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Phononic crystal (PnC) resonators of Bloch-mode resonance made by replacing periodically arranged two or three rows of air holes with one row of air holes on a two-dimensional (2-D) silicon slab with air holes of square lattice have been investigated. Piezoelectric aluminum nitride (AlN) film is employed as the interdigital transducers to transmit and detect acoustic waves, thus making the whole microfabrication process CMOS compatible. We also fabricate a PnC structure which has a stopband of 140 MHz

Two-dimensional (2-D) Silicon phononic crystal (PnC) slab of a square array of cylindrical air holes in a 10μm thick free-standing silicon plate with line defects is characterized as a cavity-mode PnC resonator. Piezoelectric aluminum nitride (AlN) film is deployed as the inter-digital transducers (IDT) to transmit and detect acoustic waves, thus making the whole microfabrication process CMOS-compatible. Both the band structure of the PnC and the transmission spectrum of the proposed PnC resonator are analyzed and optimized using finite element method (FEM). The measured quality factor (Q factor) of the microfabricated PnC resonator is over 1,000 at its resonant frequency of 152.46MHz. The proposed PnC resonator shows promising acoustic resonance characteristics for RF communications and sensing applications.

In this paper, the operation of a high Q–10 MHz micromechanical oscillator is presented. A lame-mode bulk resonator operating in nonlinear region is integrated with low noise off-chip interface circuitry. Benefiting from high quality factor as well as large energy storage capability of the bulk resonator, low phase noise performance has been achieved even when the resonator is operating in nonlinear region with a 4Vp-p oscillation output. The oscillator shows −138 dBc/Hz noise floor and −132 dBc/Hz 1 kHz away from the carrier, which meets the cellular phase noise requirement of −130 dBc/Hz at 1kHz offset for 13 MHz GSM reference oscillators.

Measured nonlinear behavior of a capacitively driven free-free micromechanical beam resonator at different driving conditions is presented. The resonator, fabricated in SOIMUMPs process, has a measured resonant frequency of 654 kHz with an average quality factor, Q value of 12,000 operating at a pressure of 37.5 μTorr. The overall nonlinearity (including mechanical and electrical) in the resonator was found to be triggered after critical ac drive voltage amplitude of about 120 mVpp was exceeded. The observed nonlinearity was relatively independent of the proof-mass dc voltage, VP, as long as the critical ac drive voltage is not exceeded. Furthermore, partial compensation of spring hardening effect (arising from mechanical nonlinearity) with spring softening effect (from capacitive force used to actuate the resonator) is observed in this work. This feature is particularly useful for MEMS oscillator applications where frequency tuning can be done by varying VP without inducing nonlinearity in the resonator.

This paper presents a behavioural modelling technique for micromechanical beam resonators that enables the simulation of MEMS resonator model in Analog Hardware Description Language (AHDL) format within a system-level circuit simulation. A 1.13 MHz clamped-clamped beam and a 10.4 MHz free-free beam resonators have been modelled into Verilog-A code and successfully simulated with Spectre in Cadence. Analysis has shown that both models behave well and their electrical characteristics are in agreement with the theory.

This paper reports a continuous-time capacitance to voltage converter (CVC), based on the charge integration circuit, for capacitive pressure sensor applications. Unlike conventional charge integrators which need a large feedback resistor for biasing, the proposed method uses low duty cycle periodic reset to establish a robust dc bias at the sensing electrode. The CVC has the merits of low noise, linear transfer characteristics and low susceptibility to system offset. A CVC has been designed with standard 0.35µm CMOS technology. For a 3.3-V supply, it achieves 1mW power consumption, 0~0.8pF detection range and 0.06% resolution.

A 2-D silicon phononic crystal (PnC) slab of a square array of cylindrical air holes in a 10-μm-thick freestanding silicon plate with line defects is characterized as a cavity-mode PnC resonator. A piezoelectric aluminum nitride (AlN) film is employed as the interdigital transducers to transmit and detect acoustic waves, thus making the whole microfabrication process CMOS compatible. Both the band structure of the PnC and the transmission spectrum of the proposed PnC resonator are analyzed and optimized using finite-element method. The measured quality factor (Q factor) of the microfabricated PnC resonator is over 1000 at its resonant frequency of 152.46 MHz. The proposed PnC resonator shows promising acoustic resonance characteristics for radio-frequency communications and sensing applications.

This paper reports experimentally measured data of two microfabricated resonators, namely a Fabry-Perot (FP) resonator and a reduced central-hole (RCH) resonator, formed by engineering different defects on an otherwise perfect phononic crystal (PnC) slab. Experimental results, which are well supported by the numerically simulated data, show that the RCH resonator has higher Q factor, higher resonant frequency and lower insertion loss than the FP resonator. Finite-element-modelling (FEM) analysed steady-state displacement profiles of the two resonators show that the higher Q factor obtained by the RCH resonator is caused by its superior ability of the energy confinement within the defected region.

In this paper, we demonstrate the experimental study of Fano resonance in a microfabricated phononic crystal (PnC) resonator by creating defects on a two-dimensional (2-D) silicon PnC slab. Our experimental results show that for this type of PnC resonator, the local resonance mechanism plays a dominant role in the acoustic wave transmission, rather than the non-resonant propagating mechanism.

In this paper, a simple and effective experimental approach has been used to extract the mechanical properties of suspended nanomechanical graphene devices using atomic force microscopy (AFM). The main objective of this work is to study the deflection behaviour of graphene devices as a function of layer number (1–5 layers) and anchor geometry which has not been widely investigated so far. Elastic and nonlinear responses of the devices were obtained using AFM nanoindentation. The estimated linear (2.5 N m−1 to 7.3 N m−1), nonlinear spring constants (1 × 1014 N m−3 to 15 × 1014 N m−3) and pretension (0.79 N m−1 to 2.3 N m−1) for the monolayer (3.35 A) to five layer (16.75 A) graphene devices of diameter 3.8 µm show an obvious increasing trend with increase in graphene thickness. The effect of anchor geometry on the force versus deflection behaviour of these devices has also been investigated. The Raman spectroscopy results confirm the absence of defects in the pristine and indented devices. Using the continuum mechanics model, the Young's modulus and 2D elastic modulus of a monolayer graphene device have been found to be 1.12 TPa and 375 N m−1 respectively. The high stiffness and low mass of these devices make them well suited for sensing applications.

This paper shows the design, fabrication and characterization of a novel design micromechanical resonators with Bloch-mode resonance by creating defects on a two-dimensional (2-D) silicon phononic crystal (PnC) slab made by etching a square array of cylindrical air holes in a 10µm thick free-standing silicon plate. Piezoelectric aluminum nitride (AlN) film is deployed as the inter-digital transducers (IDT) to transmit and detect acoustic waves, thus making the whole microfabrication process CMOS-compatible. We also fabricate a PnC structure which has a stopband of 140MHz < f

This paper investigates the potential uses of graphene nanomechanical devices for NEMS applications fabricated using Helium Ion Microscope (HIM). Suspended nanomechanical graphene drum structures of diameter (∼ 2 – 3 µm) and thickness ranging from few atomic layers (∼10 A) to about 11 nm have been fabricated and characterized using Atomic Force Microscopy (AFM). The initial suspension profile and the thickness of the fabricated structures have been obtained using AFM. FEM results suggest that these structures can vibrate in the range of several MHz. Their small size and the higher operating frequencies make them well suitable for mass sensing applications with sensitivities greater than 10−21 g Hz−1 which is more than three orders of magnitude improvement over silicon based structures. The initial suspended graphene membranes have been patterned using HIM to obtain multiple z- axis flexures with sub-10nm feature sizes.

In this paper, a 10MHz micromechanical reference oscillator is presented by combining lame-mode bulk resonator with Q above 200,000 and low noise off-chip interface circuitry. Benefiting from high quality factor as well as large energy storage capability of the bulk resonator, low phase noise performance has been achieved even when the resonator is operating in nonlinear region with a 4Vp-p oscillation output. A clear sine wave output signal is observed and the oscillator shows −138dBc/Hz noise floor and −132dBc/Hz 1kHz away from the carrier, which meets the cellular phase noise requirement of −130dBc/Hz at 1kHz offset for 13MHz GSM reference oscillators. Such oscillator does not require any gain limiting circuitry and hence makes the implementation much simpler and less noisy.

Continuous microfluidic magneto-affinity cell separator combines unique microscale flow phenomenon with advantageous nanobead properties, to isolate cells with high specificity. Owing to the comparable size of the cell-bead complexes and the microchannels, the walls of the microchannel exert a strong influence on the separation of cells by this method. We present a theoretical and experimental study that provides a quantitative description of hydrodynamic wall interactions and wall rolling velocity of cells. A transient convection model describes the transport of cells in two-phase microfluidic flow under the influence of an external magnetic field. Transport of cells along the microchannel walls is also considered via an additional equation. Results show the variation of cell flux in the fluid phases and the wall as a function of a dimensionless parameter arising in the equations. Our results suggest that conditions may be optimized to maximize cell separation while minimizing contact with the wall surfaces. Experimentally measured cell rolling velocities on the wall indicate the presence of other near-wall forces in addition to fluid shear forces. Separation of a human colon carcinoma cell line from a mixture of red blood cells, with folic acid conjugated 1 microm and 200 nm beads, is reported.

This paper presents the performance of differentiallydriven 7MHz length-extensional bulk-mode resonators using T-shaped and straight-beam anchors. Resonators with T anchor results in lower motional resistance and higher quality factor of about 717,680 which is six times higher than that achieved for straight-beam anchor. However, it was observed that the length-extensional resonance mode is dependent on the geometry of the T anchor, that is, at certain dimensions for the T structure, the T anchor significantly hinders the length-extensional mode of resonator. Differential drive of two adjoining resonators, which are normally two-port extensional-mode resonators, effectively removes parasitic feedthrough capacitances that usually suppress the transmission response.

Reliability testing of MEMS resonators has grown significantly in importance since these devices moved into high volume production. In line with this development, we present an automated phonon detection-based test setup, which utilizes a piezoelectric transducer to translate resonator mechanical motion into voltage, for investigating the long-term frequency stability of clamped-clamped beam resonators. The automated test system we have developed is able to continuously actuate up to four devices and characterize them every 30 minutes to monitor resonance frequency f 0 and Q-factor changes resultant from long-term actuation. The surface temperature of the devices is also carefully monitored and the temperature data is used to compensate for the f 0 variations caused by temperature fluctuations. The compensated f 0 measurements obtained over time can be used to determine the frequency drift of the resonators. Q-factor degradation and variations in resonator in-plane displacement can also be detected by our system. The test system was used to monitor the behaviour of a 168.502 kHz resonator over a 225-hour operating period. The device was actuated in its linear mode at 29 ±1.0 °C and ~10 -1 Pa. It showed an f 0 shift of -1.092 Hz/day with Q-factor remaining at ~27,000 throughout. Resonator displacement was also consistent over the actuation period.

In this work, three useful techniques for dynamic motion characterization of MEMS devices are presented, namely network analyzer, acoustic phonon detection and stroboscopic SEM techniques. Proof-of-concept experiments using an MEMS electrostatic resonator reveal reliable and consistent measurement results from the three techniques. The network analyzer characterization technique is most widely used in practice due to its convenience, high sensitivity and high speed. The second acoustic phonon technique features non-invasive and package level testing, but it is still an indirect characterization method, like the network analyzer. In acoustic phonon detection, mechanical waves (phonons) generated by the actuated MEMS device are used as the coupling mechanism through which information on the dynamic mechanical state of the device can be obtained. The third stroboscopic SEM technique is capable of directly measuring the device motion, but its throughput is low and hence not suitable for high volume testing. The stroboscopic SEM imaging system is based on time-gated sampling of the analogue secondary electron (SE) signal. Unlike conventional SEM, stroboscopic SEM is able to detect the actual position of the structure at a specific point in time by taking a time-gated sample of the SEM SE signal at a specific phase of the structure's motion.

Characterization of Lame-mode square resonators with different straight-beam anchor lengths, structural layer thickness, and number of anchor support reveals that there is likely an optimal range of anchor designs that provide high quality factor (Q) above one million, along with low motional resistance. Shorter anchor length restricts resonator vibrations and motional resistance could be increased by 3.5 times compared to resonators with longer anchor length. Two-anchor support design is able to achieve higher Qpsilas but results in higher motional resistance compared to four-anchor support. When structural thickness is reduced from 25 mum to 10 mum, Q gets degraded but still maintained above one million.

In this paper, we report for the first time the detailed analysis of the nonlinear behavior of a Lame-mode SOI bulk resonator. The measured resonant frequency of the resonator was 6.35 MHz with a quality factor of 1.7 million in the ambient pressure of 0.02 Pa. We used the two-step semi-analytic approach to characterize the model parameters of the resonator and the nonlinear model of the resonator was verified by the experimental results. Our study shows that the Lame-mode bulk resonator has three orders of magnitude larger maximum energy storage capability than the flexural beam resonator, leading to improved overall phase noise performance of the resonator-based oscillator.

Nonlinear behavior of a capacitively driven and sensed micromechanical free-free beam resonator is characterized, modeled and experimentally verified in this paper. Both the mechanical and electrostatic nonlinear effects are included in the resonator model. Instead of using the FEM tools which introduces uncertainties to the simulation process, an alternative semi-analytic method is proposed to identify the resonator parameters from just a few preliminary testing results. A 615kHz free-free beam resonator was designed, fabricated and studied. From the experimental results, it is observed that the nonlinear effects in the free-free beam always shift the resonant peak of the beam to a higher frequency under nonlinear vibration. In order to validate the proposed modeling approach, a nonlinear model was constructed based on the experimentally extracted parameters and numerically solved in MATLAB. The simulation results were compared with the experimental data, showing that the measured large-signal frequency domain response can be accurately reproduced by simulation. Although this work focused on the free-free beam resonator, the proposed modeling approach is not specific to flexural designs, but is valid for all types of electrostatic resonators. Such a method to predict nonlinear effects of microresonators will be especially useful for MEMS oscillator and filter applications.

In this paper, we report a 6.3 MHz Lame-mode square resonator with fully differential drive and sense electronics, exhibiting quality factor, Q values exceeding 1 million in ambient pressures as high as 100 Pa. A maximum Q value of 1.6 million was experimentally measured at vacuum pressure of 36 muTorr. It was also experimentally observed that the Q value for the bulk mode resonator was relatively independent for pressures below 100 Pa suggesting that the Q is pressure limited for pressure higher than 100 Pa. This resonator was fabricated using SOIMUMPs process from MEMSCAP.

In this paper, differentially driven 12.9 MHz square resonators in Lame mode with two different types of anchor - T-anchor and straight beam anchor are presented in an attempt to investigate how the anchor design influences the quality factor, Q values. These square resonators operated in a vacuum pressure of 36 muTorr exhibited Q values of 807,000 and 404,000, respectively. This difference in Q values for the two resonators is probably due to differing energy losses in their respective anchors. These resonators were fabricated using SOIMUMPs process from MEMSCAP.

This paper describes a fully-differential CMOS readout circuit for silicon micro-resonant accelerometer. Tested with a SOI resonator, the readout chip sustains the oscillation at 110 kHz with a phase noise of -36 dBc@1 Hz and a bias stability of 0.0035 Hz or 32 ppb, which can be translated to an amplitude noise of 1 Aring/radicHz down to 0.05 Hz and stability of 0.22 Aring up to 100 seconds. The chip is fabricated in a 0.35-mum CMOS process and draws 5 mA under a 3.3-V single supply.

This paper introduces a novel technique for dynamic motion characterization of microelectromechanical (MEMS) devices such as resonators, switches, micromirrors, accelerometers and gyroscopes. Due to the favorable generation and transmission of acoustic phonons through solids, characterization of individual MEMS devices for both dies and packaged devices can be attained non- invasively. Hence, this technique can be utilized for high volume wafer and package-level testing in MEMS manufacturing, allowing new test functionalities and cost economies in back-end wafer and package yield screens to be attained.

This paper describes an acoustic phonon-based characterization technique as a novel tool for the characterization of dynamic microelectromechanical (MEMS) devices such as resonators, switches, micromirrors, accelerometers and gyroscopes. The technique intrinsically features non-invasive characterization due to the favorable transmission properties of acoustic phonons through device packaging and high throughput due to universal detectability from a single detection point, which facilitates high volume wafer and package level testing. The dependence of phonon generation on material properties yields information not obtained in existing electrical, optical and electron beam testing techniques such as contact tribology, energy dissipation, non-linear device behavior and device resonance modes. Preliminary case study results show that phonon-based characterization not only provides efficient, non-destructive testing (NDT) of MEMS functionality, but also insights into MEMS device lifecycle behavior.

In this work, we report the experimental evidence on the capability to simultaneously improve the Q-factor (Q) and motional impedance (Z) of silicon phononic crystal (PnC) micromechanical (MM) resonators by properly engineering the cavity defects on an otherwise perfect two-dimensional (2D) silicon PnC slab. The cavity defects of the resonators in the current study are engineered by patterning additional scattering holes to the pure Fabry-Perot resonant cavity, which is created by deleting two rows of scattering air holes from the centre of the 2D square air-hole array. Experimental results show that by varying the radii of the additional scattering holes patterned in the cavity, the fabricated silicon PnC MM resonators can have their Q and Z improved simultaneously, showing great potential in overcoming the trade-off between Z and Q in conventional resonators of piezoelectric type and capacitive type.

In this paper, we report the numerical and experimental study on micromechanical resonators which are made by introducing defects on an otherwise perfect two-dimensional (2D) silicon phononic crystal (PnC) slab. The 2D PnC slab is made by etching a square array of cylindrical air holes in a free-standing silicon plate with a thickness of 10??m, while the defects are created by reducing the radii of three rows of air holes at the centre of the 2D PnC slab. Three resonators with different values of reduced radii, i.e., 2??m, 4??m and 6??m, are included in this study. The finite-element-modelling method is used to calculate the band structure of the perfect 2D PnC slab and to analyse the different mode shapes of the structure. The design, numerical modelling, fabrication process, as well as characterization results and discussions of the three PnC resonators are also included. Due to its CMOS-compatibility, aluminium nitride is chosen to be the piezoelectric material of the inter-digital transducers, which are used to generate and detect acoustic waves. Testing is done to characterize the resonant frequency (f), quality factor (Q), as well as insertion loss of each of the three microfabricated PnC resonators and the results are discussed by analysing the simulated transmission spectra, the defected band structures, and the steady-state displacement profiles of the structures at their respective resonant frequencies. The experimental results show that the designed PnC resonators with reduced central-hole radii have higher resonant frequency and higher quality factors as compared to their normal Fabry?Perot counterpart, thanks to the higher-frequency modes supported within the cavity and slow sound effect in the lateral direction introduced by the central holes with reduced radii, respectively. As a result, the achieved (f-Q) product can be as high as 2.96???1011, which is among the highest for silicon resonators operating in air.

Periodic ripples of amplitude ∼15 nm were formed in suspended bilayer graphene after nanoindentation with incremental forces up to 600 nN. The structure was annealed at ∼620 K in high vacuum and the corresponding modifications in the mechanical properties and surface morphology were investigated. The pre-tension of the pristine sample was found to be 1.46 N m−1 and after annealing it was reduced to 0.72 N m−1. The nanometre-sized ripples induced by mechanical excitation were found to be flattened after annealing. Tailoring surface corrugations in bilayer graphene through nanoindentation and thermal engineering of these ripples thus provides an innovative fabrication route for flexible electronic devices and strain sensors.

This paper shows the design, fabrication, and characterization of the Bloch-mode micromechanical resonators made by creating alternate defects to form a resonant cavity on a two-dimensional silicon phononic crystal slab of square lattice. The length of the resonant cavity (L) and the central-hole radius (r′) are varied to optimize the performance of the resonators. CMOS-compatible aluminium nitride is used as the piezoelectric material of the interdigital transducer to launch and detect acoustic waves. The extent of energy confinement within the cavity, as shown by the simulated displacement profiles of the resonators, agrees with the measured Q factors. We also quantitatively analysed the band structure of the proposed resonators and found that the Q factors are generally in an inverse relationship with the standard deviation of the band, due to the slow sound effect brought by flat bands which reduces the energy loss along the lateral direction (Y direction) and enhances the Q factor.

We present the numerical and experimental investigations of micromechanical resonators made by creating alternate defects with different central-hole radii (r′) in a two-dimensional (2-D) phononic crystal (PnC) slab. The PnC structures were fabricated by etching a square array of cylindrical air holes in a 10 μm thick free-standing silicon plate using a CMOS-compatible process. Preliminary experimental results show that the performance of the PnC resonators in terms of resonant frequency, Q factor, and insertion loss (IL) is highly dependent on r′. A Q factor of more than 3000 is achieved for the case of r′ = 6 μm while all the designed resonators with alternate defects have higher Q factor and lower IL than the resonators based on the normal Fabry-Perot structure due to the reduction in the mode mismatch.

Characterization of nanomechanical graphene drum structures is presented in this paper. The structures were fabricated by mechanical exfoliation of graphite onto pre-etched circular trenches in silicon dioxide on a silicon substrate. Drum structures with diameters ranging from 3.8 to 5.7 µm and thicknesses down to 8 nm were achieved. Mechanical characterization of the devices was then carried out by using atomic force microscopy (AFM) to measure their electrostatic deflection. The structures were found to have linear spring constants ranging from 3.24 to 37.4 N m−1 and could be actuated to about 18–34% of their thickness before exhibiting nonlinear deflection. An analytical framework was formulated to model the deflection behaviour which was verified through finite element simulations (FEM). The experimental measurements agree well with analytical and finite element results using Young's modulus of 1 TPa. The resonance characteristics of the structures were derived by both plate theory and FEM simulations. It was found that our drum structures could potentially vibrate at frequencies in excess of 25 MHz. The small size and high operating frequencies of our nanomechanical graphene devices make them very promising for resonant mass sensing applications with 10−20 g Hz−1 sensitivity, a two order of magnitude improvement over other reported silicon structures.

In this paper, a detailed study of the nonlinearities in a high-Q SOI Lame-mode bulk resonator is reported. The bulk resonator is designed to operate at 6.35 MHz with a quality factor of 1.7 million at air pressure below 100 Pa. As the vibration amplitude increases, the transmission curve of the resonator progressively bends to lower frequencies due to spring softening effects. The model parameters of the resonator are quantified based on some preliminary experimental results and verified by numerical calculation. Compared with a flexural-mode beam resonator, the Lame-mode bulk resonator is much less susceptible to nonlinear effects and thus can store three orders of magnitude more vibration energy before frequency hysteresis occurs. Closed-loop measurement further demonstrates that the ultra-high quality factor and superior power handling capability enable the Lame-mode based oscillator to achieve 42 dB lower phase noise than the flexural-mode one at 10 Hz offset from the carrier frequency.

Continuous separation of superparamagnetic nanoparticles in a microfluidic system has numerous applications, especially in novel sensors based technology platforms. We have studied a simple microfluidic system with two fluidic inlets, resulting in two-phase flow of identical aqueous fluids. Magnetic nanoparticles were entrained in de-ionized water entering one inlet channel, while the other inlet channel had only de-ionized water input. The application of a magnetic field using a simple permanent magnet causes increased migration of nanoparticles into the pure fluid channel. In the absence of the magnetic field, the particles are able to diffuse into the particle free phase. A steady state convection diffusion model describes the transport of nanoparticles in the microchannel. Particle velocities are estimated from magnetic and hydrodynamic interaction forces. It is shown how particle separation is affected by Peclet number, channel length to width ratio, and magnetic field strength and field gradient. Experiments were conducted with three particle sizes, 1000, 500, and 100 nm. Results revealed a significant discrepancy between theoretical and experimental particle separations under the applied magnetic field. A correction term was introduced into the magnetic force equation. Experiment and theory could be reconciled with the insight that the correction term scales linearly with the volume of the nanoparticle core.

In this paper, we utilize a phonon detection technique to determine the temperature coefficient of resonant frequency TCf of MEMS resonators. The technique adopted is highly sensitive to device motions and allows for TCf measurement with less than 5 ppm °C−1 error. In addition, it can also characterize multiple resonators fabricated on the same die or wafer using a single piezoelectric element. Although the multiple devices have to be measured sequentially, the data acquisition time per resonator is short, making the technique an ideal wafer level characterization tool for high volume device testing. The devices used in our TCf experiments are comb-actuated clamped–clamped beam resonators fabricated using the SOIMUMPs process from MEMSCAP. The clamped–clamped architecture of these devices makes them especially prone to thermal-induced strain. A theoretical framework for analyzing the TCf of these resonators was also derived. Experiments on 16 sample devices show that altering the length L and width w of the clamped–clamped beam improves the TCf of the devices by up to 22%. From our TCf measurements, it was also deduced that a mismatch in the thermal expansion coefficients of the SOI structural and substrate layers caused the thermal-induced strain on our samples. The mismatch was determined to be 3.8 × 10−8 °C−1 for one particular sample die.

The reported work focuses on an acoustic phonon characterisation method for MEMS devices. This technique is uniquely suited to address challenges of MEMS device characterisation as a low cost and non-destructive method. The mechanical switching action of a fixed-fixed beam MEMS switch is characterised using this acoustic phonon characterisation technique and a correlation between phonon measurements and electrical waveforms is carried out. Insights on the mechanical state of the switch are also obtained using this acoustic phonon characterisation technique.

The performance of micromechanical Lameacute-mode square resonator designs with different geometric parameter variations in structural layer thickness, length of anchor beams and the number of anchors placed at nodal points, is reported. Measured results reveal that there is an optimal range of anchor designs that provide high quality factor ( Q ) above one million, along with low motional resistance, Rm . Two-anchor-only support design is able to achieve very high Q s but results in higher motional resistance. Lower structural thickness generally reduces the quality factor Q and Rm owing to interference from out-of-plane modes.

In this paper, the performance of 6.35 MHz Lame-mode square resonators with different dimensions of straight-beam anchor supports is presented, with quality factor values exceeding one million in ambient pressures as high as 150 Pa. A maximum Q value of 1.70 million was experimentally measured for some of the square resonators at a vacuum pressure of 36 µTorr. The Q values of square resonators were relatively independent of pressure at levels below 100 Pa, which suggests that Q is pressure limited due to air damping only when pressures become higher than 100 Pa. Dimensions of straight-beam anchors placed at the four corners of the square resonator lead to tradeoffs among achievable Q, power handling capabilities and motional resistance. Longer anchor beams generally provide good signal-to-noise performance of a square resonator at lower dc bias; however, the resonator goes into the nonlinear regime at lower ac–dc drive amplitudes, which means reduced power handling capability. The benefit of shorter anchors is that the resonator is able to operate in a linear mode under high drive conditions. Depending on the type of application, anchor dimensions can be chosen such that the resonator's performance is optimal in terms of a quality factor, motional resistance and power handling. The resonators were fabricated using the silicon-on-insulator multi-user MEMS process from MEMSCAP.

This paper presents a comprehensive study of the nonlinearities in micromechanical clamped–clamped beam resonators using a stroboscopic scanning electron microscopy (SEM) technique. Stroboscopic SEM allows direct imaging and measurement of the resonator's momentary displacement, hence eliminating the uncertainties associated with the conventional characterization methods. Five different silicon-on-insulator (SOI) comb-drive clamped–clamped beam resonators with resonant frequencies ranging from 113 kHz to 239 kHz were designed, fabricated and tested to investigate how their nonlinearities are related to the device dimensions. Both the theoretical analysis and experimental results conclusively show that the critical vibration amplitude of the resonator is around 1% of the beam width in a vacuum and is relatively independent of the beam length. Furthermore, it is found that the maximum storable energy of the resonator can be significantly increased by increasing the beam width and/or reducing the beam length if there are no restrictions on these dimensions. On the other hand, if a specific resonant frequency needs to be maintained, the maximum storable energy can be improved by increasing both the beam width and length by the same factor. Such a study not only helps to reveal the intrinsic nonlinear properties of the micromechanical clamped–clamped beam resonators, but also provides useful design guidelines for engineers to optimize the overall device performance.

In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr. Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators.

In this paper, we present a systematic characterization and modeling technique for the micromechanical free?free beam resonator to analyze its nonlinear vibration behavior. Different from the conventional FEM-based approach whose simulation accuracy is usually limited around 60?70%, the proposed modeling method is able to accurately identify both the mechanical and electrostatic nonlinear parameters from just a few preliminary experimental observations. The nonlinear equation of motion is then numerically solved, demonstrating both the spring hardening and softening effects in the system. The simulated nonlinear behavior of the resonator under different driving conditions is validated by comparing them with the experimental data. In addition, based on the verified nonlinear model, design guidelines such as the nonlinearity cancellation are also highlighted. Although this work focuses on the free?free beam resonators, the proposed modeling approach can be applied to any other electrostatically driven microresonator to reveal different intrinsic nonlinear properties of the device.

The experimental realisation of a multiwall carbon nanotube (MWNT) resonator for mass sensing applications is reported. Fabricated MWNT resonators with length, inner radius and outer radius as 34.37 μm, 5.37 nm and 13.27 nm, respectively, had a measured resonant frequency around 110-120 kHz. Measured results indicate that these MWNT resonators exhibit sub-attogram reponsivity.

A report is presented, for the first time, on the effect of release etch holes on the quality factors of bulk-mode micromechanical resonators. The bulk resonators were operated in the Lame mode with frequencies around 6 MHz. Periodic 10 mum square etch holes with 30 mum spacing were placed at various locations on the surface of the resonator. A study on five such identical resonators with etch holes at various locations conclusively shows that etch holes decrease the quality factors by more than an order of magnitude from 1.67 million to 116 000 owing to two main energy loss mechanisms. Furthermore, it is demonstrated that the quality factor depends on the location of etch holes on the resonator.

A 6.3 MHz Lame-mode square resonator with fully differential drive and sense electronics, exhibiting quality factor (Q) values over 1 million in ambient pressures as high as 200 Pa is reported. A maximum Q value of 1.6 million was experimentally measured for the resonator designed for this study. It was also experimentally observed that the Q value for the designed bulk mode resonator was relatively independent for pressures below 200 Pa, suggesting that the Q is pressure limited for pressure higher than 200 Pa.

An innovative gap reduction technique is reported to achieve sub-micron capacitive gaps for micromechanical resonators to boost the output signal using the standard low-cost 2 µm commercially available foundry process from MEMSCAP. Electrostatic actuation was used to reduce the gap size below the fabrication limitation. To demonstrate the proposed idea, a 6.35 MHz Lame-mode square resonator was designed, fabricated and tested. The resonator gap size was experimentally measured to be 0.64 µm, which boosted the resonance peak by 20 dB.

The authors describe an acoustic-phonon technique for dynamic microelectromechanical device characterization. Proof of concept experiments using electrostatic resonators reveal a linear phonon to displacement relationship, with detection gain factors up to 25.2mV∕μm attained for packaged devices. Q values of 21 600 and 465 obtained at operating pressures of 6.0×10−6 and 760Torr, respectively, conform to theoretical estimates. Duffing behavior for nonlinear resonator operation was also characterized as a third order response. As acoustic phonons are well detected on any external location for packaged devices, destructive depackaging for die probing is unnecessary, allowing noninvasive testing and high measurement throughput to be attained.