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DYNAMIC MODELING CONTROL AND MANIPULATION AT THE NANOSCALE

# DMCMN: In Depth Characterization and Control of AFM Cantilevers With Integrated Sensing and Actuation

[+] Author and Article Information
Georg E. Fantner1 n2

Department of Materials Science, Massachusetts Institute of Technology, Cambridge, MA 02139fantner@mit.edu

Daniel J. Burns2

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139danburns@mit.edu

Angela M. Belcher

Department of Materials Science and Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139belcher@mit.edu

Ivo W. Rangelow

Department of Micro-Nanoelectronical Systems, Technical University Ilmenau, Ilmenau 98693, Germanyivo.rangelow@tu-ilmenau.de

Kamal Youcef-Toumi

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139youcef@mit.edu

We want to point out that these reductions in instrument size are possible with these technologies. For the purpose of this paper, we use an instrument capable of both conventional (laser) detection and piezo actuation to conduct accurate performance comparison. Our system is therefore not smaller nor more automated than a regular AFM system.

It should be noted here that the optical deflection sensitivity depends strongly on the alignment of the laser on the cantilever. Therefore, the optical deflection sensitivity will be somewhat different each time the laser is readjusted on the cantilever before imaging.

The large variations in the phase at frequencies not close to the resonances are due to the fact that the amplitude at those frequencies is below the noise floor.

The absolute value of the gain in this simulation does not describe the direct coupling in the actual device because in the simulation we did not take the gain from heater-bimorph-cantilever into account. A crosstalk gain is therefore physically possible.

The purpose of this system identification effort is to characterize the cantilever response in the frequency band over which mean deflection will track topographic changes, see Eq. 1, and not to characterize the resonance behavior. Measurements of the resonance modes are provided in Figs.  56.

The mean cantilever deflection $D=⟨d⟩$, changes with applied voltage $Vb$, but because the sample is retracted and piezo extension does not influence the cantilever $(z=0)$, the transfer function to $δ$ is obtained (see Fig. 1).

We use a calibration grating to have a standardized sample to compare the performance with other measurements. However a sample with smaller topography might show more differences in the behavior using the different actuation and sensing schemes.

1

Corresponding author.

2

GEF and DJB contributed equally to this manuscript.

J. Dyn. Sys., Meas., Control 131(6), 061104 (Nov 06, 2009) (13 pages) doi:10.1115/1.4000378 History: Received June 22, 2008; Revised June 27, 2009; Published November 06, 2009; Online November 06, 2009

## Abstract

New developments in MEMS (microelectromechanical systems) fabrication allowed the development of new types of atomic force microscopy (AFM) sensor with integrated readout circuit and actuator built in on the cantilever. Such a fully instrumented cantilever allows a much more direct measurement and actuation of the cantilever motion and interaction with the sample. This technology is expected to not only allow for high speed imaging but also the miniaturization of AFMs. Based on the complexity of these integrated MEMS devices, a thorough understanding of their behavior and a specialized controls approach is needed to make the most use out of this new technology. In this paper we investigate the intrinsic properties of such MEMS cantilevers and develop a combined approach for sensing and control, optimized for high speed detection and actuation. Further developments based on the results presented in this paper will help to expand the use of atomic force microscopy to a broad range of everyday applications in industrial process control and clinical diagnostics.

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## Figures

Figure 1

AFM images of E. coli in tapping mode in air. (a) and (b) are amplitude images. (c) and (d) are phase images for better clarity of the finer features on the cell surface.

Figure 2

AFM setup for detection and actuation of instrumented cantilever.

Figure 3

Contact mode approach curves (a) deflection readout with optical lever deflection. (b) Deflection readout with sensing resistor. The gain of the sensor resistor readout electronics is adjusted to roughly match the deflection sensitivity of the optical lever detection. The graphs are drawn such that the curves have equal height to allow better comparison of curve shape and noise levels.

Figure 4

Low frequency behavior of cantilever actuator. (a) Deflection of the cantilever for a given applied dc-voltage. (b) Step-response of heater actuation with laser readout.

Figure 5

Sinusoidal frequency sweep over the first two resonant modes. Excitation with microheater, readout with optical lever detection.

Figure 6

Swept sine wave tuning curves of active cantilever using optical deflection readout, sensing resistor readout, tapping piezo actuation and heater actuation: (a) optical lever detection and tapping piezo actuation (classical AFM setup), (b) optical lever detection and heater actuation, (c) sensing resistor readout and tapping piezo actuation, and (d) sensing resistor readout and heater actuation.

Figure 7

Connection of thermal actuator and sensing resistor with description of crosstalk between heating signal and resistor sensing signal.

Figure 8

Swept sine wave tuning curves of active cantilever using the sensing resistor readout, and heater actuation as modeled with the LABVIEW simulation interface toolkit. The individual traces represent different values of gain for the cross-coupling. Left: amplitude, right: phase. The same simulations at gain 30 and 40 show qualitatively the same behavior as in Fig. 6.

Figure 9

Influence of dc-offset on ac behavior: (a) Frequency sweep of cantilever measured with laser and driven by thermal actuator at different drive amplitudes (100 mV, 200 mV, 400 mV, 800 mV, 1600 mV, and 3200 mV). (b) Tapping mode deflection as function of dc-offset. The dc-offset is linearly ramped from −10 V to +10 V and the mean value of the oscillating cantilever is measured. (Insert is zoom in around zero dc-voltage). (c) RMS amplitude of oscillating cantilever as function of dc-offset. (d) Phase of cantilever oscillation as function of dc-offset. (Insert shows flat region between 6 V and 10 V).

Figure 10

Influence of dc-offset on ac behavior when driven at half the resonance frequency: (a) time domain signals—upper trace is excitation and lower trace is response, (b) tapping mode deflection as function of dc-offset—the dc-offset is linearly ramped from −10 V to +10 V and the mean value of the oscillating cantilever is measured, (c) tapping amplitude as function of dc-voltage, and (d) tapping phase as a function of dc-voltage.

Figure 11

Frequency response of the thermally driven cantilever with and without compensation. Deflection is measured with the AFM laser and photodiode. Compensation provides a flat frequency response up to 10 kHz.

Figure 12

Block diagram describing the relationship between all the components

Figure 13

Image quality dependent on sensor/actuator combination. (a) sensor: laser, actuator: mechanical (standard AFM configuration, amplitude setpoint is 360 mV). (b) sensor: laser, actuator: thermal (amplitude setpoint is 96 mV). (c) sensor: resistor, actuator: mechanical (amplitude setpoint is 156 mV). (d) sensor: resistor, actuator: thermal (amplitude setpoint is 56.6 mV).The tapping frequency for this cantilever was 56.8 kHz.

Figure 14

Quality of AFM image in tapping mode at different scan speeds. (a) 9.8 Hz linerate, (b) 19.5 Hz linerate, (c) 25 Hz linerate, and (d) 78 Hz linerate. For this measurement, we have used the bridge resistor for detection and the regular piezo scanner for feedback. The cantilever was excited using inertial drive at 57 kHz with an amplitude setpoint of 600 mV.

Figure 15

Scan lines taken during imaging demonstrate increased stability of the thermal actuator under compensation. For the same imaging parameters (controller gains, scan speed, etc.) the frequency of parasitic oscillation is increased from 175 Hz to 524 Hz and the amplitude is dramatically reduced, indicating better closed-loop stability margins. Inset: AFM image from which the scan lines are taken.

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