Unoccupied states of individual silver clusters and chains on Ag(111)

Size-selected silver clusters on Ag(111) were fabricated with the tip of a scanning tunneling microscope. Unoccupied electron resonances give rise to image contrast and spectral features which shift toward the Fermi level with increasing cluster size. Linear assemblies exhibit higher resonance energies than equally sized compact assemblies. Density functional calculations reproduce the observed energies within $0.6\mathrm{eV}$ and enable an assignment of the resonances to hybridized atomic $5s$ and $5p_z$ orbitals with silver substrate states.

Figure 1

(Color online) STM images of silver monomer, dimer, trimer, tetramer, and pentamer (from left to right) together with sketches of the proposed atomic arrangements (dark and bright circles depict substrate atoms and adsorbed atoms, respectively). Sample voltage and tunneling current were $V=100\mathrm{mV}$ and $I=0.1\mathrm{nA}$. Image sizes: $2.1\times 2.1{\mathrm{nm}}^2$ for ${\mathrm{Ag}}_1,\dots ,{\mathrm{Ag}}_5$ and $3\times 3{\mathrm{nm}}^2$ for the linear tetramer and pentamer.

Figure 2

Normalized spectra of $dI∕dV$ acquired on clean Ag(111), monomers $\left({\mathrm{Ag}}_1\right)$, dimers $\left({\mathrm{Ag}}_2\right)$, trimers $\left({\mathrm{Ag}}_3\right)$, tetramers $\left({\mathrm{Ag}}_4\right)$, and pentamers $\left({\mathrm{Ag}}_5\right)$. A compact silver assembly $\left({\mathrm{Ag}}_n\right)$ with probably $n\approx 10$ was also analyzed. The tunneling gap for the spectra was set at $1\mathrm{nA}$ and $3.5\mathrm{V}$ (${\mathrm{Ag}}_1$ and ${\mathrm{Ag}}_2$), $3.0\mathrm{V}$ $\left({\mathrm{Ag}}_3\right)$, and $2.5\mathrm{V}$ (${\mathrm{Ag}}_4$, ${\mathrm{Ag}}_5$, and ${\mathrm{Ag}}_n$). Spectra of ${\mathrm{Ag}}_n$ $(n⩾1)$ are vertically offset for clarity. The dashed lines indicate the respective zero of the spectra.

Figure 3

(Color online) Contour plots of the absolute square of the Kohn-Sham wave function at $\overline{\Gamma }$ for (a) the silver monomer and (b) the silver chain. The corresponding Kohn-Sham eigenenergies relative to the Fermi level are $2.66\mathrm{eV}$ for the Ag monomer and $1.37\mathrm{eV}$ for the Ag chain.

Figure 4

Experimentally determined and calculated energies of unoccupied resonances as a function of cluster size. Resonance energies for compact (triangles) and linear (circles) assemblies are presented. Error margins for experimental energies $(\approx \pm 0.05\mathrm{eV})$ are the standard deviation resulting from a statistical analysis of spectra of a variety of clusters. Theoretical values calculated within a tight-binding model described in the text (open circles and triangles) are compared to ab initio Kohn-Sham eigenenergies (filled circles). The dashed line denotes the lower band edge of the dispersion of the chain states as obtained from density functional calculations. For each geometry, the lowest tight-binding eigenenergy is given. The island configurations refer to those displayed in Fig. 1. The compact islands enfold the trimer, the tetramer, and the pentamer.

Figure 5

(Color online) $dI∕dV$ spectra acquired at indicated (1,2,…,8) positions of a linear pentamer. Inset: STM image of linear pentamer showing the positions at which spectra were taken. The tunneling gap was set at $1\mathrm{nA}$ and $3.5\mathrm{V}$.

Figure 6

Normalized spectrum of $dI∕dV$ at the center of an $\approx 45\mathrm{nm}$ long and monatomically wide silver chain. The tunneling gap was set at $0.6\mathrm{nA}$ and $3\mathrm{V}$.

Figure 7

(Color online) (a) Cross-sectional profiles in a map of $dI∕dV$ taken at the indicated voltages along the middle axis of the chain showing the increase of the signal at the end of the chain at a lateral displacement of $\approx 1.5\mathrm{nm}$. The profiles acquired at voltages $⩾1.6\mathrm{V}$ are vertically offset for clarity. (b) Apparent height of the chain as a function of the applied voltage. (c) Like (b) for the full width at half maximum of the chain. Dashed lines in (b) and (c) indicate the chain resonance energy. Apparent heights and widths were taken close to the middle of the chain.

Figure 8

(Color online) Calculated LDOS for a silver monomer (bottom), a silver dimer (middle), and an infinitely long silver chain (top) on Ag(111). Resonance energies inferred from these calculations are $2.3\mathrm{eV}$, $1.9\mathrm{eV}$, and $1.5–1.6\mathrm{eV}$, respectively. The LDOS has been computed atop a silver adatom in the case of the monomer and the chain, and atop the center of the silver dimer. The dimer and chain LDOS were shifted vertically, with dashed lines indicating the respective zero LDOS.