Understanding the Atomic-Scale Contrast in Kelvin Probe Force Microscopy

A numerical analysis of the origin of the atomic-scale contrast in Kelvin probe force microscopy is presented. Atomistic simulations of the tip-sample interaction force field have been combined with a noncontact atomic force microscope simulator including a Kelvin module. The implementation mimics recent experimental results on the (001) surface of a bulk alkali halide crystal for which simultaneous atomic-scale topographical and contact potential difference contrasts were reported. The local contact potential difference does reflect the periodicity of the ionic crystal, but not the magnitude of its Madelung surface potential. The imaging mechanism relies on the induced polarization of the ions at the tip-surface interface owing to the modulation of the applied bias voltage. Our findings are in excellent agreement with previous theoretical expectations and experimental observations.

Figure 1

(a) Sketch of the numerical tip-surface setup. We have set $z_m=5\mathrm{mm}$ compared to $z$, which scales in the sub-nm range. (b) Sketch of the NaCl unit cell showing the $17\times 17$ mesh used to calculate the ($x$, $y$, $z$, $V$) four-dimensional tip-surface force field. We have focused on four particular sites: anionic ($A$), cationic ($C$), and hollow ($H_1$, $H_2$) sites.

Figure 2

(a) Force vs distance curves measured above the four sites at $V_{\mathrm{dc}}=0\mathrm{V}$. Below 0.45 nm the tip becomes unstable. (b) Force vs $V_{\mathrm{dc}}$ curves at $z=0.45\mathrm{nm}$. The dependence is not parabolic. (c) $V_{\mathrm{dc}}$ dependence of the displacement of the foremost ${\mathrm{Na}}^{+}$ ion of the tip, ${\delta }_{\mathrm{Na}}^T$ (dashed curve), at $z=0.45\mathrm{nm}$ on top of ${\mathrm{Na}}^{+}$ of the slab and corresponding ${\delta }_{\mathrm{Na}}^S$ displacement. The ac bias modulation (shaded area) triggers the dynamic displacement of the ions at the interface (${\delta }_{\mathrm{Na}}^{T,S,\mathrm{mod}}$). (d) Same as (c) except that the tip is now placed on top of ${\mathrm{Cl}}^{-}$. Scheme of the induced ionic displacements as a function of the sign of the bias voltage on top of (e) ${\mathrm{Na}}^{+}$ and (f) ${\mathrm{Cl}}^{-}$.

Figure 3

(a) Spectroscopic curves computed above the four sites at $z=0.45\mathrm{nm}$. A shift of 0.87 V is noticed between anionic ($A$) and cationic ($C$) sites. (b) Distance dependence of the LCPD above the four sites derived from the spectroscopic curves. In the short-range regime, the LCPD exhibits a resonancelike and site-dependent behavior.

Figure 4

(a) Topographical image computed with the noncontact AFM/KPFM simulator. The vertical contrast is 38 pm. (b) Simultaneously computed LCPD image. The contrast ranges from $-2.24$ to $-1.69\mathrm{V}$ (0.56 V, full scale). (c) LCPD image computed at constant height, $z=0.45\mathrm{nm}$. The contrast ranges from $-2.24$ to $-1.38\mathrm{V}$ (0.86 V, full scale), consistently with the expected range deduced from Fig. 3b. (d) Evolution of the magnitude of the LCPD contrast (circles) and of the average LCPD (squares) as a function of the distance.