The band structure of WO₃and non-rigid-band behaviour in Na_0.67WO₃derived from soft x-ray spectroscopy and density functional theory

Abstract

The electronic structure of single-crystal WO3 and Na0.67WO3 (a sodium-tungsten bronze) has been measured using soft x-ray absorption and resonant soft x-ray emission oxygen K-edge spectroscopies. The spectral features show clear differences in energy and intensity between WO3 and Na0.67WO3. The x-ray emission spectrum of metallic Na0.67WO3 terminates in a distinct Fermi edge. The rigid-band model fails to explain the electronic structure of Na0.67WO3 in terms of a simple addition of electrons to the conduction band of WO3. Instead, Na bonding and Na 3s-O 2p hybridization need to be considered for the sodium-tungsten bronze, along with occupation of the bottom of the conduction band. Furthermore, the anisotropy in the band structure of monoclinic γ-WO3 revealed by the experimental spectra with orbital-resolved geometry is explained via density functional theory calculations. For γ-WO3 itself, good agreement is found between the experimental O K-edge spectra and the theoretical partial density of states of O 2p orbitals. Indirect and direct bandgaps of insulating WO3 are determined from extrapolating separations between spectral leading edges and accounting for the core-hole energy shift in the absorption process. The O 2p non-bonding states show upward band dispersion as a function of incident photon energy for both compounds, which is explained using the calculated band structure and experimental geometry.

Band gap states in nanocrystalline WO3thin films studied by soft x-ray spectroscopy and optical spectrophotometry

“…We have previously shown that DC magnetron sputtered films are composed of the monoclinic γ-WO 3 phase (space group P2 1 /n) together with small amounts of the monoclinic ε-WO 3 (space group Pc), both shown in Figure 1, with varying oxygen vacancy concentration depending on deposition conditions [9]. Recent density functional theory (DFT) calculations show that the electronic structure of the different WO 3 phases is a result of varying W-O bond lengths along the x, y, and z directions in the crystal, with resulting bonding-antibonding orbital interactions, which give rise to (mainly) hybridized W5d and O2p conduction and valence band states, respectively [10,11,13,14]. It has been predicted that for the monoclinic Pc and P2 1 /n phases W-O bond splitting occurs in all directions, and gives rise to an increased band gap compared to other phases [11].…”

“…X-ray spectroscopy techniques provide means to explore the valence and conduction band structure in detail. With tunable light sources available at synchrotron beam-lines they provide means to selectively probe symmetry and energy selected portions of the band structure [14,[29][30][31]. For example, in x-ray emission spectroscopy (XES) the total density of (filled) valence band states can be probed, and in x-ray absorption spectroscopy (XAS) the density of (empty) conduction band states is probed.…”

“…x-ray absorption and emission spectroscopy offers means to extract information about the electronic bands in semiconductors, which favorably can be used to compare with theoretical calculations [14,31,34].…”

First-principles reinvestigation of bulk WO3

“…WO 3 shows no proper melt; surface melting of crystalline 48 material occurs at 1746 K. Crystal growth proceeds typically 49 by sublimation and gas transport at temperatures below 50 1400 K. At the highest temperatures the structure is tetrag-51 onal (space group P 4/nmm) with strong antiferrodistortive 52 cation movements so that the WO 6 octahedra are strongly 53 distorted [30] in an antipolar pattern. Additional rotational 54 octahedral distortions condense in addition to the initial 55 tetragonal displacements when lowering the temperature.…”

“…Numerous first-principles studies were performed on WO 3 79 in order to characterize its electronic structure (bulk, thin films, 80 and cluster phases [35][36][37][38][39][40][41]), the role of oxygen vacancies 81 [42][43][44][45], and cation doping [46][47][48][49][50][51][52][53]. In this paper we do not 82 only focus on the electronic structure but also extensively 83 study the structural stabilities and metastabilities of the 84 various phases.…”