Site Determination and Thermally Assisted Tunneling in Homogenous Nucleation

A combined low-temperature scanning tunneling microscopy and density functional theory study on the binding and diffusion of copper monomers, dimers, and trimers adsorbed on Cu(111) is presented. Whereas atoms in trimers are found in fcc sites only, monomers as well as atoms in dimers can occupy the fcc as well as the metastable hcp site. In fact the dimer fcc-hcp configuration is only 1.3 meV less favorable with respect to the fcc-fcc configuration. This enables a confined intracell dimer motion, which at temperatures below 5 K is dominated by thermally assisted tunneling.

Figure 1

By means of an extended site-mapping technique the adsorption site of $\mathrm{C}\mathrm{u}/\mathrm{C}\mathrm{u}(111)$ was determined to be the fcc site. Individual adatoms were repeatedly repositioned using lateral manipulation at a temperature of 7 and 11 K. One STM image of a series and the corresponding model are shown. In the topmost part of the figure, the positions of these individual adatoms (circles at 7 K, crosses at 11 K) as well as of a dimer and a trimer (arrows) with respect to the row are shown.

Figure 2

(a) At $T=7\mathrm{K}$ Cu dimers appear unstable in STM images, showing that local diffusion takes place during scanning. (b) Long-range interactions with a monomer close by can stabilize the dimer. (c) At a temperature of 5 K, the dimer diffusion is slow enough to trace individual diffusion steps. The white arrows indicate the fast scan direction. The crystal orientation corresponds to the one in Fig. 1.

Figure 3

Arrhenius plot of the dimer ff to fh hopping rate. The hopping rate is determined by direct thermal activation (process A) at temperatures above 6 K and by thermally assisted tunneling to the ground state (process B) below 5 K. The dashed line represents a fit, taking only these two processes into account. At $4.5\le T\le 6\mathrm{K}$ an even better fit (dotted line) is obtained by including also thermally assisted tunneling for all intermediate energies (process C). Scanning at $U=10\mathrm{m}\mathrm{V}$, $I=10\mathrm{p}\mathrm{A}$ excluded tip-induced diffusion.

Figure 4

Illustration of the DFT analysis of the dimer intracell dynamics [13] observed on Cu(111). Solid (dashed) lines illustrate the variation in the fully relaxed dimer-configuration energies calculated using the $4\times 4$ ($2\times 2$) $k$-point sampling.