Micromechanical Cantilever Research Articles

Annealing effect on the fracture toughness of CrN/TiN superlattices

Superlattice films are generally known for their exceptional high hardness compared to their monolithic constituents. Recently, we have shown that CrN/TiN superlattice films exhibit a peak in fracture toughness for a bilayer period of 6.0nm, similar to the former reported peak in hardness. We propose that a dominating factor for obtaining such favourable material properties is the interface constitution between the individual layers.To proof this notion, we have intentionally modified the interface sharpness by post-deposition vacuum annealing of the samples at different temperatures. This promotes interdiffusion of Ti or Cr into its adjacent layers and gradually changes the interfaces to interphases (because TiN and CrN form a solid solution). In order to obtain reliable KIC fracture toughness values as a function of the annealing temperature, in-situ micromechanical cantilever bending tests on ex-situ vacuum annealed freestanding films were performed. High temperature loads take also place during machining processes like dry cutting or high-speed cutting, and are thus of high practical relevance.

Inertial mass sensing with low Q-factor vibrating microcantilevers

Mass sensing using micromechanical cantilever oscillators has been established as a promising approach. The scientific principle underpinning this technique is the shift in the resonance frequency caused by the additional mass in the dynamic system. This approach relies on the fact that the Q-factor of the underlying oscillator is high enough so that it does not significantly affect the resonance frequencies. We consider the case when the Q-factor is low to the extent that the effect of damping is prominent. It is shown that the mass sensing can be achieved using a shift in the damping factor. We prove that the shift in the damping factor is of the same order as that of the resonance frequency. Based on this crucial observation, three new approaches have been proposed, namely, (a) mass sensing using frequency shifts in the complex plane, (b) mass sensing from damped free vibration response in the time domain, and (c) mass sensing from the steady-state response in the frequency domain. Explicit closed-form expressions relating absorbed mass with changes in the measured dynamic properties have been derived. The rationale behind each new method has been explained using non-dimensional graphical illustrations. The new mass sensing approaches using damped dynamic characteristics can expand the current horizon of micromechanical sensing by incorporating a wide range of additional measurements.

A calibration method for the higher modes of a micro-mechanical cantilever

Micro-mechanical cantilevers are increasingly being used as a characterisation tool in both material and biological sciences. New non-destructive applications are being developed that rely on the information encoded within the cantilever's higher oscillatory modes, such as atomic force microscopy techniques that measure the non-topographic properties of a sample. However, these methods require the spring constants of the cantilever at higher modes to be known in order to quantify their results. Here, we show how to calibrate the micro-mechanical cantilever and find the effective spring constant of any mode. The method is uncomplicated to implement, using only the properties of the cantilever and the fundamental mode that are straightforward to measure.

Thermal Characterization of Dynamic Silicon Cantilever Array Sensors by Digital Holographic Microscopy.

In this paper, we apply a digital holographic microscope (DHM) in conjunction with stroboscopic acquisition synchronization. Here, the temperature-dependent decrease of the first resonance frequency (S1(T)) and Young’s elastic modulus (E1(T)) of silicon micromechanical cantilever sensors (MCSs) are measured. To perform these measurements, the MCSs are uniformly heated from T0 = 298 K to T = 450 K while being externally actuated with a piezo-actuator in a certain frequency range close to their first resonance frequencies. At each temperature, the DHM records the time-sequence of the 3D topographies for the given frequency range. Such holographic data allow for the extracting of the out-of-plane vibrations at any relevant area of the MCSs. Next, the Bode and Nyquist diagrams are used to determine the resonant frequencies with a precision of 0.1 Hz. Our results show that the decrease of resonance frequency is a direct consequence of the reduction of the silicon elastic modulus upon heating. The measured temperature dependence of the Young’s modulus is in very good accordance with the previously-reported values, validating the reliability and applicability of this method for micromechanical sensing applications.

Molecularly imprinted polymer based micromechanical cantilever sensor system for the selective determination of ciprofloxacin

The main objective of this study is to develop molecularly imprinted polymer (MIP) based micromechanical cantilever sensor system that has high specificity, fast response time and is easily applicable by user for the detection of ciprofloxacin (CPX) molecule in water resources. Highly specific CPX imprinted nanoparticles were synthesized by miniemulsion polymerization technique. The average size of the synthesized nanoparticles was measured about 160nm with high monodispersivity. Covalent and monolayer binding of the MIP nanoparticles on cantilevers was provided by EDC/NHS activation. Validation of the developed cantilever nanosensor was performed in air with dip-and-dry technique by employing the dynamic sensing mode. According to the results obtained, micromechanical cantilever sensor system worked linearly for the concentration range of 1.5–150.9μM. This concentration range resulted with 18.4–48.9pg mass load on the MIP modified cantilever. The sensitivity of the developed sensor was calculated as 2.6Hz/pg. To control the specificity of MIPs, a different antibiotic enrofloxacin (ENF), with a similar physical and chemical structure with CPX, was used, which showed 7 folds low binding affinity. The developed highly specific microcantilever sensor has a response time of approximately 2min and is reusable up to 4 times. The results indicate that the MIP based AFM nanosensor has high sensitivity for the CPX molecule. This combination of MIP nanoparticles with micromechanical sensors is one of the pioneer studies in the mass sensing applications. This fast, low cost and highly sensitive CPX specific MIP nanoparticle based nanosensor developed in this research have the potential to pave the way for further studies.

Superlattice effect for enhanced fracture toughness of hard coatings

Coherently grown nanolayered TiN/CrN thin films exhibit a superlattice effect in fracture toughness, similar to the reported effect in indentation hardness. We found –by employing in-situ micromechanical cantilever bending tests on free-standing TiN/CrN superlattice films– that the fracture toughness increases with decreasing bilayer period (Λ), reaching a maximum at Λ~6nm. For ultrathin layers (Λ~2nm), the fracture toughness drops to the lowest value due to intermixing and loss of superlattice structure. Both, fracture toughness and hardness peak for similar bilayer periods of TiN/CrN superlattices.

Adhesive behaviour of bonded paper layers: Mechanical testing and statistical modelling

In this study, an experimental methodology based on micromechanical testing inside a scanning electron microscope is proposed to characterise bonding of paper layers connected by wet pressing. The peeling force–displacement evolution law that characterises the delamination of micromechanical double cantilever beam specimens of paper tissue have been extracted from such peeling tests. It is observed that the force–displacement evolution curve achieves a steady-state value related to the effective adhesive energy of the interface. This behaviour is explained by examining the complex load transfer mechanism between the layers exerted by cellulose fibrils. A statistical approach is used for the computation of the effective adhesive energy. It is argued that the observed force–displacement evolution law may be satisfactory described by a stochastic model that depends on the distribution function of the fibrils strength, and on two geometrical distribution functions related to the in-plane and out-of-plane fibrils angles with respect to the undeformed interface configuration. Some applications of the proposed model are demonstrated on examples.

Micromechanical measurement of beating patterns in the quantum oscillatory chemical potential of InGaAs quantum wells due to spin-orbit coupling

The quantum oscillatory magnetization M(B) and chemical potential μ(B) of a two-dimensional (2D) electron system provide important and complementary information about its ground state energy at low temperature T. We developed a technique that provides both quantities in the same cool-down process via a decoupled static operation and resonant excitation of a micromechanical cantilever. On InGaAs/InP heterostructures, we observed beating patterns in both M(B) and μ(B) attributed to spin-orbit interaction. A significantly enhanced sensitivity in μ enabled us to extract Rashba and Dresselhaus parameters with high accuracy. The technique is powerful for detailed investigations on the electronic properties of 2D materials.

Fabrication of piezoelectric thick films for development of micromechanical cantilevers

We fabricated a piezoelectric thick film, whose electromechanical properties are optimized, for development of micromechanical cantilever as a sensor and actuator. Specifically, we studied the electromechanical properties of piezoelectric thick films made of different kinds of piezoelectric powders with their different sizes. The electromechanical properties of piezoelectric thick film are optimized when it is made of both micro- and nano-sized piezoelectric particles. Moreover, we fabricated a micromechanical cantilever using piezoelectric thick film, and investigated the vibrational characteristics of piezoelectric thick film-based microcantilevers. It is shown that a cantilever made of optimized piezoelectric thick film exhibits the excellent vibrational properties such as high Q-factor even in a viscous fluid, and that the resonance behavior of such a cantilever is very stable when compared with cantilevers made of other piezoelectric thick films. Our study provides the design rule of piezoelectric thick film for further development of micromechanical devices based on such a piezoelectric film.

Dynamics of impurity attraction and repulsion of an intrinsic localized mode in a driven 1-D cantilever array.

Both low frequency and high frequency impurity modes have been produced in a SiN micromechanical cantilever array by illumination with either an infrared or visible laser. When such laser-induced impurities are placed near a driven intrinsic localized mode (ILM), it is either repelled or attracted. By measuring the linear response spectrum for these two cases, it was found that vibrational hopping of the ILM takes place when the natural frequency of the ILM and an intrinsic even symmetry linear local mode are symmetrically located about the driven ILM frequency so that parametric excitation of these two linear modes is enhanced, amplifying the lateral motion of the ILM. Numerical simulations are consistent with these signature findings. It is also demonstrated that the correct sign of the observed interaction can be found with a harmonic lattice-impurity model but the magnitude of the effect is enhanced in a nonlinear lattice.

Bidirectional and location-dependent frequency tuning of single crystal 4H-SiC micromechanical cantilevers

In this paper, bidirectional and location-dependent frequency tuning of single crystal 4H silicon carbide (4H-SiC) cantilever resonators was investigated. 4H-SiC is a superior material platform for MEMS devices operated in harsh environments. A passive tuning method was employed using focused ion beam (FIB) deposition of platinum (Pt) and milling of Pt and SiC material at different locations on cantilever beams. Linear downward shifts in resonant frequency were observed with Pt films deposited at the free end of cantilever, which is attributed to the increase in effective mass. Subsequent FIB milling reduced Pt mass and therefore restored the resonant frequency to previous values, showing the advantage of FIB for fine-tuning of frequency by precise adjustment of Pt mass. Location dependence of frequency tuning was investigated by measuring frequency shifts when removing SiC material at different locations by FIB milling, which leads to changes in effective mass and effective stiffness. Results show that resonant frequency increases when removing SiC at the free end, and decreases when close to the fixed anchor. These results demonstrate the capability of bidirectional frequency tuning of SiC cantilever resonators.

Spin–orbit interaction in the magnetization of two‐dimensional electron systems

We review recent experimental and theoretical work on the quantum oscillations of the magnetization M, i.e., the de Haas–van Alphen (dHvA) effect, in two‐dimensional electron systems (2DESs) with spin–orbit interaction (SOI). We focus first on a theoretical modeling by numerically solving the Hamiltonian including the Rashba (R) and Dresselhaus (D) SOI and the Zeeman term in an arbitrarily tilted magnetic field B. We second present experimental data on the SOI‐modified quantum oscillations of in 2DESs formed in the InGaAs/InP and AlGaAs/GaAs material systems for different tilt angles between the 2DES normal and the direction of B. We find pronounced beating patterns in InGaAs/InP that are described quantitatively by assuming a dominant R‐SOI except for a distinct frequency anomaly in M present in nearly perpendicular B. In AlGaAs/GaAs, beating patterns occur at large tilt angles. Here, anomalies in the dHvA wave form occur. The findings demonstrate that the understanding of the ground state energy of a 2DES is incomplete when SOI is present. Finally, we predict that the amplitude and anisotropy of specific dHvA oscillations with respect to the in‐plane magnetic field component allow one to quantify the magnitude and relative signs of both R‐SOI and D‐SOI when simultaneously present.Calculated fan chart of Landau levels and oscillatory Fermi energy in a 2DES subject to SOI. The beating patterns in contain information on the SOI. They manifest itself in a variety of experimentally accessible observables. In this feature article, we focus on the magnetization M as a thermodynamic state variable. The inset sketches a micromechanical cantilever magnetometer used to measure M using the torque .

A study on feedback control of intrinsic localized modes in a micro-mechanical cantilever array

ySchool of Engineering, The University of Shiga Prefecture2500 Hassaka-cho, Hikone, Shiga 522-8533, JapanzDepartment of Electrical Engineering, Kyoto UniversityKatsura, Nishikyo, Kyoto 615-8510, JapanEmail: kimura.m@e.usp.ac.jp, matsushita.y@e.usp.ac.jp, hikihara.takashi.2n@kyoto-u.ac.jpAbstract —Intrinsic localized mode (ILM), which isalso called discrete breather (DB), is an energy localizedvibration in nonlinear coupled oscillators. It is well knownthat the ILM can move in the system without decay of itsenergy concentration. This paper shows that the positionof ILM can be controlled by proportional-derivative con-trol. To create a force to the ILM, linear on-site coe cientsare modulated linearly with respect to the lattice number.Namely, value of the linear on-site coe cients linearly in-crease/decrease as the lattice number increases. Magnitudeof the tilt is adjusted with PD control scheme. As a result ofnumerical simulations, a standing ILM is successfully con-trolled toward a reference position with keeping its energyconcentration.1. IntroductionSpatially localized and temporary periodic vibrations of-ten appear in nonlinear coupled oscillators [1]. The energylocalized vibration in discrete media which is rst discov-ered by A. J. Sievers and S. Takeno [2] is called intrinsic lo-calized mode(ILM) or discrete breather(DB). Experimentalobservations of ILM have been reported for a variety ofphysical system in this decade as well as theoretical andnumerical studies. In particular of them, the observationin micro-mechanical cantilever array allow us to expectthe realization of applications using ILM in micro/nano-engineering [3], because it was also observed that ILM canmove without decaying its energy concentration and can bemanipulated by an extraneous stimulus [4].For the realization of such application, the controlscheme for the ILM should be established. In our previ-ous research, it has been shown that a standing ILM losesits stability by parametric excitation [5]. This result impliesthat appropriately adjusting parameter can creates a force tostanding ILM, because the parametric resonance is usuallycaused by changing a potential shape. Therefore, if the pa-rameter of the system is changed appropriately based on thedistance from the reference position, the position of ILMcan be controlled by using an ordinary control method. Inthis paper, proportional-derivative control is applied to thecontrol of the position of ILM. First, an approximate equa-tion describing the motion of traveling ILM is derived. Sec-ond, behavior of moving ILM is shown when on-site linearcoe cients are gradually changed with respect to the lat-tice number. Finally, the proportional-derivative control ofILM is demonstrated and discussed.2. Coupled Cantilever Array and Standing ILMMicro-cantilever array is one of nonlinear coupled oscil-lators having ILM [3]. By focusing on the rst mode ofbeam vibrations, motions of each cantilever's tip are ap-proximately described by the following ordinary di eren-tial equation [4,6,7],¨u

A numerical study on parametric resonance of intrinsic localized modes in coupled cantilever arrays

ySchool of Engineering, The University of Shiga Prefecture2500 Hassaka-cho, Hikone, Shiga 522-8533, JapanzDepartment of Electrical Engineering, Kyoto UniversityKatsura, Nishikyo, Kyoto 615-8510, JapanEmail: kimura.m@e.usp.ac.jp, matsushita.y@e.usp.ac.jp, hikihara.takashi.2n@kyoto-u.ac.jpAbstract —In a coupled cantilever array modeled as acoupled ordinary di erential equation, symmetric and an-tisymmetric intrinsic localized modes (ILMs) exist. Thesymmetric ILM is stable while the other is unstable underthe regime in which the ratio in nonlinearities of inter-siteand on-site potentials is less than the critical value at whichthe stability change occurs. This paper shows that a sta-ble ILM loses its stability when the system is parametri-cally excited. If the amplitude of parametric excitation islarge enough, the destabilized ILM wanders in the wholesystem. The parameter region where the instability occursare numerically investigated and compared with that in theMathieu equation. The similarity of the shape of the re-gions strongly suggests that the instability is caused by theparametric resonance.1. IntroductionSpatially localized and temporary periodic vibrations of-ten appear in nonlinear coupled oscillators [1]. The energylocalized vibration in discrete media which is rst discov-ered by A. J. Sievers and S. Takeno [2] is called intrinsic lo-calized mode(ILM) or discrete breather(DB). Experimentalobservations of ILM have been reported for a variety ofphysical system in this decade as well as theoretical andnumerical studies. In particular of them, the observationin micro-mechanical cantilever array allow us to expectthe realization of applications using ILM in micro/nano-engineering [3], because it was also observed that ILM canmove without decaying its energy concentration and can bemanipulated by an extraneous stimulus [4].For the realization of such application, the controlscheme for the ILM should be established. The capture andrelease manipulation using the stability change is proposedas an alternative method to manipulate ILM in a micro-cantilever array [5]. For the manipulation method, it isutilized that a stable ILM begins to move after it loses itsstability. Therefore, the manipulation is a way to generatemoving ILM. In this paper, we propose another method togenerate moving ILM by parametric excitation of the ratioin nonlinearities. We rst investigate how moving ILMsbehave around a stable ILM. The motion of moving ILM isapproximated by a simple equation of pendulum. Then, be-haviors of moving ILM created by parametric excitation areshown. Finally, the region where a stable solution loses itsstability by parametric excitation is computed for an ILM,and is compared with that of the Mathieu equation.2. Coupled Cantilever ArrayCantilever array, which is often used as a coupled me-chanical resonator in nano/micro-engineering, is one ofnonlinear coupled oscillators in which ILM can be ob-served experimentally [3]. The motion of cantilevers canapproximately be described by ordinary di erential equa-tion [4–6],u¨

Nanomechanical sensors for single microbial cell growth monitoring.

A nanomechanical technique for rapid real time detection and monitoring of microorganism growth will significantly reduce costs and diagnosis times in industrial and clinical settings. Owing to their label free detection mechanism and unprecedented sensitivity to the mass and elastic modulus of biological structures, dynamically operated cantilever arrays provide an opportunity to rapidly detect and track the evolution of microbial growth. Here we report the monitoring of the growth of single Aspergillus niger spores via the multimode response of microcantilevers. The fungal hyphal structure affects the cantilevers' nanomechanical properties as it propagates along the sensor. We demonstrate, for the first time, the mapping of cellular events with great accuracy using a cantilever frequency response. Imaging of growth conditions on the cantilever, which is performed in parallel, allows for verification of these results. Theoretical comparison and finite element modelling confirm experimental findings and allow for determination of the hyphal elastic modulus.

Effective Young's Modulus Measurement of Thin Film Using Micromechanical Cantilever Sensors

Determination of mechanical properties of thin films, such as the Young's modulus, is of fundamental importance when the films are used for coating or for materials of microelectromechanical systems (MEMS). We show a simple method to calculate the effective Young's modulus of thin films by comparing lateral and vertical expansions. The stress of the film due to expansion in the lateral direction was measured using micromechanical cantilever sensor (MCS) techniques which allow for a calculation of the lateral expansion ratio of the film. The vertical expansion was measured using ellipsometry, surface plasmon resonance (SPR) and other film thickness meters. There is no limitation by the method for a measurement of Young's modulus, even if soft and thin polymer film. We detected the influence of humidity on effective Young's modulus of a polymer material by the method, as an example.

Dynamic interactions between oscillating cantilevers: Nanomechanical modulation using surface forces

Dynamic interactions between two oscillating micromechanical cantilevers are studied. In the experiment, the tip of a high-frequency cantilever is positioned near the surface of a second low-frequency cantilever. Due to the highly nonlinear interaction forces between the two surfaces, thermal oscillations of the low-frequency cantilever modulate the driven oscillations of the high-frequency cantilever. The dissipations and the frequencies of the two cantilevers are shown to be coupled, and a simple model for the interactions is presented. The interactions studied here may be useful for the design of future micro and nanoelectromechanical systems for mechanical signal processing; they may also help realize coupled mechanical modes for experiments in non-linear dynamics.

A Label-Free Detection of Biomolecules Using Micromechanical Biosensors

A Microcantilevers resonator is used to detect a protein biomarker called prostate specific antigen (PSA), which is associated with prostate cancer. Different concentrations of PSA in a buffer solution are detected as a function of deflection of the beams. For this purpose, we use a surface micromachined, antibody-coated polycrystalline silicon micromechanical cantilever beam. Cantilevers have mass sensitivities of the order of 10–17 g/Hz, which result from their small mass. This matter allows them to detect an immobilized antibody monolayer corresponding to a mass of about 70 fg. With these devices, concentrations as low as 150 fg/mL, or 4.5 fM, could be detected from the realistic samples.

Efficient parametric excitation of silicon-on-insulator microcantilever beams by fringing electrostatic fields

Large amplitude flexural vibrations have been excited in single layer silicon-on-insulator micromechanical cantilever beams in ambient air environment. Our driving approach relies on a single co-planar electrode located symmetrically around the actuated grounded cantilever. Electrostatic forces are created via tailored asymmetries in the fringing fields of deformed mechanical states during their electric actuation, with strong restoring forces acting in a direction opposite to the deflection. This results in an effective increase in the structure stiffness in its elastic regime. The devices had been fabricated using deep reactive ion etching based process and their responses were characterized in a laser Doppler vibrometer under ambient conditions. Harmonic voltages applied to the electrode result in the periodic modulation of the effective stiffness and lead to strong parametric excitation of the structure. As opposed to close gap actuators, where high-amplitude drives are severely limited by pull-in instabilities, squeezed gas damping, and stiction, our resonators exhibit very large vibration amplitudes (up to 8 in terms of the amplitude to thickness ratio in the strong parametric regime), with no apparent damage, via the application of highly tunable distributed forces. A reduced order model, based on the Galerkin decomposition, captures the main dynamical features of the system, and is consistent with the observed beam characteristics.

Resonance Based Micromechanical Cantilever for Gas Sensing

Resonance Based Micromechanical Cantilever for Gas Sensing