Signals and Systems Tools for Advanced Nanoscale Investigation with Atomic Force Microscopy

University of Minnesota Ph.D. dissertation. March 2017. Major: Electrical Engineering. Advisor: Murti Salapaka. 1 computer file (PDF); ix, 158 pages.The atomic force microscope (AFM) is one of the major advancements in recent science that has enabled imaging of samples at the nanometer and sub-nanometer scale. Over the years, different techniques have been developed to improve the speed, resolution and accuracy of imaging using AFM. Further, the application spectrum of AFMs has extended beyond topography imaging, examples of which include material characterization, probe based data storage systems, and also single molecule force spectroscopy. In spite of the remarkable achievements by AFM technologies, many challenges exist. While majority of this thesis aims to address important challenges that exist with state of the art AFM methodologies using tools from signal processing and systems theory, it also reports some surprising new phenomena that are observed from AFM based mechanical characterization of protein molecules. The techniques developed in each chapter are extensively verified with simulation and experimental results. A key issue that remains largely unaddressed in the AFM literature is the assessment of fidelity of the measurement data. The first contribution of this thesis is to develop a quantitative measure for the fidelity of images obtained from a fast dynamic mode AFM technique. The developed paradigm facilitates user specific priority for either detection of sample features with high decision confidence or on not missing detection of true features. The fidelity measures developed in this thesis are suitable for real-time implementation. The second contribution of this thesis is to develop and compare the performance of different methods to characterize mechanical properties of materials utilizing the dynamic mode of AFM operation. The dynamic mode AFM is particularly suitable for investigating soft-matter. Here, an important enabler is the viewpoint of an equivalent cantilever. The parameters of the equivalent cantilever need to be estimated to derive material properties. In this thesis, we develop a new steady-state based estimation of equivalent parameters (SEEP) and compare it with the recursive estimation of equivalent parameters (REEP). We show that the SEEP is considerably simpler to implement, however, SEEP is a low bandwidth method when compared to REEP. Both methods yield material parameters that quantitatively agree in the domain of validity of the methods. This thesis also streamlines the process of material identification and outlines the key pitfalls that need to be avoided for quantitative estimation of material parameters. Extensive design of a system identification module is reported which implements the REEP algorithm on modern field programmable gate arrays (FPGA). The step by step design procedure of the module explained in this thesis is employable to the development of a wide variety of FPGA based signal processing systems. The third contribution of this thesis is a new system model detection technique called the innovations squared mismatch. Such detection of a model from a set of models that best describes the behavior of a system is of primary importance in many applications. Here, two discriminating signals are derived from measurements for a plant that switches between two model behaviors, where the transfer functions from inputs to the two signals are identical when one model is effective while they are negative of one another when the other model is effective. Further, we report sequence based detection approaches to extend the use of the signals for high bandwidth applications. In such applications the plant behavior can switch from one model to another at high rates and the transients from a previous behavior affect the current behavior causing inter-symbol interference (ISI). Methods developed are specialized for probe based data storage where experimental data demonstrates that they offer significant advantages over current methods. The fourth contribution of this thesis is the first ever characterization of mechanical properties of utrophin protein molecule and its different terminal fragments using AFM based force spectroscopy experiments. Utrophin and its homologue dystrophin are proteins which are believed to play vital roles in mechanically stabilizing the muscle cells during stretch and relax cycles. These proteins are also under active research for finding possible cure for the disease muscular dystrophy. In this thesis we report markedly different mechanical characteristics for the utrophin constructs where previous thermodynamic studies measured identical thermal denaturation profiles. Our findings signify the need for force spectroscopy based characterization of molecules that are believed to play important mechanical roles in human body