Dynamics of structures

Pull-in instability as an inherently nonlinear and crucial effect continues to become increasingly important for the design of electrostatic MEMS and NEMS devices and ever more interesting scientifically. This review reports not only the overview of the pull-in phenomenon in electrostatically actuated MEMS and NEMS devices, but also the physical principles that have enabled fundamental insights into the pull-in instability as well as pull-in induced failures. Pull-in governing equations and conditions to characterize and predict the static, dynamic and resonant pull-in behaviors are summarized. Specifically, we have described and discussed on various state-of-the-art approaches for extending the travel range, controlling the pull-in instability and further enhancing the performance of MEMS and NEMS devices with electrostatic actuation and sensing. A number of recent activities and achievements methods for control of torsional electrostatic micromirrors are introduced. The on-going development in pull-in applications that are being used to develop a fundamental understanding of pull-in instability from negative to positive influences is included and highlighted. Future research trends and challenges are further outlined.

Electrostatic pull-in instability in MEMS/NEMS: A review

This paper reports on glass frit wafer bonding, which is a universally usable technology for wafer level encapsulation and packaging. After explaining the principle and the process flow of glass frit bonding, experimental results are shown. Glass frit bonding technology enables bonding of surface materials commonly used in MEMS technology. It allows hermetic sealing and a high process yield. Metal lead throughs at the bond interface are possible, because of the planarizing glass interlayer. Examples of surface micromachined sensors demonstrate the potential of glass-frit bonding.

Glass frit bonding : An universal technology for wafer level encapsulation and packaging

This paper reports an acceleration sensing method based on two weakly coupled resonators (WCRs) using the phenomenon of mode localization. When acceleration acts on the proof masses, differential electrostatic stiffness perturbations will be applied to the WCRs, leading to mode localization, and thus, mode shape changes. Therefore, acceleration can be sensed by measuring the amplitude ratio shift. The proposed mode localization with the differential perturbation method leads to a sensitivity enhancement of a factor of 2 than the common single perturbation method. The theoretical model of the sensitivity, bandwidth, and linearity of the accelerometer is established and verified. The measured relative shift in amplitude ratio ( $\sim 312162$ ppm/g) is 302 times higher than the shift in resonance frequency ( $\sim 1035$ ppm/g) within the measurement range of ±1 g. The measured resolution based on the amplitude ratio is 0.619 mg and the nonlinearity is $\sim 3.5$ % in the open-loop measurement operation. [2015-0247]

An Acceleration Sensing Method Based on the Mode Localization of Weakly Coupled Resonators

A new micromachined uniaxial silicon resonant accelerometer characterized by a high sensitivity and very small dimensions is presented. The device's working principle is based on the frequency variations of two resonating beams coupled to a proof mass. Under an external acceleration, the movement of the proof mass causes an axial load on the beams, generating opposite stiffness variations, which, in turn, result in a differential separation of their resonance frequencies. A high level of sensitivity is obtained, owing to an innovative and optimized geometrical design of the device that guarantees a great amplification of the axial loads. The acceleration measure is obtained, owing to a properly designed oscillating circuit. In agreement with the theoretical prediction, the experimental results show a sensitivity of 455 Hz/ ( g being the gravity acceleration) with a resonant frequency of about 58 kHz and a good linearity in the range of interest.

A Resonant Microaccelerometer With High Sensitivity Operating in an Oscillating Circuit

The combination of multiaxis and multiparameter microelectromechanical systems (MEMS) in the same technology would result in very cheap and smart inertial measurement units (IMUs). In this paper, a $Z$ -axis Lorentz-force-based magnetometer whose design and optimization are reviewed taking into account the constraints of an industrial MEMS technology (process and packaging) already used for accelerometers and gyroscopes is presented. How this impacts the design guidelines is shown; in particular, a very compact device that can fit in the same package of the gyroscope to realize an all-MEMS seven-degree-of-freedom IMU is proposed and experimentally tested. The device shows a mechanical sensitivity of around 0.8 $\hbox{aF}/(\mu\hbox{T} \cdot \hbox{mA})$ with a resolution of 520 $(\hbox{nT} \cdot \hbox{mA})/\sqrt{\hbox{Hz}}$ over a signal bandwidth of 50 Hz at room temperature. Coupled to a transimpedance amplifier, the system shows an overall sensitivity of 150 $\mu\hbox{V}/\mu\hbox{T}$ at 250 $\mu\hbox{A}$ of peak driving current.

$Z$ -Axis Magnetometers for MEMS Inertial Measurement Units Using an Industrial Process

This paper reports the developments toward an integrated, tri-axial, frequency-modulated, consumer-grade, and microelectromechanical system (MEMS) gyroscope. A custom low-power (160 μ A), low-phase-noise integrated circuit is designed specifically for frequency-modulated operation. Both yaw- and pitch-rate sensing systems are demonstrated by coupling the circuit with two novel micromachined structures fabricated with a 24- μ m-thick industrial process. In operation, both gyroscopes show a repeatable and stable scale factor, with less than 0.55% of part-to-part variability, obtained with no any calibration, and 35 ppm/ $^{\circ }$ C of variability over a 25–70  $^{\circ }$ C temperature range.

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High Scale-Factor Stability Frequency-Modulated MEMS Gyroscope: 3-Axis Sensor and Integrated Electronics Design

This paper discusses the constraints in the design of circuits for microelectromechanical systems (MEMS) resonant sensors in consumer applications, presents a novel integrated circuit implementation, and shows that this approach can be competitive with respect to the mostly used capacitive readout. From a circuit design perspective, it is shown how the large equivalent resistance typical of MEMS resonators, their operation close to mechanical nonlinearity, and the effect of feedthrough capacitances on the oscillating loop constrain the power requirements of the driving/readout electronics. As a case study, a resonant accelerometer built in an industrial process is coupled to a suitably designed transimpedance amplifier with a low-power “hard limiter.” The performance shown in terms of linearity across the measurement range (±8 g), minimum measurable acceleration (1 mg with a readout bandwidth of 100 Hz), and power consumption (≈ 100 μW per axis) is comparable to those of state-of-the-art capacitive inertial sensors.

Design Criteria of Low-Power Oscillators for Consumer-Grade MEMS Resonant Sensors

The paper discusses the operation of Lorentz-force-based microelectromechanical magnetometers at a driving-current frequency slightly lower than the device resonance frequency. Among the advantages with respect to operation at resonance, there are a higher achievable signal to noise ratio (thanks to the lower permitted pressure and damping coefficient, which have now no influence on the maximum sensing bandwidth) and the possibility of driving more magnetometers in series through a single current source, enabling the fabrication of low-power 3-axis magnetic field sensors. A partial drawback is represented by a loss in gain-factor. Experimental results obtained on a sample device confirm the trade-off between gain-factor decrease and bandwidth increase. Guidelines for an optimized design of Lorentz force magnetometers are given together with a comparison with other state-of-the-art technologies through the introduction of a figure of merit. In particular, it is shown how Lorentz force devices can reach better performance in terms of minimum detectable magnetic flux density per unit current consumption and bandwidth.

Alessandro Tocchio

Papers

A Resonant Microaccelerometer With High Sensitivity Operating in an Oscillating Circuit

$Z$ -Axis Magnetometers for MEMS Inertial Measurement Units Using an Industrial Process

High Scale-Factor Stability Frequency-Modulated MEMS Gyroscope: 3-Axis Sensor and Integrated Electronics Design

Design Criteria of Low-Power Oscillators for Consumer-Grade MEMS Resonant Sensors

Operation of Lorentz-Force MEMS Magnetometers With a Frequency Offset Between Driving Current and Mechanical Resonance