Martin Stark

Inverting dynamic force microscopy: From signals to time-resolved interaction forces

Transient forces between nanoscale objects on surfaces govern friction, viscous flow, and plastic deformation, occur during manipulation of matter, or mediate the local wetting behavior of thin films. To resolve transient forces on the (sub) microsecond time and nanometer length scale, dynamic atomic force microscopy (AFM) offers largely unexploited potential. Full spectral analysis of the AFM signal completes dynamic AFM. Inverting the signal formation process, we measure the time course of the force effective at the sensing tip. This approach yields rich insight into processes at the tip and dispenses with a priori assumptions about the interaction, as it relies solely on measured data. Force measurements on silicon under ambient conditions demonstrate the distinct signature of the interaction and reveal that peak forces exceeding 200 nN are applied to the sample in a typical imaging situation. These forces are 2 orders of magnitude higher than those in covalent bonds.

From Images to Interactions: High-Resolution Phase Imaging in Tapping-Mode Atomic Force Microscopy

In tapping-mode atomic force microscopy, the phase shift between excitation and response of the cantilever is used as a material-dependent signal complementary to topography. The localization of information in the phase signal is demonstrated with 1.4-nm lateral resolution on purple membrane of Halobacterium salinarum in buffer solution. In a first-order approximation, the phase signal is found to correlate with modulations of the tip oscillation amplitude, induced by topography. Extending the analysis to contributions of the tip-sample interaction area as a second-order approximation, a method is proposed to extract information about the interaction from the phase signal for surfaces with a roughness in the order of the tip radius.

Higher-harmonics generation in tapping-mode atomic-force microscopy: Insights into the tip–sample interaction

We present an experimental analysis of the nonlinear tip–sample interaction in tapping-mode atomic-force microscopy by exploiting anharmonic contributions of the cantilever motion. Two aspects of a concept aiming at a full reconstruction of the tip–sample interaction are demonstrated: higher flexural eigenmode vibrations excited by the impact of the oscillating tip on the sample are used to measure the tip–sample interaction time; by imaging at higher harmonics of the driving frequency material contrast is obtained.

Spectroscopy of the anharmonic cantilever oscillations in tapping-mode atomic-force microscopy

By spectroscopic analysis of the cantilever oscillation in tapping-mode atomic-force microscopy (TM–AFM), we demonstrate that the transition from an oscillatory state dominated by a net attractive force to the state dominated by repulsive interaction is accompanied by the enhanced generation of higher harmonics. The higher harmonics are a consequence of the nonlinear interaction and are amplified to significant amplitudes by the eigenmodes of the cantilever. The results show that in a quantitative description of TM–AFM higher eigenmode excitation must be considered to account for internal energy dissipation.

Chaos in dynamic atomic force microscopy

In tapping mode atomic force microscopy (AFM) the highly nonlinear tip-sample interaction gives rise to a complicated dynamics of the microcantilever. Apart from the well-known bistability under typical imaging conditions the system exhibits a complex dynamics at small average tip-sample distances, which are typical operation conditions for mechanical dynamic nanomanipulation. In order to investigate the dynamics at small average tip sample gaps experimental time series data are analysed employing nonlinear analysis tools and spectral analysis. The correlation dimension is computed together with a bifurcation diagram. By using statistical correlation measures such as the Kullback-Leibler distance, cross-correlation and mutual information the dataset can be segmented into different regimes. The analysis reveals period-3, period-2 and period-4 behaviour, as well as a weakly chaotic regime.

FAST LOW-COST PHASE DETECTION SETUP FOR TAPPING-MODE ATOMIC FORCE MICROSCOPY

A fast low-cost device to detect the phase shift between the excitation and the response of a cantilever in tapping-mode atomic force microscopy is described. For cantilever signals with a good signal to noise ratio, as is commonly found, the device presented can replace a lock-in amplifier. The setup is based on indirect time measurements realized by a combination of commonly used analog and digital integrated circuits. Phase measurement can already be achieved within one cycle. Signal output rates up to 100 kHz allow the use of the phase shift as an auxiliary imaging channel. Cantilever frequencies may range from 6 to more than 500 kHz. The principle of the setup is illustrated together with technical data. Images of a hydrophobic–hydrophilic structured silicon surface obtained in air and of purple membrane obtained in fluid are presented.

Stabilized atomic force microscopy imaging in liquids using second harmonic of cantilever motion for setpoint control

We present an automated stabilization of the imaging process in tapping mode atomic force microscopy. For biological applications, the requirement of stable imaging conditions to achieve reliable high resolution is contradicted by the necessity to work in solution to ensure biological functionality: thermal and saline variations of the viscosity, in particular when exchanging the solution the sample is surrounded with, strongly affect the cantilever motion rendering the imaging process instable. Using anharmonic contributions in the deflection signal, the amplitude setpoint is controlled to compensate for unavoidable drift in the free oscillation. By this additional feedback, the tip–sample interaction is maintained stable at a low value, making the instrument robust against drift and tolerant to environmental changes. As a delicate test sample, the “single ring”-mutant of the bacterial chaperonin GroEL from E. coli was imaged. To prove the efficiency of our setup, we show highly stabilized, continuous imaging with minimized user interaction while strong perturbations by exchange of the buffer solution were imposed during the scanning.

Correlation between spin structure oscillations and domain wall velocities

Magnetic sensing and logic devices based on the motion of magnetic domain walls rely on the precise and deterministic control of the position and the velocity of individual magnetic domain walls in curved nanowires. Varying domain wall velocities have been predicted to result from intrinsic effects such as oscillating domain wall spin structure transformations and extrinsic pinning due to imperfections. Here we use direct dynamic imaging of the nanoscale spin structure that allows us for the first time to directly check these predictions. We find a new regime of oscillating domain wall motion even below the Walker breakdown correlated with periodic spin structure changes. We show that the extrinsic pinning from imperfections in the nanowire only affects slow domain walls and we identify the magnetostatic energy, which scales with the domain wall velocity, as the energy reservoir for the domain wall to overcome the local pinning potential landscape.

Estimating the transfer function of the cantilever in atomic force microscopy: A system identification approach

Dynamic atomic force microscopy (AFM) offers many opportunities for the characterization and manipulation of matter on the nanometer scale with a high temporal resolution. The analysis of time-dependent forces is basic for a deeper understanding of phenomena such as friction, plastic deformation, and surface wetting. However, the dynamic characteristics of the force sensor used for such investigations are determined by various factors such as material and geometry of the cantilever, detection alignment, and the transfer characteristics of the detector. Thus, for a quantitative investigation of surface properties by dynamic AFM an appropriate system identification procedure is required, characterizing the force sensor beyond the usual parameters spring constant, quality factor, and detection sensitivity. Measurement of the transfer function provides such a characterization that fully accounts for the dynamic properties of the force sensor. Here, we demonstrate the estimation of the transfer function in a b...

A simple and accurate method for calibrating the oscillation amplitude of tuning-fork based AFM sensors

We have developed a simple and accurate method for calibrating the amplitude of vibration of quartz tuning fork sensors commonly used in atomic force- and near field optical-microscopy. Unlike interferometric methods, which require a complex optical setup, the method we present requires only a simple measurement of the electro-mechanical properties of the tuning-fork oscillator and can be performed in a matter of minutes without disturbing the experimental setup. Comparison with interferometric methods shows that an accuracy of better than few percent can be routinely achieved.