Sensors and Actuators B 107 (2005) 587–599

A rate equation approach to the gas sensitivity of thinfilm metal oxide materials

S. Ahlersa,∗, G. Mullera, T. Dollb

a Corporate Research Centre, EADS Deutschland GmbH, D-81663 M¨unchen, Germanyb IMM Institut fur Mikrotechnologie Mainz GmbH, Mainz, Germany

Received 14 July 2004; received in revised form 26 October 2004; accepted 12 November 2004Available online 6 January 2005

Abstract

Thin film metal oxide materials exhibit a bell-shaped variation of the gas sensitivity with sensor operation temperature. With respectto the temperatureTM at which a sensitivity maximum occurs, the distribution of the gas sensitivity is asymmetric exhibiting a relativelysteep increase belowTM and a more moderate drop-off aboveTM. In this paper a rate equation approach is described, which successfullyreproduces temperature- and gas-concentration dependent sensitivity distributionsS(T, c ) experimentally determined for a number ofr cific for thesb face oxygeni©

K

1

rtwcbitaTb

ti

nsoreen

plied,yteiationture,d inrousns

ofilesdelsion ofWithyvitygas. Theined

0d

gas

educing analyte gas molecules. We show that such distributions are determined by two energetic parameters, which are spepecial adsorbate/adsorbent system involved. These are (i) the strength of adsorption of neutral analyte gas moleculesEadsand (ii) the kineticarrierEa that needs to be overcome to induce a surface combustion event involving an adsorbed analyte gas molecule and a sur

on.2004 Elsevier B.V. All rights reserved.

eywords:Metal oxide; Modeling; Thin film; Adsorption

. Introduction

Metal oxide gas sensors sensitively respond to a wideange of oxidising and reducing analyte gases via conduc-ivity changes. The gas response profilesS(T, cgas) varyith sensor operation temperatureT and analyte gas con-entrationcgas in a manner specific for the particular adsor-ate/adsorbent system involved. In general, such profiles vary

n a bell-shaped manner with temperature, exhibiting a sensi-ivity maximumSM at an analyte-specific temperatureTM and

lower sensitivity above and below this temperature[1–3].he variation with gas concentration is universally found toe sublinear[4].

Recently, there have been several attempts at explaininghe peculiarities of metal oxide gas-sensing materials. Thosencluded in the review of Barsan et al.[4] are concerned

∗ Corresponding author. Tel.: +49 89 607 21074; fax: +49 89 607 24001.E-mail address:simon.ahlers@eads.net (S. Ahlers).

with the kinetics of adsorption and desorption on the sesurface. These models yield functional relationships betwthe sensor signal and the analyte gas concentration api.e. the calibration curve for a particular kind of analgas at a fixed sensor operation temperature. The varof the gas sensitivity with sensor operation temperaon the other hand, has been more explicitly considerea second group of papers, which is concerned with pothick-film materials. In this latter group of publicatio[5–10] diffusion–reaction theory[11,12] is invoked tocalculate temperature-dependent gas penetration prwithin a porous thick-film sensing layer. These latter mosuccessfully reproduce the observed bell-shaped variatthe gas sensitivity with sensor operation temperature.regard to the temperatureTM of maximum gas sensitivitSM, the low-temperature drop-off of the gas sensitiis explained by a decreasing reactivity of the analytemolecules and a concomitantly deeper gas penetrationhigh-temperature drop-off, on the other hand, is expla

925-4005/$ – see front matter © 2004 Elsevier B.V. All rights reserved.

oi:10.1016/j.snb.2004.11.020

588 S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599

by an increasing reactivity and an increasingly shorter gaspenetration into the sensing layer. The intriguing aspectwith these latter models is that they predict a continuouslyincreasing gas sensitivity with sensor operation temperaturein the limit of very thin films. As such an effect is notobserved in reality, it is suggested that the basic reasonsfor the high-temperature drop-off of the gas sensitivityare more likely due to adsorption–desorption rather thandiffusion–reaction phenomena.

In the present paper, we present gas sensitivity measure-ments on thin-film tin dioxide films as a function of sensoroperation temperature and analyte gas concentration. Thesemeasurements confirm that both films with smooth and gran-ular surface morphology exhibit qualitatively the same kindsof bell-shaped gas sensitivity profiles as porous thick-filmmaterials. We then proceed to develop a simple rate equa-tion approach for the thin-film gas sensitivity that builds onearly ideas of Windischmann and Mark[13] and later elab-orations by Barsan and Weimar[14]. The model proposeddescribes the sensitivity towards reducing gases in terms ofadsorption–desorption processes involving both analyte gasand oxygen molecules. We show that once the sensor baselineresistance has been fixed by assuming appropriate rate con-stants for the oxygen adsorption and desorption, the exper-imentally observed gas sensitivity profiles can be describedin terms of two energetic parameters that are specific for thep gth ofa urfacea om-b e anda lex-i ort data.A , andi poni

g de-t crib-i ichi oreb

2

lay-e xhibita epa-r rsa n theg elowa ighd asesi thata rcialm

Fig. 1. Side view of a compact tin dioxide film generated by e-beam evap-oration of SnO2 material.

Aiming at modelling gas sensor behaviour, it is advisableto reduce the number of poorly controlled parameters witha wide statistical distribution as far as possible. Sensor mor-phology clearly is such a problem parameter as the size of themetal oxide grains and the shape of sintering necks betweenadjacent grains cannot be controlled tightly enough (note ex-cept[28]), or even determined experimentally. As compacttin oxide layers do not exhibit such complicated morphol-ogy, such films are best suited to serve as a model system forstudying gas surface interactions.

The method used to deposit compact sensing layers waselectron beam evaporation (PVD) of pure SnO2 pellets. Theresulting material turns out to be slightly oxygen-deficient,which results in a finite electrical conductivity, which isneeded for supporting a gas sensing effect. In order to putthe gas response of such compact layers into perspective with“typical” porous gas sensing films, precursor films of metal-lic tin were evaporated and oxidised afterwards to form tindioxide by thermal annealing at 600◦C in ambient air.

The following two SEM images (Figs. 1 and 2) reveal themorphology of the two different types of sensing layers.

Granular tin dioxide films were also used to study theimpact of noble-metal dopants on the gas sensitivity distri-

F rationo

articular analyte gas species. These are: (i) the strendsorption of the analyte gas molecules on the sensor snd (ii) the activation energy for triggering a surface custion reaction between an adsorbed analyte moleculsurface oxygen ion. By leaving out some of the comp

ty of the Barsan model[14], we are able to gain values fhe two energy parameters from fits to the experimentaln encouraging feature is that both energy parameters

n particular, the activation energy are clearly lowered untroducing catalyst impurities.

With the values of these two energy parameters beinermined it is also possible to generalise our model to desng porous thick-film materials. This generalisation, whncludes diffusion–reaction processes in addition to the masic surface interactions, will be presented elsewhere[15].

. Preparation of thin-film tin oxide materials

Throughout the literature available today metal oxiders, which are considered for gas sensor applications, every porous morphology, almost regardless of the pr

ation method employed[16–21]. Porous metal oxide layere of interest for two reasons: firstly, a sharp increase ias sensitivity is observed as the grain size is reduced bbout 30 nm[22–27]; secondly, small grains give rise to a hegree of porosity which enhances the penetration of g

nto thick-film sensing layers, i.e. into those materialsre almost exclusively employed in present-day commeetal oxide sensor devices.

ig. 2. View onto a porous tin oxide layer as obtained by e-beam evapof Sn and subsequent thermal oxidation in laboratory air.

S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599 589

Fig. 3. PVD deposition of noble metal doped thin film sensors. A sandwichconsisting of 10 nm tin and 5 nm catalyst layers is first evaporated onto thesubstrate. Subsequently the layer stack is subjected to thermal oxidationin ambient air, resulting in a catalytically enhanced tin oxide sensor withgranular morphology.

butions. In order to obtain such doped material, multi-layerstacks of tin and dopant materials were evaporated as indi-cated inFig. 3and annealed in ambient air after deposition toobtain SnO2 material containing agglomerates of dispersednoble metal.

3. Results of gas measurements

In the following we will use the terms “response” and“sensitivity” synonymously. Mathematically the responseSis defined as follows:

S = R0

Rgas− 1 (1)

whereR0 is the sensor resistance in clean air andRgas is thesensor resistance under the influence of a reducing gas.

This formula is used because it produces reasonable valuesranging from 0 for clean air to high positive values for stronginteractions with reducing gas species. The values generatedare consistent with those obtained by the common formulaS=Rgas/R0 − 1 for oxidising gases.

Turning to the results of our gas sensing experiments, wefirst compare the gas response of tin dioxide films with a com-pact and a granular morphology. This response was measuredfor various reducing gases over a range of sensor operationtm m-m

deri

r isl di e ac-c spac

TT

G

CCH

Fig. 4. Maximum responseSM of a compact (dark grey) and a porous (lightgrey) tin dioxide layer to reducing gases. Whereas a compact film morphol-ogy reduces the gas sensitivity, it is more convenient to analyse theoretically.The operating temperature of the sensors is not fixed in this graph, rather theoptimum is chosen for each gas species.

charge regions. Such modulation effects, however, are muchmore pronounced at the sintering necks of a porous layerbecause of the associated small cross sections of the currentpaths. This matter has already been discussed in considerabledetail in the literature[23,30–32].

In the following, only results on compact layers will beconsidered. Relevant results on such layers are presented inFigs. 5–7. Granular layers will be considered in Section4.2.

The sensitivity profiles reported inFigs. 5–7exhibit sev-eral characteristics, which are common to a wide variety ofother metal oxide sensing layers: (i) the sensitivity at roomtemperature and up to about 100◦C is small for all gases andgas concentrations considered; (ii) with rising temperaturethe response increases up to a certain temperatureTM where

Fig. 5. Gas response of a compact tin dioxide layer to hydrogen. The bell-s ture ist 0 ppm(

emperatures. Specifically the gases ethene (C2H4), carbononoxide (CO) and hydrogen (H2) were considered as suarised inTable 1.Fig. 4displays the response of both kinds of layers un

dentical conditions of gas exposure.Obviously, the response of a porous tin dioxide laye

arger than that of a compact layer[29]. In both cases – anndependent of the film morphology – gas reactions at thessible surface area cause a modulation of the surface

able 1est gases used

as Concentration (ppm)

2H4 20–5000O 2–500

2 100–10000

e

haped variation of the gas sensitivity with sensor operation temperaypical of metal oxide gas sensors. The maximum response to 10.00=1%) H2 is comparably weak.

Fig. 6. Gas response of a compact tin dioxide layer to ethene (C2H4).

590 S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599

Fig. 7. Gas response of a compact tin dioxide film to carbon monoxide CO.

a sensitivity maximumSM occurs. This temperature dependsboth on the kind and on the concentration of analyte gas ap-plied; (iii) at sensor operation temperatures higher thanTMthe response drops again, however, more slowly than belowTM. In particular, a vanishing gas response is not reached,even at the highest temperatures applied.

Considering these results, it is not very surprising to findthat the temperature of maximum responseTM is gas-speciesdependent. It is perhaps more surprising thatTM also dependson the analyte gas concentration. This is not at all obviousat first sight. The theoretical considerations in the next sec-tion, however, indicate that, in principle,TM should exhibita much stronger gas concentration dependence than actuallyobserved.

As will be discussed below, the relatively weak depen-dence ofTM on the gas concentration is evidence for aconcentration-dependence of the thermodynamic and kineticparameters that characterise a particular adsorbent/adsorbatesystem.

Turning to SnO2 layers with a granular surface morphol-ogy, we demonstrate the effect of incorporating noble metalimpurities.Figs. 8–10display the gas response of granularSnO2 films with regard to H2, C2H4 and CO. In addition,these plots contain data for materials that were doped by theaddition of several percent of platinum (Pt) and gold (Au).These latter data vividly demonstrate that noble metal dopingc e gasr ym ticalc cata-

F fort s ofna

Fig. 9. Variation of the C2H4 sensitivity with sensor operation temperaturefor tin dioxide samples with granular morphology containing different typesof noble metal impurities. The test gas mixture applied was 5000 ppm C2H4

in synthetic air.

Fig. 10. Variation of the CO sensitivity with sensor operation temperaturefor tin dioxide samples with granular morphology containing different typesof noble metal impurities. The test gas mixture applied was 500 ppm CO insynthetic air.

lysts see[3,33–40]. We will see in the discussion below thatthe strong effects of noble metal catalysts on the response tosome gases is reflected in the physical parameters that governthe sensing behaviour. Especially the lowering of the reac-tion activation energy (introduced in Section4.1.1), whichis commonly associated with catalysts, can be directly ob-served.

4. Modelling the sensing behaviour

4.1. Compact films

Throughout this section, we consider our metal oxide lay-ers as being compact slabs as displayed inFig. 11. This means

Fig. 11. The assumed metal oxide layer geometry. The layer is compact andas gas/surface interactions are confined to the free surface, gas penetratione

an have a very severe impact on the magnitude of thesponseSand on the temperatureTM at which the sensitivitaximumSM occurs. For phenomenological and theore

onsiderations about the effects of adding noble metal

ig. 8. Variation of the H2 sensitivity with sensor operation temperaturein dioxide samples with granular morphology containing different typeoble metal impurities. The test gas mixture applied was 1% H2 in syntheticir.

ffects do not need to be considered.

S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599 591

that gas diffusion into the sensing layer can be neglected andthat all gas interactions take place at the free surface of theslab. This also means that there is only one single surfacedepletion layer, which can become modulated in response tothe gas/surface interactions. Because of the simple geometry,the depletion layer can be described by a single parameter,i.e. the space charge widthWSCR.

Changes in the depletion layer width modulate the cur-rent through the undepleted bulk very much in the same wayas in a depleted thin film transistor. As metal oxide surfacescan interact with an adjoining gas phase in a chemically re-versible way, the arrangement ofFig. 11basically representsa chemically sensitive thin film transistor. The properties ofsuch transistors are discussed in more detail below.

4.1.1. Surface combustion of reducing moleculesUnder clean air conditions, the surface of a metal oxide is

covered by adsorbed oxygen. Depending on the temperatureof the sensor, there are different forms of adsorbate possi-ble[4,41]. At typical sensor operation temperatures of above150◦C the prevailing adsorbate is O−. The surface coveragewith the latter creates a space charge region and thus con-trols the baseline of the sensor resistance. The surface bandbendingqVs associated with this space charge region is:

qVs = q2 N2O (2)

w ;tm oft

nt at-m rfacei takep orre-sm gasp att con-d knesst

tod sses,t at am m thei

O

i ther-m bar-r d-s rmedg ativet rfaceo ss ane

Fig. 12. Exchange of electronic charge across the surface barrier. In additionto thermionic emission over the surface barrier hopping through localiseddonor states may occur in the limit of high oxygen vacancy concentrationsand thin surface barriers. More details are given inAppendix A.

In this spirit the following rate equation can be written:

d

dtNO = κf0pO2N

2C exp

(−2(EC + qVs − EF bulk)

kBT

)

− κr0N2O exp

(−2(EC − EO minus)

kBT

)(4)

whereNO is the surface density of surface oxygen ions;pO2

is the oxygen partial pressure;κf0 and κr0 are the kineticparameters for adsorption and desorption.

Considering the fact that Eq.(4)contains the band bendingqVs on the right-hand side and that the band bending in turndepends on the surface ion densityNO through Eq.(2), it isclear that(4) is an implicit equation that can only be solvedby numerical means.

We now generalise this equation to the case that reducinganalyte gas molecules are present. In this case reactions takeplace which reduce the density of surface oxygen ionsNO.In order for those reactions to take place, the following stepsneed to be considered: first, reducing gas molecules need toadsorb on the metal oxide surface. This will lead to a certainsurface coverage with this new kind of adsorbate. A frac-tion of the adsorbed molecules in turn may exchange chargewith the metal oxide bulk, but these adsorbates will then befi avelc em l ox-i y runi rgoa a re-a ergyE uallyC onsf o thec

2εε0 nD

hereNO is the surface density of surface oxygen ionsnDhe donor density;qVs the surface band bending;q the ele-entary charge;ε0 andε the absolute and relative values

he dielectric constant.In case reducing analyte gases prevail in the ambie

osphere, the areal density of oxygen ions on the sus changed. In this case, surface combustion reactionslace, transforming the reducing gas species and a cponding number of surface oxygen ions into CO2 and H2Oolecules, which are subsequently desorbed into thehase again[35,42–44]. The electrons formerly trappedhe surface oxygen ions are returned to the metal oxideuction band, which causes the space charge layer thic

o shrink and the sensing layer resistance to decrease.In order to arrive at a rate-equation formalism able

escribe gas detection via surface combustion procehe rate of adsorption and desorption of oxygen ionsetal oxide surface needs to be considered. Starting fro

onosorption reaction

2(g)+ 2e− ↔ 2O(s)−, (3)

t is seen that ionosorption requires two electrons to beally emitted from the Fermi energy across the surface

ier (EC +qVs−EF bulk) to become trapped at a pair of aorbed oxygen atoms. As the surface oxygen ions foive rise to energy levels whose positions are fixed rel

o the position of the band edges, desorption of the suxygen ions requires re-emission of two electrons acronergy barrier of height (EC −EO minus) (Fig. 12).

xed on the surface and therefore likely to be unable to trlose to one of the surface oxygen ions[43]. Those analytolecules, which did not exchange charge with the meta

de surface, are able to diffuse along the surface until thento a surface oxygen ion, where they are likely to unde

catalysed surface combustion event. Triggering suchction, a kinetic barrier, represented by an activation ena, needs to be overcome. The reaction products – usO2 or H2O – will then leave the surface and the electr

ormerly trapped at surface oxygen ions are released tonduction band.

592 S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599

In this spirit Eq.(5) is modified by a reaction termRetoreflect the additional possibility of surface combustion:

d

dtNO = κf0pO2N

2C exp

(−2(EC + qVs − EF bulk)

kBT

)

− κr0N2O exp

(−2(EC − EO minus)

kBT

)− Re (5)

Re = LNOk0 exp

(− Ea

kBT

)(6)

The termReitself contains a number of important factors:first, a Langmuir relative surface coverageL, which reflectsthe adsorption of the reducing gas without charge transfer.

L in turn contains several important parameters[45]:

L = pgas

pgas+ p0(7)

P0 = kBT

VQexp

(−Eads

kBT

)(8)

VQ =(

2πh

MgasM0kBTgas

)1.5

(9)

whereVQ is the quantum volume of the reducing gas;pgasit re;E su her

lds,t shesa aceo cingat ight-f henm tailedi tob ase,Ee in[

thea

0

thes gasa entedb

N

NO air =√

κf0

κr0

pO2n2D (12)

with the value ofNO being determined, the width of the spacecharge layer can be calculated:

WSCR = NO

nD(13)

With the total film thickness beingD, the actual resistanceof the metal oxide layerRMOX turns out to be:

RMOX = 1

σMOX

Ls

Bs(Ds − WSCR)(14)

σMOX = µnqns (15)

whereLs is the contact distance;Bs is the contact width;Dsis the thickness of the metal oxide;WSCR is the width ofthe space charge region;nS is the conduction electron con-centration (≈nD at elevated temperatures);µn is the electronmobility.

As one is usually not so much interested in the baselineresistance of the sensor itself, but in its gas response, we use

S = Rair

Rgas− 1 (16)

t se:

S

w air;W e ofr

o-

p yerc verye onsep

theg eter-m andti st turei co-o onse.T ep ivitym tem-p e wills litya ximaim

s the partial pressure of the reducing gas;Tgas is the gasemperature (300 K);T is the sensor operation temperatuadsis the binding energy of adsorbate;M0 is the atomic masnit (1.67× 10−27 kg);Mgasis the relative atomic mass of teducing gas (e.g. 28 for CO and 2 for H2).

Assuming that a situation of dynamical equilibrium hohe time rate of change of the oxygen ion density vanind Eq.(5) can be solved to obtain the density of surfxygen ions both under clean-air as well as under redunalyte gas conditions. Again Eq.(5) is an implicit equation

hat can only be solved by numerical means. A more straorward analytical solution, however, can be obtained wore restrictive assumptions are made. For reasons de

n Appendix A, we will consider the barriers at the surfacee transparent for tunnelling by electrons. In this latter cq. (4) reduces to the form put forth by Barsan et al. in[4],ither (Eq. (2) in[4]) without a reaction term, or (Eq. (31)

4]) with a reaction term.Assuming steady-state conditions, an equation for

real density of surface oxygen ions can then written:

= κf0pO2n2D − κr0N

2O − LNOk0 exp

(− Ea

kBT

)(10)

This latter equation can be analytically solved to obtainurface oxygen ion density both under reducing analytend clean air conditions (clean air conditions are represy cgas= 0, and thereforeL= 0):

O =Lk0 exp

(− Ea

kBT

)+

√[Lk0 exp

(− Ea

kBT

)]2+ 4κr0κf0pO2n

2D

2κr0

(11)

o deduce from Eq.(14)a final formula for the gas respon

(T, cgas) = DS − WSCR gas

DS − WSCR air− 1 (17)

hereWSCRair is the space charge region width in cleanSCRgasis the space charge region width in the presenc

educing gas;Ds is the metal oxide layer thickness.In this latter formula the electrical parametersµn andnD

f the sensing layer cancel out.Combining Eqs.(7)–(9), (11), (13)and(17), an explicit ex

ressionS(T, cgas) for the gas response of a metal oxide laan be given. This expression is very lengthy and notnlightening. Rather than presenting it, simulated respatterns are displayed in Section5 below (seeFig. 15).

It is relevant to note that the bell-shaped variation ofas sensitivity with sensor operation temperature is dined by the cooperation of the Langmuir adsorption

he first-order reaction terms in Eq.(6). This latter fact isllustrated by the data plotted inFigs. 13 and 14. Whereahe first plot shows how these terms vary with temperandividually, the second plot illustrates how both termsperate in reproducing the peculiar form of the gas resphe striking fact brought out byFig. 14 is that due to throperties of the Langmuir adsorption term, the sensitaximum should shift towards higher sensor operationeratures once higher gas concentrations are applied. Wee in Section5 that this latter effect is not observed in reand that the absence of a major shift in the sensitivity ma

s due to a decrease of the adsorption energyEadsof analyteolecules with increasing surface coverage.

S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599 593

Fig. 13. Variation of the first-order reaction term (broken line) and of theLangmuir adsorption terms (full lines) with sensor operation temperature.Higher analyte gas pressure causes the decrease of the Langmuir adsorptionterm to shift towards higher sensor operation temperatures.

Fig. 14. The cooperative effect of the first-order reaction term and the Lang-muir adsorption term accounts for the bell-shaped variation of the gas sensi-tivity with sensor operation temperature. Concentration-independent valuesof the kinetic barrier and Langmuir adsorption energies cause the temper-ature of maximum gas response to shift towards higher sensor operationtemperature.

4.2. Granular thin films

In the case of compact films, the geometry is simple andthe influence of the gases on the conduction straightforward.With granular films, this situation becomes more difficult.To a first approximation the thickness of the space chargeregion does not change, but it now applies to grains and necksbetween grains instead of the compact layer. This fact can beaccounted for by exchanging the layer thickness with theaverage neck diameter, arriving at the following equation:

S = dneck− 2WSCR gas

dneck− 2WSCR air− 1 (18)

The factor of 2 reflects the fact that now the gas–surface-interactions can take place on both sides of a grain or neck,instead of only the top surface as in the compact case. Unfor-tunately, with small grains and, by implication, small necksthe space charge region may extend over most or all of agrain. If this is the case, the influence on the conductivityof the film is changed not only in quantity, but also in qual-ity. This has been suggested in[20,26]and further discussedin [14]. The models discussed there clearly show differentregions of grain sizes where different mathematical formula-tions should be used.

It is our intention in this paper to arrive at a description ofthe sensor with which it is possible to fit experimental resultsto the mathematical formulae and get an impression of thevalues for some of the physical parameters that cannot beobtained otherwise. The grain diameter can be estimated byXRD or REM imaging. However, the neck diameter is not aseasily accessible, but can be just as important.

Therefore, instead of using a formalism that we cannotjustify by experimental evidence, we make a simplificationhere by simply introducing a factor that allows an enhance-ment of the sensitivity of a granular metal oxide film over acompact one. This takes away some of the sophistication thatis already present in published models[14], but allows on theother hand fitting experimental data, which is a valuable step.

5. Extraction of adsorbate/adsorbent-specificparameters

In this final section, we apply the mathematical expres-sions derived above to the analysis of thin-film gas sensorbehaviour. Before we start, we recall that these expressions re-late the temperature- and concentration dependence of the gassensitivityS to the energiesEa andEads, which are analyte-gas-specific and to the kinetic parametersκf0 andκr0, whichdetermine the sensor baseline resistance in ambient air. Allo n ei-t g lit-e thesep

sis-t on ofa as allo inga oiceo a fit-t cificp iouro

so , wec at isc anda

f tind db e-q thesi ev a. Int s andt en-t hats ntra-t

ther parameters relate to material properties, which caher be extracted from measurements or estimated usinrature values. For the sake of clarity we summarisearameters inTable 2below.

As the ratioκf0/κr0 determines the sensor baseline reance, which is independent of the type and concentratinalyte gas considered, this latter parameter as wellther constants inTable 2have been kept constant durll fitting procedures described below. Making such a chnly leaves two parameters to be determined from dat

ing. We now go on showing how the two analyte-gas-spearametersEa andEadsdetermine the gas sensing behavf thin film metal oxide sensing layers.

The sensitivity enhancement factorAsimplifies the effectf granularity. As this factor is fixed for any single sensoronsider it is merely a morphology-related constant thommon to all fits relating to different analyte speciesnalyte gas concentrations.

As a first example we consider thin compact layers oioxide. As described in Section2, these films were formey evaporating SnO2 powder and by performing a subsuent annealing step in ambient air afterwards. Whileensitivity of these films towards H2, CO and ethene (C2H4)s displayed inFigs. 5–7in Section3; Fig. 15shows responsalues towards CO in combination with fits to these dathe latter figure measured data are indicated by symbolhe bell-shaped curves interpolating through the experimal data are fits to Eq.(17). Comparing these fits it is seen tensitivity curves relating to different analyte gas conceionscgasexhibit sensitivity maximaSM that tend to shift to

594 S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599

Table 2Parameters entering the fit equationS= f(T, cgas) which stands for the sensor response as a function of sensor operation temperature and gas concentration

pgas Reducing gas partial pressure Fit variableT Sensor operation temperature Fit variableEa Reaction activation energy; analyte-gas-dependent Fit parameterEads Binding energy of reducing gas upon chemisorption;

analyte-gas-dependentFit parameter

κf0, κr0 Unknown; ratioκf0/κr0 fixed by clean air oxygencoverage; independent of reducing gas type

Fit parameter

NO clean Clean air oxygen coverage 2.6× 1012 cm−2 [46]PO2 Atmospheric oxygen partial pressure 2× 104 PaTgas Gas temperature 300 KMgas Relative mass of the reducing gas MH2 = 2; MCO = MC2H4 = 28ma Atomic mass unit (AMU) 1.67× 10−27 kgk0 Surface phonon frequency, reaction attempt frequency 1013 Hz [43]nD Doping concentration of the metal oxide bulk 1018 cm−3 [4,47]kB Boltzmann constant 8.617× 10−5 eV/KA Sensitivity enhancement factor Fit parameter in porous layers,

fixed to 1 for the compact layers

Fig. 15. Gas response of a compact tin oxide layer to carbon monoxide(CO) as a function of the sensor operation temperature. The symbols standfor measured sensitivity values; the lines are fits to the functionS(T, cgas)(Eq.(17)).

slightly higher temperaturesTM as larger gas concentrationsare applied. Sticking to a constant sensor operation temper-ature close toTM, it is further revealed that the gas responseS increases in a sub-linear manner with increasingcgas. Allthese characteristics are quite generally observed in all kindsof metal oxide materials.

From the fits above, values for the energy parametersEaandEads can be obtained. The next series of graphs displaythose values ofEa andEadsthat were determined from thesefits. The most striking feature in these data is that both energyparameters turn out to be concentration-dependent. On thewhole these data show that reaction thresholds with surfaceoxygen ions are lowered and that the strength of adsorptionof the analyte gases is reduced as higher analyte gas concen-trations are applied (Figs. 16–18).

This concentration-dependence of the two energy param-eters deserves more attention. In Section4.1, where the func-tionS(T, cgas) was derived, it was shown that the bell-shapedvariation of the gas sensitivity arises from the cooperation oftwo opposing effects: (i) an increasing probability of trigger-ing detection reactions as the sensor operation temperature israised and (ii) an increasing probability of adsorbed analytegas molecules to desorb prior to suffering a detection reactionas the sensor operation temperature is further increased. In

Fig. 16. Fitted values for the strength of adsorption (top) and the reactionactivation energy (bottom) for the pure tin dioxide film and 20–5000 ppmethene as reducing gas. The magnitude of both energies drops with increasinganalyte gas concentration.

particular, the temperatureTM, at which the sensitivity maxi-mumSM occurs, was shown to coincide with the temperatureat which the Langmuir isobar starts to fall from a relativesurface coverage ofΘ= 1 towardsΘ= 0. As, due to the prop-erties of the Langmuir isobar this temperature is stronglyconcentration-dependent, the maximum ofS(T, cgas) is ex-pected to experience a considerable shift towards higher sen-sor operation temperatures as long as constant values ofEadsare assumed (seeFig. 14). In view of the relatively constantvalues ofTM that emerge from the data ofFigs. 5–7, sim-

Fig. 17. Fitted values for the strength of adsorption (top) and the reactionactivation energy (bottom) for the pure tin dioxide film and 2–500 ppm COas reducing analyte gas.

S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599 595

Fig. 18. Fitted values for the strength of adsorption (top) and the reactionactivation energy (bottom) for the pure tin dioxide film and 100 ppm to 1%H2 as reducing analyte gas.

ple mathematical reasons demand concentration-dependentvalues ofEa andEads to be inferred to obtain fits to the ex-perimental data.

Supporting evidence for concentration-dependent energyparameters comes from the literature on heterogeneous catal-ysis. In this field it is well known that heats of chemisorp-tion generally depend on the surface coverageΘ. Turningto the subject of chemisorption of CO and its catalytic con-version to CO2 via reaction with adsorbed oxygen species,it is found that adsorption energies are strongly coverage-dependent. Dulaurent et al.[48], for instance, find that theheat of adsorption of CO on a Ru/Al2O3 catalyst decreasesfrom about 1.8 eV atΘ= 0 down to 1.2 eV atΘ= 1. In[49] theauthors find that there seems to be no competition betweenoxygen and CO in finding adsorption sites on a Pt/SiO2 cata-lyst because the two species do not tend to adsorb at the samesites. Considering this strong coverage-dependence ofEadson catalytic surfaces, on the one hand, and the very moderateconcentration dependence ofEads on SnO2 sensor surfaces,on the other hand, it is suggested that the surface coverage COon a SnO2 surface is already close toΘ= 1, even at low COconcentrations in the ambient air. In this way, the very moder-ate decrease inEadsfrom 1.33 to 1.18 eV can be explained asthe CO concentration ranges from 2 to 500 ppm. Comparedto this amount of variation, the concentration-dependence ofE is much smaller, amounting to 3–6 meV only. We there-f thisl

A possible alternative reason for a seeming concentration-dependence ofEa andEadscould originate also in part fromthe mathematical simplifications that had been introducedinto the derivation of the simplified rate Eq.(10). In order toobtain a simple explicit equation forNO, the assumption ofa constant surface electron densityns needed to made. Thevalidity of this assumption will break down in case surfacebarrier profiles are no longer transparent to tunnelling. In thislatter case, a concentration-dependence ofns will arise as in-creasing concentrations of analyte gases are applied. Even inthis latter case the assumption of a constant (although low-ered)ns is correct as long as one is dealing with a small-signalsituation, i.e. with very low analyte gas concentrations. In thisspirit, we prefer to interpret as true analyte-specific energiesthose values ofEa andEads that can be extracted from thefitted values by extrapolation towards zero analyte gas con-centration.

After these initial considerations we should like to turnour attention to metal oxide materials which are more sim-ilar to commercially applied materials. Such films exhibit agranular morphology and these are also likely to be dopedwith catalytic noble metal materials such as Au and Pt. Asan approximation to such materials we consider thin SnO2films with a granular surface morphology, which had beenformed using the two-step approach also described in Sec-tion 2. In this approach metal evaporation is followed bys sist-i ate-r h asA yd verys nd onto

gasr atione

t int lt e cans pera-t inp rved

TM

1 sens-atTM

P

P

TT

C ChangE

aore do not attempt to provide a physical explanation foratter effect.

able 3easured and fitted results for 1% H2

% H2 Temperature of max-imum sensitivityTM (◦C)

Maximumitivity SM

re tin oxide(smooth)

400 15

re tin oxide(granular)

370 85

in oxide:Pt 220 2100inoxide:Au

370 43

atalyst doping influences the directly measurable parametersSM andTM.

ads.

ubsequent annealing in ambient air to form films conng of nanometer-sized metal oxide grains. Into such mials, it is easy to introduce noble metal impurities sucu and Pt. The data inFigs. 8–10(Section3) have alreademonstrated that such noble metal doping can have aevere impact on the magnitude of the gas response ahe temperatureTM at which the sensitivity maximumSMccurs.

Tables 3–5, in turn, show how such changes in theesponse are reflected in the fitted values of the activnergyEa and the adsorbate binding energyEads.

A first inspection of the experimental data shows thahe case of pure SnO2 the temperatureTM is quite high for alhree reducing gases investigated. From the literature onee that such sensors generally exhibit high reaction temures for reducing gases such as CO, H2, hydrocarbons andarticular CH4. Somewhat lower temperatures are obse

Reaction activ-ation energyEa (eV)

Adsorption energyEads(eV)

0.44 1.07

0.57 0.96

0.31 0.660.42 0.89

es in these parameters are reflected in the fitted energy parametersEa and

596 S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599

Table 4Measured and fitted results for 0.5% ethene (C2H4)

5000 ppm Ethene Temperature of maximumsensitivityTM (◦C)

Maximum sensitivitySM atTM

Reaction activationenergyEa (eV)

Adsorption energyEads(eV)

Pure tin oxide 400 4 0.53 1.3Pure tin oxide (granular) 490 14 0.78 1.4Tin oxide:Pt 290 314 0.52 1.0Tin oxide:Au 490 24 0.61 1.4

The influence of the catalysts on the ethene response resembles that on the H2 one.

Table 5Measured and fitted results for 500 ppm CO

500 ppm CO Temperature of maximumsensitivityTM (◦C)

Maximum sensitivitySM atTM

Reaction activationenergyEa (eV)

Adsorption energyEads(eV)

Pure tin oxide 330 2 0.52 1.3Pure tin oxide (granular) 410 0.8 1.45Tin oxide:Pt 420 1 0.87 1.3Tin oxide:Au 550 4 0.82 1.7

The influence of the catalyst doping on the CO response differs strongly from that on the C2H4 and H2 one.

in the case of NO2 and O3, which are less stable oxidisinggases[50].

Considering undoped material first and comparing the dataobtained for the three reducing gases, it is seen that the sensi-tivity profiles are quite similar, exhibiting different absolutevalues of the gas sensitivitySonly. This similarity is reflectedin the fitted energy parameters, which are similar in all threegases. According to these, the gas with the highest responsevalue (H2) also exhibits the lowest activation barrier withregard to detection.

Noble-metal-doped sensors, on the other hand, exhibitquite different behaviour. The data inTables 3–5clearly re-veal a similar impact on the two energy parameters both forH2 and for C2H4. Both catalysts vastly enhance the reactionwith hydrogen, thereby reducing the maximum temperatureTM and raising the maximum sensitivitySM. The ethene sen-sitivity is also promoted, although this effect is not as strongas in the case of H2.

Pt is the noble metal catalyst most widely used in industrialapplications. Examples are automobile exhaust gas cleaning,ammonia oxidation and petrochemical applications like fab-rication of plastics from natural oil[50,51]. On a Pt surfaceH2 molecules tend to dissociate into single hydrogen atoms.Such single atoms are more likely to react with other adsor-bents, which reduces the activation energyEa. Concomitantlythe adsorption energyE is also reduced. This latter reduc-t ino tionsr s thisw thisw fur-t ciple[

us-te lf re-

flected in concomitant changes in the two energy parame-ters.

The case of CO is somewhat different. In this latter case,the effect on the experimentally accessible quantitiesSM andTM is marginal (Pt doping) or even counter-productive in thesense that detection reactions are inhibited rather than be-ing promoted (Au doping). As far as the consistency of ourmodel is concerned, the changes in the measurable quanti-tiesSM andTM are also reflected in concomitant changes inthe fitted values of the energy parametersEa andEads. In thecase of Au doping, in particular, the inhibition of detectionreactions is reflected in increased values ofEa andEads. Atthis point, however, it should be noted that the two energyvalues do not simply reflect material properties of Pt or Au,respectively. Considering the fact that significant enhance-ments in the CO sensitivity can be obtained by evaporationof dispersed clusters of Au onto granular SnO2 surfaces[54],it is demonstrated that the fitted values ofEa andEads aremore representative of the manner of introducing, dispersingand binding the catalytic impurities at the metal oxide sen-sor surface than representing simple material properties of Ptor Au.

6. Conclusions

plaint rdsr

vari-a er-at ithr -pa

adsion is very important for the functioning of a catalyst:rder to be able to promote heterogeneous surface reaceactant molecules must neither be bound too loosely, aould not mediate any reactivity, nor too strongly, asould slow down surface diffusion and thus inhibit any

her reaction. This is also known as the Sabatier prin52,53].

Although Au as a catalyst is not widely used in indry, it nevertheless acts as a reaction promoter in SnO2. Theffects of Au are not as strong as those of Pt, but stilTM

or the H2 detection is lowered somewhat, which is also

, A new approach has been presented that is able to exhe gas sensitivity of thin film metal oxide materials towaeducing gases.

This approach satisfactorily explains the bell-shapedtion of the gas sensitivitySwith the sensor operation temptureT. In particular, the derived functionS(T, cgas) explains

he asymmetric deformation of the sensitivity profile wespect to the sensitivity maximumSM occurring at the temeratureTM as well as the sub-linear variation ofSwith thenalyte gas concentrationcgas.

S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599 597

The experimentally accessible parametersSM and TM,which characterise the sensitivity distributions, are relatedto the microscopic energy parametersEadsandEa. The firstof these parameters describes the strength of the analyte gasbinding on the metal oxide surface and the second the ki-netic barrier that needs to be overcome to induce a surfacecombustion event.

Fits to experimental gas sensitivity data for the gas speciesCO, C2H4 and H2 indicate thatEadsandEa tend to depend onthe analyte gas concentration and thus on the surface coverageof analyte molecules on the sensor surface.

A comparison of undoped and noble-metal-doped SnO2films illustrates that the addition of catalysts, in general, pro-motes surface reactions by changes in both energy parame-ters.

Acknowledgement

Part of this work has been financed by the Bundesminis-terium for Education and Research (BMBF) under the con-tracts 16SV1129/5 (MISSY) and 16SV 1532 (IESSICA).

Appendix A. Efficiency of electron tunnellingthrough metal oxide surface barriers

ion-dp ngt bandb ntm Oura etalo

Am

unds son’se ts ina facei de toa den-s ationo firsta e ofs rect,b pu-r y oft

thor-oi f then ched

was that under equilibrium conditions, mobile donors shouldgive rise to a narrowing of the space charge zones. More quan-titatively these authors propose that the usual parabolic bandbending profile should be replaced by a logarithmic one. Inthis way, the distance to the surface, that needs to be traversedby a tunnelling electron, is reduced.

A.2. Fermi-energy dependence of the oxygen vacancyconcentration

Additionally, the concentration of oxygen vacancies is un-likely to be constant throughout the space charge zone. Start-ing out from the undepleted bulk material, an upward bandbending causes the Fermi energy to retreat more and morefrom the conduction band edge as the free surface is ap-proached. According to Hellmich[56] a change in the Fermienergy relative to the band edges causes the vacancy concen-tration to increase. In[56] the reason for this increase hasbeen traced to the fact that part of the formation energy of anoxygen vacancy–interstitial pair is regained by statisticallydropping the two valence electrons trapped at an oxygen va-cancy onto the Fermi energy. As an upward band bendinglowers the Fermi energy with respect to the conduction bandedge, the density of oxygen vacancies should steeply increaseas the free surface is approached. This effect in turn reducesthe extent of the space charge region, so that in an equilibrateds ideb

A

xidea se tol ut 30a ex-p es ofm theb eepers n ass

edm r, ane allyas needt dingt thanb Ther ere-f ppinga r toa e de-c of theh thatr reac-t sor.

The function for the temperature- and concentratependent gas response of metal oxide materialsS(T, cgas)resented in Section4, was derived by assuming tunnelli

ransparency through the adsorption-induced surfaceending profile. In thisAppendix Awe should like to preseore supporting evidence in favour of this assumption.rguments rely on three items, which are specific for mxide semiconductors:

.1. Narrowed band bending due to oxygen vacancyobility

The surface band bending in a semiconductor with bourface charges can be determined by solving Poisquation. The standard solution to this problem resulparabolic band bending profile extending from the sur

nto the undepleted bulk material. The assumptions marrive at this standard solution are: zero mobile chargeity within the space charge region and a fixed concentrf doping atoms within the semiconductor crystal. Thessumption is generally not true, especially in the cashallow band bending profiles. The second is usually corut in the special case of metal oxides, where donor imities are relatively mobile oxygen vacancies, the validithis latter assumption is likely to break down.

The subject of oxygen vacancy motion has beenughly investigated by Kamp[55]. Rantala et al.[47] have

nvestigated the influence of this effect on the shape oear-surface band bending profile. The conclusion rea

tate, it is likely to extend only a few nm into the metal oxulk.

.3. Tunnelling through dopant states

Oxygen vacancies act as the main donors in tin ond other pure metal oxides. These vacancies give ri

ocalised levels below the conduction band edge of abond 150 meV[46]. The shallower one of these can beected to be emptied at common operating temperaturore than 300◦C (about 50 meV thermal energy). Whenand bending near the surface rises above 0.15 eV the dtate will also become emptied, resulting in a situatioketched inFig. 12above.

This latter figure displays a situation of a highly dopetal oxide layer. In a typical metal oxide gas sensolectron can travel from one state to another via thermctivated hopping to arrive at the free surface[57]. Fig. 12hows that much smaller amounts of thermal energyo be expended to arrive at the free surface by proceehrough a series of hops over localised bandgap statesy direct thermionic emission over the surface barrier.ate of charge transfer between bulk and surface will thore depend much less on temperature in the case of hos in direct thermionic emission over the barrier. In orderrive at mathematically tractable equations we thereforided to neglect the smaller temperature dependenceopping transport with regard to the much larger impacteaction activation and adsorption energies have on theion kinetics and the sensitivity of a metal oxide gas sen

598 S. Ahlers et al. / Sensors and Actuators B 107 (2005) 587–599

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