Tip size effect on the appearance of a STM image for complex surfaces: Theory versus experiment for $\mathrm{Si}\left(111\right)\text{−}(7\times 7)$

Scanning tunneling microscopy experiment and first-principles total energy calculation are combined to determine STM images for $\mathrm{Si}\left(111\right)\text{−}7\times 7$ to resolve the long-time discrepancy between theory and experiment. Our experiment resolves clearly and simultaneously the rest and adatom spots, in good agreement with theory, with the rest atom spots almost as bright as those of the central adatoms in the unfaulted-half of the unit cells. Theoretical study suggests that a geometric hindrance effect due to finite tip size could be responsible for the past experimental inability to observe the rest atoms.

Figure 1

(Color online) (a), (b) Calculated STM images for $\mathrm{Si}\left(111\right)\text{−}7\times 7$ with bias $\text{voltage}=-0.57$ and $-1.5\mathrm{V}$, respectively. The red peaks are about $2\mathrm{\AA }$ above the dark blue borderlines. The dark greys are areas without spatial resolution. (c), (d) The experimental STM images with bias $\text{voltage}=-0.57$ and $-1.5\mathrm{V}$, and tunneling $\text{current}=0.3$ and $0.41\mathrm{nA}$, respectively. The brighter triangles are the faulted halves of the $7\times 7$ unit cells.

Figure 2

(Color online) The calculated atomic structures for the $\mathrm{Si}\left(111\right)\text{−}(7\times 7)$ surface with the faulted half on the left: (a) top and (b) side views. The (large, light) red balls are the Si adatoms whereas the (small, dark) blue balls are the Si rest atoms.

Figure 3

Line-scans along the diagonal of the $7\times 7$ unit cell for bias $\text{voltage}=-1.5\mathrm{V}$: (a), (b) and (c) are the calculated height profiles with a tip apex radius $r=0.0$, 7.0, and $24.0\mathrm{\AA }$, respectively, whereas (d) is the experimental profile. Inset shows schematically an STM tip with an adsorbed atomic cluster beneath the apex.