A new dynamic mode for fast imaging in atomic force microscopes.

摘要

Video-rate imaging and property sensing with nanoscale precision is a subject of immense interest to scientists because it facilitates a deep understanding of processes and sample properties at a molecular level. This dissertation addresses the challenges of high-bandwidth imaging and real-time estimation of sample properties in an atomic force microscope (AFM). Atomic force microscopy has enabled high-resolution nanoscale imaging and manipulation of mechanical, biological and chemical properties of samples at atomic scales. However, current atomic force microscopy techniques suffer from limited imaging bandwidths making them impractical for applications requiring high throughput. A dynamic mode of imaging that achieves high imaging speeds while preserving the properties of high resolution and low forcing on the samples is developed. The proposed imaging scheme is particularly significant with the advent of high-speed nanopositioning stages and electronics. The design is accomplished by model-based force regulation that utilizes the fast cantilever de ection signal instead of its slower derivative signals used in existing methods. The control design uses the vertical and dither (shake) piezo-actuators to make the probe de ection signal track an appropriately designed trajectory. The underlying idea is to treat the nonlinear tip-sample interaction forces as an extraneous disturbance and derive an optimal control design for disturbance rejection with emphasis on robustness. The tracking objective guarantees force regulation between the probe-tip and the sample. Hinfinity stacked sensitivity framework is used to impose the control objectives and the optimal controller is derived through multiobjective optimization. The control design achieves disturbance rejection bandwidths of 0.15 -- 0.20 times the first modal frequency of cantilever used for imaging. Consequently, in the presence of appropriate lateral positioning bandwidth, imaging speeds of the order of 15 -- 20% of cantilever resonance frequency as compared to current speeds (0.5 -- 3%) are made possible. The applications of AFMs go beyond just imaging sample topography. As against conventional imaging methods where the control signal serves as an estimate of the sample surface profile, the proposed imaging mode facilitates estimation of tip-sample interaction potential. The interaction forces are nonlinear functions of the tip-sample distance and their physical properties. Hence, force estimation enables estimation of sample's topography as well as its physical properties. Force models based on the nature of sample and experimental conditions are used to interpret the force estimate data. The choice of model used, in turn, impacts property estimation. A new signal is constructed using error signal from the tracking control problem in order to estimate the tip-sample interaction forces. Thus the goals of force regulation and estimation are separated, increasing the estimation bandwidth beyond the disturbance rejection bandwidth. This allows real-time estimation of sample properties across a scan. Moreover, since the force estimates and sample properties are obtained using the tracking error signal, the role of regulation is only to ensure that the cantilever tip tracks on the sample surface. The understanding of spatial variation of properties across a sample coupled with high-speed imaging will help realize the goal of using AFM as a nano-tool for recording dynamic biological processes.