DYNAMIC ATOMIC FORCE MICROSCOPY RESOLVED BY WAVELET TRANSFORM

Atomic Force Microscopy (AFM) is perhaps the most significant member of the scanning probe microscopes family and, because of its capability of working in air and liquid environments with virtually no limitations on imaging conditions and types of samples, it is definitely one of the most widely used. It has become an indispensable tool to measure mechanical properties at the nanoscale in various research contexts. Scanning probes used in AFM are micromechanical oscillators (typically cantilevers) and the theory of AFM dynamics is based on the analysis of the oscillating modes of beam resonators or the simpler spring-mass model. Cantilevers can be driven by the thermal excitation and/or an external driver. Usually cantilevers are driven near resonances corresponding to flexural eigenmodes that can be described as damped harmonic oscillators. Advanced techniques consider multifrequency excitation or band excitation to broaden the measurable events in tip-sample interactions, thus expanding the variety of sample properties that can be accessed. Multifrequency methods imply excitation and/or detection of several frequencies of the cantilever oscillations and concern the associated nonlinear cantilever dynamics. Such excitation/detection schemes provide higher resolution and sensitivity to materials properties such as the elastic constants and the sample chemical environment with lateral resolution in the nanometer range. In order to measure these parameters, information on peak force of interaction, energy dissipation and contact dynamics is required. Techniques to measure the parameters of the cantilever in the stationary regime are well established. In dynamics methods the external driver (thermal noise, piezoelectric driver, etc.) excites the cantilever and a number of techniques have been implemented to gain information from the tip-sample interactions, but usually the interaction of the tip with the surface is revealed by the modification of the average value of the amplitude, frequency or phase shift over many oscillation cycles. Reconstruction of the complete evolution of the interaction force between the tip and the sample surface during a single interaction event is not even considered. As an alternative to these well established techniques and to push further the AFM possibilities, it is important to examine the possibility of analyzing single-event or impulsive interactions. This opens the possibility to capture the information conveyed by the sensing tip in a single interaction, in contrast to the cycle average used in many dynamic techniques. The single-event interactions are basically of the impact kind, with the simultaneous excitation of many cantilever eigenmodes and/or harmonics. The averaging techniques provide superior sensibility, allowing to probe the details of force interactions down to the molecular level, but to study single-event interactions it is mandatory to provide analysis techniques that are able to characterize all excited cantilever oscillation modes at once without averaging. The temporal evolution of the amplitude, phase and frequency during few oscillation cycles of the cantilever provides information that cannot be obtained with standard methods. In the present thesis a data analysis method allowing to retrieve these quantities during an impulsive cantilever excitation is proposed. This thesis concentrates on the dynamics of the flexural modes of the thermally driven cantilever in air when its tip is excited by a single impact on the sample surface. The signal analysis is based on the combination of wavelet and Fourier transforms that can be applied to a broad class of AFM impulsive measurements. To exemplify the method, a short time interval around the jump-to-contact (JTC) transition in ambient conditions is investigated, with the aim to characterize the transient excitation of the cantilever eigenmodes before and after the impact. The experimental evidences that high-order flexural modes are excited in air upon a single impact tip–sample interaction induced by the JTC transition are presented. The way to retrieve information about the instantaneous total force act ing on the cantilever tip, contact dynamics and energy dissipation at all frequencies simultaneously, without averaging or interruption, is developed. The exploration of these transient conditions of the cantilever is not possible with dynamic techniques based on the resonant driving or using Fourier transform analysis alone. The analysis presented in this work is useful to deal with nonrepeatable experiments and to determine the exact single interaction dynamics in terms of the full cantilever spectral excitations, features that are not normally considered in dynamical AFM techniques.