Single Atomic Contact Adhesion and Dissipation in Dynamic Force Microscopy

By combining dynamic force microscopy experiments and first-principles calculations, we have studied the adhesion associated with a single atomic contact between a nanoasperity—the tip apex—and a semiconductor surface—the $\mathrm{Ge}(111)\mathrm{\text{−}}c(2\times 8)$. The nanoasperity’s termination has been atomically characterized by extensive comparisons of the measured short-range force at specific sites with the chemical forces calculated using many atomic models that vary in structure, composition, and relative orientation with respect to the surface. This thorough characterization has allowed us to explain the dissipation signal observed in atomic-resolution images and force spectroscopic measurements, as well as to identify a dissipation channel and the associated atomic processes.

Figure 1

(a) Experimental and calculated short-range forces over specific positions of the $\mathrm{Ge}(111)\mathrm{\text{−}}c(2\times 8)$ surface. Tip model that better reproduces the experimental forces. (b) Dissipation signal measured with the forces shown in (a). Simultaneously acquired topographic and dissipation images (pattern A) of the surface; sizes: $(5\times 5){\mathrm{nm}}^2$ and $(3.6\times 2.2){\mathrm{nm}}^2$. Acquisition parameters: $f_0=183663\mathrm{Hz}$, $K=44.3\mathrm{N}/\mathrm{m}$, $A=18.2\mathrm{nm}$, $Q=259500$.

Figure 2

(a) Experimental and calculated short-range forces over specific positions of the $\mathrm{Ge}(111)\mathrm{\text{−}}c(2\times 8)$ surface with a different tip-apex termination than in Fig. 1. Tip model that better reproduces the experimental forces. (b) Dissipation signal measured with the forces shown in (a). Topographic images (pattern B) of the surface; sizes: $(6\times 6){\mathrm{nm}}^2$ and $(3.8\times 2.2){\mathrm{nm}}^2$. Acquisition parameters are exactly the same as the ones indicated in the caption of Fig. 1.

Figure 3

Calculated short-range forces for the tip A and tip B models upon approach and retraction over a Ge adatom.

Figure 4

Calculated potential energy of a Ge adatom as a function of its vertical displacement for several separation distances of the tip A from the surface. The images represent the adatom adsorption structure at the corresponding energy minima for a tip-surface separation of 4.5 Å.