Article pubs.acs.org/JPCC
Chemical Bonding and Hybridization in 5p Binary Oxide John A. McLeod,*,† Nikolai A. Skorikov,‡ Larisa D. Finkelstein,‡ Ernst Z. Kurmaev,‡ and Alexander Moewes† †
Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan S7N 5E2, Canada ‡ Institute of Metal Physics, Russian Academy of Sciences−Ural Division, 620990 Yekaterinburg, Russia ABSTRACT: We analyze the electronic structure of several 5p binary oxides (In2O3, SnO, SnO2, Sb2O3, Sb2O5, and TeO2) using density functional theory and soft X-ray spectroscopy. We find that there is bonding in hybridized cation 5s-O 2p states at the bottom of the valence band in oxides with cations in both the formal 5s2 and 5s0 valencies. We similarly find that there is antibonding in hybridized cation 5d- or 5s-O 2p states at the top of the valence band for oxides with cations in 5s2 or 5s0 valencies, respectively, and the density of O 2p states in these antibonding states is much greater in the 5s0 oxides than the 5s2 oxides. The calculated and quasi-empirical band gaps for these oxides are tabulated, and we identify the hybridizations responsible for the spectral features in the measured XES.
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INTRODUCTION The wide variety of electronic and chemical properties of metal oxides make them very exciting materials both for basic research and for technological applications.1−4 Oxides cover a wide range of electrical properties from wide band gap insulators to conductors and superconductors.5 5p binary oxides (SnO2 and In2O3 being the most well-known) belong to a class of materials that combines high electrical conductivity with optical transparency (“transparent conductors”) and, thus, constitute an important component for optoelectronic applications.6 Transparent conductivity can be realized by degenerately doping a host transparent oxide,7 although this alone does not ensure transparent conductivity; the host material also must have a suitable bandgap and a suitably broad valence or conduction band.8 Therefore, the electronic structure of these 5p oxides is very important for a general understanding of the phenomenon of transparent conductivity. Unfortunately, the main focus of studies on the electronic structures of these materials has been limited mostly to SnO2 and In2O3.9−11 In the present paper, we have performed a systematic study of the electronic structure of several 5p oxides using density functional theory and soft X-ray spectroscopy. It is well-known that the description of the electronic structure of compounds containing 3d transition elements is very difficult because of problems with treating the correlations between the 3d electrons.12 In our previous paper,13 we have shown that the O 2p states of alkaline earth oxides (BeO, MgO, CaO, SrO, and BaO), and post-transition metal oxides (ZnO, CdO, HgO) reproduce the shape and energy distribution of the cation s-, p-, and d-states. While not dominant at the Fermi level, the cation states are quite relevant to the electronic structure of these compounds. In a similar vein, with O Kα X-ray emission spectroscopy (XES) and O 1s X-ray absorption spectroscopy (XAS) we have © 2012 American Chemical Society
an opportunity to use these spectra to reproduce the relative position of s-, p-, and d-states of the cation for the 5p binary oxides In2O3, SnO, SnO2, Sb2O3, Sb2O5, and TeO2. Herein we perform an analysis of the partial density of states (DOS) and we extract the main trends in the electronic structure for the above 5p binary oxides.
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EXPERIMENTAL AND THEORETICAL METHODS The XES measurements of the 5p oxides were performed at Beamline 8.0.1 of the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory (LBNL).14 The endstation uses a Rowland circle geometry X-ray spectrometer with spherical gratings and an area sensitive multichannel detector. The O Kα XES were excited at 540 eV, just above the O 1s ionization threshold, to suppress the high-energy satellite structure.15 The spectrometer resolving power (E/ΔE) for emission measurements was about 103. The XAS measurements were performed at the spherical grating monochromator (SGM) beamline of the Canadian Light Source (CLS) at the University of Saskatchewan.16 The absorption measurements were acquired in total fluorescence mode (TFY) using a channel-plate fluorescence detector. The monochromator resolving power (E/ΔE) for absorption measurements was about 2000. TFY provides more bulk sensitivity than the other common technique for soft X-ray absorption measurements, total electron yield (TEY). All spectra were normalized to the incident photon current using a highly transparent gold mesh in front of the sample to measure the intensity fluctuations in the photon beam. Received: August 3, 2012 Revised: October 24, 2012 Published: October 29, 2012 24248
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Calculated Densities of States. The dominant contribution to the valence band of the 5s2 oxides comes from O 2p states, as shown in Figure 1 (although the O 2s states could also
The 5p oxide powders (99.99% purity) were obtained from Alfa Aesar. They were pressed into clean indium foil and were measured without further refinement. Because only the oxygen edges were measured, there was no risk that the indium foil would contaminate the measurements of In2O3. All X-ray spectroscopy measurements were preformed at room temperature in a vacuum of about 10−7 Torr. Our calculations were performed with the ab initio WIEN2k code,17 which is based on the linearized augmented plane-wave with local orbitals (LAPW+lo) method with scalar-relativistic corrections. We used calculation parameters typical for insulators (we used Rmin MTKmax = 7, nearly touching RMT spheres, a maximum of 1000 k-points divided into a grid based on the particular unit cells, and energy and charge convergence of 0.0001 Ryd and 0.001 e, respectively) and the experimentally determined unit cells. We used the Perdew−Burke−Enzerhof (PBE) generalized gradient approximation (GGA) functional to calculate the electronic structure, we also made use of the modified Becke−Johnson (mBJ) GGA functional, which is known to give better estimates of the band gaps.18 The PBE density of states (DOS) was then simply shifted to conform to the mBJ band gap. We calculated the oxygen K XES from the ground state electronic structure using the “XSPEC” package included with WIEN2k, which simulates the measured spectra by multiplying the partial density of states with a dipole transition matrix and a radial transition probability.19 For the oxygen K XAS spectra, we calculated the electronic structure of a primitive supercell with a single O 1s core hole (large enough that the periodic core holes were at least 10 Å apart; one of these calculations was performed for each inequivalent oxygen site in the fullsymmetry unit cell, the calculated XAS were then summed taking the differences in binding energies into account). The calculated XES and XAS were broadened with a Lorentzian function (with an energy-dependent width varying quadratically from 0.1 eV at the upper band edge to 0.5 eV at the lower band edge) to mimic the core hole lifetime broadening, and a Gaussian function (with an energy dependent width based on the aforementioned experimental resolving power) to mimic the instrumental resolution. Finally, to examine the bonding, we calculated the crystal orbital Hamilton population (COHP) using SIESTA, a tightbinding pseudopotential code.20,21 We used soft pseudopotentials with the same crystal structure, k-point grid, and the PBE exchange correlation functional as described above. (The one exception was that we used the local density approximation (LDA) exchange correlation functional for In2O3 because the PBE pseudopotential’s treatment of the 4d states resulted in ghost states.)
Figure 1. Calculated DOS for the 5s2 oxides. The Fermi level is at 0 eV, denoted by the dotted line, and four regions of interest are labeled a−d for each material. The cation states are labeled as X in the legend. Note how the occupied cation 5s2 states are located at the bottom and top of the valence band, regions a−d, respectively.
be considered as part of the valence band, in this manuscript we will use “valence band” to mean only the top valence band because it is our primary region of interest). However, the shape of the valence band is heavily influenced by the distribution of cation states. From Figure 1 we note that the bottom of the valence band (region a) is determined by hybridization between O 2p and cation 5s states, and there is a similar, but weaker, hybridization effect occurring at the Fermi level (region d; for brevity, we will refer to the top of the valence band as the “Fermi level”, even though the true Fermi level is undefined for insulators). This “bounding” of the valence band by cation s states is consistent with other studies of lone-pair oxides.22−24 The middle of the valence band is characterized by a dominant O 2p character, with weak hybridization with the cation 5p states (region b). The cation 5d states are essentially negligible. Finally, as the mass of the cation increases, the density of O 2p states hybridized with cation 5s states in feature a in Figure 1 decreases. While there are common aspects in the electronic structures of these materials, there is really only one common aspect in the local crystal structures; the cations in SnO (with the P4/ nmm space group25), Sb2O3 (with the Pccn space group26), and TeO2 (with the P41212 space group27) have no bonds in one hemisphere, and this hemisphere is occupied by the lone-pair 5s2 states. This structural feature is common for lone-pair oxides28 and is the only major similarity between the crystal structure of these materials. The valence bands of the 5s0 oxides are also dominated by O 2p states, as shown in Figure 2. As with the 5s2 oxides, the cation 5s states are hybridized with the oxygen 2p states at the bottom of the valence band (note that there is a small amount of hybridization between the O 2p states and the In 4d10 shell in In2O3; however, for the present discussion, we will consider this separate from the “valence band”) in region a. These cation 5s states are found at lower and lower energies with increasing cation Z, and the hybridization between these states and the O 2p states is progressively weaker, again as was found for the 5s2 oxides. The presence of these cation 5s states reminds us once
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RESULTS AND DISCUSSION Assuming complete oxidation, there are two cation ground state configurations in the oxides studied herein: the 5s0 ground state and the 5s2 ground state. The cations in In2O3, SnO2, and Sb2O5 belong in the former category, the cations of SnO, Sb2O3, and TeO2 belong in the latter. Even though it is apparent from the calculated DOS that the cation 5s states are, in all cases, at least partially occupied (and indeed, the cation 5p and 5d states are also partially occupied), there are observed differences between the two categories of oxides described above. Therefore, even though they are not completely accurate, the labels “5s0 ground state” and “5s2 ground state” will be used hereafter. 24249
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Figure 2. Calculated DOS for the 5s0 oxides. This figure is analogous to Figure 1. Note the filled 4d10 of In in In2O3 at −12 eV and the lack of a d feature (as found in the 5s2 oxides shown in Figure 1) at the Fermi level.
Figure 3. Calculated charge densities for SnO and SnO2. In (i) the charge density for SnO along a (100) plane is shown (this plane is a mirror plane for the Sn C4v point group) with the projected O 2p occupied DOS. Here the z axis is aligned with an O−Sn bond. The energy regions used for the charge densities are labeled as a and d. The same information for SnO2 is shown in (ii). Here the charge density is in the (110) plane and the z axis is out of the page and calculated for energy regions a and c are used. Each gradient line represents an increase of 0.01 eV/Bohr2, and the density has been saturated at 0.15 eV/Bohr2. The aspect ratio of the density plots is correct, but the SnO plots have slightly different length scales than the SnO2 plots.
again that the formal 5s0 character of the cation is only a label and not indicative of a lack of charge associated with the cation. Unlike the 5s2 oxides, the top of the valence band is dominated by a rather sharp distribution of O 2p states with comparatively strong hybridization with cation 5d states (region c). (The number of nodes in the wave function of the valence cation d states in In2O3 confirms that they are 5d and not antibonding 4d. The wave function changes from 4d to 5d at −7.8 eV relative to the Fermi level for the In in In2O3. For the other materials, the change from 4d to 5d wave functions in the cation happens at considerably lower energies: −18.5 eV and −15.8 eV for Sn in SnO and SnO2, respectively, −22.2 and −20.8 eV for Sb in Sb2O3 and Sb2O5, respectively, and −30.6 eV for Te in TeO2.) This hybridization between O 2p and cation 5d states at the top of the valence band in region c could perhaps be somewhat seen in the 5s2 oxides as well (refer back to Figure 1), but the dominant hybridization with O 2p states near the Fermi level was definitely from cation 5s states; this hybridization is completely absent in the 5s2 states. This observation suggests that the stereochemical lone pair states of these cations are near the Fermi level, a view that is supported by charge density plots of SnO and other lone pair oxides.23,28,29 Finally, like the 5s2 oxides, the dominant hybridization in the middle of the valence band is between O 2p and cation 5p states (in region b). Like the 5s2 oxides, the only common structural aspect of the 0 5s is the geometry of the cation environment; for In2O3 (with the Ia−3 space group30), SnO2 (with the P42/mnm space group31), and Sb2O5 (with the C2/c space group32) the cations are all coordinated by six oxygens in an approximate octahedral environment. Calculated Spatial Charge Densities. The similar electronic structures of the 5s2 and 5s0 oxides suggest that, despite the differences in crystal structure, there may be a common picture of the bonding between the cations and the oxygen in these materials. Because SnO and SnO2 have electronic structures representative of the 5s2 and 5s0 oxides, respectively, but also have very simple crystal structures, we will take a closer look at the charge distribution around the Sn and O sites in these materials. The charge density and projected O 2p occupied DOS is shown in Figure 3. The charge density is shown for two energy ranges; region a at the bottom of the valence band
corresponding to cation 5s-O 2p hybridization (refer back to Figures 1 and 2) for both materials and the region near the Fermi level (region d for SnO and c for SnO2). The charge density plots for SnO show a larger concentration of charge near the Sn atom than in SnO2, as we expect from the higher formal valence. Further, the lone pair charge is clearly seen occupying the hemisphere away from the oxygen ligands near the Fermi level. These charge density plots for SnO are in agreement with previously published results.28 Examining both the charge density and the projected O 2p DOS for SnO shows that the states at the bottom of the valence band, in region a, are along the ligand−cation axis and composed equally of px, py, and pz character. This suggests that the plane chosen for the charge density in Figure 3 is representative of the charge distribution between the oxygen and the tin atoms and that there is bonding in this region. In contrast, at the top of the valence band in region d, the O 2p states are almost entirely of px,y-character, which is not directly oriented along the bond axis. The charge density in this region also shows the bulk of the states away from the Sn−O bond axis, and the lack of charge between the O and the Sn suggests this is an antibonding region. For region a the same story holds for SnO2, the charge density plot in Figure 3 shows that charge is concentrated along the O−Sn bond axis, and the projected O 2p DOS supports this conclusion (here note that the z-axis is out of the page, and there are no pz states in this region). This again suggests that the states in region a are bonding. At the top of the valence band, in region c, the charge density plot shows a large number of ligand-oriented lobes on the Sn sites, and the projected O 2p shows a dominance of pz character. Because the Sn charge is oriented toward the O, but the O charge is out of the bonding plane, this region is characterized by antibonding (where the 24250
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In region c, the O 2p DOS of the approximately trigonal O site in Sb2O5 (coordinate system 3 in Figure 4iii) has almost exactly the same partitioning between px, py, and pz character as the O site in SnO2 (which has the same coordinate system), for the other two O sites in Sb2O5 (both two-coordinated using coordinate system 2 in Figure 4iii) there is a large off-axis px component and a significant py component, as was found in the 5s2 oxides Sb2O3 and TeO2. These similarities indicate that the bonding in region c in Sb2O5 is the same as the bonding at the top of the valence band in the other oxides studied here, namely, antibonding. The approximately tetrahedral orientation of In2O3 does not lend itself to this sort of comparison as readily, however we note that the on-axis pz component is lower than the partially off-axis px and py components, which is similar to the partial O 2p DOS for SnO. We, therefore, conclude that In2O3 follows the same trend as the other oxides in regards to the nature of the chemical bonding. For DOS calculated with the tight-binding method the bonding can be quantitatively estimated using the crystal orbital Hamilton population (COHP) approach.33 The COHP for the overlap of the O 2p and cation 5s states is shown in Figure 5.
antibonding lobes are mostly directed out of the page in Figure 3ii). Bonding and Antibonding Regions in the Valence Band. Although the large unit cells and rather low symmetry of the other materials studied herein make it impossible to find a single crystal plane that has a charge density representative of the bonding environment, we can still plot the projected O 2p DOS to see how that resembles the projected O 2p DOS of SnO and SnO2. These projected DOS are shown in Figure 4, and they reveal that the O 2p states in the other materials follow the pattern set by SnO and SnO2.
Figure 4. Projected O 2p occupied DOS. The three different coordinate systems used are shown in (i); the oxygen is the central atom. In coordinate system 3, the angle θ is the smallest of the three angles, and in both 2 and 3, the x-axis bisects the bond angle θ. The projected DOS is shown in (ii) for the 5s2 and in (iii) the 5s0 oxides. The dotted lines denote the limits of the cation 5s−O 2p hybridization regions (regions a and d for the 5s2 oxides, regions a and c for the 5s0 oxides). Note there are two inequivalent oxygen sites for Sb2O3 and TeO2 and three inequivalent oxygen sites for Sb2O5. In each case, the number just above the Fermi level denotes the appropriate coordinate system.
Figure 5. Partial DOS and COHP calculated with SIESTA. Negative COHP implies bonding states, positive COHP implies antibonding states. Note that due to different definitions of partial DOS in the tight-binding and LAPW methods the states here are not expected to be identical to those in Figures 1 and 2. We also stress that the calculated COHP and DOS should be interpreted qualitatively, because the technique used to calculated the DOS in Figures 1 and 2 is more accurate.
For the 5s2 oxides (see Figure 4ii), the O 2p states in region a are characterized by states that are along the ligand−cation axis, implying bonding. (Note that in SnO this meant equal parts px, py, pz, while since the O sites are only 2-coordinated in Sb2O3 and TeO2 this means a lack of pz states because these are projected out of the cation−ligand−cation plane.) For the states in region d, SnO had the simple situation that only px,y states had off-axis components, so their presence is denoted as antibonding. For Sb2O3 and TeO2, the situation is slightly more complicated, but we do see a large magnitude of off-axis pz states. Second, while the py states in Sb2O3 and TeO2 point partially toward the cations, the py wave function cannot have lobes of the same polarity pointed at each cation. Since the cation states are primarily of 5s character in this region (refer back to Figure 1), this supports the idea of antibonding in this region. Similarly, for the 5s0 oxides, the O 2p states in region a are again characterized by states that are along the ligand−cation axis. Bonding in this region requires that the approximately tetrahedral geometry of the O sites in In2O3 has an equal partitioning of px, py, and pz character states, while the sites in the other materials have no pz character, as is seen in Figure 4iii.
The partial O 2p and cation 5s states are plotted as well, because this calculation was performed using a pseudopotential tight-binding approach, it is important to check that the partial DOS is similar to that calculated with the more accurate fullpotential LAPW approach in Figures 1 and 2. (We do not expect the DOS to be identical, however, because the tightbinding approach requires significant overlap between the atomic spheres, while the LAPW requires no overlap.) Figure 5 shows the bonding and antibonding trend in the cation 5s−O 2p hybridization regions of the 5s2 oxides, as predicted above. Unfortunately, the tight-binding basis does not provide a realistic distribution of cation 5d states so the cation 5d−O 2p COHP is not provided here. The COHP shown here is essentially the same as other studies in the literature.29,34 X-ray Spectroscopy Measurements. To check the validity of the conclusions drawn from these calculations, we can use the O 2p DOS to calculate the expected O K XES and 24251
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XAS spectra of these materials and compare them to our measured spectra. O K XES and XAS present an excellent technique for measuring the bulk electronic structure; since both are governed by dipole selection rules the O K XES and XAS probe the occupied and unoccupied p-projected states local to the oxygen atom. When the XES is measured nonresonantly (as is the case here), the XES and XAS spectra are independent of one another and, for polycrystalline powders, the O K XES gives an excellent experimental portrayal of the O 2p states.13,23 Because the X-ray transitions are dominated by the final state rule, the O K XAS is not directly comparable to the ground-state unoccupied DOS because the O 1s core hole provides a perturbing potential. However, as mentioned above, this can be simulated by calculating the DOS with an explicit core vacancy included in a single atom in a low symmetry supercell. The O K XES calculated from the ground state DOS, the O K XAS calculated from the core hole-perturbed DOS, and the measured O K XES and XAS for the 5s2 oxides is shown in Figure 6. It is clear that the measured XES spectra reproduce
Figure 7. Measured and calculated O K XES and XAS for the 5s0 oxides. This figure is analogous to Figure 6. The inset shows the O 2p−In 4d hybridization feature in In2O3 from the calculated and measured XES (the measured spectrum has been smoothed to facilitate identifying this weak feature).
relative intensities of the XES spectral features are again incorrect for the lightest cation, In2O3, but the relative intensities improves for SnO2 and is quite good for Sb2O5. We suspect that one of the reasons for this is that the calculated DOS places the 4d10 states too high in energy; note that the calculation predicts a small O 2p−In 4d hybridization feature at ∼515 eV, while the measurements show a weaker hybridization feature at ∼512 eV. A similar result was previously found for O 2p−Ga 3d hybridization in LiGaO2; again, the calculated Ga 3d10 states were too high in energy.35 Placing the In 4d10 too close to the bottom of the valence band could lead to distortion from too much p−d repulsion; this might be why the calculated XES is in better agreement with measurements for the oxides with heavier cations. The calculated XAS is in excellent agreement with the measured XAS for In2O3 and SnO2, and the main features of the measured XAS are reproduced in the calculated XAS for Sb2O5, although the intensities are not quite correct. Band Gaps and Spectral Features. Despite the discrepancies noted above, the calculated XES and XAS reproduce all the major features of the measure XES and XAS, so we conclude that the calculated DOS is fairly accurate. In addition to testing the validity of the calculated bulk electronic structure, the comparison of calculated and measured XES and XAS presents an opportunity to estimate the band gap of these materials. We have band gaps calculated with both the PBE and mBJ functionals, while in Figures 6 and 7, we have shifted both the calculated XES and XAS to match the measured spectra. Because we have both ground state and core hole DOS calculations, we can determine the predicted shift in the conduction band onset due to the core hole in the XAS and arrive an a quasi-empirical band gap estimate: We first apply a rigid shift to both the calculated XES and XAS so that the XES are aligned with the measurements (this shift is justified because the calculations do not predict accurate binding energies), we then note the additional energy shift required to align the calculated and measured XAS, and we finally add in the band gap reduction by the core hole effect to arrive at a new estimate of the band gap. These calculated and estimated band gaps are listed in Table 1; they are in reasonable agreement with values found in the literature, given that there is a great deal of discrepancy in the
Figure 6. Measured and calculated O K XES and XAS for the 5s2 oxides. The XAS was measured in TFY mode. The calculated XES and XAS were independently shifted to agree with the measured spectra. Three XAS spectral features, denoting distinct hybridization regimes, are labeled for SnO; these features are present in the other XES spectra as well.
the three main DOS features (labeled a, b, and c in Figures 1 and 2), and the slope of the measured XES at the Fermi level is in agreement with the calculated influence of DOS feature d. The relative intensities of these spectral features are somewhat incorrect for SnO, but they are improved for Sb2O3 and excellent for TeO2. The calculated XAS is also in good agreement with the measured spectra, while there are some discrepancies in intensity between the measured and the calculated features, the general shape of the measured spectrum is adequately reproduced. Given the approximations inherent in modeling the XAS transition using the fully relaxed DOS with an O 1s vacancy, the agreement is excellent. We also note that fluorescence yield XAS measurements suffer from selfabsorption, this effect could explain why the peaks in the measured XAS are less sharp and relatively less intense than in the calculated XAS. The calculated and measured O K XES and XAS for the 5s0 oxides are shown in Figure 7. The measured XES for these materials is again in good agreement with the calculated XES and the three DOS features are present. Interestingly, the 24252
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hybridization and labeled c in Figures 1 and 2) are the same in the calculated and measured XES spectra (refer back to 6 and 7). As shown in Figure 8ii, this energy splitting is essentially dependent only on the cation, not the valency. Therefore, this study of simple binary oxides may provide a guide to empirically analyzing the electronic structure based on O K XES measurements of more complicated ternary oxides, or solid solutions, or other heterostructures containing these 5p cations.
Table 1. Band Gaps Calculated with the Mbj Functional (Calc.), Estimated from Comparing the Calculated and Experimental XES and XAS Spectra (Est.), Literature Bandgaps for the 5p Binary Oxides, and the Calculated Shift in the XAS Due to the Core Holea compound
calc. (eV)
exp. (eV)
In2O3 SnO SnO2 Sb2O3 Sb2O5 TeO2
3.036 0.368 3.563 3.103 2.263 3.418
3.2 1.5 3.7 3.6 4.2 4.0
literature (eV) 2.6,36 3.75,37 2.938 2.5−3.0,39 0.7,40 0†29 3.5,41 2.6,42 3.4†43 2.4,44 3.545 3.4−4.1,3 ∼ 3.5,46 3.7647
core hole shift (eV) 0.6 0.15 0.2 ∼0.1 ∼0 ∼0.1
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CONCLUSIONS To summarize, we have shown that the valence bands of these oxides are formed by O 2p states hybridized with distinct symmetries of cation states (here 5s, 5p, and 5d) at distinct energy levels. The energy of these hybridizations decreases (i.e., is further from the Fermi level) with increasing cation atomic number, independent of crystal structure or cation valency. However, the contribution of cation 5d states to the valence band is much greater for the 5s0 oxides than the 5s2 oxides. We have also found that the chemical bonding of 5p binary oxides involves bonding of hybridized cation 5s−O 2p states at the bottom of the conduction band, and antibonding of hybridized cation 5d- or 5s-O 2p states at the Fermi level for both 5s2 and 5s0 oxides. This similarity in the type and energy of bonding and antibonding states in the high and low cation oxidation states of these oxides can explain the similarity in thermodynamic properties (formation energy, melting temperature, etc.) between them. Further, the bulk of the oxygen 2p states is coincident with the bulk of the cation 5d states, and although the cation 5d states are of relatively low intensity, they do help define this region as bonding (in the 5s2 oxides) or antibonding (in the 5s0 oxides). The dependence of the oxygen 2p states on hybridization with the cation states is the reason why many of the oxygen K XES bands are progressively reduced in energy with increasing cation atomic number. Finally, we have compared calculated O K XES and XAS spectra to measured spectra and found generally good agreement, although the band gaps were occasionally significantly underestimated even for the calculations with the mBJ functional. We have identified the hybridized states responsible for the distinct features in the measured O K XES, and since the energy splitting of these features seems dependent only on the cation species, not the crystal structure of the cation valency, these features may be used to interpret the electronic structure of more complicated oxides that involve these 5p cations. We can conclude that oxygen K XES provides powerful empirical data on hybridizations not only between oxygen and cation states, but on the distinct symmetry (5s, 5p, or 5d) of these states, the latter of which, for many formally d0 cations, is often neglected in theoretical treatment.
a All literature bandgaps are experimental save those denoted by †, which are based on calculations.
reported band gaps. Our calculated and estimated gaps are in reasonable agreement for In2O3 and SnO2. The agreement is poorer for Sb2O3 and TeO2, and the calculated gaps are considerably underestimated for SnO and Sb2O5. We stress that the core hole can generally only decrease the conduction band energies, and although it is difficult to determine the band edges from XES and XAS spectra empirically, we expect the separation between the measured XES and XAS to be generally less than the true band gap. The calculated effect of the core hole only shifts the conduction band onset to lower energies by a few tenths of an eV in all cases (as shown in Figure 1, the shift is largest for In2O3 at 0.6 eV, but all other cases are considerably smaller and Sb2O5 has no core hole shift within the experimental resolution), so even if this effect were neglected entirely the band gaps of SnO and Sb2O5 would still be too small to accurately reproduce the separation between the XES and XAS spectra. The band gaps calculated with the mBJ functional and estimated from the experimental spectra are plotted in Figure 8i. Apart from the calculated gaps for Sb2O5 (which, as
Figure 8. (i) Band gaps calculated with the mBJ functional and determined pseudoexperimentally (labeled “exp.”). (ii) Emission energy of the XES features labeled a−c in Figures 6 and 7. Note that the features are at essentially the same energy regardless of cation valency.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
mentioned above, are almost certainly underestimated), the band gap increases with increasing cation mass and cation valency for these materials. A final observation on the electronic structure of these materials is that the energy splitting between the cation 5s−O 2p hybridization feature at the bottom of the valence band (labeled a in Figures 1 and 2), the cation 5p−O 2p hybridization feature (labeled b in Figures 1 and 2), and the bulk of the O 2p states (characterized by cation 5d−O 2p
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge support of the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada Research Chair program, and the Russian Foundation for Basic Research (Projects 11-02-00022). The Canadian Light 24253
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Source is supported by the NSERC, the National Research Council (NSC) Canada, the Canadian Institutes of Health Research (CIHR), the Province of Saskatchewan, Western Economic Diversification Canada, and the University of Saskatchewan. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. The computational part of this research was enabled by the use of computing resources provided by WestGrid and Compute/Calcul Canada.
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dx.doi.org/10.1021/jp3077134 | J. Phys. Chem. C 2012, 116, 24248−24254
