906 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 5, SEPTEMBER 2007 Design and Modeling of a High-Speed AFM-Scanner Georg Schitter, Member, IEEE, Karl J. Åström, Fellow, IEEE, Barry E. DeMartini, Member, IEEE, Philipp J. Thurner, Kimberly L. Turner, and Paul K. Hansma Abstract—A new mechanical scanner design for a high-speed atomic force microscope (AFM) is presented and discussed in terms of modeling and control. The positioning range of this scanner is 13 m in the - and -directions and 4.3 m in the vertical direction. The lowest resonance frequency of this scanner is above 22 kHz. This paper is focused on the vertical direction of the scanner, being the crucial axis of motion with the highest precision and bandwidth requirements for gentle imaging with the AFM. A second- and a fourth–order mathematical model of the scanner are derived that allow new insights into important design parameters. Proportional–integral (PI)-feedback control of the high-speed scanner is discussed and the performance of the new AFM is demonstrated by imaging a calibration grating and a biological sample at 8 frames/s. Index Terms—Atomic force microscopy, fast scanning, mecha- tronics, nanotechnology, precision positioning, real time imaging. I. INTRODUCTION T HE ATOMIC force microscope (AFM) [1] is a very im- portant instrument for exploring materials at the scale of a few nanometers [2]. The principle of the AFM is to raster scan a sample in close vicinity to a probing tip that is mounted on the free end of a micromechanical cantilever. The deflection of this cantilever can be measured with subnanometer precision [3]. A feedback controller tracks the probing force by varying the po- sition of the sample in the vertical direction. Thus, the output of the feedback controller corresponds to the height of the top- ographical feature on the corresponding lateral position in the plane of the raster scan. To avoid damages to the sample or the tip, it is desirable to use a small force, particularly when imaging biological specimens. A high-performance feedback controller is required in order to minimize variations of the imaging force Manuscript received February 27, 2006; revised October 31, 2006. Manu- script received in final form February 5, 2007. Recommended by Guest Ed- itor E. Eleftheriou. This work was supported in part by the National Science Foundation through the UCSB Materials Research Laboratory under Award DMR00-80034 and Award NSF SST ECS04-28916, by the National Institutes of Health under Award RO1 GM 065354-05, by the NASA University Research, Engineering, and Technology Institute on Bio-inspired Materials under Award NCC-1-02037, by a research agreement with Veeco #SB030071, by the SNF Project PA002-108933, and the SNF Project PA002-111445. G. Schitter is with Delft University of Technology, Delft Center for Systems and Control, 2628 CD, Delft, The Netherlands (e-mail: g.schitter@tudelft.nl) K. J. Åström, B. E. DeMartini, and K. L. Turner are with the Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106 USA (e-mail: astrom@engineering.ucsb.edu; baredog@umail.ucsb.edu; turner@engineering.ucsb.edu). P. J. Thurner and P. K. Hansma are with the Department of Physics, Uni- versity of California, Santa Barbara, CA 93106 USA (e-mail: thurner@physics. ucsb.edu; prasant@physics.ucsb.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2007.902953 and to avoid loss of the tip sample contact due to a decline in the sample surface. The scanning speed of current AFM systems is limited due to the dynamic behavior of the individual microscope compo- nents. The main limitations are 1) the response time of the force sensor [4], 2) the dynamic behavior of the scanning unit [5], [6], 3) the bandwidth of the feedback loop that controls the interac- tion force between the tip and the sample [7], and 4) the speed of the data acquisition system [8], [9]. Some efforts have been made to speed up imaging by using smaller and faster force sen- sors [10], [11] and directly actuated cantilevers [12], [13], by improving the mechanical design of the scanner [14]–[16], by exploiting alternative scanning methods [17], and by utilizing advanced control methods for faster scanning [5], [6], [18]–[22] and faster vertical motion [7], [23], [24]. Parallel operation of several AFM probes has also been successfully implemented [25], [26]. In spite of all previous advances there are still needs and pos- sibilities to improve system performance, particulary in the ver- tical ( ) direction, which is the control task with the highest requirements on bandwidth and precision. From a control engineering point of view, the sample topog- raphy acts as a disturbance to the AFM in -direction, that has to be compensated by the feedback controller [23]. For AFM imaging usually no oscillations in the control action and in the cantilever deflection are required to keep image distortion at a minimum. This is achieved by setting the control bandwidth suf- ficiently low, which contradicts with the requirement of a high bandwidth for gentle imaging. However, recent developments reported methods that enable faster imaging without distortions by utilizing advanced control techniques [7], [27]. The oscilla- tory modes of the AFM system are compensated by the con- troller and the undistorted topography information is then ob- tained by model-based filtering of the high-bandwidth control action. This paper presents a new mechanical scanner design that al- lows scanning speeds that are more than two orders of mag- nitude faster than current commercial AFM systems. The goal is to develop a high-performance system by combined process and control design. We analyze the vertical motion of the new scanner, where the motivation is to gain detailed insights into the system dynamics and to understand how process design in- fluences the control design. Section II presents the mechan- ical design of the new scanner. A mathematical model of the scanner based on first principles is derived in Section III and ex- perimentally verified in Section IV. Feedback operation of the high-speed AFM is discussed (see Section V) and the perfor- mance of the new AFM is demonstrated by imaging a biological sample. 1063-6536/$25.00 © 2007 IEEE