Model mismatch paradigm for probe based nanoscale imaging.

Abstract

Scanning Probe Microscopes (SPMs) are widely used for investigation of material properties and manipulation of matter at the nanoscale. These instruments are considered critical enablers of nanotechnology by providing the only technique for "direct" observation of dynamics at the nanoscale and affecting it with sub Angstrom resolution. Current SPMs are limited by low throughput and lack of quantitative measurements of material properties. Various applications like the high density data storage, sub-20 nm lithography, fault detection and functional probing of semiconductor circuits, direct observation of dynamical processes involved in biological samples viz. motor proteins and transport phenomena in various materials demand high throughput operation. Researchers involved in material characterization at nanoscale are interested in getting quantitative measurements of stiffness and dissipative properties of various materials in a least invasive manner. In this work, system theoretic concepts are used to address these limitations. The central tenet of the thesis is to model, the known information about the system and then focus on perturbations of these known dynamics or model, to sense the effects due to changes in the environment such as changes in material properties or surface topography. Thus a model mismatch paradigm for probe based nanoscale imaging is developed. The topic is developed by presenting physics based modeling of a particular mode of operation of SPMs called the dynamic mode operation. This mode is modeled as a forced Lure system where a spring mass damper system is in feedback with an unknown static memoryless nonlinearity. Tools from averaging theory are used to tame this rich nonlinear system by approximating it as a linear system with time varying parameters. Material properties are thus transformed from being parameters of unknown nonlinear functions to being unknown coefficients of a linear plant. The first contribution of this thesis deals with real time detection and reduction of spurious areas in the image which are also known as probe-loss areas. These areas become critical during high speed operations. The detection strategy is based on thresholding of a distance measure, which captures the difference between the sensor models in absence and presence of probe-loss. A switching gain control strategy based on the output of a Kalman Filter is used to reduce probe-loss areas in real time. The efficacy of this technique is demonstrated through experimental results showing increased image fidelity at scan rates that are 10 times faster than conventional scan rates. The second contribution of this thesis deals with developing multi-frequency input excitation strategy and deriving a bias compensated adaptive parameter estimation strategy to determine the instantaneous equivalent cantilever model. This is used to address the challenge of quantitative imaging at high bandwidth operation by relating the estimated plant coefficients to conservative and dissipative components of tip-sample interaction. The efficacy of the technique is demonstrated for quantitative material characterization of a polymer sample, resulting in material information not previously obtainable during dynamic mode operation. This information is obtained at speeds which are two orders faster than existing techniques. Quantitative verification strategies for the accuracy of estimated parameters are presented. The third contibution of this thesis deals with developing real time tractable models and characterization methodology for an electrostatically actuated MEMS cantilever with an integrated solid state thermal sensor. Appropriate modeling assumptions are made to delineate various nonlinear forces on the cantilever viz. electrostatic force, tip-sample interaction force and capacitive coupling. Experimental strategy is presented to measure the thermal sensing transfer function from DC-100kHz. A quantitative match between experimental and simulated data is obtained for the large range nonlinearities and small signal dynamics.