Direct mapping of the lateral force gradient onSi(111)−7×7

Abstract

Lateral force gradient of down to 0.01 N/m on Si͑111͒-7 ϫ 7 was directly detected by dynamic lateral-force microscopy with an amplitude of 81 pm. Positive and negative torsional resonance frequency shifts of a silicon cantilever caused by the attractive interaction inward and outward tip ditherings were detected on adatom and nonadatom sites, respectively. The lateral force of down to subpiconewton was measurable with direct lateralforce spectroscopy. The converted lateral force predicts a possibility of the stick-slip motion in the noncontact region. The theoretical calculations were in good qualitative agreement with the experiments.

Measuring Electric Field Induced Subpicometer Displacement of Step Edge Ions

“…The CPD value is affected by the potential difference between tip and sample so that a differently charged tip apex results in the different CPD values as shown by the fitted quadratic functions with selected bias regions. However, since such a difference of the tip potential is not expected to induce site-dependent capacitive forces, similarly to applied bias voltage on flat terraces [37], it should cause no significant shift of the lateral signal Áf TR , but surprisingly we observe a linear dependence on the bias [ Fig. 2(c)].…”

“…Instead of using two flexural modes, simultaneous detections of the vertical and lateral interactions have been demonstrated by using the torsional resonance mode. The site-independent interactions are invariant in the lateral directions so that they do not show up in the torsional signal [37]. Furthermore, the higher mechanical quality factor, compared to that of the flexural mode, can improve the force sensitivity itself [38].…”

Atom manipulation on an insulating surface at room temperature

“…10), using the second flexural [44][45][46] and first torsional resonance modes 48,47 to oscillate the tip apex vertically and laterally with respect to the sample surface, respectively. These frequency shifts were detected with two sets of a digital phase-locked loop (Nanonis: dual-OC4).…”

Energy Loss Triggered by Atomic-Scale Lateral Force

“…However, this method cannot take into account nonconservative effects happening during the lateral tip movement and their influence on the extracted forces. Alternatively, one can excite the torsional resonance of the cantilever (TR-AFM) [28,29], enabling direct detection of the lateral force gradient from the torsional frequency shift, Áf TR [30], and the energy loss in the oscillation E TR from the driving excitation signal. Since the tip oscillates laterally thousands of times while acquiring a sample, the signal gives an average value, equivalent to the measurement of several friction loops in contact mode, and the dissipated energy corresponds to the average energy loss in the loops.…”