AFM tip characterization by Kelvin probe force microscopy

Barth, Clemens; Hynninen, Teemu; Bieletzki, M.; Henry, Claude R.; Foster, Adam S.; Esch, F.; Heiz, Ueli

doi:10.1088/1367-2630/12/9/093024

Cited by 49 publications

(61 citation statements)

References 49 publications

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“…Earlier studies obtained such a term by treating native ions or charged atoms adsorbed on the sample surface and/or the tip apex as point charges. 22,23,29 Deviations from the linear behavior could occur for larger biases, especially near instabilities, as observed in computations for a charged nanotip.…”

Section: 41mentioning

confidence: 80%

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Multiscale approach for simulations of Kelvin probe force microscopy with atomic resolution

et al. 2012

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The distance dependence and atomic-scale contrast recently observed in nominal contact potential difference (CPD) signals simultaneously recorded by KPFM using non-contact atomic force microscopy (NCAFM) on defect-free surfaces of insulating, as well as semiconducting samples, have stimulated theoretical attempts to explain such effects. Especially in the case of insulators, it is not quite clear how the applied bias voltage affects electrostatic forces acting on the atomic scale. We attack this problem in two steps. First, the electrostatics of the macroscopic tip-cantilever-sample system is treated by a finite-difference method on an adjustable nonuniform mesh. Then the resulting electric field under the tip apex is inserted into a series of atomistic wavelet-based density functional theory (DFT) calculations. Results are shown for a realistic neutral but reactive silicon nano-scale tip interacting with a NaCl(001) sample. Bias-dependent forces and resulting atomic displacements are computed to within an unprecedented accuracy.Theoretical expressions for amplitude modulation (AM) and frequency modulation (FM) KPFM signals and for the corresponding local contact potential differences (LCPD) are obtained by combining the macroscopic and atomistic contributions to the electrostatic force component generated at the voltage modulation frequency, and evaluated for several tip oscillation amplitudes A up to 10 nm. For A = 0.1Å, the computed LCPD contrast is proportional to the slope of the atomistic force versus bias in the AM mode and to its derivative with respect to the tip-sample separation in the FM mode. Being essentially constant over a few Volts, this slope is the basic quantity which determines variations of the atomic-scale LCPD contrast. Already above A = 1Å, the LCPD contrasts in both modes exhibit almost the same spatial dependence as the slope. In the AM mode, this contrast is approximately proportional to A −1/2 , but remains much weaker than the contrast in the FM mode, which drops somewhat faster as A is increased. These trends are a consequence of the macroscopic contributions to the KPFM signal, which are stronger in the AM-mode and especially important if the sample is an insulator even at sub-nanometer separations where atomic-scale contrast appears.

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Section: 41mentioning

confidence: 80%

“…Because the charge or dipole are intrinsic, the interaction is proportional to V , so that this correction would give rise to long-range contributions to the slopes a and a ′ . 22,23 In the case of our neutral Si nanotip, this correction is small.…”

mentioning

confidence: 93%

Multiscale approach for simulations of Kelvin probe force microscopy with atomic resolution

et al. 2012

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“…Interatomic interactions in the surface are included via fitted Buckingham potentials [51][52][53][54]. As the tip is contacted to the surface, we expect the apex to be covered by LiF and model it as a simple dipole [45,55,56]-since we are interested in the interactions at LR, an atomistic model of the tip is unnecessary. The resulting force field is then used to run our home-built virtual DFM [57] capable of simulating Áf TR in the bimodal operation mode, enabling us to correlate the step atom displacements to the frequency shift as well as compare the latter to the experiment.…”

Section: Prl 109 146101 (2012) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…week ending 5 OCTOBER 2012 146101-3 tips [45,55,56]. The origin of the simulated Áf TR is found entirely in the atomic displacements of the step ions induced by the bias: the ions move mainly along the vertical direction by at most 2 pm [ Fig.…”

Section: Prl 109 146101 (2012) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Measuring Electric Field Induced Subpicometer Displacement of Step Edge Ions

et al. 2012

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We provide unambiguous evidence that the applied electrostatic field displaces step atoms of ionic crystal surfaces by subpicometers in different directions via the measurement of the lateral force interactions by bimodal dynamic force microscopy combined with multiscale theoretical simulations. Such a small imbalance in the electrostatic interaction of the shifted anion-cation ions leads to an extraordinary long-range feature potential variation and is now detectable with the extreme sensitivity of the bimodal detection.

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“…6,7 KPFM signal generation has been investigated for a large number of systems, 2,[7][8][9] including the contrast on different sample facets 10 and on metallic nanostructures 11,12 as well as at the atomic [13][14][15][16][17] and even submolecular 18,19 scale. Recently, a very general electrostatic model from Kantorovich et al 20 has been used in several case studies [21][22][23] to derive analytical expressions for the closed-loop amplitude modulation (AM)-KPFM and frequency modulation (FM-)KPFM signals measured for charged systems. In particular, this model separated the tip geometry from the sample charges as well as from the contact potential difference of the metallic contacts.…”

Section: Introductionmentioning

confidence: 99%

The weight function for charges—A rigorous theoretical concept for Kelvin probe force microscopy

Söngen

Rahe

Bechstein

et al. 2016

Journal of Applied Physics

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A comprehensive discussion of the physical origins of Kelvin probe force microscopy (KPFM) signals for charged systems is given. We extend the existing descriptions by including the openloop operation mode, which is relevant when performing KPFM in electrolyte solutions. We define the contribution of charges to the KPFM signal by a weight function, which depends on the electric potential and on the capacitance of the tip-sample system. We analyze the sign as well as the lateral decay of this weight function for different sample types, namely, conductive samples as well as dielectric samples with permittivities both larger and smaller than the permittivity of the surrounding medium. Depending on the surrounding medium the sign of the weight function can be positive or negative, which can lead to a contrast inversion for single charges. We furthermore demonstrate that the KPFM signal on thick dielectric samples can scale with the sample size-rendering quantitative statements regarding the charge density challenging. Thus, knowledge on the weight function for charges is crucial for qualitative as well as quantitative statements regarding charges beneath the tip. V C 2016 AIP Publishing LLC.

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AFM tip characterization by Kelvin probe force microscopy

Cited by 49 publications

References 49 publications

Multiscale approach for simulations of Kelvin probe force microscopy with atomic resolution

Multiscale approach for simulations of Kelvin probe force microscopy with atomic resolution

Measuring Electric Field Induced Subpicometer Displacement of Step Edge Ions

The weight function for charges—A rigorous theoretical concept for Kelvin probe force microscopy

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