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ELECTRONIC STRUCTURE OF FeSi

The full set of high-energy spectroscopy measurements including X-ray photoelectron valence band spectra and soft X-ray emission valence band spectra of both components of FeSi (Fe K_beta_5, Fe L_alpha, Si K_beta_1,3 and Si L_2,3) are performed and compared with the results of ab-initio band structure calculations using the linearized muffin-tin orbital method and linearized augmented plane wave method.


I. INTRODUCTION
FeSi is a non-magnetic [1], narrow-gap semiconductor [2,3] at low temperatures. Its magnetic susceptibility χ(T ) increases with temperature and passes through a maximum at T ∼ 500 K [2]. FeSi becomes metallic above 300 K [3,4]. The substitution of Co for Fe (about 10% Co) yields a magnet with a helical spin order [5]. Local density functional [6] band structure calculations [7,8,9] give the correct value of the semiconducting gap (about 0.1 eV), but can not explain the large magnitude of χ(T ). According to infrared and optical measurements [10], the gap of 50 meV is gradually filled with increasing temperature, with new spectral weight which can not be explained within the conventional band structure picture. In connection with a temperature-induced local moment, a model based on unified spin-fluctuation theory was proposed in Ref. [11] which explains χ(T ) using a model density of states (DOS).
In spite of the large number of publications devoted to measurements of X-ray photoelectron spectra (XPS) and ultraviolet photoelectron spectra (UPS) of FeSi [12,13,14,15,16,17], most measurements were performed using polycrystalline samples which do not allow precise measurements on clean surfaces free of contamination. In this paper, we present a full set of precise spectral measurements, data, including XPS of the valence band and X-ray emission valence spectra for both components of FeSi, which were obtained on the same single crystal, and providing experimental information about the distribution of total and partial DOS in the valence band.
The already published information on the calculated electronic structure of FeSi presented in Ref. [7,8,9] reveals only total DOS and Fe 3d, Si 3s partial DOS distributions in Ref. [8], and Fe 3d, Si 3p DOS for the CsCl-type structure (which is rather different from that known for the bulk FeSi [1]) in Ref. [9]. Because of this we performed a new set of band structure calculations of FeSi by two independent methods -linearized muffin-tin orbitals (LMTO) and linearized augmented plane wave (LAPW) -which give more detailed information about the total and the Fe 3d, Fe 4p, Si 3s, Si 3d and Si 3p partial DOS distributions.

II. EXPERIMENTAL
The Fe L α (2p-3d4s transition) X-ray emission spectrum was measured on the RSM-500 type X-ray vacuum spectrometer with a diffraction grating (N = 600 lines/mm and R = 6 m) and electron excitation. The spectra were recorded in the second order of reflection by a secondary electron multiplier with a CsI photocathode. The energy resolution was about 0.35-0.40 eV. The X-ray tube was operated at V = 4.6 keV, I = 0.4 mA.
The Si K β 1,3 (1s-3p transition) X-ray emission spectrum was measured using a fluorescent Johan-type vacuum spectrometer with a position-sensitive detector [18]. The Pd L-X-ray radiation from a special sealed X-ray tube was used for the excitation of the fluorescent The X-ray tube was operated at V = 25 keV, I = 50 mA.
The XPS valence band spectra of FeSi were measured using a Perkin-Elmer ESCA spectrometer (PHI 5600 ci, monochromatized Al K α radiation). The FeSi single crystal was cleaved in high vacuum prior to the XPS measurements. The XPS spectra were calibrated based on the Au 4f -spectra of Au metal (E b =84.0 eV). X-ray emission spectra have been brought to the scale of binding energies with respect to the Fermi level using the binding energies of the relevant initial (core level) states of the X-ray transitions as measured by the XPS technique. Corresponding binding energies are The values of E(Fe K α 1 ) = 6403.86 eV and E(Si K α 1 ) = 1740.1 eV were taken for comparison of Fe L α and Fe K β 5 , Si L 2,3 and Si K β 1,3 X-ray emission spectra of FeSi.
The measured XPS and X-ray emission spectra are shown in Fig. 1.

III. DETAILS OF CALCULATION
Electronic structure calculations have been performed for the cubic FeSi structure (8 atoms/cell, space group P 2 1 3) as determined in Ref. [1] and discussed in detail in Ref. [7].
We have used the cubic lattice constant of a = 4.493Å, with Fe atoms occupying the In the calculations using the tight-binding LMTO method [21], we used space-filling atomic spheres of equal size on Fe and Si sites (R = 1.394Å) and no empty spheres were introduced. The exchange-correlation potential as proposed by von Barth and Hedin [22] was used. DOS calculated by the tetrahedron method over 470 k-points in the irreducible part of the Brillouin zone are shown in Fig. 1, and compared with the experimental spectra. Our calculated electron bands are very close to those obtained by Fu et al. [8] using the augmented spherical wave method, and our calculated DOS agree well with those of Ref. [8,23]. We found a direct gap of 0.14 eV at the X point of the Brillouin zone and an indirect gap of 0.05-0.08 eV, in agreement with the resistivity measurement data reported in Ref. [8].
Some small deviations from the bands calculated in Ref. [7] using the LAPW method without any shape approximation imposed on the potential seem to have quite negligible effect on the densities of states, in the present context of making a comparison with Xray spectra using the LMTO method. We also carried out an independent LAPW [24,25] calculation, in which we used the local density approximation [6] form for exchange and correlation given by Ceperley and Alder [26], as parameterized by Perdew and Zunger [27].
In the expansion of the charge density and potential inside the muffin-tin spheres (R Fe = R Si = 1.111Å), lattice harmonics up to angular momentum of l = 8 have been used, while the interstitial region was described by a plane wave expansion. Core orbitals were treated self-consistently, retaining, however, only the spherically-symmetric part of their density. Scalar relativistic effects (neglecting spin-orbit coupling) were included for the valence states, and full relativistic effects were included for the core states. A large basis set consisting of both real-space orbitals (inside the muffin-tin regions) and plane waves was There seems to be generally good agreement between the several LDA-based band structure calculation schemes in reproducing the bands, total densities of states, and bandwidths in FeSi. Below, we concentrate on discussing particular features of partial densities of states of the constituents as revealed in the X-ray emission spectra and the present calculations.

IV. EXPERIMENTAL RESULTS AND DISCUSSION
The X-ray photoelectron valence band spectrum and X-ray emission valence band spectra of Fe (Fe L α , Fe K β 5 ) and Si (Si L 2,3 , Si K β 1,3 ) are presented in Fig. 1. As is known, the XPS valence band spectrum gives an information about the total DOS distribution (accurate up to the weight function depending on the atomic photoemission cross-sections, see Ref. [28]), whereas the Fe L α , Fe K β 5 , Si L 2,3 , Si K β 1,3 X-ray emission spectra (in accordance to dipole selection rules) -give information about partial Fe 3d4s, Fe 4p, Si 3s3d and Si 3p densities of states, respectively. These spectra are compared in Fig. 1 with the results of the LMTO band structure calculations by aligning the calculated and experimental positions of the Fermi level. We note that the experimental XPS valence band spectrum reproduces the total 5 DOS distribution of FeSi quite well. Especially, it is very important that in our experiments we have found the splitting of the main peak of XPS spectrum in the range 0-2 eV which corresponds to the Fe 3d band splitting. This distinct splitting was not found before in XPS [12] and UPS [13,14,16,17] measurements on FeSi, and its absence was attributed in Ref. [17] to a hole lifetime broadening which increases with binding energies. The similar splitting of the XPS valence band spectrum of FeSi was found in Ref. [15] only in the measurements done at low temperatures (T =120 K). In our opinion, this discrepancy between fine structure in the present and previous XPS (UPS) valence band spectra is due to the high quality of the FeSi single crystal which was used for the present measurements. The low-energy Si 3p and Si 3s subbands are reflected in the XPS valence band spectrum as low-intensity (due to low values of respective photoinization cross-sections [28]) features located at binding energies of approximately 4.5 and 9 eV, respectively.
The experimental Fe L α X-ray emission spectrum reproduces fairly well the position of the center of gravity of calculated Fe 3d DOS distribution in the valence band of FeSi, but not the splitting of the Fe 3d band. This is due to the large total distortion of the Fe L α X-ray emission spectrum which includes the instrumental distortion (about 0.4 eV) and the width of the inner (core) Fe 2p level (about 0.8-1.0 eV) which is determined by the lifetime of the core-level vacancy under an X-ray transition.
The experimental Fe K β 5 spectrum shows two maxima located at binding energies of approximately 3.5 and 9.0 eV that is in accordance with the theoretical distribution of the Fe 4p partial DOS. It is also seen from both the theoretical and experimental spectra that Fe 4p states are hybridized mostly with Si 3p and Si 3d states.
The experimental Si L 2,3 X-ray emission spectra corresponds to the 2p-3s3d transition.
Usually it is considered that the Si 3d states do not take part in the chemical bonding in 3d transition metal silicides. As was emphasized in Ref. [19], the high-energy subband of SiL 2,3 X-ray emission spectra of transition metal silicides FeSi, MnSi and NiSi, as well as that of disilicides FeSi 2 , MnSi 2 and NiSi 2 , cannot be explained without an assumption that Si 3d states contribute to the chemical bonding. Subsequently, the same conclusion was 6 drawn for Pt silicides (Pt 2 Si, PtSi) in Ref. [29] based on an analysis of the Si L 2,3 X-ray emission spectra of these compounds. This conclusion is again confirmed now for FeSi by two independent sets of band structure calculations (see Figs. 1 and 2). One can see from Fig. 1 that the Si 3s DOS is concentrated in the range of binding energies about 6-13 eV where the most intensive low-energy subband of the Si L 2,3 X-ray emission spectrum is located.
The center of gravity of the Si 3d states distribution corresponds to a binding energy about 2 eV where the high-energy maximum of the Si L 2,3 spectrum is situated. The Si 3d states are strongly hybridized with Fe3d states, and the same splitting of the Si 3d band (about 2 eV) as that in the Fe 3d subband is observed in the band structure calculations.
The energy position and fine structure of the Si K β 1,3 X-ray emission spectrum is in a good accord with the Si3 p partial DOS distribution (see Fig. 1).

V. CONCLUSION
The results of high-energy spectroscopy measurements of FeSi single crystals, including the XPS valence band spectrum and the X-ray emission valence band spectra of both constituents, are presented. They are compared with two independent ab initio band structure calculations of FeSi, performed using the LMTO and LAPW methods, and good agreement between the experimental and theoretical spectra is found.