REVIEW ARTICLE Cantilever transducers as a platform for chemical and biological sensorscau.ac.kr/~jjang14/BioMEMS/Lavrik_Datskos_RSI_Cantilever... · 2006-03-23 · REVIEW ARTICLE

REVIEW ARTICLE

Cantilever transducers as a platform for chemical and biological sensorsNickolay V. LavrikOak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6141

Michael J. SepaniakUniversity of Tennessee, Knoxville, Tennessee 37996-1200

Panos G. Datskosa)

Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6141and University of Tennessee, Knoxville,Tennessee 37996-1200

~Received 24 November 2003; accepted 10 April 2004; published online 21 June 2004!

Since the late 1980s there have been spectacular developments in micromechanical ormicroelectro-mechanical~MEMS! systems which have enabled the exploration of transductionmodes that involve mechanical energy and are based primarily on mechanical phenomena. As aresult an innovative family of chemical and biological sensors has emerged. In this article, wediscuss sensors with transducers in a form of cantilevers. While MEMS represents a diverse familyof designs, devices with simple cantilever configurations are especially attractive as transducers forchemical and biological sensors. The review deals with four important aspects of cantilevertransducers:~i! operation principles and models;~ii ! microfabrication;~iii ! figures of merit; and~iv!applications of cantilever sensors. We also provide a brief analysis of historical predecessors of themodern cantilever sensors. ©2004 American Institute of Physics.@DOI: 10.1063/1.1763252#

I. INTRODUCTION

A. General definitions and concepts

Concepts of chemical sensors have been a subject ofextensive research efforts in recent decades. According toestablished definitions, a chemical sensor consists of a physi-cal transducer~i.e., a transducer of physical quantities intoconvenient output signals! and a chemically selective layer~see Fig. 1! so that measurable output signals can be pro-duced in response to chemical stimuli.1 Specific binding sitespresent in chemically selective layers provide affinity of tar-geted analytes to the sensor active area. Highly selective re-ceptor layers can be designed using concepts of molecularand biomolecular recognition@Fig. 1~B!#. It is often thephysical transducer that imposes both fundamental and prac-tical limitations on the figures of merit achievable with therespective class of chemical sensors. As a result, implemen-tation of a transduction principle or innovative transducerdesign is always a significant milestone in the area of chemi-cal sensors.

Until the late 1980s, the main fundamental transductionmodes used in chemical sensors could be categorized as2,3

~a! thermal, ~b! mass,~c! electrochemical, and~d! optical.Each of these detection modes is associated with featuresthat are complementary rather than competitive with respectto the other, and a search of an ‘‘ideal transducer’’ has con-

tinued. During the last two decades, advances in microelec-tromechanical systems~MEMS! have facilitated develop-ment of sensors that involve transduction of mechanicalenergy and rely heavily on mechanical phenomena.4–11 De-velopment of microfabricated cantilevers for atomic forcemicroscopy~AFM!12 signified an important milestone in es-tablishing efficient technological approaches to MEMS sen-sors. However, the key concepts13–18as well as early experi-mental studies19–24 related to mechanical transducers forchemical sensors can be traced back far beyond the MEMSera as is accepted today.

Functionality of MEMS sensors is based on mechanicalmovements and deformations of their micromachined com-ponents, such as single-clamped suspended beams~cantile-vers!, double-clamped suspended beams~‘‘bridges’’ !, or sus-pended diaphragms. Cantilever structures similar to AFMprobes are some of the simplest MEMS that can also beconsidered as basic building blocks for a variety of morecomplex MEMS devices. Since the advent of scanning probemicroscopy~SPM!, the fabrication and characterization ofmicroscale cantilevers useful as AFM probes12,25have been asubject of extensive research efforts.26–28As a result of morerecent advances in several converging areas of science andtechnology, not only a variety of sophisticated probes be-came available for SPM but also an innovative family ofphysical, chemical, and biological sensors based on cantile-ver technology was shaped out.6,9–11,29–33Broader interestin MEMS transducers4 can be explained by their potentialfor applications in optical imaging,34,35 telecommunica-

a!Author to whom all correspondence should be addressed; electronic mail:[email protected]

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 75, NUMBER 7 JULY 2004

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http://dx.doi.org/10.1063/1.1763252

tions,36–38 and data storage.39–44 While MEMS transducersspan a great variety of designs,4 devices with very simplecantilever-type configurations appeared to be especially suit-able as transducers of physical, chemical, and biologicalstimuli into readily measured signals.29,45 In Figs. 2~A!–2~C!, we show examples of different cantilever devices. Fig-ure 2~A! illustrates a comparison between sizes of commer-cially available AFM cantilevers and a human hair. Designsof cantilever devices vary substantially depending on the de-sired parameters. For example, the long thin legs of the can-tilever shown in Fig. 2~B! improve thermal isolation betweenthe active part of the device and its surrounding.

The general idea behind MEMS sensors is that physical,chemical, or biological stimuli can affect mechanical charac-

teristics of the micromechanical transducer in such a waythat the resulting change can be measured using electronic,optical, or other means.46 In particular, microfabricated can-tilevers together with read-out means that are capable ofmeasuring 10212 to 1026 m displacements can operate asdetectors of surface stresses,5,47–53extremely small mechani-cal forces,54–57 charges,58–62 heat fluxes,5,63,64 and IRphotons.65–72 As device sizes approach the nanoscale, theirmechanical behavior starts resembling vibrational modes ofmolecules and atoms~Fig. 3!. Dimensional scaling of canti-levers is associated with respective scaling of their mass,frequency, and energy content. In the nanomechanical re-gime, it is possible to attain extremely high fundamental fre-quencies approaching those of vibrational molecular modes.Ultimately, very small nanomechanical transducers can beenvisioned as human-tailored molecules that interact control-lably with both their molecular environment and readoutcomponents. Nanomechanical resonators with a mass of2.34310218g and a resonance frequency of 115 MHz werefabricated and displacement of 2310215m Hz21/2 weremeasured.73 Mass sensitivity of only a few femtograms wasreported recently using nanoscale resonators.74

This article focuses almost exclusively on MEMS sen-sors with transducers in a form of cantilevers or analogousstructures with more complex shapes and one or several an-choring points. We will use the terms ‘‘cantilever’’ and‘‘bridge’’ throughout the text of this section to denote devicesanalogous to, respectively, single-clamped and double-clamped suspended beams of various sizes and shapes. Forsimplicity, we will mainly use the term ‘‘MEMS,’’ althoughderived terms, such as microoptoelectromechanical systems,and biological microelectromechanical systems could also bejustified in this content to emphasize specific features of cer-tain sensors based on micromechanical transducers. This re-view is structured largely around the four main aspects rel-evant to MEMS sensors:~i! operation principles and models;~ii ! microfabrication;~iii ! figures of merit; and~iv! applica-tions of cantilever sensors. In addition, we also provide abrief historical background on cantilever sensors over a pe-

FIG. 1. Generalized structure a chemical sensor.~A! Schematic representa-tion of a chemical sensor that produces an output signal in response to thepresence of a target analyte.~B! A chemical sensor with a molecular recog-nition receptor layer provides a highly selective response.

FIG. 2. Examples of cantilever devices.~A! Commercially available canti-levers used in AFM.~B! and ~C! Modified rectangular cantilevers with in-creased thermal isolation are optimized for calorimetric detection.

FIG. 3. Cantilevers: Spatial scaling is associated with respective scaling ofmasses, frequencies, and energies. In the nanomechanical regime, it is pos-sible to attain extremely high fundamental frequencies approaching those ofvibrational molecular modes.

2230 Rev. Sci. Instrum., Vol. 75, No. 7, July 2004 Lavrik, Sepaniak, and Datskos


riod that spans a century. Since many MEMS are truly mul-tifaceted devices that may integrate several transductionmodes, a significant part of the article is devoted to prin-ciples of their operation.

B. Early devices utilizing direct conversion ofchemical stimuli into mechanical responses

Studies of mechanical phenomena associated withchanges in the chemical environment have a substantial his-torical background. In 1924, Palmer19 studied coherence ofloosely contacting thin filaments induced by electromagneticwaves in the presence of different gases and analyzed corre-lation between the observed responses and the heat of gasabsorption. Almost at the same time, Meehan21 observedadsorption-induced expansion of yellow pine charcoal ex-posed to carbon dioxide vapors and showed that this was areversible process. Later, Yates75 conducted similar studieson the expansion of porous glass exposed to nonpolar gasessuch as Ar, N2 , O2 , H2 , and Kr. A description of a chemicaldetector based on a cantilever mechanical transducer can befound in the patent issued to Norton as early as 1943.14 Afurther refinement of this principle described by Norton wasdescribed by Shaver in 1969.15

Mechanical stresses and deformations produced in re-sponse to a changing chemical environment have also drawnattention as a principle of powering miniature mechanicaldevices. For example, in the 1960s, Kuhn76 and Steinberget al.17 developed the concept of devices that provide directconversion of chemical stimuli into mechanical energy.18,77

Work on such devices referred to asmechanochemical en-gineshas not been pursued since then primarily because ofthe difficulty associated with microfabrication. Furthermore,practical implications of these devices were limited until ad-vances in microtechnology and, more recently, in MEMSopened up an opportunity to fabricate miniaturized mechani-cal components routinely.

C. Evolution from macro- to micro-mechanicaltransducers

Long before the advent of AFM, macroscopic cantileverdevices and mechanical resonators were used by many re-searchers as very sensitive transducers and highly preciseoscillators. One of the earliest examples is an electronic cir-cuit that provided a precision time standard by using a mac-roscopic tuning fork.78 As was already mentioned in the pre-vious section, the use of macroscopic cantilevers in chemicalsensors can be traced back to the 1940s;14 Norton proposed ahydrogen detector based on a macroscopic bimetallic plate.Norton’s work was revisited almost three decades later byShaver15 who also used large 100 mm long, 125mm thickbimaterial cantilevers in a hydrogen sensor. A decade later,Taylor and coworkers from Oak Ridge National Laboratory,Oak Ridge, Tennessee studied bending induced by molecularadsorption of He, H2 , NH3, and H2S on large nickel canti-levers ~100 mm long! coated with 80 nm of gold.79 Theoperation of sensors described by Norton and Shaver wasbased on very high solubility of hydrogen gas in palladiumand concomitant expansion of the metal, i.e., the same phe-

nomenon that was used recently in an integrated on-chipMEMS-based hydrogen sensors.80 Cantilever deflections ob-served in the studies of Taylor and coworkers were associ-ated with adsorbate-induced stresses~i.e., a surface ratherthan bulk phenomenon! and indicated another fundamentalmechanism81 that was later utilized in a variety of cantilever-based chemical and biological sensors. Macroscopic cantile-ver transducers were also demonstrated to be rather sensitivecalorimetric devices useful, for instance, as IR detectors. In1957 Jones used a thin, few millimeter long metallic strip inorder to detect IR radiation due to thermal expansion of thestrip.82

Optical means for measuring mechanical responses ofmacroscopic mechanical transducers with submicrometer ac-curacy have existed since the 1920s.20 However, a simplevisual approach to cantilever readout often used in the earlystudies14,15,79,82could not provide the accuracy and the sen-sitivity required for a macroscale mechanical transducers toconstitute practically appealing chemical sensors. Yet an-other difficulty of using macroscale cantilever transducersfor practical applications was their extremely high suscepti-bility to external vibrations stemming from their large sus-pended masses and, respectively, low resonance frequencies.Hence, cantilever transducers had attained little practical ap-peal until both microscopic cantilevers and more precisemeans for their readout became widely available.

Interestingly, in the 1960s Newell and his coworkersfrom Westinghouse Research Laboratories, Pittsburgh, PA,developed a device integrating a field effect transistor and athin micromachined metal plate suspended above its gate.16

This work by Newell and his coworkers introduced the ideaof ‘‘the resonance gate transistor,’’ according to which me-chanical oscillation of a resonating microcantilever could beconverted into an oscillatory electronic signal and amplifiedby the field effect transistor. In 1967, Newell discussed ageneralized concept of electromechanical devices based on‘‘miniaturized tuning forks’’ and reported evaluation of theirfundamental parameters.83,84 While the scope of this workwas not related to chemical sensing, it represented a success-ful implementations of a microfabricated cantilever trans-ducer integrated with an electronic readout. Notably, by cre-ating a density of 500 resonance gate transistors per one-inchsilicon wafer,85 batch fabrication of MEMS devices wasdemonstrated. Nonetheless, significant technological chal-lenges of microfabricated cantilevers prevented resonant gatetransistors from becoming widespread at that time. This,however, was not the case with piezoelectric devices86 basedon bulk87 and surface acoustic waves which were explored astransducers for chemical sensors88–90 and drew significantattention in the subsequent decade.1,91–95Except for very fewstudies,96,97 the idea of microfabricated transducers based onsuspended resonating or deformable structures16,24,83–85,98,99

remained almost abandoned until the advent of AFM.12

II. FUNDAMENTAL MODELS

Analogous to contact and tapping modes of AFM,46 can-tilever based sensors also involve measurements of cantile-ver deflections, resonance frequencies and, in some cases,

2231Rev. Sci. Instrum., Vol. 75, No. 7, July 2004 Cantilevers as platforms for sensors


damping characteristics. However, the mechanisms thattranslate various components of a physical, chemical, or bio-logical environment into these parameters are generally dif-ferent from the mechanisms that are operative in AFM. Thevariety of transduction mechanisms that are involved in thefunctioning of cantilever sensors is depicted in Fig. 4. De-pending on the measured parameter—cantilever deflection orresonance frequency—the mode of cantilever operation canbe referred to as either static or dynamic. Each of thesemodes, in turn, can be associated with different transductionscenarios~Fig. 4!. Static cantilever deflections can be causedby either external forces exerted on the cantilever~as inAFM! or intrinsic stresses generated on the cantilever surfaceor within the cantilever. While cantilever microfabricationtechnology is capable of producing nearly stress-free sus-pended beams, additional intrinsic stresses may subsequentlyoriginate from thermal expansion, interfacial processes andphysicochemical changes. Cantilever sensors operating in thedynamic mode are essentially mechanical oscillators, reso-nance characteristics of which depend upon the attachedmass as well as viscoelastic properties of the medium. Forinstance, adsorption of analyte molecules on a resonatingcantilever results in lowering of its resonance frequency dueto the increased suspended mass of the resonator.

Depending on the nature of the input stimuli, microcan-tilever sensors can be referred to asphysical, chemical, orbiological sensors. The variety of transduction modes~Fig.4! stems from the fact that a stimulus of each type may affectthe mechanical state of the transducer directly or may un-dergo one or several transformations before the measuredmechanical parameter of the transducer is affected. For in-stance, biochemical interactions can be monitored by detect-ing IR photons emitted as a result of an exothermic process.In turn, IR photons can be detected by measuring mechanicalstresses produced in a MEMS detector as a direct conse-quence of the photon absorption process.67 More commonly,however, detection of IR photons by MEMS detectors con-sists in detecting the temperature increases associated withabsorption of IR photon.68,70,72Thermal sensitivity of bima-terial cantilevers13 can also be used to detect molecular and

biochemical interfacial interactions due to the heating effectsof exothermic reactions or molecular adsorption processes.5

Alternatively, cantilever transducers can detect chemical andbiochemical species more directly due to adsorption-inducedstresses47,49,53,100–103or mass loading effects.74,104,105

Modern MEMS sensors have much in common withtheir predecessors, such as resonant gate transis-tors,16,24,83,84,98,106 acoustomechanical resonancesensors,92,94,107–110 as well as macroscopic cantileverdevices.13,15,79,111,112In fact, more than 50 years separatedsome of the earliest experimental113 and theoretical13,114

studies on cantilever systems and the recognition of cantile-vers as a platform for chemical sensors by the broader re-search community.11,45,64,115–119Due to this remarkable timespan, well-established analytical models of cantilevers arenow available and can be used to design and evaluate micro-cantilever transducers or analogous MEMS for chemical ana-lytical applications. Furthermore, the classical models ofcantilever devices have been frequently revisited, refined,and compared against the results of numerical computationalmethods that become widespread in recent years.52,120 Nev-ertheless, simple classical models remain very useful for un-derstanding basic principles of MEMS sensors. Dependingon the operation mode of a MEMS sensor, static or dynamicmodels are applicable.

In the beginning of the 20th century, development of theelasticity theory by Timoshenko13,114and experimental stud-ies of thin films by Stoney113 become major milestones indeveloping fundamental analytical models that would subse-quently find wide applications in MEMS analysis. Theseclassical models13,113 focused primarily on static deforma-tions of purely elastic beams and plates have been revisitedmore recently.8,50–52,121–124As applied to various cantileversensors operating in the static mode, the expression forstrain-induced deformations of bimaterial plates derived byTimoshenko13 in the 1920s appeared to be of particular sig-nificance.

A. Static deformations

In the absence of external gravitational, magnetic, andelectrostatic forces, cantilever deformation is unambiguouslyrelated to a gradient of mechanical stress generated in thedevice. Depending on a particular origin of this stress, ana-lytical models suitable for quantitative analysis of microcan-tilever responses may or may not be available. For instance,simple models are applicable to thermally induced stressesand concomitant deformations of microcantilevers made oftwo layered materials with different coefficients of thermalexpansion. Theoretical evaluation of bimetal thermostats re-ported by Timoshenko13 provided an analytical expressionfor the radius of curvature of a bimaterial cantilever as afunction of a temperature change. This deformation resultingfrom unequal thermal expansion of each layer has been usedextensively as an operation principle of thermostats and of-ten referred to as the bimetallic effect. Taking into accountthe length of the cantileverl, the respective defection of thetip Dz@5 l 2/(2R)# can be expressed as

FIG. 4. Conversion of input stimuli into output signals by cantilever trans-ducers is associated with a number of transduction mechanisms. Dependingon the measured parameter—structural deformations or resonance frequencychanges—the mode of sensor operation can be refereed to as eitherstaticorresonant. Each of these modes, in turn, can be associated with differenttransduction scenarios.



Dz53l 2

t11t2 F S 11t1

t2D 2

3S 11t1

t2D 2

1S 11t1E1

t2E2D S t1

2

t22

1t2E2

t1E1D G

3~a12a2!DT, ~1!

where t1 and t2 is the thickness of the two layers of thebimaterial plate,E1 andE2 are the Young’s moduli, anda1 ,anda2 are the thermal expansion coefficients for the mate-rials of these layers, respectively. While the objective of Ti-moshenko’s original work was evaluation of bimaterial ther-mostats, a strain induced deformation is also an importantresponse mechanism of cantilever based chemical sensors inwhich a chemically selective layer undergoes expansionupon interaction with its chemical medium.124

More recently, various modifications of Eq.~1! havebeen used to predict thermally induced deflections of micro-scopic bimaterial cantilevers.8,63 In order to evaluate calori-metric sensitivity of a bimaterial cantilever, Barneset al.63

combined Eq.~1! with the expression for a thermal fluxalong the cantilever and found that the deflection of the can-tilever tip Dz is given by

Dz55

4~a12a2!

t11t2

t22K

l 3

l1t11l2t2P,

~2!

K5416S t1

t2D14S t1

t2D 2

1E1

E2S t1

t2D 3

1E2

E1S t1

t2D ,

wherel1 and l1 are the thermal conductivities of the twolayers andP is the absorbed power.

Femto-Joule level calorimetric sensitivity of conven-tional AFM cantilevers demonstrated experimentally by Bar-neset al. is consistent with the theoretical predictions madeusing Eq.~2!.63 As applied to chemical and biological sen-sors, cantilever based calorimetry enables two transductionscenarios~Fig. 4!. First, the presence of analyte species canbe detected due to the heat associated with their adsorptionon the transducer. Second, the heat produced in the course ofa subsequent chemical reaction on the cantilever surface canbe characteristic of the analyte presence. However, molecularadsorption processes and interfacial chemical reactions mayalso affect mechanical stresses in thin plates more directlyand independently of the thermal effects. Apart from funda-mental interest in the direct conversion of chemical energyinto mechanical energy,18,76 this mechanism means that can-tilever transducers are compatible with many responsivephases and can function in both gas and liquid environments.

It has been known since the 1960s that molecular andatomic adsorbates on atomically pure faces of single crystalstend to induce significant surface stress changes. Long beforethe first microfabricated cantilevers were created, changes insurface stresses in these systems had been studied by mea-suring minute deformations of relatively thin~up to 1 mm!plates. Using this method, often referred to as the beam-bending technique,49,111,112Koschet al. studied125,126surfacestress changes induced by adsorption of atoms on atomically

pure surfaces in vacuum. Using the Shuttleworth equation,81

the surface stresss and surface free energyg can be inter-related

s5g1S ]g

]e D , ~3!

wheres is the surface stress. The surface strainde is definedas the relative change in surface area]e5]A/A. In manycases, the contribution from the surface strain term can beneglected and the free energy change approximately equalsthe change in surface stress.

Adsorbate and chemically induced surface stresses havealso been extensively studied with regard to their role incolloidal systems. Important examples of colloidal phenom-ena associated with the surface stress changes include swell-ing of hydrogels upon hydration or formation of surfactantmonolayers at the air-water interface.127 Fundamental studiesof adsorption- and absorption-induced mechanical phenom-ena, however, had limited implications for chemical sensorsuntil mass produced AFM microcantilevers became widelyavailable. As compared with their macroscopic predecessors,microcantilevers coupled with the optical lever readoutgreatly simplified real-time measurements of surface stresschanges in the low mN m21 range.

Cantilevers intended for use as chemical sensors aretypically modified so that one of the sides is relatively pas-sive while the other side exhibits high affinity to the targetedanalyte. In order to understand how different modifying coat-ings provide responses of cantilever sensors in the staticbending mode, it is useful to consider the three distinctivemodels. The first model is most adequate when interactionsbetween the cantilever and its environment are predomi-nantly surface phenomena. Adsorption of analyte species ontransducer surfaces may involve physisorption~weak bond-ing, binding energy,0.1 eV! or chemisorption~strongerbonding, binding energy.0.3 eV!. Physisorption is associ-ated with van der Waals interactions between the adsorbateand the adsorbent substrate. As the analyte species approachthe surface, they can polarize the surface creating induceddipoles. The resulting interactions are associated with bind-ing energies less than 0.1 eV. Much higher binding energiesare characteristic of chemical bonding between the analyteand the surface in the case of chemisorption.

In general, changes in surface stresses can be largelyattributed to changes in Gibbs free energy associated withadsorption processes. An example of this situation is given inFig. 5, where chemisorption of straight-chain thiol moleculeson a gold coated cantilever is schematically depicted. Sincespontaneous adsorption processes are driven by an excess ofthe interfacial free energy, they are typically accompanied bythe reduction of the interfacial stress. In other words, sur-faces usually tend to expand~see Fig. 5! as a result of ad-sorptive processes. This type of surface stress change is de-fined as compressive, referring to a possibility of return ofthe surface into the original compressed state. The larger theinitial surface free energy of the substrate, the greater thepossible change in surface stress results from spontaneousadsorption processes. Compressive surface stresses were ex-



perimentally observed on the gold side of gold coated canti-levers exposed to vapor-phase alkanethiols.102,103

In many cases, adsorbate-induced deformations of thinplates can be accurately predicted using a modification of therelationships originally derived by Stoney and vonPreissig113,121

1

R5

6~12y!

Et2Ds, ~4!

whereR is the radius of microcantilever curvature,y andEare Poisson’s ratio and Young’s modulus for the substrate,respectively,t is the thickness of the cantilever, andds is thedifferential surface stress. Knowledge of the radius of curva-ture R allows the tip displacement of a microcantilever withlength l tip to be determined by

Dz51

2

l 2

R5

3l 2~12y!

Et2Ds. ~5!

When adsorbate-induced stresses are generated on idealsmooth surfaces or within coatings that are very thin in com-parison to the cantilever, the analysis according to Eq.~3! israther straightforward. Using Eq.~4! or ~5!, the predictionsfor the cantilever bending can be based on the expected sur-face stress change. Alternatively, responses of cantilever sen-sors converted into surface stress changes can be analyzed asthe measure of the coating efficiency independently of thetransducer geometry.

The second model of analyte-induced stresses~Fig. 6! isapplicable for a cantilever modified with a much thicker thana monolayer analyte-permeable coating.128,129Taking into ac-count interactions of the analyte molecules with the bulk ofthe responsive phase, a predominant mechanism of cantile-

ver deflection can be described as deformation due toanalyte-induced swelling of the coating~Fig. 6!. Such swell-ing processes can be quantified using approaches developedin colloidal and polymer science, i.e., by evaluating molecu-lar forces acting in the coating and between the coating andthe analyte species. In general, dispersion, electrostatic,steric, osmotic, and solvation forces,127 acting within thecoating can be altered by absorbed analytes. Depending onwhether it is more appropriate to describe the responsivephase as solid or gel-like, these altered forces can be put intoaccordance with, respectively, stress or pressure changes in-side the coating. An in-plane component of this change mul-tiplied by the coating thickness yields an apparent surfacestress change that can be used in Stoney’s model@Eq. ~4!# inorder to estimate deflections of a cantilever coated with thin,soft, responsive films. It is important to note that the magni-tude of apparent surface stress scales up in proportion withthe thickness of the responsive phase.

The third model~Fig. 7! is most relevant to nanostruc-tured interfaces and coatings, such as surface-immobilizedcolloids, that have been recently recognized as a very prom-ising class of chemically responsive phases for cantileversensors and actuators.74,130–134It is worthy to note that grainboundaries, voids, and impurities have been long known asbeing responsible for high intrinsic stresses in disordered,amorphous, and polycrystalline films.125

Analyte-induced deflections of cantilevers with struc-tured phases~Fig. 7! combine mechanisms of bulk, surface,and intersurface interactions.127 A combination of thesemechanisms facilitates efficient conversion of the energy ofreceptor-analyte interactions into mechanical energy of can-tilever bending. Recent studies demonstrated that up to twoorders of magnitude increases in cantilever responses can beobtained when receptor molecules are immobilized on nano-structured instead of smooth gold surfaces.133,135,136Further-more, nanostructured responsive phases offer an approach tosubstantially increase the number of binding sites per canti-

FIG. 5. Schematic depiction of chemisorption of straight-chain thiol mol-ecules on a gold coated cantilever. Spontaneous adsorption processes aredriven by an excess in the interfacial free energy, and accompanied byreduction of the interfacial stress.

FIG. 6. Schematic depiction of analyte-induced cantilever deformationwhen the surface is modified with a thicker analyte-permeable coating. In-teractions of the analyte molecules with the bulk of the responsive phaselead to coating swelling and can be evaluated using approaches employed incolloidal and polymer science.



lever without compromising their accessibility for the ana-lyte. In fact, many of these nanostructured phases exhibitbehaviors ofmolecular sponges. Although deflections ofcantilevers with nanostructured coatings or thicker hydrogellayers cannot be accurately predicted using the analyticalmodels mentioned above, estimates for the upper limit of themechanical energy produced by any cantilever transducercan always be based on simple energy conservation. Thisupper limit in available energy is given by the product of theenergy associated with the binding site-analyte interactionand the number of such interactions on the cantilever surface.

B. Resonance operation

Cantilever transducers operating in gases or in vacuumcan be treated as weakly damped mechanical oscillators.Their resonant behavior can be readily observed using exci-tation in alternated electric, electromagnetic, or acousticfields. Furthermore, minute sizes and mass of microfabri-cated cantilevers makes them susceptible to thermally in-duced noise, which has the same origin as Brownian motionof small particles in liquids. Therefore, cantilever sensorsmay operate in the resonant mode either with or withoutexternal excitation.

As a first approximation, it can be assumed that the can-tilever tip displacement is directly proportional to the forceexerted on the cantilever tip. Then, a simplified model of aresonating cantilever transducer can be based on the Hook’slaw applied to a rectangular leaf spring with an effectivesuspended massm0 and a spring constantk. The effectivesuspended mass of a cantilever can be related to the totalmass of the suspended portion of the beammb through therelationship:m05n mb , wheren is a geometric parameter.For a rectangular cantilever,n has a typical value of 0.24 andthe spring constantk is given by46

k5Ewt3

4l 3, ~6!

whereE is the modulus of elasticity for the material compos-ing the cantilever andw, t, l are the width, thickness, andlength of the cantilever, respectively. Assuming a spring con-stantk and an effective suspended massm0 , which consistsof both a concentrated and a distributed mass, the microcan-tilever fundamental resonance frequencyf 0 in the absence ofdamping can be approximated as46

f 051

2pA k

m0. ~7!

Equation~7! is often used as a starting point in estimating themass sensitivity of resonating cantilever sensors of variousshapes and sizes.74,104,105,115,137,138As a rule, Eq.~7! gives agood approximation of the resonance frequency for a weaklydamped mechanical resonator, such as a microscopic canti-lever in air. However, more accurate calculations of the mi-crocantilever resonance frequencies require the dissipation ofthe resonator energy through various mechanisms to be takeninto account. This can be done by introducing a mechanicalquality factor~Q-factor!. In the case of damping force beingproportional to the cantilever velocity~viscous damping!, theresonance frequency of the mechanical resonator is46,139

f 0,Q51

23/2pA k

m0

A2Q21

Q. ~8!

When Eqs.~7! and ~8! are used to analyze gravimetric re-sponses of resonating microcantilever transducers, it is rea-sonable to assume that the spring constantk remains unaf-fected. However, there is some evidence that chemical andphysical interactions between a cantilever transducer and itsenvironment do affect the cantilever spring constant thusmaking analysis of gravimetric responses less straight-forward.115,140,141For instance, appreciable changes in thecantilever spring constant were reported in response to vary-ing ionic strength of an aqueous NaCl solution. In particular,spring constant of an AFM cantilever was reported to changeby over one order of magnitude from 0.531023 to 7.531023 N/m as the NaCl concentration increased from 0.05to 0.8 M/L.141 In another study by the same group, a modelof a tout string was used in order to relate changes in thespring constant and adsorbate-induced surface stresses.142

This evaluation led to the following relationship:

Dk5p2

4n1~Ds11Ds2!, ~9!

whereDs1 andDs2 are the changes in the surface stress onthe top and bottom surface of the microcantilever~before andafter the adsorption of analytes!, n50.24 for a rectangularmicrocantilever, andn1 is another geometrical factor. Whilea spring constant change of 0.38 N/m was calculated for agold coated AFM cantilever as a result of its exposure to athiol,142 applicability of the tout spring model to microcanti-lever transducers and Eq.~9! is questionable. Unfortunately,more appropriate models that could explain effects of thechemical environment on the microcantilever stiffness are

FIG. 7. Schematic depiction of analyte-induced cantilever deformation inthe case of a structured modifying phase. Analyte-induced deflections ofcantilevers with structured phases combine mechanisms of bulk, surface,and intersurface interactions.



still lacking. When the damping effect of the medium israther strong, both resonance frequency shifts and theQ-factor can be related to changes in the viscosity of themedium. Such a dependency was experimentally observedusing standard AFM cantilevers placed in different gases143

or water-glycerol mixtures.144

In summary, the resonant operation of cantilever trans-ducers encompasses three mechanisms:~i! adsorbate-inducedmass-loading;~ii ! chemically induced changes in the cantile-ver stiffness; and~iii ! mechanical damping by the viscousmedium. A more detailed discussion of various dampingmechanisms in microcantilever transducers related to exter-nal as well as intrinsic dissipation phenomena is given in thenext section.

C. Energy dissipation in microcantilevers

Mechanical deformations in MEMS always involve ap-preciable dissipation of mechanical energy into thermal en-ergy. Mechanisms that determine this dissipation are relatedto inelastic phenomena in solids and viscous properties offluids.145 In analogy to other types of resonators, the qualityfactor ~or Q-factor! is commonly used to quantify energydissipation in MEMS. TheQ-factor is inversely proportionalto the damping coefficient146 or total energy lost per cycle ofvibration in a microcantilever transducer and can be definedas

Q52pW0

DW, ~10!

whereW0 andDW0 are, respectively, the mechanical energyaccumulated and dissipated in the device per vibration cycle.

It is important to emphasize that both the resonance be-havior of any microcantilever and its off-resonance thermalnoise are critically dependent on theQ-factor.69,146–151

Therefore, theQ-factor is one of the important characteristicof MEMS sensors operating in both resonance and static re-gimes. Based on the spectral analysis, theQ-factor can becalculated as a ratio of the resonance frequencyf 0 to thewidth of the resonance peak at its half amplitude. Hence, theQ-factor is frequently used to characterize the degree of theresonance peak sharpness. Alternatively,Q-factors of me-chanical oscillators can be related to time constants of expo-nentially decaying oscillator amplitude during a ring-downprocess150

Q5ptdf 0 , ~11!

wheretd is the time constant of the exponentially decayingring-down amplitude.

The Q-factor of microcantilevers depends on a numberof parameters, such as cantilever material, geometrical shape,and the viscosity of the medium. Obviously, increased damp-ing of a microcantilever oscillator by the medium translatesinto lowerQ-factor values143 as compared to the same oscil-lator in vacuum. Models of drag forces exerted on solid bod-ies in fluids145,152,153can be used to evaluate viscous damp-ing effects. A very important distinctive feature of viscousdamping is that the damping force is proportional to the lin-ear velocity of the vibrating cantilever. The other damping

mechanisms, involving clamping loss and internal frictionwithin the microcantilever, were reviewed in recent studiesby Yasumuraet al.150 As a rule, these dissipation mecha-nisms are associated with damping forces independent of thelinear cantilever velocity. Clamping loss has an insignificantcontribution to the total dissipation in the case of longermicrocantilever with high length-to-width and width-to-thickness ratios. However, ultimate minimization of clamp-ing loss can be achieved in oscillators with double-paddle or‘‘butterfly’’ geometries154 rather than single-clamped cantile-vers or double-clamped bridges. Hence, fundamental studiesof intrinsic friction effects in MEMS often rely on measure-ments of resonances in double-paddle resonators.Q-factorsas high as 105 were reported for torsional butterfly-shapedresonators fabricated from a single-crystal silicon.155–157

Internal friction can be linked to a variety of physicalphenomena, in particular, thermoelastic dissipation~TED!152

motion of lattice defects, phonon-phonon scattering, and sur-face effects.158,159 The TED limit and phonon-phonon scat-tering mechanisms correspond to very highQ-factors (106 to108), which can hardly be observed experimentally due tothe contribution from other dissipation mechanisms presentin real MEMS. The fact that surface effects may limitQ-factors of MEMS oscillators in vacuum can be verified byannealing the device and controllably changing its surface.150

As the thickness of the oscillator decreases, TED becomeseven a less significant mechanism of dissipation.150

As mentioned previouslyQ-factors of MEMS resonatorsin vacuum can be very high.157,160 However, Q-factors ofrectangular microcantilevers in air are typically in the rangeof 10 to 1000 while cantilever transducers in aqueous solu-tions rarely haveQ-factors above 10. Very strong viscousdamping in liquids makes resonant operation of microcanti-levers, and, in turn, measurements of adsorbed mass usingmicrocantilever sensors, rather challenging. In order to over-come the difficulties of resonant cantilever operation in liq-uids, cantilever transducers can be used as a part of a self-oscillating system with a positive feedback.46,161 Forinstance, the signal from the microcantilever readout can beamplified and fed back to a piezoelectric actuator connectedto the microcantilever. Such a self-oscillating system can bedescribed by an apparent quality factorQ8 defined as in-creased in the mean square of the cantilever deflections162

Q85^zdr

2 &

^zth2 &

Q. ~12!

It was reported that the positive feedback scheme applied tocantilevers in water results in apparentQ-factors Q8 thatexceed the intrinsicQ-factors by two to three orders ofmagnitude.161 Taking into account the apparentQ-factor, ex-pression for the cantilever response functionuG( f )u2 ~oruG(v)u2) can be rewritten as162

uG~v!u25

1

m02

~v022v!21S v0v

Q8 D 2 . ~13!



While it may be convenient to use an apparentQ-factor Q8in order to describe the spectral response of the self-oscillating system, the intrinsic thermal noiseC th(v) is al-ways a function of an intrinsicQ-factor162 as discussed later.

III. MICROFABRICATION

Microfabrication of MEMS has been a subject of exten-sive research and development efforts over the past 25 years.The relevant microfabrication processes have been describedin great detail in literature.4,163–167In general, fabrication ofMEMS devices is based on two distinct micromachiningstrategies:~i! bulk micromachining and~ii ! surface microma-chining. Bulk micromachining involve removal of substan-tial portions ~i.e., ‘‘bulk’’ ! of the substrate. Bulk microma-chining is often used to create devices with three-dimensional ~3D! architecture or suspended structures.Surface micromachining remain the original substrate mostlyintact and use it as a base for a device formed as a result ofadditive ~deposition! and subtractive~etching! processes.4

Although a variety of substrates and thin films can beused to fabricate microcantilever devices using bulk or sur-face micromachining, one of the most preferred substrates issingle crystal silicon. In fact, MEMS fabrication reliesheavily on approaches previously developed for microfabri-cation of conventional electronic devices. Silicon oxide, sili-con nitride, polycrystalline silicon~polysilicon!, and metalfilms are some of the most common films used in surfacemicromachining of both MEMS168 and more traditional mi-croelectronic devices. As applied to microcantilever fabrica-tion, low pressure chemical vapor deposition~LPCVD! andplasma-enhanced chemical vapor deposition~PECVD! tech-niques are widely used to form silicon dioxide and siliconnitride structural or sacrificial layers.4

Typically, fabrication of suspended microstructures, suchas a cantilever transducer, consists of deposition, patterning,and etching steps that define, respectively, thickness, lateralsizes, and the surrounding of the cantilever. One of the fre-quently used approaches in microcantilever fabrication in-volves deposition of a sacrificial layer on a prepatterned sub-strate followed by deposition of a structural material layer~such as a silicon nitride layer or a polysilicon layer! usingan LPCVD or PECVD processes. By varying the conditionsof these deposition processes, the stress and stress gradient inthe deposited layers can be minimized so that suspendedstructures do not exhibit significant deformation after theyare released by etching of the sacrificial layer. The cantilevershapes can be defined by patterning the silicon nitride filmon the top surface using photolithography followed by reac-tive ion etching~RIE!. Photolithographic patterning of thestructural material~silicon nitride or polysilicon! on the bot-tom surface is used to define mask for anisotropic bulk etchof Si. The silicon substrate is then etched away to producefree-standing cantilevers. Using a similar sequence of pro-cesses, single crystal silicon cantilevers can be created withthe difference that doping of silicon or epitaxy of a dopedsilicon layer substitutes deposition of a silicon nitride layer~thep-doped silicon plays a role of an etch stop layer!.116,169

In order to avoid any bulk micromachining, such as

through-etch of silicon in KOH, various cantilever fabrica-tion processes based on the use of a sacrificial layer weredeveloped.116,169,170These processes frequently rely on sili-con oxide as a material for the sacrificial layer.166,170The useof a sacrificial layer for fabrication of silicon nitride mem-branes, bridges, and cantilevers is illustrated in Fig. 8. Whilethe use of a sacrificial layer introduces additional restrictionson the material choice, it enables process flows that are fullycompatible with standard complementary-metal-oxide-semiconductor~CMOS! chip technology.117,171–173

Specialized MEMS transducers can be rapidly proto-typed by using standard rectangular cantilevers as a startingmaterial and using focused ion beam~FIB! for their struc-tural modification.74 Figure 9 shows two examples of canti-lever thermal detectors optimized for calorimetric spectros-copy applications that were fabricated by applying FIBmilling to a 500mm long and 100mm wide commerciallyavailable cantilevers. The improved calorimetric perfor-mance of the detector shown in Fig. 9 is due to a substan-tially narrowed~only 1 mm wide! region that connects thesuspended cantilevered structure and the base and provides avery low thermal conductance.

Details of cantilevers design and fabrication are largelydefined by the mode of the sensor operation, readout meth-ods, and specific applications. A 50 to 150 nm metal layerdeposited on the top side of cantilever detectors providesreflectivity required for the optical readout. Readouts usingcharge or tunneling effects also require parts of the trans-ducer to be metallized.60,174,175In the case of MEMS thermaldetectors based on the bimaterial effect, more complex con-figurations of cantilever transducers may be preferable.170,176

Metal layers with a high coefficient of thermal expansiondeposited on silicon or silicon nitride cantilevers are essen-tial for bimaterial regions in order to achieve high responsiv-ity of MEMS thermal detectors. Piezoelectric and piezo-resistive177 readout methods require one of the cantilever lay-ers or a coating on the cantilever to be made out of a piezo-electric or piezoresistive material.

FIG. 8. Illustration of the steps in a process flow used for fabrication ofsilicon nitride membranes, bridges, and cantilevers. The process involves adeposition of a structural silicon nitride layer on a silicon wafer with aprepatterned sacrificial layer. The cantilever shapes can be defined by pat-terning the silicon nitride film on the top surface using photolithographyfollowed by reactive RIE.



Commercially available AFM probes made of silicon orsilicon nitride have been used extensively in research on can-tilever based sensors.6,10,11,29–33,178In fact, main structuraland geometrical requirements to cantilever transducers forsensor applications are similar to those applicable in AFM.In analogy to AFM cantilevers~Fig. 2!, cantilever transduc-ers for MEMS sensors are usually fabricated from silicon orsilicon nitride and have typical thicknesses in the range of0.5 to 5mm. The typical lengths of cantilevers for both AFMand sensor applications are in the range of 100 to 500mmand approximately correspond to spring constants of, respec-tively, 1 to 0.01 N m21. Fabrication of AFM probes is basedon well-established process flows that provide low cost, highyield, and good reproducibility of the resulting devices.However, AFM cantilevers are designed and fabricated tosatisfy a number of the application-specific requirements,which become partly redundant in the case of cantilevertransducers for sensor applications. The most obvious ofsuch redundant features is the presence of a sharp tip on thecantilever end and the accessibility of the tip for a samplesurface. Therefore, fabrication of cantilever sensors can evenbe simplified in comparison to fabrication of AFM probes.This does not, however, take into account the fact that a

practical MEMS sensor should ultimately integrate a cantile-ver transducer, its readout, and an interface with the environ-ment.

In the case of chemical and biological sensors, noblemetal coatings provide surfaces that can be selectively modi-fied with synthetic or biological receptors using thiol-goldreaction schemes.100,101,135,179,180It was found that palladiumand gold coatings can be used in MEMS sensors in order toachieve chemical specificity to hydrogen gas and mercuryvapor, respectively.115,124 Polymeric and macromolecularcompounds in a form of 5 nm to 5mm thick films wereshown to provide sensitivity to various organic compoundsin a vapors phase117,119,128,180 as well as organic com-pounds136 and ionic species in water.181–183

IV. COMMON READOUT SCHEMES

Operation of any cantilever sensor relies on real-timemeasurements of cantilever deflections with at least nanom-eter accuracy. Therefore, an important part of any cantileversensor is a readout system capable of monitoring changes inone of the parameters directly related to the cantilever de-flection. Such parameters include cantilever tip position, spa-tial orientation, radius of curvature, and intrinsic stress. Spe-cific requirements for the readout of cantilever sensors canbe dictated by the operation mode~either static or dynamic!,cantilever design, and materials used as well as the magni-tude of expected responses. In this section, we discuss meansof cantilever readout that can be broadly classified as opticaland electrical.46 Using optical, piezoresistive, piezoelectric,capacitance, or electron tunneling methods,46 deformationsand resonance frequency shifts of cantilever transducers canbe measured with sufficient precision. All these methods arecompatible with array formats.

In order to insure the best possible performance of can-tilever sensors, inherent advantages and disadvantages of dif-ferent readout techniques were analyzed in recent studies.The optical beam deflection method was shown to have ex-cellent readout efficiency in the case of cantilevers with areflecting area of at least a 10310mm2. Optical readout tech-niques may, however, be inefficient when applied to nano-cantilevers. The shortcomings of some optical techniques, inparticular the optical deflection method, are related to loss ofintensity and directionality of optical beams reflected~scat-tered! by nanosize cantilevers. By contrast, electron transfermethods can be used with cantilevers that are only a fewhundred nanometers long. An important issue still to be ad-dressed is the readout of nanocantilevers arranged in densearrays. Among already explored readout methods, a chargeshuttling method is well suited for nanocantilevers arrays.The basic concept of this method is similar to electrostaticcharge shuttling demonstrated by Tuominenet al.184 How-ever, implementation of electron transfer signal transductionin aqueous environments is challenging. Electroactive ions inelectrolytes tend to cause parasitic currents that overwhelmelectron transfer signal. These leakage currents, however,can be significantly reduced by using proper insulation, re-ducing bias voltage, and controlling electroactive ions in thesolution.

FIG. 9. Example of silicon cantilevers modified using FIB milling. Theincreased path-length or the narrowed region connecting the suspended rect-angular structure to the base provides substantially smaller thermal conduc-tance as compared to the unmodified cantilever.



A. Optical methods

It is noteworthy that cantilever sensors inherited not onlythe unique advantages of a microfabricated AFM probe, butalso the elegant ‘‘optical lever’’ readout scheme commonlyused in modern AFM instruments. Optical methods most ex-tensively used for measurements of cantilever deflections inAFM ~Refs. 185–189! include optical beam deflection~alsoreferred to as the ‘‘optical lever’’ method!186 and opticalinterferometry.185,187In optical beam deflection technique, alaser diode is focused at the free end of the cantilever. Theoptical lever method proposed for the use in AFM by Meyerand Amer186 appeared to be simpler and at least as sensitiveas more complex interferometric schemes. In the Meyer andAmer studies,186 a small mirror was attached to a cantilever~made then out of a tungsten wire! so that a position of alaser beam bounced off this mirror could be monitored usinga position sensitive photodetector~PSD!. This particular op-tical detection scheme~Fig. 10! can discern extremely smallchanges in the cantilever bending; measurements of 10214mdisplacements were reported. A most common type of PSD isbased on a quadrant photodiode that consists of four cells: A,B, C, and D. Each of the cells is coupled to the input of aseparate transimpedance amplifier the output voltages ofwhich, VA , VB , VC, andVD , are proportional to the illumi-nation of the respective quadrant. The normalized differentialoutput, Vout5@(VA1VC)2(VB1VD)/(VA1VB1VC1VD)#,depends linearly on the vertical displacement of the weightedcenter of the light spot projected by the cantilever. The ab-sence of electrical connections to the cantilever, linear re-sponse, simplicity, and reliability are important advantagesof the optical lever method. As this method has been used inthe vast majority of the work on cantilever sensors, its limi-tations are well recognized. For instance, changes in the op-tical properties of the medium surrounding the cantilevermay interfere with the output signal. This interference canlargely be avoided by using a proper orientation of the can-tilever relative to the optical components as discussed in therecent paper of the authors.136 The effect of the refractiveindex change as well as other interfering factors can be fur-ther suppressed by using differential pairs or arrays of canti-levers. However, applications of cantilever sensors with theoptical lever readout are limited to analysis of low opacity,

low turbidity media. Another limitation of the optical levermethod is related to the bandwidth of PSDs, which typicallyon the order of several hundred kilohertz.

As the requirements of the high bandwidth become morecritical in the case of smaller and stiffer cantilevers that op-erate in the resonant mode, alternatives to the optical leverreadout were explored. For instance, motion of a micro-scopic structure, such as a cantilever, illuminated with atightly focused laser beam, produces a change in the spatialdistribution of the reflected and/or scattered light. A simplespot photodetector alone or in combination with a knife-edgeobstacle can be used to monitor these intensityfluctuations.190 The readout bandwidth of this method can beextended into the gigahertz range by using a small area,high-speed avalanche photodiode. Approaches based on asingle photodetector and light scattering, however, sufferfrom the interference with ambient light, nonlinear response,and a poorly controllable optical gain. More accurate high-bandwidth optical measurements of cantilever deflectionscan be carried out using interferometric schemes. Notably,interferometry is an optical technique used for measurementsof cantilever deflections in AFM. Interferometry was revis-ited as a MEMS readout and characterization tool more re-cently because of its potential for high-bandwidth high-resolution mapping of nanometer scale motions of smallcantilevers56,185arranged in large 2D arrays. Notably, Rugaret al.55,185 used interferometry to measure subnanometer de-flections of the ultrasensitive cantilevers designed for ultra-sensitive force measurements that could ultimately permitsingle-spin magnetic resonance microscopy.

More recently, optical detection techniques were devel-oped independently by a number of groups70,72for readout oflarge arrays of cantilevers motivated by applications of bi-material cantilevers to uncooled infrared imaging. In thoseworks a single visible laser source illuminates the whole ar-ray and the reflected light is either interferometricaly coupledwith a reference beam and detected by a charge-coupled de-vice ~CCD! imager or directly reflected onto a CCD. Thesetechniques can easily be applied to large two-dimensionalarrays limited only by the availability of large size CCD orCMOS visible imagers.

B. Piezoresistance method

Piezoresistivity is the phenomenon of changes in thebulk resistivity with applied stress. When a silicon cantileverwith an appropriately shaped doped region is deformed, thechange in the resistance of the doped region reflects the de-gree of the deformation. One of the most common materialsthat exhibit a strong piezoresistive effects is doped singlecrystal silicon.65,177,191,192However, doped polysilicon canti-lever were also fabricated that exhibited excellent piezo-resistivity.117,193The variation in resistance is typically mea-sured by including the cantilever into a dc-biased Wheat-stone bridge. Typical resistance of a silicon microcantileverwith a boron doped channel is a few kiloohms. When voltageV is applied to the Wheatstone bridge with resistors of iden-tical initial resistanceR, the differential voltage across thebridge can be expressed asDV5V(DR/4R). Piezoresis-

FIG. 10. The ‘‘optical lever’’ readout commonly used to measure deflec-tions of microfabricated cantilever probes in AFM.



tive cantilevers are usually designed to have two identical‘‘legs,’’ so that the resistance of the boron channel can bemeasured by wiring two conductive paths to the cantileverbase next to the legs~see Fig. 11!. The cantilever shown inFig. 11 is a commercially available piezoresistive cantileverused in AFM. The disadvantage of the piezoresistive tech-nique is that it requires current to flow through the cantilever.This results in additional dissipation of heat and associatedthermal drifts. When the cantilever is heated appreciablyabove the ambient temperature, any changes in the thermalconductivity of the environment will result in fluctuations ofthe cantilever temperature that, in turn, may lead to parasiticcantilever deflection and piezoresistance changes.

C. Piezoelectric method

Piezoelectric readout technique requires deposition of pi-ezoelectric material, such as ZnO, on the cantilever. Due to apiezoelectric effect, transient charges are induced in the pi-ezoelectric layer when a cantilever is deformed.7,194–196

Lee and White197 successfully micromachined self-excited piezoelectric cantilevers with resonances in theacoustic frequency range. The piezoelectric cantilever usedin these studies had a zinc oxide~ZnO! piezoelectric thinfilm sandwiched between two aluminum layers on a support-ing layer of silicon nitride. A few years later, Leeet al.198

micromachined piezoelectric cantilevers using PZT films.More recently, Adamset al.199 demonstrated a microcantile-ver chemical detection platform based on an array of piezo-electric microcantilevers with a power consumption in thenanowatts range. Leeet al.198 reported that micromachinedpiezoelectric cantilevers 100mm wide, 200mm long, and 2.1mm thick had a gravimetric sensitivity of 300 cm2/g, whichenabled detection of 5 ng mass. Characterization of thegravimetric sensitivities in this study was conducted by de-positing known amount of gold on the backside of the can-tilevers.

The main disadvantage of the piezoelectric as well aspiezoresistance readout is that they require electrical connec-tions to the cantilever. An additional disadvantage of the pi-ezoelectric technique is that in order to obtain large outputsignals it requires the thickness of the piezoelectric film to bewell above the values that correspond to optimal mechanical

characteristics. Furthermore, the piezoelectric readout is in-efficient when slowly changing cantilever deflections need tobe measured. Because of the aforementioned disadvantages,application of piezoelectric readout to MEMS sensors issomewhat limited.

D. Capacitance method

Capacitance readout is based on measuring the capaci-tance between a conductor on the cantilever and anotherfixed conductor on the substrate that is separated from thecantilever by a small gap.68,118,200Changes in the gap due tocantilever deformation result in changes in the capacitancebetween two conductor plates. Since the capacitance of a flatcapacitor is inversely proportional to the separation distance,sensitivity of this method relies on a very small gap betweenthe cantilever and the substrate. Capacitance readout suffersfrom interference with variations in the dielectric constant ofthe medium.201 While differential schemes may eliminatethis interference, electrically conductive media, such as elec-trolytes, make capacitance readout more challenging. One ofthe main advantages of capacitance readout is that it can beused in integrated MEMS devices that are fully compliantwith standard CMOS technology. An interesting variation ofthe capacitance methods is the ‘‘electron shuttling’’ regimethat is especially promising for nano-electro-mechanical sys-tems. For instance, Erbe and Blick and Erbeet al. reportedon the ‘‘quantum bell’’174,175 that consists of five metal-coated cantilever structures and operates in the radio fre-quency range.

E. Electron tunneling

Electron tunneling has been utilized to measure the de-flection of cantilevers in AFM.12 The electron tunneling oc-curs between a conducting tip and the cantilever separated bya subnanometer gap. By applying a bias voltage between thetunneling tip and the cantilever causes a flow of electronsbetween the tip and the cantilever. The tunneling current isvery sensitive to the gap and therefore positional changes ofthe cantilever. This current can be described as202,203

I}Ve2aAFs, ~14!

whereV is the bias voltage,F is the height of the tunnelingbarrier,s is the tunneling gap distance, anda is a conversionfactor with a value of 1.025 Å21 eV21/2. For typical values ofF and s, the tunneling current increases by one order ofmagnitude for each 0.1 nm change ins.202 Therefore, thetunneling readout combines very high sensitivity to relativepositional changes, nonlinear response, and a limited dy-namic range. Using an electron tunneling readout technique,cantilever displacements as small as 1024 nm have beenmeasured.202 It is worthy to note that tunneling processes aresensitive to the nature of materials between which the tun-neling process occurs, which often translated into challeng-ing requirements to device implementation. Despite its well-known limitations, electron tunneling readout was success-fully used in accelerometers,202 infrared sensors,204 and mag-netic field sensors.205

FIG. 11. Example of a piezoresistive cantilever that can be used in bothAFM and cantilever sensors.



V. FIGURES OF MERIT AND FUNDAMENTALLIMITATIONS

Some of the most important figures of merit of anychemical or biological sensor are responsivity, limit of detec-tion ~LOD!, specificity, and reproducibility. As discussed inone of the previous sections, chemical specificity of MEMSsensors may rely on the use of certain responsive phases,such as polymers, self-assembled monolayers, or biologicalreceptors that exhibit higher affinity to the targeted analytes.This reliance on the selective properties of responsive coat-ings is a common feature of microcantilever sensors operat-ing in both static and resonant regimes. However, transduc-tion efficiency of the two regimes is dictated by very distinctmodels and mechanisms. Transduction efficiency of thestatic mode increases when the stiffness of the cantilever isreduced. Therefore, longer cantilevers with very small springconstants are preferable for the use in the static mode. On theother hand, the sensitivity of the resonant mode increasesprogressively with the operation frequency. As a rule, staticand resonant operation of the same microcantilever sensor ischaracterized by the same specificity but different respon-sivities and LODs. The fundamental limits of microcantile-ver chemical transducers are determined by ratios of theirresponsivities to the levels of intrinsic noise. The next twosections focus on the models specific to optimization of mi-crocantilever sensors based on, respectively, measurementsof resonance frequency variations and adsorption-induceddeformations. In particular, noise sources that influence thesmallest detectable displacements and resonance frequencyshifts are discussed.

A. Responsivity of the resonance-based transducers

Although adsorption-induced stresses were extensivelyexplored as a transduction principle in many cantilever sen-sors, the advantage of the resonant operation is that it canpotentially provide mass detection at the single moleculelevel. The resonance frequency of a cantilever beam dependson its geometry as well as the elastic modulus and density ofits material. By changing cantilever dimensions, its reso-nance frequency can be varied from hundreds of hertz to afew gigahertz~see Fig. 3!. For a given cantilevers mass,higher spring constants correspond to higher resonance fre-quencies. For a given cantilever thickness, shorter cantilevershave higher spring constants. Depending on the cantilevermaterial, gigahertz resonance frequencies can be achieved,when the cantilever length is less than a few microns.73 Veryshort cantilevers with high resonance frequency are, there-fore, promising in extending the detection limit down to afew molecules.

The dependence of the fundamental frequency on thecantilever parameters for a rectangular cantilever with di-mensionl, w, andt, respectively, in length, width, and thick-ness can be expressed as46

f 051

2pA Ewt3

4l 3~mc10.24wtlr!, ~15!

wherer is the density of the cantilever materialmc is the

concentrated mass. The mass of the adsorbed material can bedetermined from the initial and final resonance frequencyand the initial mass of the cantilever206

f 022 f 1

2

f 02

'Dm

mor

f 02 f 1

f 0'

1

2

Dm

m, ~16!

where f 0 and f 1 are the initial and final frequency, respec-tively, andDm andm are adsorbed mass and initial mass ofthe cantilever, respectively. If the adsorption is not confinedto the very end of the cantilever,104 Eq. ~16! should be modi-fied in order to take into account the effective mass of thecantilever. For any geometry of a microcantilever sensor, themass responsivity can be defined as

Sm5 limDm→0

1

f 0

D f

DG5

1

f 0

d f

dG, ~17!

whereDG is normalized per active area of the device (DG5Dm/A, whereA is the active area of the cantilever!. Equa-tion ~16! shows that the mass responsivity is the fractionalchange of the resonant frequency of the structure with addi-tion of mass to the sensor. Using Eq.~17!, the mass respon-sivity of a resonating microcantilever sensor can be ex-pressed as104

Sm51

rt

d f

f 0, ~18!

wherer andt are the density and the thickness of the adsor-bate, respectively. Note that the responsivity of a cantileversensorSm can be calculated when adsorbate thickness anddensity are known. It is however, important to emphasizethat Sm alone can not be used to evaluate the smallest massdetectable.

Another very important figure of merit of a cantileversensor is the smallest detectable mass and respective surfacedensity. From Eqs.~17! and~18!, the smallest detectable sur-face density of the adsorbate can be defined as

DGmin51

Sm

D f min

f, ~19!

whereDGmin andD f min are the minimum detectable surfacedensity and minimum detectable frequency change, respec-tively. In principle, the smallest total detectable mass can bepredicted by knowing the detector active area, and the mini-mum detectable surface density. The estimate for the remain-ing unknown parameterD f min can be found taking into ac-count intrinsic noise mechanisms that limit ultimate stabilityof the resonance frequency. These noise mechanisms are dis-cussed later in this section.

B. Responsivity in the static deformation regime

Adsorption-induced cantilever bending enabled some ofthe most sensitive detection of trace-level analytes in gasesand is a preferable mode of cantilever operation in liquids. Adistinctive feature of microcantilever sensors operating in thestatic mode is that they convert a sum of weak intermolecu-lar forces involved in analyte-sensor interactions into readilymeasured displacements. This means, that the sensor mayrespond differently to the same amount of different analytes



depending on the sensor-analyte affinity. Furthermore,adsorbate-induced stresses and associated deformations canbe distinguished from the bulk effects, such as changes involume of thicker polymer films, which also lead to cantile-ver deformations. Currently, rigorous quantitative evaluationof the sensor responsivity according to these mechanisms islacking. Semiquantitative analysis of the static mode respon-sivity can be based on Eqs.~1!–~4! as reported in theliterature.47,124,135,147In particular, a linear relationship be-tween the cantilever tip displacement and the differential sur-face stress is given by Eq.~4!. According to Eq.~4!, there isa quadratic dependency of surface stress induced deflectionson the microcantilever length. It is worthy to note that aquadratic dependency of microcantilever deflection re-sponses on the microcantilever length is also predicted byEq. ~1! for the case of bulk interactions. For microcantileveroperating in the static mode, an increased length is, there-fore, a prerequisite of high responsivity. This conclusion isconsistent with the fact that microcantilevers 400 to 1500mm long were successfully used in chemical sensors operat-ing in the static mode.133,135,207Equations~1! and ~4! alsoindicate a strong effect of the thickness of a microcantileveron its deflection responses. In the case of very thin respon-sive phases or purely surface interactions, Eqs.~1! and ~4!predict deflection responses to be inversely proportional tothe total thickness of the microcantilever. However, morecomplex dependencies follow from Eq.~1! in the case ofresponsive coatings with the thicknesses comparable to thecantilever thickness.

C. Intrinsic noise sources

Noise processes in microcantilever sensors can be di-vided into processes intrinsic to the device and those relatedto interactions with its environment~for instance, adsorption-desorption noise! or originated from the readout. Here wefocus on the intrinsic noise mechanisms since they determineultimate fundamental limits of the microcantilever sensorsperformance. One of the essential features of microcantile-vers is that they are mechanical devices~oscillators! that canaccumulate and store mechanical energy. Over the past de-cades there have been extensive efforts to identify the fun-damental intrinsic sources of noise in mechanical systemsand identify the relationships between parameters of the me-chanical system and its noise level.148

When a microcantilever detector is equilibrated with theambient thermal environment~a thermal bath!, there is acontinuous exchange of the mechanical energy accumulatedin the device and thermal energy of the environment. Thisexchange dictated by the fluctuation dissipation theorem re-sults in spontaneous oscillation of the microcantilever so thatthe average mechanical energy per mode of cantilever oscil-lation is defined by thermal energykBT. Sarid46 referred tothis type of noise as ‘‘thermally induced lever noise.’’ Inother words, any cantilever in equilibrium with its thermalenvironment has a ‘‘built-in’’ source of white thermal noiseC th( f ) given by162

C th54m0kBT

Q. ~20!

At frequencies well below the resonance, the amplitude ofthe resulting thermally induced oscillation of a cantileverbeam is proportional to the square root of the thermal energyand can be expressed as

^dz2&1/25A2kBTB

pk f0Q, ~21!

wherekB is the Boltzmann constant (1.38310223J/K), T isthe absolute temperature~300 K at room temperature!, B isthe bandwidth of measurement. As it follows from Eq.~21!,lower cantilever stiffness corresponds to higher amplitudesof thermal noise. It should be emphasized, that an intrinsicQ-factor should always be used in Eq.~21!.

As a result of the dynamic exchange between cantilevermechanical energy and the ambient thermal energy, the ac-tual frequencyf of thermally induced cantilever oscillationsat any given moment can noticeably deviate from the reso-nance frequencyf 0 . The amplitude of such frequency fluc-tuationsd f 0 , due to the exchange between mechanical andthermal energy is162

d f 051

zmaxA2p f 0kBTB

kQ, ~22!

where zmax is the amplitude of the cantilever oscillations.Equation~22! predicts increased absolute fluctuations of theresonance frequencyd f 0 as the resonance frequencyf 0 in-creases. However, relative frequency instabilityd f 0 / f 0 de-creases in the case of higher frequency oscillators

d f 0

f 05

1

zmaxA2pkBTB

kQ f0. ~23!

Although Eqs.~21! and ~23! are valid for thermally excitedcantilevers, they can also be used to evaluate effects of ther-mal noise on the frequency instability of any externallydriven cantilever.162 As applied to cantilever sensors operat-ing in the resonance mode, an important implication of Eqs.~22! and ~23! is that frequency instability due to effects ofthermal noise can be minimized by driving the transducerwith the highest possible amplitude. In the case of self-oscillating systems with a positive feedback, however, anintrinsic Q-factor should always be used in Eq.~21! since theamplitude of cantilever oscillationzmax is already explicitlytaken into account in this analysis.

By changing the physical dimension of a cantilever, itsmass detection limit can be affected by many orders of mag-nitude. For a given cantilever design, the smallest~thermalnoise limited! detectable change in the surface density can befound by combining Eqs.~7! and ~23!

Dmth58A2p5kkBTB

f 05Q

. ~24!

The minimum detectable massDmth can then be expressedas

Dmth58G

^zth2 &1/2

m05/4

k3/4AkBTB

Q, ~25!



wherekB is the Boltzmann constant,T is the temperature ofthe cantilever,B is the bandwidth of the measurement,k isthe cantilever force constant,Q is the mechanical qualityfactor,m0 is the initial cantilever mass and^zth

2 &1/2 is the rootmean square amplitude of the cantilever motion.

Thermomechanical noise of microcantilevers is alsoknown to be a fundamental noise source in AFM.46,147Simi-lar analysis is applicable to microcantilever sensors operatingin the static regime. The analysis provided by Sarid46 in-volves theQ-factor of a vibrating microcantilever, its reso-nance frequency,v0 and stiffness,k. While Q-factor can bedefined empirically as the ratio of the resonance frequency tothe resonance peak width, knowing the exact mechanisms ofcantilever damping is important for evaluation of the thermo-mechanical noise spectrum. The model evaluated by Sarid46

assumes that damping of the cantilever is of a viscous nature.Assumption of predominantly viscous damping is valid formicrocantilevers in air or water and, therefore, justified formicromechanical devices used as force probes in SPM. In thecase of a cantilever in a viscous medium, such as air orwater, the damping force is proportional to the cantileverlinear velocity. The resulting noise density spectrum can beexpressed as146

^dzTM2 &1/25A4kBTB

Qk

v03

@~v022v2!21v2v0

2/Q2#. ~26!

The expression given by Eq.~26! predicts a frequency inde-pendent noise density for the frequencies well below the me-chanical resonance frequency,v0 , ~i.e., v!v0). At theselow frequencies, the rms of the cantilever tip displacementdue to thermo-mechanical noise is

^dzTM2 &1/25A4kBTB

Qkv0. ~27!

However, at the resonance~i.e., v5v0)46

^dzTM2 &1/25A4kBTBQ

kv0. ~28!

As follows from Eq.~26!, the density of thermomechanicalnoise follows a 1/f 1/2 dependence below the resonance@seeFig. ~12!# when the damping is due to intrinsic friction pro-cesses. Analysis of Eqs.~27! and~28! shows that, regardlessof the dissipation mechanism, the off-resonance thermome-chanical noise is lower in the case of microcantilevers withhigherQ-factor and higherk. It should be emphasized that,while predictions based on Eq.~26! are often reported in theliterature,149,208the noise density calculated according to thetwo alternative models may substantially deviate from eachother at low frequencies.146,209,210Furthermore, the intrinsicfriction model predicts the low frequency noise to be inde-pendent of the cantilever resonance frequency provided thatthe stiffnessk is constant. By contrast, the viscous dampingmodel predicts that the low frequency noise of a microcan-tilever detector can be decreased by increasing its resonancefrequency even without changes in its stiffness. Therefore,knowing the actual mechanisms of mechanical dissipation inthe microcantilever detector can be critical in analyzing ther-momechanical noise of microcantilever sensors.

In the case of layered~for instance bimaterial! microcan-tilever transducers an additional noise source needs to beconsidered. This noise mechanism is related to the tempera-ture sensitivity of bimaterial cantilevers13,64,114and the factthat local temperature undergoes appreciable fluctuation atthe microscopic scale. As discussed previously by Kruse,211

the mean square magnitude of these temperature fluctuationsis

^dT2&5kBT2

C, ~29!

wherekB is Boltzmann’s constant,T is the absolute tempera-ture, andC is the total heat capacity of the microcantilever.The temperature fluctuation̂dT2& of Eq. ~29! is the integra-tion over all frequenciesf, wheref 5v/2p. The spectral den-sity of the root mean square~rms! temperature fluctuations isgiven by211

^dT2&1/252AkBBT

G1/2A11v2t2, ~30!

whereB is the measurements bandwidth andG is the thermalconductance of the principal heat loss mechanism.

Temperature fluctuation noise of the cantilever detectormanifests itself as a fluctuation inz and exhibits a frequencydependence influenced by both the thermal response and themechanical response of the microcantilever. The spontaneousfluctuations in displacement of the microcantilever caused bytemperature fluctuations are given by

^dzTF2 &1/25

TA4kBB

G1/2A11v2t2

1

AS 12v2

v02D 2

1v2

v02Q2

, ~31!

wherev0 is resonance frequency of the microcantilever witha quality factorQ. Figure 12 illustrates, the frequency depen-dence of^dz2&1/2 for both thermomechanical and tempera-

FIG. 12. The contribution of thermomechanical and temperature fluctuationnoise to the frequency dependent^dz2&1/2. Theoretical plots calculated for a600 nm thick silicon nitride AFM cantilever coated with 50 nm of gold areshown along with the actual experimental data obtained for this cantilever.The cantilever had a mass of 30 ng, a spring constant of 0.015 N/m, aQ-factor of 100, and a resonance frequency of 6.5 KHz.



ture fluctuation noise and compares these theoretical depen-dencies with the experimentally measured noise behavior ofa standard silicon nitride AFM cantilever.

VI. DEMONSTRATED APPLICATIONS OF CANTILEVERSENSORS

A. Gas phase analytes

Detection of mercury vapors reported by Thundatet al.115 was one of the first gas sensor applications of mi-croscopic cantilevers. Commercially available delta-shapedsilicon nitride AFM cantilevers@Ultralevers, Park Scientific,Sunnyvale, CA, see Fig. 2~A!# were used in those studies.The typical length, thickness, and force constant of thesecantilevers were, respectively, 180mm, 0.6 mm, and 0.06N/m. An evaporated 50 nm gold coating provided affinity ofone side of the cantilevers to mercury. The measurements ofstatic deflections and resonance frequencies were based onthe Multi-Mode Nanoscope III AFM head~Digital Instru-ments, Santa Barbara, CA! which provided the optical leverreadout of the cantilevers. It was found that both resonancefrequencies and static deflections of the gold coated cantile-vers underwent changes in presence of mercury vapor~30mg m23! added to a nitrogen carrier gas. When one side ofthe cantilevers was completely coated with gold, the reso-nance frequency of the cantilevers increased as a result ofexposure to mercury vapors. This rather unexpected resultwas explained by competing effects of the absorbed mercuryon the cantilever force constant and on the cantilever sus-pended mass. It was concluded that interaction of mercurywith the gold coating led to a lowering of the cantileverresonance frequency as a result of a relatively small increasein the cantilever effective mass and a more significant in-crease in the cantilever force constant. This model was con-firmed by the fact that exposure to mercury vapors did lowerthe resonance frequency when only an end portion of thecantilever was coated with gold. In the latter experiment, theregion close to the clamping point~which largely defines thecantilever force constant! remained without gold and, there-fore, was unaffected in presence of mercury.

Ferrari and coworkers7 used ceramic cantilevers actuatedby piezoelectric excitation to measure resonant frequencychanges due to adsorption of water. Ferrariet al.7 usedpoly~N-vinylpyrrolidinone! and poly~ethyleneglycol! as hy-drophilic coating materials and obtained frequency shifts ofabout 500 and 1400 Hz for relative humidity changes from12% to 85%, respectively.

Dual ~static/dynamic! mode responses of gold coatedcantilevers were reported for several other gaseous phaseanalytes, in particular, 2-mercaptoethanol.138 In the case of2-mercaptoethanol, analyte-induced deflections rather thanchanges in the resonance frequency of gold-coated AFM can-tilevers was found to be a preferable mode of sensor opera-tion. Measurements of cantilever deflections permitted detec-tion of mercaptoethanol vapor at concentrations down to 50part per billion~ppb!. The calibration curve obtained in thestatic deflection mode had a slope of 0.432 nm per ppb in theconcentration range of 0–400 ppb.

Fairly high sensitivity and selectivity demonstrated inthe early studies on cantilever sensors relied on properties ofsome metals used as active coatings. For instance, gold is avery chemically inert metal that, nevertheless has very highreactivity toward mercaptans~or thiols!, i.e., compoundswith one or more sulfohydryl~-SH! groups. High solubilityof hydrogen in palladium and palladium based alloys is an-other mechanism that leads to selective interaction of metalcoatings with gas-phase analytes. Good sensitivity of Au andPd coated cantilevers to, respectively, mercury and hydrogenwas subsequently used to implement a palm-sized, self-contained sensor module with spread-spectrum-telemetryreporting.118 The device utilized polysilicon cantilevers oper-ating in the static deflection mode and integrated with CMOScircuitry that provided their capacitive read-out as well asradio-frequency output for telemetry. The implemented pro-totype provided reversible, real-time hydrogen sensing anddosimetric ~cumulative! mercury-vapor sensing. It wasshown in a separate study212 that a dosimetric mode of hy-drogen sensing can also be realized using cantilevers trans-ducers. For this purpose, alpha platinum oxide was used as acoating that undergoes reduction and, therefore, irreversiblemass loss in presence of hydrogen. Commercially availableAFM cantilevers were coated with 20–50 nm platinum oxidefilms using reactive sputtering of platinum. Exposure of thesensor to 4% hydrogen in argon resulted in both static can-tilever and resonance frequency changes. These changesreached saturation in about 30 min, thus indicating completereduction of platinum oxide. Overall changes in the coatingmass were estimated to be less than a nanogram. In additionto steady the state responses associated with irreversiblechemical and physical changes in the coating, the observedtransient features in the bending response were consistentwith the expected thermal response due to the exothermicoxidation of hydrogen.

As inorganic coatings alone cannot provide the selectiv-ity patterns sought in many applications, modification of can-tilevers with chemically selective organic layers has been asubject of more recent studies. One of the first cantileversensors with organic coatings was a humidity sensor de-scribed by Thundatet al.144 In those studies, silicon nitrideAFM cantilevers were coated with gelatine, by contactingone side of the cantilever with a 0.1% gelatine solution indistilled water. The deposited gelatine solution was dried byplacing the cantilever in the desiccator for two days. Whenthe thus prepared cantilever was exposed to atmosphere ofgradually increased humidity, both cantilever deflections andincreases in the resonance frequency were observed. Thesensor sensitivity measured in the static deflection mode wasvery high, which even somewhat limited the dynamic rangeof this sensor@0%–60% relative humidty~R.H.!#. The cali-bration slope reported for the resonance mode was 55 Hz per% R.H. Another design of a cantilever humidity sensor em-ployed cantilevers with integrated piezoresistive readout.117

The design included both humidity sensitive and referencecantilevers as a part of a Wheatstone bridge. The layeredsilicon/silicon oxide cantilevers were 200mm long, 50mmwide, 1.5mm thick with deflection sensitivityz21 (DR/R) ofapproximately 1026 nm21. Using a glass capillary and a mi-



cromanipulator, the active~humidity sensitive! cantileverwas additionally coated with 10mm photoresist. Swelling ofthe photoresist layer in presence of water vapor providedsensor responses that were nearly proportional to R.H.% inthe range of 2% to 60%. The reference cantilever providedtemperature compensation and could also be used for tem-perature measurements.117 The reference channel is also use-ful to minimize effects of other noise sources. It should benoted, however, that the photoresist coating used in thesestudies was not highly specific to water vapor and respondedto alcohol vapor as well.117 In the case of ethanol, concen-tration levels as low as 10 ppm could be easily detected.Somewhat different responsivities were obtained in the caseof methanol, ethanol and 2-propanol.

In analogy to chemical sensors based on surface acousticwave ~SAW! transducers,110 cantilevers coated with variouscommercially available polymers were proposed for distin-guishing between different volatile organic compounds~VOCs! in air. Bergeret al.30 and Balleret al.119 reported ona multicantilever sensor, in which signals were collected in aquasisimultaneous~time-multiplexing! manner from eight in-dividual cantilever transducers, each modified with a differ-ent coating.207,213–215This design allowed the researchers totransfer the concept of a ‘‘chemical nose’’ from more con-ventional transduction principles2 to innovative nanome-chanical devices. Poly-methylmethacrylate~PMMA! as wellas Pt metal coatings were used in some of these studies inorder to demonstrate versatility of the cantilever arrays. Us-ing a cantilever sensor with a PMMA coating, responses to aseries of alcohols were obtained in both resonance and staticdeflection mode. Based on the differences in the shapes ofresponse curves~either static deflection or resonance fre-quency change plotted as a function of time!, the presence ofdifferent alcohols could be differentiated. In this case, theobserved selectivity was primarily related to the fact thatalcohols with different molecular weight and/or molecularstructure have different diffusion rates in the PMMA coating.Therefore, the use of a multicantilever array with differentpolymeric coatings was the next logical step in developing a‘‘chemical nose’’ based upon the cantilever platform. It wasshown that cantilevers coated with several readily available‘‘generic’’ polymers, such as polymethylmethacrylate, poly-styrene, polyurethane, and their blends or copolymers, re-spond differently to various VOCs.207,213 By applying prin-cipal component or artificial neuron network analysis toresponse patterns from arrays of such polymer-modified can-tilevers, the concept of an ‘‘electronic nose’’ was imple-mented.

Selectivity of cantilever gas sensors can also be con-trolled by coating the transducer surface with stationaryphases developed for chemical separation applications, suchas gas-chromatography~GC!. Such coatings were previouslyused to impart chemical selectivity to sensors based on elec-troacoustic SAW transduces.94 More recently, this approachhas been extended to cantilever sensors.128 In one study, thinfilms of commercially available GC polysilane phases,SP2340~polycyano-phase! and OV25 ~polymethyl-phenyl-phase! were deposited on one side of the Si cantilevers usinga combination of spin-coating and FIB milling.128 The thick-

nesses of both the polysilane film and the cantilever materialwere varied by adjusting the conditions of spin-coating andFIB milling. The selectivity pattern of polysilane coated Sicantilevers was assessed by measuring bending responses toa series of VOCs with different polarities. For 300 nm thicksilicon cantilevers, maximal responses were observed withapproximately 100 nm of the polysilane modifying coatings.Selectivity was shown to be consistent with a common GCphase classification scheme.128

In order to create cantilever sensors with even more dis-tinctive selectivity patterns with regard to different classes ofVOCs, sol-gel coatings as well as covalently attached orevaporated films of synthetic receptors were found to beuseful.10,129,180Thin films of sol-gels were formed on oneside of 600 nm thick silicon cantilevers using aqueous solu-tions of organosilane precursors and spin coatingprocedures.129 The cantilevers with sol-gel coatings exhib-ited strong bending in response to vapors of polar VOCs, inparticular ethanol, while sensitivity to less polar compoundswas relatively low. Additional chemical modification of thesol-gel coated cantilevers with a hydrophobic organosilane~hexamethyldisilazane! resulted in partial reversal of thistrend and an eightfold increase in the response ton-pentane~the least polar compound among the screened analytes!. De-spite these promising results, obtaining uniform coatings oncantilevers using spin coating procedures was challenging.Alternative methods of physical and chemical modificationof microcantilever transducers for gas sensors were investi-gated by the authors of this review in the recent studies.180

An ultrathin layer of thiol-modified receptors of the cyclo-dextrin family was formed preferentially on one side of goldcoated cantilevers using self-assembling procedures similarto those used previously with other types of transducers withnoble metal surfaces. The coatings of this type can be ex-pected to provide the sensor specificity based on molecularrecognition mechanisms as well as size exclusion effects. Forinstance, sensor responsivities varied for trichloroethylene,tetrachloroethylene, and 2,7-dimethylnaphthalene.180 Cova-lent attachment of the reactive receptor molecules onto nano-structured noble metal surfaces was found to be particularlysuitable for creating highly efficient cantilever sensors. In thecase of cantilevers with smooth gold surfaces, the magnitudeof cantilever responses was only moderate. However, dra-matic enhancements of responses were achieved when thesame receptor layers were deposited on cantilevers withnanostructured~granular! gold films.135 Using cantilever sen-sors with nanostructured surfaces, LODs as low as 0.17 ppband 0.28 ppm were obtained for, respectively, 2,7-dimethylnaphtalene and tetrachloroethylene.

A microcantilever chemical detection platform based onan array of piezoelectric microcantilevers was demonstratedby applying this platform to detection of ethanol vapor.199

The presence of ethanol vapor was found to be manifested inNovolac-coated cantilevers as a decrease in resonantfrequency.199 The measured response was found to be fourtimes larger than the response measured for the same canti-lever in the presence of water vapor. Those studies have alsoshown that ethanol vapor causes an increase inQ-factor forthe Novolac-coated cantilever, which we attribute to a loos-



ening of the uncured gel-like coating that ordinarily has ahigher damping coefficient; another possible explanation is astiffening of the Novolac due to swelling, but this is lesslikely since gram-sized samples of uncured Novolac weretested in the laboratory and were shown to dissolve inethanol.199A similar but lesser effect was also observed withthe Novolac coated cantilevers in water.199

More recently, microcantilevers were used for the detec-tion of explosives.134,216 Pinnaduwageet al.216 reported de-tection of 10 to 30 ppt levels of pentaerythritol tetranitrate~PETN! and hexahydro-1,3,5-triazine~RDX! using commer-cially available cantilevers coated with a gold layer thatwas functionalized with a self-assembled monolayer of4-mercaptobenzoic acid. Pinnaduwageet al. reported216 thatthose measurements corresponded to a limit of detection of afew femto-grams. Lavriket al.134 used trimaterial cantileversmodified with a tert-butylcalix6 arene coating and reportedlarge bending responses in presence of vapor phase TNT andits analogs, 2-mononitrotoluene~2-MNT! and 2,4-dinitrotoluene ~2,4-DNT!. Lavrik et al. estimated that thenoise limited TNT detection threshold was 520 ppt.134 A dif-ferent approach to the detection of explosives in air usinguncoated cantilever was reported by Pinnaduwageet al.217

Those workers utilized the deflagration of TNT in a smalllocalized explosion on an uncoated piezoresistive microcan-tilever. After removing the TNT source, the TNT moleculeswere slowly desorbed from the cantilever, and could beheated above the deflagration point by applying a voltagepulse to a piezoresistor integrated in the cantilever. The pres-ence of TNT could be detected due to a small deflagration217

that occurred when the cantilever temperature reached theTNT deflagration point.

In addition to sensors that utilize static or dynamic~reso-nance! cantilever responses due to adsorption~or absorption!of analyte molecules, bimaterial cantilevers can detect localtemperature changes associated with a chemical reaction thatinvolves analyte molecules and is catalyzed by a catalyst onthe cantilever surface. One of the first implementations ofthis detection scheme was reported by Barneset al.63 Bymeasuring deflections of a 1.5mm thick Si cantilever with a0.4 mm Al coating heat flux generated by a gas-phase cata-lytic reaction between O2 and H2 over a Pt surface was de-tected. For a standard AFM bimaterial cantilever and AFMoptical cantilever readout, the limits of detection were esti-mated to be 1 pJ of thermal energy and 1025 K of localtemperature differences.63 Even higher sensitivity of thismethod can be achieved using modified silicon or siliconnitride cantilevers with increased thermal isolation betweentheir active regions~catalytic areas! and supporting bases~‘‘heat sinks’’!. When heat escape through the surroundingenvironment becomes the principal path for the heat ex-change, the sensitivity of cantilever based calorimetric sen-sors reaches its fundamental limit. While practical applica-tions of cantilever based calorimetric detectors that involvecatalytic reactions can be somewhat limited, much more ver-satile detection and identification of species adsorbed on can-tilevers can be achieved using photothermal spectroscopymethods.218–220 For instance, the authors of this reviewshowed that analytes present on cantilevers in a form of thin

coatings~about 100 nm average thickness! can be detected ina calorimetric spectroscopy mode.219,220While such cantile-ver based spectroscopic instruments may not satisfy rigorousdefinitions of chemical sensors they offer excellent portabil-ity combined with inherent to vibrational spectroscopy dif-ferentiating power.

We should point out that the static bending mode wasused extensively in the majority of studies on cantilever sen-sors. However, resonating cantilevers scaled down to thenanoscale offer uniquely high mass sensitivity that cannot beachieved by using the static bending mode.74 Therefore,resonating nanocantilevers may be indispensable in applica-tions where species to be detected and analyzed are availablein very minute quantities.

B. Liquid phase analytes

Early works on cantilever based chemical detection inliquids involved standard AFM cantilevers and AFM headsfor their readout. Buttet al.221 studied responses of 190mmlong, 0.6mm thick, gold coated, silicon nitride AFM canti-levers to various chemical factors and found that the steadystate deflections depend upon both pH and ionic strength ofthe aqueous medium. The ionic strength was varied by ad-justing the concentration of KNO3 varied from 0 to 1 M. ThepH calibration plot acquired in 0.1 M KNO3 was representedby two roughly linear regions corresponding to pH of 2–5.5and pH of 8–11, respectively. This broad calibration plotwith a relatively flat region at pH of 5.5–8 is qualitativelyconsistent with existing models of silicon nitride surfacedissociation.221 The average slope of the calibration curvewas approximately 9 nm per pH~at 0.1 M KNO3). Furtherresearch in this direction focused on surface modifications ofcantilevers that can lead to improved or modified pH sensi-tivity. Alkylthiols terminated with different chemical groupswere most extensively used as modifying agents for gold-coated cantilevers. The other modification procedures in-volved silane-oxide chemistry and spontaneous oxidation ofevaporated aluminum films. When pH responses of cantile-vers modified with carboxylic acid, hydroxyl, and aminogroups were analyzed in several independent studies,100,182

reasonable correlation between the experimental calibrationplots and expected protonation-deprotonation behavior of thecantilever surfaces was found. The reported pH responsivi-ties varied from 15 to 50 nm/pH and was dependent on thesurface treatment, cantilever type, and pH range.

Some of the most impressive figures of merit demon-strated with cantilever sensors are related detection of heavymetal ions. In particular, Jiet al.222 reported on highly sen-sitive and selective detection of Cs1 ions using a cantileversensor with a self-assembled responsive layer of the molecu-lar recognition type. The responsive layer for this sensor wasformed using a synthesized receptor compound which com-bined calixarene and crown-ether macrocycles and had areactive-SH group that provided its covalent attachment togold surfaces. Using a cantilever transducer with this respon-sive layer, Cs1 ions could be detected in the concentrationrange of 10211 to 1027 M. The observed cantilever deflec-tions in response to Cs1 ions reached a steady state in less



than 5 min. Cantilever deflections up to 350 nm were docu-mented in this study. Importantly, Na1 ions had almost noeffect on the cantilever bending while rather good selectivitywas observed with respect to K1 ~a steady state response of115 nm corresponded to 5310210M Cs1 or 1024 M K1).By modifying gold coated cantilever transducers with an-other self-assembled responsive monolayer, triethyl-12-mercaptododecylammonium bromide, a detector of traceamounts of CrO4

22 was implemented.181 It was reported that,while 1029 M CrO4

22 could be detected, other anions, suchas Cl2, Br2, CO3

22 , and SO422 , had a minimal affect on the

sensor response. As an extension of this approach, detectionof trace levels of Ca21 was also achieved using cantilevertransducers modified with Ca21 selective self-assembled re-sponsive layers.141 Two alternative chemical functionaliza-tion procedures were used in this study and resulted in thetwo kinds of self-assembled monolayers terminated with, re-spectively, with phosphate and N,N-diethyl-acetamide moi-eties. Cantilever sensors with these two types of selectivecoatings were shown to be practically useful in complemen-tary ranges of Ca21 concentrations spanning from 1029 to1022 M. At the same time, Na1 and K1 cations at theirphysiological concentrations had negligible interfering effecton these sensors. Self-assembled monolayers of yet anotherlong-chain thiol compound were found to improve selectivityof gold coated cantilevers towards Hg21 cations. Hg21 atconcentrations as low as 10211 could be detected using thisapproach, while other cations, such as K1, Na1, Pb21,Zn21, Ni21, Cd21, Cu21, and Ca21 had little or no effecton the cantilever deflections.

Cantilevers modified with synthetic receptor compoundsof the molecular recognition type were also found to be use-ful for detection of various neutral aromatic compounds inaqueous solutions.136,223In particular, self-assembled mono-layers of a thiolated beta-cyclodextrin derivative and evapo-rated thin films of heptakis~2,3-O-diacetyl-6-O-tertbutyl-dimethylsilyl!-beta-cyclodextrin were studied on smooth andnanostructured gold-coated microcantilever surfaces. Inthose studies, micro- and nano-structural modifications ofmicrocantilevers chemical sensors were shown to improvethe stress transduction between the chemical coating and thetransducer. Structural modifications of microcantilever sur-faces were achieved using either chemical dealloying136 orfocused ion beam milling.223 The dealloyedsurfaces133,135,136,180,223contained nanometer-sized featuresthat enhanced the transduction of molecular recognitionevents into cantilever response, as well as increased coatingsstability in the case of thicker films. The observed responsefactors for the analytes studied varied from 0.02–604 nm/ppm. Calibration plots obtained for 2,3-dihydroxy-naphthalene and several volatile organic compounds revealedproportionality between the analyte concentrations and can-tilever deflections in the range of up to several hundred na-nometers. By manipulating surface morphologies and filmthicknesses, improvements in the limits of detection as greatas 2 orders of magnitude were demonstrated.136,223

C. Biosensors

An attempt to combine the biosensor concept and a can-tilever transducer took advantage of the ultrahigh calorimet-ric sensitivity of a bimaterial microcantilever.10,218By immo-bilizing glucose oxidize on the surface of 320-mm long, goldcoated silicon nitride cantilevers, Subramanianet al. createda glucose sensor that responded to presence of glucose in theaqueous medium due to the enzyme-induced exothermicprocesses.224 This sensor exhibited a good linear calibrationcurve for glucose concentrations in the range of 5–40 mM.Specificity of the sensor to glucose was confirmed in controlexperiments, in which responses to mannose were approxi-mately 25% of responses to glucose of the same concentra-tion. Control experiments also revealed subtle glucose re-sponsivity of the cantilever transducer without immobilizedenzyme.

Another indirect method of detecting biological speciesusing micromachined cantilevers was proposed by Baseltand coworkers.225,226Their force amplified biological sensor~FABS! utilized a micromachined cantilever placed in astrong magnetic field. Similar to many conventional biologi-cal assays, such as the enzyme-linked immunosorbent assay,the FABS method relied on labeled biological material, how-ever, magnetic beads rather than enzymes or fluorophoreswere used as a label. It was shown that an important advan-tage of the FABS method over existing bioassays is its capa-bility to detect trace amounts of extremely dilute biologicalsamples.

More recently, significant attention has been drawn todirect conversion of various biological receptor-ligand inter-actions into mechanical responses using cantilevertransducers.31,33,101,179,227–233Raiteriet al.explored high sen-sitivity of cantilever transducers to interfacial stresschanges227 in their work on a biosensor for a herbicide. Theresearchers reported bending responses of microfabricatedcantilevers associated with interaction between the surface-immobilized herbicide~2,4-dichlorophenoxyacetic! and themonoclonal antiherbicide antibody in an aqueous solution.The optical lever method was used to monitor deflections ofa cantilever placed in a liquid flow-through cell with a flowrate of 0.5 mL/min that was provided by a peristaltic pump.In the described experiments, standard gold coated siliconnitride AFM cantilevers were successively incubated in cys-teamine and glutaraldehyde solutions in order to activatethem for preferential binding of the 2,4-dichloro-phenoxyacetic-albumin conjugate on the gold surface. Thecantilever with thus immobilized herbicide exhibited par-tially reversible bending in response to the antiherbicide an-tibodies at the concentrations of 5 and 25mg/mL in a phos-phate buffer saline. The magnitude of the measuredresponses was about 50 nm, which significantly exceeded thereadout accuracy~0.1 nm!. Unfortunately, no clear correla-tion between the antibody concentration and the bendingmagnitude was observed in this study.

Despite the excellent sensitivity of cantilever transducersand their capability to detect receptor-ligand interactions di-rectly, the static deflection mode is not free from long-termdrifts and instabilities inherent to other types of biosensors.



In addition to temperature-induced drifts, it was also estab-lished that both specific binding and nonspecific adsorptionof proteins on various surfaces are accompanied with veryslow surface stress changes.230 Moulin et al.230 used micro-fabricated cantilevers to measure surface stress changes as-sociated with nonspecific adsorption of immunoglobulin G~IgG! and bovine serum albumin~BSA! on gold surfaces.Compressive and tensile surface stress changes were ob-served upon adsorption of, respectively, IgG and BSA. Thisdifference was attributed to different packing and deforma-tion of each protein on the gold surface. It was also con-cluded that biological assays based on surface stress mea-surements are sensitive to subtle differences in preparationand purification of proteins that are otherwise identical andcannot be differentiated using other techniques.230 Takinginto account extremely high sensitivity of cantilever bendingto interfacial biomolecular binding events, Moulinet al.31

proposed a clinically relevant cantilever biosensor for differ-entiation of low density lipoproteins~LDL ! and their oxi-dized form~oxLDL!. For this purpose, silicon nitride canti-levers with freshly evaporated gold were modified withheparin. The modification procedure included successive in-cubation of the cantilevers in 2-aminoethanethiol hydrochlo-ride and heparin solutions, and saturation of nonspecificbinding sites with BSA~each incubation was followed byrinsing in purified water!. The resulting cantilevers exhibitedpronounced bending in opposite directions upon exposure to120 mg/mL of LDL and 10mg/mL of oxLDL, respectively.The adsorption induced surface stress changes measured us-ing the cantilever biosensor were notably slower in compari-son to the binding kinetics observed in the control surfaceplasmon resonance measurements. Therefore, a conclusioncan be made that post-adsorption molecular rearrangementprocesses play an important role in generating prolonged re-sponses of the cantilever sensor.

A significant milestone in developing cantilever basedbiosensors was demonstration of their applicability to DNAanalysis.101,179,232,233Fritz et al. reported on sensitive andspecific monitoring of oligonucleotide hybridization usingarrays of functionalized cantilevers and optical readout oftheir deflections.101Arrays of 1mm thick, 500mm long rect-angular silicon cantilevers, custom designed and microfabri-cated at IBM Zurich Research Laboratory~Ruschlikon, Swit-zerland! were used in these studies. A thin layer of gold onone side of the cantilevers permitted controllable immobili-zation of thiomodified oligonucleotides. When 12-mer oligo-nucleotides with different degree of complementarity wereused in the hybridization assay, a single base pair mismatchwas clearly detectable. The use of a differential pair of can-tilever transducers, i.e., functionalized and ‘‘blank,’’ andanalysis of the differential deflections was an important re-finement that minimized interfering effects of temperature,mechanical vibrations, and fluid flow in the cell and, there-fore, provided more reliable differentiation of the responsesthat accompanied specific biomolecular interactions. The re-sidual noise in the differential signal corresponded to ap-proximately 0.5 nm. The LOD of the proposed method de-fined on the basis of this noise was estimated to be 10 nM. Inaddition to oligonucleotide hybridization assays, differential

cantilever deflection method was shown to be very promis-ing for monitoring a wide range of biological affinity inter-actions. In particular, irreversible differential responses wereobserved in the course of protein A–IgG interactions.31 In asimilar study reported by Raiteriet al.,228 85 ng/mL myoglo-bin in an aqueous solution was detected using a differentialpair of cantilevers, one of which was functionalized withmonoclonal antimyoglobin antibodies.

Nevertheless, under carefully controlled experimentalconditions ~temperature, pH, ionic strength, etc.!, even asingle cantilever transducer provides a sensitive means fordetection of various biomolecular interactions. For instance,Thundat and coworkers succeeded in differentiating a single-nucleotide mismatch using a cantilever transducer placed ina thermally stabilized flow cell.179,232Within approximately30 to 60 min after the sample injection, the cantilever deflec-tions reached a steady state that was typically in the range of225 to 10 nm. Both the rate and the magnitude of deflectionresponse were dependent on the length and sequence mis-match of the analyzed oligonucleotide. The same group ofresearchers also reported232 on detection of ultralow concen-trations~0.2 ng/ml! of prostate specific antigen~PSA! usinga similar thermoelectrically stabilized cell housing a singlecantilever transducer. In that clinically relevant study, thecalibration curve for PSA at the concentrations of 1022 to106 ng/mL was measured using a series of similar cantilevertransducers and plotted in terms of the generated surfacestress change. It is important to emphasize that backgroundbuffered solutions in these experiments contained physi-ological levels~1 mg/mL! of both human serum albumin andhuman plasminogen, thus making the reported results espe-cially clinically relevant.

Biotin-streptavidin is yet another example of high-affinity biomolecular interactions that was successfullymonitored using cantilever transducers. Raiteriet al. usedbiotin functionalized silicon nitride cantilevers and measuredtheir deflection responses in presence of 100 nMstreptavidin.228 These responses that reached approximately50 nm in magnitude within 10 min were largely reversible.In the case of high-affinity streptavidin-biotin interactions,the reversible nature of the responses is especially unex-pected and apparently indicates a nontrivial relationship be-tween the surface coverage of streptavidin molecules on thecantilever surface and the associated surface stress change.

It is important to note that the deflection responses ofcantilever based biosensors rarely exceed 100 nm regardlessof the chosen biological affinity system. This implies thatsignal-to-noise ratios and sensitivities achievable with con-ventionally designed cantilever biosensors may be limited bycommon fundamental mechanisms. A question arises as towhether such limitations can be surmounted. Recent studiesconduced by the authors of this article addressed this ques-tion by exploring cantilevers with asymmetrically nanostruc-tured surfaces and demonstrated feasibility of cantilever bio-sensors with dramatically enhanced responsivities. It wasfound that interfacial biomolecular recognition events wereconverted into mechanical responses much more efficientlywhen high density of nanosize features were present on oneside of the cantilever transducers. Creating of such interfaces



may rely on surface immobilization of gold nanospheres ordealloying of coevaporated Au:Ag films. The most efficienttransduction was achieved when the cantilevers were modi-fied with 50 to 75 nm thick dealloyed Au:Ag films. Unlikeconventional cantilevers with smooth surfaces, these nano-structured transducers exhibited up to several micron deflec-tions upon adsorption of protein A and biotin-labeled albu-min on nanostructured gold surfaces. Additional micrometerscale deflections of the cantilevers were observed upon inter-action of the surface immobilized receptors with, respec-tively, immunoglobulin G and avidin.10

Yet, another promising approach to ultrasensitive detec-tion of biological species in air was demonstrated by Ilicet al. using smaller cantilevers operating in the resonancemode.105,234The silicon nitride cantilevers used in these stud-ies were about 5mm long, had resonance frequencies in themegahertz range, and permitted detection of minute amountsof biological molecules or cells. In Fig. 13~top image!, weshow a micrograph of the cantilever used by Ilicet al.wherea single E. coli cell is present at the tip of the cantilever.Mass sensitivity of the designed cantilever sensor was suffi-cient to detect mass changes due to attachment of a singlemicrobial cell while modification of the cantilever surfacewith appropriate biological receptors, for instance antibodies,provided high detection specificity.

VII. DISCUSSION

Cantilever transducers are recognized as a promisingplatform for the next generation of chemical and biologicalsensors. It is anticipated that microfabricated cantilevers canprovide a versatile platform for real-time,in situ measure-ments of physical, chemical, and biochemical properties ofphysiological fluids. In general, the MEMS platform offers

an unparalleled capability for the development and mass pro-duction of extremely sensitive, low-cost sensors suitable forrapid analysis of many chemical and biological species.Compared with more conventional sensors, cantileversensors offer improved dynamic response, greatly reducedsize, high precision, and increased reliability. A plethoraof physical, chemical, and biological sensors based on themicromachined cantilever transducers have already beendemonstrated.7,30,45,63,66,115,119,136,137,207,218,137,207,218

An important advantage of microcantilever sensors isthat they can operate in vacuum, gases, and liquids. A com-pelling feature of the cantilever-based sensors operating inthe resonant mode is that four response parameters~reso-nance frequency, phase, amplitude, andQ-factor, measuredsimultaneously! may provide complementary informationabout the interactions between the sensor and the environ-ment. The damping effects of a liquid medium, however,reduce resonance responses of cantilever devices. In mostcommon liquids, such as aqueous solutions, the amplitude ofthe cantilever oscillations at the resonance can be orders ofmagnitude lower as compared to the same resonating canti-lever operating in air. On the other hand, operation in thestatic mode is unaffected by viscous properties of the me-dium. Therefore, microcantilever sensors operating in thestatic mode are especially attractive as a platform for nano-mechanical biochemical assays and other biomedical appli-cations.

Another unique advantage of cantilever sensors is thatdeformations and resonance frequency shifts measured si-multaneously provide complementary information about theinteractions between the transducers and the environment.Micro- and nano-scale cantilevers have extremely small ther-mal masses and can be heated and cooled with thermal timeconstants of less than a millisecond. This is advantageous forrapid reversal of molecular absorption processes and regen-eration purposes. Both static and dynamic responses of can-tilever sensors can be measured with very high precisionusing several readout techniques46 based on optical beamdeflection, interferometry, electron transfer, piezoresistance,capacitance, and piezoelectric properties. Other resonanceparameters of cantilever transducers, such as amplitude andQ-factor, can be extracted from these responses measured inan appropriate frequency or time domain.

Cantilevers operating in the static mode often surpass inperformance cantilevers operating in the resonant operation.However, the mass sensitivity of cantilever transducers oper-ating in the resonance mode increases as their dimensions arereduced. Therefore, cantilever sensors with progressively in-creased mass sensitivity can be fabricated by simply reduc-ing the transducer dimensions.74,151,235,236As the technologyof nanosize mechanical structures advances, nanomechanicaldevices approach the gigahertz frequency domain that is al-ready widely explored with electronic and optical devices. Inorder to achieve fundamentally limited performance of reso-nating cantilever sensors, it is necessary to delineate thenoise present in micromechanical systems. The type of noisein cantilever devices referred to as ‘‘thermomechanical’’46,148

or ‘‘mechanical-thermal noise’’237,238 arises from the dy-namic equilibrium between mechanical energy of the device

FIG. 13. Resonating cantilever devices that provide mass sensitivity suffi-cient for a single cell detection. These sensors were described in studies by~a! Ilic et al. ~Ref. 105! and ~b! Lavrik and Datskos~Ref. 74!.



and thermal energy of the surrounding environment at non-zero temperatures. This type of noise imposes the ultimatelimits on the performance of microcantilever sensors operat-ing in the resonance mode.

The advantages of cantilever sensors can be further ex-panded by arranging individual cantilever transducers intolarge multisensor arrays integrated with on-chip electroniccircuitry.239 One-dimensional and two-dimensional arrays ofcantilever transducers offer additional advantages that cannotbe overlooked. In particular, such arrays provide a viableplatform for the development of high-performance ‘‘elec-tronic noses.’’

ACKNOWLEDGMENTS

The authors would like to acknowledge support from theDefense Advanced Research Projects Agency, the NationalScience Foundation, and the U.S. Department of Energy.This work was performed in part at the Cornell Nanofabri-cation Facility ~a member of the National NanofabricationUsers Network! which is supported by the National ScienceFoundation under Grant No. ECS-9731293, Cornell Univer-sity and industrial affiliates. This work was partially sup-ported by the Laboratory Director’s Research and Develop-ment Program of Oak Ridge National Laboratory. Oak RidgeNational Laboratory is operated for the U.S. Department ofEnergy by UT-Battelle under contract DE-AC05-96OR22464.

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REVIEW ARTICLE Cantilever transducers as a platform for chemical and biological sensorscau.ac.kr/~jjang14/BioMEMS/Lavrik_Datskos_RSI_Cantilever... · 2006-03-23 · REVIEW ARTICLE