Nonlinear dynamic atomic force microscopy

Most physical phenomena be it mechanical, chemical or biological are inherently nonlinear in nature. In fact, it is the linear phenomenon that is the exception rather than the rule. By harnessing these nonlinearities one can obtain far greater information about the underlying physics and develop more sensitive and efficient devices. This is especially true at the micro and nanoscale world where the forces tend to be highly nonlinear and the go-to tool for studying such forces is the atomic force microscopy (AFM). Ever since its inception, AFMhas revolutionized theworld of nanotechnology through its ability to manipulate and characterize matter with atomic resolution. With the gradual development of novel characterization techniques, AFM has slowly transitioned from a traditional imaging technique to a powerful nanomechanical characterization tool capable of estimating material properties of wide variety of samples with ease. This transition is fueled by the greater interest in understanding the highly nonlinear tip-sample interaction forces that exist between an AFM probe and the sample of interest. However, in order to advance our understanding of nanoscale interactions, one must fully embrace the nonlinear nature of the system and develop parameter identification techniques based on nonlinear dynamics. In this regard, this thesis focusses on both fundamental and applied nonlinear dynamical studies to develop novel identification techniques for dynamic AFM applications.