Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Generation of picosecond pulses with a repetition frequency of 100 GHz by a multicomponent injection laser

A mode for generating a sequence of spectrally limited pulses with a duration of 2 nsec and a repetition frequency of approximately 100 GHz in AlGaAs/GaAs by an injection heterolaser, which has amplifying and absorbing parts combined in a common resonator, is discussed.

DIRECT DETECTION OF PICOSECOND PULSES EMITTED BY AN INJECTION LASER WITH ACTIVE MODE LOCKING.

An Agat-SF linear-scan streak image-converter camera was used to record output pulses of 2. 7 psec duration generated by an injection laser with an external dispersive resonator operated in the active mode-locking regime. The duration of the pulses was determined by the reciprocal of the spectral width and the product of the duration and the spectral width was 0. 30.

A single FBAR-based temperature and pressure sensors

A novel temperature and pressure sensor based on a single film bulk acoustic resonator (FBAR) is designed. This FBAR support two resonant modes, which response opposite to the change of temperature. By sealed the back cavity of a back-trench membrane type FBAR with silicon wafer, an on-chip single FBAR sensor suitable for measuring temperature and pressure simultaneously is proposed. For unsealed device, the experimental results show that the first resonant mode has a temperature coefficient of frequency (TCF) of 69.5ppm/K, and the TCF of the second mode is -8.1ppm/K. After sealed the back trench, it can be used as a pressure sensor, the pressure coefficient of frequency (PCF) for the two resonant mode is -17.4ppm/kPa and -6.1 ppm/kPa respectively, both of them being more sensitive than other existing pressure sensors. © 2013 Trans Tech Publications Ltd, Switzerland.

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a 'high-lift' and an 'ultra high-lift' turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in 'ultra high-lift' design when compared to the 'high-lift' design. Stronger 'Klebanoff streaks' are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The 'part-span' Kelvin-Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging. © 2013 Elsevier Inc.

High resolution direct measurement of temperature distribution in silicon nanophotonics devices.

Following the miniaturization of photonic devices and the increase in data rates, the issues of self heating and heat removal in active nanophotonic devices should be considered and studied in more details. In this paper we use the approach of Scanning Thermal Microscopy (SThM) to obtain an image of the temperature field of a silicon micro ring resonator with sub-micron spatial resolution. The temperature rise in the device is a result of self heating which is caused by free carrier absorption in the doped silicon. The temperature is measured locally and directly using a temperature sensitive AFM probe. We show that this local temperature measurement is feasible in the photonic device despite the perturbation that is introduced by the probe. Using the above method we observed a significant self heating of about 10 degrees within the device.

Acoustic properties of carbon nanotube electrodes in BAW resonators

In this paper the acoustic characterization of a layer of carbon nanotubes (CNT) deposited on AlN solidly mounted resonators is described. The structure of the CNT layer is analyzed by scanning electron microscopy and Raman spectroscopy. The electrical sheet resistance is derived from 4 point probe measurements and from the fitting of the electrical response of the resonators. Values of sheet resistance around 100 Ω/□ are measured. The longitudinal acoustic velocity is derived from the fitting of the electrical response of the resonators using Mason's model, by adjusting the overtones produced in the CNT layer. A mean value of 62000 m·s-1 is obtained, although some devices show values around 90000 m·s -1, close to the theoretical value of 100000 m·s-1. Some results on the deposition of CNT layers on metallic top electrodes and their influence on the performance of the resonator are also presented. © 2013 IEEE.

Numerical study of the impact of process variations on the motional resistance of weakly coupled MEMS resonators

This paper presents a numerical study of the impact of process-induced variations on the achievable motional resistance Rx of one-dimensional, cyclic and cross-coupled architectures of electrostatically transduced MEMS resonators operating in the 250 kHz range. Monte Carlo numerical simulations which accounted for up to 0.75% variation in critical resonator feature sizes were initiated on 1, 2, 3, 4, 5 and 9 coupled MEMS resonators for three distinct coupling architectures. Improvements of 100X in the spread of Rx and 2.7X in mean achievable Rx are reported for the case of 9 resonators when implemented in the cross-coupled topology, as opposed to the traditional one-dimensional chain. © 2013 IEEE.

MEMS-based mechanical AGC for oscillator circuits

This paper investigates a nonlinear amplitude saturation behavior in an electrostatically transduced, silicon MEMS disk resonator operating in its secondary elliptical bulk-mode (SEBM) at 3.932 MHz towards its implementation as an all-mechanical automatic gain control (AGC) element. The nonlinear vibration behavior of the SEBM mode is experimentally observed in open-loop testing such that above a threshold small signal drive voltage at a given polarization voltage, the vibration amplitude of the SEBM mode saturates. We also study this nonlinearity in an oscillator circuit designed such that the driving power level at the resonator input can be manually tuned as the circuit operates. The measurements of the voltage amplitudes show a clear transition from the linear to the nonlinear saturation region as the driving power is increased. Short-term frequency stability measurements were also conducted for different v ac and the resulting Allan deviation plots show an improvement in the short-term stability from 1.4 ppb in the linear region to 0.4 ppb in the amplitude saturation region. © 2013 IEEE.

High-frequency programmable acoustic wave device realized through ferroelectric domain engineering

Surface acoustic wave devices are extensively used in contemporary wireless communication devices. We used atomic force microscopy to form periodic macroscopic ferroelectric domains in sol-gel deposited lead zirconate titanate, where each ferroelectric domain is composed of many crystallites, each of which contains many microscopic ferroelastic domains. We examined the electro-acoustic characteristics of the apparatus and found a resonator behavior similar to that of an equivalent surface or bulk acoustic wave device. We show that the operational frequency of the device can be tailored by altering the periodicity of the engineered domains and demonstrate high-frequency filter behavior (>8GHz), allowing low-cost programmable high-frequency resonators. © 2014 AIP Publishing LLC.

Synchronization in a coupled architecture of microelectromechanical oscillators

There has been much recent interest in engineering the phenomenon of synchronization in coupled micro-/nano-scale oscillators for applications ranging from precision time and frequency references to new approaches to information processing. This paper presents descriptive modelling detail and further experimental validation of the phenomenon of mutual synchronization in coupled MEMS oscillators building upon recent experimental validation of this concept by the present authors. In particular, the underlying dependence of the observation of synchronization on system parameters is studied through numerical and analytical modelling while considering essential nonlinearities in both the resonator and circuit domain. Experimental results demonstrating synchronized response are elaborated based on the realization of electrically coupled MEMS resonator based square-wave oscillators. The experimental results on frequency entrainment are found to be in general agreement with results obtained through analytical modeling and numerical simulation. The concept presented here is scalable and could be used to investigate the dynamics of large-arrays of coupled MEMS oscillators. © 2014 AIP Publishing LLC.

Parametric resonance for vibration energy harvesting with design techniques to passively reduce the initiation threshold amplitude

A vibration energy harvester designed to access parametric resonance can potentially outperform the conventional direct resonant approach in terms of power output achievable given the same drive acceleration. Although linear damping does not limit the resonant growth of parametric resonance, a damping dependent initiation threshold amplitude exists and limits its onset. Design approaches have been explored in this paper to passively overcome this limitation in order to practically realize and exploit the potential advantages. Two distinct design routes have been explored, namely an intrinsically lower threshold through a pendulum-lever configuration and amplification of base excitation fed into the parametric resonator through a cantilever-initial-spring configuration. Experimental results of the parametric resonant harvesters with these additional enabling designs demonstrated an initiation threshold up to an order of magnitude lower than otherwise, while attaining a much higher power peak than direct resonance. © 2014 IOP Publishing Ltd.

Output Characteristics of an InP/InGaAsP Triangle Microcavity Laser

Mode competitions between modes with different output coupling efficiencies can result in optical bistability under certain asymmetric nonlinear gain. For a GaInAsP/InP equilateral triangle microlaser with the side length of 10 mu m, the drop of the output power with the increase of the injection current is observed corresponding to transverse mode transitions. Furthermore, the measured laser spectra up to 270 K show that lasing modes coexist with the wavelength interval of 39 nm at 240 K. The emission at 5.2 THz can be expected by the mode frequency beating with the 39 nm interval.

Mode Characteristics for Square Resonators With a Metal Confinement Layer

Microsquare resonators laterally confined by SiO2/Au/air multilayer structure are investigated by light ray method with reflection phase-shift of the multiple layers and two-dimensional (2-D) finite-difference time-domain (FDTD) technique. The reflectivity and phase shift of the mode light ray on the sides of the square resonator with the semiconductor/SiO2/Au/air multilayer structure are calculated for TE and TM modes by transfer matrix method. Based on the reflection phase shift and the reflectivity, the mode wavelength and factor are calculated by the resonant condition and the mirror loss, which are in agreement well with that obtained by the FDTD simulation. We find that the mode factor increases greatly with the increase of the SiO2 layer thickness, especially as d < 0.3 mu m. For the square resonator with side length 2 mu m and refractive index 3.2, anticrossing mode couplings are found for confined TE modes at wavelength about 1.6 mu m at d = 0.11 mu m, and confined TM modes at d = 0.71 mu m, respectively.

Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators

The enhancement of quality factor for TE whispering-gallery modes is analyzed for three-dimensional microcylinder resonators based on the destructive interference between vertical leakage modes. In the microcylinder resonator, the TE whispering-gallery modes can couple with vertical propagation modes, which results in vertical radiation loss and low quality factors. However, the vertical loss can be canceled by choosing appropriate thickness of the upper cladding layer or radius of the microcylinder. A mode quality factor increase by three orders of magnitude is predicted by finite-difference time-domain simulation. Furthermore, the condition of vertical leakage cancellation is analyzed.