Dithering-amplitude dependence of STM-regulated dynamic lateral force microscopy maps on $\text{Si}\left(111\right)7\times 7$

Model simulation of dynamic lateral force microscopy (DLFM) regulated by scanning tunneling microscopy (STM) has been performed. The simulated STM/DLFM maps on $\text{Si}\left(111\right)7\times 7$ exhibit marked transitions depending on the lateral dithering amplitude, and they can successfully reproduce the experimentally acquired maps for a wide range of operating conditions. This work describes the direct calibration of dithering-amplitude-induced artifacts of STM/DLFM maps on $\text{Si}\left(111\right)7\times 7$ for a small time-averaged tunneling current corresponding to a tip-sample distance larger than $5\text{Å}$, where the atomic relaxation of the tip and the sample is sufficiently small.

Figure 1

(Color online) (a) Algorithm of the simulation method for STM/DLFM. (b) Schematic illustration of the rigid model: half part of the $\text{Si}\left(111\right)7\times 7$ surface and the ${\text{Si}}_4\left[111\right]$ tip. (c) $y\text{−}z$ maps of the total energy $V$, (d) lateral force $F_y$, and (e) lateral force gradient $F_y^{\prime }$ along P-Q. The approximately vertical lines in (d) indicate the positions corresponding to $F_y=0$.

Figure 2

(Color online) (a) Simulated (left) and experimental (right) STM topographies for $A_{\text{dith}}=$ (a) .37, (b) 1.9, (c) 2.5, (d) 2.9, (e) 3.4, (f) $3.8\left(\simeq L/2\right)$, (g) 4.3, (h) 4.9, (i) 6.1, (j) 6.8, and (k) $7.6\left(\simeq L\right)\text{Å}$. Imaging parameters: ${\overline{I}}_t=0.5\text{nA}$ and $V_{\text{bias}}=1.8\text{V}$.

Figure 3

(Color online) Simulated (left) and experimental (right) DLFM images for $A_{\text{dith}}=$ (a) .37, (b) 1.9, (c) 2.5, (d) 2.9, (e) 3.4, (f) $3.8\left(\simeq L/2\right)$, (g) 4.3, (h) 4.9, (i) 6.1, (j) 6.8, and (k) $7.6\left(\simeq L\right)\text{Å}$. Imaging parameters: $f_{\text{TR}}=2.2\text{MHz}$, $Q_{\text{TR}}\simeq 1.1\times {10}^5$, ${\overline{I}}_t=0.5\text{nA}$, and $V_{\text{bias}}=1.8\text{V}$. The lateral position of the DLFM images is calibrated by considering the thermal drift.

Figure 4

(Color online) Simulated maps of (a) $z_{\text{STM}}\left(A_{\text{dith}},y\right)$ and (b) $\Delta f_{\text{TR}}\left(A_{\text{dith}},y\right)$ for ${\overline{I}}_t=0.5\text{nA}$. (c) and (d) correspond to the cross sections of (a) and (b) at Ce and M. White broken curves in (d) show Eq. (4), $R\left(A_{\text{dith}}\right)=\Delta f_{\text{TR}}\left(A_{\text{dith}}\right)/\Delta f_{\text{TR}}\left(A_{\text{dith}}=0\right)$ at Ce and M.