2666 IEEE SENSORS JOURNAL, VOL. 12, NO. 8, AUGUST 2012

Deflection Sensitivity Calibration of HeatedMicrocantilevers Using Pseudo-Gratings

Jungchul Lee∗, Bong Jae Lee, and William P. King

Abstract— We report a technique to calibrate the sensitivityof sensor-integrated atomic force microscope cantilevers usingpseudo-gratings. An offset signal superposed onto the cantilevercontrol signal modulates the cantilever position over a flatsurface, driving the cantilever toward and away from thesurface in a controlled way. The relationship between thecantilever sensor signal and displacement provides the cantilevercalibration. We show how this technique can be used to calibrateheated microcantilever sensors.

Index Terms— Atomic force microscopy, calibration, deflectionsensitivity, heated microcantilever.

I. INTRODUCTION

THE ATOMIC force microscope (AFM) is the mostwidely used instrument for measuring nanometer-scale

phenomena [1]. The most common AFM apparatus usesa laser and a position sensitive photodetector (PSPD) todetect cantilever deflections. Other approaches for measuringcantilever deflection include piezoresistive [2], [3] or thermalsensing [3], [4]. Regardless of the transduction mechanism,it is necessary to calibrate the deflection sensitivity of amicrocantilever before it is used for a measurement. The keyadvantage of cantilevers with integrated deflection sensorsis that they can operate without a laser-based deflectionmeasurement. This advantage is diminished when the lasermust be used for calibration. Thus there is a need fornon-optical calibration techniques.

This letter introduces a technique to calibrate deflectionsensitivity of heated microcantilevers using deflections that arecontrolled through the feedback loop of the AFM system.

II. EXPERIMENT

Fig. 1(a) shows the experimental setup. The setupincludes an AFM system, a Wheatstone bridge, a differentialamplifier, and a low pass filter. The microcantilever has an

Manuscript received February 2, 2012; accepted May 14, 2012. Date ofpublication May 24, 2012; date of current version June 13, 2012. Thiswork was supported in part by the National Research Foundation Grantfunded by the Korean Government NRF-2011-220-D00014 and the SogangUniversity Research Grant of 2010 (201010087.01). The associate editorcoordinating the review of this paper and approving it for publication wasProf. Bernhard Jakoby. Asterisk indicates corresponding author.∗J. Lee is with the Department of Mechanical Engineering, SogangUniversity, Seoul 121-742, South Korea (e-mail: jayclee@sogang.ac.kr).

B. J. Lee is with the Department of Mechanical Engineering, KoreaAdvanced Institute of Science and Technology, Daejeon 305-701, South Korea(e-mail: bongjae.lee@kaist.ac.kr).

W. P. King is with the Department of Mechanical Science and Engineering,University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (e-mail:wpk@illinois.edu).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2012.2200971

Fig. 1. (a) Schematic for the deflection sensitivity calibration of functionalmicrocantilevers using the pseudo-grating concept. (b) Experimental setup.Amplified and filtered signals are fed into a commercial AFM control andrecorded in PC.

integrated resistive heater-thermometer [5]. All resistors in thecircuit including the heated microcantilever are about 2 k�.The Wheatstone bridge output is nulled out upon initial contactof the heated microcantilever to a flat substrate. An offsetsignal determines the initial contact position and contact force.Once the X–Y scan starts, a voltage drive signal is superposedinto the control loop, moving the Z scanner up and down.In this way, the cantilever deflection is modulated as it wouldbe if moving over a grating, hence the name pseudo-grating.The cantilever thermal signal varies with the deflection [3]–[6].We set the gain of 10 in the differential amplifier stage andgain of additional 3.16 in the low pass filter stage (Fig. 1(b)).The thermal signal from the heated microcantilever isamplified and recorded.

Fig. 2 shows a block diagram of the pseudo-grating tech-nique, a function generator drive signal and the correspondingpseudo-gratings. The feedback integral gain (KI ) is muchgreater than the proportional gain (K P) and thus the shape ofthe pseudo-gratings is the integral of drive signal. In our exper-iments, a square drive signal produces a triangular pseudo-grating, where KI varies between 80 and 200, and K P = 0. AsKI decreases, the amplitude of the pseudo-grating decreases.For example, the peak to peak amplitude becomes 0.50 μmwith KI = 80 and K P = 0. The scan size is 5 μm and the scan

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LEE et al.: DEFLECTION SENSITIVITY CALIBRATION OF HEATED MICROCANTILEVERS USING PSEUDO-GRATINGS 2667

Fig. 2. (a) Block diagram for the pseudo-grating technique. (b) Functiongenerator drive signals and corresponding pseudo-gratings. (c) Triangu-lar pseudo-gratings generated using square wave drives from the functiongenerator have a peak to peak amplitude of 2.28 μm and a pitch of 1.12 μm.

(a)

(b)

Fig. 3. (a) Substrate-dependent thermal signal as a function of verticaldeflection. (b) Sensitivity as a function of the triangular pseudo-gratingamplitude for glass and silicon substrates.

rate is fixed at 0.25 Hz. Because this frequency modulationis well below the thermal cut-off of the heated cantilever,thermal signals were relatively insensitive to frequency.

We calibrated the cantilever for 5 different deflectionamplitudes on two different substrates. With KI = 200, thepeak to peak deflection is 2.279 ± 0.015 μm when thebridge bias is 4V DC. The deflection sensitivity of the heatedcantilever is 14.3 mV/μm for the glass substrate and24.4 mV/μm for the silicon substrate. With the springconstant calibration (k = 0.92 N/m), the force sensitivity is15.5 mV/μN for the glass substrate and 26.5 mV/μN for thesilicon substrate.

Fig. 3(a) shows substrate-dependent thermal signal as afunction of vertical deflection. The thermal signal on glassis nearly symmetric while the thermal signal on siliconis asymmetric and concave. The difference is due to the

higher in-plane temperature gradient in the silicon substratecompared to the glass substrate. Fig. 3(b) shows the peakto peak deflection sensitivity as a function of the grat-ing amplitude varying from 0.5 to 2.0 μm. As the ampli-tude increases, the deflection sensitivity for glass substratedecreases, while that for silicon substrate increases, whichis expected from the substrate-dependent thermal signals ofFig. 3(a).

The substrate-dependent deflection sensitivity of the heatedcantilever can be attributed to the difference in substratethermal conductivities. During deflection, the thermal signalchanges as the average air gap between the cantilever andthe substrate changes [3]–[6]. While the thermal conductivityof the glass is about 100X less than that of the silicon, themeasured deflection sensitivity on the glass substrate is onlyabout 40 % lower than that on the silicon substrate. This resultis expected from previous publications [3], [4]. The cantileverthermal conductance depends upon the distance between thecantilever and the substrate, the thermal conductivity of thesurrounding medium (air), and the thermal conductivity of thesubstrate. The heat flux to the silicon substrate is expectedto be about 5X larger than that to the glass substrate. Theheated region in the silicon substrate is about 10X larger thanthat in the glass. Taken together, we expect the sensitivity tobe approximately 2X larger in the for the silicon substratecompared to the glass substrate, which is consistent with themeasured result.

III. CONCLUSION

We have demonstrated a calibration technique for thedeflection sensitivity of heated microcantilevers by introducingartificial periodic patterns on flat substrates. With the pseudo-grating amplitude of 2.28 μm, the deflection sensitivity of theheated cantilever was 14.3 mV/μm for the glass substrate and24.4 mV/μm for the silicon substrate. The technique couldbe further applied to any functional microcantilever, such aspieozoresistive or piezoelectric cantilevers.

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[3] J. Lee and W. P. King, “Improved all-silicon microcantilever heaters withintegrated piezoresistive sensing,” J. Microelectromech. Syst., vol. 17,no. 2, pp. 432–445, Apr. 2008.

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[5] J. Lee, T. Beechem, T. L. Wright, B. A. Nelson, S. Graham, and W.P. King, “Electrical, thermal, and mechanical characterization of siliconmicrocantilever heaters,” J. Microelectromech. Syst., vol. 15, no. 6, pp.1644–1655, Dec. 2006.

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