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The screening response of a dilute electron gas in core level photoemission from Sb-doped SnO2
Journal of Electron Spectroscopy and Related Phenomena 128 (2003) 59–66 www.elsevier.com / locate / elspec
The screening response of a dilute electron gas in core level photoemission from Sb-doped SnO 2 a, a b R.G. Egdell *, T.J. Walker , G. Beamson a
b
Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3 QR, UK Research Unit for Surfaces Transforms and Interfaces, Daresbury Laboratory, Warrington, Cheshire WA4 4 AD, UK Received 2 July 2002; received in revised form 19 August 2002; accepted 26 August 2002
Abstract The variation of core lineshape with carrier concentration in Sb-doped SnO 2 has been studied by high-resolution X-ray photoemission spectroscopy. The Sn 3d core levels display an asymmetric lineshape which may be fitted with components associated with screened and unscreened final states. The separation between the two fitted peaks and the relative intensity of the screened component both increase with increasing carrier concentration. The satellite energies are of the order expected for a screening mechanism involving excitation of plasmons. 2002 Elsevier Science B.V. All rights reserved. Keywords: Antimony-doped tin oxide; Core-hole screening; Plasmons
1. Introduction It was recognized early in the application of photoemission techniques to simple metallic solids that plasmon satellites make a significant contribution to core level structure in X-ray photoelectron spectra. Much of the early work in this area was concerned with unravelling the relative contributions of intrinsic and extrinsic structure and with rationalising the pattern of multiple plasmon excitations [1]. The weak coupling models developed 30 years ago suggested that the intrinsic plasmon satellite intensity I should increase as the conduction electron density n decreases according to the expression I~n 21 / 3 [2]. Interest in this area was rekindled *Corresponding author. Tel.: 144-1865-275-965; fax: 144-1865272-690. E-mail address: [email protected] (R.G. Egdell).
by the observation of very strong satellites in core photoemission of ‘narrow band’ metallic oxides including the sodium tungsten bronzes NaxWO 3 [3– 6]; the superconducting spinel LiTi 2 O 4 [7,8]; dioxides such as MoO 2 [8] and RuO 2 [9]; and the ternary metallic pyrochlore ruthenates Pb 2 Ru 2 O 7 and Bi 2 Ru 2 O 7 [10]. These materials all have a much more dilute electron gas than that in conventional metals and the plasmon energies are only around 1–2 eV, as compared with values usually well in excess of 5 eV for simple metals. Weak coupling models therefore suggest that there should be very strong low energy plasmon satellites in core photoemission from these materials. However, it is obvious that this conclusion calls into question the applicability of a weak coupling model in the first place. Moreover, in the ‘simple’ metals the overall lineshape involves multiple plasmon loss satellites, whereas for the ‘narrow band’ metals only a single satellite is
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observed. Wertheim and co-workers [3–5] suggested an alternative limiting model for the screening response in a narrow band metal. This involves a screening mechanism in which the Coulomb potential of the core hole at an ionised atom creates a localised trap state. In this situation two different final states are then accessible depending on whether the localised state remains empty (giving an unscreened states) or is filled by transfer of an electron from the conduction band (to give a screened final state). In the model developed by Kotani and Toyazawa [11] the screened final state gives rise to an asymmetric line to low binding energy of the lifetime broadened peak associated with the unscreened final state. In the alternative language of the plasmon model the high binding energy unscreened peak corresponds to an extrinsic plasmon satellite whose Lorentzian linewidth will be determined by the conduction electron scattering rate. Our recent interest in this longstanding problem has been stimulated by the observation of very strong satellite structure in core XPS of oxides such as Sb-doped SnO 2 [12] and Sn-doped In 2 O 3 [13]. These oxides are well-known as transparent conducting materials which transmit visible light but reflect infrared radiation. The plasmon energies in transparent conducting oxides are at most around 0.7 eV, which is of course comparable with intrinsic core linewidths. Plasmon satellite structure is therefore expected to overlap the ‘main’ core level peak to give an asymmetric core lineshape. In the present communication we make a systematic study of the variation in core lineshape with carrier concentration in Sb-doped SnO 2 . Satellite energies and intensities derived by curve fitting the Sn 3d 5 / 2 core line to two components vary qualitatively in the way expected on the basis of the plasmon model, although the quantitative agreement is not perfect.
2. Experimental High purity tin(IV) oxide was obtained from Johnson Matthey. Phase pure antimony-doped tin oxide was prepared by a co-precipitation procedure, as described previously [14–16]. The powders were pressed into 13-mm pellets and sintered in air at
1000 8C for several days to yield strong ceramic discs. Surface plasmon energies were determined from electron energy loss spectra measured in an ESCALAB spectrometer (VG Scientific). The mode of operation of this spectrometer and its application to the study of electron spectra of SnO 2 has been described in detail elsewhere [14–16]. High-resolution X ray photoemission spectra were measured in a Scienta ESCA 300 spectrometer located in the Research Unit for Surfaces, Transforms and Interfaces (RUSTI) at Daresbury Laboratory. This incorporates a rotating anode X-ray source, a seven-crystal X-ray monochromator and a 300-mm mean radius spherical sector electron energy analyser with parallel electron detection system. The X-ray source was run with 200 mA emission current and 14 kV anode bias, whilst the analyser operated at 150 eV pass energy with 0.5-mm slits. Gaussian convolution of the analyser resolution with a linewidth of 260 meV for the X-ray source gives an effective instrument resolution of 350 meV. Binding energies are referenced to the Fermi energy of an ion bombarded silver foil which is regularly used to calibrate the spectrometer. The ceramic pellets of undoped SnO 2 and Sbdoped SnO 2 were cleaned in situ in the preparation chamber of the Scienta spectrometer by annealing in UHV at about 750 8C for 2–3 h, heating being effected by an electron beam heater. Surfaces prepared in this way were free of structure due to carbon or other contaminants and remained clean for the duration of the spectroscopic measurements.
3. Results and discussion Fig. 1a shows X-ray photoelectron spectra in the region of the Sn 3d, Sb 3d and O1s core levels. The Sb 3d 5 / 2 peak overlaps the O1s core peak, but the surface Sb concentration can be estimated by comparing the Sb 3d 3 / 2 and Sn 3d 3 / 2 intensities after subtraction of a Shirley background. Fig. 1(b) shows the apparent Sb / Sn atomic ratios derived by dividing the 3d intensities by the relevant ionisation crosssections. This figure also shows the corresponding data derived from Sb 4d1Sn 4d, Sb 3p 3 / 2 1Sn 3p 3 / 2 , and MNN Auger peaks. Note that the Auger
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Fig. 1. (a) Core level XPS encompassing the Sn 3d, Sb 3d and O1s regions for Sb-doped SnO 2 at the various doping levels indicated. Note that a Sb 3d 3 / 2 peak is visible in all spectra. The Sb 3d 5 / 2 peak overlaps the O1s peak. Binding energies are referenced to the Fermi energy of an Ag sample used to calibrate the spectrometer. (b) Intensity ratios between Sb and Sn core level peaks, corrected for ionisation atomic cross-sections. Uncorrected data for MNN Auger peaks are also shown. Note that the intensity axis is logarithmic.
intensities are uncorrected. The atomic ratios are all much bigger than the nominal doping levels due to Sb surface segregation. It has been argued that the
segregation is restricted to the topmost ionic layer [14–16]. In agreement with this idea the apparent Sb / Sn ratio increases with decreasing electron kinet-
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ic energy, i.e., the ratio increases in the sequence 4d,3d,3p,Auger. This is attributed to the fact that as the electron inelastic pathlength decreases, the topmost ionic layer makes an increasing contribution to the overall photoemission intensity. Segregated antimony ions at external or grain boundary interfaces do not act as n-type donors but instead trap an electron pair in a lone pair-like state deep in the bulk bandgap. For this reason the carrier concentration is always lower than expected from the nominal Sb doping level [12]. Fig. 2 shows valence band X-ray photoemission spectra acquired over a period of around 12 h. This enables us to achieve adequate signal to noise to identify structure arising from occupation of the conduction band. The conduction band structure straddles zero binding energy, confirming the integrity of the binding energy calibration procedure. We are thus able to identify binding energy shifts in valence band and core level features as small as 0.05 eV with some confidence. The Sn 3d 5 / 2 core line for undoped SnO 2 displays a simple Voigt lineshape with a full width at half maximum height (FWHM) of 1.04 eV. With increasing Sb doping the core line broadens, becomes increasingly asymmetric and displays a shift to high binding energy. Fig. 3 shows curve fits to the Sn 3d 5 / 2 peak using a Shirley background along with two Voigt components for the doped samples and a single Voigt component for the undoped sample. The extent of Gaussian–Lorentzian mixing was allowed to vary freely in the fits. The reproducibility of the curve fitting was checked by launching the fits with different starting parameters. As might be expected from visual inspection, the fits are least robust for low doping level where the screened final state component becomes very weak. Overall excellent fits are obtained with just two components. The low binding energy peak associated with the screened final state has a halfwidth somewhat smaller than typically found for core lines of insulating oxides because coupling to phonons of the oxide lattice is attenuated by the short Thomas–Fermi screening length of the degenerate electron gas. The high binding energy peak associated with the unscreened final state gives a broader peak that always has dominant Lorentzian character. In the plasmon model the width reflects the plasmon lifetime, which
Fig. 2. Valence band XPS for 3% and 0.6% Sb-doped SnO 2 . Binding energies are referenced to the Fermi energy of an Ag sample used to calibrate the spectrometer. Weak structure associated with electrons in the Sn 5s conduction band is evident from the 350 expansions of the structure around zero binding energy. The Fermi Dirac onset in the conduction band is seen to straddle zero binding energy (indicated by vertical dashed lines).
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Fig. 3. Fits of the Sn 3d 5 / 2 peaks in Sb-doped SnO 2 to two Voigt components associated with screened and unscreened final states for the different doping levels indicated. The positions of the components in the curve fits are indicated by dotted lines.
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in turn depends on the conduction electron relaxation rate: in the alternative Kotani model the width reflects the lifetime of the ‘split off’ localised state. It should be noted that no significant improvement to the curve fits (which extended over a wider energy range than shown in the figures) resulted from introduction of extra components associated with multiple plasmon satellites. It also proved to be impossible to investigate the possibility of an asymmetric lineshape in the low binding energy screened peak, as required by the Kotani local screening model. A quantitative discussion of the core and valence XPS data requires values for the carrier concentrations at the various different doping levels. These were derived from surface plasmon energies measured in electron energy loss spectroscopy [14–16]. The surface plasmon frequency is given by vsp where: Ne 2 v 2sp 5 ]]]]] m*e0 [e (`) 1 1]
(1)
where N is the concentration of conduction electrons, e the electronic charge, e (`) the high-frequency dielectric constant, m* the effective mass of conduction electrons at the Fermi level, and e0 the permittivity of free space. Note that the ratio between ]]]]] surface and bulk frequencies is œe (`) / [e (`) 1 1]. With e (`)53.91, the ratio is 0.892. The effective mass m* relevant to EELS depends on the dispersion of energy with wavevector k at EF dE U] U dk
" 2K ]] 5 E5E F m*
(2)
where K is the Fermi wavevector. The conduction band in SnO 2 is not strictly parabolic and m* increases slightly with increasing occupation of the conduction band. Published values of m* at different doping levels [17,18] can be fitted to a simple heuristic expression of the sort: m* 5 m *0 1 an 5 m *0 1 ck 3
(3)
where the constants are related by a 5 3p 2 c and m *0 is the effective mass at the bottom of the conduction band. This fit gives m *0 /m e 50.192 and a /m e 5 0.0259310 220 cm 3 , where m e is the electron mass. From Eqs. (1) and (3) it is possible to derive values
of the surface plasmon energy as a function of carrier concentration and hence to use the measured plasmon energy to fix the carrier concentration. The characteristics of the Sn 3d 5 / 2 core lines as a function of carrier concentration derived in this way are shown in Fig. 4. Firstly 4(a) shows the variation in the full width at half maximum height (FWHM) of the peak. There is a pronounced broadening from just over 1.0 eV for nominally undoped material to about 1.5 eV at the highest carrier concentration. Fig. 4(b) shows the variation in the intensity ratio between the low binding energy screened and the high binding energy unscreeened final state components derived from curve fitting. In the plasmon model, the high binding energy unscreened peak corresponds to the plasmon satellite and therefore in the weak coupling limit one expects Iscreened /Iunscreened to be proportional to n 1 / 3 . The solid line in 4(b) is a best fit of the experimental data points to bn 1 / 3 where b is a constant. The fit is clearly far from perfect and the data points conform better to an n 1 / 2 dependence on carrier concentration. Next Fig. 4(c) shows the corresponding separation between the screened and unscreened components. As in 4(b) the increase in the size of the error bars as the carrier concentration decreases reflects the fact that the curve fits become less robust as the separation between the two peaks decreases and the screened final state component becomes progressively weaker. Superimposed on 4(c) are the bulk and surface plasmon energies over the range of carrier concentrations investigated. It is seen that both the satellite intensity and the separation between the two final state peaks are broadly in line with the plasmon model, although again it could not be claimed that the quantitative agreement is perfect. Finally Fig. 4(d) shows the variation in the baricentre binding energy of the 3d 5 / 2 peak. These values are obtained by weighting the binding energies of the screened and unscreened components with their relative intensities. The variation in the binding energy of the first peak in the valence band spectrum is also plotted. Whatever the model for the screening response, the unrelaxed Koopmans’ state is not an eigenstate of the ionised system and must be projected onto screened and unscreened final states. Assuming that there is no satellite intensity in the ˚ valence region, the Manne–Aberg theorem [19]
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Fig. 4. (a) Variation in the full width at half maximum height for the Sn 3d 5 / 2 core line of Sb-doped SnO 2 for the differing carrier concentrations indicated. (b) The screened to unscreened intensity ratio as a function of carrier concentration derived from curve fitting. The solid line is a best fit with a function of the sort bn 1 / 3 , whilst the dashed curve is best fit with a function bn 1 / 2 . (c) Separation between screened and unscreened component peaks resulting from curve fits to the Sn 3d 5 / 2 core line as a function of carrier concentration. The dashed and solid lines show the respective energies of the surface and bulk plasmons. (d) Variation in the baricentre of the Sn 3d 5 / 2 binding energy (solid squares) and of the binding energy of the first peak in the valence band spectrum (solid circles) as a function of carrier concentration. The solid line shows the variation in the width of the occupied part of the conduction band.
therefore suggests that the shift in the baricentre core binding energy equates to the energy shift of the Koopmans state and should be equal to the valence level binding shift. This is observed. In the simplest model the shift to high binding energy with doping may be simply equated with the upward shift in the Fermi level within the conduction band with increasing carrier concentration: since binding energies are referenced to the Fermi energy they should show a corresponding shift to high binding energy. The solid line in 4(d) therefore shows the calculated variation in the width of the occupied part of the conduction band, i.e., the variation in the Fermi energy relative to the bottom of the conduction band. This is obtained from a modified free electron model as follows. The effective mass shows a linear variation with carrier concentration and hence varies linearly with the cube of the wavevector k. The Fermi energy
EF relative to the bottom of the conduction band is given by the integral: K
EF 5 "
2
k E ]]] dk m * 1 ck
(4)
3
0
0
As before, K is the wavevector at the Fermi energy. This is given by K 5 (3p 2 N)1 / 3 , where N is the carrier concentration. The definite integral is evaluated to give:
F
" 2b 2 1 K 3 1 b3 ]] ] ]]] EF 5 ln m *0 6 sK 1 bd 3
S
1 p 21 2K 2 b ]] ] 1] tan 1 ] ] Œ3 Œ3b 6
DG
(5)
where b5(3p 2 m *0 /a)5(m 0* /a). Thus from N we can calculate EF .
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It is quite clear from 4(d) that at the higher doping levels there is an increasing discrepancy between the measured binding energy shifts and the occupied conduction bandwidth. This is attributed to a shrinkage or renormalisation of the gap between the bottom of the conduction band and the top of the valence band which arises from Coulombic attraction between dopant atoms and conduction electrons and from screening of the repulsion between valence and conduction electrons due to conduction band occupancy [20–22]. The bandgap shrinkage implied from Fig. 4(c) at a carrier concentration of 3.5310 20 cm 23 is about 0.6 eV. This value is consistent with estimates of 0.572 eV at n52.2310 20 cm 23 and 0.744 eV at n54.0310 20 cm 23 derived from analysis of optical absorption spectra of SnO 2 thin films with differing carrier concentrations induced by oxygen deficiency [17]. The bandgap shrinkage is also similar to that found by analysis of photoemission data for In doped CdO [21,22].
4. Concluding remarks Sb-doped SnO 2 provides a simple model system in which to investigate the evolution in the screening response of a dilute electron gas to the creation of a core hole as the carrier concentration decreases toward zero. As expected, the probability of final state screening decreases as the conduction electron concentration decreases. The separation between the screened and unscreened final states is of the same order of magnitude as the plasmon energy although the variation of the satellite energy and intensity do not conform exactly to the predictions of the plasmon model of screening.
References ¨ ¨ [1] P. Steiner, H. Hochst, S. Hufner, in: L. Ley, M. Cardona (Eds.), Photoemission in Solids II, Springer, Berlin, 1979.
[2] D.C. Langreth, Nobel Symp. 24 (1973) 210. [3] M. Campagna, G.K. Wertheim, H.R. Shanks, F. Zumsteg, E. Banks, Phys. Rev. Lett. 34 (1975) 738. [4] J.N. Chalzalviel, M. Campagna, G.K. Wertheim, Phys. Rev. B 16 (1977) 697. [5] G.K. Wertheim, Chem. Phys. Lett. 65 (1979) 377. [6] R.G. Egdell, H. Innes, M.D. Hill, Surf. Sci. 149 (1985) 33. [7] P.P. Edwards, R.G. Egdell, I. Fragala, J.B. Goodenough, M.R. Harrison, A.F. Orchard, G. Scott, J. Solid State Chem. 54 (1984) 127. [8] N. Beatham, P.A. Cox, R.G. Egdell, A.F. Orchard, Chem. Phys. Lett. 69 (1980) 475. [9] P.A. Cox, J.B. Goodenough, P. Tavener, D. Telles, R.G. Egdell, J. Solid State Chem. 62 (1986) 36. [10] P.A. Cox, R.G. Egdell, J.B. Goodenough, A. Hamnett, C.C. Naish, J. Phys. C 16 (1983) 6221. [11] A. Kotani, Y. Toyazawa, J. Phys. Soc. Jpn. 37 (1974) 912. [12] R.G. Egdell, J. Rebane, T.J. Walker, D.S. L Law, Phys. Rev. B 59 (1999) 1792. [13] V. Christou, M. Etchells, O. Renault, P. J Dobson, O.V. Salata, G. Beamson, R.G. Egdell, J. Appl. Phys. 88 (2000) 5180. [14] P.A. Cox, R.G. Egdell, C. Harding, A.F. Orchard, W.R. Patterson, P.J. Tavener, Solid State Commun. 44 (1982) 837. [15] P.A. Cox, R.G. Egdell, C. Harding, W.R. Patterson, P.J. Tavener, Surf. Sci. 123 (1982) 179. [16] R.G. Egdell, W.R. Flavell, P.J. Tavener, J. Solid State Chem. 51 (1984) 345. [17] G. Sanon, R. Rup, A. Masingh, Phys. Rev. B 44 (1991) 5672. [18] R.G. Egdell, in: J. Nowotny (Ed.), The Science of Ceramic Interfaces II, Materials Science Monographs, Vol. 81, Elsevier, Amsterdam, 1994, p. 527. ˚ [19] R. Manne, T. Aberg, Chem. Phys. Lett. 7 (1970) 282. [20] I. Hamberg, K.F. Bergren, L. Engstrom, C.G. Granquist, B.E. Sernelius, Phys. Rev. B 30 (1984) 3240. [21] Y. Dou, T. Fishlock, R.G. Egdell, D.S.L. Law, G. Beamson, Phys. Rev. B 55 (1997) R13381. [22] Y. Dou, R.G. Egdell, T.J. Walker, D.S.L. Law, G. Beamson, Surf. Sci. 398 (1998) 241.
The screening response of a dilute electron gas in core level photoemission from Sb-doped SnO 2 a, a b R.G. Egdell *, T.J. Walker , G. Beamson a
b
Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3 QR, UK Research Unit for Surfaces Transforms and Interfaces, Daresbury Laboratory, Warrington, Cheshire WA4 4 AD, UK Received 2 July 2002; received in revised form 19 August 2002; accepted 26 August 2002
Abstract The variation of core lineshape with carrier concentration in Sb-doped SnO 2 has been studied by high-resolution X-ray photoemission spectroscopy. The Sn 3d core levels display an asymmetric lineshape which may be fitted with components associated with screened and unscreened final states. The separation between the two fitted peaks and the relative intensity of the screened component both increase with increasing carrier concentration. The satellite energies are of the order expected for a screening mechanism involving excitation of plasmons. 2002 Elsevier Science B.V. All rights reserved. Keywords: Antimony-doped tin oxide; Core-hole screening; Plasmons
1. Introduction It was recognized early in the application of photoemission techniques to simple metallic solids that plasmon satellites make a significant contribution to core level structure in X-ray photoelectron spectra. Much of the early work in this area was concerned with unravelling the relative contributions of intrinsic and extrinsic structure and with rationalising the pattern of multiple plasmon excitations [1]. The weak coupling models developed 30 years ago suggested that the intrinsic plasmon satellite intensity I should increase as the conduction electron density n decreases according to the expression I~n 21 / 3 [2]. Interest in this area was rekindled *Corresponding author. Tel.: 144-1865-275-965; fax: 144-1865272-690. E-mail address: [email protected] (R.G. Egdell).
by the observation of very strong satellites in core photoemission of ‘narrow band’ metallic oxides including the sodium tungsten bronzes NaxWO 3 [3– 6]; the superconducting spinel LiTi 2 O 4 [7,8]; dioxides such as MoO 2 [8] and RuO 2 [9]; and the ternary metallic pyrochlore ruthenates Pb 2 Ru 2 O 7 and Bi 2 Ru 2 O 7 [10]. These materials all have a much more dilute electron gas than that in conventional metals and the plasmon energies are only around 1–2 eV, as compared with values usually well in excess of 5 eV for simple metals. Weak coupling models therefore suggest that there should be very strong low energy plasmon satellites in core photoemission from these materials. However, it is obvious that this conclusion calls into question the applicability of a weak coupling model in the first place. Moreover, in the ‘simple’ metals the overall lineshape involves multiple plasmon loss satellites, whereas for the ‘narrow band’ metals only a single satellite is
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observed. Wertheim and co-workers [3–5] suggested an alternative limiting model for the screening response in a narrow band metal. This involves a screening mechanism in which the Coulomb potential of the core hole at an ionised atom creates a localised trap state. In this situation two different final states are then accessible depending on whether the localised state remains empty (giving an unscreened states) or is filled by transfer of an electron from the conduction band (to give a screened final state). In the model developed by Kotani and Toyazawa [11] the screened final state gives rise to an asymmetric line to low binding energy of the lifetime broadened peak associated with the unscreened final state. In the alternative language of the plasmon model the high binding energy unscreened peak corresponds to an extrinsic plasmon satellite whose Lorentzian linewidth will be determined by the conduction electron scattering rate. Our recent interest in this longstanding problem has been stimulated by the observation of very strong satellite structure in core XPS of oxides such as Sb-doped SnO 2 [12] and Sn-doped In 2 O 3 [13]. These oxides are well-known as transparent conducting materials which transmit visible light but reflect infrared radiation. The plasmon energies in transparent conducting oxides are at most around 0.7 eV, which is of course comparable with intrinsic core linewidths. Plasmon satellite structure is therefore expected to overlap the ‘main’ core level peak to give an asymmetric core lineshape. In the present communication we make a systematic study of the variation in core lineshape with carrier concentration in Sb-doped SnO 2 . Satellite energies and intensities derived by curve fitting the Sn 3d 5 / 2 core line to two components vary qualitatively in the way expected on the basis of the plasmon model, although the quantitative agreement is not perfect.
2. Experimental High purity tin(IV) oxide was obtained from Johnson Matthey. Phase pure antimony-doped tin oxide was prepared by a co-precipitation procedure, as described previously [14–16]. The powders were pressed into 13-mm pellets and sintered in air at
1000 8C for several days to yield strong ceramic discs. Surface plasmon energies were determined from electron energy loss spectra measured in an ESCALAB spectrometer (VG Scientific). The mode of operation of this spectrometer and its application to the study of electron spectra of SnO 2 has been described in detail elsewhere [14–16]. High-resolution X ray photoemission spectra were measured in a Scienta ESCA 300 spectrometer located in the Research Unit for Surfaces, Transforms and Interfaces (RUSTI) at Daresbury Laboratory. This incorporates a rotating anode X-ray source, a seven-crystal X-ray monochromator and a 300-mm mean radius spherical sector electron energy analyser with parallel electron detection system. The X-ray source was run with 200 mA emission current and 14 kV anode bias, whilst the analyser operated at 150 eV pass energy with 0.5-mm slits. Gaussian convolution of the analyser resolution with a linewidth of 260 meV for the X-ray source gives an effective instrument resolution of 350 meV. Binding energies are referenced to the Fermi energy of an ion bombarded silver foil which is regularly used to calibrate the spectrometer. The ceramic pellets of undoped SnO 2 and Sbdoped SnO 2 were cleaned in situ in the preparation chamber of the Scienta spectrometer by annealing in UHV at about 750 8C for 2–3 h, heating being effected by an electron beam heater. Surfaces prepared in this way were free of structure due to carbon or other contaminants and remained clean for the duration of the spectroscopic measurements.
3. Results and discussion Fig. 1a shows X-ray photoelectron spectra in the region of the Sn 3d, Sb 3d and O1s core levels. The Sb 3d 5 / 2 peak overlaps the O1s core peak, but the surface Sb concentration can be estimated by comparing the Sb 3d 3 / 2 and Sn 3d 3 / 2 intensities after subtraction of a Shirley background. Fig. 1(b) shows the apparent Sb / Sn atomic ratios derived by dividing the 3d intensities by the relevant ionisation crosssections. This figure also shows the corresponding data derived from Sb 4d1Sn 4d, Sb 3p 3 / 2 1Sn 3p 3 / 2 , and MNN Auger peaks. Note that the Auger
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Fig. 1. (a) Core level XPS encompassing the Sn 3d, Sb 3d and O1s regions for Sb-doped SnO 2 at the various doping levels indicated. Note that a Sb 3d 3 / 2 peak is visible in all spectra. The Sb 3d 5 / 2 peak overlaps the O1s peak. Binding energies are referenced to the Fermi energy of an Ag sample used to calibrate the spectrometer. (b) Intensity ratios between Sb and Sn core level peaks, corrected for ionisation atomic cross-sections. Uncorrected data for MNN Auger peaks are also shown. Note that the intensity axis is logarithmic.
intensities are uncorrected. The atomic ratios are all much bigger than the nominal doping levels due to Sb surface segregation. It has been argued that the
segregation is restricted to the topmost ionic layer [14–16]. In agreement with this idea the apparent Sb / Sn ratio increases with decreasing electron kinet-
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ic energy, i.e., the ratio increases in the sequence 4d,3d,3p,Auger. This is attributed to the fact that as the electron inelastic pathlength decreases, the topmost ionic layer makes an increasing contribution to the overall photoemission intensity. Segregated antimony ions at external or grain boundary interfaces do not act as n-type donors but instead trap an electron pair in a lone pair-like state deep in the bulk bandgap. For this reason the carrier concentration is always lower than expected from the nominal Sb doping level [12]. Fig. 2 shows valence band X-ray photoemission spectra acquired over a period of around 12 h. This enables us to achieve adequate signal to noise to identify structure arising from occupation of the conduction band. The conduction band structure straddles zero binding energy, confirming the integrity of the binding energy calibration procedure. We are thus able to identify binding energy shifts in valence band and core level features as small as 0.05 eV with some confidence. The Sn 3d 5 / 2 core line for undoped SnO 2 displays a simple Voigt lineshape with a full width at half maximum height (FWHM) of 1.04 eV. With increasing Sb doping the core line broadens, becomes increasingly asymmetric and displays a shift to high binding energy. Fig. 3 shows curve fits to the Sn 3d 5 / 2 peak using a Shirley background along with two Voigt components for the doped samples and a single Voigt component for the undoped sample. The extent of Gaussian–Lorentzian mixing was allowed to vary freely in the fits. The reproducibility of the curve fitting was checked by launching the fits with different starting parameters. As might be expected from visual inspection, the fits are least robust for low doping level where the screened final state component becomes very weak. Overall excellent fits are obtained with just two components. The low binding energy peak associated with the screened final state has a halfwidth somewhat smaller than typically found for core lines of insulating oxides because coupling to phonons of the oxide lattice is attenuated by the short Thomas–Fermi screening length of the degenerate electron gas. The high binding energy peak associated with the unscreened final state gives a broader peak that always has dominant Lorentzian character. In the plasmon model the width reflects the plasmon lifetime, which
Fig. 2. Valence band XPS for 3% and 0.6% Sb-doped SnO 2 . Binding energies are referenced to the Fermi energy of an Ag sample used to calibrate the spectrometer. Weak structure associated with electrons in the Sn 5s conduction band is evident from the 350 expansions of the structure around zero binding energy. The Fermi Dirac onset in the conduction band is seen to straddle zero binding energy (indicated by vertical dashed lines).
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Fig. 3. Fits of the Sn 3d 5 / 2 peaks in Sb-doped SnO 2 to two Voigt components associated with screened and unscreened final states for the different doping levels indicated. The positions of the components in the curve fits are indicated by dotted lines.
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in turn depends on the conduction electron relaxation rate: in the alternative Kotani model the width reflects the lifetime of the ‘split off’ localised state. It should be noted that no significant improvement to the curve fits (which extended over a wider energy range than shown in the figures) resulted from introduction of extra components associated with multiple plasmon satellites. It also proved to be impossible to investigate the possibility of an asymmetric lineshape in the low binding energy screened peak, as required by the Kotani local screening model. A quantitative discussion of the core and valence XPS data requires values for the carrier concentrations at the various different doping levels. These were derived from surface plasmon energies measured in electron energy loss spectroscopy [14–16]. The surface plasmon frequency is given by vsp where: Ne 2 v 2sp 5 ]]]]] m*e0 [e (`) 1 1]
(1)
where N is the concentration of conduction electrons, e the electronic charge, e (`) the high-frequency dielectric constant, m* the effective mass of conduction electrons at the Fermi level, and e0 the permittivity of free space. Note that the ratio between ]]]]] surface and bulk frequencies is œe (`) / [e (`) 1 1]. With e (`)53.91, the ratio is 0.892. The effective mass m* relevant to EELS depends on the dispersion of energy with wavevector k at EF dE U] U dk
" 2K ]] 5 E5E F m*
(2)
where K is the Fermi wavevector. The conduction band in SnO 2 is not strictly parabolic and m* increases slightly with increasing occupation of the conduction band. Published values of m* at different doping levels [17,18] can be fitted to a simple heuristic expression of the sort: m* 5 m *0 1 an 5 m *0 1 ck 3
(3)
where the constants are related by a 5 3p 2 c and m *0 is the effective mass at the bottom of the conduction band. This fit gives m *0 /m e 50.192 and a /m e 5 0.0259310 220 cm 3 , where m e is the electron mass. From Eqs. (1) and (3) it is possible to derive values
of the surface plasmon energy as a function of carrier concentration and hence to use the measured plasmon energy to fix the carrier concentration. The characteristics of the Sn 3d 5 / 2 core lines as a function of carrier concentration derived in this way are shown in Fig. 4. Firstly 4(a) shows the variation in the full width at half maximum height (FWHM) of the peak. There is a pronounced broadening from just over 1.0 eV for nominally undoped material to about 1.5 eV at the highest carrier concentration. Fig. 4(b) shows the variation in the intensity ratio between the low binding energy screened and the high binding energy unscreeened final state components derived from curve fitting. In the plasmon model, the high binding energy unscreened peak corresponds to the plasmon satellite and therefore in the weak coupling limit one expects Iscreened /Iunscreened to be proportional to n 1 / 3 . The solid line in 4(b) is a best fit of the experimental data points to bn 1 / 3 where b is a constant. The fit is clearly far from perfect and the data points conform better to an n 1 / 2 dependence on carrier concentration. Next Fig. 4(c) shows the corresponding separation between the screened and unscreened components. As in 4(b) the increase in the size of the error bars as the carrier concentration decreases reflects the fact that the curve fits become less robust as the separation between the two peaks decreases and the screened final state component becomes progressively weaker. Superimposed on 4(c) are the bulk and surface plasmon energies over the range of carrier concentrations investigated. It is seen that both the satellite intensity and the separation between the two final state peaks are broadly in line with the plasmon model, although again it could not be claimed that the quantitative agreement is perfect. Finally Fig. 4(d) shows the variation in the baricentre binding energy of the 3d 5 / 2 peak. These values are obtained by weighting the binding energies of the screened and unscreened components with their relative intensities. The variation in the binding energy of the first peak in the valence band spectrum is also plotted. Whatever the model for the screening response, the unrelaxed Koopmans’ state is not an eigenstate of the ionised system and must be projected onto screened and unscreened final states. Assuming that there is no satellite intensity in the ˚ valence region, the Manne–Aberg theorem [19]
R.G. Egdell et al. / Journal of Electron Spectroscopy and Related Phenomena 128 (2003) 59–66
65
Fig. 4. (a) Variation in the full width at half maximum height for the Sn 3d 5 / 2 core line of Sb-doped SnO 2 for the differing carrier concentrations indicated. (b) The screened to unscreened intensity ratio as a function of carrier concentration derived from curve fitting. The solid line is a best fit with a function of the sort bn 1 / 3 , whilst the dashed curve is best fit with a function bn 1 / 2 . (c) Separation between screened and unscreened component peaks resulting from curve fits to the Sn 3d 5 / 2 core line as a function of carrier concentration. The dashed and solid lines show the respective energies of the surface and bulk plasmons. (d) Variation in the baricentre of the Sn 3d 5 / 2 binding energy (solid squares) and of the binding energy of the first peak in the valence band spectrum (solid circles) as a function of carrier concentration. The solid line shows the variation in the width of the occupied part of the conduction band.
therefore suggests that the shift in the baricentre core binding energy equates to the energy shift of the Koopmans state and should be equal to the valence level binding shift. This is observed. In the simplest model the shift to high binding energy with doping may be simply equated with the upward shift in the Fermi level within the conduction band with increasing carrier concentration: since binding energies are referenced to the Fermi energy they should show a corresponding shift to high binding energy. The solid line in 4(d) therefore shows the calculated variation in the width of the occupied part of the conduction band, i.e., the variation in the Fermi energy relative to the bottom of the conduction band. This is obtained from a modified free electron model as follows. The effective mass shows a linear variation with carrier concentration and hence varies linearly with the cube of the wavevector k. The Fermi energy
EF relative to the bottom of the conduction band is given by the integral: K
EF 5 "
2
k E ]]] dk m * 1 ck
(4)
3
0
0
As before, K is the wavevector at the Fermi energy. This is given by K 5 (3p 2 N)1 / 3 , where N is the carrier concentration. The definite integral is evaluated to give:
F
" 2b 2 1 K 3 1 b3 ]] ] ]]] EF 5 ln m *0 6 sK 1 bd 3
S
1 p 21 2K 2 b ]] ] 1] tan 1 ] ] Œ3 Œ3b 6
DG
(5)
where b5(3p 2 m *0 /a)5(m 0* /a). Thus from N we can calculate EF .
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It is quite clear from 4(d) that at the higher doping levels there is an increasing discrepancy between the measured binding energy shifts and the occupied conduction bandwidth. This is attributed to a shrinkage or renormalisation of the gap between the bottom of the conduction band and the top of the valence band which arises from Coulombic attraction between dopant atoms and conduction electrons and from screening of the repulsion between valence and conduction electrons due to conduction band occupancy [20–22]. The bandgap shrinkage implied from Fig. 4(c) at a carrier concentration of 3.5310 20 cm 23 is about 0.6 eV. This value is consistent with estimates of 0.572 eV at n52.2310 20 cm 23 and 0.744 eV at n54.0310 20 cm 23 derived from analysis of optical absorption spectra of SnO 2 thin films with differing carrier concentrations induced by oxygen deficiency [17]. The bandgap shrinkage is also similar to that found by analysis of photoemission data for In doped CdO [21,22].
4. Concluding remarks Sb-doped SnO 2 provides a simple model system in which to investigate the evolution in the screening response of a dilute electron gas to the creation of a core hole as the carrier concentration decreases toward zero. As expected, the probability of final state screening decreases as the conduction electron concentration decreases. The separation between the screened and unscreened final states is of the same order of magnitude as the plasmon energy although the variation of the satellite energy and intensity do not conform exactly to the predictions of the plasmon model of screening.
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