H. Hölscher

Measurement of three-dimensional force fields with atomic resolution using dynamic force spectroscopy

Using dynamic force microscopy and spectroscopy in an ultrahigh vacuum (“noncontact atomic force microscopy”) at low temperatures, we measured three-dimensional force fields with atomic resolution. The method is based on the systematic recording of the frequency shift of a cantilever oscillating near the sample surface. The presented experimental results were obtained on a NiO(001) sample surface with an iron-coated silicon tip, but the measurement principle can be extended to any tip–sample system.

Calculation of the frequency shift in dynamic force microscopy

Abstract A theoretical study of the quality and the range of validity of different numerical and analytical methods to calculate the frequency shift in dynamic force microscopy is presented. By comparison with exact results obtained by the numerical solution of the equation of motion, it is demonstrated that the commonly used interpretation of the frequency shift as a measure for the force gradient of the tip–sample interaction force is only valid for very small oscillation amplitudes and leads to misinterpretations in most practical cases. Perturbation theory, however, allows the derivation of useful analytic approximations.

Principles of atomic friction: from sticking atoms to superlubric sliding

Tribology—the science of friction, wear and lubrication—is of great importance for all technical applications where moving bodies are in contact. Nonetheless, little progress has been made in finding an exact atomistic description of friction since Amontons proposed his empirical macroscopic laws over three centuries ago. The advent of new experimental tools such as the friction force microscope, however, enabled the investigation of frictional forces occurring at well-defined contacts down to the atomic scale. This research field has been established as nanotribology. In the present article, we review our current understanding of the principles of atomic-scale friction based on recent experiments using friction force microscopy.

Modelling of the scan process in lateral force microscopy

Abstract A model for the simulation of the profiling process of a scanning force microscope tip scanning a sample surface is introduced. Starting from the equations of motion, complete lateral force microscopy images as well as individual scan lines can be calculated. The model is applied to the constant-force mode of a lateral force microscope using a model potential for the tip-sample interaction which has the translational symmetry of a MoS 2 (001) surface. Comparison with recent experimental data shows good agreement. Subsequent analysis of the tip movement demonstrates the characteristic two-dimensional stick-slip behavior of the tip. In addition, the influence of the scan speed on the measured lateral forces is discussed.

Theory of Q-Controlled dynamic force microscopy in air

The theory of dynamic force microscopy in air is developed with respect to the application of the Q-Control technique, which allows to increase or decrease the effective Q factor of the cantilever via an active external feedback. Analytical as well as numerical approaches are applied to solve the equation of motion describing the cantilever dynamics with and without Q-Control in the presence of a model tip-sample interaction force. Based on this analysis, the characteristics of Q-Controlled dynamic force microscopy are compared to conventional dynamic force microscopy carried out in amplitude modulation mode without active Q-Control (“tapping mode”). In the case of negligible tip-sample interaction (i.e., with the tip “far” from the surface), the theory describes how Q-Control alters the shape of the resonance curves of the cantilever by modifying the effective Q factor and shifting the resonance peak. Explicit consideration of tip-sample forces then permits insight into the imaging properties of Q-Contro...

Increasing the Q factor in the constant-excitation mode of frequency-modulation atomic force microscopy in liquid

By adding a Q-control electronics to the setup of the constant-excitation mode of the frequency-modulation atomic force microscope, the authors are able to increase the effective Q factor of a self-oscillated cantilever in liquid to values comparable to ambient conditions. During imaging of soft biological samples adsorbed on a mica substrate, the authors observed an increased corrugation of the topography with increased Q factors. This effect is caused by the reduction of tip-sample indentation forces as demonstrated by numerical simulations and an analytical approach.

Q-controlled amplitude modulation atomic force microscopy in liquids: An analysis

An analysis of amplitude modulation atomic force microscopy in liquids is presented with respect to the application of the Q-Control technique. The equation of motion is solved by numerical and analytic methods with and without Q-Control in the presence of a simple model interaction force adequate for many liquid environments. In addition, the authors give an explicit analytical formula for the tip-sample indentation showing that higher Q factors reduce the tip-sample force. It is found that Q-Control suppresses unwanted deformations of the sample surface, leading to the enhanced image quality reported in several experimental studies.

Dynamic force spectroscopy using the constant-excitation and constant-amplitude modes

Dynamic force spectroscopy experiments were conducted with a silicon tip on graphite in ultrahigh vacuum. Spectroscopy curves were acquired in the constant-amplitude as well as in the constant-excitation mode. From both modes we extract quantitative force and energy dissipation curves. We show that the calculated tip–sample interaction curves are independent of the operational mode. This proves that quantitative dynamic force spectroscopy is also possible in the constant-excitation mode.

Dynamic force microscopy with atomic resolution at low temperatures

Abstract In this paper, we review some of the most important results obtained with our low-temperature force microscope operated in ultrahigh vacuum. In particular, we stress the resolution capabilities on the atomic scale. After describing some recent modifications of our earlier published setup, we first compare quasi-atomic resolution in the contact mode with true-atomic resolution in the non-contact mode on graphite. On xenon, we demonstrate that weak Van der Waals interactions are sufficient to achieve atomic resolution. Thereafter, atomic scale contrast with ferromagnetic tips on nickel oxide, an insulating antiferromagnet, is discussed with respect to recent theoretical calculations regarding the detection of exchange forces. Finally, tip-induced relaxation is visualized by imaging a point defect on indium arsenide at different tip–sample distances.

Three‐Dimensional Force Field Spectroscopy

A method is presented that utilizes the frequency modulation technique in ultra‐high vacuum to measure the tip‐sample force field in all three dimensions with atomic resolution. It is based on a systematic procedure to record frequency shift versus distance curves. After their conversion into the tip‐surface potential landscape the complete force field in all three dimensions can be calculated. Experimental results obtained in the non‐contact regime on NiO(001) with an iron‐coated silicon tip are presented to demonstrate that interatomic vertical and lateral forces can be determined and assigned to specific sites within the surface unit cell.