Direct mapping of the lateral force gradient on $\text{Si}\left(111\right)\text{−}7\times 7$

Lateral force gradient of down to 0.01 N/m on $\text{Si}\left(111\right)\text{−}7\times 7$ was directly detected by dynamic lateral-force microscopy with an amplitude of 81 pm. Positive and negative torsional resonance frequency shifts of a silicon cantilever caused by the attractive interaction inward and outward tip ditherings were detected on adatom and nonadatom sites, respectively. The lateral force of down to subpiconewton was measurable with direct lateral-force spectroscopy. The converted lateral force predicts a possibility of the stick-slip motion in the noncontact region. The theoretical calculations were in good qualitative agreement with the experiments.

Figure 1

(Color online) (a) Schematic drawing of $\text{Si}\left(111\right)\text{−}7\times 7$. Simulated (b) potential map $U\left(X,Z\right)$, (c) lateral-force map $F_X\left(X,Z\right)$, and (d) lateral-force-gradient map $F_X^{\prime }\left(X,Z\right)$ in the $X$ direction.

Figure 2

(Color online) (a) Experimentally obtained frequency shift map and (b) STM topographic map with a fast scan direction of $X$. (c) Experimentally obtained frequency-shift map and (d) STM topographic map with a fast scan direction of $Y$. (e) Simulated-frequency map and (f) STM topographic map. Arrow shows the direction of the fast scan. Imaging and simulation parameters; $f_{\text{TR}}=2.216275\text{MHz}$, $Q_{\text{TR}}=110810$, $A_{\text{dith}}=81\text{pm}$, ${\overline{I}}_t=0.6\text{nA}$, and $V_{\text{bias}}=1.8\text{V}$.

Figure 3

(Color online) (a) ${\overline{F}}_Y^{\prime }\left(X,Y\right)$ map. Solid lines show the positions with ${\overline{F}}_Y^{\prime }=0\text{N}/\text{m}$ for ${\overline{I}}_t=1.0\text{nA}$. (b) ${\overline{F}}_Y^{\prime }\left(X,Z\right)$ map along $A\text{−}{A}^{\prime }$. ${\overline{I}}_t=0.1\sim 1.0\text{nA}$ and $V_{\text{bias}}=1.8\text{V}$. CoH is the corner hole and CoA and CeA are the corner and center adatoms, respectively.

Figure 4

(Color online) (a) Line profile of $\Delta f_{\text{TR}}$ along $B\text{−}{B}^{\prime }$ in Fig. 3a. ${\overline{I}}_t=0.25\text{nA}$. (b) Converted lateral-force curve. (c) Simulated lateral force detected with $k_{\text{TR}}$ of 0.003 and 0.03 N/m in static LFM.