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Temperature dependent photoemission spectroscopy on lightly-doped sodium tungsten bronze
Solid State Communications 152 (2012) 493–496
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Temperature dependent photoemission spectroscopy on lightly-doped sodium tungsten bronze Sanhita Paul a , Anirudha Ghosh a , Anirban Chakraborty b , Luca Petaccia c , D. Topwal c , D.D. Sarma b , S. Oishi d , Satyabrata Raj a,∗ a
Department of Physical Sciences, Indian Institute of Science Education and Research-Kolkata, Mohanpur Campus, Nadia 741252, India
b
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India
c
Sincrotrone Trieste S.C.p.A., Strada Statale 14 km 163.5, I-34149 Trieste, Italy
d
Faculty of Engineering, Shinshu University, Nagano 380-8553, Japan
article
info
Article history: Received 28 October 2011 Accepted 30 December 2011 by C.S. Sundar Available online 5 January 2012 Keywords: A. Disordered systems A. Insulator D. Electronic band structure E. Photoelectron spectroscopies
abstract Temperature dependent photoemission studies on lightly doped (x = 0.025) sodium tungsten bronzes, Nax WO3 have been investigated by high-resolution photoemission spectroscopy. The experimental results show evidence for polaron formation at the valence band edge and the photoemission spectra taken in different modes of the electron analyzer suggest that the density of states at the valence band edge gradually moves to other k-points in the Brillouin zone with increasing temperature and explain the dynamics of polarons in the insulating disordered sodium tungsten bronzes. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Alkali metal doped tungsten–oxide materials have been known for their potential technological implications in material science for a long time [1,2]. It is possible to insert sodium (Na) in bulk-WO3 , thus forming the series of sodium tungsten bronze (Nax WO3 ), which has very interesting optical properties [3]. Many properties such as the electronic, optical, and transport properties have been studied extensively in sodium tungsten bronzes. The metal–insulator transition (MIT) observed as a function of x is also an interesting electronic property in this compound. Nax WO3 becomes nonmetallic for low Na doping and metallic for x ≥ 0.25 [4]. Sodium tungsten bronze shows a very rich phase diagram [5] with increasing x and is also very interesting to study from structural evolution point of view. The crystal structure changes from monoclinic, to orthorhombic, to tetragonal, and finally to cubic with increasing x. For x ≥ 0.5, Nax WO3 is highly metallic with perovskite-type crystal structure with cubic crystal symmetry, while for x ≤ 0.4, it exists in a variety of structural modifications. For low doping the system can be considered to have a more or less pseudo-cubic crystal structure. Fig. 1(a) shows the crystal structure of NaWO3 . Na ions occupy the center of the cube, while the WO6 octahedra are located at the cube corners. The
∗
Corresponding author. Tel.: +91 33 25873118; fax: +91 33 25873020. E-mail address: [email protected] (S. Raj).
0038-1098/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2011.12.045
octahedral crystal field of the six oxygen neighbors of the W split the W 5d bands into triply degenerate t2g and doubly degenerate eg bands. In WO3 , the Fermi level (EF ) lies at the top of the O 2p bands, and WO3 is a band insulator. Within a rigid band model, the band structure of both WO3 and NaWO3 should be identical, with EF at different positions. In NaWO3 , the Na 3s electrons are transferred into the W 5d t2g band and the system should behave metallic for any value of x. However, for lower concentrations of x ≤ 0.25, the material is insulating and the cause of the MIT was a matter of debate for a long time. The electrochromic property of sodium doped WO3 is another interesting subject of research, where even after a substantial effort, understanding on the mechanism behind electrochromic property is not yet fully achieved. Low sodium doped tungsten bronzes are nonmetallic with localized W5+ ions scattered in a background of W6+ ions. Absorption of light occurs by the excitation of an electron from a site with W5+ ion to a neighboring W6+ ion around it. The excited electron modifies the local lattice and the electrochromic properties can be explained by the language of ‘‘polaron’’ physics. Schirmer et al. [6] explained the optical absorption of WO3 as small polaron absorption. Recently photoemission spectroscopy has found a signature of polaron formation in non-metallic Nax WO3 [7]. In spite of having indications regarding the formation of polarons in the non-metallic Nax WO3 , a clear understanding on the dynamics of polarons has not yet been achieved. In this paper, we have investigated the change of density of states (DOS) with temperature at the valence-band edge along the Γ − X high-symmetry direction in the Brillouin zone (BZ)
494
S. Paul et al. / Solid State Communications 152 (2012) 493–496
a
b
Na W O
d Binding Energy (eV)
c
Laue Diffraction
EF 0.2 0.4 0.6 -0.2 0.0 0.2 Wave Vector (Å-1)
Fig. 1. (Color online) (a) Cubic crystal structure of NaWO3 showing corner sharing WO6 octahedra. (b) Brillouin zone of cubic NaWO3 showing high-symmetry lines. (c) Laue diffraction pattern of single crystal Nax WO3 (x = 0.025). (d) Experimental near EF band mapping of Nax WO3 (x = 0.025) along the Γ − X high symmetry direction. Circles are a guide to the eyes to follow the band dispersion. Band moves towards EF but never crosses EF showing the insulating character of the system.
(see Fig. 1(b)). We found the signature of polaron formation in this non-metallic system. The DOS at valence band edge gradually decreases around the Γ point and increases at other k-points with increasing temperature implying the delocalization of polaron. The different photoemission modes (i.e., HAD, LAD, and WAM, see results and discussion) of measurements helped us to understand the dynamics of polaron formation in the lightly doped sodium tungsten bronzes. 2. Experiments Single crystals of insulating Nax WO3 (x = 0.025) were grown from high temperature solution of 15 mol% of Na2 O with WO3 by a slow cooling method [8]. Fig. 1(c) shows the Laue diffraction pattern of the insulating sample, which indicates that the samples were single crystals. High-resolution ARPES experiments were performed at the BaD ElPh beamline installed at the Elettra synchrotron, Italy. Photon energy of 22 eV was used to excite the photoelectrons, which were detected with a Phoibos 150 hemispherical electron analyzer and the overall instrumental resolution was better than 40 meV. The measurements for insulating Na0.025 WO3 were performed at 50–300 K in a vacuum better than 5 × 10−11 Torr. A clean surface of the sample for photoemission measurements was obtained by in situ cleaving along (001) surface. The possibility of charging in the insulating sample was checked by reducing the photon flux. We found no shift in the valence band peaks, which confirms that there is no charging in the sample. The Fermi level (EF ) of the sample was referred to that of a copper prepared freshly by Ar sputtering on the sample substrate. All the spectra were collected within 24 h after cleaving, during which we did not observe any significant changes in the spectra indicative of the contamination and/or degradation of the sample surface. 3. Results and discussion A typical near-EF band mapping of Nax WO3 (x = 0.025) by ARPES is shown in Fig. 1(d) around the Γ point of BZ. An electron-like dispersive band is observed around the Γ point which never crosses EF , showing that the system is insulating. The dispersive band represents the conduction band of Nax WO3
(x = 0.025), which is assigned as the W 5d t2g orbitals from the band calculations. The insulating behavior arises from the Anderson localization [9] of all the states near EF due to the strong disorder caused by inserting Na in a WO3 lattice. As a result of the localization, a soft Column gap arises at EF and consequently the DOS vanishes at EF . This gap arises due to the long-range interaction of the electrons trapped due to the strong disorder caused by the random distribution of Na in WO3 lattice. It is important to mention that in Anderson localization model [9] single electron DOS has no singularity and remains finite near the Fermi level. A truly Anderson localized system is called ‘‘gapless’’ as the insulating state does not have any gap in a DOS near EF but has a ‘‘mobility gap’’ between the Fermi level and the mobility edge. As soon as the Coulomb interaction among carriers sets in the insulating state, a gap opens up at EF [10–14]. The temperature dependence of the valence-band spectra has been investigated by carrying out photoemission spectroscopy (PES) on Na0.025 WO3 around Γ (X ) point (with different acceptance angles of detector) with the variation of temperature, and the results are shown in Fig. 2(a)–(c). The angle-resolved Phoibos 150 hemispherical electron analyzer has a provision to set different acceptance angles of the detector namely: High-Angular Dispersion (HAD) mode with ±3°, Low-Angular Dispersion (LAD) mode with ±7°, and Wide-Angle Mode (WAM) with ±13°. The PES spectra see mostly the angle-integrated spectra around the Γ (X ) point with ±3°, ±7°, and ±13° acceptance angle of the analyzer for HAD, LAD, and WAM modes, respectively. The acceptance angle of the analyzer for HAD, LAD, and WAM modes correspond to 13%, 30%, and 55% of the BZ of Na0.025 WO3 for 22 eV photon energy. All the spectra have been normalized under the curve within the energy range shown in the figure. The variation of the intensity of the 2.5-eV peak with temperature is clearly observed. The change in 2.5-eV peak intensity is more visible in HAD mode (Fig. 2(a)) than in WAM mode (Fig. 2(c)). It indicates that the intensity around Γ point for the HAD mode varies a lot with change in temperature whereas for the WAM mode the intensity variation is minimal. We believe that this behavior is because of the formation of polarons with lowering of temperature. It is believed that at low sodium doping levels, the sodium tungsten bronzes are nonmetallic with localized W5+ and W6+ ions and show polaronic states [15,16]. Polaron formation can take place in the insulating system, particularly when the doped charge carriers are in a comparatively narrow d band and are contributed by donors distributed at random in the lattice. The polaron formation in the lightlydoped tungsten bronzes had been studied with electron spin resonance, optical absorption, and Raman spectroscopy [15–18]. In fact, in Na0.025 WO3 the carriers are self-trapped by inducing an asymmetric local deformation in the WO3 lattice. Even though the carrier is confined to a single lattice site, the tunneling between different lattice sites is still relevant and a self-trapped carrier resides in an itinerant polaron state [19–21]. This is most likely to occur when the band edge is degenerate and the valence-band edge is more often degenerate than the conductionband edge. Hence an effect of polaron formation should be reflected significantly at the valence-band edge as compared to the conduction band. The intensity ratio of the valence-band edge (2.5-eV peak) to the 4-eV peak is shown in Fig. 3(a). The valence band photoemission spectra shown in Fig. 2 is fitted with a curve fitting program and the intensity ratio is determined by the area under the peak with centroid at 2.5 and 4-eV. It is observed that the intensity of 2.5-eV peak decreases with increasing temperature (from 50 to 200 K the intensity ratio is weakly decreasing, while there is a strong decrease around 220 ± 15 K) and reaches a minimum above 230 K for all the modes of detection. As earlier mentioned, we
S. Paul et al. / Solid State Communications 152 (2012) 493–496
Binding Energy (eV)
Intensity (arb. units)
c
Intensity (arb. units)
b
Intensity (arb. units)
a
495
Binding Energy (eV)
Binding Energy (eV)
Fig. 2. (Color online) Valence-band PES spectra around Γ (X ) point of Nax WO3 (x = 0.025) at several temperatures showing the signature of polaron formation below 230 K at valence-band edge (∼2.5 eV binding energy) for different acceptance angles of the electron analyzer (a) High Angular Dispersion (HAD) mode with ±3° (b) Low Angular Dispersion (LAD) mode with ±7° (c) Wide Angle Mode (WAM) with ±13°.
4. Conclusion We have carried out high-resolution photoemission spectroscopy on insulating Nax WO3 (for x = 0.025) with variation of temperature from 50 to 300 K. We found a direct evidence of polaron formation from the temperature dependence of the photoemission spectra. The DOS at valence band edge gradually decreases around the Γ point and increases at other k-points with
a (2.5 eV peak/4eV peak)
Intensity Ratio
0.25
0.20
0.15
0.10 50
100
150
200
250
300
Temperature (K)
b Low Temperature / High Temperature 2.5 eV Peak Intensity Ratio
think that the reduction in the intensity of the 2.5-eV peak is due to the breakdown of polaron formation at higher temperatures (above 230 K), where the charge carriers are no longer self-trapped. A polaron can be considered to be a local deformation/defect in the lattice and a truly localized defect level is derived primarily from the Γ point (k = 0) with far less weight from other k-points. A more delocalized defect level is derived from k-points other than Γ [22]. As the polaron becomes more delocalized, there is a spectral weight transfer from Γ point to other k-points. A comparison among different modes of PES shows that the intensity ratio, especially at low temperature, decreases with increasing acceptance angle of the detector. The total DOS of 2.5-eV peak is constant (if integrated over the full BZ) and in the WAM mode the detector integrates all the DOS arising from ±13° (corresponding to 55% of the BZ for photon energy of 22 eV) around the Γ point. With increasing temperature a fraction of 2.5-eV DOS moves from the Γ point to other k-points because of the delocalization of polarons. That is why in the WAM mode, the photoemission spectra show less variation of 2.5-eV peak intensity as compared to the HAD mode, where the integration is only for ±3° around the Γ . For a better understanding the ratio of low (average of 80–200 K) and high (275 K) temperature DOS of the 2.5-eV peak is shown in Fig. 3(b). For WAM, the ratio is less as compared to HAD (1 is expected value for integrations over the full BZ). Because of polaron formation the DOS of 2.5-eV peak accumulates around the Γ point at lower temperatures, whereas the intensity decreases with increasing temperature. This is well reflected in HAD mode PES where the observed intensity is only around the Γ point. The optical absorption of W5+ in WO3−x shows signature of polaron formation in low-temperature and vanishes at 300 K [15,16]. This adds additional support to our conclusion that the increase in the intensity of the valence-band edge below 230 K is due to the formation of polarons.
3.0
2.5
2.0
1.5 +7 + 13 3 – – Analyzer Acceptance Angle (degree)
+ –
Fig. 3. (Color online) (a) Temperature dependence of the intensity ratio of the 2.5-eV peak to the 4.0-eV peak for different measurement modes of PES showing the delocalization of polaron above 230 K temperature. (b) Low- to hightemperature intensity ratio of 2.5-eV peak vs. analyzer acceptance angle (errors are given as vertical bar). This ratio is less in WAM mode than HAD mode, which explains the transfer of 2.5-eV DOS at Γ point to other k-points with increasing temperature.
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S. Paul et al. / Solid State Communications 152 (2012) 493–496
increasing temperature implying the delocalization of polaron. After 230 K, the polaron has less effect on the variation of DOS at different k-points implying the delocalization of the trapped charge carriers within the disordered lattice for the low doped sodium tungsten bronzes. Acknowledgments The work at Elettra was supported by Indian DST and Italian MAE under the bilateral program of collaboration. We acknowledge E. Nicolini for the Laue diffraction measurements and D. Lonza for his technical assistance during the photoemission experiments. References [1] C.G. Granqvist, Handbook of Inorganic Electrochromic Materials, Elsevier, Amsterdam, 1995. [2] P.M.S. Monk, R.J. Mortimer, D.R. Rosseinsky, Electrochromism: Fundamentals and Applications, VCH, Weinheim, 1995.
[3] J.B. Goodenough, in: H. Reiss (Ed.), Progress in Solid State Chemistry, vol. 5, Pergamon, Oxford, 1971, p. 145. [4] H.R. Shanks, P.H. Slides, G.C. Danielson, Adv. Chem. Ser. 39 (1963) 237. [5] A.S. Ribnick, B. Post, E. Banks, Adv. Chem. Ser. 39 (1963) 246. [6] O.F. Schirmer, V. Wittwer, G. Baur, G. Brandt, J. Electrochem. Soc. 124 (1977) 749. [7] S. Raj, D. Hashimoto, H. Matsui, S. Souma, T. Sato, T. Takhashi, D.D. Sarma, P. Mahadevan, S. Oishi, Phys. Rev. Lett. 96 (2006) 147603. [8] S. Oishi, N. Endo, K. Kitajima, Nippon Kagaku Kaishi, vol. 11, The Chemical Society of Japan, Japan, 1995, p. 891. [9] P.W. Anderson, Phys. Rev. 109 (1958) 1492. [10] A.L. Efros, B.I. Shklovskii, J. Phys. C 8 (1975) L49. [11] M. Pollak, Discuss. Faraday Soc. 50 (1970) 13. [12] M. Pollak, J. Non-Cryst. Solids 11 (1972) 1. [13] V. Ambegaokar, B.I. Halperin, J.S. Langar, Phys. Rev. B 4 (1971) 2612. [14] G. Srinivasan, Phys. Rev. B 4 (1971) 2581. [15] O.F. Schirmer, E. Salje, Solid State Commun. 33 (1980) 333. [16] O.F. Schirmer, E. Salje, J. Phys. C 13 (1980) L1067. [17] R.G. Egdell, G.B. Jones, J. Solid State Chem. 81 (1989) 137. [18] T. Mertelj, D. Mihailovic, Eur. Phys. J. B 23 (2001) 325. [19] H. DeRaedt, A. Lagendijk, Phys. Rev. B 27 (1983) 6097. [20] H. Lowen, Phys. Rev. B 37 (1988) 8661. [21] J. Ranninger, U. Thibblin, Phys. Rev. B 45 (1992) 7730. [22] G.F. Koster, J.C. Slater, Phys. Rev. 95 (1954) 1167.
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Temperature dependent photoemission spectroscopy on lightly-doped sodium tungsten bronze Sanhita Paul a , Anirudha Ghosh a , Anirban Chakraborty b , Luca Petaccia c , D. Topwal c , D.D. Sarma b , S. Oishi d , Satyabrata Raj a,∗ a
Department of Physical Sciences, Indian Institute of Science Education and Research-Kolkata, Mohanpur Campus, Nadia 741252, India
b
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India
c
Sincrotrone Trieste S.C.p.A., Strada Statale 14 km 163.5, I-34149 Trieste, Italy
d
Faculty of Engineering, Shinshu University, Nagano 380-8553, Japan
article
info
Article history: Received 28 October 2011 Accepted 30 December 2011 by C.S. Sundar Available online 5 January 2012 Keywords: A. Disordered systems A. Insulator D. Electronic band structure E. Photoelectron spectroscopies
abstract Temperature dependent photoemission studies on lightly doped (x = 0.025) sodium tungsten bronzes, Nax WO3 have been investigated by high-resolution photoemission spectroscopy. The experimental results show evidence for polaron formation at the valence band edge and the photoemission spectra taken in different modes of the electron analyzer suggest that the density of states at the valence band edge gradually moves to other k-points in the Brillouin zone with increasing temperature and explain the dynamics of polarons in the insulating disordered sodium tungsten bronzes. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Alkali metal doped tungsten–oxide materials have been known for their potential technological implications in material science for a long time [1,2]. It is possible to insert sodium (Na) in bulk-WO3 , thus forming the series of sodium tungsten bronze (Nax WO3 ), which has very interesting optical properties [3]. Many properties such as the electronic, optical, and transport properties have been studied extensively in sodium tungsten bronzes. The metal–insulator transition (MIT) observed as a function of x is also an interesting electronic property in this compound. Nax WO3 becomes nonmetallic for low Na doping and metallic for x ≥ 0.25 [4]. Sodium tungsten bronze shows a very rich phase diagram [5] with increasing x and is also very interesting to study from structural evolution point of view. The crystal structure changes from monoclinic, to orthorhombic, to tetragonal, and finally to cubic with increasing x. For x ≥ 0.5, Nax WO3 is highly metallic with perovskite-type crystal structure with cubic crystal symmetry, while for x ≤ 0.4, it exists in a variety of structural modifications. For low doping the system can be considered to have a more or less pseudo-cubic crystal structure. Fig. 1(a) shows the crystal structure of NaWO3 . Na ions occupy the center of the cube, while the WO6 octahedra are located at the cube corners. The
∗
Corresponding author. Tel.: +91 33 25873118; fax: +91 33 25873020. E-mail address: [email protected] (S. Raj).
0038-1098/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2011.12.045
octahedral crystal field of the six oxygen neighbors of the W split the W 5d bands into triply degenerate t2g and doubly degenerate eg bands. In WO3 , the Fermi level (EF ) lies at the top of the O 2p bands, and WO3 is a band insulator. Within a rigid band model, the band structure of both WO3 and NaWO3 should be identical, with EF at different positions. In NaWO3 , the Na 3s electrons are transferred into the W 5d t2g band and the system should behave metallic for any value of x. However, for lower concentrations of x ≤ 0.25, the material is insulating and the cause of the MIT was a matter of debate for a long time. The electrochromic property of sodium doped WO3 is another interesting subject of research, where even after a substantial effort, understanding on the mechanism behind electrochromic property is not yet fully achieved. Low sodium doped tungsten bronzes are nonmetallic with localized W5+ ions scattered in a background of W6+ ions. Absorption of light occurs by the excitation of an electron from a site with W5+ ion to a neighboring W6+ ion around it. The excited electron modifies the local lattice and the electrochromic properties can be explained by the language of ‘‘polaron’’ physics. Schirmer et al. [6] explained the optical absorption of WO3 as small polaron absorption. Recently photoemission spectroscopy has found a signature of polaron formation in non-metallic Nax WO3 [7]. In spite of having indications regarding the formation of polarons in the non-metallic Nax WO3 , a clear understanding on the dynamics of polarons has not yet been achieved. In this paper, we have investigated the change of density of states (DOS) with temperature at the valence-band edge along the Γ − X high-symmetry direction in the Brillouin zone (BZ)
494
S. Paul et al. / Solid State Communications 152 (2012) 493–496
a
b
Na W O
d Binding Energy (eV)
c
Laue Diffraction
EF 0.2 0.4 0.6 -0.2 0.0 0.2 Wave Vector (Å-1)
Fig. 1. (Color online) (a) Cubic crystal structure of NaWO3 showing corner sharing WO6 octahedra. (b) Brillouin zone of cubic NaWO3 showing high-symmetry lines. (c) Laue diffraction pattern of single crystal Nax WO3 (x = 0.025). (d) Experimental near EF band mapping of Nax WO3 (x = 0.025) along the Γ − X high symmetry direction. Circles are a guide to the eyes to follow the band dispersion. Band moves towards EF but never crosses EF showing the insulating character of the system.
(see Fig. 1(b)). We found the signature of polaron formation in this non-metallic system. The DOS at valence band edge gradually decreases around the Γ point and increases at other k-points with increasing temperature implying the delocalization of polaron. The different photoemission modes (i.e., HAD, LAD, and WAM, see results and discussion) of measurements helped us to understand the dynamics of polaron formation in the lightly doped sodium tungsten bronzes. 2. Experiments Single crystals of insulating Nax WO3 (x = 0.025) were grown from high temperature solution of 15 mol% of Na2 O with WO3 by a slow cooling method [8]. Fig. 1(c) shows the Laue diffraction pattern of the insulating sample, which indicates that the samples were single crystals. High-resolution ARPES experiments were performed at the BaD ElPh beamline installed at the Elettra synchrotron, Italy. Photon energy of 22 eV was used to excite the photoelectrons, which were detected with a Phoibos 150 hemispherical electron analyzer and the overall instrumental resolution was better than 40 meV. The measurements for insulating Na0.025 WO3 were performed at 50–300 K in a vacuum better than 5 × 10−11 Torr. A clean surface of the sample for photoemission measurements was obtained by in situ cleaving along (001) surface. The possibility of charging in the insulating sample was checked by reducing the photon flux. We found no shift in the valence band peaks, which confirms that there is no charging in the sample. The Fermi level (EF ) of the sample was referred to that of a copper prepared freshly by Ar sputtering on the sample substrate. All the spectra were collected within 24 h after cleaving, during which we did not observe any significant changes in the spectra indicative of the contamination and/or degradation of the sample surface. 3. Results and discussion A typical near-EF band mapping of Nax WO3 (x = 0.025) by ARPES is shown in Fig. 1(d) around the Γ point of BZ. An electron-like dispersive band is observed around the Γ point which never crosses EF , showing that the system is insulating. The dispersive band represents the conduction band of Nax WO3
(x = 0.025), which is assigned as the W 5d t2g orbitals from the band calculations. The insulating behavior arises from the Anderson localization [9] of all the states near EF due to the strong disorder caused by inserting Na in a WO3 lattice. As a result of the localization, a soft Column gap arises at EF and consequently the DOS vanishes at EF . This gap arises due to the long-range interaction of the electrons trapped due to the strong disorder caused by the random distribution of Na in WO3 lattice. It is important to mention that in Anderson localization model [9] single electron DOS has no singularity and remains finite near the Fermi level. A truly Anderson localized system is called ‘‘gapless’’ as the insulating state does not have any gap in a DOS near EF but has a ‘‘mobility gap’’ between the Fermi level and the mobility edge. As soon as the Coulomb interaction among carriers sets in the insulating state, a gap opens up at EF [10–14]. The temperature dependence of the valence-band spectra has been investigated by carrying out photoemission spectroscopy (PES) on Na0.025 WO3 around Γ (X ) point (with different acceptance angles of detector) with the variation of temperature, and the results are shown in Fig. 2(a)–(c). The angle-resolved Phoibos 150 hemispherical electron analyzer has a provision to set different acceptance angles of the detector namely: High-Angular Dispersion (HAD) mode with ±3°, Low-Angular Dispersion (LAD) mode with ±7°, and Wide-Angle Mode (WAM) with ±13°. The PES spectra see mostly the angle-integrated spectra around the Γ (X ) point with ±3°, ±7°, and ±13° acceptance angle of the analyzer for HAD, LAD, and WAM modes, respectively. The acceptance angle of the analyzer for HAD, LAD, and WAM modes correspond to 13%, 30%, and 55% of the BZ of Na0.025 WO3 for 22 eV photon energy. All the spectra have been normalized under the curve within the energy range shown in the figure. The variation of the intensity of the 2.5-eV peak with temperature is clearly observed. The change in 2.5-eV peak intensity is more visible in HAD mode (Fig. 2(a)) than in WAM mode (Fig. 2(c)). It indicates that the intensity around Γ point for the HAD mode varies a lot with change in temperature whereas for the WAM mode the intensity variation is minimal. We believe that this behavior is because of the formation of polarons with lowering of temperature. It is believed that at low sodium doping levels, the sodium tungsten bronzes are nonmetallic with localized W5+ and W6+ ions and show polaronic states [15,16]. Polaron formation can take place in the insulating system, particularly when the doped charge carriers are in a comparatively narrow d band and are contributed by donors distributed at random in the lattice. The polaron formation in the lightlydoped tungsten bronzes had been studied with electron spin resonance, optical absorption, and Raman spectroscopy [15–18]. In fact, in Na0.025 WO3 the carriers are self-trapped by inducing an asymmetric local deformation in the WO3 lattice. Even though the carrier is confined to a single lattice site, the tunneling between different lattice sites is still relevant and a self-trapped carrier resides in an itinerant polaron state [19–21]. This is most likely to occur when the band edge is degenerate and the valence-band edge is more often degenerate than the conductionband edge. Hence an effect of polaron formation should be reflected significantly at the valence-band edge as compared to the conduction band. The intensity ratio of the valence-band edge (2.5-eV peak) to the 4-eV peak is shown in Fig. 3(a). The valence band photoemission spectra shown in Fig. 2 is fitted with a curve fitting program and the intensity ratio is determined by the area under the peak with centroid at 2.5 and 4-eV. It is observed that the intensity of 2.5-eV peak decreases with increasing temperature (from 50 to 200 K the intensity ratio is weakly decreasing, while there is a strong decrease around 220 ± 15 K) and reaches a minimum above 230 K for all the modes of detection. As earlier mentioned, we
S. Paul et al. / Solid State Communications 152 (2012) 493–496
Binding Energy (eV)
Intensity (arb. units)
c
Intensity (arb. units)
b
Intensity (arb. units)
a
495
Binding Energy (eV)
Binding Energy (eV)
Fig. 2. (Color online) Valence-band PES spectra around Γ (X ) point of Nax WO3 (x = 0.025) at several temperatures showing the signature of polaron formation below 230 K at valence-band edge (∼2.5 eV binding energy) for different acceptance angles of the electron analyzer (a) High Angular Dispersion (HAD) mode with ±3° (b) Low Angular Dispersion (LAD) mode with ±7° (c) Wide Angle Mode (WAM) with ±13°.
4. Conclusion We have carried out high-resolution photoemission spectroscopy on insulating Nax WO3 (for x = 0.025) with variation of temperature from 50 to 300 K. We found a direct evidence of polaron formation from the temperature dependence of the photoemission spectra. The DOS at valence band edge gradually decreases around the Γ point and increases at other k-points with
a (2.5 eV peak/4eV peak)
Intensity Ratio
0.25
0.20
0.15
0.10 50
100
150
200
250
300
Temperature (K)
b Low Temperature / High Temperature 2.5 eV Peak Intensity Ratio
think that the reduction in the intensity of the 2.5-eV peak is due to the breakdown of polaron formation at higher temperatures (above 230 K), where the charge carriers are no longer self-trapped. A polaron can be considered to be a local deformation/defect in the lattice and a truly localized defect level is derived primarily from the Γ point (k = 0) with far less weight from other k-points. A more delocalized defect level is derived from k-points other than Γ [22]. As the polaron becomes more delocalized, there is a spectral weight transfer from Γ point to other k-points. A comparison among different modes of PES shows that the intensity ratio, especially at low temperature, decreases with increasing acceptance angle of the detector. The total DOS of 2.5-eV peak is constant (if integrated over the full BZ) and in the WAM mode the detector integrates all the DOS arising from ±13° (corresponding to 55% of the BZ for photon energy of 22 eV) around the Γ point. With increasing temperature a fraction of 2.5-eV DOS moves from the Γ point to other k-points because of the delocalization of polarons. That is why in the WAM mode, the photoemission spectra show less variation of 2.5-eV peak intensity as compared to the HAD mode, where the integration is only for ±3° around the Γ . For a better understanding the ratio of low (average of 80–200 K) and high (275 K) temperature DOS of the 2.5-eV peak is shown in Fig. 3(b). For WAM, the ratio is less as compared to HAD (1 is expected value for integrations over the full BZ). Because of polaron formation the DOS of 2.5-eV peak accumulates around the Γ point at lower temperatures, whereas the intensity decreases with increasing temperature. This is well reflected in HAD mode PES where the observed intensity is only around the Γ point. The optical absorption of W5+ in WO3−x shows signature of polaron formation in low-temperature and vanishes at 300 K [15,16]. This adds additional support to our conclusion that the increase in the intensity of the valence-band edge below 230 K is due to the formation of polarons.
3.0
2.5
2.0
1.5 +7 + 13 3 – – Analyzer Acceptance Angle (degree)
+ –
Fig. 3. (Color online) (a) Temperature dependence of the intensity ratio of the 2.5-eV peak to the 4.0-eV peak for different measurement modes of PES showing the delocalization of polaron above 230 K temperature. (b) Low- to hightemperature intensity ratio of 2.5-eV peak vs. analyzer acceptance angle (errors are given as vertical bar). This ratio is less in WAM mode than HAD mode, which explains the transfer of 2.5-eV DOS at Γ point to other k-points with increasing temperature.
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increasing temperature implying the delocalization of polaron. After 230 K, the polaron has less effect on the variation of DOS at different k-points implying the delocalization of the trapped charge carriers within the disordered lattice for the low doped sodium tungsten bronzes. Acknowledgments The work at Elettra was supported by Indian DST and Italian MAE under the bilateral program of collaboration. We acknowledge E. Nicolini for the Laue diffraction measurements and D. Lonza for his technical assistance during the photoemission experiments. References [1] C.G. Granqvist, Handbook of Inorganic Electrochromic Materials, Elsevier, Amsterdam, 1995. [2] P.M.S. Monk, R.J. Mortimer, D.R. Rosseinsky, Electrochromism: Fundamentals and Applications, VCH, Weinheim, 1995.
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