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Optics and Lasers in Engineering 47 (2009) 217– 222

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Optics and Lasers in Engineering

0143-81

doi:10.1

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journal homepage: www.elsevier.com/locate/optlaseng

Interferometric profiling of microcantilevers in liquid

Jason Reed a,c, Joanna Schmit b,�, Sen Han b, Paul Wilkinson a, J.K. Gimzewski a,c

a Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA 90095, USAb Veeco Instruments, Inc., 2650 E. Elvira RD, Tucson, AZ 85706, USAc California Nanosystems Institute (CNSI) 570 Westwood Plaza, Los Angeles, CA 90095, USA

a r t i c l e i n f o

Available online 9 June 2008

Keywords:

Interferometric microscope

Optical profiler

Biosensor

Microcantilever

Liquid environment

66/$ - see front matter & 2008 Elsevier Ltd. A

016/j.optlaseng.2008.04.024

esponding author.

ail address: JSCHMIT@veeco.com (J. Schmit).

a b s t r a c t

Silicon micro cantilevers are used as highly sensitive transducers for a wide range of physical, chemical

and biochemical stimuli. Vibrating the cantilevers at higher-order resonant modes can achieve extra

sensitivity, but the difficulty lies in determining exactly which modes are excited in the cantilever. This

problem is exacerbated for cantilever sensors operating in liquid where the computational analysis of

the resonance modes is very challenging. Using strobed interferometric microscopy, we are able to

image the dynamic behavior of individual (100�500�1 mm3) cantilevers in an eight cantilever array

over frequencies from 0–1 MHz. We show how some modifications to the interferometric microscope

allow for the spatial visualization of 16 longitudinal modes of cantilevers working in liquid with

nanometer-scale amplitudes. We also compare the shift in frequency response and reduction in quality

factor for cantilevers resonating in liquid versus in air and simulations in vacuum. Because the resonant

frequency spectrum is fairly complex and does not follow simple intuition, our work maps the actual

behavior of cantilevers without having any specific knowledge of the sample and environment

parameters and without the necessity of involved simulations and calculations.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Silicon cantilever structures (MEMS cantilevers) were firstused to transduce local forces in the atomic force microscope [1]through their static bending properties; very precise measure-ments of surface topography as well as other material propertieswere achieved. The transduction of the cantilever motion typicallyuses a single point detection method such as optical deflection, aninterferometer or an electrical means such as piezoresistorsintegrated on the cantilever surface.

These delicate micromechanical cantilever structures have alsoproven to be extremely precise free-standing sensors of a varietyof properties with a sensitivity that far exceeds conventionalmethods [2]. Properties these structures have measured includeheat, mass changes, surface stress, nuclear spins and a singleelectron spin [3–8]. In addition to static bending, the dynamic orresonant properties of cantilever sensors can be used to translatepractically any physical signal domain into mechanical motionwith higher sensitivity.

The cantilever’s surface can also be coated with a material thatselectively adsorbs or binds to a given target substance. In thisway the cantilever can be converted into a selective chemical orbiochemical sensor. When the cantilever comes in contact with

ll rights reserved.

the target substance, it generates a mechanical response; eitherthe cantilever bends or changes its resonance frequency. Bothsignals can be measured with extremely high accuracy, allowingfor identification and quantitative detection of the targetsubstance or its concentration.

Typically, for these purposes cantilevers are placed in cham-bers with vacuum, gas or liquid. Sensing in liquids is one of theprimary applications of MEMS-based bio/chemical transducers.Microcantilevers used as sensors in biochemistry, genomics andproteomics must by necessity operate in aqueous saline solution(salt water), and many other organic and inorganic chemicalsensing of dissolved heavy metals or organic toxins requireoperating in water. In addition, using arrays of cantilevers [9]functionalized differently made it possible to specifically dis-criminate different chemical [10] and biochemical bindingprocesses. Other MEMS devices have also begun to be packagedin liquid chambers but for different reasons. For example, MEMStunable capacitors are placed in liquids in order to improve theirperformance by reducing mechanical ringing and sensitivity tovibrations.

Extra sensitivity of cantilever sensors can be achieved by theuse of higher-order harmonics created at high-frequency reso-nances [11–16]; the difficulty lies in determining exactly whichmodes are excited in the cantilever. At higher-order harmonicswhere the standing wave approaches the dimension of thecantilever width, one can expect that two-dimensional (2D)modes will also be excited in addition to linear modes [17–19].

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We previously used stroboscopic full field interferometricprofiling to detail the higher resonance modes of an eightmicrocantilever sensor array in air [20]. We found that thefrequencies and shapes of the modes in air corresponded well tothe prediction of a finite element simulation and some observeddiscrepancies were shown to be related to differences incantilevers thickness. In liquid, however, simulation of micro-cantilever structure dynamics becomes very challenging, madeeven more so by complicated MEMS structures. Thus, experi-mental characterization of modes in liquid is necessary. Themeasurement of cantilevers in liquid requires specific modifica-tions to the interferometric microscope detection system.

This paper describes how interferometric techniquesand system modification provide viable measurements of micro-cantilever MEMS structures’ dynamic behavior in liquid.We present experimental data of 16 modes of cantileversvibrating in water. This specific cantilever geometry was the basisof a number of previously published reports, where the cantileverarray was used for a variety of sensing purposes [21,22]. Our dataare compared with finite element calculations of cantilevervacuum modes. We describe our findings made in visualizingthe modes.

2. Imaging microcantilevers in liquid with interferometricprofiler

Interferometric profilers have been widely employed in thesemiconductor, data storage, and MEMS industries for more thantwo decades. These systems produce rapid, accurate, andrepeatable characterizations of surface roughness, form and filmthickness. Recently these profilers have been adapted to capturethe dynamic behavior of MEMS, even through protective coversand in liquids.

The measurement of the dynamic modes of cantilevers inliquid was performed on the Veeco interference microscopeDMEMS 1100 with a red LED (light emitting diode) (644 and18 nm bandpass) used for stroboscopic illumination and 5�0.13numerical aperture special TTM (through transmissive media)Michelson objective (Fig. 1). The DMEMS uses an interferenceobjective that allows for the observation of not only lateralfeatures with typical optical resolution but also height dimensionsbelow the scale of 1 nm [23].

The height profile is obtained by scanning the objective in thez-axis and analyzing the interference at each pixel. Interferencemay be achieved with a wide spectral band light source such as a

Fig. 1. Schematics of optical profiler for measurement of vibrating cantilevers in

liquid chamber.

halogen lamp or a white LED or with quasi-monochromaticillumination filtered from the white light source or directly from acolor LED. Different white light or phase-shifting interferometry(PSI) algorithms may be applied when appropriate. Objects withsteps as small as 1 nm and as big as a few mm can easily bemeasured. Fields of view from tens of microns to a fewmillimeters square can be observed.

2.1. Dynamic motion measurement

Determining the shape of the cantilevers that are vibrating at agiven frequency entails modifying the interference microscopedescribed above, because the vibration washes out the inter-ference pattern making measurement impossible [19,24]. Thecrux of the modification lies in freezing the motion of the object soas to observe a static interference pattern; this freezing isachieved by strobing the illumination in sync with the piezo-electric transducer driving the cantilevers. Under these conditionsthe motion appears to be frozen at a given position of thecantilever’s periodic motion. The motion of the cantil-ever thorough its complete cycle is recorded by applying a seriesof offsets in the phase between the driving and strobing signals(Fig. 2).

The maximum measurable vibrational frequency dependsmainly on the rise and fall times of the LED pulses, which areon the order of a few hundreds to a few tens of nanoseconds,allowing for the measurement of maximum frequencies from afraction to a few MHz. In addition, the detected signal has to bestrong enough to analyze. Signal strength depends on the sourceitself, camera sensitivity, reflectivities of the sample and thereference mirror, and also on magnification used.

2.2. Measurement through transmissive media (TTM)

Because MEMS devices are often covered in protective glass,testing has to occur through the glass. Optical, non-contactmethods are well suited for this kind of test with some systemmodifications [25]. First, an interference objective with a longerworking distance was developed so as to accommodate the beam-splitter and cover glass of the objective. In addition, becauseaberrations are introduced into the system by the beam-splitterand cover glass, the objective has to be compensated for in orderto obtain good quality images. For this task we use an industrialtype of objective with compensation for certain glass thicknesses.In cases where the total thickness of the glass exceeds thethickness for which typical objectives are compensated for, apellicle as a beam-splitter in the Michelson interferometer set-upis used so that objects can be tested through these thicker glassplates. Finally, the interference objective requires the insertion ofan almost identical glass plate into the reference arm ofinterferometer to compensate for dispersion. Otherwise theinterferometer is imbalanced and fringe quality may be poor.

Fig. 2. Relative signals for strobing the light, driving the sample motion and data

collection by detector with time.

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Fig. 3. TTM objective (middle) and fringes for pitch standard as observed in air

through a 3 mm cover glass using a standard and TTM objective of magnification

20� and numerical aperture 0.28.

J. Reed et al. / Optics and Lasers in Engineering 47 (2009) 217–222 219

Fig. 3 shows fringes for a pitch standard as observed in air througha 3 mm cover glass using a standard and TTM objective ofmagnification 20� and numerical aperture 0.28, respectively.

The visibility of fringes in an imbalanced interfero-meter depends on the spectral bandwidth of the source andthe numerical aperture of the objective. Compensation fordispersion does not have to be perfect if the spectral bandwidthand numerical aperture are sufficiently narrow. For an NA ¼0.13 and 40 nm bandpass filter the typical difference in glassplate thickness can be tens of microns. For objectives with highernumerical apertures so as to reduce the influence of the NAon fringe quality, the illumination can be delivered from theside underneath the objective and not through the objective.Illumination delivered in this way reduces the illuminating NA,while the imaging NA remains that of the objective as shown inFig. 3. With this technique the fringe visibility is greatly improvedso that the TTM objective performs at the same level as a standardobjective.

Fig. 4. Cantilever array used in measurement.

2.3. Measurements in liquid

The measurement of dynamic MEMS structures in liquidrequires further modification to the interferometric setup. Insteadof a compensating glass plate in TTM interference objective, acompensating fluid cell is inserted into the setup. The fluid cell is0.7 mm thick and bounded on both sides by 0.5 mm opticalwindows. This cell matches the optical path length of the reflectedbeam from the fluid test chamber, which is covered by a 1 mmoptical window. Fluid fully fills the chamber, so that no air gapbetween the fluid and cover glass exists, which eliminates thepossibility of the fluid surface varying during cantilever motion.We used a 5�0.13 NA objective with red LED of 18 nm bandpass.Having a quasi-monochromatic source with some bandpass, whileallowing more light into the system, prevents the creation ofspeckles that would introduce noise into the measurement. Thecompensating plate prevents fringe degradation. Because canti-levers are smooth and without discontinuities, a PSI mode wasused for the measurement.

Since cantilevers work in liquid the index of refraction for theilluminating wavelength needs to be taken into account for thesurface topography measurement. Because it is a phase measure-ment with quasi-monochromatic illumination, the result needs tobe corrected by a phase index of refraction of the environment. Forwater this index of refraction equals 1.33 [26]. If the index ofrefraction of liquid is not known, a standard or well-knownsample can be measured and the ratio of the height measured inliquid versus air will deliver information about the scaling factorthat needs to be used, and thus the index of refraction.

2.4. Cantilevers

Eight silicon cantilevers were vibrating in liquid. They werearranged in an array on a silicon base, each of which is 500 mmlong by 100 mm wide and 0.9 mm thick, with a nominal springconstant of 0.02 N/m (Fig. 4). The cantilever pitch is 250mm, whichwas originally chosen to make optical communication arrays.

These commercially available arrays were produced by IBMZurich Research Laboratories using a proprietary dry etch, silicon-on-insulator (SOI) process. They were fabricated from /10 0Soriented wafers; so any horizontal face on the chip is oriented/10 0S. The cantilevers are extended in the /110S direction. Thecantilever array was firmly fixed to a cylindrical piezo with siliconadhesive paste. The piezo actuator was driven in the z-axis by asinusoidal signal (0–50 V; 0–150 nm) at the observation frequen-cies (0–1 MHz). The free cantilever versus the fixed base isautomatically recognized in the image and measured by SureVi-sion multiple region analysis software. SureVision employs a user-defined template as a reference, against which subsequentmeasurements of a similar sample (or the same sample underdynamic conditions) are compared [27]. The template ensuresthat analyses performed on the devices are all based on the samecorresponding regions.

3. Visualization of longitudinal modes in liquid versusvacuum

First, we recorded the response for the cantilever motion as afunction of frequency over the range 0–1 MHz by driving thecantilever array with a piezoelectric actuator with a motion ofapproximately 150 nm peak-to-peak (Fig. 5). The peaks areassigned to the longitudinal (L) resonance modes of a singlecantilever assignment discussed below. We have compared theseresonant frequencies to the simulations of resonant frequencies ofsuch geometry of cantilevers in vacuum. Our previous measure-ments of cantilevers in air well agreed with simulations invacuum. The amplitude in Fig. 5 is the modulus of thedeformation at phase 01 and 901. Thus, two data points weretaken at each frequency. This representation better depicts themaximum height of the resonant peaks, because it takes intoaccount the in- and out-of-phase components of the motion.

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Fig. 5. Cantilever amplitude motion as a function of frequency over the range

0–1 MHz by driving the cantilever array in air. The peaks are assigned to the

longitudinal (L) modes.

Fig. 6. 3D and cross-sectional profile of an individual cantilever excited at

755 kHz—14th longitudinal mode L.

Fig. 7. L1–L9 spatially resolved lateral modes from cantilever simulation in

vacuum and experimental measurement in liquid.

J. Reed et al. / Optics and Lasers in Engineering 47 (2009) 217–222220

Fig. 6 shows the 3D and cross-sectional profile of an individualcantilever excited at 755 kHz, which is the 14th longitudinalmode. The peak-to-valley amplitude of this mode is �100 nm.

Fig. 8. L10–L16 spatially resolved lateral modes from cantilever simulation in

vacuum and experimental measurement in liquid.

3.1. Modeling of cantilever in vacuum

The theoretical calculations of natural frequencies and modeshapes for the undamped free vibration of the cantilever in avacuum were performed using a finite element analysis (FEA)with the software package ABAQUS. A single cantilever of length500 mm, width 100mm, and thickness 0.9mm was modeled as anorthotropic elastic plate with mass density r ¼ 2.33 gm/cm3,Young’s modulus E11 ¼166 GPa, E12 ¼ 64 GPa, E44 ¼ 80 GPa,and Poisson’s ratio n ¼ 0.266, reflecting the material propertiesof the silicon crystal [28]. The plate is discretized into 1600uniformly sized 4-noded quadrilateral finite elements with a totalof 1717 nodes. Encastre-type boundary conditions are applied atthe base of the cantilever, constraining to zero all translationaland rotational degrees of freedom along that edge. The first 100modes were calculated using FEA.

3.2. Comparison of resonant modes from modeling in vacuum and

experiment in water

Figs. 7 and 8 show a comparison of the spatially resolvedlongitudinal resonances of a representative cantilever observed inwater (right column) and modes with the expected profiles in a

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vacuum determined from the FEA model (left column). Theamplitudes are normalized with height scale blue (lower) to red(higher).

We have observed that in water higher modes at frequencies423 and 527 kHz have some 2D components. It is expected thatwhen the standing wave approaches the dimension of thecantilever width a 2D mode can be excited in addition to linearmode [17–19]. These are ‘true’ resonances but cannot be classifiedas pure longitudinal or pure torsional, though for the purposes ofthis paper we are calling them longitudinal. The reason for 2Dcomponents may be also, for example, slight mechanical im-perfections of cantilever such as non-uniformity in dimension,mass, internal stresses, etc.

A plot of the frequencies of the longitudinal modes observed inwater versus the vacuum FEA simulation show a marked down-shift in the resonant frequencies in water (Fig. 9).

The corresponding modes in the vacuum vary from roughly6� higher frequency (modes L2–L5) to 3� higher frequency(modes L10–L16). The viscosity of the environment has clearly aninfluence on the vibrations of the cantilevers. In addition, the

Fig. 9. Frequencies of the longitudinal modes observed in water versus the

vacuum FEA.

Fig. 10. Cantilever amplitude motion as a function of frequency over the range 0–1 MHz

approximately 150 nm peak-to-peak. The peaks are assigned to the longitudinal (L) mo

resonant peaks of the microcantilever are broadened by thedamping effects of the viscous medium. The ratio of peak-width toamplitude is known as the Q or quality factor, and Q isproportional to mass sensitivity. Microcentilevers operating invacuum have very high Q-factors (b100), while in water theQ-factor can be dramatically reduced (o50). Fig. 10 shows, aspreviously measured by us, a frequency response with very high-quality factor of similar cantilevers but working in air, whosepeaks are indeed narrower than for cantilevers working in liquidas shown in Fig. 5. Interest in operating microcantilever sensors athigher resonant modes, particularly in viscous media, is partlydriven by the fact that in this environment the Q-factor can beincreased substantially at higher frequencies.

At higher frequencies, the resonant peaks become spacedcloser together, and can nearly overlap (see our previous paper[20]). In this case it can be difficult to select the appropriateresonance mode reliably, particularly in the case where the Q-factor is reduced. In addition, damping effects, time-varyingperturbations and slight mechanical imperfections (mass, internalstresses, etc.) can cause unstable frequency, amplitude and phasebehavior, which compromise sensor performance. This problembecomes exacerbated in MEMS structures of more complexgeometry than a cantilever.

4. Conclusion

We described modifications to an interferometric profilerthat enables the measurement of vibrations of MEMS elementsin liquid. Then we discussed the high-resolution, 3D dynamicbehavior of microcantilever MEMS structures in water, identicalto ones used for a variety of sensing applications. We obtainedinterferometric height profiles from selected longitudinalresonance modes L2–L16. We observed the down shift infrequency and degradation of Q-factor for cantilevers in liquidas compared to simulations for vacuum or measurements in air.We found that while the operation of the AFM and other resonantsensing devices at higher frequencies have some consider-able advantages, it is necessary to experimentally characterizethe nano-mechanical response of the system in detail. Theadvantage of the experiment over the simulation lies in theconvenience that the properties of the MEMS and environment donot need to be known to predict devices’ behavior and the result

by driving the cantilever array in air with a piezoelectric actuator with a motion of

des.

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of any deviations from the assumed parameters will be readilyvisible.

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