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Tip-NP tunnel gaps are ∼2 nm in air due to a reduced work function compared to vacuum. Gap changes are significantly smaller. For example, in Figs. 1(c) and 1(d), the top of the cantilever deflects about 0.5 nm. The tip-NP gap changes by a smaller amount due to a "lever" effect that arises since the tip-NP gap is lower than the top of the cantilever. The reduced work function also mitigates a convolution effect inherent in the STM-AFM geometry where cantilever motion can give rise to strong current changes. Note that, in Figs. 1(c) and 1(d), a roughly linear cantilever motion does not give rise to strong asymmetry in current magnitudes with respect to plus/minus bias voltages.
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18
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0034668528
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Given our current set point of ∼0.1 nA and a typical value for work functions (∼ 1 eV) under ambient conditions, we estimate the distance between tip and NP to be ∼2 nm. The cantilever's force constant k is estimated to be ∼ 1 N/m, larger than a factory value (∼0.2 N/m, thermomicroscope) because of the presence of a thin layer of water between tip and cantilever under ambient conditions. See T. Stifter, O. Marti, and B. Bhushan, Phys. Rev. B 62, 13 667 (2000). STM images of NP's were stable to repeated scanning, implying that the tip is not in direct contact with the NP's under these conditions.
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33646603344
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NP-T to reproduce non-linearity in current as in Refs. 17 and 19.
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33646630550
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2+⋯], where r=a/2(a +d).
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