Long-Range Electron Interferences at a Metal Surface Induced by Buried Nanocavities

Apparent $c(2\times 2)$ superstructures within the narrow beams of an interference pattern spreading in the $⟨100⟩$ directions at the surface of Cu(001) are observed by scanning tunneling microscopy. These features are induced by electron scattering from Ar- and Ne-filled subsurface nanocavities. The beams originate from electron anisotropy resulting in focusing of bulk electrons. We developed a model providing a good agreement between simulations and experiments. Particularly, a simple explanation of the angular distribution for the interference pattern and the period in the superstructure is found.

Figure 1

XPS spectra of the Cu sample after implantation of Ar without annealing (1) and annealing at (2) 1000 K, (3) 1050 K, and at (4) 1075 K. The positions of Ar $2p_{1/2}$ and $2p_{3/2}$ maxima of binding energy are marked by the vertical bars. For better visibility the curves 2 and 3 are shifted down by 30 and 60 counts, respectively. The corresponding structure is shown in the inset.

Figure 2

Two couples of differential conductance maps of the same Cu surfaces after implantation of Ar (a),(b), $60\times 60{\mathrm{nm}}^2$, or Ne (c),(d), $15\times 15{\mathrm{nm}}^2$, and annealing at 1050 K. The bias voltages $V_b$ of (a) 400 mV, (b) 600 mV, (c) 500 mV, and (d) 800 mV were applied at the STS scanning with tunnel current 5 nA stabilized by the closed feedback loop.

Figure 3

(a),(b) and (c) STM images of Cu surface above the nanocavities with atomic resolution: (a) typical interference pattern above a single Ar-filled nanocavity, $15\times 15{\mathrm{nm}}^2$, $V_b=46\mathrm{mV}$, $R_t=2\mathrm{M}\Omega$; (b) several Ar-filled nanocavities induce overlapping beams of interference fringes, $18\times 18{\mathrm{nm}}^2$, $V_b=7\mathrm{mV}$, $R_t=0.05\mathrm{M}\Omega$; (c) a $c(2\times 2)$ superstructure within the interference beam near a Ne-filled nanocavity, $12\times 12{\mathrm{nm}}^2$, $V_b=7\mathrm{mV}$, $R_t=0.1\mathrm{M}\Omega$; (d) schematic drawing similar to (c) (scale not corresponding) illustrating the shift of the rows within the superstructure.

Figure 4

Examples of nonequivalent beams of interference: (a) one beam, (b) two aligned beams, (c) two adjacent beams in the left corners. In (b) the extra beam on top of the main structure belongs to a neighboring nanocavity located out of the scanned field. In (c) very weak beams are still visible in the right corners. The field of view is $15\times 15{\mathrm{nm}}^2$. Scanning parameters (a) $V_b=-10\mathrm{mV}$, $R_t=0.1\mathrm{M}\Omega$; (b) $V_b=9\mathrm{mV}$, $R_t=0.4\mathrm{M}\Omega$; (c) $V_b=10\mathrm{mV}$, $R_t=0.4\mathrm{M}\Omega$.

Figure 5

(a) Simulated conductance map of Cu(001) above a nanocavity showing the $c(2\times 2)$ structure within the beams induced by the nanocavity buried 5.5 nm below the surface, and with the size of the $\{001\}$ facets of $2.2\times 2.2{\mathrm{nm}}^2$, and the $\{110\}$ facets of $3.3\times 0.7{\mathrm{nm}}^2$; (b) schema of the formation of the interference pattern at the Cu(001) surface (green line) due to the wave concentrated in the $⟨101⟩$ directions; (c) origin of the $c(2\times 2)$ superstructure and the shift of rows. The grid corresponds to the crystalline lattice of Cu while the apparent $c(2\times 2)$ superstructure is shown by spots. The arrows in (a),(c) and guiding lines are to indicate the shifted rows of the superstructure.