The objective of this proposal is the development and implementation of a systems-theory framework for modeling, analyzing, and designing microprobe-based systems that will enable high-speed and reliable imaging of surface topographies, matter properties, and probe-and-matter interaction forces with nanoscale precision.
The intellectual merit of this proposal leverages a systems-theoretic approach for analysis and design which uses real-time model-based techniques to address critical challenges associated with microprobe based nanoscale investigation. One of the primary challenges encountered is the control of the main probe; a microcantilever. Currently, most approaches do not exploit models of the probe to achieve its control. Also, models of probe-sample interaction in the dynamic mode operation have not been employed. In this proposal, relevant models for real-time control of the main probe will be developed and subsequently employed for engendering high bandwidth and high resolution. The approach, , will provide significant advances in imaging capabilities, by up to two-orders faster imaging than existing modes. An important need for probe based nanoscale investigation is that of increasing the range of the positioning devices, to the millimeter scale without sacrificing high resolution (nanometer scale). In the proposal, modern control paradigm is proposed for long-range high resolution positioning which will enable critical nanoscale-investigation studies, especially in biology. Model-based techniques are proposed that will resolve a significant challenge of matter-property and lateral-forces characterization in real time as the matter is scanned for surface imaging.
The broader impacts will include transformative technologies that will enable high precision, high bandwidth and large range nano investigation capabilities. Thus, proposed research will translate into technological and economic gains. This work is at the confluence of dynamic systems and control theory, control applications, and instrumentation technology. The graduate students involved will be trained in a unique interdisciplinary manner that exposes them to the diverse research areas and interaction with industry. Besides its direct impact on graduate education, this program will provide workshops for advanced graduate students and research engineers, research experience for undergraduates, internet-based access to SPM-devices for high-school teachers and students.
Atomic Force Microscopes are devices that are capable of providing images of samples with atomic-scale resolution. In most common AFMs this high resolution is achieved by moving a cantilever probe on the sample surface (much like running a finger on a material) which deflects up and down due to the interatomic forces between the cantilever tip and the sample. However the efficacy of this method depends on maintaining the probe in the close vicinity of samples (on the order of atomic distances) since the interatomic forces are effective only over atomic distances. This obstacle is typically overcome by force- regulation, where the sample is moved up and down with respect to the probe to compensate for the topographic features on the sample so as to maintain a constant force between them; the amount by which the sample is moved gives a measure of the feature height. Thus the control signal that achieves force regulation also gives an image of sample topography. One of our main finding in the course of this project is a design scheme that separates the regulation and the sample-topography estimation. In this scheme, design for estimation of sample topography (feature height) is independent of the design for regulation of tip-sample interaction force. The force regulation objective is achieved through an appropriate design without giving any regard for the estimation objective. Also, for any linear design scheme, our design for estimation achieves the maximum estimation bandwidth (through our model matching formulation) for a given controller for regulation. Thus improvements in the regulation design for larger disturbance rejection bandwidths (better robustness) lead to larger (and the maximum possible bandwidths through linear designs) estimation bandwidth. For regulation designs, PID-based methods are most commonly used. Our recent efforts using H∞ synthesis design methods did give about 20% improvement in the bandwidth over the PID designs (exhaustively searched over the parameter space); however these improvements are restricted since the linearization errors are large which limit the disturbance-rejection bandwidth of any linear robust control design. In many AFM imaging, especially in soft sample applications, dynamic-mode imaging is used where the cantilever is oscillated and the changes in the cantilever oscillations (typically changes in oscillation amplitude or phase) are used for imaging. Our another achievement from this project is a new dynamic mode of operation in the AFM where the deflection signal is used for force regulation in the place of its derivatives such as the amplitude and phase. This mode is especially useful in AFMs with high speed positioning systems with bandwidths of the order of ≈ 1/10 times the natural frequency of the scanning probe. In the presence of high speed positioning systems, methods that enforce amplitude regulation do not provide reliable results. We have formulated this model based force regulation problem in an optimal control setting and employed multi-objective optimization techniques to design the regulating controller. Furthermore, we have a design to estimate the tip-sample interaction forces and extract the sample topography information from this estimate. The overall scheme facilitates high-speed imaging that can potentially exploit fast scanning devices without compromising on the bandwidth and resolution. Simulation results show a regulation bandwidth of 10−15% of the natural frequency of the probe and also good estimation of the tip sample interaction forces. In depth simulation results confirm this methodology. We are currently in the process of developing a FPGA based hardware module, which can handle high-speed data acquisition rates, to implement our design on an MFP-3D AFM. A proof of concept was demonstrated on a cantilever (resonant freq 8kHz); electronic components as well as fast positioning systems are being developed to adopt this methodology for fast (resonant freq >100 kHz) cantilevers. The project outcomes are applicable to the industry and is expected to foster transfer of the theory and technology developed in this program between the academic institution of the PI and the SPM industry. I was invited to present these results in a workshop coorganized by the IBM-Zurich. I presented a talk titled "Research Workshop on Dynamics and Control of Micro and Nanoscale Systems" at this workshop held at the University of Newcastle in Australia (Feb 2012), where experts from all over the world were invited to discuss on the upcoming trends and control tools in micro/nanoscales systems. The results developed in this proposal required Methods from dynamic systems and control theory, control applications, and instrumentation technology. The graduate students involved were trained in a unique interdisciplinary manner that exposed them to the diverse set of expertise . They were trained both in the theoretical and experimental aspects. They attended workshops (NSF sponsored and others) where they interacted with people from industry as well as academia. The work in this proposal resulted in a Ph. D. thesis.
