MEMS Mass Sensors Research Articles

Introducing a novel piezoelectric-based tunable design for mode-localized mass micro-sensors

This investigation focuses on developing a new sensitivity-improving approach for high-order mode-localized mass micro-sensors by utilizing the capabilities of piezoelectric materials. To this end, an electrostatically coupled micro-beam as the building block of MEMS mass sensors is considered. The present design includes the incorporation of a patterned arrangement of piezoelectric thin films placed on the lower electrode of the system. The nonlinear reduced equations of motion for the introduced tunable system are derived by employing the Hamilton principle in conjunction with the Euler-Bernoulli beam theory and the Ritz discretization procedure. These equations are subsequently solved using the harmonic balance method. The present findings are validated by those available in the literature for the case of static excitation. In addition, the eigenvalue loci of the proposed system have been compared and verified by those obtained through three-dimensional finite element simulations carried out in COMSOL Multiphysics commercial software. Taking the shift of the amplitude ratio as the measure demonstrating the sensitivity of the proposed design, it is observed that incorporating piezoelectric excitation can significantly enhance the efficiency of these systems more than two times in comparison to conventional mode-localized mass micro-sensors without piezoelectric layers.

On the equivalence between mass perturbation and DC voltage bias in coupled MEMS resonators: Theoretical and experimental investigation

In this work, we consider MEMS devices made of mechanically coupled microbeams under electric actuation. We conduct an experimental study to identify the occurrence of veering and then investigate its dynamic response for different electric actuations. A slight change in the DC voltage bias from the veering point is observed to affect significantly the frequency response. Indeed, jump to large orbits occurred when perturbing the applied DC voltage while operating near the cyclic-fold bifurcation point. We also develop and validate a mathematical model to simulate the response of the device. The model showed similarities in the softening effect of the DC voltage bias and an added mass when matching their induced shift in the natural frequency. As such, one can discern the inherent nonlinear effects of DC voltage bias on coupled resonators and exploit them for mass sensing applications without going over the hassle of mass deposition, which requires the deployment of complex processes. We also investigate different mass detection mechanisms. We show the potential of mode localization and the significant and abrupt jumps in the deflection of the coupled microbeams due to mass perturbation to enhance the sensitivity of MEMS mass sensors.

Simple and Robust Microfabrication of Polymeric Piezoelectric Resonating MEMS Mass Sensors.

Resonating MEMS mass sensors are microdevices with broad applications in fields such as bioscience and biochemistry. Their advantageous surface-to-volume ratio makes their resonant frequency highly sensitive to variations in their mass induced by surface depositions. Recent global challenges, such as water quality monitoring or pandemic containment, have increased the need for low-cost (even disposable), rapidly fabricated microdevices as suitable detectors. Resonant MEMS mass sensors are among the best candidates. This paper introduces a simple and robust fabrication of polymeric piezoelectric resonating MEMS mass sensors. The microfabrication technology replaces the traditional layer-by-layer micromachining techniques with laser micromachining to gain extra simplicity. Membrane-based resonant sensors have been fabricated to test the technology. Their characterization results have proven that the technology is robust with good reproducibility (around 2% batch level variations in the resonant frequency). Initial tests for the MEMS mass sensors’ sensitivity have indicated a sensitivity of 340 Hz/ng. The concept could be a starting point for developing low-cost MEMS sensing solutions for pandemic control, health examination, and pollution monitoring.

Enhancing the linear dynamic range of a mode-localized MEMS mass sensor with repulsive electrostatic actuation

This letter demonstrates the linear dynamic range enhancement of a mode-localized microelectromechanical systems sensor based on two weakly coupled cantilevers under electrostatic actuation resulting in a repulsive force. An analytical model is proposed to design the sensor, and the expression of the electrostatic force is obtained using a finite element simulation. Compared to attractive electrostatic actuation, the intensity of the resulting force is less sensitive to the change in the cantilever’s displacement, with negligible electrostatic nonlinearities. This result is confirmed by experimental measurements showing linear vibrations up to 70% of the gap, which is almost three times higher than the electrostatic critical amplitude of a similar device using attractive electrostatic force. Finally, the mass sensing capability is highlighted by depositing a few picograms of platinum on the sensor.

Bifurcation-based MEMS mass sensors

Linear mass or gas micro-sensors are based on detecting a shift in the response frequency as associated with the deposited mass. To enhance the sensitivity of these sensors, it has been suggested to relate the deposited mass to a change in the response amplitude over a specified hysteretic range where multiple solutions coexist. We expand on this notion and show that the sensitivity of micro electromechanical sensors can be enhanced further by exploiting specific qualitative changes induced by deposited masses to yield a binary response. Specifically, rather than depending on small quantitative shifts in response frequency, in the jump frequency or in the amplitude of a response that may require a change in the excitation frequency and may be hard to evaluate, we propose two binary sensing approaches based on a change in the type of bifurcation or a finite amplitude response that would be associated with a deposited mass under specified and fixed excitation conditions. Both approaches are based on the capability to establish a relation between the target mass and the required detuning to result in the binary response. We derive the governing equations from first principles and implement the method of multiple scales to quantify this relation for two sensors and show that such sensors can be designed to meet enhanced and specified mass sensing requirements.

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped-Clamped Microbeams for Mass Sensing.

This paper details study of the anti-symmetric response to the symmetrical electrostatic excitation of a Micro-electro-mechanical-systems (MEMS) resonant mass sensor. Under higher order mode excitation, two nonlinear coupled flexural modes to describe MEMS mass sensors are obtained by using Hamilton’s principle and Galerkin method. Static analysis is introduced to investigate the effect of added mass on the natural frequency of the resonant sensor. Then, the perturbation method is applied to determine the response and stability of the system for small amplitude vibration. Through bifurcation analysis, the physical conditions of the anti-symmetric mode vibration are obtained. The corresponding stability analysis is carried out. Results show that the added mass can change the bifurcation behaviors of the anti-symmetric mode and affect the voltage and frequency of the bifurcation jump point. Typically, we propose a mass parameter identification method based on the dynamic jump motion of the anti-symmetric mode. Numerical studies are introduced to verify the validity of mass detection method. Finally, the influence of physical parameters on the sensitivity of mass sensor is analyzed. It is found that the DC voltage and mass adsorption position are critical to the sensitivity of the sensor. The results of this paper can be potentially useful in nonlinear mass sensors.

Distributed MEMS Mass-Sensor Based on Piezoelectric Resonant Micro-Cantilevers

We have realized a distributed mass-sensor using micro-cantilevers. The micro-cantilevers were actuated using piezoelectric ZnO thin films. The micro-cantilevers layer stack consists of Si/SiO2/Pt/ZnO/Pt layers for self-actuation of devices. The mass sensing performance was evaluated by laser Doppler vibrometer. Experimentally, micro-cantilever length was varied in the 100–300- $\mu \text{m}$ range, and it is established that mass-sensitivity increases with reducing length of cantilevers. New relationship has been derived between mass sensitivity (S) and cantilever length (l), which follows the modified power law as S $\propto 1/l^{2.8}$ . Remarkable mass-sensitivity (S = 0.3138 Hz/pg) was obtained for a smallest size cantilever, which has dimensions $100\,\,\times \,\,50\,\,\times \,\,8.3 \mu \text{m}^{3}$ . Optimal mass sensor shows high-quality factor (Q ~ 234) at room temperature and one atmospheric pressure. Such ZnO-based mass sensors are biocompatible, safe, and promising candidate for chemical and bio-sensing applications. [2018-0243]

Attogram mass sensing based on silicon microbeam resonators

Using doubly-clamped silicon (Si) microbeam resonators, we demonstrate sub-attogram per Hertz (ag/Hz) mass sensitivity, which is extremely high sensitivity achieved by micro-scale MEMS mass sensors. We also characterize unusual buckling phenomena of the resonators. The thin-film based resonator is composed of a Si microbeam surrounded by silicon nitride (SiN) anchors, which significantly improve performance by providing fixation on the microbeam and stabilizing oscillating motion. Here, we introduce two fabrication techniques to further improve the mass sensitivity. First, we minimize surface stress by depositing a sacrificial SiN layer, which prevents damage on the Si microbeam. Second, we modify anchor structure to find optimal design that allows the microbeam to oscillate in quasi-one dimensional mode while achieving high quality factor. Mass loading is conducted by depositing Au/Ti thin films on the local area of the microbeam surface. Using sequential mass loading, we test effects of changing beam dimensions, position of mass loading, and distribution of a metal film on the mass sensitivity. In addition, we demonstrate that microbeams suffer local micro-buckling and global buckling by excessive mass loading, which are induced by two different mechanisms. We also find that the critical buckling length is increased by additional support from the anchors.

Mass and position determination in MEMS mass sensors: a theoretical and an experimental investigation

We present a method to determine accurately the position and mass of an entity attached to the surface of an electrostatically actuated clamped–clamped microbeam implemented as a mass sensor. In the theoretical investigation, the microbeam is modeled as a nonlinear Euler–Bernoulli beam and a perturbation technique is used to develop a closed-form expression for the frequency shift due to an added mass at a specific location on the microbeam surface. The experimental investigation was conducted on a microbeam made of Polyimide with a special lower electrode to excite both of the first and second modes of vibration. Using an ink-jet printer, we deposited droplets of polymers with a defined mass and position on the surface of the microbeam and we measured the shifts in its resonance frequencies. The theoretical predictions of the mass and position of the deposited droplets match well with the experimental measurements.

Mass detection based on pure parametric excitation of a micro beam actuated by piezoelectric layers

In this research, nonlinear dynamics of a parametrically excited clamped---clamped micro-beam is investigated for mass sensing applications. The ability to detect mass change opens up implementation of various precise chemical and biological sensors due to their small size and high sensitivity; one of the factors which limit the sensitivity of the MEMS mass sensor is the quality factor (Q). In the proposed model, the micro beam is sandwiched with two piezoelectric layers undergoing a combination of DC and AC voltages which leads to a parametric excitation. The governing differential equation of the motion is derived by the minimization of the Hamiltonian and discretized to a single-degree of freedom system in terms of nonlinear damped Mathieu equation. Based on shooting method, the periodic solutions are captured, the stability of the periodic solutions is determined by means of Floquet theory and the stability margins are determined. We showed that in the plane of excitation frequency and the amplitude of harmonic voltage, there are two distinctive regions, including damped and parametrically resonated regions; these regions are separated via limit cycles (periodic motions). The micro beam is set to operate in the damped region in the vicinity of the limit cycles, before the response is damped once the added mass is deposited on the micro beam the response is pushed inside the resonance region and the amplitude magnification is used as a measure of mass detection. The effect of geometric nonlinearity on the system response is investigated.

Issues associated with scaling up production of a lab demonstrated MEMS mass sensor

This work reports on the development of a lab demonstrated resonant mass sensor towards mid-size production. The issues associated with scaling-up production of the microfabricated chip are discussed with particular focus on yield and device reproducibility, as well as the constraints imposed on the design and manufacturing of the device when packaging and integration must be taken into account. Issues of modal alignment and ambient operational pressure are discussed. Fabricated devices show a 4.81 Hz pg−1 mass sensitivity with a temperature sensitivity of typically 10 Hz °C−1.

Flambage et vibrations non-linéaires d'une plaque stratifiée piézoélectrique. Application à un capteur de masse MEMS

Mots cles : Plaque stratifiee / non-linearites geometriques / flambage / vibrations / piezoelectrique Abstract - Buckling and non-linear vibrations of a piezoelectric stratified plate. Application to a MEMS mass sensor. This study proposes a model of a circular, non-symetrically laminated, piezoelectric plate, subjected to non-linear large amplitude vibrations. This model is built to simulate the behavior of a MEMS bio-sensor, designed to detect, automatically and autonomously, the presence of a given molecule in an aqueous solution. Because of both the laminated structure and the fabrication process, prestresses are observed, with different signs and intensities from one layer to another. This is responsible of a non-planar deformed geometry of the plate at rest. Moreover, experimental results show that a geometrically non-linear response is observed, with curved freqeuncy responses. A continuous non- linear model of the von-Karman type is used and discretized by an expansion of the solution onto the mode shape basis of the plate without prestresses. It's response is numerically computed by a continuation method, in order to predict the system's non-linear behavior.

Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Parametric resonance has been well established in many areas of science, including the stability of ships, the forced motion of a swing and Faraday surface wave patterns on water. We have previously investigated a linear parametrically driven torsional oscillator and along with other groups have mentioned applications including mass sensing, parametric amplification, and others. Here, we thoroughly investigate the design of a highly sensitive mass sensor. The device we use to carry out this study is an in-plane parametrically resonant oscillator. We show that in this configuration, the nonlinearities (electrostatic and mechanical) have a large impact on the dynamic response of the structure. This result is not unique to this oscillator—many MEMS oscillators display nonlinearities of equal importance (including the very common parallel plate actuator). We report the effects of nonlinearity on the behavior of parametric resonance of a micro-machined oscillator. A nonlinear Mathieu equation is used to model this problem. Analytical results show that nonlinearity significantly changes the stability characteristics of parametric resonance. Experimental frequency response around the first parametric resonance is well validated by theoretical analysis. Unlike parametric resonance in the linear case, the jumps (very critical for mass sensor application) from large response to zero happen at additional frequencies other than at the boundary of instability area. The instability area of the first parametric resonance is experimentally mapped. Some important parameters, such as damping co-efficient, cubic stiffness and linear electrostatic stiffness are extracted from the nonlinear response of parametric resonance and agree very well with normal methods.