PHYSICAL REVIEW B VOLUME 51, NUMBER 20 15 MAY 1995-II

Electronic structure of antimony-doped tin oxide

K. C. MishraCentral Research, Osram Sylvania Inc. , 100Endicott Street, Danvers, Massachusetts 01923

K. H. JohnsonDepartment ofMaterials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

P. C. SchmidtInstitut Fu'r Physikalische Chemic, Technische Hochschule Darmstadt, Darmstadt, Germany

(Received 1 February 1995)

The electronic structure and associated properties of antimony-doped tin (IV) oxide have been studiedusing both the self-consistent-field scattered-wave molecular-orbital cluster approach and the augment-ed-spherical-wave supercell band-structure approach. The calculated molecular-orbital energy eigenval-ues and wave functions have been used to interpret several interesting optoelectronic properties of thisdefect semiconductor. The nature and origin of the energy gap from optical-absorption studies and thevalence-band structure from ultraviolet photoelectron spectroscopy (UPS) have been satisfactorily ex-plained using the band structure of pure and antimony-doped tin oxide. It is observed that the antimonyion leads to an impurity band in the band gap and increases the forbidden gap of the host material. Thispartially filled free-electron-like band is the origin of the UPS peak near the band edge whose intensitygrows with the dopant concentration.

I. INTRGDVCTION

Tin (IV) oxide is a semiconductor with many interest-ing optoelectronic properties. Tin oxide with a high dop-ant concentration of antimony exhibits quasimetallic con-ductivity while maintaining its transparency in the opti-cal region. ' This interesting optoelectronic property isexploited in solar cells and optical devices. The mixedoxides of antimony and tin are often used as catalysts inthe oxidation and ammoxidation of hydrocarbons, name-ly propylene to acrolein and acrylonitrile. It is be-lieved that the surface chemical composition critical tocatalytic properties differs significantly from that of thebulk; therefore, considerable attention has been paid toanalyzing the surface composition and segregation of an-timony atoms by surface-sensitive techniques.

The physics of group-V impurities in group-IV semi-conductors is fairly well understood in terms of the bandstructure of the bulk material and the donor levels fromthese impurities and subsequent n-type conductivity ofthese materials. One can explain the quasimetallicbehavior of tin oxide using a similar picture, but its tran-sparency in the visible region presents a conceptualdi%culty that requires a careful consideration of this ma-terial as an ionic system with impurity states. In ioniccrystals, the effect of a similar substitution on the elec-tronic structure is usually interpreted in terms of local-ized defect levels with an accompanying charge-com-pensating mechanism to stabilize the valence state of thedopant ion. Because of the charge compensation, the im-purity levels are usually empty with no conduction elec-trons, thus retaining most of the characteristics of the

host material. For example, one may consider a penta-valent antimony ion at a tetravalent tin site being chargecompensated by cation vacancies. The extra electroncontributed by antimony compensates for the absenttetravalent ion in fulfilling the valence of the oxygen ions,i.e., in maintaining a filled valence band. The multiplevalency of antimony can provide an alternate scenario ofcharge compensation without cation vacancies. In fact,Mossbauer studies have indicated segregation of tri-valent ions in the surface layer and pentavalent ions inthe bulk, suggesting an effective valence of 4. Tin oxidedoped with antimony presents a real challenge to elec-tronic-structure calculation in order to explain its op-toelectronic properties, since the explanations must tran-scend formal descriptions of a material in terms of ionicand semiconducting properties.

The electronic structure of pure tin oxide has beenstudied extensively by various theoretical' ' and exper-imental studies in the past. ' ' In this paper, we haveextended the electronic-structure calculations to includethe antimony ions in tin oxide. Similar to our previousworks on defects in ionic crystals, ' both the real-spacecluster approach and the k-space band-structure ap-proach have been used in a complementary manner to de-velop a consistent picture of its electronic structure. Be-ginning with pure tin oxide, the changes in the electronicstructure of the host material due to the presence of theantimony atom has been traced through cluster andband-structure calculations. It will be shown that the an-timony atoms in tin oxide lead to an impurity band witha significant free-electron-like character that provides asatisfactory explanation for many of its interesting op-toelectronic properties.

0163-1829/95/51(20)/13972(5)/$06. 00 13 972 1995 The American Physical Society

ELECTRONIC STRUCTURE OF ANTIMONY-DOPED TIN OXIDE 13 973

II. THEORY III. RESULTS AND DISCUSSION

A. Structure A. Cluster calculation

Tin oxide crystallizes in the rutile structure with twoformula units per unit cell, the space group symmetry be-ing P42/mnm, with a and c lattice constants being 4.737

O

and 3.186 A. ' Every unit cell contains two formulaunits of Sn02 with tin and oxygen atoms occupying theWyckoff positions a and f. The site symmetry of the tinatoms is D2&. Cluster calculations were performed usingthese structural parameters to generate the positions ofatoms in the clusters while retaining the site symmetry inall the cases. Additionally, calculations were also per-formed assuming higher-order symmetry groups to devel-op an understanding of how the degeneracy of variousmolecular orbitals are removed. The band-structure cal-culation for pure tin oxide is performed using the conven-tional unit cell as the building unit. For the supercell cal-culation, the lattice constant c is doubled to define a su-percell which includes two old primitive cells in whichone of the tin atoms was replaced by an antimony atomcorresponding to an impurity concentration of 8 at. %.This is comparable to the antimony concentration in tinoxide for optimal catalytic activity.

B. Computational procedure

The calculations are performed using the scattered-wave molecular-orbital (SW-Xa ) method and theaugmented-spherical-wave (ASW) band-structure meth-od. ' The cluster results are based on three difIerent clus-ters: a tin-centered cluster with six nearest neighbors; acluster containing two tin atoms and ten oxygen atomswith the two tin atoms being located on the c axis of thecrystal; and a cluster similar to the second one with anantimony atom replacing one of the tin atoms. The cal-culations are repeated with difFerent exchange potentialapproximations, but the energy eigenvalues change byless than 1%. The results presented in this work derivemostly from calculations based on the Xa approximationof the exchange correlation potential.

The band-structure calculations are done using theHedin-Lundquist exchange-correlation potential. Inthe ASW procedure, the unit-cell volume is partitionedinto overlapping atomic spheres, the sphere radii beingcritical in the determination of the energy gaps. Howev-er, the overall features of the bands do not change withthe sphere radii, and the radii are in most cases transfer-able. In the present calculation, we have used atomicspheres of radii 1.24 and 1.30 A for the tin and oxygenatoms, respectively. Additionally, empty spheres of ra-dius equal to 0.87 and 0.76 A are placed at the WyckofT'position c and f, respectively, to fill up the empty space.The present choice of sphere radii not only gives thecorrect optical gap but also reproduces the essentialfeatures of the valence band as revealed by the ultravioletphotoemission spectroscopy (UPS) measurements. Theseradii are subsequently used for the supercell calculationincluding the antimony atom, its sphere radius beingchosen to be the same as that for tin.

The electronic structure of pure tin oxide is studied us-ing two clusters: one consisting of seven atoms, with thetin atom being at the center, and the other centered be-tween two tin atoms on the c axis with 12 atoms. In thefirst calculation, the crystallographic a axis coincideswith the z axis of the cluster, while in the second the crys-tallographic c axis is the z axis of the cluster. For allclusters studied in this work, the standard embeddingscheme with a Watson sphere is used. The 4d, 5s, and 5porbitals of tin and 2s and 2p orbitals of oxygen are treatedas valence orbitals. The molecular energy levels com-posed of oxygen 2s- and 2p-like states and the 4d-like or-bitals of tin appear as bands separated by well-definedgaps. The highest occupied molecular-orbital (HOMO)level composed predominantly of oxygen 2p-like statesbelongs to the b&g representation of the D2& point groupwith a significant admixture of the tin 4d-like orbital.The lowest unoccupied molecular orbital (LUMO) be-longs to the a representation and is composed tin 5s-likeand oxygen 2p-like states indicating strong covalency anddelocalization of the conduction-band states. TheHOMO-LVMO separation is calculated to be 5.3 eV.However, an optical transition between a~ and b&~ statesis not allowed. The lowest-energy allowed transition cor-responds to an excitation from a b3„ level with significantSn 5p-like character to the LUMO at 6.07 eV. This tran-sition corresponds to the optical excitation across the en-ergy gap. However, the calculated gap is approximately60%%uo greater than the observed gap [3.8 eV (Ref. 17)].This is partly due to perturbations caused by four levels(b,g, as, b~g, and

b2s ) at the top of the valence band withsignificant mixing with tin d-like character that are most-ly associated with the surface states of the cluster.

The width of the oxygen 2p-like band, i.e., the width ofthe energy interval containing discrete molecular orbitalsassociated with the oxygen 2p-like states for this cluster,is found to be 4.8 eV, indicating the strong covalency ofthe system. The gap between the oxygen 2p-like bandand 2s-like band, and between the oxygen 2s-like bandand tin 4d-like band, are found to be 9.9 and 3.1 eV. Thetin 4d-like band has a very narrow bandwidth (0.5 eV),indicative of the localized nature of these states.

Our past experience with ionic crystals has been thatone does not really need very large clusters to explain theoptical properties. This is because photoexcitation ofelectrons in solids is a local process and therefore de-pends largely on the local electronic structure. However,in the present case, the discrepancy between the observedand predicted values is large, and the degree of covalencyis very strong, which prompted us to study a larger clus-ter consisting of 12 atoms including two tin atoms todetermine the extent of second-nearest-neighbor interac-tion. For this cluster, the LUMO and HOMO levelsbelonged to as and bg representations (note the differentorientations of the clusters mentioned earlier) with a sep-aration of 2.3 eV. The ungerade molecular orbital withsignificant Sn p character is found to be a b3„orbital at

13 974 K. C. MISHRA, K. H. JOHNSON, AND P. C. SCHMIDT 51

3.2 eV below the LUMO level. This compares reasonablywell with the observed gap for tin oxide (3.8 eV). Theband widths and band gap also change with the increasedcluster sizes, but less severely: the oxygen 2p-like band-width increases to 5.6 eV, the bandwidths of oxygen 2s-like bands and tin 4d-like bands increase from 1.8 and 0.5eV to 2.6 and 0.6 eV, respectively, and the gaps betweenthe oxygen 2p-like and 2s-like bands and oxygen 2s-likeband and tin 4d-like bands change to 8.9 and 3.8 eV.These changes in most cases refiect a better agreementwith experimental data, to be discussed later in the text.

The e6'ect of antimony substitution is studied using acluster similar to the 12-atom cluster described earlier,with one of the tin atoms being replaced by an antimonyatom in a pentavalent state which lowers the site symme-try to C2, . The LUMO level (a, ) is found to havesignificantly more antimony Ss-like character. The next-higher level is an antibonding combination of tin and an-timony 5s-like states in b, representation. The separationbetween these levels is 0.7 eV, suggesting that antimonyintroduces a donorlike level. This separation is expectedto decrease when the LUMO is occupied by an electron,indicating that the ionization energy associated with thisdonor state is less than 0.7 eV. The band-gap transitionis found to be 3.3 eV, corresponding to an excitation froma b& level in the valence band to the a& donor state. Thisis comparable to the band gap (3.2 eV) obtained for thepure tin oxide calculated from the earlier cluster, indicat-ing that the impurity level perturbs the local electronicstructure, leading to an increase in the band gap of thehost system. However, the donor level remains practical-ly at the same place on the energy scale where the bottomof the conduction band of the pure tin oxide used to be.This feature is confirmed by the band-structure calcula-tion discussed below.

A number of changes are also noted in the energy-levelstructure of this cluster compared to the pure tin oxidecluster. The band widths of the oxygen p-like, oxygen2s-like, and tin 4d-like bands increase to 7.3, 3.3, and 0.5eV. The gaps between the oxygen 2p-like, oxygen 2s-like,and tin 4d-like bands are found to be 7.0 and 3.2 eV. Theantimony 4d-like band appears 9.3 eV below the tin 4d-like band. Significant admixture of the tin or antimony5s-like states is observed in the deep valence-band levels.

15.0

10.0

0.0

—5.0

—10.0

—15.0

—20.0

A R

FIG. 1. The band structure of Sn02 ~ The zero of the energyscale is the Fermi energy EI;.

15.0—Dos Sn s Sn p Sn d 0 s 0 p

10.0—

5.0—

band gap of tin oxide has been measured by a number ofworkers, and varies from 4.3 to 2.25 eV, ' ' '" which ispossibly due to variations in the purity of samples. Themost probable value is 3.89 eV, "which agrees very wellwith the calculated gap from the band structure and thecluster calculation. The analysis of the partial density ofstates (Fig. 2) suggests the band-gap transition involves

B. Band-structure calculation

The band structure calculated for the pure tin oxide isshown in Fig. 1, and has features similar to those report-ed by Robertson. ' The Fermi level is chosen to be thezero of the energy scale. The ordering of the energybands is similar to that in the cluster calculation, i.e., theoxygen 2p-like, oxygen 2s-like, and tin 4d-like bands (notshown in Fig. l) follow the same ordering as the corre-sponding molecular orbitals. The conduction band ex-hibits significant free-electron-like character in thedirection (r-X direction) or A direction (1 -M direction),unlike the band structure reported by Jacquemin andBrodure. " The minimum gap is observed at the I point,the direct gap being 3.7 eV. The present results do notindicate the presence of any lower indirect gap. The

—5.0—

—10.0—

—15.0 —.

—20.0 ——--I I I I I I

2.0 4, 0 6.0 8.0 10.0 0.5 0.5w(E) (ev ')

1.5 1.5

FIG. 2. The density of states (DOS) of Sn02. The firstcolumn shows the total density of states. The followingcolumns contain the partial densities and consecutively, the s-,p-, and d-like partial DOS of Sn and the s- and p-like DOS of O.

51 ELECTRONIC STRUCTURE OF ANTIMONY-DOPED TIN OXIDE 13 975

15.0

10.0

5.0

0.0C3

V3

—5.0

—10.0

—15.0

—20.0

A R X I' Z

FIG. 3. The band structure for lines of symmetry in the Bril-louin zone of Sn3SbO8. The Fermi energy EF of SnQ~ is thezero of the energy scale.

excitations from an oxygen 2p-like state to tin s-likeconduction-band states. The density of states plotted inFig. 2 indicates a bandwidth of 7.0 eV, which is compara-ble to the p bandwidth from the cluster calculation andalso to that reported from the UPS measurements[ —10.0 eV (Refs. 7—9 and 23)]. The three peaks associ-ated with the valence band appear at 4.3, 7.3, and 11.1eV, which compare well with the UPS peaks at 4.8, 7.4,and 11.2 eV. The partial-density-of-states calculation in-dicates a significant admixture of tinlike states deep in-side the valence band.

In Fig. 3 we show the band structure of the Sn3Sb08system. In this calculation, we have assumed no chargecompensation; therefore one expects that this system willbe metallic with one of the low-lying states half-filled.The question is whether this is a predominantly an-timonylike or tinlike band. In the latter case, one canthink of the antimony atoms donating their last electronto the tinlike state, and the conductivity is essentially dueto a tinlike conduction band as speculated in Ref. 9. Inthe former case, two things may happen. We may get animpurity band in the gap which is very localized andhalf-filled. Thus one will need to supply energy to excitethese electrons to a free-electron-like conduction bandwith significant tin character, and the conduction will bedue to the electrons in this band. This would give a semi-conductorlike behavior with an activation energy. Alter-natively, the donor band itself may be free-electron-likeand give the conductive properties of the material. Ofcourse, it would exhibit a quasi-semiconductor-likebehavior corresponding to excitation of electrons to thetinlike band. The last case appears to be true. An addi-tional band (Fig. 3) appears in the forbidden gap withfree-electron-like character near the I point. The

15.0—DOS Sns'Snp Snd Sbs Sbp Sbd 01s 01p 02s 02p

10.0—

5.0 —

)

oV3

—5.0—

—15.0—

partial-density-of-states calculation indicates that theelectronic states associated with this band have antimony5s-like character (Fig. 4), which mixes more strongly withthe oxygen 2p-like states than with the tin 5s-like state.The gap near the I point is 2.9 eV, the Fermi level being4.1 eV above the top of the valence band. The minimumof the tin 5s-like band now appears at 5.6 eV above thevalence band, suggesting that the donor state repels thehost states, increasing the apparent gap. This feature wasalso observed in the cluster calculations.

In Fig. 4, the total density of states of antimony-dopedtin oxide is shown. The p-band-width is found to be 8.1

eV, with three major peaks at 4.3, 7.5, and 10.3 eV. Thepeaks have changed very little from the position of thepeaks for pure tin oxide, and agree very well with thepeaks observed by Cox et aI. Considering the antimonyconcentration assumed in this work, it is rather a veryminor perturbation. It is then not surprising that theUPS measurements indicate almost no change in thevalence-band region with antimony doping. The band-widths of the oxygen 2s-like band and tin 4d-like band arefound to be 3.6 and —1.0 eV, respectively, the corre-sponding energy gaps being 7.3 and 1.7 eV. The two d-like bands due to tin and antimony are separated by—8.0 eV, which compares well with the x-ray photoemis-sion spectroscopy (XPS) data.

IV. CONCI. USION

In this paper, an attempt has been made to develop acoherent picture of the electronic structure of antimony-

'g Rm0. 0I I I I

8.0 0.5 0.5 0.5 0.5 0.5 0 5 1.0 1.0 1.0 1.0

x(E) (ev ')

FIG. 4. The density of states (DOS) of Sn3SbO8. The firstcolumn shows the total density of states. The foHowingcolumns contain the partial densities, consecutively the s-, p-,and d-like partial DOS of Sn, the s-, p-, and d-like partial DOSof Sb, and the s- and p-like DOS of O1 and O2.

13 976 K. C. MISHRA, K. H. JOHNSON, AND P. C. SCHMIDT 51

doped tin oxide by first-principles calculations. Using theenergy eigenvalues, we have provided a satisfactory ex-planation of the experimentally observed electronic struc-ture of this material, namely the UPS peaks and the opti-cal gap. It is shown that the positions of the peaks in thedensity of states with respect to the Fermi surface in thecase of antimony-doped material, or with respect to thebottom of the conduction band for the pure tin oxide,remain nearly identical. This is responsible for nearlyidentical UPS spectra for the pure and antimony-dopedmaterials. A nearly identical picture emerged from thecluster calculations.

The metallic nature of the electrons led to the con-clusion that the conductivity is due to the tin Ss-likeband. Our calculation suggests, at least for systems withhigh concentrations of antimony, that the impurity bandhas a nearly free-electron-like structure and can in princi-ple behave like a half-filled metallic band. Additionally,the conductivity of this material will increase with

thermal excitation of electrons to the tinlike bands. This,in addition, can lead to absorption of excitation near 1.5eV resulting in a blue coloration. An alternative ex-planation based on surface plasmons has been presentedon the basis of electron-energy-loss spectroscopy mea-surements. They are not necessarily mutually exclusiveand may contribute conjointly to the coloration of thematerial.

It has been shown that neither a pure ionic model nor asemiconductor model is adequate to explain the behaviorof antimony-doped Sn02. For such systems, one needsdetailed electronic-structure calculations to build a reli-able picture of the electronic structure of the materialfrom the experimental observations.

ACKNOWLEDGMENT

The authors wish to thank Dr. B. G. DeBoer fromOSI, Towanda for many helpful discussions.

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