Relationship between strain and the surface electronic structure of Cu(111) films on Ru(0001): Theory and experiment

The relationship between strain and surface electronic structure of Cu(111) films grown on Ru(0001) is studied by a combination of tunneling spectroscopy and ab initio theoretical calculations. Experimentally, the relaxation of the 5.5% in-plane lattice mismatch between Ru(0001) and Cu(111) changes layer-by-layer the lateral lattice parameter of the Cu film, while the surface state, that is above the Fermi level for the pseudomorphic monolayer of Cu, shifts down in energy with increasing thickness until it becomes the occupied surface state of Cu(111). The effects due to strain in the Cu films are distinguished from those due to the proximity to the Ru substrate by detailed comparisons with theoretically expanded Cu(111) and $\mathrm{Cu}∕\mathrm{Ru}\left(0001\right)$ surfaces. Our ab initio calculations indicate that the observed energy shift must be essentially assigned to the decreasing tensile stress of the deposited film.

Figure 1

(Color online) Left panel: Scanning tunneling spectroscopy (STS) spectrum of Cu(111) recorded at $300\mathrm{K}$. Right panel: Partial density of states (DOS) of $s$ and $p_z$ orbitals at the surface of 5 (broken line) and 15 (continuous line) layers thick slabs of Cu(111). The DOS was integrated in a region around the center of the Brillouin zone, $1∕4$ of its maximum size to compare with the experiments.

Figure 2

(Color online) Left panel: $10\mathrm{nm}\times 8.3\mathrm{nm}$ STM image of Ru(0001); Right panel: Tunneling spectrum recorded at $300\mathrm{K}$ on the clean Ru(0001) surface. The tunneling gap was stabilized at $0.4\mathrm{V}$ and $0.3\mathrm{nA}$.

Figure 3

(Color online) The upper panel shows a $160\mathrm{nm}\times 127\mathrm{nm}$ STM image of a 2 ML Cu film grown on Ru(0001). The image has been taken with a gap resistance of $2\mathrm{M}\Omega$. The brighter parts of the image corresponds to subsurface Ar bubbles (see text). The lower panel shows a $10\mathrm{nm}\times 8\mathrm{nm}$ STM image with the atomic details of the reconstruction of 2 ML of Cu on Ru(0001).

Figure 4

(Color online) The upper panel shows a $200\mathrm{nm}\times 200\mathrm{nm}$ STM image of a Cu film grown on Ru(0001) with local thicknesses of 1 and 2 MLs. The regions 1 ML-thick are seen flat. The areas 2 ML-thick are easily recognized by the characteristic strain-relief reconstruction pattern. A fraction of the derivative of the image has been added to increase the contrast in the presence of steps. The lower panel shows differential conductance versus voltage spectra recorded on the 1 and 2 ML patches of the upper panel. The spectra have been shifted vertically for clarity.

Figure 5

(Color online) Calculated partial LDOS projected on $d$ orbitals (left panels) or on $s$ and $p_z$ (right panels) for (a) 15 ML of fcc Cu(111). The continuous line corresponds to bulk distances $a_{xy}=2.55\mathrm{\AA }$, $a_z=2.08\mathrm{\AA }$, where $a_{xy}$ is the nearest neighbor distance in the surface plane and $a_z$ is the distance between layers. The broken line corresponds to a uniformly expanded lattice $a_{xy}=2.70\mathrm{\AA }$, $a_z=2.20\mathrm{\AA }$, while the dashed-dotted line shows the results for an expanded lattice with just the surface contracted to $a_z=1.94\mathrm{\AA }$, and (b) 1 ML of Cu on 13 ML of Ru(0001). The lateral distances are $a_{xy}=2.70\mathrm{\AA }$, and the $\mathrm{Ru}\mathrm{Ru}$ distances, $a_z=2.14\mathrm{\AA }$, while the $\mathrm{Cu}\mathrm{Ru}$ distance at the interface is $2.10\mathrm{\AA }$ (continuous line) and $1.94\mathrm{\AA }$ (dashed-dotted line), respectively.

Figure 6

(Color online) Calculated evolution of the partial LDOS at the surface projected on $d$ orbitals (left panels) and on $s$ and $p_z$ (right panels) for increasing Cu thickness in $\mathrm{Cu}∕\mathrm{Ru}\left(0001\right)$. The solid lines represent the results obtained by taking the experimental interatomic distances for each coverage (see Table ), while the dashed lines correspond to the results for a Cu film that keeps strictly pseudomorphism with the Ru substrate.

Figure 7

(Color online) The left panel shows the tunneling conductance vs. sample voltage measurements on clean Ru(0001) (continuous line) and (from bottom to top) 1, 2, and 4 ML-thick Cu films grown on Ru(0001). The $I∕V$ curves were measured at constant height above the Cu surfaces. The initial tunneling conditions were stabilized at a sample voltage of $0.1\mathrm{V}$ and a tunnel current of $0.3\mathrm{nA}$. The right panel shows the calculated DOS of $s$ and $p_z$ character at the surface atoms for clean Ru(0001), 1 and 2 ML-thick Cu films and Cu(111). All the spectra have been shifted in the vertical direction for clarity.

Figure 8

(Color online) Upper panel: $23.2\mathrm{nm}\times 14\mathrm{nm}$ STM image of the pseudomorphic monolayer of Cu on Ru(0001) recorded at $300\mathrm{K}$. Lower panel: STS spectra taken above the Ar bubbles (noted as A) and on the flat terrace (noted with B).