ is expected to beabout 10% lower than that of grains with R > Λ because ofthe decrease of surface state density.It must be observed that the density of electrons decreasesexponentially with the distance of Ec from EF in the samemanner as the thermionic contribution increases due to thelower barrier. As explained in [8, equation (7)], if we callΔE the barrier height and eV ′s the distance between Ec andEF , then the Fermi level is eV ′s − ΔE below the bottom ofthe conduction band. The carrier density is then reducedby a factor Exp[−(eV ′s − ΔE)/kT]. Consequently the totalthermionic contribution to conductance is proportional toExp[−(eV ′s −ΔE)/kT]×Exp(−ΔE/kT), where the first termis the change in carrier density and the second one is theprobability of barrier crossing. This product gives exactlyExp[−eV ′skT]= Exp[−Ec − EFkT]. (6)Therefore, if we do not invoke tunnelling, it is necessaryfor a semiconductor with lower distance between Ec andEF to exhibit higher conductivity, which is contradicted byexperimental evidence.If the mechanism of barrier crossing were purelythermionic, the smaller grains would show less resistivityat every temperature, being the resistivity an exponentialfunction of the barrier height; see (6). At the highertemperature, the number of electrical active grains, of thesamples S2, competes with its higher resistivity making theresistance of the two samples almost equal, R(S1) = 1.3R(S2).Instead, at 280◦C where the tunneling contribution (I1) isdominant with respect to the thermionic (I2) because atlower temperature E00 ∼= kT , the effect of grain size iscrucial. In the case of small grains, the actual barrier to becrossed, E, is much lower than that of the larger grains,and, in the case of lower barrier, the relative tunnelingcontribution is reduced with respect to the thermionic one.In fact, at R = 25 nm the overlapping of potential barrierstakes place, see Figure 5, and ΔE < V ′s < Vs. Therefore alarger resistance for smaller grains is to be expected at thelower temperature. If instead the phenomenon were purelydetermined by thermionic emission, the barrier lowering ofsmall grains could not produce different effects at differenttemperatures, the effect being only that of reducing theresistance of the small grains with respect to that of largeones. It would not then be possible to explain why R(S1) =5.4R(S2) at 280◦C.5. ConclusionsThe resistance behavior of the two samples in oxygen hasbeen explained in terms of barrier variations due to surfacereactions. In the case of vacuum, to explain the greaterresistance (Table 1) of small grains with respect to largerones, in spite of the fact that the barrier of the latter ishigher, it is necessary to invoke tunneling. It turns outthat the relative tunneling contribution in the case of smallgrains is smaller because intergranular barriers are lower asa consequence of the lift of the potential at the centre of thegrain.Therefore, if the sensors are working at temperatures atwhich the tunneling crossing is dominant with respect tothermionic, it is possible that the decrease of the formercontribution results in a very big increase in resistance forsamples with a grain radius smaller than depletion width.This evidence could not be taken into account by barethermionic emission.AcknowledgmentThis work has been possible thanks to the project ofScientific Cooperation between CNR (Italy) and CONICET(Argentina).References[1] W. Göpel and K. D. Schierbaum, “SnO2 sensors: current statusand future prospects,” Sensors and Actuators B, vol. 26, no. 1–3,pp. 1–12, 1995.[2] N. Barsan and U. Weimar, “Conduction model of metal oxidegas sensors,” Journal of Electroceramics, vol. 7, no. 3, pp. 143–167, 2001.[3] G. Gaggiotti, A. Galdikas, S. Kaciulis, G. Mattogno, and A.Setkus, “Surface chemistry of tin oxide based gas sensors,”Journal of Applied Physics, vol. 76, no. 8, pp. 4467–4471, 1994.[4] S. Capone, P. Siciliano, F. Quaranta, R. Rella, M. Epifani, and L.Vasanelli, “Moisture influence and geometry effect of Au andJournal of Sensors 5Pt electrodes on CO sensing response of SnO2 microsensorsbased on sol-gel thin film,” Sensors and Actuators B, vol. 77,no. 1-2, pp. 503–511, 2001.[5] C. Xu, J. Tamaki, N. Miura, and N. Yamazoe, “Grain size effectson gas sensitivity of porous SnO2-based elements,” Sensors andActuators B, vol. 3, no. 2, pp. 147–155, 1991.[6] J. W. Orton and M. J. Powell, “The Hall effect in polycrystallineand powdered semiconductors,” Reports on Progress in Physics,vol. 43, no. 11, pp. 1263–1307, 1980.[7] P. Romppainen and V. Lantto, “The effect of microstructure onthe height of potential energy barriers in porous tin dioxidegas sensors,” Journal of Applied Physics, vol. 63, no. 10, pp.5159–5165, 1988.[8] C. Malagú, G. Martinelli, M. A. Ponce, and C. M. Aldao,“Unpinning of the Fermi level and tunneling in metal oxidesemiconductors,” Applied Physics Letters, vol. 92, no. 16,Article ID 162104, 3 pages, 2008.[9] C. R. Crowell and V. L. Rideout, “Normalized thermionic-field(T-F) emission in metal-semiconductor (Schottky) barriers,”Solid State Electronics, vol. 12, no. 2, pp. 89–105, 1969.[10] B. D. Cullity, “Elements of X-Ray Diffraction,” Addison-Wesley, Reading, Mass, USA, 1978.[11] G. Blaustein, M. S. Castro, and C. M. Aldao, “Influenceof frozen distributions of oxygen vacancies on tin oxideconductance,” Sensors and Actuators B, vol. 55, no. 1, pp. 33–37, 1999.[12] M. A. Ponce, C. Malagu, M. C. Carotta, G. Martinelli, and C.M. Aldao, “Gas indiffusion contribution to impedance in tinoxide thick films,” Journal of Applied Physics, vol. 104, no. 5,Article ID 054907, 5 pages, 2008.[13] G. Sakai, N. S. Baik, N. Miura, and N. Yamazoe, “Gassensing properties of tin oxide thin films fabricated fromhydrothermally treated nanoparticles: dependence of CO andH2 response on film thickness,” Sensors and Actuators B, vol.77, no. 1-2, pp. 116–121, 2001.[14] M. A. Ponce, C. M. Aldao, and M.S . Castro, “Influence ofparticle size on the conductance of SnO2 thick films,” Journalof the European Ceramic Society, vol. 23, no. 12, pp. 2105–2111,2003.[15] T. G. G. Maffeıs, G. T. Owen, C. Malagú, et al., “Directevidence of the dependence of surface state density on thesize of SnO2 nanoparticles observed by scanning tunnellingspectroscopy,” Surface Science, vol. 550, no. 1–3, pp. 21–25,2004.

Field-Assisted and Thermionic Contributions to Conductance in SnO2 Thick-Films

CONICET Digital

Hindawi Publishing CorporationJournal of SensorsVolume 2009, Article ID 402527, 5 pagesdoi:10.1155/2009/402527Research ArticleField-Assisted and Thermionic Contributions toConductance in SnO2 Thick-FilmsC. Malagu`,1 M. C. Carotta,1 G. Martinelli,1 M. A. Ponce,2 M. S. Castro,2 and C. M. Aldao21 Department of Physics, University of Ferrara, Via Saragat 1/C, 44100 Ferrara, Italy2 Institute of Materials Science and Technology (INTEMA), National University of Mar del Plata, CONICET, Juan B. Justo 4302,B7608FDQ Mar del Plata, ArgentinaCorrespondence should be addressed to C. Malagu`, malagu@fe.infn.itReceived 27 January 2009; Revised 27 May 2009; Accepted 23 June 2009Recommended by Giorgio SberveglieriA deep analysis of conductance in nanostructured SnO2 thick films has been performed. A model for field-assisted thermionicbarrier crossing is being proposed to explain the film conductivity. The model has been applied to explain the behavior of resistancein vacuum of two sets of nanostructured thick-films with grains having two well-distinct characteristic radii (R = 25 nm andR = 125 nm). In the first case the grain radius is shorter than the depletion region width, a limit at which overlapping of barrierstakes place, and in the second case it is longer. The behavior of resistance in the presence of dry air has been explained through themechanism of barrier modulation through gas chemisorption.Copyright © 2009 C. Malagu` et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.1. IntroductionIn the last two decades, gas sensors based on SnO2 thick filmsbecame the dominant solid state devices for the gas detectionin domestic, commercial, and industrial alarms [1, 2]. Itis widely accepted that, when oxygen chemisorbs, electronstransfer from the bulk to the surface of the grain modifyingthe barriers at the grain boundaries [3]. In particular,after oxygen chemisorption, the barrier height, Vs, and thedepletion width, Λ, become larger and, as a consequence,the sample resistance increases. Diﬀerent factors (such astype of defects, morphology, and additives) contribute to theelectrical response of the gas sensor [4, 5].The film resistivity (or conductivity) is broadly usedto characterize a sensor, and the widely acknowledgedphenomenological equation [2, 6, 7] isρ = ρoExp(eVskT), (1)where ρo is the bulk resistivity, k the Boltzmann constant, andT the absolute temperature.In this work, the resistance of undoped SnO2 thick-film gas sensors is analyzed as a function of temperaturein vacuum and in dry air atmosphere. In order to explainthe results, thermionic and tunneling contributions to theelectrical conduction have been considered.2. ExperimentalCommercial high-purity SnO2 (Aldrich, medium particlesize 0.4 μm) was ground until a medium particle size of0.1 μm (labeled powders P1). A calcination process carriedout at 1100◦C for 2 hours led to powders with larger particlesize (labeled powders P2). Then, a paste was prepared withan organic binder (glycerol) and the powders P1 and P2. Theused solid/organic binder ratio was 1/2. No dopants wereadded.Thick, porous film samples were made by painting ontoinsulating alumina substrate on which electrodes with aninterdigit shape have been deposited by sputtering. Finally,samples were thermally treated for 2 hours in air at 500◦C.Samples were labeled S1 (small particle size) and S2 (largeparticle size). The thickness of the films was measured with aSurtronic 3+ (Taylor Hobson) profilometer with a diamondstylus (radius: 1 μm). To image the tin oxide surfaces aJEOL JSM 6700F SEM was employed. The X-ray data werecollected with a Siemens D-500 difractometer using CuKαradiation.2 Journal of SensorsDynamical resistance curves were measured while chang-ing the vacuum into air flux and, after having reachedquasisaturation, changing the dry air flux back into vacuum(10−4 mmHg). In temperature cycling experiments, resis-tance was measured while raising and then decreasing thetemperature from room temperature up to 420◦C at a rateof ∼2◦C/min with the sample kept in air (40 mmHg).3. ModellingTo model the resistance of the two sets of sensors, a field-assisted mechanism for barrier crossing is proposed (see [8]).We applied the WKB approximation to a double parabolicbarrier of the following form:V(r) =⎧⎪⎪⎨⎪⎪⎩VsΛ2(r + Λ)2, −Λ ≤ r ≤ 0,VsΛ2(r −Λ)2, 0 ≤ r ≤ Λ.(2)The tunnelling and thermionic contributions to the currentdensity, with respect to the flat band case, were calculatedfollowing the classical work of Crowell and Rideout for asingle parabolic barrier [9]. The whole calculation resultedin a factor two in the exponent of the tunneling partof [9, equation (13)]. Thus, we found for the tunnelingcontribution, here called I1, and for the thermionic one, herecalled I2, respectively,I1 = eVskT∫ 10Exp{−eVskT[α +2kTy(α)E00]}dα,I2 = Exp(−eVskT),(3)wherey(α) = (1− α)0.5 − αLn[1 + (1− α)0.5α0.5],α = EeVs,E00 = eh4π(Ndm∗ ε)1/2,(4)with E being the energy of an electron in the conductionband. From numerical solutions of (3) it turns out that therelative tunneling emission with respect to the thermionicone (I1/I2) is an increasing function of E00/kT ratio. For agiven material, E00 is fixed; thus the tunneling contribution ismore eﬀective at lower temperatures. Moreover the solutionof (3) at a fixed temperature shows, as discussed in [8] (ourfactor two does not alter the trend), that the lower the barrierthe more important the relative thermionic contributionwith respect to the field assisted one. This phenomenongives an explanation to the experimental evidence presentedbelow.4. Results and DiscussionIn Figures 1(a) and 1(b), SEM micrographs of the samplesS1 and S2 are shown. Both samples present homogeneous200 nm Mag = 150 kX EHT = 3 kV WD = 1mm Signal = 1 Signal B = InLens Signal A = InLens(a)200 nm Mag = 80 kX EHT = 4.99 kV WD = 3mm Signal = 1 Signal B = InLens Signal A = InLens(b)Figure 1: (a) SEM micrograph for a sample labeled S1 (R < Λ). (b)SEM micrograph for a sample labeled S2 (R > Λ).microstructures. From SEM micrographs a significant diﬀer-ence in the microstructures of S1 and S2 is observed. Thesamples showed the presence of agglomerates, but samplesmade with larger particle size (S2) showed a highly porousmicrostructure with the presence of some cracks (not shownin this figure). The average particle radius of samples labeledS1 was determined to be 25 nm, while for samples labeled S2it was determined to be 125 nm. The mean thickness of thefilms determined by the profilometer was 100 μm for samplesS1 and 440 μm for samples S2.Since SEM imager for sample S1 is not clear enough toprovide reliable grain size determination, we have performedX-Ray Diﬀraction (XRD) on this sample for comparison.From XRD, the film is found to be composed of SnO2with a high degree of crystalline. In Figure 2, the peakcorresponding to the (211) plane is showed. The grain sizesof the samples were calculated following Scherrer’s law [10]:t = 0, 9 · λB · cos(θB) , (5)where t is the SnO2 particle size; λ is the wavelength (Co =1.788 A˚); B is the angular width (in terms of 2θB) measured inradians that corresponds to the full width at half-maximum;θB is the value of the angle of the peak of the highestintensity. Through this equation, a particle size, t, of 41 nmJournal of Sensors 30200400600800100012001400160018002000Intensity30 30.2 30.4 30.6 30.8 31 31.2 31.4 31.6 31.8 322θSample 130.97B = 0.264.01× 10−3Figure 2: XRD of sample 1 to compare with SEM measurement.was calculated for sample S1. This result is in agreement withthat found using SEM.Figure 3 shows the electrical response (resistance versustime) of the sample with smaller particle size after changingthe vacuum (10−2 mmHg) into air flux (t = 0) and backinto vacuum. In Figure 3, curve A—experiment carried outat 280◦C—after a quick increasing due to air exposure,the electrical resistance is almost constant over a lapse of700 seconds. On the other hand, at the temperature of420◦C (Figure 3, curve B) a diminution in the resistanceafter a quick increase is observed. Figure 4 shows electricalresponses (resistance versus time) of the sample S2 afterchanging the vacuum into air flux (t = 0) and back intovacuum. Curve A shows an electrical response similar tothose observed in sample S1 at the low temperature (Figure 3,curve A). When the temperature is increased at values closeto 420◦C, a slow decreasing in the resistance with exposuretime was registered (Figure 4, curve B). This behavior issimilar to that observed at the high temperature in sample S1for the longest exposition times. However, due to the greaterthickness in sample S2, a slower electrical response withrespect to S1 in the studied temperature range is detected.Resistance versus time curves can be understood byconsidering that intergranular potential barriers are respon-sible for the observed electrical response [11]. The rapidincrease of the resistance, when samples are exposed to air,indicates that equilibrium at the surface is quickly reached.The interaction of oxygen with grain surfaces produces thetransfer of electrons from the bulk to the surface. From thisprocess, Vs and Λ become larger and, as a consequence,the sample resistance increases. The long term changes inthe resistance observed after a quick initial change in theatmosphere can be explained in terms of oxygen in- and out-diﬀusion [12] that reflects in a slow change of the dopinglevel, Nd.Samples with larger particle size (S2) showed a relativelyslower response than samples with smaller particle size (S1).This result could be explained by considering that samples02468Resistance(KΩ)0 200 400 600 800 1000 1200Time (s)280 ◦C420 ◦CVacuumABAirFigure 3: Dynamical response (resistance versus time) of S1 afterchanging the vacuum into air flux (t = 0) and back into vacuum.(a) T = 280◦C. (b) T = 420◦C.0123×103Resistance(Ω)0 5000 10000Time (s)280 ◦C420 ◦CVacuumABAirFigure 4: Dynamical response (resistance versus time) of S2 afterchanging the vacuum into air flux (t = 0) and back into vacuum.(a) T = 280◦C. (b) T = 420◦C.S2 are thicker than S1. It has long been suggested that theresponse time of a semiconductor gas sensor could be relatedto the reactivity and diﬀusion of gas molecules inside gassensing layers [13, 14].Regarding the behaviour of resistance in vacuum a moresubtle analysis is required. The values of resistance in vacuumfor the samples S1 and S2 are reported in Table 1 at thetemperatures of 280 and 420◦C, respectively.Samples S2 show a lower resistance than samples S1 atboth temperatures due to the lower number of grains. But itis worth noticing that, whereas at the high temperature thevalue of the resistance is comparable to that of the smaller4 Journal of Sensors−25 250V′sΔEr(nm)R < ΛBarrier(V)Figure 5: R < Λ, the potential is not zero at the centre of the grain.The potential barrier that electrons have to cross is ΔE < eV ′s . V′s isthe distance between the conduction band at surface and the Fermilevel; it holds V ′s < Vs [13].Table 1: Average resistance values in vacuum of samples S1 and S2at the two operating temperatures.S1 (R = 25 nm) S2 (R = 125 nm)280◦C R = 0.565 kΩ R = 0.105 kΩ420◦C R = 0.110 kΩ R = 0.085 kΩgrained sample, at the low temperature the resistance of S1 isfive times larger than that of S2. The case of grains with R < Λ(S1) is sketched in Figure 5. In a previous work [15] we havedemonstrated that the barrier height in vacuum, which wewill call here V ′s , of SnO2 grains with R < Λ is expected to beabout 10% lower than that of grains with R > Λ because ofthe decrease of surface state density.It must be observed that the density of electrons decreasesexponentially with the distance of Ec from EF in the samemanner as the thermionic contribution increases due to thelower barrier. As explained in [8, equation (7)], if we callΔE the barrier height and eV ′s the distance between Ec andEF , then the Fermi level is eV ′s − ΔE below the bottom ofthe conduction band. The carrier density is then reducedby a factor Exp[−(eV ′s − ΔE)/kT]. Consequently the totalthermionic contribution to conductance is proportional toExp[−(eV ′s −ΔE)/kT]×Exp(−ΔE/kT), where the first termis the change in carrier density and the second one is theprobability of barrier crossing. This product gives exactlyExp[−eV ′skT]= Exp[−Ec − EFkT]. (6)Therefore, if we do not invoke tunnelling, it is necessaryfor a semiconductor with lower distance between Ec andEF to exhibit higher conductivity, which is contradicted byexperimental evidence.If the mechanism of barrier crossing were purelythermionic, the smaller grains would show less resistivityat every temperature, being the resistivity an exponentialfunction of the barrier height; see (6). At the highertemperature, the number of electrical active grains, of thesamples S2, competes with its higher resistivity making theresistance of the two samples almost equal, R(S1) = 1.3R(S2).Instead, at 280◦C where the tunneling contribution (I1) isdominant with respect to the thermionic (I2) because atlower temperature E00 ∼= kT , the eﬀect of grain size iscrucial. In the case of small grains, the actual barrier to becrossed, E, is much lower than that of the larger grains,and, in the case of lower barrier, the relative tunnelingcontribution is reduced with respect to the thermionic one.In fact, at R = 25 nm the overlapping of potential barrierstakes place, see Figure 5, and ΔE < V ′s < Vs. Therefore alarger resistance for smaller grains is to be expected at thelower temperature. If instead the phenomenon were purelydetermined by thermionic emission, the barrier lowering ofsmall grains could not produce diﬀerent eﬀects at diﬀerenttemperatures, the eﬀect being only that of reducing theresistance of the small grains with respect to that of largeones. It would not then be possible to explain why R(S1) =5.4R(S2) at 280◦C.5. ConclusionsThe resistance behavior of the two samples in oxygen hasbeen explained in terms of barrier variations due to surfacereactions. In the case of vacuum, to explain the greaterresistance (Table 1) of small grains with respect to largerones, in spite of the fact that the barrier of the latter ishigher, it is necessary to invoke tunneling. It turns outthat the relative tunneling contribution in the case of smallgrains is smaller because intergranular barriers are lower asa consequence of the lift of the potential at the centre of thegrain.Therefore, if the sensors are working at temperatures atwhich the tunneling crossing is dominant with respect tothermionic, it is possible that the decrease of the formercontribution results in a very big increase in resistance forsamples with a grain radius smaller than depletion width.This evidence could not be taken into account by barethermionic emission.AcknowledgmentThis work has been possible thanks to the project ofScientific Cooperation between CNR (Italy) and CONICET(Argentina).References[1] W. Go¨pel and K. D. Schierbaum, “SnO2 sensors: current statusand future prospects,” Sensors and Actuators B, vol. 26, no. 1–3,pp. 1–12, 1995.[2] N. Barsan and U. Weimar, “Conduction model of metal oxidegas sensors,” Journal of Electroceramics, vol. 7, no. 3, pp. 143–167, 2001.[3] G. Gaggiotti, A. Galdikas, S. Kaciulis, G. Mattogno, and A.Setkus, “Surface chemistry of tin oxide based gas sensors,”Journal of Applied Physics, vol. 76, no. 8, pp. 4467–4471, 1994.[4] S. Capone, P. Siciliano, F. Quaranta, R. Rella, M. Epifani, and L.Vasanelli, “Moisture influence and geometry eﬀect of Au andJournal of Sensors 5Pt electrodes on CO sensing response of SnO2 microsensorsbased on sol-gel thin film,” Sensors and Actuators B, vol. 77,no. 1-2, pp. 503–511, 2001.[5] C. Xu, J. Tamaki, N. Miura, and N. Yamazoe, “Grain size eﬀectson gas sensitivity of porous SnO2-based elements,” Sensors andActuators B, vol. 3, no. 2, pp. 147–155, 1991.[6] J. W. Orton and M. J. Powell, “The Hall eﬀect in polycrystallineand powdered semiconductors,” Reports on Progress in Physics,vol. 43, no. 11, pp. 1263–1307, 1980.[7] P. Romppainen and V. Lantto, “The eﬀect of microstructure onthe height of potential energy barriers in porous tin dioxidegas sensors,” Journal of Applied Physics, vol. 63, no. 10, pp.5159–5165, 1988.[8] C. Malagu´, G. Martinelli, M. A. Ponce, and C. M. Aldao,“Unpinning of the Fermi level and tunneling in metal oxidesemiconductors,” Applied Physics Letters, vol. 92, no. 16,Article ID 162104, 3 pages, 2008.[9] C. R. Crowell and V. L. Rideout, “Normalized thermionic-field(T-F) emission in metal-semiconductor (Schottky) barriers,”Solid State Electronics, vol. 12, no. 2, pp. 89–105, 1969.[10] B. D. Cullity, “Elements of X-Ray Diﬀraction,” Addison-Wesley, Reading, Mass, USA, 1978.[11] G. Blaustein, M. S. Castro, and C. M. Aldao, “Influenceof frozen distributions of oxygen vacancies on tin oxideconductance,” Sensors and Actuators B, vol. 55, no. 1, pp. 33–37, 1999.[12] M. A. Ponce, C. Malagu, M. C. Carotta, G. Martinelli, and C.M. Aldao, “Gas indiﬀusion contribution to impedance in tinoxide thick films,” Journal of Applied Physics, vol. 104, no. 5,Article ID 054907, 5 pages, 2008.[13] G. Sakai, N. S. Baik, N. Miura, and N. Yamazoe, “Gassensing properties of tin oxide thin films fabricated fromhydrothermally treated nanoparticles: dependence of CO andH2 response on film thickness,” Sensors and Actuators B, vol.77, no. 1-2, pp. 116–121, 2001.[14] M. A. Ponce, C. M. Aldao, and M.S . Castro, “Influence ofparticle size on the conductance of SnO2 thick films,” Journalof the European Ceramic Society, vol. 23, no. 12, pp. 2105–2111,2003.[15] T. G. G. Maﬀeıs, G. T. Owen, C. Malagu´, et al., “Directevidence of the dependence of surface state density on thesize of SnO2 nanoparticles observed by scanning tunnellingspectroscopy,” Surface Science, vol. 550, no. 1–3, pp. 21–25,2004.

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Field-Assisted and Thermionic Contributions to Conductance in SnO2 Thick-Films

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