An analytical formulation for phase noise in MEMS oscillators.

In recent years, there has been much interest in the design of low-noise MEMS oscillators. This paper presents a new analytical formulation for noise in a MEMS oscillator encompassing essential resonator and amplifier nonlinearities. The analytical expression for oscillator noise is derived by solving a second-order nonlinear stochastic differential equation. This approach is applied to noise modeling of an electrostatically addressed MEMS resonator-based square-wave oscillator in which the resonator and oscillator circuit nonlinearities are integrated into a single modeling framework. By considering the resulting amplitude and phase relations, we derive additional noise terms resulting from resonator nonlinearities. The phase diffusion of an oscillator is studied and the phase diffusion coefficient is proposed as a metric for noise optimization. The proposed nonlinear phase noise model provides analytical insight into the underlying physics and a pathway toward the design optimization for low-noise MEMS oscillators.The authors would like to thank the UK-Indian Education and Research Initiative (grant SA06-250) and the Cambridge Trusts for funding support.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TUFFC.2014.00651

Damping of piezoelectric MEMS oscillators – fundamentals and applications

A limiting parameter for the performance of micromechanical oscillators is the damping induced by the surrounding medium. In this work, the damping losses of micromechanical oscillators with piezoelectric actuation and detection are investigated in nine different gas atmospheres over a pressure range of six decades. In addition, the influence of the distance to a spatial boundary is examined, covering a range from narrow gaps with squeeze film damping to an almost freely oscillating structure. This reveals a superposition of four different damping mechanisms, which occur in varying strength depending on pressure, distance and eigenmode. Using an analytical approach, the individual damping phenomena can be separated from each other and subsequently evaluated in a targeted manner. Based on these results, new insights are gained for the molecular flow regime as well as the transitional flow regime, which include the impact of the number of active degrees of freedom of the gas molecules as well as thermal resonance effects. In addition, an electrical equivalent circuit was designed for the entire measurement range, which shows very good agreement with the experimental data. Finally, the damping effects are exploited for applications in sensor technology and a wide range pressure sensor using the nonlinear regime of the oscillators as well as a concept for the measurement of the oxygen concentration are presented.Eine für die Leistungsfähigkeit mikromechanischer Oszillatoren limitierende Größe stellt die Dämpfung durch das umgebende Medium dar. In dieser Arbeit werden daher die Dämpfungsverluste mikromechanischer Oszillatoren mit piezoelektrischer Anregung und Detektion in neun verschiedenen Gasatmosphären über einen Druckbereich von sechs Dekaden untersucht. Zusätzlich wird der Einfluss des Abstandes zu einer räumlichen Begrenzung betrachtet und dabei ein Bereich von engen Spalten mit Squeeze Film Dämpfung bis hin zu fast frei schwingenden Strukturen untersucht. Dabei ergibt sich eine Überlagerung von vier verschiedenen Dämpfungsmechanismen, welche in Abhängigkeit von Druck, Abstand und Eigenmode in unterschiedlich starker Ausprägung auftreten. Durch einen analytischen Ansatz lassen sich die einzelnen Dämpfungsphänomene voneinander separieren und in der Folge gezielt auswerten. Anhand dieser Ergebnisse wurden für den molekularen sowie den Übergangsbereich neue Erkenntnisse gewonnen, welche die Anzahl aktiver Freiheitsgrade der Gasmoleküle sowie thermische Resonanzeffekte miteinbeziehen. Darüber hinaus wurde für den gesamten Messbereich ein elektrisches Ersatzschaltbild konzipiert, das eine sehr gute Übereinstimmung mit den experimentellen Daten zeigt. Abschließend werden die Dämpfungseffekte für Anwendungen in der Sensorik erschlossen und ein Mehrbereichsdrucksensor mit Hilfe des nichtlinearen Bereichs der Oszillatoren sowie ein Konzept zur Messung des Sauerstoffgehaltes präsentiert.German Research Foundation (DFG

Classical and fluctuation-induced electromagnetic interactions in micronscale systems: designer bonding, antibonding, and Casimir forces

Whether intentionally introduced to exert control over particles and macroscopic objects, such as for trapping or cooling, or whether arising from the quantum and thermal fluctuations of charges in otherwise neutral bodies, leading to unwanted stiction between nearby mechanical parts, electromagnetic interactions play a fundamental role in many naturally occurring processes and technologies. In this review, we survey recent progress in the understanding and experimental observation of optomechanical and quantum-fluctuation forces. Although both of these effects arise from exchange of electromagnetic momentum, their dramatically different origins, involving either real or virtual photons, lead to different physical manifestations and design principles. Specifically, we describe recent predictions and measurements of attractive and repulsive optomechanical forces, based on the bonding and antibonding interactions of evanescent waves, as well as predictions of modified and even repulsive Casimir forces between nanostructured bodies. Finally, we discuss the potential impact and interplay of these forces in emerging experimental regimes of micromechanical devices.Comment: Review to appear on the topical issue "Quantum and Hybrid Mechanical Systems" in Annalen der Physi

DESIGN, COMPACT MODELING AND CHARACTERIZATION OF NANOSCALE DEVICES

Electronic device modeling is a crucial step in the advancement of modern nanotechnology and is gaining more and more interest. Nanoscale complementary metal oxide semiconductor (CMOS) transistors, being the backbone of the electronic industry, are pushed to below 10 nm dimensions using novel manufacturing techniques including extreme lithography. As their dimensions are pushed into such unprecedented limits, their behavior is still captured using models that are decades old. Among many other proposed nanoscale devices, silicon vacuum electron devices are regaining attention due to their presumed advantages in operating at very high power, high speed and under harsh environment, where CMOS cannot compete. Another type of devices that have the potential to complement CMOS transistors are nano-electromechanical systems (NEMS), with potential applications in filters, stable frequency sources, non-volatile memories and reconfigurable and neuromorphic electronics

Complex dynamical networks constructed with fully controllable nonlinear nanomechanical oscillators

Control of the global parameters of complex networks has been explored experimentally in a variety of contexts. Yet, the more difficult prospect of realizing arbitrary network architectures, especially analog physical networks that provide dynamical control of individual nodes and edges, has remained elusive. Given the vast hierarchy of time scales involved, it also proves challenging to measure a complex network’s full internal dynamics. These span from the fastest nodal dynamics to very slow epochs over which emergent global phenomena, including network synchronization and the manifestation of exotic steady states, eventually emerge. Here, we demonstrate an experimental system that satisfies these requirements. It is based upon modular, fully controllable, nonlinear radio frequency nanomechanical oscillators, designed to form the nodes of complex dynamical networks with edges of arbitrary topology. The dynamics of these oscillators and their surrounding network are analog and continuous-valued and can be fully interrogated in real time. They comprise a piezoelectric nanomechanical membrane resonator, which serves as the frequency-determining element within an electrical feedback circuit. This embodiment permits network interconnections entirely within the electrical domain and provides unprecedented node and edge control over a vast region of parameter space. Continuous measurement of the instantaneous amplitudes and phases of every constituent oscillator node are enabled, yielding full and detailed network data without reliance upon statistical quantities. We demonstrate the operation of this platform through the real-time capture of the dynamics of a three-node ring network as it evolves from the uncoupled state to full synchronization

Multiphysics modelling and experimental validation of microelectromechanical resonator dynamics

The modelling of microelectromechanical systems provides a very challenging task in microsystems engineering. This field of research is inherently multiphysics of nature, since different physical phenomena are tightly intertwined at microscale. Typically, up to four different physical domains are usually considered in the analysis of microsystems: mechanical, electrical, thermal and fluidic. For each of these separate domains, well-established modelling and analysis techniques are available. However, one of the main challenges in the field of microsystems engineering is to connect models for the behavior of the device in each of these domains to equivalent lumped or reduced-order models without making unacceptably inaccurate assumptions and simplifications and to couple these domains correctly and efficiently. Such a so-called multiphysics modelling framework is very important for simulation of microdevices, since fast and accurate computational prototyping may greatly shorten the design cycle and thus the time-to-market of new products. This research will focus on a specific class of microsystems: microelectromechanical resonators. MEMS resonators provide a promising alternative for quartz crystals in time reference oscillators, due to their small size and on-chip integrability. However, because of their small size, they have to be driven into nonlinear regimes in order to store enough energy for obtaining an acceptable signal-to-noise ratio in the oscillator. Since these resonators are to be used as a frequency reference in the oscillator circuits, their steady-state (nonlinear) dynamic vibration behaviour is of special interest. A heuristic modelling approach is investigated for two different MEMS resonators, a clamped-clamped beam resonator and a dog-bone resonator. For the clamped-clamped beam resonator, the simulations with the proposed model shows a good agreement with experimental results, but the model is limited in its predictive capabilities. For the dogbone resonator, the proposed heuristic modelling approach does not lead to a match between simulations and experiments. Shortcomings of the heuristic modelling approach serve as a motivation for a first-principles based approach. The main objective of this research is to derive a multiphysics modelling framework for MEMS resonators that is based on first-principles formulations. The framework is intended for fast and accurate simulation of the steady-state nonlinear dynamic behaviour of MEMS resonators. Moreover, the proposed approach is validated by means of experiments. Although the multiphysics modelling framework is proposed for MEMS resonators, it is not restricted to this application field within microsystems engineering. Other fields, such as (resonant) sensors, switches and variable capacitors, allow for a similar modelling approach. In the proposed framework, themechanical, electrical and thermal domains are included. Since the resonators considered are operated in vacuum, the fluidic domain (squeeze film damping) is not included. Starting from a first-principles description, founded on partial differential equations (PDEs), characteristic nonlinear effects from each of the included domains are incorporated. Both flexural and bulk resonators can be considered. Next, Galerkin discretization of the coupled PDEs takes place, to construct reduced-order models while retaining the nonlinear effects. The multiphysics model consists of the combined reduced-order models from the different domains. Designated numerical tools are used to solve for the steady-state nonlinear dynamic behaviour of the combined model. The proposed semi-analytical (i.e. analytical-numerical) multiphysics modeling framework is illustrated for a full case study of an electrostatically actuated single-crystal silicon clamped-clamped beam MEMS resonator. By means of the modelling framework, multiphysics models of varying complexity have been derived for this resonator, including effects like electrostatic actuation, fringing fields, shear deformation, rotary inertia, thermoelastic damping and nonlinear material behaviour. The first-principles based approach allows for addressing the relevance of individual effects in a straightforward way, such that the models can be used as a (pre-)design tool for dynamic response analysis. The method can be considered complementary to conventional finite element simulations. The multiphysics model for the clamped-clamped beam resonator is validated by means of experiments. A good match between the simulations and experiments is obtained, thereby giving confidence in the proposed modelling framework. Finally, next to themodelling approach for MEMS resonators, a technique for using these nonlinear resonators in an oscillator circuit setting is presented. This approach, called phase feedback, allows for operation of the resonator in its nonlinear regime. The closedloop technique enables control of both the frequency of oscillation and the output power of the signal. Additionally, optimal operation points for oscillator circuits incorporating a nonlinear resonator can be defined

7th International Conference on Nonlinear Vibrations, Localization and Energy Transfer: Extended Abstracts

International audienceThe purpose of our conference is more than ever to promote exchange and discussions between scientists from all around the world about the latest research developments in the area of nonlinear vibrations, with a particular emphasis on the concept of nonlinear normal modes and targeted energytransfer

The 2017 Terahertz Science and Technology Roadmap

Science and technologies based on terahertz frequency electromagnetic radiation (100GHz-30THz) have developed rapidly over the last 30 years. For most of the 20th century, terahertz radiation, then referred to as sub-millimeter wave or far-infrared radiation, was mainly utilized by astronomers and some spectroscopists. Following the development of laser based terahertz time-domain spectroscopy in the 1980s and 1990s the field of THz science and technology expanded rapidly, to the extent that it now touches many areas from fundamental science to “real world” applications. For example THz radiation is being used to optimize materials for new solar cells, and may also be a key technology for the next generation of airport security scanners. While the field was emerging it was possible to keep track of all new developments, however now the field has grown so much that it is increasingly difficult to follow the diverse range of new discoveries and applications that are appearing. At this point in time, when the field of THz science and technology is moving from an emerging to a more established and interdisciplinary field, it is apt to present a roadmap to help identify the breadth and future directions of the field. The aim of this roadmap is to present a snapshot of the present state of THz science and technology in 2016, and provide an opinion on the challenges and opportunities that the future holds. To be able to achieve this aim, we have invited a group of international experts to write 17 sections that cover most of the key areas of THz Science and Technology. We hope that The 2016 Roadmap on THz Science and Technology will prove to be a useful resource by providing a wide ranging introduction to the capabilities of THz radiation for those outside or just entering the field as well as providing perspective and breadth for those who are well established. We also feel that this review should serve as a useful guide for government and funding agencies

Frequency Stability in Thin-film Piezoelectric-on-substrate Oscillators

For many years, crystal oscillators have been used as the de facto frequency reference in almost all electronic platforms because they offer excellent stability and superior phase noise. This is mainly due to the high quality factor (Q) and exceptional temperature stability of quartz crystals. However, the size of quartz resonators is relatively large, and they cannot be readily integrated with microelectronics. This ultimately impedes the complete integration of the high-performance oscillators with the electronics. Achieving such integration will enable frequency control devices with a smaller form factor, lower cost, greater flexibility, and potentially higher reliability. Microelectromechanical systems (MEMS) resonator technology is gradually gaining popularity as a solution for the integration barrier and high-performance micro-machined oscillators have been presented by researchers and companies recently. However, one of the most important drawbacks of MEMS resonators has been their relatively large and linear temperature coefficient of frequency (TCF) (e.g., around -30 ppm/C for Si-based). The subject of this presentation is on the frequency stability in thin-film piezoelectric-on-substrate oscillators (TPoS). In this regard, jitter and temperature dependency of the oscillation frequency are studied. The dependency of jitter of TPoS on the resonator characteristics (i.e. quality factor and motional impedance) is studied where the results provide experimental validation for the suppression of overall oscillator circuit noise through the operation of the resonator beyond the bifurcation.A novel temperature compensation technique for silicon-based lateral-extensional MEMS oscillators is introduced, which is based on the properly orienting an extensional-mode resonator on a highly doped n-type silicon substrate. The existence of a local zero temperature coefficient of frequency (i.e., turnover point) in extensional-mode silicon microresonators, fabricated on highly n-type-doped substrates and aligned to the [100] crystalline orientation is demonstrated. It is shown that the turnover point in TPoS resonators is a function of doping concentration and orientation. Moreover, the turnover point can be adjusted by changing the thickness ratio of Si and the piezoelectric film (e.g., AlN) in the resonant structure. MEMS oscillators with controlled temperature coefficient of frequency (TCF), assembled through mixing the frequencies of two oscillators that are made of silicon micro-resonators with known and dissimilar TCF, are also introduced. Based on this method, a TPoS MEMS oscillator is assembled in which the first-order TCF is virtually cancelled resulting in a parabolic TCF curve (second-order TCF).The frequency tuning in TPoS resonators is also reported which results show a great potential application in temperature compensated oscillators. Tuning is demonstrated through varying the termination load connected to an isolated tuning port. The dependency of frequency tuning on the design features of the resonator is studied as well.Electrical Engineerin