Probing theSi(001)surface with a Si tip: Anab initiostudy

Abstract

Topographic noncontact atomic force microscopy (NC-AFM) images of the $p(2\ifmmode\times\else\texttimes\fi{}1)$ and $c(4\ifmmode\times\else\texttimes\fi{}2)$ reconstructions of the $\mathrm{Si}(001)$ surface are simulated for the cases of weak and strong tip-surface interactions and various temperatures using ab initio density functional theory. In the simulations the surface is imaged by a sharp silicon tip with a single dangling bond at its apex. At a very close approach to the surface, the tip flips a surface dimer when positioned close to its lower atom. The energy barriers for an individual flipped surface dimer to regain its initial configuration are calculated to be $\ensuremath{\sim}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, implying that the surface should be able to ``heal'' itself at all but extremely low temperatures during one oscillation cycle of the cantilever. Thus, at small enough temperatures, $T\ensuremath{\leqslant}70\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and large frequency shifts, the imaging process is dominated by tip induced dimer flip events resulting in a permanent deformation of the surface and an apparent $p(2\ifmmode\times\else\texttimes\fi{}1)$ symmetric phase to be observed. No dissipation is expected as the tip oscillations are conservative at these conditions. At intermediate temperatures, $70\phantom{\rule{0.3em}{0ex}}\mathrm{K}\ensuremath{\leqslant}T\ensuremath{\leqslant}200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the flipped dimers are able to return to the ground state during each tip oscillation, resulting in continuous healing of the surface and thus large dissipation is expected. At $T\ensuremath{\geqslant}200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ dimers flip back and forth easily resulting in an apparent symmetric $p(2\ifmmode\times\else\texttimes\fi{}1)$ phase and noticeable dissipation. At small frequency shifts the dimers do not flip, still the upper dimer atoms are imaged as bright so that surface reconstruction can easily be determined. The possibility of manipulating the orientation of dimers at low temperatures and large frequency shifts by means of preprogrammed scan directions, is also discussed.