Structure and one-dimensional metallicity of rare-earth silicide nanowires on Si(001)

Rare-earth deposition on Si(001) substrates and thermal treatment lead to the formation of metastable silicide nanowires with extremely high aspect ratios and quasi-one-dimensional metallicity. In this work, the prototypical erbium silicide nanowires are investigated theoretically by ab initio thermodynamics, considering a multitude of possible nanowire structures. The calculations indicate that the nanowires consist of hexagonal ${\mathrm{ErSi}}_2$ with two possible orientations with respect to the substrate, that they are partially buried into the substrate, and that they are electronically decoupled from the substrate. However, wires of finite width are predicted to be less favorable than planar silicide structures, demonstrating that the wires are metastable and suggesting that their formation is more governed by kinetic effects than by thermodynamics.

Figure 1

(a) STM image of Tb silicide nanowires on Si(001) ($V_{\mathrm{sample}}=-2.5\mathrm{V},I=100\mathrm{pA}$), (b) detailed STM image of one nanowire bundle ($V_{\mathrm{sample}}=-1.5\mathrm{V},I=100\mathrm{pA}$), (c) ARPES measurement along the nanowires with the most pronounced dispersive bands around $\overline{\mathrm{\Gamma }}$ ($k_{\parallel }=0$) and $\overline{\mathrm{J}}$ (edge of nanowire Brillouin zone).

Figure 2

Optimized structures of $5a$ wide and two layers high nanowires buried into the substrate by one layer (a) with the hexagonal $c$ axis perpendicular (labeled R) and (b) parallel to the nanowire direction (labeled H), in cross-sectional view (left) and side view (right). Blue circles indicate Si substrate atoms, light blue circles the Si dimers of the clean Si(001) surface, magenta circles Si atoms in the nanowires, and green circles Er atoms. $A_{\mathrm{W}}$ and $A_{\mathrm{C}}$ indicate the areas of the nanowire and of the clean substrate, respectively. The schematic representation shown in the central part will be used in the following to indicate the discussed structures [28].

Figure 3

Variation of the Landau potential [(a) and (d)] for different burial depths, [(b) and (e)] for different nanowire heights, and [(c) and (f)] for different nanowire widths, [(a)–(c)] for the R and [(d)–(f)] for the H structures. 0–III denote the depths varying from 0 to 3 silicon monolayers, S, D, and T stand for single, double, and triple height, respectively, and 3a–9a and $\infty$ indicate the widths of the nanowire in multiples of silicide unit cells.

Figure 4

Simulated STM-images (sample voltage $V_{\mathrm{sample}}=-1.5$ V, filled states) for slabs modeling the ${\mathrm{ErSi}}_2$ nanowires (a) with R structure and (b) with H structure according to the thermodynamically stable models of $5a$ width.

Figure 5

[(a) and (b)] Band structure (left-hand side) and DOS (right-hand side) for the (a) R and (b) H structures of $5a$ broad nanowires with double height and buried into the substrate by two silicon layers. The intensity of the color in the band structure is proportional to the Er contribution. The gray overlay is the silicon bulk band structure projected onto the surface Brillouin zone. The panels on the right-hand side of (a) and (b) show the density of states (DOS/a.u.) integrated over the whole Brillouin zone and projected onto the Er atoms. The corresponding unfolded band structures are shown in (c) and (d). Panel (e) shows a sketch of the surface Brillouin zone with the relevant high symmetry points. All energies are given with respect to the slab Fermi energy $E_{\mathrm{F}}$.

Figure 6

Electronic states of the (a) $5a$-R and (b) $5a$-H structures [calculated for nanowires of double height and buried into the substrate by two silicon layers] overlaid to the measured ARPES data. See text for details.