Force spectroscopy using bimodal atomic force microscopy

In atomic force microscopy (AFM) achieving compositional contrast while mapping topographical features is a challenging task. Conventional single mode frequency and amplitude modulation AFM techniques are sensitive to the properties of the tip sample interaction, however in the absence of additional information channels, compositional features such as elasticity and density cannot be distinguished from topographical variations. To tackle this problem bimodal excitation techniques are introduced. In bimodal amplitude modulation AFM, sensitivity to compositional features improves by recording the phase of the higher order vibrations, while the topography is acquired using the amplitude of the first order vibrations. Increased sensitivity to mechanical properties allows imaging delicate samples such as organic molecules using gentle forces. In this thesis we propose a force spectroscopy technique in which two modes of a cantilever are excited in such a way that the amplitudes of the components of the vibration stay constant. Presence of the force field modulates the properties of the primarily bi-harmonic vibration of the cantilever, which is, in our case, the instantaneous frequencies of vibration modes. The frequency shift of the first mode remains sensitive to topographical variation, whereas the frequency shift of the higher mode samples the gradient of the tip sample forces and allows us to extract the tip sample interaction as a function of separation within a single cycle of the slow oscillation. We provide an analytic treatment of the proposed scheme and confirm our predictions by numerical simulations. We present an analysis of the sensitivity of higher mode frequency shifts to compositional features in the presence of thermal and sensor noise. We demonstrate that the method is suitable for the fast acquisition of contact properties, especially in vacuum environment where the large quality factor of the cantilever limits the available bandwidth of the amplitude modulation techniques. Finally we investigate phase shifts in bimodal amplitude modulation AFM using the developed formalism and show that phase contrast can be optimized by solving a simpler problem in single mode amplitude modulation AFM.