biosensors and bioelectronics - · pdf filebiosensors and bioelectronics 32 (2012) 1–18...

Biosensors and Bioelectronics 32 (2012) 1– 18

Contents lists available at SciVerse ScienceDirect

Biosensors and Bioelectronics

j our na l ho me page: www.elsev ier .com/ locate /b ios

Biosensing using dynamic-mode cantilever sensors: A review

Blake N. Johnson, Raj Mutharasan ∗

Department of Chemical and Biological Engineering, Drexel University, Philadelphia, PA 19104, United States

a r t i c l e i n f o

Article history:Received 26 July 2011Received in revised form 25 October 2011Accepted 27 October 2011Available online 4 November 2011

Keywords:Dynamic-modeResonant frequencySensitivity

a b s t r a c t

Current progress on the use of dynamic-mode cantilever sensors for biosensing applications is criticallyreviewed. We summarize their use in biosensing applications to date with focus given to: cantileversize (milli-, micro-, and nano-cantilevers), their geometry, and material used in fabrication. The reviewalso addresses techniques investigated for both exciting and measuring cantilever resonance in variousenvironments (vacuum, air, and liquid). Biological targets that have been detected to date are summa-rized with attention to bio-recognition chemistry, surface functionalization method, limit of detection,resonant frequency mode type, and resonant frequency measurement scheme. Applications published todate are summarized in a comprehensive table with description of the aforementioned details includingcomparison of sensitivities. Further, the general theory of cantilever resonance is discussed includ-

BiosensingResonant cantilever

ing fluid–structure interaction and its dependence on the Reynolds number for Newtonian fluids. Thereview covers designs with frequencies ranging from ∼1 kHz to 10 MHz and cantilever size ranging from
millimeters to nanometers. We conclude by identifying areas that require further investigation.
© 2011 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. Dynamic-mode cantilever theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1. Transverse modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2. Torsional modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3. Lateral modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4. Longitudinal modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.5. Mass-change and stiffness-change effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3. Geometries and materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.1. Materials of fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2. Single-layer geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3. Multi-layer geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.4. Length scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4. Exciting and measuring resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.1. Techniques for exciting and measuring resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2. Combinations used for exciting and measuring resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5. Surface functionalization and bio-recognition agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.1. Antibody-based bio-recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.2. Nucleic acid-based bio-recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.3. Alternative bio-recognition agents and surface reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6. Sensing using high-order modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7. Fluid–structure interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
7.1. Reynolds number and fluid effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147.2. Q-value enhancement strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

∗ Corresponding author. Tel.: +1 215 895 2236; fax: +1 215 895 5837.E-mail address: [email protected] (R. Mutharasan).

0956-5663/$ – see front matter © 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.bios.2011.10.054

dx.doi.org/10.1016/j.bios.2011.10.054

http://www.sciencedirect.com/science/journal/09565663

http://www.elsevier.com/locate/bios

mailto:[email protected]

dx.doi.org/10.1016/j.bios.2011.10.054

9. Sensitivity characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1610. Conclusions and future trends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

tmmfmi(besGb1esmttctLa2tg2aeeo

rbis(ccbonbii

taartvrb

where L is the length, t is the thickness, E is the Young’s modulus,

. Introduction

Over the past two decades, the field of biosensing has evolvedo include a wide range of methods and devices aimed towards

easuring biological targets and processes that are important inedical diagnostics, environmental monitoring, bio-warfare, and

undamental research (Van Emon, 2007; Cooper, 2009). Commonethods-based biosensing approaches include enzyme-linked

mmunosorbent assay (ELISA) and polymerase chain reactionPCR), while common device-based approaches include optics-ased devices, such as surface plasmon resonance (SPR) (Hoat al., 2007; Fan et al., 2008), electrochemical-based devices,uch as amperometric and potentiometric sensors (Wang, 2006;rieshaber et al., 2008; Pohanka and Skládal, 2008), and acoustic-ased devices, such as quartz crystal microbalance (QCM) (Hepel,999; Marx, 2003) and surface acoustic wave (SAW) sensors (Länget al., 2008). Cantilever sensors, a class of acoustic-based sen-ors, are highly sensitive devices capable of label-free quantitativeeasurement of biomolecular interactions. They are a platform

echnology and adaptable for various diverse biosensing applica-ions. Cantilever sensors have been used to measure the mass ofells and biomolecules (Ilic et al., 2001; Burg et al., 2007), concentra-ions of dilute cell suspensions (Campbell and Mutharasan, 2007b;i et al., 2009), nucleic acids (Su et al., 2003; Ilic et al., 2005), as wells bacterial and fungal growth (Gfeller et al., 2005b; Nugaeva et al.,005). They have been extensively investigated for low-level detec-ion applications and for studying biomolecular interactions. Manyeneral reviews on cantilever sensors have appeared (Raiteri et al.,001; Lavrik et al., 2004; Ziegler, 2004; Craighead, 2007; Waggonernd Craighead, 2007; Fritz, 2008; Goeders et al., 2008; Singamanenit al., 2008; Boisen and Thundat, 2009; Datar et al., 2009; Mutyalat al., 2009; Alvarez and Lechuga, 2010). The current review focusesn biosensing applications only.

There are two modes in which cantilever sensors are used,eferred to as the static-mode and the dynamic-mode. Sensingiomolecular interactions in the static-mode relies on binding-

nduced changes in the cantilever deflection caused by differentialurface stress. On the other hand, sensing in the dynamic-modealso called resonant-mode) relies on binding-induced changes inantilever resonant frequency caused by mass-change or stiffness-hange. Thus, in the dynamic-mode, the surface biochemicalinding is sensed directly since the resonant frequency is a functionf the cantilever mass. In the static-mode, the sensing medium isot a limiting environment, as long as the cantilever deflection cane measured accurately. However, in the dynamic-mode, the sens-

ng medium is of concern since cantilever dynamics can be stronglynfluenced by fluid effects, such as viscous damping.

In this review, we limit our discussion to dynamic-mode can-ilever sensors because they have shown the highest potential forchieving the most sensitive measurements of biomolecular inter-ctions. Also, due to the breadth of the field, only those applicationselated specifically to biosensing will be included. This review con-ains a basic discussion of resonating cantilever structures, their
arious resonant modes, surface functionalization techniques, bio-ecognition agents, and a comprehensive summary of reportediosensing applications to date. The sensitivity data published over
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

the past decade is found to show a complex correlation betweensensitivity and device characteristics, such as size and resonantfrequency. The analysis indicates that the correlation between sen-sitivity and device size is not a simple one due to the use ofhigh-order modes and non-uniform cantilever design.

2. Dynamic-mode cantilever theory

The International Union of Pure and Applied Chemistry (IUPAC)defines a biosensor as a device that uses specific biochemicalreactions mediated by isolated enzymes, immune-systems, tis-sues, organelles, or whole cells to detect chemical compounds(McNaught and Wilkinson, 1997). The sensor transduces directinteraction with a specific target analyte through electrical, ther-mal, or optical signals that can be both measured and recorded.Sensor features are shown schematically in Fig. 1. As illustrated,dynamic-mode cantilevers respond to surface biochemical inter-actions through resonant frequency change caused by a change inits mass or stiffness. Although the resonant frequency is used to dis-cern molecular binding, a variety of different resonant modes maybe used for sensing. The various mode types that arise in a can-tilever sensor are illustrated in Fig. 2, which shows schematics ofthe various possible resonant mode shapes. In general, the motionis described as either out-of-plane or in-plane with respect to theplane formed by the cantilever’s two largest dimensions. Out-of-plane vibrations include transverse, also called bending or flexural,and torsional motion. In-plane vibrations include lateral, also calledin-plane bending, and longitudinal, also called extensional or axial,motion. Equations of motion for all of the aforementioned vibra-tions can be found in the following references (Timoshenko, 1937;Timoshenko and Goodier, 1970).

Each of the four aforementioned modes exhibit resonance whenexcited at their characteristic frequency, known as the resonantfrequency or eigen frequency. Further, certain cantilevers mayexhibit mode coupling depending on the device characteristics.Analytical expressions for various mode shapes can be derivedmathematically from the corresponding equations of motion underthe following assumptions: the aspect ratio is sufficiently large, thedeflection is small compared to cantilever thickness, the geom-etry is of single-layer uniform rectangular cross-section, and thematerial is isotropic.

2.1. Transverse modes

The nth order transverse mode resonant frequency is given by(Timoshenko, 1937; McFarland et al., 2005a):

f nTr = t

4�

�2n

L2

√E

3�c(1)

2 B.N. Johnson, R. Mutharasan / Biosensors and Bioelectronics 32 (2012) 1– 18

8. Biosensing application formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158.1. Dip-dry-measure format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158.2. Continuous-measurement format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

�c is the cantilever material density, �n is the eigenvalue given bythe nth positive root of 1 + cos(�n)cosh(�n) = 0, and n is a positiveinteger. The first three eigenvalues are 1.875, 4.694, and 7.855.

B.N. Johnson, R. Mutharasan / Biosensors and Bioelectronics 32 (2012) 1– 18 3

mic-m

2

(

f

wPa

�

F(s

Fig. 1. General schematic of dyna

.2. Torsional modes

The nth order torsional mode resonant frequency is given byTimoshenko and Goodier, 1970; McFarland et al., 2005a):

nTo = (2n − 1)

4L

√G�

�cIp(2)

here G = E/2(1 + �) is the shear modulus, w is the width, � is theoisson ratio, Ip = (tw3 + t3w)/12 is the polar moment of inertia, n is

positive integer, and � is defined as:

= 13

t4[

w

t− 192

�5

∑∞

n=1

1n5

tanhn�w

2t

](3)

ig. 2. General schematic of a traditional cantilever (A) and various types of resonant modC), lateral mode (D), and longitudinal mode (E) are shown. Only fundamental mode shapehape clarity. Dashed arrows represent cantilever motion through the resonant cycle.

ode cantilever sensing principle.

2.3. Lateral modes

The nth order lateral mode resonant frequency is given by(Timoshenko, 1937; McFarland et al., 2005a):

f nLa = w

4�

�2n

L2

√E

3�c(4)

where �n is the nth positive root of 1 + cos(�n)cosh(�n) = 0. Note thateigenvalues are the same as for out-of-plane transverse modes.

2.4. Longitudinal modes

The nth order longitudinal mode resonant frequency is given by
(Timoshenko, 1937; Castille et al., 2010):
f nLo = (2n − 1)

4L

√E

�c(5)

es found in idealized cantilever sensors (B–E). Transverse mode (B), torsional modes of each mode are shown for clarity. Displacements are arbitrarily scaled for mode

4 B.N. Johnson, R. Mutharasan / Biosensors

Table 1Summary of cantilever resonant modes in terms of the simple harmonic oscillatormodel where m = �cLwt is the cantilever mass.

Mode Resonant Frequency Constant (ci,n) Spring Constant (ki)

Transverse cTr,n

√kTrm

�2n

2�Ewt3

12L3

Torsional cTo,n

√kTom

2n−14

G�wtIpL√

�2 3

roa

f

w(saffsletc(l1flimffa

2

tfate

�

citccru

cs(Gtt

Lateral cLa,nkLam

n2�

Ew t12L3

Longitudinal cLo,n

√kLom

2n−14

EwtL

It is customary to express resonant frequency as a square rootatio of effective spring constant (ki) and mass (m) for comparisonf each mode with an equivalent harmonic oscillator model givens:

ni = ci,n

√ki

m(6)

here i = Transverse (Tr), Torsional (To), Lateral (La), or LongitudinalLo) modes and ci,n is a mode-type and mode-order dependent con-tant. Therefore, Eqs. (1), (2), (4), and (5) have been cast into such

form and are summarized in Table 1. One notes that the constantor bending and lateral modes is the same. Similarly, the constantor torsional and longitudinal modes is the same. However, thepring constants are significantly different. Given that L > w, theowest spring constant is achieved with the flexural mode. Forxample, a 500-100-10 �m3 (L-w-t) silicon micro-cantilever withhe following material properties, Young’s modulus (E) = 150 GPa,antilever density (�c) = 2300 kg/m3, and Poisson ratio (�) = 0.17Petersen, 1982; Spiering et al., 1993), has transverse, torsional,ateral, and longitudinal mode spring constants (ki) of 10, 4.7e3,e3, and 3e5 kg/s2, respectively, and fundamental mode resonantrequencies of 52.2, 507.9, 522.0, and 4040 kHz, respectively. Theowest spring constant is found in the flexural mode and the highestn the longitudinal mode. Thus, for practical purposes the flexural

ode can be thought of as the mode that manifests at the lowestrequency. The torsional and lateral modes occur at similar resonantrequencies because of the nature of both the leading constant (ci,n)nd the spring constant (ki).

.5. Mass-change and stiffness-change effects

Sensing events in dynamic-mode cantilevers cause changes inhe resonant frequency. The primary mechanism of the resonantrequency change occurs through binding-induced mass-changend/or spring constant-change (stiffness-change). The effects onhe resonant frequency can be expressed most simply by (Chent al., 1995):

f = 12

fn

(�k

k− �m

mn

)(7)

Eq. (7) indicates that the resonant frequency decreases as theantilever mass increases, but increases if its spring constantncreases. In Eq. (7), the mass or stiffness changes are assumedo occur uniformly over the entire cantilever (Ziegler, 2004), aondition which is often not satisfied in practical biosensing appli-ations due to localized binding areas selected for optimum sensoresponse. Therefore, Eq. (7) is an approximation. Nevertheless, it isseful for interpreting sensor response.

Although various reports have observed resonant frequencyhanges attributed to adsorption-induced changes in cantileverpring constant or surface stress even though mass was attached
Thundat et al., 1995; Rogers et al., 2003; McFarland et al., 2005b;upta et al., 2006; Hwang et al., 2006; Tamayo et al., 2006),
he majority of reports to date found the resonant frequencyo decrease upon analyte binding attributed to an increase in

and Bioelectronics 32 (2012) 1– 18

cantilever mass. This indicates that the mass-change binding effectis often dominant relative to the stiffness-change effect in mostbiosensing applications. Therefore, the stiffness term in Eq. (7)is often neglected which gives rise to a relation dependent onlyon mass-change effects. The resulting relation can be restated todefine mass-change sensitivity:

�n = �f

�m= −1

2fn

mn(8)

The mass-change sensitivity has also been defined as the inverseof Eq. (8) in several reports. Another related characterization ofsensitivity is the minimum mass capable of being sensed, referredto as the limit of detection (LOD). Solving Eq. (8) for the minimumdetectable added-mass (�mmin) shows that the LOD depends onthe effective sensor mass and quality factor (Q) = fn/�fPWHM, where�fPWHM is the peak width at half-maximum:

LOD ≡ �mmin ∝ mn

Q(9)

As can be seen from the above equation, both values are relatedto the resonant frequency and mode order, and thus, the simplelooking relationship is actually quite complex. We emphasize thatthe above is the best sensitivity possible and should be used asa guideline since it is derived from idealized models. AlthoughQ-value is related to uncertainty in the resonant frequency mea-surement, the realizable LOD must be determined experimentallysince acceptable signal-to-noise ratio (SNR) is a practical consid-eration in biosensing applications. Therefore, the experimentallymeasured sensitivity may differ from values predicted by Eqs.(7)–(9), especially for sensors which use high-order resonantmodes and are of non-uniform designs. In addition, differencesmay arise between experiments and theory because the assump-tions used in developing Eqs. (7)–(9) are purely mechanical anddeflection-based, while a variety of new electromechanical designshave evolved that measure analyte binding through ways that areindirectly related to deflection, such as bulk active layer prop-erty changes. For high-order mode characterization in non-uniformsensor designs, both numerical techniques and experiments arenecessary for evaluating device sensitivity and LOD.

3. Geometries and materials

A wide range of design materials, sizes, and geometries havebeen extensively investigated since the dynamic-mode cantileverwas originally introduced (Binnig et al., 1986). We summarize herethe main features that have appeared in biosensing applications.

3.1. Materials of fabrication

Traditionally, silicon-based materials, such as silicon, siliconnitride, and silicon dioxide, are popular materials because theyexhibit relatively low energy dissipation and resonate with high Q-values (Ilic et al., 2000; Su et al., 2003; Gupta et al., 2004a). Further,such materials are suitable for fabricating cantilevers at micro- andnano-scales using semi-conductor fabrication processes. In addi-tion to silicon-based materials, materials with unique properties,such as piezoelectric and magnetoelastic materials, have also beenused in many designs (Yi et al., 2002; Lee et al., 2004a; Li et al.,2009). Such materials offer alternative techniques for both excitingand measuring cantilever resonance. Polymers that show compa-rable elastic characteristics to the more traditional materials have
also been investigated (McFarland et al., 2004). Designs of similargeometry but different material will have different mass and springconstant (Table 1), and therefore, different resonant frequenciesand sensitivities.

nsors

uccb2d(w2tiqasS

3

hcod2nrFsli(2ilafl

a2rmestdmrewct2c

3

ctdte2ap

B.N. Johnson, R. Mutharasan / Biose

Due to the large number of possible materials that can besed for fabricating dynamic-mode cantilevers, biosensing appli-ations have been carried out using a wide variety of differentantilever designs. For example, silicon-based cantilevers haveeen used to estimate the mass of a single cell (Ilic et al., 2000,001). Piezoelectric-based cantilevers were shown to measure veryilute bacterial pathogen concentrations continuously in liquidCampbell and Mutharasan, 2007b). Metal oxide-based cantileversere used to detect prostate cancer biomarkers (Vancura et al.,

007). In Table 2, the majority of biosensing applications reportedo date are summarized with a description of materials usedn the design. While material impacts both the resonant fre-uency and the Q-value, it also appears that sensitivity and LODre influenced by techniques used for both exciting and mea-uring resonance. These considerations are further discussed inection 4.

.2. Single-layer geometry

Besides the materials reported, cantilever designs investigatedave a large variety in geometry. They fall broadly into designsonsisting of either a single-layer or multi-layers. The geometryf the layers can vary in both shape and size. The single-layeresigns often have uniform rectangular cross-section (Ilic et al.,000; Davila et al., 2007; Park et al., 2008) due to fabrication conve-ience and advantage of using analytical theory to interpret sensoresponse. Examples of such designs are shown in Fig. 3A and B.ig. 3A shows a cantilever array (Nugaeva et al., 2007), while Fig. 3Bhows a single cantilever (Johnson et al., 2006). Such rectangu-ar cross-section designs also vary in aspect ratio, since changesn aspect ratio have been shown to impact device performanceLee et al., 2007a; Vazquez et al., 2009; Waggoner and Craighead,009). For example, a decrease in the aspect ratio was shown to

mprove the sensitivity to molecular binding of angiopoietin-1 iniquid (Ricciardi et al., 2010). Such a result is not surprising as thespect ratio directly affects both the resonant frequency and theuid–structure interaction.

Single-layer designs with non-rectangular cross-section havelso been investigated (Lee et al., 2006; Jin et al., 2007; Liu et al.,009). Arguments for exploring new geometry include: selectiveesonant-mode actuation, Q-value enhancement, fluid dampinginimization, and increased sensitivity. For example, some inter-

sting highlights include the paddle geometry, also called T-shaped,hown in Fig. 3C (Pang et al., 2006; Xia and Li, 2008) and theriangular geometry, also called V-shaped (Su et al., 2003). Suchesigns can also be highly sensitive and have unique resonantodes due to non-uniform design. The T-shaped piezoelectric

esonators shown in Fig. 3C showed femtogram sensitive lateral-xtensional modes (Pang et al., 2006). As shown in Fig. 3D, designsith small tip extensions have been examined for minimizing the

antilever mass while at the same time maintaining the integrity ofhe actuating active layer (Salehi-Khojin et al., 2009; Vazquez et al.,009). In the summary Table 2, geometric data are included foromparison.

.3. Multi-layer geometry

In addition to single-layer designs, many multi-layer designsonsisting of multiple materials have been investigated. Evenhough the cantilever mass is increased relative to single-layeresigns because of added layers, the added layers provide advan-ages to the sensor, such as eliminating the need for external
xcitation and measurement components (for example; Shih et al.,003). Multi-layer designs typically have a single-layer devoted toctuation, called an active layer. The active layer is often either aiezoelectric (for example; Hwang et al., 2004; Lee et al., 2005) or
and Bioelectronics 32 (2012) 1– 18 5

magnetoelastic material (Li et al., 2009). Further, the active layercan also be used to measure resonance. In addition to active layers,multi-layer designs also contain inactive, sometimes called pas-sive, layers for modifying geometry and cantilever properties, suchas the spring constant, or to inhibit active layer deformation (Shihet al., 2003; Campbell and Mutharasan, 2005a). Bi-layer designswith equal length layers, called unimorphs and bimorphs, wereamong the first of such designs to be investigated (Smits et al.,1991; Itoh et al., 1996; Coughlin et al., 1997; Gaucher et al., 1998;Yi et al., 2002; Shih et al., 2003). Although they are of similargeometry, unimorphs and bimorphs differ based on the number ofactive layers they contain. Subsequently, the multi-layer designsevolved to include designs in which the layers were no longerof the same length (Yi et al., 2003; Campbell and Mutharasan,2005a). Such designs intrinsically contain step-discontinuities incross-section which were shown to introduce unique resonanceproperties (Mahmoodi and Jalili, 2007, 2008, 2009; Johnson andMutharasan, 2011a). Examples of designs with unequal lengthswere investigated by several research groups (Hwang et al., 2004;Lee et al., 2004a; Campbell and Mutharasan, 2005b; Lee et al.,2008). The non-uniform multi-layer designs have shown uniqueresonance properties relative to the single-layer designs. Such aconsequence is analogous to the unique resonant modes that arisein non-uniform single-layer designs relative to traditional modesfound in uniform rectangular cross-section designs. For example,multi-layer piezoelectric sensors with step-discontinuities give riseto femtogram sensitive high-order longitudinal-bending modes(Maraldo et al., 2007b; Johnson and Mutharasan, 2011a). Also, it hasbeen suggested that geometric non-linearity of the piezoelectriclayer can play a significant role in the dynamic range (Mahmoodiet al., 2008).

3.4. Length scales

Cantilever sensors of length ranging from millimeters tonanometers have been investigated (see Table 2). The trend ofreducing the size is motivated by deflection-based models, Eqs.(7)–(9), for achieving high sensitivity. At the same time investiga-tion of larger cantilevers operating in high-order modes have beenpursued in parallel. High-order modes have provided an alternativemethod for achieving femtogram sensitivity without drasticallyreducing device size, and are further discussed in Section 6. Thus,cantilever devices used in biosensing may differ in size by ordersof magnitude.

In addition to the resonant frequency and the sensitivity, sizeaffects other characteristics. It is well-known that as the cantileverdimensions decrease, a greater amount of energy is dissipated byviscous damping (Sader, 1998). Thus, maintaining high Q-values innon-vacuum environments becomes difficult without adding addi-tional energy to the resonator with amplification strategies, whichis further discussed in Section 7. Cantilever size also directly affectsthe probability of sensing the target on a practical time scale. Sincesensing will only take place when analyte binds to the cantilever,the size directly influences the detection time, an important con-cern for detection-based biosensing applications. In the summarygiven in Table 2, we see that there are both advantages and dis-advantages associated with both small and large cantilevers. Thesuitable choice depends on the intended application. Regardless ofthe heuristics guiding cantilever biosensor design, the goal is todevelop sensors that show: (1) sensitive resonant modes to molec-ular binding, (2) provide large dynamic range, (3) high probabilityof encountering the target on a practical time scale, and (4) the abil-
ity to measure in liquids. As should be noted from the past threesections, researchers have reported a variety of designs of differentsizes, shapes, and materials in attempts to achieve the identifiedperformance metrics.

6B.N

. Johnson,

R.

Mutharasan

/ Biosensors

and Bioelectronics

32 (2012) 1– 18Table 2Overview of dynamic-mode cantilever devices and applications. Abbreviations used: immunoglobulin (Ig), colony-forming unit (CFU), not available (N/A).

Material & Size Geometry/Design Actuationmethod/Sensingmethod

Mode type, Modeorder, & Resonantfrequency

Measurementmedium & Q-value

Target or application,Recognition agent (RA), &Sensitivity (S)

Resonantfrequencymeasurementformat

Reference

MicrobesSilicon-based,L = N/A

Suspendedmicrochannelresonator,Hollow internalchannels

N/A N/A N/A Single cell B. subtilis,E. coli, S. cerevisiae, &L1210 lymphoblastsgrowth rate,RA: Buoyant mass

Continuous Godin et al. (2010)

Silicon-based,L = N/A

Suspendedmicrochannelresonator,Hollow internalchannels

N/A N/A N/A Growth cycle variationson mass, density, andvolume in yeast,RA: Buoyant massS: ∼3 fg

Continuous Bryan et al. (2010)

Piezoelectric- andsilicon-based,L ∼ 2 mm

Composite,rectangularcross-section,step-discontinuity

Active piezoelectriclayer/Impedance

mode N/A,n = N/A,f = 865 kHz

Liquid:Q = 30

C. parvum oocystdetection,RA: IgG and IgM,S: 5 oocysts/mL

Continuous Xu and Mutharasan(2010a)




mode N/A,n = N/A,f ∼ 856 kHz

Liquid:Q = 30

A. laidlawii mycoplasmadetectionRA: Ig,S: <103 CFU/mL

Continuous Xu et al. (2010)

Piezoelectric- andsilicon-based,L = 2.7 mm




Liquid:Q = 26

G. lamblia cyst detection,RA: Ig,S: <10 cysts/mL

Continuous Xu and Mutharasan(2010b)

Magnetoelastic-andmetal-based,L ∼ 3 mm

Rectangular-cross-section,bimorph

Activemagnetostrictivelayer/Magnetic

Transverse,n = 1,f ∼ 2.6 kHz

Liquid:Q ∼ 20

B. anthracis detection,RA: phage,S: ∼105 CFU/mL

Continuous Li et al. (2009)

Piezoelectric- andsilicon-basedL ∼ 3.0 mm




Liquid:Q = 15

C. parvum oocystdetection,RA: IgM,S: 100 oocysts/mL

Continuous Campbell andMutharasan (2008)

Silicon-based,L = 25–40 �m

Single-layer,rectangularcross-section, array

Electrical/Optical

Transverse,n = 1,f ∼ 35 kHz

Liquid:Q = N/A

Single HeLa cell mass,RA: Poly-L-lysine

Batch Park et al. (2008)

Silicon-based,L = 596 �m

Single-layer,triangular (wedge)tip

Piezoceramic base/Optical

Transverse &Torsional,n = 1, 2,f ∼ 30–285 kHz

N/A Ragweed pollendetection,RA: physisorption,S: single pollen

Batch Xie et al. (2008)

Silicon-based,L = N/A

Suspendedmicrochannelresonator, hollowinternal channels

N/A N/A Vacuum(liquid-filledchannel):Q ∼ 8000–15,000

E. coli and human redblood cell mass densities,RA: Buoyant mass

Continuous Godin et al. (2007)


Single-layer,uniformrectangularcross-section

Thermal noise/Optical

Transverse,n = 1,f = N/A

Liquid:Q < 5

B. anthracis detection,RA: Ig,S: 50 spores

Batch Davila et al. (2007)

Piezoelectric- andsilicon-based,L ∼ 3.0 mm




Liquid:Q ∼ 12

B. anthracis detection,RA: Ig,S: 38 spores/L (airconcentration)

Continuous Campbell et al.(2007a)

B.N.

Johnson, R

. M

utharasan /

Biosensors and

Bioelectronics 32 (2012) 1– 18

7





Liquid:Q ∼ 15

B. anthracis detectionamong B. cereus & B.thuringiensis,RA: Ig,S: 333 spores/mL

Continuous Campbell andMutharasan(2007a)





Liquid:Q ∼ 20–30

E. coli O157:H7 detectionin food matrices,RA: Ig,S: 1–100 cells/mL

Continuous Campbell et al.(2007b), Maraldoand Mutharasan(2007a,c)



Electrostatic/Optical

Transverse,n = N/Af ∼ 200 kHz

Liquid-filled:Q = 15,000

Single E. coli and B.subtilis cell mass,RA: Buoyant mass

Continuous Burg et al. (2007)

Piezoelectric- andsilicon-based,L = 3 mm



Transverse,n = 1,f = 31 kHz

Air:Q = 39

E. coli JM101 growth rate,RA: agar layer

Continuous Detzel et al. (2006)



N/A/Optical

Transverse,n = 5,f = 280 kHz

Air:Q = N/A

B. subtilis detection,RA: polypeptide,S: 1e5 spores/mL

Batch Dhayal et al. (2006)

Silicon-based,L = 250, 500 �m

Composite,rectangularcross-section, array

N/A/Optical

Transverse,n = N/Af ∼ 30–135 kHz

Air:Q = 116

A. niger & S. cerevisiaegrowth and detection,RA: concanavalin A,fibronectin, & IgG,S: 10e3 CFU/mL

Batch Nugaeva et al.(2005)


Single-layerrectangularcross-section, array

N/A/Optical

Transverse,n = N/A,f ∼ 33 kHz

Air:Q = N/A

E. coli XL1-Blue growth,RA: agar layer,S: ∼100–200 cells,50–140 pg/Hz

Continuous Gfeller et al.(2005a,b)

Piezoelectric- andsilicon-based,L = 3–5 mm



Transverse,n = 2f ∼ 55 kHz

Liquid:Q = 30–100

E. coli O157:H7 detectionamong E. Coli JM101,RA: Ig,S: 700 cells/mL

Continuous Campbell andMutharasan(2005b)


Single layer,rectangularcross-section


Transverse,n = 1f ∼ 85 kHz

Air:Q ∼ 55

L. innocua detection,RA: Ig,S: 65–90 Hz/pg

Batch Gupta et al. (2004a)

Silicon-basedL = 15–25 �m



Transverse,n = 1,f ∼ 1 MHz

Air:Q ∼ 50

Single cell E. coliO157:H7 detection,RA: Ig,S: 1–7 Hz/fg

Batch Ilic et al. (2001)

Silicon-basedL = 100–200 �m




Air:Q = 5–8

E. coli O157:H7 detection,RA: Ig,S: ∼6 Hz/pg, 14.7 fg


ProteinsSilicon-based,L ∼ 200 �m


N/A Transverse,n = N/A,f = 200 kHz

Vacuum (liquidfilled channel):Q = N/A

Human recombinantactivated leukocyte celladhesion molecule(ALCAM) detection inundiluted serum,RA: IgG,S: 10 ng/mL

Continuous von Muhlen et al.(2010)


Single-layer,T-shapedcross-section

Lorentz force/Piezoresistive

Torsional,n = N/A,f = 95–99 kHz

Air:Q = 3500–4000

Alpha-fetoprotein (AFP)detection,RA: Ig,S: 2 ng/mL

Continuous Liu et al. (2009)

8B.N

. Johnson,

R.

Mutharasan

/ Biosensors

and Bioelectronics

32 (2012) 1– 18

Table 2 (Continued )






Reference


Single-layer,uniform-rectangular

N/A/Optical

Transverse,n = 1, 2f = 12–74 kHz

Vacuum:Q = N/A

Anti-IgG detection,RA: IgG,S: 0.4–2.5 Hz/pg

Batch Oliviero et al.(2009)

Piezoelectric- andsilicon-based,L = 30–240 �m



Transverse,n = N/A,f ∼ 0.03–3.3 MHz

N/A:Q = 213–677

Human IgG detection,RA: reactive thiol-basedSAM,S: 3 fg/Hz

Batch Shin et al. (2008)

Piezoelectric- andsilicon-based,L = 100 �m


Active piezoelectriclayer/Impedance &Optical

Transverse,n = 1,f ∼ 1.2 MHz

Air:N/A

Carcinoembryonicantigen (CEA) detection,RA: Ig,S: 30 pM (5 ng/mL)

Batch Lee et al. (2008)


Single-layer,cross-shaped


Torsional,n = 2,f = 525 kHz

Air:Q = 11–45

Alpha-fetoprotein (AFP)detection,RA: Ig,S: ∼9 fg

Batch Xia et al. (2008)


Single-layer,cross-shapedT-shaped, &rectangular


Transverse &Torsional,n = 1,2f = 47–518 kHz

Air:Q ∼ 1000–10,000

Streptavidin detection,RA: biotinylatedthiol-based SAMS: 0.33–5.1 Hz/pg

Batch Xia and Li (2008)

Metal oxide -based,L = 150 �m

Single-layer,uniform-cross-section

LorentzForce/Piezoresistive

Transverse,n = 1,2,3,f ∼ 200–700 kHz

Liquid:Q ∼ 10–20

Prostate specific antigen(PSA) detection,RA: Ig,S: 10 ng/mL

Continuous Vancura et al.(2007), Li et al.(2008)





Liquid:Q = 28–35

Staphylococcylenterotoxin B (SEB)detection in foodmatrices,RA: Ig,S: 100 fg

Continuous Maraldo andMutharasan(2007b)





Liquid:Q = 28–31

Alpha-methylacyl-CoAracemase (AMACR)detection in urine,RA: Ig,S: 3 fg/mL

Continuous Maraldo et al.(2007a)

Silicon-basedL = 300 �m

Single-layer,T-shaped

Lorentz Force/Piezoresistive

Torsional,n = 1f = 97 kHz

Air:Q = 3,725

Streptavidin detection,RA: biotinylatedthiol-based SAM,S: ∼23 fg

Batch Jin et al. (2007)


Single layer,rectangularcross-section, array

Active piezoelectriclayer/Piezoelectric

Transverse,n = 1f = 66 kHz

Air:Q = N/A

Hepatitis C virus helicasedetection,RA: RNA aptamerS: 100 pg/mL

Batch Hwang et al. (2007)

B.N.

Johnson, R

. M

utharasan /

Biosensors and

Bioelectronics 32 (2012) 1– 18

9

Piezoresistive-based,L = 335 �m

Single layer,triangularcross-section

Piezoelectricbase/Piezoresistive

Transverse,n = N/A,f = 265 kHz

Liquid:Q = 294

Egg albumin (OVA)detection,RA: IgG,S: 200 fg/Hz

Continuous Hosaka et al. (2006)

Piezoelectric-based,L = 150 �m

Single layer,rectangularcross-section, array


Transverse,n = 1,2,f = 77, 487 kHz

Air:Q = N/A

Myoglobin detection,RA: Ig

Batch Hwang et al. (2006)

Piezoelectric- andmetal-based,L = 3.5 mm




Liquid:Q = 43

Human serum albumindetection,RA: variousfunctional-headgroupSAMs

Continuous Campbell andMutharasan (2006)


Compositetriangularcross-section,step-discontinutiy


Transverse,n = 1,f ∼ 1.3 MHz

Air:Q = N/A

Human insulin detection,RA: Ig

Batch Lee et al. (2006)


Composite,rectangularcross-section,step-discontinuity,array

Piezoelectric/Impedance &Optical

N/A Air:Q = N/A

Myoglobin detection,RA: biotinylated Ig,S: 1 ng/mL

Batch Kang et al. (2006)



Electrical/Optical


Vacuum (liquidfilled channel):Q ∼ 400–1700

Biotinylated bovineserum albumindetection,RA: avidin,S: 0.8 ng cm−2

Continuous Burg et al. (2006)


Composite,rectangularcross-section,step-discontinuity,array

Active piezoelectriclayer/Piezoresistive& Optical

Transverse,n = N/A,f = 16–61 kHz

Air & Liquid:Q = N/A

Prostate specific antigen(PSA) detection,RA: Ig,S: ∼10 pg/mL

Batch & Continuous Hwang et al.(2004), Lee et al.(2005)



Active piezoelectriclayer/Electrical & Optical

Transverse,n = 1f = 25 kHz

Air:Q = N/A

C-reactive protein (CRP)detection,RA: Ig,S: <nM

Continuous Lee et al. (2004a,b)



Electrostatic/Optical


Vacuum (liquidfilled channels):Q ∼ 90

Avidin detection,Biotinylated bovineserum albumin,S: 10−17 g/�m2

Continuous Burg and Manalis(2003)


Single layer,v-shapedcross-section

Piezoelectric base&Electromagnetic/Optical

Transverse,n = N/A,f ∼ 16 MHz

Liquid:Q = 625

anti-STAR71,RA: anti-BRAC30

Continuous Tamayo et al.(2001)

VirusesPiezoelectric- andmetal-basedL = 715 �m

Composite,rectangularcross-section


Longitudinal,n = 1,f ∼ 1 MHz

Liquid:Q ∼ 25

White spot syndromevirus detection,RA: IgGS: ∼100 virions/mL

Continuous Capobianco et al.(2010)



Piezoelectric base/Optical

Transverse,n = 10–15,f = N/A

Liquid:Q = N/A

Bacterial T5 phagedetection,RA: E. colitransmembrane Fhu Aprotein,S: ∼300 fM

Continuous Braun et al. (2009)

Silicon-based,L = 6, 21 �m

Single-layer,rectangularcross-section

Thermal noise&Piezoelectricbase/Optical

Transverse,n = N/A,f = 0.5–5.5 MHz

medium N/A:Q = 707

Vaccinia virusdetection–single virusmass determination,RA: physisorption,S: ∼1–20 fg

Batch Johnson et al.(2006)

10B.N

. Johnson,

R.

Mutharasan

/ Biosensors

and Bioelectronics

32 (2012) 1– 18

Table 2 (Continued )






Reference


Single-layer,rectangularcross-section,rounded-tip

N/A/Optical

Transverse,n = N/A,f ∼ 1–3 MHz

N/A Vaccinia virusdetection–recognitionlayer effect on frequencychange,RA: Ig,

Batch Gupta et al. (2006)


Single-layer,rectangularcross-section withtip paddle

Piezoelectric base/Optical

Transverse,n = N/Af ∼5.5–10 MHz

Vacuum:Q ∼ 104

Insect baculovirusdetection,RA: Ig,S: ∼0.4–1 ag/Hz,105–107 PFU/mL





Transverse,n = 1f ∼ 1.3 MHz

Air:Q ∼ 5–7

Vaccinia virusdetection–single virusmass determination,RA: physisorption,S: ∼6.3 Hz/ag

Batch Gupta et al. (2004b)

Nucleic AcidsPiezoelectric- andsilicon-based,L = 90 �m

Composite,cross-section N/A,array

Active piezoelectriclayer/Optical

N/A Liquid:Q = N/A

Hepatitis B Virus DNA(27-bp) detection,RA: thiolated DNA probes

Continuous Zheng et al. (2011)



Thermal noise/N/A

Transverse,n = 1,f = 167–365 kHz

Air & Liquid:Q = N/A

20-bp thiolated DNAdetection,RA: N/A

Continuous Kim et al. (2010)


Composite,rectangularcross-section


N/A Air:Q = N/A

Hepatitis B Virus DNA(243-bp) detection,RA: thiolated DNAprobes,S: fM with nanoparticleenhancement

Batch Cha et al. (2009)

Piezoelectric- andsilicon-based,L = 3 mm



mode N/A,n = N/Af ∼ 900 kHz

Liquid:Q ∼ 19

10-bp DNA detection inhuman serum,RA: 15-bp thiolated DNAprobe,S: ∼10 aM

Continuous Rijal andMutharasan (2007)

Silicon-based, L = 3.5 - 5 �m Single-layer,rectangularcross-section

Optical/Optical

Transverse,n = N/Af ∼ 11 MHz

Vacuum:Q ∼ 3000–5000

1587-bp thiolated DNAdetection,S: ∼0.23 ag


Silicon-based, L = 150 �m Single-layer,triangularcross-section

N/A/Optical


Air:Q = N/A

30-bp DNA detectionwith and without SNP,RA: thiolated DNA &nanoparticle probe,S: 23 pM

Batch Su et al. (2003)

B.N. Johnson, R. Mutharasan / Biosensors and Bioelectronics 32 (2012) 1– 18 11

Fig. 3. (A) Image of a cantilever array with 500 micrometer long cantilevers which give rise to resonant modes from ∼40 to 135 kHz depending on the mode order. Reprintedwith permission from Nugaeva et al. (2007). Copyright 2007, Cambridge University Press. (B) Uniform cross-section micro-cantilever which gives rise to resonant modes at∼550 kHz depending on the mode order. Bar corresponds to 5 �m. Reprinted with permission from Johnson et al. (2006). Copyright 2005, Elsevier. (C) T-shaped cantilever withf et al.s st, secs ican In

4

4

citphedetbmt2ot

ciatEtt2it

emtogram sensitive lateral extensional mode. Reprinted with permission from Pangilicon micro-cantilever with a non-uniform tip extension gives rise to sensitive firensitive. Reprinted with permission from Salehi-Khojin et al. (2009). © 2009 Amer

. Exciting and measuring resonance

.1. Techniques for exciting and measuring resonance

Measuring the resonant frequency changes of dynamic-modeantilevers first requires them to be excited by a perturbing driv-ng force so that the resonant frequency can be realized. Second,he resulting motion must be both measured and gathered forost-processing by a read-out technique. As previous sectionsave shown, cantilever designs are quite diverse; therefore, bothxciting and measuring resonance is accomplished by a variety ofifferent techniques. The exciting and measuring components canither be internal or external to the cantilever. As shown in Fig. 4,he various excitation techniques reported in the literature may beroadly classified into five categories: thermal, optical, electrical,agnetic, and acoustic. An excellent discussion on the details of

he various methods can be found in earlier reviews (Lavrik et al.,004; Ziegler, 2004). Due to the constraint of space, we discuss herenly the diversity of combinations that have been investigated, nothe detailed physical principles involved.

As shown in the sensor schematic in Fig. 1, analyte bindingauses the resonant frequency to change. In order for the binding-nduced changes to be measured, the cantilever must be actuatednd its motion must then be measured. The energy used to excitehe sensor comes either from an internal or an external source.xciting vibrations using an external source has been done throughhe use of electrostatic forces (Burg and Manalis, 2003), piezoelec-
ric base elements (Tamayo et al., 2001), thermal noise (Ilic et al.,000), and optics (Ilic et al., 2005). On the other hand, exciting by
nternal means has been done via piezoelectric and magnetoelas-ic active layers (Campbell and Mutharasan, 2005b; Li et al., 2009),

(2006). Copyright 2006, American Institute of Physics. (D) Composite piezoelectric-ond, and third order resonant modes. The second mode was found to be the moststitute of Physics.

and by generating Lorentz forces from embedded circuits (Xia et al.,2008; Xia and Li, 2008). Measurement of resonant frequency usingan external component has been done through the use of opticalor capacitive techniques. In contrast, measurement using an inter-nal component has been done by measuring property changes ofthe active layer. Examples include electrical impedance changesof the active layer or property changes of embedded resistivecomponents in areas of the sensor that undergo significant mechan-ical deformation (for example; Lee et al., 2006; Vancura et al.,2007).

4.2. Combinations used for exciting and measuring resonance

The aforementioned techniques for exciting and measuring res-onance have been combined in three ways: (1) both the excitingand the measuring components are external, (2) both the excitingand the measuring components are internal, and (3) the excitingcomponent is external, while the measuring component is inter-nal, or vice versa. For example, the case in which a sensor is excitedvia a piezoelectric base element and its motion is measured usingan optical technique (Xie et al., 2008), such as by optical lever orlaser Doppler vibrometry, falls into the first category. In contrast,the case where the sensor is both excited and measured by a piezo-electric active layer, falls into the second category (Yi et al., 2003;Campbell and Mutharasan, 2005a). Such a design has come to bereferred to as self-sensing and self-exciting, since the same com-ponent is used to do both (Itoh et al., 1996; Itoh and Suga, 1996).
Another commonly used scheme in which the sensor is excitedusing an active layer and its motion is measured externally usingoptical techniques (Lee et al., 2004a,b), falls into the third category.In Table 2 we summarize the techniques used for both exciting and


ureme

md

nsos(ahnem2feSqpc

5

dAtcmhBbnbnmet(i

t

Fig. 4. Schematic of excitation and meas

easuring resonance used in biosensing applications to show theiversity in both techniques and combinations used.

In fact, the techniques used for exciting and measuring reso-ance can affect the measured frequency response. For example,ome techniques measure motion based on deflection at a portionf the cantilever (for example; Stark, 2004), while others mea-ure motion of the entire cantilever via a bulk property changefor example; Yi et al., 2003). Also, micro-cantilevers excited by

piezoelectric ceramic showed almost two orders of magnitudeigher Q-value than did the same cantilever excited by thermaloise (Johnson et al., 2006). Further, the frequency response ofxcited cantilevers measured both optically and using impedanceeasurement was shown to have noted differences (Sanz et al.,

007). Thus, although sensors may be of similar geometry, theirrequency response can differ if different techniques are used forxcitation and measurement (for example; Johnson et al., 2006;anz et al., 2007; Johnson and Mutharasan, 2010). Since the fre-uency response is an indicator of the mode characteristics, it isrobable that the technique used may also affect other relatedharacteristics such as sensitivity.

. Surface functionalization and bio-recognition agents

Biosensing using dynamic-mode cantilevers has involvedetection of microbes, viruses, and biological macromolecules.pplications have been designed for both the detection of such

argets and for measuring interactions among them. These appli-ations hinge on functionalizing the sensor with recognitionolecules or entities, called bio-recognition agents, that have both

igh affinity and selectivity for the intended biological targets.efore a recognition agent can be used for target binding, it muste chemically attached to the cantilever surface. A number of tech-iques for immobilizing the recognition agent to a surface haveeen developed (Hermanson, 1996). The immobilization mecha-ism is ultimately determined by both the chemical nature of theolecular probe and its reactive functional groups. Although the

arliest chemical sensing applications with dynamic-mode can-ilevers used chemically sensitive polymers for analyte sorption
Lang et al., 1998; Battiston et al., 2001; Adams et al., 2003), biosens-ng applications require more selective recognition chemistry.
In general, functionalizing a surface for a biosensing applica-ion can be looked at as a three step process. First, the cantilever

nt in dynamic-mode cantilever sensors.

surface must be chemically modified if it does not already con-tain appropriate reactive functional groups to bind the recognitionagent. Second, the recognition agent must be immobilized to thesurface by reaction with surface chemical groups in an orientationthat accommodates interaction with the biological target. Third,if non-selective reactive areas remain on the cantilever surface,they must be passivated to prevent non-specific adsorption of non-target constituents. The steps can be done in either batch or flowformat. As many designs are based on miniaturized cantilevers, cap-illary incubation, inkjet printing, and contact printing techniquesare common batch techniques (Nugaeva et al., 2007; Braun et al.,2009). Alternatively, the functionalization steps can also be carriedout directly in a flow cell prior to sensing of the target.

5.1. Antibody-based bio-recognition

The bulk of targets sensed in biosensing applications have beenrelated to sensing pathogenic microbes and toxic proteins. There-fore, many applications have used antibodies as highly selectiverecognition agents. Antibodies have copious peripheral carboxyland amine groups. Thus, antibodies are immobilized to cantileversurface by reacting carboxyl or amine functional groups with thesurface. For silicon-based surfaces, silanization introduces surfaceamine or carboxyl groups for binding the antibody (Nugaeva et al.,2005; Maraldo et al., 2007b; Liu et al., 2009). For gold (Au)-basedsurfaces, antibody binding proteins, such as Protein A or G, havebeen used since they adsorb to Au (Nugaeva et al., 2005; Maraldoet al., 2007b). Mercaptans with amine or carboxyl functional endgroups have also been used on Au-coated sensors for immobilizingantibodies (Liu et al., 2009). It has also been shown that sulfur atomscan be incorporated into peripheral amino acid residues of proteinsfor immobilization on Au surfaces using iminothiolane chemistry(Caruso et al., 1996; Oh et al., 2004) or by adding cysteine moietiesthrough genetic engineering (Lee et al., 2007b). Native thiol groupsof antibodies have also been used for immobilizing antibodies ongold (Karyakin et al., 2000). Likewise, histidine residues have beenincorporated by genetic engineering for binding proteins to sur-faces with accessible metal ions (Hochuli et al., 1988). Although
these techniques have been investigated for immobilizing proteinsand antibodies on surfaces in other applications, they have not beentested in biosensing applications using dynamic-mode cantilevers.Less selective methods such as reactive polymer coatings have also

nsors

betcbidue

5

hatstMbAap(ma2

5r

hs2nbblaidca

asmag2tfsT

6

wtbcrpg


een investigated, but they suffer the disadvantage of random ori-ntation of recognition agents (Oliviero et al., 2009). Subsequento immobilizing the bio-recognition agent, the vacant areas of theantilever surface are often passivated using albumins, such asovine serum albumin (BSA). Such a preparation reduces false pos-

tive results due to contaminant binding, which is a concern whenetecting biological samples. Rinsing with surfactants is also oftensed post-functionalization for removing non-specifically boundntities (Liu et al., 2009).

.2. Nucleic acid-based bio-recognition

Besides sensing of microbes and protein targets, nucleic acidsave also been sensed in various applications. Biosensing of nucleiccids has typically been carried out on Au-coated sensors. Theargets have been sensed in two ways. One method uses highlyelective thiolated DNA probes of exact complementary sequenceo the target as recognition agents (Su et al., 2003; Rijal and

utharasan, 2007; Zheng et al., 2011). The target is then sensedy hybridizing with the immobilized DNA probe after the emptyu sites are filled with small mercaptans, such as mercaptohex-nol. Another approach reported in the literature is the use ofolymerase chain reaction to amplify target with thiolated primersIlic et al., 2005) prior to detection on Au-coated sensors. Both

ethods use the strength of the sulfur-Au <111> bond which has binding energy comparable to covalent bonding (Love et al.,005).

.3. Alternative bio-recognition agents and surfaceeproducibility

For sensing non-nucleic acid targets and those that do notave suitable antibodies available, alternate bio-recognition agentsuch as peptide ligands (Dhayal et al., 2006), phages (Fu et al.,011), aptamers (Hwang et al., 2007), and various other recog-ition proteins (Nugaeva et al., 2005; Gupta et al., 2006) haveeen used. Avidin has been reported as a bio-recognition agent,ut the scheme has the disadvantage of requiring the target to be

abeled with biotin (see Table 2). Electrostatic interactions between charged surface, such as polylysine, and the target have also beennvestigated (Park et al., 2008), but the approach has the severeisadvantage of low selectivity. In the summary of biosensing appli-ations in Table 2, we include both the biological target detectednd the recognition agent used.

Another important practical issue one must be aware of ischieving reproducible immobilization. For example, in a recenttudy it was shown that surfaces can be difficult to reproduce onicro-cantilevers (Mertens et al., 2007). Furthermore, the mass

nd stiffness contributions from a binding event have been sug-ested to depend on the recognition chemistry used (Gupta et al.,006). Thus, direct comparison of sensor responses for the samearget requires careful analysis of the recognition chemistry. There-ore, a description of bio-recognition agent used in the varioustudies is included in the biosensing application summarized inable 2.

. Sensing using high-order modes

The early sensing applications of dynamic-mode cantileversere carried out with fundamental resonant modes. Thus, some of

he earliest investigations to increase sensitivity were attemptedy reducing device size as is suggested by Eqs. (7)–(9). As dis-
ussed in Section 2, not only do cantilevers have fundamentalesonant modes, they also have higher-order modes due to theeriodic nature of eigenfunctions. The same models that sug-est miniaturization as a method for achieving high sensitivity

also indicate the higher-order modes as an alternative for achiev-ing the same goal. The mode order affects both the magnitudeof resonant frequency, and also the mode shape. Since high-order modes contain nodes, there are locations on the dynamiccantilever which have zero deflection and are therefore static.Thus, the effective mass of the cantilever in high-order modesis lower relative to the fundamental mode. If one examines theassociated physics in this way, the high-order mode effective res-onating mass decreases, and thus as per Eqs. (7)–(9), sensitivityincreases.

Many sensitive high-order modes have been reported in bothsingle-layer and multi-layer cantilevers (Lochon et al., 2005;Ghatkesar et al., 2007; Maraldo et al., 2007a; Xie et al., 2008;Narducci et al., 2009). In single-layer uniform rectangular cross-section sensors, behavior of high-order modes can be obtainedusing analytical models. The mode shape of transverse modes asa function of mode order is given by (Sader, 1998; Yu and Li,2009):

u(x) = cos(�nx) − cosh(�nx) − cos(�nL) + cosh(�nL)sin(�nL) + sinh(�nL)

× [sin(�nx) − sinh(�nx)] (10)

where u(x) is the position dependent transverse deflection. In con-trast, understanding the nature of high-order modes in multi-layercantilevers requires numerical or approximate analytic techniques.One can assert without fault that high-order modes of multi-layer cantilevers behave quite differently than those found insingle-layer cantilevers because of variations in elastic propertiesand geometry discontinuity. The unique properties of high-ordermodes have expanded both sensing capabilities and applications.For example, the unique combination modes observed in multi-layer piezoelectric sensors with step-discontinuities have enabledmilli-cantilevers to make measurements at femtogram levels (Rijaland Mutharasan, 2007). In addition to increased sensitivity, high-order modes give the potential for sensing multiple targets (Yu andLi, 2009). As illustrated in Fig. 5A, they make possible the simulta-neous measurement of binding response using multiple modes foradded control in biosensing (Sharma et al., 2011). In Table 2, thevarious biosensing applications that used high-order modes havebeen summarized.

To illustrate the sensitivity dependence on mode order, vari-ous sensing examples that used high-order modes are shown inFig. 5. For example, Fig. 5B shows the net frequency response ofthe first three modes caused by depositing a platinum mass on anon-uniform cross-section multi-layer micro-cantilever. The sec-ond mode was the most sensitive of the first three modes andgave a maximum shift of 2.031 kHz (Salehi-Khojin et al., 2009).Fig. 5C shows the first and second mode responses in 400 �mT-shaped micro-cantilevers to mass addition using polystyrenemicrospheres. The sensitivity of the first and second modes were0.07 Hz/pg and 0.3 Hz/pg, respectively, which shows sensitivityincreases with mode order (Narducci et al., 2009). High-ordertransverse and torsional modes in 300 �m uniform rectangularcantilevers and T-shaped cantilevers showed highest sensitivity tobiotin-streptavidin interaction (Fig. 5D). In that study, the secondtorsional mode in cantilever number four showed the largest shiftof the first two bending and torsional modes of 2330 Hz (Xia andLi, 2008). Analysis summarized in Table 2 clearly shows how themagnitude of sensing resonant frequency in micro-cantilevers andmilli-cantilevers can be comparable although device size differ by
an order of magnitude or more. It is to be emphasized that fabricat-ing cantilever devices which express high resonant frequency is themain goal, and the technique used to accomplish this is a secondaryconcern.


Fig. 5. (A) Responses of the first and second mode in ∼2.5 mm long piezoelectric cantilevers with asymmetric anchor to molecular binding of an alkanethiol on gold in liquidshows a 23 and 123 Hz frequency shift, respectively. Reprinted with permission from Sharma et al. (2011). Copyright 2011, Elsevier. (B) The net frequency shift for depositionof a platinum mass on a non-uniform cross-section multi-layer micro-cantilever made of a piezoelectric material and silicon shows the second mode as the most sensitiveof the first three modes with a maximum shift of 2.031 kHz. Reprinted with permission from Salehi-Khojin et al. (2009). Copyright 2009, American Institute of Physics. (C)Responses of the first and second modes in 400 micrometer long T-shaped micro-cantilevers to mass addition using polystyrene microspheres. The sensitivities of the firstand second modes were 0.07 Hz/pg and 0.3 Hz/pg, respectively, which shows the high-order mode has higher sensitivity. Reprinted with permission from Narducci et al.(2009). Copyright 2009, Elsevier. (D) Responses of both the first and second transverse modes and the first and second torsional modes in a 300 micrometer long uniformr . Cans shiftw

7

tilmi1em

7

ceasihaGctl

ectangular cantilevers and T-shaped cantilevers to biotin-streptavidin interactionecond transverse mode shift of 591.2 Hz, cantilever No. 3 shows first torsional modeith permission from Xia and Li (2008). © 2008 American Institute of Physics.

. Fluid–structure interaction

Traditionally, sensing applications using dynamic-mode can-ilevers were carried out in vacuum to achieve high Q-value, andn turn, high sensitivity. However, biosensing applications haveed to their use in air and liquid environments. In particular,

easurements in liquids are significant, and thus a number ofnvestigations have examined fluid-structure interactions (Sader,998; Bergaud and Nicu, 2000; Chon et al., 2000; Boskovict al., 2002; Green and Sader, 2002). We summarize here theain ideas.

.1. Reynolds number and fluid effects

The earliest attempts to model fluid-structure interaction ofantilevers treated the fluid as inviscid (Chu, 1963; Lindholmt al., 1965; Fu and Price, 1987). Although the inviscid modelccurately predicts the resonant frequency in fluids, it gaveignificant error for cantilevers with micrometer-sized widthn liquids. This problem was addressed later using improvedydroelastic theory that could predict the frequency response ofn excited cantilever immersed in viscous fluids (Sader, 1998;
reen and Sader, 2002). A detailed discussion on the theory ofantilever dynamics immersed in viscous fluids can be found inhe aforementioned references. Because of space constraints, weimit the discussion to Reynolds number (Re) and appropriate
tilever No. 1 shows first transverse mode shift of 57.5 Hz, cantilever No. 2 shows of 443 Hz, cantilever No. 4 shows second torsional mode shift of 2330 Hz. Reprinted

corrections to the inviscid fluid model using hydrodynamicfunctions ( ).

The deviation from the inviscid model can be addressed usingRe arguments (Sader, 1998). The Re for a cantilever vibrating in aviscous fluid neglecting the nonlinear inertial terms of the Navier-Stokes Equation is given as:

Re = �f ωw2

4�(11)

where �f is the density of the fluid, ω is the angular frequency,w is the width, and � is the viscosity of the fluid. For practi-cal cases where Re � 1, a viscous fluid can be treated as inviscidwith little error; thus, the inviscid fluid model is applicable. How-ever, as cantilever width is reduced, Re decreases, and viscouseffects are no longer negligible. When Re is ∼ O(1), the inviscidfluid approximation does not hold, and results in significant errors(Sader, 1998). In such a situation, the dimensionless hydrodynamicfunction accounts for viscous effects. Thus, the nth order resonantfrequency in a fluid (ωR,n) in the limit for small dissipative effectsis given by (Sader, 1998):

ωR,n

[��f w2

]−1/2

ωvac,n= 1 +

4�r(ωR,n) (12)

where ωvac,n is the nth order resonant frequency in vacuum, � isthe mass per unit length of the cantilever, and r is the real part

nsors

oT(c

wBfTaf2

pTo2Ts2iisd(

7

vattpuaebFQMQccisht

taet2m(

8

pq(


f the appropriate hydrodynamic function for the given geometry.he hydrodynamic function for rectangular cross-section geometry rect) is given by a corrected hydrodynamic function developed forircular cross-section geometry:

rect(ω) = ˝(ω)

[1 + 4iK1(−i

√iRe)√

iReK0(−i√

iRe)

](13)

here ˝(ω) is the correction function, and K0 and K1 are modifiedessel functions of the third kind. Expressions for the correction

unction can be found in the following reference (Sader, 1998).he mode dependent hydrodynamic functions for both transversend torsional vibration was recently reported by Sader’s group tourther extend the aforementioned theory (Van Eysden and Sader,007).

A few reports have experimentally characterized Re to inter-ret fluid effects on the resonant frequency using Eqs. (11)–(13).he Re of nano- and micro-cantilevers are very low, in the rangef 10−2–102 (Kirstein et al., 1998; Paul and Cross, 2004; Lee et al.,007a,b). Such results are anticipated based on Eqs. (1) and (11).he Re in non-uniform cross-section cantilevers with a micrometer-ized tip extension has been reported as 103–104 (Vazquez et al.,009). The Re in transverse and torsional modes in milli-cantilevers

n water has been reported in the range of 105 which indicates thatnertial effects are dominant (Rijal and Mutharasan, 2007). Mea-urements of these modes in high viscosity liquids also showedeviation from the inviscid fluid model at values of Re ∼ O(10)Johnson and Mutharasan, 2011b).

.2. Q-value enhancement strategies

The discussion on Re shows the importance of accounting foriscous effects on micro- and nano-scale cantilevers since theyre typically ∼ O(1). As a result, the Q-value, which is indica-ive of energy losses, is reduced significantly in a fluid relativeo vacuum, and compromises achievable sensitivity. However theroblem can somewhat be addressed if amplification strategies aresed to enhance Q-value. Thus far, excellent discussions of Q-valuemplification and control strategies have been reported (Abadalt al., 2001; Tamayo and Lechuga, 2003; Lavrik et al., 2004). Control-ased amplification strategies have been among the most common.or example, various control strategies have been used to amplify-value by orders of magnitude (Albrecht et al., 1991; Sarid, 1991;ehta et al., 2001; Manzaneque et al., 2011). In spite of the various-value amplification methods reported, its use in sensing appli-ations and direct effect on sensitivity has not yet been extensivelyharacterized. The guiding principle is that LOD can be improved byncreasing Q-value according to Eq. (9). However, the effect on sen-itivity still remains to be investigated. For example, in one study itas been shown that signal-to-noise ratio remained constant evenhough Q-value amplification was used (Tamayo, 2005).

Besides control-based amplification strategies, other creativeechniques have also been reported. A noteworthy strategy thatvoids damping of micro-cantilevers in liquid was achieved bymbedding microfluidic channels within a resonating cantilever sohat the cantilever could be operated in vacuum (Burg and Manalis,003; Burg et al., 2006). Such a design has enabled single-celletabolic studies in liquid that would not otherwise be possible

Godin et al., 2010).

. Biosensing application formats

Resonant frequency change in a sensing context is measuredrimarily in two different ways: (1) by measuring the resonant fre-uency at end points; namely, prior to and after a sensing event, or2) by measuring the resonant frequency continuously throughout


the entire course of a sensing event. Often the choice is not deter-mined by the user, but is determined by the sensor design as waspreviously discussed in Section 4. The latter technique is advanta-geous since the sensor is exposed to minimal or no disturbance orcontamination, and the environment in which the biosensing inter-action takes place remain constant throughout the measurement.It also can provide kinetic information on the molecular bindingnot given by the former technique.

8.1. Dip-dry-measure format

The dip-dry-measure technique is among one of the earliest andmost simple biosensing measurement formats. It consists of a threestep process: (1) immerse the prepared sensor in the sample for anappropriate time period, (2) remove, rinse, and dry the sensor, and(3) measure the resonant frequency. This method relies on the stateof the sensor, both with and without bound target, to be identicalin order to have confidence in attributing the measured frequencyshift to the target binding. For confidence in obtaining accurate sen-sor response, avoiding potential alterations during the transfer anddrying steps is crucial. Therefore, biosensing applications using thistechnique typically involve control experiments for characterizingthe effects of transfer, rinsing, and drying. Additionally, rinsing anddrying the sensor can change the state of the biochemical inter-actions on the surface relative to the native state. Therefore, thesignificance of the measurement is reduced due to lack of biolog-ically relevant binding environment. Such a consequence is not amajor concern if the goal of the biosensing application is detection-based, but becomes important if the application is intended to studyinteraction between biological targets, such as protein, microbe orDNA.

8.2. Continuous-measurement format

In contrast to the dip-dry-measure technique, the continuousmeasurement technique involves measuring the resonant fre-quency throughout the entire biosensing application. Since mostbiological interactions take place in liquid, continuous measure-ment in the biological environment adds considerable validity tothe sensing application. This has typically been done while the fluidis continuously flowing past the sensor. This technique has advan-tages of avoiding unnecessary disturbance and contamination ofthe sensor. It also gives the user the ability to rinse the sensor in situwhich adds a confirmation step that the sensor response is due totarget binding and not due to extraneous effects (see Fig. 6A). Sub-sequent to the in situ rinse step, a secondary binding amplificationstep can be used, analogous to a “sandwich assay,” to enhance sen-sitivity and the reliability of measurement (see Fig. 6D). The secondbinding step or target amplification can be done either using anti-bodies, nanoparticles, or other proteins that have affinity for thetarget (Su et al., 2003; Maraldo and Mutharasan, 2007b; Cha et al.,2009).

Assays that measure the resonant frequency continuously dur-ing a sensing event also include control experiments which are onthe same time scale as the measured sensing event. Examples areshown in the biosensing applications presented in Figs. 6A–D. Sucha measurement method adds confidence by showing the sensorresponse is indeed due to binding and not sensor drift caused bytemperature, non-specific binding, or other extraneous factor. Forsensors that exhibit small signal-to-noise ratios this is paramountfor confidence in results. Further confidence in the measurement
may be gained by repeating the experiment using various targetconcentrations. Since the target concentration has direct impact onthe binding response, it is to be expected that one should be ableto observe concentration-dependent changes in sensor response


Fig. 6. (A) Continuously measured response due to thiolated DNA probe immobilization on piezoelectric cantilever sensors, followed by back-filling of empty sites withmercaptohexanol, and subsequent hybridization of DNA strands of complementary sequence at nM–fM ranges. Reprinted with permission from Rijal and Mutharasan (2007).Copyright 2007, American Chemical Society. (B) Binding of S. typhimurium to a gold coated PZT cantilever at various concentrations. Reprinted with permission from Zhu et al.(2007). Copyright 2007, Elsevier. (C) Continuously measured resonant frequency response to prostate specific antigen binding to an antibody functionalized metal-oxidec ra et

o nd Ma

wf

9

ertcsfi(vtntdt(idtptrs

antilever at three different concentrations. Reprinted with permission from Vancuf avidin and subsequent binding to biotin. Reprinted with permission from Burg a

ith respect to both binding time scale and magnitude of resonantrequency change (see Figs. 6A–C).

. Sensitivity characterization

Sensitivity has been defined in a variety of ways in the lit-rature. One is the mass-change sensitivity, defined as the massequired to cause a unit change in frequency, and the other ishe inverse of this quantity, the frequency change for a unit masshange as given in Eq. (8). A second definition is given as themallest level of added-mass that can be reliably sensed at suf-cient signal-to-noise ratio and is called the limit of detectionLOD). The LOD is typically defined based on the measured Q-alue and cantilever effective mass. It may also be obtained usinghe mass-change sensitivity and minimum acceptable signal-to-oise ratio. Another way sensitivity is reported is in terms ofhe lowest concentration at which the target may be reliablyetected at acceptable signal-to-noise ratio. For viable cell detec-ion, the sensitivity is typically reported as colony forming unitsCFU) per milliliter of fluid. For dead cell detection, the sensitiv-ty is typically reported in cells per milliliter of fluid. All previousefinitions of sensitivity are related to the minimum amount ofarget capable of being sensed. However, an equally important
arameter in sensor development is the range over which thearget may be sensed, called the dynamic range. The dynamicange is often reported in units of mass or concentration. Onehould be aware that often there is a trade-off between the LOD
al. (2007). (D) Response of a suspended microchannel resonator to immobilizationnalis (2003). © 2003 American Institute of Physics.

and the dynamic range. In practice, the goal is to optimize bothvalues.

While comparing sensor performance in biosensing applica-tions, it is important to recognize that the sensitivity depends onthe target of interest, the recognition molecule, and the surfaceimmobilization method used. Target size can range from microm-eters to nanometers, shape can range from linear to globular, masscan range from kiloDaltons to picograms, and binding chemistrycan range from covalent bonds to electrostatic interactions. There-fore, even if the same concentration of two different targets arebound to the cantilever, the sensitivity for the target that causeslower stiffness contribution and binds with greater affinity willbe superior. Additionally, the ratio of available targets in solutionto available binding sites can significantly affect binding kinetics.As shown in Table 2, very few reports have examined the issueof interfering background material, such as non-target proteinsand microbes. However, a few studies have shown that extraneousentities can affect both the sensitivity and the binding kinet-ics (Campbell and Mutharasan, 2007a; Maraldo and Mutharasan,2007c). In these investigations, the minimal non-specific bindingobserved was attributed to the fact that sensor surface was in con-stant vibration. Although such a hypothesis has not been rigorouslytested, studies have shown the ability to detach bound species using
vibrations in resonating beam systems (Ilic et al., 2007). Since thepractical concentrations of interest in biosensing range from sin-gle molecule to millimolar (mM) and device sensing area rangesfrom mm2 to nm2, comparing the results can be complicated. In

nsors

TcsidsetwLvtiettbcdrnatLbtpP

1

tfmomQogIaoaueo(sicmc

A

Cwi

R

A


able 2 the wide range of sensitivity reported using dynamic-modeantilevers and the various ways it has been reported to date isummarized. Care should be exercised when interpreting sensitiv-ty reported in Table 2. For example, some cantilevers have beenesigned to resolve the mass of a single cell or virion and are highlyensitive based on a numerical value of LOD in mass units. How-ver, such devices would typically not be suitable for detectingargets over concentration ranges spanning orders of magnitudehich can be achieved by other cantilever designs, and vice versa.

ikewise, sensors designed to measure analyte sorption in air andacuum at very sensitive levels would often not have such sensi-ivities in liquid. Such a conclusion is clear from the distributionn results found in Table 2. It is not only due to cantilever prop-rties, but also the sensing environment, Q-value amplificationechnique, and target sensed. Therefore, direct comparison of can-ilever sensors based on LOD can be erroneous and misleading if theiosensing application differs. A compilation of biosensing appli-ations using dynamic-mode cantilever sensors is presented withescription of probe, target, Q-value, cantilever design, LOD, andesonant frequency measurement format in Table 2. It should beoted that dynamic-mode cantilevers have been investigated for

large number of biosensing applications. Therefore, it is impor-ant to analyze existing and future sensor characteristics, such asOD, in reference to practical levels of pathogen infectious dose,iomarker gene expression levels, and environmental contamina-ion based on the specific biosensing application to realize mostractical options (Kothary and Babu, 2001; Leclerc et al., 2002;olanski and Anderson, 2006).

0. Conclusions and future trends

A critical review of the current state of dynamic-mode can-ilever sensors in biosensing applications was presented with aocus on the designs investigated. A comprehensive table sum-

arizing the reported applications in biosensing with a focusn resonant frequency, mode order, mode type, size, geometry,aterial, resonance excitation-sensing method, sensing medium,-value, recognition chemistry, probe used, target detected, limitf detection, and resonant frequency measurement scheme wasiven. Biosensing applications were organized by target detected.n spite of the extensive published literature, several importantreas remain relatively unexplored. These are: (1) the use of high-rder modes with localized and optimized sensing regions, (2)pplication of sensor non-linearity in biosensing applications, (3)nderstanding of the influence of vibration on binding kinetics,quilibrium, and non-specific adsorption, (4) developing meth-ds of in situ surface renewal for high-throughput applications,5) design of continuous resonant frequency measurement-basedensing applications in liquid, (6) examination of repeatabilityn sensor response, (7) improved understanding of recognitionhemistry–target interaction mechanics for distinguishing added-ass effects from stiffness contribution, and (8) assessment of

ellular viability.

cknowledgements

The authors are grateful for the generous support of NSF GrantBET-0828987 which provided the entire funding for the reportedork. The authors acknowledge Ms. Jennifer Bing for the graphics

n Fig. 1.

eferences

badal, G., Davis, Z.J., Helbo, B., Borrise, X., Ruiz, R., Boisen, A., Campabadal, F.,Esteve, J., Figueras, E., Perez-Murano, F., Barniol, N., 2001. Nanotechnology 12(2), 100–104.


Adams, J.D., Parrott, G., Bauer, C., Sant, T., Manning, L., Jones, M., Rogers, B., McCorkle,D., Ferrell, T.L., 2003. Appl. Phys. Lett. 83 (16), 3428–3430.

Albrecht, T.R., Grutter, P., Horne, D., Rugar, D., 1991. J. Appl. Phys. 69 (2), 668–673.Alvarez, M., Lechuga, L.M., 2010. Analyst 135 (5), 827–836.Battiston, F.M., Ramseyer, J.P., Lang, H.P., Baller, M.K., Gerber, C., Gimzewski, J.K.,

Meyer, E., Guntherodt, H.J., 2001. Sens. Actuators, B 77 (1–2), 122–131.Bergaud, C., Nicu, L., 2000. Rev. Sci. Instrum. 71 (6), 2487–2491.Binnig, G., Quate, C.F., Gerber, C., 1986. Phys. Rev. Lett. 56 (9), 930–933.Boisen, A., Thundat, T., 2009. Mater. Today 12 (9), 32–38.Boskovic, S., Chon, J.W.M., Mulvaney, P., Sader, J.E., 2002. J. Rheol. 46 (4), 891–899.Braun, T., Ghatkesar, M.K., Backmann, N., Grange, W., Boulanger, P., Letellier, L., Lang,

H.P., Bietsch, A., Gerber, C., Hegner, M., 2009. Nat. Nanotechnol. 4 (3), 179–185.Bryan, A.K., Goranov, A., Amon, A., Manalis, S.R., 2010. PNAS 107 (3), 999–1004.Burg, T.P., Godin, M., Knudsen, S.M., Shen, W., Carlson, G., Foster, J.S., Babcock, K.,

Manalis, S.R., 2007. Nature 446 (7139), 1066–1069.Burg, T.P., Manalis, S.R., 2003. Appl. Phys. Lett. 83 (13), 2698–2700.Burg, T.P., Mirza, A.R., Milovic, N., Tsau, C.H., Popescu, G.A., Foster, J.S., Manalis, S.R.,

2006. J. Microelectromech. Syst. 15 (6), 1466–1476.Campbell, G.A., Delesdernier, D., Mutharasan, R., 2007a. Sens. Actuators, B 127 (2),

376–382.Campbell, G.A., Mutharasan, R., 2005a. Biosens. Bioelectron. 21 (4), 597–607.Campbell, G.A., Mutharasan, R., 2005b. Biosens. Bioelectron. 21 (3), 462–473.Campbell, G.A., Mutharasan, R., 2006. Anal. Chem. 78 (7), 2328–2334.Campbell, G.A., Mutharasan, R., 2007a. Anal. Chem. 79 (3), 1145–1152.Campbell, G.A., Mutharasan, R., 2007b. Environ. Sci. Technol. 41 (5), 1668–1674.Campbell, G.A., Mutharasan, R., 2008. Biosens. Bioelectron. 23 (7), 1039–1045.Campbell, G.A., Uknalis, J., Tu, S.I., Mutharasan, R., 2007b. Biosens. Bioelectron. 22

(7), 1296–1302.Capobianco, J.A., Shih, W.H., Leu, J.H., Lo, G.C.F., Shih, W.Y., 2010. Biosens. Bioelectron.

26 (3), 964–969.Caruso, F., Rodda, E., Furlong, D.N., 1996. J. Colloid. Interface Sci. 178 (1), 104–115.Castille, C., Dufour, I., Lucat, C., 2010. Appl. Phys. Lett. 96 (15), 154102.Cha, B.H., Lee, S.M., Park, J.C., Hwang, K.S., Kim, S.K., Lee, Y.S., Ju, B.K., Kim, T.S., 2009.

Biosens. Bioelectron. 25 (1), 130–135.Chen, G.Y., Thundat, T., Wachter, E.A., Warmack, R.J., 1995. J. Appl. Phys. 77 (8),

3618–3622.Chon, J.W.M., Mulvaney, P., Sader, J.E., 2000. J. Appl. Phys. 87 (8), 3978–3988.Chu, W.H., 1963. Tech. Rep. No. 2, DTMB, Contract NObs-86396(X). South-west

Research Institute, San Antonio, Texas.Cooper, M.A., 2009. Label-Free Biosensors: Techniques and Applications, first ed.

Cambridge University Press, New York.Coughlin, M.F., Stamenovic, D., Smits, J.G., 1997. IEEE Trans. Ultrason. Ferroelectr.

Freq. Control 44 (4), 730–732.Craighead, H., 2007. Nat. Nanotechnol. 2 (1), 18–19.Datar, R., Kim, S., Jeon, S., Hesketh, P., Manalis, S., Boisen, A., Thundat, T., 2009. MRS

Bull. 34 (6), 449–454.Davila, A.P., Jang, J., Gupta, A.K., Walter, T., Aronson, A., Bashir, R., 2007. Biosens.

Bioelectron. 22 (12), 3028–3035.Detzel, A.J., Campbell, G.A., Mutharasan, R., 2006. Sens. Actuators, B 117 (1), 58–64.Dhayal, B., Henne, W.A., Doorneweerd, D.D., Reifenberger, R.G., Low, P.S., 2006. J.

Am. Chem. Soc. 128 (11), 3716–3721.Fan, X., White, I.M., Shopova, S.I., Zhu, H., Suter, J.D., Sun, Y., 2008. Anal. Chim. Acta

620, 8–26.Fritz, J., 2008. Analyst 133 (7), 855–863.Fu, L.L., Li, S.Q., Zhang, K.W., Chen, I.H., Barbaree, J.M., Zhang, A.X., Cheng, Z.Y., 2011.

IEEE Sens. J. 11 (8), 1684–1691.Fu, Y., Price, W.G., 1987. J. Sound Vib. 118 (3), 495–513.Gaucher, P., Eichner, D., Hector, J., Von Munch, W., 1998. J. Phys. IV 8 (P9), 235–238.Gfeller, K.Y., Nugaeva, N., Hegner, M., 2005a. Biosens. Bioelectron. 21 (3),

528–533.Gfeller, K.Y., Nugaeva, N., Hegner, M., 2005b. Appl. Environ. Microbiol. 71 (5),

2626–2631.Ghatkesar, M.K., Barwich, V., Braun, T., Ramseyer, J.P., Gerber, C., Hegner, M., Lang,

H.P., Drechsler, U., Despont, M., 2007. Nanotechnology 18 (44), 445502.Godin, M., Bryan, A.K., Burg, T.P., Babcock, K., Manalis, S.R., 2007. Appl. Phys. Lett. 91

(12), 123121.Godin, M., Delgado, F.F., Son, S.M., Grover, W.H., Bryan, A.K., Tzur, A., Jorgensen, P.,

Payer, K., Grossman, A.D., Kirschner, M.W., Manalis, S.R., 2010. Nat. Methods 7(5), 387–U370.

Goeders, K.M., Colton, J.S., Bottomley, L.A., 2008. Chem. Rev. 108 (2), 522–542.Green, C.P., Sader, J.E., 2002. J. Appl. Phys. 92 (10), 6262–6274.Grieshaber, D., MacKenzie, R., Vörös, J., Reimhult, E., 2008. Sensors 8 (2), 1400–1458.Gupta, A., Akin, D., Bashir, R., 2004a. J. Vac. Sci. Technol. B 22 (6), 2785–2791.Gupta, A., Akin, D., Bashir, R., 2004b. Appl. Phys. Lett. 84 (11), 1976–1978.Gupta, A.K., Nair, P.R., Akin, D., Ladisch, M.R., Broyles, S., Alam, M.A., Bashir, R., 2006.

PNAS 103 (36), 13362–13367.Hepel, M., 1999. In: Wieckowski, A. (Ed.), Interfacial Electrochemistry: Theory,

Experiment, and Applications. Marcel Dekker Inc., New York, pp. 599–635.Hermanson, G.T., 1996. Bioconjugate Techniques, First ed. Elsevier, San Diego, CA.Hoa, X.D., Kirk, A.G., Tabrizian, M., 2007. Biosens. Bioelectron. 23, 151–159.Hochuli, E., Bannwarth, W., Döbeli, H., Gentz, R., Stüber, D., 1988. Nat. Biotechnol. 6

(11), 1321–1325.Hosaka, S., Chiyoma, T., Ikeuchi, A., Okano, H., Sone, H., Izumi, T., 2006. Curr. Appl.

Phys. 6 (3), 384–388.Hwang, K.S., Eom, K., Lee, J.H., Chun, D.W., Cha, B.H., Yoon, D.S., Kim, T.S., 2006. Appl.

Phys. Lett. 89, 173905.

1 nsors

H

H

I

I

I

I

IIIJ

JJJJ

K

K

KKKL

LLLL

LL

L

L

LLLL

LL

LL

M

MMMM

MMMMM

MM

M

M

M

M

M

8 B.N. Johnson, R. Mutharasan / Biose

wang, K.S., Lee, J.H., Park, J., Yoon, D.S., Park, J.H., Kim, T.S., 2004. Lab. Chip. 4 (6),547–552.

wang, K.S., Lee, S.M., Eom, K., Lee, J.H., Lee, Y.S., Park, J.H., Yoon, D.S., Kim, T.S., 2007.Biosens. Bioelectron. 23 (4), 459–465.

lic, B., Czaplewski, D., Craighead, H.G., Neuzil, P., Campagnolo, C., Batt, C., 2000. Appl.Phys. Lett. 77 (3), 450–452.

lic, B., Czaplewski, D., Zalalutdinov, M., Craighead, H.G., Neuzil, P., Campagnolo, C.,Batt, C., 2001. J. Vac. Sci. Technol. B 19 (6), 2825–2828.

lic, B., Krylov, S., Kondratovich, M., Craighead, H.G., 2007. Nano Lett. 7 (8),2171–2177.

lic, B., Yang, Y., Aubin, K., Reichenbach, R., Krylov, S., Craighead, H.G., 2005. NanoLett. 5 (5), 925–929.

lic, B., Yang, Y., Craighead, H.G., 2004. Appl. Phys. Lett. 85 (13), 2604–2606.toh, T., Lee, C., Suga, T., 1996. Appl. Phys. Lett. 69 (14), 2036–2038.toh, T., Suga, T., 1996. Sens. Actuators, A 54 (1–3), 477–481.in, D.Z., Li, X.X., Bao, H.H., Zhang, Z.X., Wang, Y.L., Yu, H.T., Zuo, G.M., 2007. Appl.

Phys. Lett. 90 (4), 041901.ohnson, B.N., Mutharasan, R., 2010. Rev. Sci. Instrum. 81 (12), 125108.ohnson, B.N., Mutharasan, R., 2011a. Sens. Actuators 155 (2), 868–877.ohnson, B.N., Mutharasan, R., 2011. J. Appl. Phys. 109 (6), 066105.ohnson, L., Gupta, A.T.K., Ghafoor, A., Akin, D., Bashir, R., 2006. Sens. Actuators, B

115 (1), 189–197.ang, G.Y., Han, G.Y., Kang, J.Y., Cho, I.H., Park, H.H., Paek, S.H., Kim, T.S., 2006. Sens.

Actuators B 117 (2), 332–338.aryakin, A.A., Presnova, G.V., Rubtsova, M.Y., Egorov, A.M., 2000. Anal. Chem. 72

(16), 3805–3811.im, S., Yi, D.C., Passian, A., Thundat, T., 2010. Appl. Phys. Lett. 96 (15), 153703.irstein, S., Mertesdorf, M., Schonhoff, M., 1998. J. Appl. Phys. 84 (4), 1782–1790.othary, M.H., Babu, U.S., 2001. J. Food Safety 21 (1), 49–68.ang, H.P., Berger, R., Battiston, F., Ramseyer, J.P., Meyer, E., Andreoli, C., Brugger, J.,

Vettiger, P., Despont, M., Mezzacasa, T., Scandella, L., Guntherodt, H.J., Gerber,C., Gimzewski, J.K., 1998. Appl. Phys. A 66, 61–64.

änge, K., Rapp, B.E., Rapp, M., 2008. Anal. Bioanal. Chem. 391, 1509–1519.avrik, N.V., Sepaniak, M.J., Datskos, P.G., 2004. Rev. Sci. Instrum. 75 (7), 2229–2253.eclerc, H., Schwartzbrod, L., Dei-Cas, E., 2002. Crit. Rev. Microbiol. 28 (4), 371–409.ee, J.H., Hwang, K.S., Park, J., Yoon, K.H., Yoon, D.S., Kim, T.S., 2005. Biosens. Bioelec-

tron. 20 (10), 2157–2162.ee, J.H., Kim, T.S., Yoon, K.H., 2004a. Appl. Phys. Lett. 84 (16), 3187–3189.ee, J.H., Lee, S.T., Yao, C.M., Fang, W.L., 2007a. J. Micromech. Microeng. 17 (1),

139–146.ee, J.M., Park, H.K., Jung, Y., Kim, J.K., Jung, S.O., Chung, B.H., 2007b. Anal. Chem. 79

(7), 2680–2687.ee, J.H., Yoon, K.H., Hwang, K.S., Park, J., Ahn, S., Kim, T.S., 2004b. Biosens. Bioelec-

tron. 20 (2), 269–275.ee, Y., Lee, S., Seo, H., Jeon, S., Moon, W., 2008. J. Assoc. Lab. Autom. 13, 259–264.ee, Y., Lim, G., Moon, W., 2006. Sens. Actuators, A 130, 105–110.i, S.Q., Fu, L.L., Barbaree, J.M., Cheng, Z.Y., 2009. Sens. Actuators, B 137 (2), 692–699.i, Y., Vancura, C., Kirstein, K.U., Lichtenberg, J., Hierlemann, A., 2008. IEEE Trans.

Circuits Syst. Regul. Pap. 55 (9), 2551–2560.indholm, U.S., Kana, D.D., Chu, W.H., Abramson, H.N., 1965. J. Ship Res. 9 (1), 11–36.iu, Y.J., Li, X.X., Zhang, Z.X., Zuo, G.M., Cheng, Z.X., Yu, H.T., 2009. Biomed. Microde-

vices 11 (1), 183–191.ochon, F., Dufour, I., Rebiere, D., 2005. Sens. Actuators, B 108 (1–2), 979–985.ove, J.C., Estroff, L.A., Kriebel, J.K., Nuzzo, R.G., Whitesides, G.M., 2005. Chem. Rev.

105 (4), 1103–1169.ahmoodi, S.N., Afshari, M., Jahli, N., 2008. Commun. Nonlinear Sci. Numer. Simul.

13 (9), 1964–1977.ahmoodi, S.N., Jalili, N., 2007. Int. J. Nonlinear Mech. 42 (4), 577–587.ahmoodi, S.N., Jalili, N., 2008. J. Vib. Acoust. 130 (6), 061003.ahmoodi, S.N., Jalili, N., 2009. Sens. Actuators, A 150 (1), 131–136.anzaneque, T., Hernando-Garcia, J., Ababneh, A., Schwarz, P., Seidel, H., Schmid, U.,

Sanchez-Rojas, J.L., 2011. J. Micromech. Microeng. 21 (2), 025007.araldo, D., Garcia, F.U., Mutharasan, R., 2007a. Anal. Chem. 79 (20), 7683–7690.araldo, D., Mutharasan, R., 2007a. J. Food Protect. 70 (7), 1670–1677.araldo, D., Mutharasan, R., 2007b. Anal. Chem. 79 (20), 7636–7643.araldo, D., Mutharasan, R., 2007c. J. Food Protect. 70 (11), 2651–2655.araldo, D., Rijal, K., Campbell, G., Mutharasan, R., 2007b. Anal. Chem. 79 (7),

2762–2770.arx, K.A., 2003. Biomacromolecules 4 (5), 1099–1120.cFarland, A.W., Poggi, M.A., Bottomley, L.A., Colton, J.S., 2004. Rev. Sci. Instrum. 75

(8), 2756–2758.cFarland, A.W., Poggi, M.A., Bottomley, L.A., Colton, J.S., 2005a. J. Micromech.

Microeng. 15 (4), 785–791.cFarland, A.W., Poggi, M.A., Doyle, M.J., Bottomley, L.A., Colton, J.S., 2005b. Appl.

Phys. Lett. 87 (5), 053505.cNaught, A.D., Wilkinson, A., 1997. IUPAC-Gold Book, Second ed. Blackwell Scien-

tific Publications, Oxford, UK.ehta, A., Cherian, S., Hedden, D., Thundat, T., 2001. Appl. Phys. Lett. 78 (11),

1637–1639.ertens, J., Calleja, M., Ramos, D., Taryn, A., Tamayo, J., 2007. J. Appl. Phys. 101 (3),

034904.

and Bioelectronics 32 (2012) 1– 18

Mutyala, M.S.K., Bandhanadham, D., Pan, L., Pendyala, V.R., Ji, H.F., 2009. Acta Mech.Sin. 25 (1), 1–12.

Narducci, M., Figueras, E., Lopez, M.J., Gracia, I., Santander, J., Ivanov, P., Fonseca, L.,Cane, C., 2009. Microelectron. Eng. 86 (4–6), 1187–1189.

Nugaeva, N., Gfeller, K.Y., Backmann, N., Duggelin, M., Lang, H.P., Guntherodt, H.J.,Hegner, M., 2007. Microsc. Microanal. 13 (1), 13–17.

Nugaeva, N., Gfeller, K.Y., Backmann, N., Lang, H.P., Duggelin, M., Hegner, M., 2005.Biosens. Bioelectron. 21 (6), 849–856.

Oh, B., Lee, W., Kim, Y., Lee, W.H., Choi, J., 2004. J. Biotechnol. 111 (1), 1–8.Oliviero, G., Bergese, P., Canavese, G., Chiari, M., Colombi, P., Cretich, M., Damin, F.,

Fiorilli, S., Marasso, S.L., Ricciardi, C., Rivolo, P., Depero, L.E., 2009. Anal. Chim.Acta 630 (2), 161–167.

Pang, W., Yan, L., Zhang, H., Yu, H.Y., Kim, E.S., Tang, W.C., 2006. Appl. Phys. Lett. 88(24), 243503.

Park, K., Jang, J., Irimia, D., Sturgis, J., Lee, J., Robinson, J.P., Toner, M., Bashir, R., 2008.Lab. Chip 8 (7), 1034–1041.

Paul, M.R., Cross, M.C., 2004. Phys. Rev. Lett. 92 (23), 235501.Petersen, K.E., 1982. Proc. IEEE 70 (5), 420–457.Pohanka, M., Skládal, P., 2008. J. Appl. Biomed. 6, 57–64.Polanski, M., Anderson, N.L., 2006. Biomarker Insights 2, 1–48.Raiteri, R., Grattarola, M., Butt, H.J., Skladal, P., 2001. Sens. Actuators, B 79 (2–3),

115–126.Ricciardi, C., Canavese, G., Castagna, R., Ferrante, I., Ricci, A., Marasso, S.L., Napione,

L., Bussolino, F., 2010. Biosens. Bioelectron. 26 (4), 1565–1570.Rijal, K., Mutharasan, R., 2007. Anal. Chem. 79 (19), 7392–7400.Rogers, B., Manning, L., Jones, M., Sulchek, T., Murray, K., Beneschott, B., Adams, J.D.,

Hu, Z., Thundat, T., Cavazos, H., Minne, S.C., 2003. Rev. Sci. Instrum. 74 (11),4899–4901.

Sader, J.E., 1998. J. Appl. Phys. 84 (1), 64–76.Salehi-Khojin, A., Bashash, S., Jalili, N., Muller, M., Berger, R., 2009. J. Appl. Phys. 105

(1), 013506.Sanz, P., Hernando, J., Vazquez, J., Sanchez-Rojas, J.L., 2007. J. Micromech. Microeng.

17 (5), 931–937.Sarid, D., 1991. Scanning Force Microscopy. Oxford University Press, New York, NY.Sharma, H., Lakshmanan, R.S., Johnson, B.N., Mutharasan, R., 2011. Sens. Actuators,

B 153 (1), 64–70.Shih, W.Y., Campbell, G., Yi, J.W., Mutharasan, R., Shih, W.H., 2003. J. Am. Chem. Soc.

Abstr. 225, U991.Shin, S., Kim, J.P., Sim, S.J., Lee, J., 2008. Appl. Phys. Lett. 93 (10), 102902.Singamaneni, S., LeMieux, M.C., Lang, H.P., Gerber, C., Lam, Y., Zauscher, S., Datskos,

P.G., Lavrik, N.V., Jiang, H., Naik, R.R., Bunning, T.J., Tsukruk, V.V., 2008. Adv.Mater. 20 (4), 653–680.

Smits, J.G., Dalke, S.I., Cooney, T.K., 1991. Sens. Actuators, A 28 (1), 41–61.Spiering, V.L., Bouwstra, S., Spiering, R., 1993. Sens. Actuators, A 39 (2), 149–156.Stark, R.W., 2004. Rev. Sci. Instrum. 75 (11), 5053–5055.Su, M., Li, S.U., Dravid, V.P., 2003. Appl. Phys. Lett. 82 (20), 3562–3564.Tamayo, J., 2005. J. Appl. Phys. 97 (4), 044903.Tamayo, J., Humphris, A.D.L., Malloy, A.M., Miles, M.J., 2001. Ultramicrosc 86 (1–2),

167–173.Tamayo, J., Lechuga, L.M., 2003. Appl. Phys. Lett. 82 (17), 2919–2921.Tamayo, J., Ramos, D., Mertens, J., Calleja, M., 2006. Appl. Phys. Lett. 89 (22), 224104.Thundat, T., Chen, G.Y., Warmack, R.J., Allison, D.P., Wachter, E.A., 1995. Anal. Chem.

67 (3), 519–521.Timoshenko, S., 1937. Vibration Problems in Engineering, Second ed. Van Nostrand

Company, Inc., New York, NY.Timoshenko, S., Goodier, J., 1970. Theory of Elasticity. McGraw-Hill, New York, NY.Van Emon, J.M., 2007. Immunoassay and Other Bioanalytical Techniques. CRC Press,

Boca Raton, FL.Van Eysden, C.A., Sader, J.E., 2007. J. Appl. Phys. 101 (4), 044908.Vancura, C., Li, Y., Lichtenberg, J., Kirstein, K.U., Hierlemann, A., Josse, F., 2007. Anal.

Chem. 79 (4), 1646–1654.Vazquez, J., Rivera, M.A., Hernando, J., Sanchez-Rojas, J.L., 2009. J. Micromech. Micro-

eng. 19 (1), 015020.von Muhlen, M.G., Brault, N.D., Knudsen, S.M., Jiang, S.Y., Manalis, S.R., 2010. Anal.

Chem. 82 (5), 1905–1910.Waggoner, P.S., Craighead, H.G., 2007. Lab. Chip 7 (10), 1238–1255.Waggoner, P.S., Craighead, H.G., 2009. J. Appl. Phys. 105 (5), 054306.Wang, J., 2006. Biosens. Bioelectron. 21 (10), 1887–1892.Xia, X.Y., Li, X.X., 2008. Rev. Sci. Instrum. 79 (7), 074301.Xia, X.Y., Zhang, Z.X., Li, X.X., 2008. J. Micromech. Microeng. 18 (3), 035028.Xie, H., Vitard, J., Haliyo, D.S., Regnier, S., 2008. Meas. Sci. Technol. 19 (5), 055207.Xu, S., Mutharasan, R., 2010a. Anal. Chim. Acta 669 (1–2), 81–86.Xu, S., Mutharasan, R., 2010b. Environ. Sci. Technol. 44 (5), 1736–1741.Xu, S., Sharma, H., Mutharasan, R., 2010. Biotechnol. Bioeng. 105 (6), 1069–1077.Yi, J.W., Shih, W.Y., Mutharasan, R., Shih, W.H., 2003. J. Appl. Phys. 93 (1), 619–625.Yi, J.W., Shih, W.Y., Shih, W.H., 2002. J. Appl. Phys. 91 (3), 1680–1686.
Yu, H.T., Li, X.X., 2009. Appl. Phys. Lett. 94 (1), 011901.Zheng, S., Choi, J.H., Lee, S.M., Hwang, K.S., Kim, S.K., Kim, T.S., 2011. Lab. Chip 11 (1),
63–69.Zhu, Q., Shih, W.Y., Shih, W.H., 2007. Sens. Actuators, B 125 (2), 379–388.Ziegler, C., 2004. Anal. Bioanal. Chem. 379 (7–8), 946–959.

biosensors and bioelectronics - · pdf filebiosensors and bioelectronics 32 (2012) 1–18...

Documents