Self-sensing, estimation and control in multifrequency atomic force microscopy

Despite the undeniable success of the Atomic Force Microscope (AFM), dynamic techniques still face limitations in terms of spatial resolution, imaging speed and high cost of acquisition. In order to expand the capabilities of the instrument, it was realized that the information about the nanomechanical properties of a sample are encoded over a range of frequencies and the excitation and detection of higher order eigenmodes of the microcantilever open up further information channels. The ability to control these modes and their fast responses to excitation is believed to be the key to unraveling the true potential of these methods. This work highlights a number of drawbacks of the standard AFM setup, which limit the realizability of multifrequency approaches. First, a class of probes based on microelectromechanical system (MEMS) design is motivated, which enable the development of novel self-sensing/self-actuating techniques. Specifically, these piezoelectric transduction schemes enable the miniaturization of the AFM towards a cost-effective on-chip device with nanoscale precision in a much smaller form factor than that of conventional macroscale instruments. Second, the integrated actuation enables the development of a multimode controller which exhibits remarkable performance in arbitrarily modifying the quality factor of multiple eigenmodes and comes with inherent stability robustness. The experimental results demonstrate improved imaging stability, higher scan speeds and adjustable contrast when mapping nanomechanical properties of soft samples. Lastly, in light of the demand for constantly increasing imaging speeds while providing multifrequency flexibility, the estimation of multiple components of the high-frequency deflection signal is performed with a linear time-varying multifrequency Kalman filter. The chosen representation allows for an efficient high-bandwidth implementation on a Field Programmable Gate Array (FPGA). Tracking bandwidth, noise performance and trimodal AFM imaging on a two-component polymer sample are verified and shown to be superior to that of the commonly used lock-in amplifier.