# Fileset

[s-info3.pdf](https://mdr.nims.go.jp/filesets/4be508c5-2fb4-421d-a52c-a714c70bcbf8/download)

## Creator

[Nobuyuki Ishida](https://orcid.org/0000-0003-0161-0583), [Takaaki Mano](https://orcid.org/0000-0002-6955-260X)

## Rights

[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

## Other metadata

[Quantitative theoretical analysis of the electrostatic force between a metallic tip and semiconductor surface in Kelvin probe force microscopy](https://mdr.nims.go.jp/datasets/4161da21-8b1e-438a-a15a-d13ae45307ca)

## Fulltext

Supplementary information:Quantitative theoretical analysis of the electrostatic forcebetween a metallic tip and semiconductor surface in Kelvin probeforce microscopyNobuyuki Ishida1 and Takaaki Mano11National Institute for Materials Science,1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan1FIG. S1: Scripts added to the line 345 in the ”semitip_v4.f” file to output the coordinates (r andz values) of grid points in the vacuum region and the electrostatic potential at each grid point.2TABLE I: The input parameters used for the electrostatic potential calculation in the SEMITIP.3FIG. S2: z component of the electrostatic force per unit area (fzelec) acting on the tip surfaceplotted as a function of radial distance. The forces are expressed as absolute values. The range ofr on the tip surface extended from 0 nm to approximately 2100 nm.FIG. S3: F zelec(U) spectrum in (a) was converted into ∆ν(U) spectrum in (b) using Eq. 2 inthe main article. Both curves exhibited parabolic-like behavior, with the minimum of the absolutevalues appearing at the bias voltage corresponding to the input contact potential difference (CPD),as indicated by dashed vertical lines.4FIG. S4: Magnitude of tip-induced band bending (TIBB) as a function of bias voltage. The TIBB(φsurf) was measured relative to the potential energy at a point far inside the semiconductor.ECEFENEV0.756 eV0.3 eVFIG. S5: Virtual surface states introduced to simulate the effect of Fermi level pinning. The surfacestates had a Gaussian type energy distribution, with the centroid energy located at the center ofthe band gap, i.e., 0.756 eV above the valence band edge. The full width at half maximum of theGaussian distribution was 0.3 eV. The charge neutrality level EN was located at the center of theGaussian distribution. Due to the occupation of these states, the band bending occurred even inthe absence of the tip near the semiconductor surface, a phenomenon referred to as Fermi levelpinning.5FIG. S6: Normalized ∆ν(U) curves simulated with tip radii of 5 (solid circles) and 100 nm (solidtriangles). The ∆ν signals were normalized using the values at a bias voltage of 2.1 V. Thenormalization highlights the difference in curvature between the two curves across the entire biasrange.FIG. S7: Estimation of the radius of the W tip used in the experiment, performed using scanningelectron microscopy (SEM). The contour of the tip apex was fitted with a hyperbolic curve (dashedline), using the tip radius and opening angle as fitting parameters. For the tip in the SEM image,a reasonable fit was obtained with a tip radius of 10 nm and an opening angle of 7 ◦.6ExperimentSimulationFIG. S8: Simultaneous fitting of the simulated tunneling current (It) and ∆ν data to the ex-periment. (a) Experimentally obtained ∆ν(U) curve on the GaAs(110) surface (solid line). Theoscillation amplitude of the qPlus sensor was 580 pm. Solid circles show the simulated ∆ν(U) curveusing parameter values of 10 nm, 1.53 nm, and 0.933 V for Rtip, s, and CPD, respectively. Theinput CPD value was determined from curve fitting of a 9th-order polynomial to the ∆ν(U) curvein the experiment. The values of Rtip and s were determined so that both simulated ∆ν(U) andIt(U) curves reproduced the experimental values. (b) Experimentally obtained It(U) spectrum atthe same location as the ∆ν(U) spectrum in (a) (solid line). The excitation of the qPlus sensor wasturned off during tunneling spectroscopy. Solid circles represent the simulated It(U) spectroscopydata using the same parameter values as in the ∆ν(U) spectroscopy case, except for s, which wasset to 0.9 nm. The difference in s from the value used for the ∆ν(U) simulation arose from thedifferences between the two spectroscopies in the values of the oscillation amplitude and the offsetadded in the tip-sample separations from the set point separation during the bias spectroscopymeasurements.7FIG. S9: The solid line shows the experimental ∆ν(U) spectrum. The radius of the W tip usedfor this experiment was estimated from the curve fitting to be 10 nm. Blue solid circles and redsolid triangles display the ∆ν(U) curves calculated using tip radii of 5 nm and 15 nm, respectively.The coefficient term (− ν0kA2 ), treated as a fitting parameter (as discussed in the main article),was adjusted to ensure good fits to the experimental data on the left side of the inflection point.This parameter optimization resulted in deviations from the experiment on the right side of theinflection point. Conversely, when the parameter was adjusted to achieve good fits on the rightside, deviations were observed on the opposite side.8�� �� � ������������
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����������� ��FIG. S10: Tip-sample separation dependence of the experimental ∆ν(U) spectra (solid lines)obtained using a W tip with a large radius. The lift heights of the tip for the bias spectroscopy,relative to the tip-sample separation regulated by the STM feedback, were 0.1, 0.5, 1.0, and 3.0 nm.Solid circles represent ∆ν(U) spectra from the simulations. To determine the parameters for thesimulations, we first performed curve fitting of the simulation to the data obtained with a lift heightof 0.1 nm. The tip radius estimated from the parameter optimization was 105 nm. Subsequently,we computed the ∆ν(U) spectra by only changing the tip-sample separation according to the liftheights of the tip. While we achieved good agreement between theory and experiment for the datawith a tip lift of 0.1 nm after the parameter optimization, slight deviations between theory andexperiment were observed for the data of increased tip-sample separations.9