J. MATER. CHEM., 1991, 1(3), 451-455 451 Infrared Reflectance Spectra of Sb-doped SnO, Ceramics C. Stephan Rastomjee," P. Anthony COX,"Russell G. Egdell,*" Jeremy P. Kemp" and Wendy R. Flavellb a Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, UK Department of Chemistry, UMIST, P.O. Box 88, Manchester M60 1QQ UK Infrared specular reflectance spectra of Sn,-$b,O, ceramics have been measured over a range of bulk doping levels extending up to x=O.O3. At low doping levels conduction electrons screen out coupling of the infrared radiation to bulk phonon modes in a way expected from a model in which reflectivity is calculated from the bulk dielectric function. However, at higher doping levels a reflectivity minimum develops at ca. 800 cm-'. This is interpreted in terms of a model where a surface layer with low carrier concentration sits on top of an undepleted bulk.Keywords: Antimony-doped tin oxide ceramic; Infrared reflection spectroscopy; Depletion layer 1. Introduction Stoichiometric SnO, is a semiconductor with a bandgap of 3.89 eV, adopting the tetragonal rutile structure. The oxide may be doped n-type by oxygen deficiency or substitutional replacement of Sn with Sb or of 0 with F.' At doping levels above 5 x lo'* cm-3 the material becomes a metallic conduc- tor and carriers occupy an essentially free-electron-like con- duction band of dominant Sn 5s atomic character. The plasma energy of Sb-doped SnO, increases with doping level, reaching ca. 0.55 eV (4400cm-') in 3% Sb-doped Sn02.2-4 Owing to the low plasma frequency, doped SnO, retains good trans- parency in the visible regi~n.~ This property, in combination with high reflectivity at lower frequencies, leads to applications in infrared reflecting windows for both domestic and special- ised applications.Technological interest in tin oxide also includes its application as a sensor material for reducing gases such as CO and CH4.6 The generally accepted model for sensor activity is as follows. Chemisorbed oxygen on the SnO, surface under ambient conditions depletes carriers in the near- surface region. Surface oxygen is removed by catalytic oxi- dation of reducing gases, thus releasing carriers back into the surface and producing a rise in conductivity.In previous publications we have reported the use of techniques including ultraviolet photoemission (UPS) and high-resolution electron energy loss spectroscopy (HREELS) to measure the concentration of n-type carriers at doped SnO, surfaces under ultra-high vacuum In the present study we extend the scope of the earlier work by applying infrared reflectance spectroscopy to examine phonon structure in Sb-doped SnO, ceramics as a function of bulk doping level. Screening of phonons by the carriers provides a probe of carrier distribution close to the surface under ambient conditions. Evidence emerges from our work that for highly doped Sn0, there is significant carrier depletion in the near-surface region for samples held in air. 2. Experimental Samples were prepared by a coprecipitation method.Weighed quantities of Sn shot (Aldrich Gold Label, 99.999%) and Sb powder (Koch Light, 99.999%) were dissolved separately in aqua regia made from BDH AnalaR grade acids. The solutions were then mixed to give the required doping level and made alkaline with excess AnalaR grade ammonia solution. After the solutions had been boiled for at least 1 h the white gelatinous precipitate was allowed to settle overnight before collection and washing in a Buchner funnel. The precipitate was dried overnight at 100°C and then slowly heated to 1000 "C in recrystallised alumina crucibles. After sintering for 14 days this temperature with occasional regrinding, samples were finely ground in an agate mortar and pressed into 13 mm diameter pellets between optically smooth tungsten carbide dies. They were then sintered in air for at least 24 h to yield mechanically robust ceramic discs.X-Ray powder diffractometer traces from samples prepared in this way contained only peaks attributable to a well crystallised rutile phase with lattice parameters not signifi- cantly different from those of tin dioxide itself. Analytical electron microscopy and atomic absorption spectroscopy con- firmed that the Sb doping level was close to the nominal value for the more highly doped samples. Some of the samples were studied by a range of surface analytical techniques including X-ray photoelectron spectroscopy (XPS), UPS and HREELS, as detailed Specular infrared reflectance spectra were measured using unpolarised radiation incident at 20" to the surface normal in a Mattson Alpha Centauri FTIR spectrometer, incorporat- ing a Nichrome wire radiation source, KBr beamsplitter and DTGS detector.The experimental resolution was set at 16 cm- I. Background interferograms were recorded from an aluminium mirror, which was assumed to be 100% reflecting over the region of interest. 3. Results The experimental infrared spectra are shown in Fig. 1A. Undoped SnOz displays a spectrum with two reflectivity maxima above 400 cm-', peaking at 620 and 480 cm- '. The higher-energy peak is the stronger and has a pronounced shoulder on its high-energy side. The reflectivity declines to a minimum at 800 cm-I and remains low at higher frequency. The drop in reflectivity below 800 cm-' corresponds to the longitudinal optical (LO) phonon frequencies of the highest- energy E, and the A," modes, which are at 757 and 704 cm- ', re~pectively.~The initial effect of doping is to produce an increasing reflectivity across the infrared region, especially at low frequency.Maxima in reflectivity corresponding to those of undoped SnO, persist in the experimental spectra, although the maxima are less pronounced as the doping level increases. At higher doping levels a shallow trough in the spectra develops at CQ. 750 cm-l. In making a comparison between experimental reflectance data and simulations of the spectra (section 4, below) it should be remembered that the absolute 452 A B 20 40 10 20 20 30Y860 o b 20401 80Ol--+-+- 10 20 iJ!? 0 n 1300 800 400 1200 800 400 waven urn ber/cm -Fig.1 A, Experimental infrared specular reflection spectra of Sb-doped SnO, ceramics as a function of bulk doping level; B, simulated spectra, using Dresselhaus averaging procedure and flat-band carrier distribution (see text). Doping level, Sb (YO):(a) 3.0; (b)0.6; (c) 0.1; (40 value of the reflectivity is lower than expected when dealing with ceramic pellets owing to optical imperfection of the sample surface. 4. Discussion 4.1 Modelling of Data with Reflectivity from Bulk Dielectric Function Tin(1v) oxide adopts the tetragonal rutile structure with space group Dit.There are two formula units per cell and the 15 optical modes span irreducible representations r as follow^:^^* r=Ai,+ A2,+ A2, +Big+ B2,+2Bi,+ E,+ 3E, (1) The dipole-moment operator spans representations E, and A2, and hence only the four optical modes of these symmetries involve the dipole-moment change necessary for infrared activity. Moreover, inspection of the basis vectors shows that the E, modes involve atomic displacements perpendicular to the c axis and the A2, mode displacements parallel to the c axis. The infrared reflectance R(o)at normal incidence is given by R(4= IC1-&4I/C1 ++M2 ={[n(o)-1l2 +k(o)2)/{[n(o)+1]2+k(o)2) (2) where &(a) =[n(o)+ik(o)12 (3)=~(0)~ and the complex dielectric function &(a)is given by n =&(a)~(o) + 1 R:/(w? -o2-ioy,) (4)i= 1 J.MATER. CHEM., 1991, VOL 1 The summation in eqn.(4) extends over the dipole active modes and Ri, mi and yi are respectively the dipole strength, transverse resonance frequency and damping constant for the ith oscillator. For single-crystal SnO, with the electric vector polarised parallel to the c axis, only the one term associated with the Azu mode contributes to the summation (4), giving a dielectric function E,,(o). However, with the electric vector polarised perpendicular to the c axis the summation extends over the three E, modes, giving the function E,,(w). Addition-ally, it is necessary to select the value of E(m) appropriate to the relevant polarisation.The ‘parallel’ and ‘perpendicular’ reflectivities of single-crystal Sn02 calculated from eqn. (2) are shown in Fig. 2, the relevant parameters in eqn. (4)being obtained from the experiments of S~mmitt.~For both polaris-ations a single broad Reststrahlen band appears above 400 cm-’, two of the E, bands in the parallel polarisation being below the wavenumber range available on our spec-trometer. Evidently, the experimental spectrum for our polycrystalline ceramic sample is completely unlike the single-crystal spectra and cannot be obtained by a suitably weighted summation of the reflectances for the two polarisations. We have explored two approaches for calculation of spectra for ceramic samples. The first uses an ‘average’ dielectric function given by &a,(@) =$zz(a) +&xx(a) (5) cav(o)is then inserted into eqn.(2) to calculate the reflectivity. This approach gives two reflectivity maxima above 400 cm-’, although the two peaks are of comparable intensity and the trough between them is much more pronounced than found experimentally [Fig. 3(b)]. An alternative to this ad hoc approach, taking proper account of the random orientation of crystallites, has recently been suggested by Dresselhaus and co-worker~.~This assumes that the grain size is larger than the wavelength of the infrared radiation and involves an integration over the angle 8 between the c axis of a crystallite and the Poynting vector of the 80 60 40 20 hZo 0 80 -c’60 1200 1000 800 600 400 wavenurnber/crn -Fig.2 Simulated infrared reflection spectra for single-crystal SnOJ 1lo), (a)with electric vector polarised parallel to c axis, (b) with electric vector polarised perpendicular to c axis J. MATER. CHEM., 1991, VOL 1 80 60 40 20 50 a, c 80 a, c '60 40 20 0 1200 1000 800 600 400 wavenum ber/cm -' Fig. 3 Simulated infrared reflection spectra of polycrystalline SnO, (a)using the Dresselhaus method for averaging reflectivity over crystal orientation (b)using ad hoc effective medium method for averaging the dielectric function before calculating the reflectivity. See text for details of these procedures where K~(o) =[E,,(o) COS~e +E,,(o) sin2 (7) "&4=C&XX(4l 1'2 (8) This approach gives two Reststrahlen peaks of roughly the correct relative intensity [Fig.3(a)] and the overall spectral profiles are in reasonable agreement with experiment, except that the shoulder on the higher-frequency peak in the model spectrum is less pronounced than that found experimentally, and the peak itself is less sharp than in the experimental spectra. The reasons for the discrepancies are unclear to us at present, although one possibility is that there is significant texturing of the ceramic close to the pellet surface so that the averaging procedure used in eqn. (6)is not quite correct. To model the effects of doping on experimental spectra it is necessary to introduce a term into eqn. (4)to represent the dielectric response of the conduction electrons introduced by doping.In place of eqn. (4)we write n =~(m)&(a) + 1 QT/(o:-o2-ioy,) -sZi/(02-ior,) (9)i= 1 where rpis the plasmon damping parameter and the unscre- ened plasma frequency, R,, is given by R, =(ne2/&om*)1/2 (10) Here, e is the charge on the electron, E~ is the permittivity of free space, n is the carrier concentration and m* is the electron effective mass. The value of m* was fixed by reference to our own previous HREELS data2-4 for 3% Sb doped SnO,. Here a surface plasmon loss is observed at 0.55eV. The surface loss condition Re E(o)= -1 (11) leads to the following expression for the surface plasmon energy ESP: ESP=hR,/[&(m) +1]'12 =(ne2/com*[&(.o)+1]}1/2 (12) Hence we find m*/me=0.75, where me is the electron rest mass.We assume an average value for &(a)in eqn. (12); the possibility of anisotropy in m* does not enter into our analysis. However, some anisotropy in the plasma response is incorpor- ated into our calculations of the reflectivity by the use of different values of &(a)in E,,(o) and E,,(o). Calculated reflectivities for the different doping levels are shown in Fig. 1B. The plasmon energy for 0.1% doped SnO, is only ca. 1000 cm-', so that at this doping level the reflectivity drops markedly across the infrared region extending up to 1200cm-'. The drop becomes less pro- nounced as the plasmon energy increases with increasing doping level. Phonon structure is superimposed on the plas- mon background and becomes progressively weaker with increasing doping level. At higher doping levels, the phonon structure takes the form of two fairly sharp maxima, the highest energy peak occurring at the E, transverse optical (TO) phonon frequency.No well defined structure is found around the LO frequency, corresponding to the minimum in reflectivity for undoped Sn02. Qualitatively, the disappear- ance of structure at the LO frequency can be understood in terms of screening of the long-range coupling that leads to the LO-TO splitting. In view of the model calculations, the experimental data for the highly doped samples, showing a pronounced trough in the reflectivity around the A,,/E, LO phonon frequency, must be regarded as extremely puzzling. 4.2 Modelling of Data using Two-layer Model The discrepancy between experimental data and results from model calculations using the bulk dielectric function leads us to consider analysis of the data using a model where a layer with a carrier concentration lower than that of the bulk sits on top of the undepleted bulk.Details of this model have been given in a recent publication." The rationale for intro- ducing this approach is as follows. It is well known from experiments on thin layers of dielectrics on metals that, at non-normal incidence, reflectivity minima corresponding to LO frequencies of the dielectric overlayer can be observed in experimental spectra." In the present context we suppose that a carrier-free layer can arise from band bending at the surface, mimicking the dielectric layer of the classical experi- ments.The undepleted bulk then functions as the highly reflecting metal underlayer. In experiments on Sb-doped Sn02 using electron spectroscopic techniques under ultrahigh vac- uum (UHV) conditions we find no evidence of surface carrier depletion so that the origin of depletion layers seen in the reflectance experiments carried out in air must lie in depletive adsorption of oxygen on the ceramic surface. The model for the reflectivity is based on a general theory of surface response to electromagnetic fields advanced by Flores and Garcia-Moliner.12 They introduce a surface impedance tensor 2 which can be defined through the equa- tion (SI) EllS=Z*(nx Hs) (13) where c is the speed of light, n the unit outer normal vector from the surface, HSthe magnetic field at the surface and EllS the electric field parallel to the surface, evaluated at the surface.Matching conditions applied to electric and magnetic 454 fields for incident, transmitted and reflected waves at the air/ depletion layer, and depletion layer/bulk interfaces leads to a reflectivity R for p-polarised radiation (H parallel to surface): R= ICzeff-(1/c&o) cosei)/CZeff +(I/CEO) cos @ill2 (14) where Bi is the angle of incidence of the radiation relative to the surface normal and Zeff is the effective impedance of the two-layer system. This is given in terms of impedances of surface and bulk layers 2, and zb, respectively: Zeff=Z,(1 + D2A)/(1 -D2A) (15) where A = (zb -zs)/(zb + zs) (16) and D is the damping factor, D =exp [-dlIm E~(O)O~/C' -q211/2] (17) where E, is the dielectric function for the surface layer of thickness d, and q is the x component of the wavevector of the incident radiation.Note the expected limiting behaviour d+O, Zeff+Zb and d+m, Zeff+Zs. Similar expressions can be derived for s-mode radiation. Results of a calculation based on this model assuming unpolarised radiation (i.e. mixed s and p polarisation) are shown in Fig. 4 for a 200 A depletion layer on 3% Sb-doped SnO,. This thickness is based on the following considerations. I I I 76 t I I I 1 I 1200 1000 800 600 400 wavenumber/cm -' Fig.4 Simulated infrared reflection spectra of 3% Sb-doped SnO, with surface depletion layer 200 8, thick. (a) Carrier free depletion layer, (b)depletion layer supporting plasmon mode of wavenumber 484 cm-' (60 meV), (c) depletion layer supporting plasmon mode of wavenumber 726 cm-I (90 meV). In (b)and (c) it is assumed that the plasmon damping parameter r in the surface layer is given by hT= 50 meV J. MATER. CHEM., 1991, VOL 1 At the (001) surface of SnO, there is one cation per cell. Suppose that oxygen chemisorption on these surface cations depletes four electrons per adsorbed molecule (corresponding to reduction to 02-).Given that there are two cations per cell in the bulk and that the lattice parameter c= 3.185 A, at 3% doping the carrier depletion will extend over a length range d=(4 x 3.185 x 100/3x 2) 8,~200A.Of course, we are not implying that the polycrystalline surface is strongly (001) textured in adopting this approach to estimating the depletion layer thickness. For simplicity, the dielectric function for bulk and surface layers is averaged using the ad hoc procedure of eqn. (5). As expected, a dip in the experimental spectra develops at the LO frequency at the highest E, mode just below 800cm-', but this is much sharper and weaker than in the experimental data. One possibility is that the relaxation time for LO phonons in the surface layer is much shorter than for bulk LO phonons, thus broadening the absorption dip. However, the intensity of the dip still remains too low.This leads us in turn to consider an alternative model where the surface layer supports a reduced (but non-zero) carrier concentration as compared with the bulk. If the plasmon frequency in the surface layer is similar to that of the LO phonons, strong coupling occurs to give modes of mixed plasmon-phonon character. In the reflection experiment, absorption then occurs at the longitudinal frequency of the coupled modes within the surface layer. For plasmon frequen- cies ca. 560-800 cm- (70-100 meV) the simulated spectra bear a striking qualitative resemblance to those measured experimentally. We thus identify the unexpected broad dip in reflection spectra of highly doped SnO, as being associated with a surface layer of reduced carrier concentration.In speculating as to the mechanism of carrier depletion, we are guided by the following considerations. First, as noted above, the depletion layer is not found in UHV experiments and so appears to be related to oxygen adsorption on the ceramic surface. Secondly, major qualitative discrepancies between experimental spectra and simulations based on the bulk dielectric function only become apparent at high doping levels. Previous work has shown that at the higher doping level surface cation sites are increasingly occupied by segre- gated Sb ions, the fractional Sb surface coverage being close to unity at 3% Sb bulk doping It thus appears that segregated Sb cations act as sites for the depletive adsorption of oxygen.This in turn can be rationalised in terms of competition between atmospheric 0, and H20 for surface cation sites. Segregated Sb ions are essentially Sb"' species3 carrying a directional sp hybrid lone pair of electrons. Such ions are likely to be weak Lewis-acid centres, with a low heat of adsorption for HzO. Thus 0, is able to adsorb on the surface Sb sites, producing the depletion layer. 5. Concluding Remarks The present study clearly shows that infrared reflectance spectra of tin dioxide are very sensitive to the bulk carrier concentration, the major effect of doping being to screen out coupling between lattice phonon modes and external electro- magnetic fields. However, the existence of surface depletion layers allows appearance of new reflectance features associated with longitudinal optical modes in the surface layer.Ani- sotropy of the dielectric function introduces further complex- ities into analysis of the reflectance data. C.S.R. is grateful to British Gas for the Award of a Research Scholarship. J. MATER. CHEM., 1991, VOL 1 455 References 7 R. Summitt, J. Appl. Phys., 1968, 39, 3762. Z. M. Jarzebski and J. P. Marton, J. Electrochem SOC., 1976, 123, 8 P. A. Cox, R. G. Egdell, W. R. Flavell and R. Helbig, Vacuum, 1983, 33, 835. 229C. 9 G. L. Doll, J. Steinbeck, G. Dresselhaus, M. S. Dresselhaus, A. J. P. A. Cox, R. G. Egdell, A. F. Orchard, C. Harding, W. R. Pat-terson and P. W. Tavener, SoIid State Commun., 1982,44, 837. P. A. Cox, R. G. Egdell, C. Harding, W. R. Patterson and P. W. 10 Strauss and H. J. Zeiger, Phys. Rev. B, 1987,36, 8884. J. P. Kemp, P.A. Cox, R.G. Egdell and K. Kang, J. Phys. Condens. Matter, 1989, 1, SB123. Tavener, Surf: Sci., 1982, 123, 179. R. G. Egdell, W. R. Flavell and P. W. Tavener, J. Solid State 11 C. Kittell, Introduction to Solid State Physics, John Wiley, New York, 5th edn., 1976. Chem., 1984,51, 345. Z. M. Jarzebski and J. P. Marton, J. Electrochem. SOC., 1976, 123, 333C. 12 F. Flores and F. Garcia-Moliner, Introduction to the Theory of Solid Surfaces, Cambridge University Press, Cambridge, 1979. e.g. J. F. McAleer, P. T. Moseley, J. 0.W. Norris and D. E. Williams, J. Chem. SOC.,Faraday Trans. I, 1987, 83, 1323. Paper 1/00073J;Received 7th January, 1991