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TECHNICAL PAPERS

Design and Control of Optimal Scan Trajectories: Scanning Tunneling Microscope Example

[+] Author and Article Information
Hector Perez, Qingze Zou, Santosh Devasia

Department of Mechanical Engineering, Box 352600, University of Washington, Seattle, WA, 98195

J. Dyn. Sys., Meas., Control 126(1), 187-197 (Apr 12, 2004) (11 pages) doi:10.1115/1.1636770 History: Received March 12, 2002; Revised May 12, 2003; Online April 12, 2004
Copyright © 2004 by ASME
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Figures

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Scan trajectory consisting two parts: Tracking (active-scan) section (t0<t<ti); and the transition (retrace) section (ti≤t≤tf). The desired output trajectory is pre-specified in the active-scan section; it is not pre-specified during the retrace section.
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STM scanner scheme (plot (a)) and scan trajectory (plot (b)); figures are not to scale.
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System consisting of Prefilter and STM scanner.
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Inputs obtained in simulation for Case I with Ttran=Ttrack=5 ms (left column) and case II (right column) with Ttrack=5 ms,Ttran=2 ms, using three approaches: (i) the polynomial trajectory with the DC-gain approach (plot (a1) and (a2)), (ii) the polynomial trajectory with the inversion-based approach (plot (b1) and (b2)), (iii) the optimal scan-trajectory approach (plot (c1) and (c2)), where u (solid line) is the input before the pre-filter, and u⁁ (dashed line) is the input after pre-filter (see Figure 3).
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Simulation results of the output tracking using DC-gain approach for Case I with Ttran=Ttrack=5 ms (plot (a)) and case II with Ttrack=5 ms,Ttran=2 ms (plot (b)).
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Experimental results, images of graphite surface: For Case I (K=1, left column), and case II (K=0.4, right column), the images were acquired using inputs found from the three approaches: (i) the polynomial trajectory with the DC-gain approach (plots (a1) and (a2)); (ii) the polynomial trajectory with the inversion-based approach (plots (b1) and (b2)); and (iii) the optimal scan-trajectory approach (plots (c1) and (c2)).
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Experimental STM image of graphite acquired using polynomial trajectory with inversion-based approach for K=1 (plot (a)), and the plot of the connected atom centers (plot (b)) for the image shown on the left. In plot (b), the atom-spacing where the maximum error occurred (δmax) is indicated as the thick line between two atoms.
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Simulation results: optimal scanning cost Jtran* for different K: Transition Time/Tracking Time, where Tracking time is fixed to be 5 ms.

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