High-Q longitudinal block resonators with annexed platforms for mass sensing applications

Disclosed are sensing apparatus, such as mass sensors, comprising longitudinal block resonators having annexed platforms that offer the improved mass sensitivity at micron scale, high-Q in air, simplicity of fabrication, and improved reliability. Exemplary mass sensors comprise a central block separated from a substrate. Two annexed platforms are coupled to the central block by way of two separating beams that are separated from the substrate. One or more anchors are coupled to the central block by way of support beams that are separated from the substrate by insulating material. One or more transducers are provided for actuating and sensing vibration of the central block and the annexed platforms. The transducers may employ capacitive and piezoelectric drive and sense schemes.

BACKGROUND

The present invention relates generally to micromachined block resonators, and more particularly, to high-Q longitudinal block resonators with annexed platforms for use in mass sensing applications.

Resonant micro- and nano-cantilevers as mass sensors have demonstrated adsorption-induced stiffness variation, complicating interpretation of experimental results for calculating adsorbed mass from frequency shift. This is discussed by S. Cherian and T. Thundat, in Applied Physics Letters, 80 (2002), pp. 2219-2221, for example. Moreover, cantilevers need to be scaled down to the nanometer range for high sensitivity, imposing fabrication difficulty and long-term stability. This is discussed by A. Gupta, J. Denton, et. al., in J. Microelectromech. Syst., 12, (2003), pp. 185-192, for example. While FBAR-based mass sensors can achieve high sensitivity at micron scale, the dependence of the mass sensitivity on the FBAR design, such as acoustic isolation for separating the vibrations from the substrate, complicates the fabrication processes. This is discussed by R. Gabi, E. Green, et. al., in IEEE Sensors 2003, pp. 1184-1188.

MEMS/NEMS (MicroElectroMechanical Systems or NanoElectroMechanical Systems) based resonators coated with selective binding layers are of great interest for detecting chemical or biological species. This is discussed by P. G. Datskos, et al., in “Micro and Nanocantilever Sensors”, Encyclopedia of Nanoscience and Technology, Edited by H. S. Nalwa, American Publishers (2004). They have found numerous potential applications. For instance, they can be used to monitor patients at home, provide tools for life science study, monitor environmental conditions, and contribute to homeland security.

By monitoring its resonant frequency variation, a mechanical resonant structure coated with a particular sensitive binding layer can detect the existence and measure the concentration of a particular target species in the analyte of interest, to be specific, the adsorbed mass of that species. Although this basic concept of species or mass sensing has been demonstrated for a long time, some key technical challenges prevent it from practical applications. For instance, most of the MEMS/NEMS based mass sensors developed so far have utilized a flexural-mode cantilever as the resonant structure. Cantilever-based mass sensors have demonstrated attogram-level sensitivity in vacuum and femtogram-level sensitivity in air. This is discussed by B. Llic, et al., in “Attomgram Detection Using Nanoelectromechanical Oscillators”, Journal of Applied Physics, Vol. 95, No. 7, April 2004, pp. 3694-3703, K. L. Ekinci, et al., in “Ultrasensitive Nanoelectromechanical Mass Detection”, Applied Physics Letters, Vol. 84, No. 22, May 2004, pp. 4469-4471, and Nickolay V. Lavrik et al., in “Femtogram Mass Detection Using photothermally Actuated Nanomechanical Resonators”, Applied Physics Letters, Vol. 82, No. 16, April 2003, pp. 2697-2699. However, their low quality factors (Q) demonstrated in air make them unsuitable for real-world detection. Especially, a higher Q in a resonant mass sensor is desirable in that it translates to a higher signal-to-noise ratio, lower motional resistance for its interface circuit, and a lower minimum detectable mass. This is discussed by Yu-Wei Lin, et al., in “Series-Resonant VHF Micromechanical Resonator Reference Oscillators,” Resistance” IEEE Journal of Solid-State Circuits, Vol. 39, No. 12, December 2004, pp. 2477-2491, and K. L. Ekinci, Y et al., in “Ultimate Limits to Inertial Mass Sensing Based Upon Nanoelectromechanical Systems”, Journal of Applied Physics, Vol. 95, No. 5, March 2004, pp. 2682-2689. Due to their complicated assembly of photothermal actuation and optical readout disclosed in the Lavrik et al. paper, integration and packaging of cantilever-based sensors present a major bottle block to the implementation of sensor-array configurations.

Besides the above-mentioned challenges, there are other technical issues pertinent to cantilever-based mass sensors. For instance, resonant frequency shift should ideally be caused only by the mass of an absorbed species. However, the adsorption process introduces stiffness variation of a cantilever, and complicates the interpretation of experimental results. This is discussed by G. Y. Chen, et al., “Adsorption-Induced Surface Stress and Its Effects on Resonance Frequency of Microcantilevers”, Vol. 77, No. 8, Journal of Applied Physics, April 1995, pp. 3618-3622, and Suman Cherian and Thomas Thundat, in “Determination of Adsorption-Induced Variation in the Spring Constant of a Microcantilever”, Applied Physics Letters, Vol. 80, No. 12, March 2002, pp. 2219-2221. Since the same amount of adsorbed mass at different locations along the length of a cantilever has different distributed modal mass, non-uniform adsorption of a target species will further introduce error in experimental measurement. This is discussed by Don L. Devoe, in “Piezoelectric Thin Film Micromechanical Beam Resonators”, Sensors and Actuators, Vol. 88, 2001, pp. 263-272.

It would be desirable to have micromachined longitudinal block resonators that have improved sensitivity and reliability.

DETAILED DESCRIPTION

Disclosed are high-Q length-extensional mass sensors, featuring both annexed sensing platforms and on-chip integrated transducers. The annexed sensing platforms incorporated into the sensors greatly alleviate the technical issues pertinent to cantilever-based mass sensors. The utilization of the length-extensional bulk-mode vibrations of a resonant microstructure enables the advantages as follows: 1) higher mass sensitivity at a large scale, relative to cantilever-based sensors; 2) high-Q in air; 3) on-chip integrated transducers; and 4) compatibility with sensor array configurations.

Concept

Working Principle

Referring to the drawing figures,FIGS. 1aand1billustrate the working principle of a length-extensional mass sensor10with annexed sensing platforms12, whereinFIG. 1ashows the sensor10before absorbing a target species17andFIG. 1bshows the sensor10after absorbing the target species17. As shown inFIGS. 1aand1b, the mechanical resonant structure of a length extensional mass sensor10is comprised of a central block11and two sensing platforms12annexed to the block11by way of separation beams13. This resonant structure is suspended from a substrate14by two support beams15. A selective binding layer16is disposed (coated) on top of the two annexed sensing platforms12. Symmetric about a central line of its support beams14, the resonant microstructure operates in a length-extensional bulk-mode, as illustrated inFIGS. 2a-2c. From its bulk-mode vibrations, this microstructure lends itself to high-Q in air, a key factor determining practical applications and performance merits of a mass sensor10.

FIGS. 2a-2cillustrate length-extensional bulk-mode vibrations of a resonant microstructure shown inFIGS. 1aand1bshowing translation motion in the annexed sensing platforms12.FIG. 2ashows the mode shape without mass loading.FIG. 2bshows the mode shape with a loaded mass of 26.35 pg on one platform12.FIG. 2cshows the mode shape with a total loaded mass of 52.7 pg on both platforms12. The legend shows the resonant displacement distribution across the resonant structure and the solid line denotes the undeformed shape.)

Initially, the resonant structure with the selective binding 16 layer vibrates at its original resonant frequency, fo. Once a target species appears in the analyte under test, the binding layer16will adsorb the species17and give rise to a lower resonant frequency, fs. By measuring resonant frequency shift, Δf=fo−fs, this mass sensor monitors mass loading, Δm, from species adsorption.

Annexed Sensing Platforms

As illustrated inFIGS. 2a-2c, by introducing slim separation beams13into the resonant microstructure, the deformation in the annexed sensing platforms12is greatly alleviated, compared to that in a rectangular block or beam, and results in a translational-dominant motion. Therefore, species17absorption on the platforms12has much less effect on the equivalent modal stiffness (Δk˜0), and mass loading becomes the main mechanism for the shift in resonant frequency. This is verified by numerical simulation results. As shown inFIGS. 2a-2c, the frequency shift is proportional to the loaded mass.

Due to the near-uniform motion of the platforms12, especially in areas sufficiently away from the separation beams13, the adsorbed species17across the platforms12has the same distributed modal mass, and hence non-uniform adsorption does not complicate the interpretation of experimental results. Moreover, since the annexed platforms12experience the maximum vibration amplitude in the whole structure, the adsorbed species introduces the largest distributed modal mass and maximizes the shift in resonant frequency of the device.

As is shown inFIG. 3a, the mass sensor10comprises a central longitudinal block11that is coupled (clamped or attached) along a lateral axis by way of two support beams15to two lateral anchors21. The longitudinal block11is coupled along an orthogonal longitudinal axis by way of two slim separating beams13to two annexed platforms12. A selective binding layer16is disposed (coated) on top of the two annexed sensing platforms12. The resonant structure of the mass sensor10comprises the longitudinal block11, the two lateral anchors21and support beams15, the two annexed platforms12, and the separating beams13. One annexed platform12is coupled to a sense electrode22. The other annexed platform12is coupled to a drive electrode23. The sense and drive electrodes22,23shown inFIG. 4acomprise a capacitive drive and sense scheme. The drive electrode23is operative to resonant vibrations. The sense electrode22is operative to sense motion of the longitudinal block11. An insulating material24, such as buried oxide24is disposed on bottom surfaces of the sense and drive electrodes22,23and the lateral anchors21that insulate them from an underlying substrate14, which may be silicon, for example.

As is shown inFIG. 3b, the mass sensor10comprises a longitudinal block11that is coupled (clamped or attached) along one axis to two lateral anchors21by way of two support beams15. The longitudinal block11is coupled along an orthogonal longitudinal axis to two annexed platforms12by way of two slim separating beams13. A selective binding layer16is disposed (coated) on top of the two annexed sensing platforms12. The resonant structure of the mass sensor10comprises the longitudinal block11, the lateral anchors21, the support beams15, the annexed platforms12, and the two separating beams13. An insulating material24, such as buried oxide24is disposed on bottom surfaces of the two lateral anchors21that insulate them from an underlying substrate14. A piezoelectric layer25, such as zinc oxide, for example, is disposed on top surfaces of the longitudinal block11and lateral anchors21. Conductive electrodes22,23, such a aluminum, for example, are disposed on top surfaces of the longitudinal block11and piezoelectric layer25which comprise a piezoelectric drive and sense scheme. The drive electrode23is operative to resonant vibrations. The sense electrode22is operative to sense motion of the longitudinal block11.

As is illustrated inFIG. 3a, the mass sensor10can be operated with on-chip integrated capacitive transducers18with a two-port configuration. The resonant microstructure is connected to a DC polarization voltage (Vp). An AC voltage (Vd) is applied to the drive electrode, while a sensing current (is) is detected from the sense electrode. Capacitive transducers are used to demonstrate the proof of concept.

Alternatively, the mass sensor10can be operated with on-chip integrated piezoelectric transducers18, as shown inFIG. 3b. Compared with their capacitive counterpart, piezoelectric transducers18do not need a DC polarization voltage for resonant operation and provide large electromechanical coupling, further easing its interface circuit design. Since the resonant microstructure is not necessary to be conductive for its piezoelectric transducers,18this feature lends itself to higher compatibility with various bio-sensitive materials than capacitive transducers18.

Design and Modeling

The length-extensional bulk-mode vibrations of the mass sensor10will now be discussed.FIG. 4shows geometrical design parameters of half of the symmetric resonant microstructure and coordinates used for analysis. The microstructure includes three regions, identified as Region I: half of the central block11; Region II: separating beam13; and Region III: sensing platform12.

Close-up views of modal displacement distribution in different regions of the microstructure are illustrated inFIGS. 5a-5c. The deformation mainly exists in the central block11and the separating beams13. While it undergoes longitudinal deformation, the function of the separating beam13is to prevent the longitudinal elastic waves in the central block11from propagating into the annexed sensing platforms12.

Therefore, the equivalent modal stiffness, k, of the length-extensional vibrations is from the central block11and the separating beams13. The annexed platforms12undergo primarily translational-motion while suffering slightly deformation in the area close to the separating beams13. Because the annexed platforms12experience the maximum vibration amplitude, it is reasonable to consider that the equivalent modal mass, M, is mainly from them.

Simulated in ANSYS/Multiphysics,FIG. 6shows a modal displacement distribution along the x-axis of the resonant microstructure, with different distances from the x-axis. The slope of the tangent along each solid line indicates the level of deformation. Consider the modal displacement distribution at y=0.0 μm (the x-axis). The separating beams13undergo the most deformation from its sharp slope, while the annexed sensing platform12experiences trivial deformation but mainly translational motion. Especially, as the location in the annexed platform12is away from the x-axis, the slope of the tangent gets flatter, indicating that the deformation in that area is even smaller. This feature is important because it means that adsorption of a target species will not vary the equivalent modal stiffness of the mass sensor10but its equivalent modal mass only.

A comparison of the modal displacement distribution along the length of the structures used for mass sensing is illustrated inFIG. 7. The equivalent distributed modal mass of the adsorbed species at the location, x, is written as:
m(x)=ms·φ(x)  (1)
where msand φ(x) denote the adsorbed mass and modal displacement at the location, x.

Based on the above equation, the equivalent distributed modal mass of the same amount of adsorbed mass can vary from zero at x=0 to twice of its physical value at the edge of either a cantilever or a rectangular block. Thus, the nonuniform adsorption of a target species17on such types of resonant structures will complicate the interpretation of the adsorbed mass. In contrast, the adsorbed species across the platforms12has the same contribution to the equivalent distributed modal mass, greatly alleviating the non-uniform absorption of any species17.

As may be observed fromFIGS. 5a-5c, a 2-D effect is noticeable due to the different cross-sections in the microstructure. For simplicity, this effect will be neglected to derive a simple expression for providing design guidance for initial design parameters and rough predictions. Since the resonant frequency is a critical design parameter for the mass sensor10, numerical simulation are used to provide accurate prediction and further refine the design parameters. A numerical simulation is inevitable for taking two-dimensional (2-D) effect into account.

Since the sensing platform12undergoes negligible deformation, the 1-D governing equation for the length-extensional bulk-mode vibrations in the microstructure may be expressed as:

When the resonator undergoes time-harmonic vibrations, it can be assumed that:
u(x,t)=U0(x)·eiω·t(3)
where ω denotes the angular resonant frequency.

By using the boundary condition at x=0, requiring that the displacement be zero, the solution to Region I may be written as:
Uc=Uc0·sin(c·x)Region I  (4)
where c=ω/√{square root over (E/ρ)} and Uc0is the vibration amplitude in Region I

The solution to Region II may be written as:
Ub=Ub1·cos(c·x)+Ub2·sin(c·x)Region II  (5)
where Ub1and Ub2are the vibration amplitudes in Region II.

For Region II, the boundary condition at x=L+Lb requires that the normal force be equal to the acceleration of the mass of the annexed sensing platform12:

-ma·Ub·ω2=E·Ab·∂Ub∂x(6)
where ma=ρ·La·b·h is the physical mass of the annexed sensing platform12.

The boundary condition at x=L requires that the normal force and the longitudinal displacement from the central block11be equal to the corresponding values from the separation beam13:

The combination of Equations (6) and (7) yields the expression for the following relation:

[a11a12a13a21a22a23a31a32a33]·[Uc⁢⁢0Ub⁢⁢1Ub⁢⁢2]=0(8)
where the matrix is associated with the geometrical parameters and the physical properties of the structural material used.

In order to obtain nontrivial solutions to Uc0, Ub1, and Ub2, the determinant of the matrix in Equation (8) must be set to zero. It is the eigenvalue causing the determinant to vanish that corresponds to the resonant frequency of the bulk-mode vibrations of the microstructure. Therefore, the eigenvalue equation for the resonant frequency can be expressed as:

By expanding tangent and cotangent functions into series and neglecting higher orders (c·Lb)2and (c·L)2, Equation (9) can be simplified as:

fth=12⁢π·AbL·Ema·1(1-γA)·[1-γL1-γA](10)
where fthis the theoretical resonant frequency and γL=Lb/L is the ratio of the length of the separation beam13to half the length of the central block11.

FIGS. 8aand8bshow a comparison between the theoretical calculated and numerical simulated resonant frequencies.FIG. 8ashows the resonant frequency versus the sensing platform length (Ls) for a microstructure (L=10 μm, b=10 μm, Lb=2 μm, and bb=1 μm), andFIG. 8bshows the resonant frequency versus the width of the separation beams (bb) of a microstructure (L=50 μm, b=40 μm, Lb=4 μm, La=50 μm, and bb=1 μm)

As illustrated inFIG. 8a, the resonant frequency decreases with the length of the annexed platform12, while it increases with the width of the separation beam13. From the frequency difference between the theoretical and numerical calculations, numerical simulation is necessary to provide accurate performance prediction. However, according to the theoretical derivation, the width of separation beams13, the length of the central block11, and the mass of the annexed platform12are identified as the main design parameters for this mass sensor10. By varying them, different types of mass sensors can be designed to meet different performance specifications.

Equivalent Lumped-Element Model

The equivalent modal stiffness of the device can be obtained using two numerical simulations. As shown inFIG. 2a, the first simulation is to calculate the original resonant frequency, expressed as:

Given in eitherFIG. 2bor2c, the second simulation gives rise to the resonant frequency with a known adsorbed mass, Δm:

Through combining Equations (11) and (12), the accurate equivalent modal stiffness of this mass sensor10can be obtained using the following expression:

Then, the equivalent modal mass of the mass sensor10can be written as:

M=k(2⁢π⁢⁢fo)2=2·λeff·ρ·La·b·h(14)
where λeffis a coefficient, which is larger than the value of 1 and can be determined from numerical simulation. The dynamic vibration behavior of the microstructure can be described by an equivalent lumped-element model:

M⁢ⅆ2⁢xⅆt2+D·ⅆxⅆt+k·x=Fe(15)
where D is the damping coefficient, which is determined by experiment. The capacitive force, denoted by F, is from the on-chip integrated capacitive transducers18.

With the assumption of a parallel-plate model, which neglects the fringing effect, the capacitive force with the resonant frequency, ω, applied to the two ends of the sensing platforms12can be calculated as below:

Fd=-Cdodd·Vp·vd+Cdo·Vp2ddo2·u(16⁢a)Fs=Cso·Vp2dso2·u(16⁢b)
where Fdand Fs, denote the terms from the drive electrode and sense electrode, respectively; and vdis an ac voltage of frequency, ω. Cdoand Csoare the static capacitances of the drive and sense electrodes23,22, respectively.

Incorporating the capacitive force into Equation (15) leads to the expression modeling electromechanical coupling behavior of the mass sensor10:

M⁢ⅆ2⁢xⅆt2+D·ⅆxⅆt+(k-ke)·x=-Cdodd·Vp·vd(17)
where the term at the right side of the equation is the driving force, and keis the electrostatic stiffness, expressed as below:

Therefore, taking electrostatic stiffness into account, the resonant frequency of the capacitive mass sensor10is calculated as:

To aid in the design and analysis of the device, an admittance model is derived, by combining the capacitive equations with the second-order equation of the resonant microstructure. The overall transfer function describing the admittance, Ysd, between the drive electrode23(input) and sensed electrode22(output) of the mass resonator depicted inFIG. 3ais defined by:

Ysd⁡(jω)=is⁡(jω)vd⁡(jω)(20)
where vdis the drive voltage, and isthe current measured at the sense electrode22.

Equation (20) can also be expressed as the product of the mechanical force-displacement transfer function for the microstructure, x(jω)/F(jω), the electromechanical coupling at the input, ηd=F(jω)/vd(jω), and the electromechanical coupling at the output port, ηs(jω)=is(jω)/[jω·x(jω)]. Therefore, Equation (20) can be rewritten as:

While Equation (17) can be written in the following format:

Based on the above equations, an equivalent electrical model describing the dynamic behavior of the two-port configuration of the capacitive mass sensors10is illustrated inFIG. 9.FIG. 9shows an equivalent P-SPICE electrical model of the two-port configuration of the capacitive mass sensor shown inFIG. 3a. Its corresponding equivalent inductance (Lio), motional resistance (Rio), and equivalent capacitance (Cio) can be expressed as below:

Lio=(k-ke)·ddo·dsoCdo·Cso·Vp2·(2⁢π·ftune)2(23⁢a)Rio=(k-ke)·(M+Δ⁢⁢m)·ddo·dsoCdo·Cso·Vp2·Q(23⁢b)Cio=Cdo·Cso·Vp2ddo·dso·(k-ke).(23⁢c)
where TX1, and TX2denote the coupling of the drive side and the sense side, respectively, which are both equal to 1. Rnetis the resistor of 50Ω in a network analyzer, which is connected to the mass sensor10for performance characterization.

According to Equation (23b), a high quality factor is critical for reducing the motional resistance of the mass sensor10. Correspondingly, a high resonant sense current going through the mass sensor10can be expected:

The vibration amplitude at the end of the annexed sensing platform12is calculated as:

Figures of Merit

The mass sensitivity (Sm) of this device can be expressed as:

According to Equation (26), by varying the length (Ls) of the annexed sensing platform12, this design can cover a large range of mass sensitivity within one single sensor-array chip.

The theoretical minimum detectable mass (Δmmin) of this mass sensor10may be expressed as:

Δ⁢⁢mmin=4⁢kb·T·Bx⁢2⁢ρ·b·h·LS·λeffQ·(2⁢π)3·f03(27)
where kband T denote the Boltzman constant and the environment temperature, respectively; B is Bandwidth; and q is the vibration amplitude. Both a high-Q and a large vibration amplitude help reduce the Δmmin.

With the known design and operation parameters, k, ke, and ftune, and the measured parameter, fs, the actual loaded mass, Δm, can be calculated using the following relation:

Experimental Verification

Experimental Procedure

The length-extensional capacitive mass sensors10with on-chip integrated capacitive transducers18have been fabricated on a 4.3 μm-thick SOI (silicon-on-insulator) wafer using a one-mask fabrication process. Exemplary one-mask fabrication processes are disclosed by Reza Abdolvand and Farrokh Ayazi, in “A Gap Reduction and Manufacturing Technique for Thick Oxide Mask Layers with Multiple-Size Sub-Micron Openings,” to be published in Journal of Microelectromechanical Systems, and in “Single-Mask Reduced-Gap Capacitive Micromachined Devices,”Proc. IEEE MicroElectro Mechanical Systems Conference (MEMS2005), Miami, Fla., 2005, pp. 151-154, for example.FIG. 10shows SEM pictures of length-extensional capacitive mass sensors10with the capacitive gaps in the range of 600 nm.

To evaluate the performance of this mass sensor10, certain amount of nanoparticles (Ceria from nGimat Co., diameter<20 nm) was placed on its annexed platforms12, using a very fine probe tip (radius=2.5 μm) under a microscope. This has the same effect as mass loading due to species adsorption.FIGS. 11a-11cshow SEM pictures of the mass sensor10with clusters of nanoparticles loaded on the sensing platforms12.

To measure the mass sensitivity of this device, the resonant frequencies of the mass sensor10were measured before and after mass loading, as illustrated inFIGS. 12aand12b, where the resonant frequency decreases due to a mass load of ˜1 pg. At the top right corner ofFIGS. 12band12cis the insertion loss between the input and the output (before Rnet). From this loss, the measured motional resistance of a mass sensor10can be expressed as:
Rmeasured=50·10Loss/20(29)

Experimental Results

FIGS. 13a,13b,14a,14b,15a,15b,16aand16bare graphs that show measured resonant frequency shifts at various bias voltages and different loaded mass of exemplary mass sensors10. Parameters for exemplary devices are L=50 μm, b=40 μm, and vd=1.26V, with a sensing platform length of 35 μm. The quality factor measured in air is in the range of 4,000.FIGS. 14a,14bandFIGS. 15a,15bshow the measured frequency shifts at various bias voltages and the corresponding Q of the devices (L=50 μm, b=40 μm, and vd=1.26V) with the sensing platform length of 40 μm and 45 μm, respectively. The measured Q ranges from 3,800 to 4,400 in air, clearly showing that mass loading does not affect the Q values. Taking experimental errors and fabrication tolerances into account, the measured loaded mass is approximately consistent at different bias voltages for these devices and is in good agreement with theoretical calculation from Equations (26) and (28).

The performance of exemplary mass sensors10shown inFIGS. 13a,13b,14a,14b,15a,15b,16aand16bis summarized in Table 1.

Both theoretical (23b) and measured (29) motional resistances of the mass sensors are 2.4 MΩ or so. The vibration amplitude at ˜12 nm leads to leads to a sense current of 0.5 μA going through the mass sensors. A stiffness in the table is the equivalent modal stiffness, and varies with fabrication tolerance of the width of the separation beams. By varying the length of the sensing platform from 35 μm to 45 μm, the mass sensitivity can be tuned from 215 Hz/pg to 151 Hz/pg. Both the mass sensitivity and the quality factor of this device are much larger than the corresponding values (66 Hz/pg and Q<100 at freq<100 kHz) of a sub-micron thick cantilever, such as is disclosed by Amit Gupta, et al., in “Novel Fabrication Method for Surface Micromachined Thin Single-Crystal Silicon Cantilever Beams”, Journal of Microelectromechanical Systems, Vol. 12, No. 2, April 2003, pp. 185-192. Based on Equation (27), the theoretical Δmminof this device in air is at the attogram level, which is comparable to that of a nanocantilever in vacuum.

Thus, high-Q length-extensional mass sensors10have been disclosed, that exhibit numerous advantages over micro/nano-cantilever-based mass sensors. With no need of a transducer assembly and with a large Q, the mass sensors10show better performance in air and compatibility with sensor array configuration. To lower the bias voltage, a HARPSS-on-SOI process can be used to reduce the capacitive gaps (<200 nm). Alternatively, piezoelectric transduction18can be used on the central block11of the sensor10, providing more flexibility for using the device in various detection environments. The disclosed mass sensors10can be further integrated into oscillator circuits for sensor array configurations and further parallel detection.

The above-disclosed high quality factor (Q) mass sensors10having annexed platforms12offer the advantages of improved mass sensitivity at micron scale, high-Q in air, simplicity of fabrication, and improved reliability. The mass sensors10are capable of detecting sub-picogram mass change in air and in liquid. The sensitivity of such mass sensors10depends on lateral dimensions, and is independent of thickness. Un-deformed annexed platforms12, coated with the selective binding layer16adsorbs agents, and may be used to avoid adsorption-induced stiffness changes, which lead to improved reliability of the mass sensors10. The adsorption-induced stiffness change is negligible and the mass change is solely the reason for the frequency shift of the mass sensors10.

The operating resonant mode shape of the mass sensors10shows that the annexed platforms13do not experience deformation but only translational movement. This feature is enabled by the use of slim separating beams13, which prevent longitudinal waves from propagating to the platforms12.

Compared with either cantilever-based or FBAR-based mass sensors, the high-Q mass sensors10having annexed platforms12offers the advantages of improved mass sensitivity at micron scale, high-Q in air, simplicity of fabrication, and improved reliability. The sensitivity of 60 Hz/picogram has been demonstrated at ˜12 MHz. The mass sensors10use the longitudinal bulk-mode of a very simple structure with relatively large dimensions (208 μm×48 μm×10 μm) to achieve picogram-level sensitivity.

Thus, improved micromachined mass sensors have been disclosed. It is to be understood that the above-described embodiments are merely illustrative of some of the many specific embodiments that represent applications of the principles discussed above. Clearly, numerous and other arrangements can be readily devised by those skilled in the art without departing from the scope of the invention.