Surface structure and electronic states of epitaxial $\beta -{\mathrm{FeSi}}_2$(100)/Si(001) thin films: Combined quantitative LEED, ab initio DFT, and STM study

The surface structure of epitaxial $\beta \text{−}{\mathrm{FeSi}}_2$(100) thin film grown on Si(001) was analyzed using the quantitative low-energy electron diffraction intensity-voltage (LEED I-V) method, ab initio density functional theory (DFT) calculations, and scanning tunneling microscopy (STM). LEED patterns measured on the $\beta \text{−}{\mathrm{FeSi}}_2$(100) surface reveal two domains of a $p(2\times 2)$ reconstruction with $p2gg$ diffraction symmetry. The iron-silicide film truncation and atomic surface structure were determined by LEED I-V method: The smallest Pendry's reliability factor $R_P=0.22\pm 0.02$ was achieved for the bare $\beta \text{−}{\mathrm{FeSi}}_2$ film truncated by an Si layer, whereas Si and Fe ad-atom structures were excluded. Significant atomic relaxations within the topmost surface layers were revealed by the LEED I-V method and confirmed by DFT. The simulated STM patterns from the best-fit model agree well with the measured STM images on the $\beta \text{−}{\mathrm{FeSi}}_2\left(100\right)/\mathrm{Si}\left(001\right)\text{−}p(2\times 2)$ surface: Four Si atoms on a surface form one bright protrusion on STM patterns. Electronic band structure analysis of the bulk and epitaxial $\beta \text{−}{\mathrm{FeSi}}_2$(100) was carried out. A bare truncated epitaxial film was found to be metallic. Surface electronic states were identified by a partial $k$-resolved atomic-orbital based local density-of-state analysis.

Figure 1

LEED patterns measured on the epitaxial $\beta \text{−}{\mathrm{FeSi}}_2$(100)/Si(001)-$p(2\times 2)$ surface at electron beam energies of (a) $E=35$ eV and (b) $E=65$ eV. A Si(001)-$(1\times 1)$ unit cell is marked with a dashed square. $(h/2,0)$ and $(0,k/2)$ reflections, where $h$ and $k$ are odd integers, are forbidden due to $p2gg$ symmetry. Equivalent diffraction beam intensities are shown schematically using circles of the same color in (c). Two ${90}^{\circ }$-rotated equivalent domains of iron silicide were confirmed on a surface. (d) Measured and (e) simulated filled state ($U=-1.5$ V) STM images of the $\beta \text{−}{\mathrm{FeSi}}_2$ surface. Si(001) substrate with $(2\times 1)$ protrusions is seen in (d). A magnified region of the $\beta \text{−}{\mathrm{FeSi}}_2$ film is shown; a $p(2\times 2)$ unit cell of 7.8 $\AA$ $\times$ 7.8 $\AA$ area is marked by a white square. Each bright protrusion is formed by four Si atoms on a surface [see relaxed layer 1 in Fig. 2]

Figure 2

(a) Top and side views of bulk $\beta \text{−}{\mathrm{FeSi}}_2$ unit cells. Fe and Si atoms are marked with red and green spheres, respectively. Layers 6–10 are shifted with respect to layers 1–5 by $\left|\mathbf{b}\right|/2$ distance along the [010] direction. Layer-resolved structures of bulk unit cells are shown in (b). The adatom models consist of Si or Fe atoms on ${\mathrm{H}}_1$, ${\mathrm{H}}_2$ sites. The $p2gg$ symmetry is preserved for bare truncated and adatom ${\mathrm{H}}_1$, ${\mathrm{H}}_2$ structure models. The ${\mathrm{H}}_3$ model with vacancies (v) has $p2$ symmetry. Twofold rotation axis and glide planes are indicated (layer 5). The glide operations translate atoms along the glide planes by $\left|\mathbf{b}\right|/2$ or $\left|\mathbf{c}\right|/2$, and mirror them against these planes. The topmost relaxed layer of the best-fit ${\mathrm{L}}_1$ model is shown on the right-hand side of layer 1. The coordinates of the relaxed structure are presented in Table 2.

Figure 3

Comparison of experimental (black) and theoretical (red dashed) LEED I-V curves of the best-fit Si-bare model of the $\beta \text{−}{\mathrm{FeSi}}_2$(100)/Si(001)-$p(2\times 2)$ surface. Pendry's reliability factor $R_P=0.22\pm 0.02$ was achieved for the Si-bare structure with $p2gg$ symmetry. Symmetrically equivalent reflections were averaged according to a scheme presented in Fig. 1.

Figure 4

Electronic band structures of $\beta \text{−}{\mathrm{FeSi}}_2$. (a) Schematic Brillouin zone of the bulk $\beta \text{−}{\mathrm{FeSi}}_2$. Surface Brillouin zone of the $\beta \text{−}{\mathrm{FeSi}}_2-(1\times 1)$ reconstruction is shown by blue rectangle. (b) Computed bulk band structure. There is indirect band gap between $Y-0.6\Lambda$ points. (c) Surface band structure. Grey shaded areas represent projected bulk bands. Black dots correspond to the electronic states of the ${\mathrm{L}}_1$ model. Surface states induced by the topmost Si layer are marked by red stars. Surface states were identified from the $k$-projected atomic-orbital based local density of states in (d). Intensity contrast was modulated according to Eq. (2).