The effect of stray capacitance on potential measurements was investigated using Kelvin probe force microscopy (KPFM) at room temperature under ultra-high vacuum (UHV). The stray capacitance effect was explored in three modes, including frequency modulation (FM), amplitude modulation (AM) and heterodyne amplitude modulation (heterodyne AM). We showed theoretically that the distance-dependence of the modulated electrostatic force in AM-KPFM is significantly weaker than in FM- and heterodyne AM-KPFMs and that the stray capacitance of the cantilever, which seriously influences the potential measurements in AM-KPFM, was almost completely eliminated in FM- and heterodyne AM-KPFMs. We experimentally confirmed that the contact potential difference (CPD) in AM-KPFM, which compensates the electrostatic force between the tip and the surface, was significantly larger than in FM- and heterodyne AM-KPFMs due to the stray capacitance effect. We also compared the atomic scale corrugations in the local contact potential difference (LCPD) among the three modes on the surface of Si(111)-7 × 7 finding that the LCPD corrugation in AM-KPFM was significantly weaker than in FM- and heterodyne AM-KPFMs under low AC bias voltage conditions. The very weak LCPD corrugation in AM-KPFM was attributed to the artefact induced by topographic feedback.

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In this paper, the crosstalk in potential measurements caused by the topographic feedback and the resonance frequency in Kelvin probe force microscopy (KPFM) was investigated in frequency modulation (FM), amplitude modulation (AM) and heterodyne amplitude modulation (heterodyne AM) modes. We showed theoretically that the distance-dependence of the modulated electrostatic force in AM-KPFM is significantly weaker than in FM-and heterodyne AM-KPFMs. We experimentally confirmed that the crosstalk in FM-KPFM and heterodyne AM-KPFM is weak than that in AM-KPFM due to the bigger difference of the modulated frequencies in topographic and potential measurements in FM and heterodyne AM-KPFMs. We also compared the corrugations in the local contact potential difference (LCPD) on the surface of Si (001) show that difference on topographic (potential) images is approximately 15 pm (10 mV) between the faulted and unfaulted parts using heterodyne AM-KPFM, on the other hand, this difference cannot be observed using AM-KPFM mode. Original of this was attributed to the low crosstalk between the topographic and the LCPD measurements in heterodyne AM-KPFM.

We construct a kink solution on a non-BPS D-brane using Berkovits' formulation of superstring field theory in the level truncation scheme. The tension of the kink reproduces 95% of the expected BPS D-brane tension. We also find a lump-like solution which is interpreted as a kink-antikink pair, and investigate some of its properties. These results may be considered as successful tests of Berkovits' superstring field theory combined with the modified level truncation scheme.

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