Accurate Extraction of Electrostatic Force by a Voltage-Pulse Force Spectroscopy

The classification of interaction forces between two approaching bodies is important in a wide range of research fields. Here, we propose a method to unambiguously extract the electrostatic force ($F_{\text{ele}}$), which is one of the most significant forces. This method is based on the measurement of the energy dissipation under applied voltage pulse between an atomic force microscopy (AFM) tip and sample. It allowed us to obtain $F_{\text{ele}}$ as a function of the tip-sample distance and voltage including the distance-independent part, to which conventional AFM is insensitive. The obtained $F_{\text{ele}}$ curves nicely fit the analytical model, enabling estimation of the geometry of the tip. The distance-dependent contact potential difference could also be correctly obtained by the measured $F_{\text{ele}}$, opening an alternative route to quantitative Kelvin probe force microscopy.

Figure 1

(a) Schematic diagram of experimental setup of the voltage-pulse method for measurement of electrostatic force. Bias voltage pulse applied to the sample is synchronized with the cantilever oscillation. (b) Schematic $F(z)$ curves during cantilever oscillation. Forward and backward curves are shown by green and red, respectively. It is assumed that $|F(z,V=V_0+V_p)|$ is larger than $|F(z,V=V_0)|$. Bias jump from $V_0$ to $V_0+V_p$ produces hysteresis of $F$ curves in each oscillation cycle. Energy dissipation $D^{+}$ is generated.

Figure 2

(a) $D^{+}(\tau )$ and (b) $D^{-}(\tau )$ curves measured on the $\mathrm{Si}(111)\text{−}(7\times 7)$ surface. Pulse conditions and $F$ vs $V$ parabolic curves are schematically shown in the insets. (c) $D^{+}(\tau )$ and (d) $D^{-}(\tau )$ curves with different $V_p$ values using a different cantilever from (a, b). (e) $(D^{+}+D^{-})/(2V_p^2)$ vs $\tau$ and (f) $(D^{+}-D^{-})/(2V_p)$ vs $\tau$. We set $w=50\mathrm{ns}$ for all measurements. The acquisition parameters are summarized in the Supplemental Material [21].

Figure 3

(a) Extracted $a(z)$ and (b) $V_{\text{cpd}}(z)$ curves with eight different tips. Tip 1 and tip 2 correspond to Figs. 2 and 2 and Figs. 2, respectively. The fitting curves based on Eq. (7) are shown in (a). The values of $R$ ($\theta$) are determined to be 6.0 nm (6.2°), 24.7 nm (12.9°), 11.1 nm (11.3°), 5.7 nm (11.2°), 25.2 nm (10.5°), 27.0 nm (13.6°), 10.2 nm (16.7°), and 8.5 nm (15.3°) for tips 1–8, respectively. The tip model is illustrated in the inset. $z=0$ is defined as the divergence point of $a(z)$. The acquisition parameters are summarized in the Supplemental Material [21].

Figure 4

(a) FM-KPFM measurements: $\mathrm{\Delta }f(V)$ curves at different heights on the Cu(001) surface. (b) $V_{\text{cpd}}(z)$ obtained by pulse method (black curve) and $V_{\text{cpd}}^{FM}(z)$ obtained by FM-KPFM experiments of (a) (blue circles). The simulated $V_{\text{cpd}}^{FM}(z)$ is also shown by the green curve. One cannot calculate $V_{\text{cpd}}^{FM}(z)$ at far distances in the region of $2A$ since $F_{\text{ele}}$ data are missing to calculate $\mathrm{\Delta }f$ in this region. The acquisition parameters for pulse measurements were $f=287480.6\mathrm{Hz}$, $A=125\AA$, and $k=26.3\mathrm{N}/\mathrm{m}$, respectively. $A$ is reduced to $A=19.6\AA$ for FM-KPFM measurements, and for the simulation of $V_{\text{cpd}}^{FM}(z)$.