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Influence of carrier-free surface layers on infrared reflectance spectra of n-type metallic oxides
Journal of Electron Spectroscopy and Related Phenomena, 54155 (1990) 1173-1182 Elsevier Science Publishers B.V., Amsterdam
1173
Influence of carrier-free surface layers on infrared reflectance spectra of n-type metallic oxides.
P.A. Coxa, R.G. Egdellb,
W.R. Flavellc,
J.P. Kempc,
F.H. Potterb
and C.S.
Rastomjeeb.
a Inorganic Chemistry Laboratory, bDepartment 2Az, UK.
of Chemistry,
CDepartment of Chemistry,
S. Parks Road, Oxford OX1 3QR, UK.
Imperial
College, South Kensington,
UMIST, PO Box 88, Manchester
London SW7
M60 l&D, UK.
Abstract. The influence of carrier-free surface layers on infrared reflection spectra of metallic oxides has been explored using model calculations on two-layer systems. Reflectivity minima are found at LO phonon frequencies. Comparison is made with preliminary experimental data from Sb-doped SnOz ceramics and Nao.eWOs single crystal surfaces oxidised in air at 500°C.
1. INTRODUCTION. Infrared reflectance spectra of solid oxides depend critically upon the electronic properties of the material. It is well-known that for non-metallic oxides, the reflectivity is low above the frequency of phonon modes, being essentially given by (~~(~)-1)~/(~&(~)+1)2, with ~(-1 values of at most 5-6. However, between longitudinal optical (LO) and transverse optical (TO) phonon frequencies, a high reflectivity is found, giving rise to so-called Reststrahlen spectra [l]. In metallic oxides, by contrast, there is high reflectivity at all frequencies below the plasmon frequency. The carriers in metallic materials
0368-2048/90/$03.50
0 1990 Elsevier Science Publishers B.V.
1174
screen out coupling between lattice vibrations and external fields, as well as the long range Coulombic interactions that produce LO-TO splittings 121. Thus to a first approximation, the reflectance spectrum of a metallic oxide will contain only weak features at TO phonon frequencies. In fact the screening is not perfect due to the non-zero screening length, allowing weak structure to appear close to the LO phonon frequency in both high-resolution electron energy loss spectroscopy (HREELS) [31 and infrared reflectance [41. It is obvious that carrier-free surface layers may exert a pronounced influence on infrared reflectance spectra of metallic oxides by allowing coupling of IR radiation to phonons within an ‘unscreened’ layer. Carrier-free or depleted layers may arise in two distinct ways. Firstly, surface states intrinsic to the solid or associated with chemisorption on the crystal surface may trap charge. For large band bending a carrier-free surface layer arises with thickness equal to the two-dimensional surface state concentration divided by the bulk carrier concentration. The second mechanism involves macroscopic oxidation or reduction in the near surface region, which will deplete carriers in n- and p-type oxides respectively. (Out-diffusion of dopant ions can usually be described in redox terms and should be viewed as special case of surface oxidation/reduction.). Here the thickness of carrier-free layers may be very much greater than those produced by chemisorption. Depletion layers or carrier-free layers on conducting oxide surfaces are of interest in relation to a diverse range of areas, These include conductivity sensors based on tin or zinc oxide whose response to reducing gases is believed to be intimately connected with depletive adsorption of oxygen [5]; and high temperature oxide superconductors where recent HREELS experiments indicate the existence of carrier-free layers even on high quality cleavage surfaces 161. The obvious advantage of IR spectroscopy as compared with HREELS is the ability of the former to interrogate surfaces under ambient pressure conditions. In the present communication we use simple model calculations to explore the effects of carrier-free layers on reflectance spectra of two prototype n-type-metallic oxides. These are the sodium tungsten bronzes NaxWOa and Sb-doped SnOz, Sn&lbxO~. In the former case, Na acts as an interstitial dopant and with x values in the range 0.6-0.8, the plasmon energy is just below 2eV 171. The doping level produced by substitution of Sn by Sb is restricted to x values below 0.03, and the highest plasmon energy for doped SnOa ceramics is around 0.5eV [83. Comparison is made with experimental reflectance
spectra measured in air. In the case of single crystal Nao.sWOa, an
increasingly thick carrier-free surface layer is produced by oxidation in air at 5OO”C, whilst for Sno.97Sbo.oa02 a depletion layer arises spontaneously in air, presumably
due to oxygen chemisorption.
1175
2. MODEL CALCULATIONS. A simple model for the reflectivity of a two-layer system consisting of a carrier-free or carrier-depleted surface layer on top of an undepleted bulk has been given elsewhere [4,91. The model takes account of interference between waves reflected from the air/surface-layer and surface layer/bulk interfaces, as well as damping of radiation across the depletion layer due to absorption. The essential inputs to the model are the thickness of the depletion layer and complex dielectric functions for bulk and surface layers. Results for calculations on Nao.eWOa(lOO)with a WOa overlayer of varying thickness are shown in figure 1 for the wavenumber range 6OOcm-1to 1400 cm-l. The essentially cubic structure of the sodium tungsten bronzes for x values greater than 0.4 supports 3 IR active phonon modes of T1, symmetry. In decreasing order of frequency, these may be described as W-O stretch, W-O bend and Na+ rattle relative to WOs octahedra 131.Of these modes, only the W-O stretch mode is of high enough frequency to appear in figure 1. Dielectric function parameters were derived from previous HREELS work [2,3]. It was assumed that the WO3 over-layer retained the cubic structure of the tungsten bronze substrate and that the phonon parameters were the same as those of the bulk: the overlayer is distinguished from the bulk by not supporting a plasmon mode or a sodium rattling mode. In the absence of a depletion layer, the spectra show a high reflectivity throughout the IR, with only a weak feature close to the TO frequency of the highest T1, mode at 766cm-1. Even with a depletion layer only 1OA thick, a dip has appeared close to the LO phonon frequency at 96&m-1 with intensity comparable to that of the TO feature. The LO phonon absorption becomes stronger with increasing thickness of the WO3 overlayer and dominates spectra for thicknesses between 102A and 105A. Finally when the carrier-free layer becomes much thicker than the wavelength of the infrared radiation, the spectra evolve into a typical Reststrahlen spectrum for a solid with a single IR active phonon mode. The appearance of LO phonon absorption in the carrierfree layer is analogous to excitation of LO phonons in thin films of dielectric materials such as LiF on metallic silver substrates 1101. SnO2 is a little more complicated because the tetragonal rutile structure supports four IR active phonon modes: three E, modes with dipole change perpendicular to the c-axis and a single Azu mode polarised parallel to the caxis [ll]. To make contact with experimental data on polycrystalline samples (section 3), we have evaluated the reflectivity with an ud hoc procedure using an average dielectric function E,,(O) = (l/3)& 1I to)+ (2/3)&.(o). Structure above 490cm-1 involves both the Asu mode and the highest energy E, mode. In figure
1176
0.916
-
OA
0.916t
/
Wavenumber /cm-l
Figure 1. Calculated IR reflectance varying thickness. Unpolarised
spectra of Na0.6W03( 100) with cubic WO3 overlayer of
radiation incident at 45’ relative to surface normal. The dip
below SO&m-1 is due to the screened W-O stretch TO phonon mode. The increasingly
strong
dip just below lOOOcm-* is due to the corresponding LO phonon. Note how spectra evolve into a Reststrahlen-like spectrum for a thick WOg overlayer. 2a we show the reflectivity layer
20081 thick.
IR measurements from our own
Dielectric
for polycrystalline parameters
Sn0.&3b0.0302
for undoped
of Summitt [ll]. Plasmon previous HREELS experiments
feature (at about 750cm-1) again corresponds associated with both E, and Aau modes.
with a carrier
SnOa were taken
parameters [8]. The to LO phonon
free
from the
were again taken highest frequency absorption,
now
1177
82 -
a
78 76 -
82.
b
80. 78
82.
76 I200
C
I
I
I
1000
800
600
400
Wavenumber I cm-l Figure 2. Calculated IR reflectance spectra of Sn0.g7Sb0.0302 with 200A depletion layer. Unpolarised radiation incident at 45’ angle of incidence relative to surface normal. In (a) the depletion layer is assumed to be carrier-free, but in (b) and (c) the depletion layer supports plasmon modes with wavenumber484cm-1 and 726cm-1 respectively. Doped
SnOz differs further from Na,WOa
in that carrier self trapping
to
give localised small polaron states does not occur at low doping levels. Thus in the latter system when the composition parameter drops below x-O.3 there is a transition to a non-metallic state and the plasmon found at higher doping levels is replaced by an intervalence charge transfer excitation at 1.4eV whose frequency shows little change on further lowering the doping level 112,131. By
1178
contrast SnOa remains metallic for carrier concentrations
down to 5xlOlVcm3
1
corresponding to x values of 1.8x10-4 [141. The possibility thus emerges of low frequency plasmon modes in surface layers where the carrier concentration is reduced below the bulk value, but not reduced to zero. In figures 2b and 2c we have therefore explored the effects of a 2OOA layer supporting plasmon modes with frequencies close to those of the LO phonons. In this situation there is strong coupling between plasmon and phonon modes and broad reflectivity minima between 700cm-1 and 900cm-1 corresponding found in the simulations.
3. COMPARISON
to the coupled modes are
WITH EXPE RIMEWI’AL DATA
We have attempted to produce carrier-free layers of varying thickness on single crystal Na,W03(100) surfaces by oxidation in air at temperatures between 5OO’C and 6OO’C. The most likely mode of oxidation involves reversal of the electrolytic reduction process used to grow the tungsten bronze crystals in the first instance 141: Na,WO+)+
(x/4)02(g)-+
(~-x/‘&WO&)+
M2)Na2WOdd
Thus the carrier free surface layers investigated in our experiments are considerably more complicated than the idealised cubic WO3 layer entering into the spectral simulations. Some typical reflectance spectra are shown in figure 3. The reflectivity
is
initially high over the complete wavenumber range up to 8000cm-1, but after oxidation for 2.5 hours at 5OO’C the reflectivity drops noticeably across this range with a shallow minimum at 6500cm- 1. With further oxidation a broad pattern of reflectivity maxima and minima develops, with progressively decreasing separation between the features. The broad structure is interpreted as arising from the differing phase relationships between waves reflected from the air/carrier-free and carrier-free/bulk interfaces. Assuming a value s(oo)=B for the dielectric constant of the carrier-free layer, the spacing between successive reflectivity minima allows us to make rough estimates of the thicknesses of the carrier-free surface layers, as indicated in the caption to figure 3. Associated with the interference fringes, a well-defined pattern of sharp reflectivity minima develops below lOOOcm-1, as shown in the right hand panel of figure 3. Clearly this low frequency structure is more complex than in the simulations. This must be due to the fact that oxidation does not produce an ideally cubic WO3 surface layer but a multiphase mixture of probably noncubic WO3 1151 and Na2W04 , as indicated above. However,
the simulations
are relevant in rationalising
the appearance
of
8000 4000 Wavenumber /
400 cm-l
1400 1000 Wavenumber
500 / cm-l
Figure 3. Infrared reflection spectra of Nao_eW03(100) oxidised in air at 500°C measured with unpolarised radiation incident at 14’ to sample surface using Perkin Elmer 1760X FTIR spectrometer with wideband MCT detector. (a) polished crystal washed in distilled water (b) after oxidation for 2.5 hours (c) 36 hours (d) 54 hours (e) 78 hours (f) 132 hours. In the left hand panel the reflectivity scale runs from O-100% in each case, but in the right hand panel the scale for (a) and (b) is from 90% to 100%. The thickness of the oxidised surface layer is estimated to be XNIOA, WooA, 1OOOOAand 15oo0Ain (c), (d), (e) and (f) respectively. Details of crystal preparation are given in reference (4). absorption-like features with low reflectivity at the phonon frequencies and high reflectivity at either side, rather than Reststrahlen-like features with high reflectivity between LO and TO frequencies and low reflectivity to higher and lower frequency.
1180 Next we consider
reflection
spectra of Sb-doped
SnOz ceramics.
Details of
sample preparation and characterisation are given elsewhere [81. Experimental reflection spectra for a range of bulk doping levels up to x=0.03 are shown in the left hand panel of figure 4. In the right hand panel are shown simulations assuming that the carrier concentration does not vary with depth. The dielectric parameters in these simulations are essentially the same as those in figure 2, but with the plasmon energy scaled for the varying doping levels. However, we have averaged the reflectivity over crystal orientation according to the method outlined by Dresselhaus El61 rather than calculate the reflectivity from an averaged dielectric function. The Dresselhaus averaging procedure is appropriate to situations where the grain size in the solid is greater than the wavelength of the IR radiation, as in the case for our wellsintered ceramic samples. However, there is in fact little difference between spectra simulated through the two differing procedures. The model spectra of figure 4 nicely illustrate the expected effects of doping through to a metallic state on IR reflectance of a metal oxide. Changes in reflectivity at phonon frequencies in the metallic samples are superimposed on a background reflectivity that becomes stronger and flatter with increasing doping level. At the same time the phonon structure becomes weaker and marked reflectivity changes are found only at TO frequencies. The simulated spectra of figure 4 are in broad agreement with the experimental spectra at low doping level, although the detailed lineshape of the first Reststrahlen band of undoped SnOa is not perfectly reproduced. Note also that the experimental reflectivity for ceramic samples does not reach the same high values as found in simulations owing to optical imperfection of the ceramics. However, at high doping levels major discrepancies between experimental and simulated spectra become apparent , with development of a broad reflectivity minimum around 750cm-1 in the experimental spectrum of 0 2.Comparison with the simulated spectra of figure 2 immediately S"o.97Sb 0.03 suggests that the broad feature is associated with coupled plasmon-phonon modes in surface layer with reduced, but non-zero, carrier concentration or ,alternatively, with significantly broadened LO phonon absorption in a carrierfree surface layer. The IR results are at variance with HREELS and photoemission experiments on the same ceramic samples, which give no indication of carrier depleted surface layers 18,171. However, the former experiments are conducted in UHV and the latter in air, thus suggesting that oxygen chemisorption is an important factor in producing the carrier depletion. Further IR experiments, preferably on single crystal samples under controlled atmosphere conditions, are needed to clarify this matter.
1181 3.0% Sb
80.. 60.. 40.. 20.. 0 40
0.
30 20
40..
10
20.. 0. 8. 0.1% Sb
5’
40
0. Pure Sn02
80..Pure Sn02
30
60..
20
40..
10
20..
0 Ld!? 1200 800 Wavenumber
400 /cm-l
10200
) 800
Wavenumber
400 /cm-l
Figure 4. Left hand panel: IR reflection spectra of Sb-doped SnO2 ceramics measured with unpolarised radiation incident at 20’ to sample surface using Mattson Alpha-Centaur-i FIIR spectrometer with DTGS detector. Right hand panel: simulated spectra using dielectric parameters for undoped SnO2 from reference 11 and plasmon parameters from reference 8. The reflectivity has been averaged over crystallite orientation using procedure of reference 16.
4. CONCLUDING R&MARKS. Simple simulations of IR reflection spectra show the way in which the technique is expected to be sensitive to carrier-free surface layers with
1182
thicknesses extending from a few Angstroms at the one extreme to several thousand Angstroms at the other. Comparison with some preliminary experiments further emphasises the potential power of IR reflectance in this area.
5. ACKNOWTJ3DGl3MENTS. We are grateful to British Gas PLC for the award of a Research Scholarship to CSR and to the Queen’s College Oxford for the award of a Junior Research Fellowship to JPK.
6. REFJ3RENCES. 1. 2. 3. 4. 5. 6. 7. B, 8. 9.
C. Kittel, Introduction to Solid State Physics, John Wiley, New York, 1976. P.A. Cox and J.P. Kemp, Surf. Sci., 210 (1989) 225. P.A.Cox, M.D. Hill, F. Peplinskii and R.G.Egdell, Surf. Sci., 141 (1984) 13. J.P. Kemp, P.A. Cox, R.G. Egdell and K. Kang, J. Phys. Condens. Matter 1 (1989) SB123. J.F. McAleer, P.T. Moseley, J.O.W. Norris and D.E. Williams, J.C.S. Faraday Trans. I, 83 0.987) 1323. J.E. Demuth, B.N.J. Persson, F. Holtzberg and C.V. Chandrasekhar, Phys. Rev. Letters, 64 (1990) 603. R.E. Dietz, M. Campagna, J.N. Chalzalviel, and H.R. Shanks, Phys. Rev. 17 (1978) 3790. R.G. Egdell, W.R. Flavell and R.G. Egdell, J. Solid State Chem., 51 (1984) 345. F. Flares and F. Garcia-Moliner, Introduction to the Theory of Solid Surfaces, Cambridge University Press, Cambridge, 1979.
10. D.W. Berreman, Phys. Rev. B, 130 (1963) 2193. 11. R. Summitt, J. Appl. Phys., 39 (1968) 3762. 12.0.F. Schirmer, V. Wittwer, G. Baur and G. Brandt, J. Electrochem. Sot., 124 (1977) 749. 13. R.G. Egdell and G.B. Jones, J. Solid State Chem., 81(1989) 137. 14. Z.M. Jarzebski and J.P. Marton, J. Electrochem. Sot., 123 (1976) 299C. 15. E. Salje, Acta Crystogr. Sect. A, 31(1975) 360. 16. G.L. Doll, J. Steinbeck, G. Dresselhaus, M.S. Dresselhaus, A.J. Strauss and H.J. Zeiger, Phys. Rev. B, 36 (1987) 8884, 17. P.A. Cox, R.G. Egdell, C. Harding, W.R. Patterson and P.J. Tavener, Surf. Sci., 123 (1982) 179.
1173
Influence of carrier-free surface layers on infrared reflectance spectra of n-type metallic oxides.
P.A. Coxa, R.G. Egdellb,
W.R. Flavellc,
J.P. Kempc,
F.H. Potterb
and C.S.
Rastomjeeb.
a Inorganic Chemistry Laboratory, bDepartment 2Az, UK.
of Chemistry,
CDepartment of Chemistry,
S. Parks Road, Oxford OX1 3QR, UK.
Imperial
College, South Kensington,
UMIST, PO Box 88, Manchester
London SW7
M60 l&D, UK.
Abstract. The influence of carrier-free surface layers on infrared reflection spectra of metallic oxides has been explored using model calculations on two-layer systems. Reflectivity minima are found at LO phonon frequencies. Comparison is made with preliminary experimental data from Sb-doped SnOz ceramics and Nao.eWOs single crystal surfaces oxidised in air at 500°C.
1. INTRODUCTION. Infrared reflectance spectra of solid oxides depend critically upon the electronic properties of the material. It is well-known that for non-metallic oxides, the reflectivity is low above the frequency of phonon modes, being essentially given by (~~(~)-1)~/(~&(~)+1)2, with ~(-1 values of at most 5-6. However, between longitudinal optical (LO) and transverse optical (TO) phonon frequencies, a high reflectivity is found, giving rise to so-called Reststrahlen spectra [l]. In metallic oxides, by contrast, there is high reflectivity at all frequencies below the plasmon frequency. The carriers in metallic materials
0368-2048/90/$03.50
0 1990 Elsevier Science Publishers B.V.
1174
screen out coupling between lattice vibrations and external fields, as well as the long range Coulombic interactions that produce LO-TO splittings 121. Thus to a first approximation, the reflectance spectrum of a metallic oxide will contain only weak features at TO phonon frequencies. In fact the screening is not perfect due to the non-zero screening length, allowing weak structure to appear close to the LO phonon frequency in both high-resolution electron energy loss spectroscopy (HREELS) [31 and infrared reflectance [41. It is obvious that carrier-free surface layers may exert a pronounced influence on infrared reflectance spectra of metallic oxides by allowing coupling of IR radiation to phonons within an ‘unscreened’ layer. Carrier-free or depleted layers may arise in two distinct ways. Firstly, surface states intrinsic to the solid or associated with chemisorption on the crystal surface may trap charge. For large band bending a carrier-free surface layer arises with thickness equal to the two-dimensional surface state concentration divided by the bulk carrier concentration. The second mechanism involves macroscopic oxidation or reduction in the near surface region, which will deplete carriers in n- and p-type oxides respectively. (Out-diffusion of dopant ions can usually be described in redox terms and should be viewed as special case of surface oxidation/reduction.). Here the thickness of carrier-free layers may be very much greater than those produced by chemisorption. Depletion layers or carrier-free layers on conducting oxide surfaces are of interest in relation to a diverse range of areas, These include conductivity sensors based on tin or zinc oxide whose response to reducing gases is believed to be intimately connected with depletive adsorption of oxygen [5]; and high temperature oxide superconductors where recent HREELS experiments indicate the existence of carrier-free layers even on high quality cleavage surfaces 161. The obvious advantage of IR spectroscopy as compared with HREELS is the ability of the former to interrogate surfaces under ambient pressure conditions. In the present communication we use simple model calculations to explore the effects of carrier-free layers on reflectance spectra of two prototype n-type-metallic oxides. These are the sodium tungsten bronzes NaxWOa and Sb-doped SnOz, Sn&lbxO~. In the former case, Na acts as an interstitial dopant and with x values in the range 0.6-0.8, the plasmon energy is just below 2eV 171. The doping level produced by substitution of Sn by Sb is restricted to x values below 0.03, and the highest plasmon energy for doped SnOa ceramics is around 0.5eV [83. Comparison is made with experimental reflectance
spectra measured in air. In the case of single crystal Nao.sWOa, an
increasingly thick carrier-free surface layer is produced by oxidation in air at 5OO”C, whilst for Sno.97Sbo.oa02 a depletion layer arises spontaneously in air, presumably
due to oxygen chemisorption.
1175
2. MODEL CALCULATIONS. A simple model for the reflectivity of a two-layer system consisting of a carrier-free or carrier-depleted surface layer on top of an undepleted bulk has been given elsewhere [4,91. The model takes account of interference between waves reflected from the air/surface-layer and surface layer/bulk interfaces, as well as damping of radiation across the depletion layer due to absorption. The essential inputs to the model are the thickness of the depletion layer and complex dielectric functions for bulk and surface layers. Results for calculations on Nao.eWOa(lOO)with a WOa overlayer of varying thickness are shown in figure 1 for the wavenumber range 6OOcm-1to 1400 cm-l. The essentially cubic structure of the sodium tungsten bronzes for x values greater than 0.4 supports 3 IR active phonon modes of T1, symmetry. In decreasing order of frequency, these may be described as W-O stretch, W-O bend and Na+ rattle relative to WOs octahedra 131.Of these modes, only the W-O stretch mode is of high enough frequency to appear in figure 1. Dielectric function parameters were derived from previous HREELS work [2,3]. It was assumed that the WO3 over-layer retained the cubic structure of the tungsten bronze substrate and that the phonon parameters were the same as those of the bulk: the overlayer is distinguished from the bulk by not supporting a plasmon mode or a sodium rattling mode. In the absence of a depletion layer, the spectra show a high reflectivity throughout the IR, with only a weak feature close to the TO frequency of the highest T1, mode at 766cm-1. Even with a depletion layer only 1OA thick, a dip has appeared close to the LO phonon frequency at 96&m-1 with intensity comparable to that of the TO feature. The LO phonon absorption becomes stronger with increasing thickness of the WO3 overlayer and dominates spectra for thicknesses between 102A and 105A. Finally when the carrier-free layer becomes much thicker than the wavelength of the infrared radiation, the spectra evolve into a typical Reststrahlen spectrum for a solid with a single IR active phonon mode. The appearance of LO phonon absorption in the carrierfree layer is analogous to excitation of LO phonons in thin films of dielectric materials such as LiF on metallic silver substrates 1101. SnO2 is a little more complicated because the tetragonal rutile structure supports four IR active phonon modes: three E, modes with dipole change perpendicular to the c-axis and a single Azu mode polarised parallel to the caxis [ll]. To make contact with experimental data on polycrystalline samples (section 3), we have evaluated the reflectivity with an ud hoc procedure using an average dielectric function E,,(O) = (l/3)& 1I to)+ (2/3)&.(o). Structure above 490cm-1 involves both the Asu mode and the highest energy E, mode. In figure
1176
0.916
-
OA
0.916t
/
Wavenumber /cm-l
Figure 1. Calculated IR reflectance varying thickness. Unpolarised
spectra of Na0.6W03( 100) with cubic WO3 overlayer of
radiation incident at 45’ relative to surface normal. The dip
below SO&m-1 is due to the screened W-O stretch TO phonon mode. The increasingly
strong
dip just below lOOOcm-* is due to the corresponding LO phonon. Note how spectra evolve into a Reststrahlen-like spectrum for a thick WOg overlayer. 2a we show the reflectivity layer
20081 thick.
IR measurements from our own
Dielectric
for polycrystalline parameters
Sn0.&3b0.0302
for undoped
of Summitt [ll]. Plasmon previous HREELS experiments
feature (at about 750cm-1) again corresponds associated with both E, and Aau modes.
with a carrier
SnOa were taken
parameters [8]. The to LO phonon
free
from the
were again taken highest frequency absorption,
now
1177
82 -
a
78 76 -
82.
b
80. 78
82.
76 I200
C
I
I
I
1000
800
600
400
Wavenumber I cm-l Figure 2. Calculated IR reflectance spectra of Sn0.g7Sb0.0302 with 200A depletion layer. Unpolarised radiation incident at 45’ angle of incidence relative to surface normal. In (a) the depletion layer is assumed to be carrier-free, but in (b) and (c) the depletion layer supports plasmon modes with wavenumber484cm-1 and 726cm-1 respectively. Doped
SnOz differs further from Na,WOa
in that carrier self trapping
to
give localised small polaron states does not occur at low doping levels. Thus in the latter system when the composition parameter drops below x-O.3 there is a transition to a non-metallic state and the plasmon found at higher doping levels is replaced by an intervalence charge transfer excitation at 1.4eV whose frequency shows little change on further lowering the doping level 112,131. By
1178
contrast SnOa remains metallic for carrier concentrations
down to 5xlOlVcm3
1
corresponding to x values of 1.8x10-4 [141. The possibility thus emerges of low frequency plasmon modes in surface layers where the carrier concentration is reduced below the bulk value, but not reduced to zero. In figures 2b and 2c we have therefore explored the effects of a 2OOA layer supporting plasmon modes with frequencies close to those of the LO phonons. In this situation there is strong coupling between plasmon and phonon modes and broad reflectivity minima between 700cm-1 and 900cm-1 corresponding found in the simulations.
3. COMPARISON
to the coupled modes are
WITH EXPE RIMEWI’AL DATA
We have attempted to produce carrier-free layers of varying thickness on single crystal Na,W03(100) surfaces by oxidation in air at temperatures between 5OO’C and 6OO’C. The most likely mode of oxidation involves reversal of the electrolytic reduction process used to grow the tungsten bronze crystals in the first instance 141: Na,WO+)+
(x/4)02(g)-+
(~-x/‘&WO&)+
M2)Na2WOdd
Thus the carrier free surface layers investigated in our experiments are considerably more complicated than the idealised cubic WO3 layer entering into the spectral simulations. Some typical reflectance spectra are shown in figure 3. The reflectivity
is
initially high over the complete wavenumber range up to 8000cm-1, but after oxidation for 2.5 hours at 5OO’C the reflectivity drops noticeably across this range with a shallow minimum at 6500cm- 1. With further oxidation a broad pattern of reflectivity maxima and minima develops, with progressively decreasing separation between the features. The broad structure is interpreted as arising from the differing phase relationships between waves reflected from the air/carrier-free and carrier-free/bulk interfaces. Assuming a value s(oo)=B for the dielectric constant of the carrier-free layer, the spacing between successive reflectivity minima allows us to make rough estimates of the thicknesses of the carrier-free surface layers, as indicated in the caption to figure 3. Associated with the interference fringes, a well-defined pattern of sharp reflectivity minima develops below lOOOcm-1, as shown in the right hand panel of figure 3. Clearly this low frequency structure is more complex than in the simulations. This must be due to the fact that oxidation does not produce an ideally cubic WO3 surface layer but a multiphase mixture of probably noncubic WO3 1151 and Na2W04 , as indicated above. However,
the simulations
are relevant in rationalising
the appearance
of
8000 4000 Wavenumber /
400 cm-l
1400 1000 Wavenumber
500 / cm-l
Figure 3. Infrared reflection spectra of Nao_eW03(100) oxidised in air at 500°C measured with unpolarised radiation incident at 14’ to sample surface using Perkin Elmer 1760X FTIR spectrometer with wideband MCT detector. (a) polished crystal washed in distilled water (b) after oxidation for 2.5 hours (c) 36 hours (d) 54 hours (e) 78 hours (f) 132 hours. In the left hand panel the reflectivity scale runs from O-100% in each case, but in the right hand panel the scale for (a) and (b) is from 90% to 100%. The thickness of the oxidised surface layer is estimated to be XNIOA, WooA, 1OOOOAand 15oo0Ain (c), (d), (e) and (f) respectively. Details of crystal preparation are given in reference (4). absorption-like features with low reflectivity at the phonon frequencies and high reflectivity at either side, rather than Reststrahlen-like features with high reflectivity between LO and TO frequencies and low reflectivity to higher and lower frequency.
1180 Next we consider
reflection
spectra of Sb-doped
SnOz ceramics.
Details of
sample preparation and characterisation are given elsewhere [81. Experimental reflection spectra for a range of bulk doping levels up to x=0.03 are shown in the left hand panel of figure 4. In the right hand panel are shown simulations assuming that the carrier concentration does not vary with depth. The dielectric parameters in these simulations are essentially the same as those in figure 2, but with the plasmon energy scaled for the varying doping levels. However, we have averaged the reflectivity over crystal orientation according to the method outlined by Dresselhaus El61 rather than calculate the reflectivity from an averaged dielectric function. The Dresselhaus averaging procedure is appropriate to situations where the grain size in the solid is greater than the wavelength of the IR radiation, as in the case for our wellsintered ceramic samples. However, there is in fact little difference between spectra simulated through the two differing procedures. The model spectra of figure 4 nicely illustrate the expected effects of doping through to a metallic state on IR reflectance of a metal oxide. Changes in reflectivity at phonon frequencies in the metallic samples are superimposed on a background reflectivity that becomes stronger and flatter with increasing doping level. At the same time the phonon structure becomes weaker and marked reflectivity changes are found only at TO frequencies. The simulated spectra of figure 4 are in broad agreement with the experimental spectra at low doping level, although the detailed lineshape of the first Reststrahlen band of undoped SnOa is not perfectly reproduced. Note also that the experimental reflectivity for ceramic samples does not reach the same high values as found in simulations owing to optical imperfection of the ceramics. However, at high doping levels major discrepancies between experimental and simulated spectra become apparent , with development of a broad reflectivity minimum around 750cm-1 in the experimental spectrum of 0 2.Comparison with the simulated spectra of figure 2 immediately S"o.97Sb 0.03 suggests that the broad feature is associated with coupled plasmon-phonon modes in surface layer with reduced, but non-zero, carrier concentration or ,alternatively, with significantly broadened LO phonon absorption in a carrierfree surface layer. The IR results are at variance with HREELS and photoemission experiments on the same ceramic samples, which give no indication of carrier depleted surface layers 18,171. However, the former experiments are conducted in UHV and the latter in air, thus suggesting that oxygen chemisorption is an important factor in producing the carrier depletion. Further IR experiments, preferably on single crystal samples under controlled atmosphere conditions, are needed to clarify this matter.
1181 3.0% Sb
80.. 60.. 40.. 20.. 0 40
0.
30 20
40..
10
20.. 0. 8. 0.1% Sb
5’
40
0. Pure Sn02
80..Pure Sn02
30
60..
20
40..
10
20..
0 Ld!? 1200 800 Wavenumber
400 /cm-l
10200
) 800
Wavenumber
400 /cm-l
Figure 4. Left hand panel: IR reflection spectra of Sb-doped SnO2 ceramics measured with unpolarised radiation incident at 20’ to sample surface using Mattson Alpha-Centaur-i FIIR spectrometer with DTGS detector. Right hand panel: simulated spectra using dielectric parameters for undoped SnO2 from reference 11 and plasmon parameters from reference 8. The reflectivity has been averaged over crystallite orientation using procedure of reference 16.
4. CONCLUDING R&MARKS. Simple simulations of IR reflection spectra show the way in which the technique is expected to be sensitive to carrier-free surface layers with
1182
thicknesses extending from a few Angstroms at the one extreme to several thousand Angstroms at the other. Comparison with some preliminary experiments further emphasises the potential power of IR reflectance in this area.
5. ACKNOWTJ3DGl3MENTS. We are grateful to British Gas PLC for the award of a Research Scholarship to CSR and to the Queen’s College Oxford for the award of a Junior Research Fellowship to JPK.
6. REFJ3RENCES. 1. 2. 3. 4. 5. 6. 7. B, 8. 9.
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