Toward quantitative Kelvin probe force microscopy of nanoscale potential distributions

Kelvin probe force spectroscopy (KPFS) and finite-element method (FEM) simulations were employed to investigate the averaging effect of the work function signals of nanoscale potential distributions in Kelvin probe force microscopy (KPFM). A KPFS routine is presented that enables meaningful experimental results even for electronically inhomogeneous KPFM tips. By use of this routine a strong distance dependence of the averaging effect is revealed. A combination of KPFS experiments and FEM simulations is applied to quantify the averaging effect, which simplifies comparison among different experiments and to theory. No influence of surface topography on the averaging effect was observed.

Figure 1

KPFM line profiles of topography and relative work function (${\Phi }_{\mathrm{rel}}$) across the various NPDs from Table , obtained at the minimum tip-sample distances stated in Table . All work function line profiles were shifted in such a way that ${\Phi }_{\mathrm{rel}}$ outside the NPD is at 0.

Figure 2

KPFM line profiles (ten lines averaged) of (a) topography and (b) work function ($\Phi$) behavior across step 1, obtained at a tip-sample distance $z_{\min }=2.7$ nm. $500\times 5$ nm images of the corresponding surface area are shown as insets. (c) KPFS work function spectra at step 1, taken directly at the center of the NPD and in the background. The positions at which the spectra were taken are indicated in the insets of Fig. 2b.

Figure 3

KPFS difference spectra of the NPD work function signal ($\Delta \Phi$) of step 1, determined experimentally (line) and by simulations (squared line) (Ref. 38). Inset 1 shows an SEM image of the tip used for the experiment. Inset 2 shows the 3D tip geometry used for the simulation.

Figure 4

KPFS work function spectra taken at various NPDs of CIGSe grain boundaries and GaAs surface steps (see Table ). Spectra taken (a) at the center of the NPDs and (b) in the corresponding backgrounds. All work function spectra were shifted in such a way that the relative work function (${\Phi }_{\mathrm{rel}}$) is at 0 for large tip-sample distances.

Figure 5

(a) Experimental KPFS difference spectra of the NPD work function signal ($\Delta \Phi$) taken at GB1–GB3, step 1, and step 2. All spectra were normalized to the absolute NPD signal percentage from Fig. 3 at the smallest common tip-sample distance $z=9.7$ nm. The inset shows an SEM image of the tip used for the KPFS experiments at GB1–GB3 and step 2. (b) Simulated (Ref. 40) KPFS difference spectra of the NPD work function signal ($\Delta \Phi$) with and without the surface topography displayed in the inset.

Figure 6

Simulated (Ref. 41) KPFS difference spectra of the NPD work function signal ($\Delta \Phi$) for different radii $r$ of the tip apex.