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Sensors and Actuators B 126 (2007) 204–208

Ab initio DFT computation of SnO2 and WO3

slabs and gas–surface interactions

Michel Levy, Thierry Pagnier ∗Laboratoire d’Electrochimie et de Physicochimie des Materiaux et des Interfaces, ENSEEG 1130 rue de la Piscine,

BP75 F-38402 Saint Martin d’Heresm, France

Available online 3 January 2007

bstract

Slabs of SnO2 and WO3 were computed by ab initio DFT technique, in order to model nanoribbons. Atomic positions, electron density andlectronic density of states were calculated for perfect, vacancy free materials. In these conditions, oxygen is shown to adsorb as a neutral species,ut this adsorption creates acceptor states in the gap which can trap the electrons due to O vacancies in real materials.

2006 Elsevier B.V. All rights reserved.

eywords: Ab initio; DFT; SnO2; WO3; O adsorption; DOS

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. Introduction

SnO2 and WO3 are both n-type semiconductors with a wideandgap. The n-type conduction is due to the presence of oxy-en vacancies, which create electrons in the conduction bandhrough:

O ⇔ 12 O2 + VO

•• + 2e′ (1)

here the Kroger notation is used.In SnO2, these donor levels are found very close to the top

f the conduction band, at 0.15 and 0.03 eV from its bottom1]. It is generally accepted that oxygen atoms adsorb as O−,hus creating an electron-depleted area at the surface of oxiderains. As a consequence, the electrical resistance of the oxidencreases. When oxidizing (e.g. NO2) or reducing (e.g. CO)olecules co-adsorb, the depleted area is modulated. This is

he reason for the very high gas sensing properties of SnO2,nd to a lesser extent of WO3.

Despite the wide acceptance of this model, there are veryew experimental evidences. Ab initio computations, which areecoming powerful enough for the study of large atom assem-lies, could be a way to better understand the interactions of

∗ Corresponding author.E-mail address: Thierry.Pagnier@lepmi.inpg.fr (T. Pagnier).

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925-4005/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.snb.2006.11.047

xide surfaces with gases and their influence on the electricalroperties.

In this paper, we present the first results obtained on the com-utation of oxide slabs and on the interactions of the calculatedurfaces with adsorbed oxygen atoms.

. Computation procedure

The code used is ABINIT [2], which is distributed underhe GNU General Public Licence. The software allows cal-ulations of the ground state of periodic systems using theensity functional theory (DFT). Our computations were car-ied out within the local density approximation (LDA) withhe Hartwigsen–Goedecker–Hutter pseudopotentials found onhe Abinit WEB site [3]. These pseudopotentials include fouralence electrons for Sn, and six for O. Most of the cal-ulations were carried out on Apple workstations (PowerPCrocessor working at 2.5 or 2.7 GHz, 4 GB of memory).he base structure of WO3 was calculated at IDRIS on

he ZAHIR machine. Crystal structures of rutile SnO2 andonoclinic WO3 were computed in order to check the

onsistency of the parameters used. Table 1 gives a com-

arison between the results obtained and the experimentalata. As customary, calculations within the LDA approxi-ation give a forbidden gap narrower than experimentallyeasured.

M. Levy, T. Pagnier / Sensors and Ac

Table 1Experimental and calculated data for SnO2 and WO3 crystals

Parameter Experimental Calculated

WO3

a 7.306 7.459b 7.540 7.455c 7.692 7.778β 90.88 90.895Gap 2.62 2.045

SnO2

a 4.737 4.712c 3.188 3.174x 0.307 0.306

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ashown in Fig. 4. A positive difference indicates an excess of

Fs

Gap 3.60 3.167

xperimental data are from ref. [8] for WO3 and ref. [9] for SnO2.

Slabs were calculated with surfaces parallel to the (0 0 1)lane for WO3 and (1 −1 0) plane for SnO2. In both cases, theattice parameters of the planes parallel to the surfaces were keptonstant and equal to their values in the crystal. The z-axis washosen to be perpendicular to the ab plane in WO3, and parallel tohe (1 −1 0) direction in SnO2. Because of the slight monoclinicistortion of the WO3 cell, the z-axis is not strictly perpendic-lar to the surfaces of the slab, but this has no influence on theomparisons made between free surfaces and surfaces havingdsorbed atoms. The origin of the z-axis was taken in the centerf the slab and the atoms of the corresponding plane were fixedo their position in the crystal during the relaxation of the struc-ure. Relaxed structures were considered to be obtained whenorces on free atoms were lower than 5 × 10−2 eV A−1. Once

quilibrium positions were obtained, the electron density wasalculated. In SnO2 slab, a symmetry plane remains (z = 0) andalculations were carried out in the P11m space group. For WO3

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ig. 1. View of the SnO2 (left) and WO3 (right) slabs with three metal planes. (Largurface (rotated for WO3) showing the alignment of surface O atoms and metal-expo

tuators B 126 (2007) 204–208 205

owever, there is no symmetry except identity and the C1 spaceroup was used.

. Slab calculation and oxygen adsorption

Fig. 1 shows the structure of the slabs. In both cases, in ordero keep the slab electroneutrality, one surface oxygen over twoave been removed. The remaining oxygen atoms form lines athe surface, the difference being that these oxygens are con-ected to one tungsten atom or two tin atoms. In all cases,ve-fold exposed cations have a tendency to shift towards the

nterior of the slab.Adsorption of one oxygen atom per unit cell is allowed on

ach SnO2 surface. In order to keep the plane symmetry of thelab, oxygen atoms were simultaneously added on each side ofhe slab. Two positions were tested: the adsorbed oxygen onop of the five-coordinated Sn atom (called apical from now), orridging between two Sn atoms (Fig. 2). For WO3, there are twoositions per side of the slab. One or two oxygen atoms weredded in apical position. A there was no symmetry to keep,xygen atoms were added only on one side of the slab.

One of the standards outputs of ABINIT is the electron den-ity along the z-axis direction ρz(z), obtained by integrating theocal electron density ρ(x, y, z):

z(z) =∫∫

ρ(x, y, z) dx dy (2)

Fig. 3 shows ρz(z) for the SnO2 slab without and with anpical oxygen added. The difference between both curves is

lectrons when the O atom is absorbed, a negative value a lack oflectrons (depleted area). The number of electrons involved cane obtained by a numerical integration of the difference in each

e spheres) O atoms. (Small spheres) Metal atoms. (Bottom) View of each slabsed atoms.

206 M. Levy, T. Pagnier / Sensors and Actuators B 126 (2007) 204–208

Fig. 2. Slab surfaces showing adsorbed apical O on WO3 (a), apical O on S

Fig. 3. Electron density along the z-axis (perpendicular to the slab surface) fortTp

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iTemperature programmed desorption (TPD) experiments [6]have shown that O coverage is almost unity. For the slabs studiedhere, it means that there is one adsorbed oxygen per unit cell, or

he SnO2 slab (thin line) and after adsorption of one apical oxygen (thick line).he origin of the z-axis is at the center of the slab. Maxima correspond to thelanes occupied by nuclei.

one. When an O atom is absorbed, a depleted zone is observedbout 4 A from the slab center, and involves 0.34 electron. Thisocal charge is compensated by two excess zones from z = 2.2o 3.4 A and for z > 4.4 A, each one carrying a negative chargef 0.17 electron. At the position of the adsorbed oxygen (theucleus is located at z = 5.4 A), the electron excess is solely dueo the six valence electrons brought by the O atom. A similarbservation can be made for WO3 slab.

These results strongly suggest that there is no significant elec-ron transfer from the “bulk” of the slab to the adsorbed oxygentom: O adsorbs as a neutral species.

. Electron density of states

Fig. 5 shows a schematic view of the electron density of statesDOS), calculated by the tetrahedron method with 8k points inhe Brilloin zone for the SnO2 slab, apical O adsorbed and bridg-ng O adsorbed. The forbidden gap decreases from 3.17 eV (bulknO2) to 1.8 eV (slab). When O is adsorbed, half filled statesppear in the gap. For bridging oxygen, these states appear asne filled band and one empty band. For apical oxygen, theres only one band half filled. In both cases, the empty states canccommodate two electrons per adsorbed oxygen, thus suggest-ng that oxygen charge can go up to −2. For apical oxygen, the

efect band is located 0.54 eV from the top of the valence band.hese states cannot be filled with electrons originating from thelab, except through thermal population for T > 0. But they canrap the electrons coming from the oxygen vacancies through Eq.

Fadzs

nO2 (b) and bridging O on SnO2 (c). Adsorbed O atoms are darker.

1). Donor levels due to oxygen vacancies were observed verylose to the bottom of the conduction band [4,5]. As acceptorevels due to the adsorbed oxygens are localized at the surfacef SnO2, only the vacancies near this surface are involved. Therder of magnitude of the depth at which a vacancy can interactith adsorbed oxygen is given by the Debye length.As adsorbed oxygen compensates oxygen vacancies, it is

nteresting to determine which of these defects is predominant.

ig. 4. (Left) Difference between electron density along the z-axis for Odsorbed SnO2 slab and without O adsorbed. (Right) Integral of the electronifference showing that there are as many electrons from the slab center to= 0.46 nm in both cases, suggesting no transfer from the slab to the SnO2

urface.

M. Levy, T. Pagnier / Sensors and Actuators B 126 (2007) 204–208 207

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ig. 5. Schematic electron density of states (DOS) for SnO2 slab (A), with bridgands coming from adsorbed oxygen. In both cases, the levels added in the gap

.7 × 1014 O cm−2. The number of oxygen vacancies, estimatedither by TPD [6] or by electrical measurements [7], falls within016 to 1017 cm−3. For a Debye length of 10 nm, there is only× 10−4 oxygen vacancy per surface unit cell. This result indi-ates that only a small fraction of adsorbed oxygen is negativelyharged (roughly 1 over 5000), and that, in the region close tohe surface, all free carriers are trapped by adsorbed oxygen.

. Effect of foreign gases and conduction model

The model that comes from the present calculations is basedn: (i) the presence of a large number of unoccupied acceptortates in the gap and (ii) a region close to the slab surface virtu-lly free of charge carriers due to oxygen vacancies. Within thisodel, it is hardly understandable why gases such as NO2 or CO

an strongly affect the electrical properties, especially at the parter million level. Actually, air remains the major constituent ofhe gas phase and the oxygen coverage of the surface will remainigh. We can therefore estimate that numerous acceptor levelsemain. Addition of new acceptor molecules (e.g. NO2) will nothange this situation. Nor will the presence of donor moleculese.g. CO), because adsorbed neutral oxygen will trap these newlectrons.

We therefore suggest a defect conduction in a region closeo the surface of SnO2. For example, electrons could jump fromn adsorbed O− to a neutral adsorbed O, with a mechanismimilar to polaronic hopping. In this case, the number of chargearriers could be the number of adsorbed O− species, and the

ffect of donor (resp. acceptor) molecules will be to increaseresp. decrease) this number. As the fraction of charged oxygens about 10−4, even gases at the ppm ratio will have a significantnfluence on this number.

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sorbed oxygen (B) and with apical adsorbed oxygen (C). Stars denote the extrai) located below those of donor states coming from Eq. (1) and (ii) half filled.

. Conclusion

By using a DFT ab initio calculation of SnO2 and WO3 slabs,nd by adding adsorbed oxygen atoms to the slab, we have shownhat O adsorbs as neutral on perfect (vacancy free) oxide. Theecrease of the electrical conductivity observed experimentallyhen O is adsorbed to the oxide surface is more likely due to

he presence of acceptor states in the bottom of the gap whenadsorbs. We have shown that only a small fraction of the

dsorbed oxygen atoms are charged and that a region close tohe surface is virtually free of charge carriers, thus becominglectrically insulating. We suggest that the conduction is due tourface (or near-surface) defect transport. We propose that theumber of charge carriers could be assimilated to the numberf charged oxygen adsorbed atoms. In this case, the effect ofonor or acceptor co-adsorbed molecules would be to modifyhe number of charge carriers.

cknowledgements

This work was carried out in the framework of the Nanos-ructured Solid-State Gas Sensors with Superior PerformanceNANOS4) Project (No. 001528), funded by the European Com-unity through the Sixth Framework Program.Part of the calculations were performed at IDRIS within the

ANOVIB Project.

eferences

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2 nd Ac

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6] J. Mizusaki, H. Koinuma, J.I. Shimoyama, M. Kawasaki, K. Fueki, Hightemperature gravimetric study on nonstoichiometry and oxygen adsorptionof SnO2, J. Solid State Chem. 88 (1990) 443–450.

7] H. Ogawa, M. Nishikawa, A. Abe, Hall measurement studies and an electricalconduction model of tin oxide ultrafine particle films, J. Appl. Phys. 53

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8] B.O. Loopstra, H.M. Rietveld, Further refinement of the structure of WO3,Acta Crystallogr. B 25 (1969) 1420–1421.

9] A. Svane, E. Antoncik, Electronic structure of rutile SnO2, GeO2 and TeO2,J. Phys. Chem. Solids 48 (1987) 171–180.