Figure 1

Dual-mode setup. (a) Sketch of the dual-mode sensor. The DFM/STM tuning-fork sensor, to which the tip is connected, is glued onto the MACOR carrier. DFM is performed by detecting the signal from the tuning fork via contacts T1 and T2. P1 and P2 are the contacts of the excitation piezo, which excites vibration of the tuning fork. By means of the $\mu$m wire, the tunneling current can be recorded. With this setup, the frequency shift and the tunneling current can be recorded simultaneously with the same microscopic tip configuration. This enables the spectroscopy of the frequency shift vs bias voltage (b) and vs $z$ displacement (c), as well as the tunneling current vs bias voltage (d) and vs $z$ displacement (e).Reuse & Permissions

Figure 2

Frequency shift as a function of the bias voltage $V_{\mathrm{bias}}$ and of the tip-sample distance $z$ as following from Eqs. (3) and (4). (a) Surface plot and (b) contour plot. The Lennard-Jones parameters are $\epsilon =2.8\times {10}^{-18}$ J and $\sigma =1.6$ nm and the effective contact potential is $\Delta {\Phi }_{\mathrm{eff}}=-0.15$ eV. A sphere with a radius of $95$ nm in front of a plane wall (Ref. 25) is used to model the capacity $C_{\mathrm{series}}$. The amplitude of the tuning fork is $a=3\times {10}^{-10}$ m, the spring constant is $k=21$ kN ${\mathrm{m}}^{-1}$, and the unperturbed resonance frequency is $f_0=21$ kHz.Reuse & Permissions

Figure 3

Frequency shift experimentally determined by DFM as a function of the bias voltage $V_{\mathrm{bias}}$ and the $z$ displacement. (a) Surface plot and (b) contour plot. The amplitude of the tuning fork is $a=3\times {10}^{-10}$ m, the spring constant is $k\approx 21$ kN ${\mathrm{m}}^{-1}$, and the unperturbed resonance frequency is $f_0=21$ kHz (Ref. 26).Reuse & Permissions

Figure 4

Frequency shift vs (a) the tip-sample distance and (b) the bias voltage. The experimental data (thick lines)correspond to cuts through Fig. 3. The thin dotted lines are calculated by Eqs. (4) and (3) with the parameters shown in the caption of Fig. 2. An experimentally recorded $z$ displacement of 0 corresponds to a tip-sample distance of $z=3.4$ nm.Reuse & Permissions

Figure 5

(a) Frequency shift with varying bias voltage at fixed tip-sample distance on Ag(001) and 3 ML MgO/Ag(001). The indicated effective contact potential shift of $\Delta {\Phi }_{\mathrm{eff}}=-1.2$ eV results from the shift of the Ag(001) work function induced by the MgO overlayers, reducing the surface dipole. Graph (b) shows the derivatives of the parabolic fits to the data.Reuse & Permissions

Figure 6

Ratio of the tip-sample interactions resulting from the atom directly beneath the tip (atom $j$) and the full tip-sample interaction of all surface atoms with the tip $F_{\mathrm{ts}}$. The inset shows the tip-sample arrangement.Reuse & Permissions