Quantitative analysis of dynamic-force-spectroscopy data on graphite(0001) in the contact and noncontact regimes

Hölscher, Hendrik; Schwarz, Alexander; Allers, W.; Schwarz, Udo D.; Wiesendanger, R.

doi:10.1103/physrevb.61.12678

Cited by 96 publications

(63 citation statements)

References 23 publications

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“…Several methods give similar results [17][18][19] and the dependence of the converted force on the oscillation amplitude has been thoroughly checked. 20 The data was cut at small tip-sample distances such that the part where differences between the two equivalent bridge sites occur is eliminated. The average over both bridge sites is used for the analysis.…”

Section: A Experimentsmentioning

confidence: 99%

Sublattice identification in noncontact atomic force microscopy of the NaCl(001) surface

et al. 2009

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We compare the three-dimensional force field obtained from frequency-distance measurements above the NaCl͑001͒ surface to atomistic calculations using various tip models. In the experiments, long-range forces cause a total attractive force even on the similarly charged site. Taking force differences between two sites minimizes the influence of such long-range forces. The magnitude of the measured force differences are by a factor of 6.5-10 smaller than the calculated forces. This is an indication that for the particular tip used in this experiment several atoms of the tip interact with the surface atoms at close tip-sample distances. The interaction of these additional atoms with the surface is small at the imaging distance, because symmetric images are obtained. The force distance characteristics resemble those of a negative tip apex ion which could be explained, e.g., by a neutral Si tip.

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Section: A Experimentsmentioning

confidence: 99%

Sublattice identification in noncontact atomic force microscopy of the NaCl(001) surface

et al. 2009

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“…In the z-range from 0 to -100 pm where the short-range chemical bonding forces start to emerge, the magnitude of γ increases exponentially (see inset). It is believed, that the shortrange forces between AFM tips and graphite originate from van-der-Waals forces [16] with their typical 1/z 7 -distance dependence. The experimental data shows that when the interatomic distance approaches the atomic diameters, an exponential force dependence prevails.…”

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confidence: 99%

“…For graphite, the interlayer bonds are much weaker and the potential of Eq. 1 in [16]). Because this value is more than two orders of magnitude greater than the estimate above, it is expected that long-range forces have caused a large contribution in that experiment.…”

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Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

et al. 2005

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Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be similar to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM-and STM images differ substantially depending on distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.The capability of scanning tunneling microscopy (STM) [1] and atomic force microscopy (AFM) [2] to resolve single atoms in real space makes them powerful tools for surface science and nanoscience. When operating AFM in the repulsive mode, protrusions in the images simply relate to the atoms because of Pauli's exclusion law. In contrast, the interpretation of STM images is more complicated. The Tersoff-Hamann approximation [3], valid for tips in an s-state, interprets STM images as a map of the charge density of the sample at the Fermi energy. Depending on the state of the tip, atoms can either be recorded as protrusions or holes, and tip changes can reverse the atomic contrast [4,5]. Theoretical predictions regarding the relation of forces and tunneling currents I state that tunneling currents and attractive forces are directly related, thus AFM would not provide any new physical insights over STM. Chen [5] has found that the square of the attractive energy between tip and sample should be proportional to I with experimental evidence in [6]. Hofer and Fisher [7] suggested that the interaction energy and I should be directly proportional, experimentally found in [8,9]. In this Letter, we investigate the experimental relationships between tunneling currents and conservative as well as dissipative forces for graphite probed with a W tip by performing local spectroscopy on specific lattice sites. While force spectroscopy on specific lattice sites [10] and combined force and tunneling spectroscopy on unspecific sample positions [8,9] have been performed before, the measurements reported here encompass site-specific spectra of currents and forces, supplemented by simultaneous constant-height measurements of currents and forces that allow a precise assessment of the validity of the theories regarding currents and forces in scanning probe experiments.In graphite (see Fig. 1), the electrons at E F are concentrated at the β sites, and only these atoms are 'seen' by STM at low-bias voltages. The state-of-theart method for atomic resolution force microscopy is frequency modulation AFM (FMAFM) [11], where the frequency shift ∆f of an oscillating cantilever with stiffness k, eigenfrequency f 0 and oscillation amplitude A is used as the imaging signal [12,13]. The b...

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“…Dynamic AFM [1] in the frequency modulation (FM) mode [2] has resolved the true geometric structure of a broad range of materials [3][4][5]. FM AFM experiments on carbon-based materials [6][7][8][9][10][11][12][13] show atomic contrast in Δf images and, depending on the setup, in the dissipation channel. While the origin of the dissipation is not well understood, the Δf contrast has been linked with the nature of the tip-sample interaction [14].…”

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Atomic-Scale Variations of the Mechanical Response of 2D Materials Detected by Noncontact Atomic Force Microscopy

et al. 2016

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We show that noncontact atomic force microscopy (AFM) is sensitive to the local stiffness in the atomicscale limit on weakly coupled 2D materials, as graphene on metals. Our large amplitude AFM topography and dissipation images under ultrahigh vacuum and low temperature resolve the atomic and moiré patterns in graphene on Pt(111), despite its extremely low geometric corrugation. The imaging mechanisms are identified with a multiscale model based on density-functional theory calculations, where the energy cost of global and local deformations of graphene competes with short-range chemical and long-range van der Waals interactions. Atomic contrast is related with short-range tip-sample interactions, while the dissipation can be understood in terms of global deformations in the weakly coupled graphene layer. Remarkably, the observed moiré modulation is linked with the subtle variations of the local interplanar graphene-substrate interaction, opening a new route to explore the local mechanical properties of 2D materials at the atomic scale. DOI: 10.1103/PhysRevLett.116.245502 Atomic force microscopy (AFM) and scanning tunneling microscopy (STM) are tools of choice for characterizing the unique mechanical and electronic properties of graphene (G) and other 2D materials. Dynamic AFM [1] in the frequency modulation (FM) mode [2] has resolved the true geometric structure of a broad range of materials [3][4][5]. FM AFM experiments on carbon-based materials [6][7][8][9][10][11][12][13] show atomic contrast in Δf images and, depending on the setup, in the dissipation channel. While the origin of the dissipation is not well understood, the Δf contrast has been linked with the nature of the tip-sample interaction [14].G properties can be efficiently tuned by the interaction with metals [15,16]. The interaction strength varies widely from the strong coupling with Rh [17,18] and Ru [19] to the weak limit (Ir [20], Pt [21]), where G retains its unique electronic properties [22]. The different lattice parameters of G and the metal underneath are accommodated through the formation of commensurate structures known as moiré patterns, where C atoms become inequivalent due to their different bonding configuration with the metal. The resulting "true" topographic corrugation of G-the difference in height among the topmost and the bottom C atom-varies widely, even in the weakly interacting cases, where it ranges from ≈50 pm on Ir [23,24] to practically flat (≤ 3 pm) on Pt [21].While STM can easily resolve these moiré patterns, even in the G=Pt case [21,25], AFM experiments have only been reported in highly corrugated cases as Ru [26], Rh [27], and Ir [12,28]. Focusing on the most challenging case, G=Ir, experiments with a Kolibri sensor using a W tip clearly resolved the moiré in constant height (CH) AFM images [28]. Measurements with a tuning fork using both inert (CO-terminated) and reactive (Ir-terminated) tips [12] were able to identify the atoms with both tips at any tip-sample distance. This atomic-scale resolution allowed the ...

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Quantitative analysis of dynamic-force-spectroscopy data on graphite(0001) in the contact and noncontact regimes

Cited by 96 publications

References 23 publications

Sublattice identification in noncontact atomic force microscopy of the NaCl(001) surface

Sublattice identification in noncontact atomic force microscopy of the NaCl(001) surface

Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

Atomic-Scale Variations of the Mechanical Response of 2D Materials Detected by Noncontact Atomic Force Microscopy

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