Hydrodynamic Loading on Vibrating Piezoelectric Microresonators

The dynamics of micro-piezoelectric resonators can be profoundly affected by immersion in fluids. Aluminum nitride-based piezoelectric microresonators are fabricated and tested under controlled pressures in several gases. The cases on microresonator vibrating in fluid can be broadly divided into: (i) those that deal with vibration in free space and (ii) close to a surface. For the first case, experimental and analytical results for the hydrodynamic loading characteristics of the resonators at different resonant modes have been investigated, as well as the influences of fluid viscosity and compressibility. For the second case, most prior efforts have been focused on squeeze-film damping with very narrow gaps, while in many practical applications, the resonators vibrate close to a surface with a moderate distance. Experiments by using a micro-bridge resonator with a big range of gaps are performed and compared with predictions from theoretical models

Forecasting the Risk of Speculative Assets by Means of Copula Distributions

The GARCH(1,1) model and its extensions have become a standard econometric tool for modeling volatility dynamics of financial returns and port-folio risk. In this paper, we propose an adjustment of GARCH implied conditional value-at-risk and expected shortfall forecasts that exploits the predictive content of uncorrelated, yet dependent model innovations. The adjustment is motivated by non-Gaussian characteristics of model residuals, and is implemented in a semiparametric fashion by means of conditional moments of simulated bivariate standardized copula distributions. We conduct in-sample forecasting comparisons for a set of 18 stock market indices. In total, four competing copula-GARCH models are contrasted against each other on the basis of their one-step ahead forecasting performance. With regard to forecast unbiasedness and precision, especially the Frank-GARCH models provide most conservative risk forecasts and out-perform all rival models

Generalized Damping Model for MEMS Oscillators from Molecular to Viscous Flow Regime

In this study, we investigate the damping phenomena acting on piezoelectrically driven MEMS oscillators. Three different geometrical shapes of MEMS oscillators are presented, including cantilevers, bending oscillators, and paddle oscillators. An analytical model for their resonance frequencies is derived. The bending modes of these micro-oscillator structures are characterized regarding their resonance frequency and their quality factor as a function of the ambient pressure in a nitrogen atmosphere as well as the dependence on the distance to a neighboring plate representing a geometrical boundary (e.g., to the package or to the mounting). The investigations cover a pressure range from 10−3 mbar up to 900 mbar and a gap width from 150 µm to 3500 µm. Consequently, a Knudsen number range over six orders of magnitude from 100 to 10−4 is covered. The measurement data are evaluated with a generalized damping model consisting of four parts representing the individual damping mechanisms (intrinsic, molecular, transitional, and viscous). The evaluated parameters are analyzed as a function of the resonance frequency and the gap width. The data reveal an exponential growing saturation behavior, which is determined by two characteristic lengths, being correlated with the viscous and the thermal boundary layer thickness, respectively. This leads to an estimation of the strength and of the range of the damping effect just by calculating the boundary layer thicknesses given by the resonance frequency and the gas properties. From these results, we gain fundamental insights on the viscous and transitional damping mechanisms as well as on the intrinsic losses. In conclusion, a basic concept is provided to reduce the damping of micro-oscillator bending modes and thus increase the quality factor. Additionally, the results are supported by finite element simulations revealing the temperature and pressure distribution within the gap

Using the Nonlinear Duffing Effect of Piezoelectric Micro-Oscillators for Wide-Range Pressure Sensing

This paper investigates the resonant behaviour of silicon-based micro-oscillators with a length of 3600 µm, a width of 1800 µm and a thickness of 10 µm over a wide range of ambient gas (N2 ) pressures, extending over six orders of magnitude from 10−3 mbar to 900 mbar. The oscillators are actuated piezoelectrically by a thin-film aluminium-nitride (AlN) layer, with the cantilever coverage area being varied from 33% up to 100%. The central focus is on nonlinear Duffing effects, occurring at higher oscillation amplitudes. A theoretical background is provided. All relevant parameters describing a Duffing oscillator, such as stiffness parameters for each coverage size as well as for different bending modes and more complex modes, are extracted from the experimental data. The so-called 2nd roof-tile-shaped mode showed the highest stiffness value of −97.3·107 m−2 s −2 . Thus, it was chosen as being optimal for extended range pressure measurements. Interestingly, both a spring softening effect and a spring hardening effect were observed in this mode, depending on the percentage of the AlN coverage area. The Duffing-effect-induced frequency shift was found to be optimal for obtaining the highest pressure sensitivity, while the size of the hysteresis loop is also a very useful parameter because of the possibility of eliminating the temperature influences and long-term drift effects of the resonance frequency. An reasonable application-specific compromise between the sensitivity and the measurement range can be selected by adjusting the excitation voltage, offering much flexibility. This novel approach turns out to be very promising for compact, cost-effective, wide-range pressure measurements in the vacuum range

Design and Characterization of a Planar Micro-Conveyor Device Based on Cooperative Legged Piezoelectric MEMS Resonators

This paper reports the design, fabrication, and performance of a hybrid piezoelectric planar micro-conveyor based on Micro-Electromechanical Systems (MEMS) bridge resonators and featuring 3D-printed vertical legs. The device includes two cooperating silicon plate resonators with an area of 5 × 1 mm2 , actuated by an integrated aluminum-nitride (AlN) piezoelectric thin film. An optimally designed array of 3D-printed projection legs was attached to the plates, to convert the standing-wave (SW) vertical vibrations into horizontal rotations or translations of the supported slider. An open-loop control strategy based on burst-type driving signals, with different numbers of sinusoidal cycles applied on each of the resonators, allowed the cooperation of the two bridges to set up prescribed trajectories of small flat objects, up to 100 mg, with positional accuracy below 100 nm and speeds up to 20 mm/s, by differential drive actuation. The effect of the leg tip and sliders’ surface finish on the conveyor performance was investigated, suggesting that further optimizations may be possible by modifying the tribological properties. Finally, the application of the micro-conveyor as a reconfigurable electronic system, driven by a preprogrammed sequence of signals, was demonstrated by delivering some surface-mount technology (SMD) parts lying on a 65 mg glass slider

MEMS-based Gyroscopes as Physical Unclonable Functions

We are at the dawn of a hyper connectivity age otherwise known as the Internet of Things (IoT). It is widely accepted that to be able to reap all benefits from the IoT promise, device security will be of paramount importance. A key requirement for most security solutions is the ability to provide secure cryptographic key storage in a way that will easily scale in the IoT age. In this paper, we focus on providing such a solution based on Physical Unclonable Functions (PUFs). To this end, we focus on microelectromechanical systems (MEMS)-based gyroscopes and show via wafer-level measurements and simulations, that it is feasible to use the physical and electrical properties of these sensors for cryptographic key generation. After identifying the most promising features, we propose a novel quantization scheme to extract bit strings from the MEMS analog measurements. We provide upper and lower bounds for the minimum entropy of the bit strings derived from the measurements and fully analyze the intra- and inter-class distributions across the operation range of the MEMS device. We complement these measurements via Monte-Carlo simulations based on the distributions of the parameters measured on actual devices. We also propose and evaluate a key derivation procedure based on fuzzy extractors for Hamming distance, using the min-entropy estimates obtained to derive a full entropy 128-bit key, requiring 1219-bits of helper data with an (authentication) failure probability of 4x10^-7. Thereby, we present a complete cryptographic key generation chain. In addition, we propose a dedicated MEMS-PUF design, which is superior to our measured sensor, in terms of chip area, quality and quantity of key seed features

Piezoelectric MEMS Linear Motor for Nanopositioning Applications

This paper reports the design, fabrication, and performance of piezoelectric bidirectional conveyors based on microelectromechanical systems (MEMS) and featuring 3D-printed legs in bridge resonators. The structures consisted of aluminum-nitride (AlN) piezoelectric film on top of millimeter-sized rectangular thin silicon bridges and two electrode patches. The position and size of the patches were analytically optimized for travelling or standing wave generation, while the addition of 3D-printed legs allowed for a controlled contact and amplified displacement, a further step into the manufacturing of efficient linear motors. Such hybrid devices have recently demonstrated the conveyance of sliders of several times the motor weight, with speeds of 1.7 mm/s by travelling waves generated at 6 V and 19.3 kHz. In this paper both travelling and standing wave motors are compared. By the optimization of various aspects of the device such as the vibrational modes, leg collocation and excitation signals, speeds as high as 35 mm/s, and payloads above 10 times the motor weight were demonstrated. The devices exhibited a promising positional resolution while actuated with only a few sinusoidal cycles in an open-loop configuration. Discrete steps as low as 70 nm were measured in the conveyance of 2-mg sliders

A Geometrical Study on the Roof Tile-Shaped Modes in AlN-Based Piezoelectric Microcantilevers as Viscosity–Density Sensors

Cantilever resonators based on the roof tile-shaped modes have recently demonstrated their suitability for liquid media monitoring applications. The early studies have shown that certain combinations of dimensions and order of the mode can maximize the Q-factor, what might suggest a competition between two mechanisms of losses with different geometrical dependence. To provide more insight, a comprehensive study of the Q-factor and the resonant frequency of these modes in microcantilever resonators with lengths and widths between 250 and 3000 µm and thicknesses between 10 and 60 µm is presented. These modes can be efficiently excited by a thin piezoelectric AlN film and a properly designed top electrode layout. The electrical and optical characterization of the resonators are performed in liquid media and then their performance is evaluated in terms of quality factor and resonant frequency. A quality factor as high as 140 was measured in isopropanol for a 1000 × 900 × 10 µm3 cantilever oscillating in the 11th order roof tile-shaped mode at 4 MHz; density and viscosity resolutions of 10−6 g/mL and 10−4 mPa·s, respectively are estimated for a geometrically optimized cantilever resonating below 1 MH

Bidirectional Linear Motion by Travelling Waves on Legged Piezoelectric Microfabricated Plates

This paper reports the design, fabrication and performance of MEMS-based piezoelectric bidirectional conveyors featuring 3D printed legs, driven by linear travelling waves (TW). The structures consisted of an aluminium–nitride (AlN) piezoelectric film on top of millimetre-sized rectangular thin silicon bridges and two electrode patches. The position and size of the patches were analytically optimised for TW generation in three frequency ranges: 19, 112 and 420 kHz, by the proper combination of two contiguous flexural modes. After fabrication, the generated TW were characterized by means of Laser–Doppler vibrometry to obtain the relevant tables of merit, such as the standing wave ratio and the average amplitude. The experimental results agreed with the simulation, showing the generation of a TW with an amplitude as high as 6 nm/V and a standing wave ratio as low as 1.46 for a device working at 19.3 kHz. The applicability of the fabricated linear actuator device as a conveyor was investigated. Its kinetic performance was studied with sliders of different mass, being able to carry a 35 mg silicon slider, 18 times its weight, with 6 V of continuous sinusoidal excitation and a speed of 0.65 mm/s. A lighter slider, weighting only 3 mg, reached a mean speed of 1.7 mm/s at 6 V. In addition, by applying a burst sinusoidal excitation comprising 10 cycles, the TW generated in the bridge surface was able to move a 23 mg slider in discrete steps of 70 nm, in both directions, which is a promising result for a TW piezoelectric actuator of this size

Generation of Linear Traveling Waves in Piezoelectric Plates in Air and Liquid

A micro- to milli-sized linear traveling wave (TW) actuator fabricated with microelectromechanical systems (MEMS) technology is demonstrated. The device is a silicon cantilever actuated by piezoelectric aluminum nitride. Specifically designed top electrodes allow the generation of TWs at different frequencies, in air and liquid, by combining two neighboring resonant modes. This approach was supported by analytical calculations, and different TWs were measured on the same plate by laser Doppler vibrometry. Numerical simulations were also carried out and compared with the measurements in air, validating the wave features. A standing wave ratio as low as 1.45 was achieved in air, with a phase velocity of 652 m/s and a peak horizontal velocity on the device surface of 124 μm/s for a driving signal of 1 V at 921.9 kHz. The results show the potential of this kind of actuator for locomotion applications in contact with surfaces or under immersion in liquid