A theoretical and experimental investigation of the electronic structure of α-Fe2O3 thin films

Ground and excited states of α-Fe2O3 have been investigated by determining the spinpolarized wavefunctions and eigenvalues of an embedded Fe2O 12− 9 cluster using the discrete variational Xα method. The computed transition energies compare reasonably well with the recorded experimental spectrum of high-purity α-Fe2O3 thin films obtained by the sol–gel technique. The theoretical data herein reported predict a very high valence–conduction band gap incompatible with the experimental outcomes, which were routinely interpreted as originated by an interband transition. In contrast to this, the lowest-energy optical transitions have a charge transfer nature, involving excitation of electrons from the occupied O 2p-based spin down levels to the empty Fe atom-like spin down orbitals. Iron (III) oxide thin films are particularly appealing for experimental and theoretical investigations in view of their technological applications. Actually, they can be used as catalysts in dehydrogenation reactions [1], magnetic devices [2], temperature and water sensors and optical filters [3, 4]. Furthermore, the applicability of Fe2O3 thin films in the relatively new field of non-linear optics has been suggested [5]. The UV–VIS absorption spectra of ferric oxides have received great attention in the past in order to understand the role of the ground and excited electronic states in determining their electronic properties. Unfortunately, in the case of measurements carried out on bulk samples, a very strong absorption starting at about 2.45 eV obscures a large section of the UV–VIS spectrum, preventing any analysis of the energy region above such an edge. As as consequence, in these kinds of sample, the only bands for which an assignment can be attempted are the very weak ones lying at about 1.85 eV, which, on the basis of crystal field calculations [6, 7], are assigned as a whole to the formally doubly forbidden d–d electronic transitions within the d5 configuration of the iron (III) ion. In a recent contribution, some of us [8] investigated by means of x-ray photoelectron (XPS), UV–VIS and Mössbauer spectroscopies high-purity Fe2O3 thin films prepared by the sol–gel technique. In detail, XPS measurements revealed that iron is only present (within the sensitivity of the technique, <1%) in the ferric form and that films without any carbon contamination are obtained at temperatures above 400 ◦C. The absence of any absorption in the near-IR range confirmed the absence of the ferrous species for all the heat treatment temperatures. Furthermore, Mössbauer spectroscopy detected exclusively the presence of iron (III) ions with an octahedral environment in the amorphous phase as well as in 0953-8984/95/230299+07$19.50 c © 1995 IOP Publishing Ltd L299 L300 Letter to the Editor nanocrystals. As far as the UV–VIS data are concerned, a fairly resolved structure in the 2.5–6.0 eV spectral region was obtained for films heated above 500 ◦C. In the present letter we extend the analysis to UV–VIS spectra for Fe2O3 coatings heated from 200 ◦C to 1000 ◦C. Moreover, a detailed assignment of absorption bands for samples heated above 500 ◦C [9] is reported. The theoretical analysis of the experimental data is based on calculations carried out within the discrete variational (DV) Xα approach [10] through the use of the cluster embedding procedure of Ellis et al [10], which, incidentally, has been widely applied in the last decade to study the electronic structure of metal oxides and of defect centres in these materials [11]. The DV Xα procedure [10] has been used to determine the spin-polarized wave functions and the eigenvalues of a cluster. The rest of the solid has been mimicked by providing an electrostatic crystal field and charge field in which the cluster is embedded (see the article by Ellis et al [10]). This is done by generating a microcrystal surrounding the cluster and placing the atoms at specified lattice positions. This approach has proved to be very appropriate to investigate systems where the conventional band structure formalism turns out to be intractable or computationally expensive. More details about the computational procedure are reported by Bertoncello et al [11]. Numerical atomic orbitals (AOs) generated by Hartree–Fock–Slater calculations on free Fe3+ and O2− ions were used as basis functions. An extended basis set was used for both atoms (1s–4d for Fe and 1s–3p for O). Spherical wells (2 Ryd deep) having internal and external radii of 4.0 and 6.0 au, respectively, were added to the atomic potentials. The crystal structure of haematite, α-Fe2O3, is typified by that of corundum, rather common in sesquioxides (α-Al2O3, Cr2O3, Ti2O3, α-Fe2O3). The hexagonal unit cell, containing 12 Fe cations and 18 O anions is shown in figure 1, while in figure 2 the rather small cluster (Fe2O9) we have adopted to carry out our calculations is displayed (see below). Geometrical parameters relative to the cluster employed have been taken from [12], where the crystal structure of hexagonal Fe2O3 is reported. The Fe2O3 precursor solution was prepared by dissolving Fe(OCH2CH3)3 in dehydrated ethanol. Iron (III) ethoxide was synthesized in our laboratory according to the published procedure [13]. The oxide concentration in the solution was 20 g l−1. Films were obtained by dipping spectrograde silica slides in the precursor solution with a withdrawal speed of 12 cm min−1. Depositions were carried out at room temperature and at a relative humidity of 60%. Heat treatments were performed in air by using a programmable furnace (Heraeus Thermicon P) from 200 ◦C to 1000 ◦C, holding the samples for 1 h at each temperature. Films 1000 (± 100) Å thick, as measured by a Tencor Alpha Step profilometer, were obtained. The UV–VIS spectra were finally recorded using a double-beam CARY5E spectrophotometer with a spectral bandwidth of 1 nm. The contribution due to the silica substrate was subtracted. In a series of papers dealing with the electronic structure of sapphire (with both bulk and surface states taken into account) Ellis and coworkers [11] have pointed out that only for quite large and compact clusters, containing more than 30 embedded atoms, does the density of states (DOS) not show significant variations when increasing the cluster size. With this in mind, our first numerical experiments were carried out by running spin-polarized DV Xα calculations on an embedded 33-atom cluster of symmetry C3v containing 15 Fe atoms. As usual, when carrying out molecular cluster calculations, the first problem to be solved is the choice of the correct number of electrons to be used to fill the DV Xα self-consistent cluster energy levels. In principle, any number of electrons between the neutral cluster and the ionic extreme would be correct [14]. In this regard, it is worthwhile to mention that in a rather ionic material such as ZnO the use of the ionic extreme provided very good results (see the Letter to the Editor L301 Figure 1. A schematic representation of the hexagonal unit cell of haematite. The dark thick lines correspond to the short Fe– O bonds (1.97 Å) while the thin ones refer to the long Fe–O (2.12 Å) bonds. Figure 2. A schematic representation of the Fe2O9 cluster. In the adopted framework the z axis is coincident with the Fe–Fe internuclear