Microelectromechanical components in electrical metrology

Microelectromechanical systems (MEMS) can offer a competitive alternative for conventional technology in electrical precision measurements. This article summarises recent work in development of MEMS solutions for electrical metrology. MEMS-based voltage references, RMS-to-DC converters, high frequency power sensors, and reference oscillators are discussed. The main principle of operation of the components is the balance between electrical forces and mechanical spring forces in micromachined silicon structures. In RMS sensors and RMS-to-DC converters, the quadratic voltage dependence of the force between plates of a moving-plate capacitor is utilised, and the operation of the MEMS voltage reference is based on the pull-in phenomenon of a moving-plate capacitor. Advantages of MEMS devices compared to more conventional solutions include small size, low power consumption, low price in mass production, and stability. The drift caused by electrostatic charging effects has turned out to be a major problem. This problem has not yet been solved in DC applications, but it can be circumvented by using AC actuation instead of DC and by compensating the internal DC voltages of the component. In this way, an AC voltage reference with relative drift rate below 2 ppm during a three-week test period has been constructed. Even better stability has been demonstrated with a MEMS-based reference oscillator: no changes in resonance frequency were observed at relative uncertainty level of about 0.01 ppm in a measurement which was continued for more than a month. MEMS components have also been developed for measuring RF and microwave power up to frequencies of about 40 GHz. Unlike conventional high frequency power sensors, which measure the absorbed power, the MEMS device measures the power that is transmitted through the sensor

Robust Controller Design for an Electrostatic Micromechanical Actuator

In this paper, a robust feedback controller is developed on an electrostatic micromechanical actuator to extend the travel range of it beyond pull-in limit. The actuator system is linearized at multiple operating points, and the controller is constructed based on the linearized model. Two kinds of controller designs are developed for set-point tracking of the actuator despite the presences of sensor noise and external disturbance. One of them is a regular fourth order Active Disturbance Rejection Controller (ADRC) and is able to achieve 97% of the maximum travel range. And the other one is a novel multi-loop controller with a second order ADRC in an inner loop and a PI controller in an outer loop. The multi-loop controller can achieve 99% of the maximum travel range. Transfer function representations of both controller designs are developed. The controllers are successfully applied and simulated on a parallel-plate electrostatic actuator model. The simulation results and frequency domain analyses verified the effectiveness of the controllers in extending the travel range of the actuator, in disturbance rejection, and in noise attenuation

Robust Controller Design for an Electrostatic Micromechanical Actuator

In this paper, a robust feedback controller is developed on an electrostatic micromechanical actuator to extend the travel range of it beyond pull-in limit. The actuator system is linearized at multiple operating points, and the controller is constructed based on the linearized model. Two kinds of controller designs are developed for set-point tracking of the actuator despite the presences of sensor noise and external disturbance. One of them is a regular fourth order Active Disturbance Rejection Controller (ADRC) and is able to achieve 97% of the maximum travel range. And the other one is a novel multi-loop controller with a second order ADRC in an inner loop and a PI controller in an outer loop. The multi-loop controller can achieve 99% of the maximum travel range. Transfer function representations of both controller designs are developed. The controllers are successfully applied and simulated on a parallel-plate electrostatic actuator model. The simulation results and frequency domain analyses verified the effectiveness of the controllers in extending the travel range of the actuator, in disturbance rejection, and in noise attenuation

Pull-in dynamics of overdamped microbeams

We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At DC voltages close to the pull-in voltage, experiments and numerical simulations have reported `bottleneck' behaviour in which the transient dynamics slow down considerably. This slowing down is highly sensitive to external forces, and so has widespread potential for applications that use pull-in time as a sensing mechanism, including high-resolution accelerometers and pressure sensors. Previously, the bottleneck phenomenon has only been understood using lumped mass-spring models that do not account for effects such as variable residual stress and different boundary conditions. We extend these studies to incorporate the beam geometry, developing an asymptotic method to analyse the pull-in dynamics. We attribute bottleneck behaviour to critical slowing down near the pull-in transition, and we obtain a simple expression for the pull-in time in terms of the beam parameters and external damping coefficient. This expression is found to agree well with previous experiments and numerical simulations that incorporate more realistic models of squeeze film damping, and so provides a useful design rule for sensing applications. We also consider the accuracy of a single-mode approximation of the microbeam equations --- an approach that is commonly used to make analytical progress, without systematic investigation of its accuracy. By comparing to our bottleneck analysis, we identify the factors that control the error of this approach, and we demonstrate that this error can indeed be very small.Comment: 18 page

Doctor of Philosophy

dissertationThis thesis presents the design, fabrication and characterization of a microelectromechanical system (MEMS) based complete wireless microsystem for brain interfacing, with very high quality factor and low power consumption. Components of the neuron sensing system include TiW fixed-fixed bridge resonator, MEMS oscillator based action-potential-to-RF module, and high-efficiency RF coil link for power and data transmissions. First, TiW fixed-fixed bridge resonator on glass substrate was fabricated and characterized, with resonance frequency of 100 - 500 kHz, and a quality factor up to 2,000 inside 10 mT vacuum. The effect of surface conditions on resonator's quality factor was studied with 10s of nm Al2O3 layer deposition with ALD (atomic layer deposition). It was found that MEMS resonator's quality factor decreased with increasing surface roughness. Second, action-potential-to-RF module was realized with MEMS oscillator based on TiW bridge resonator. Oscillation signal with frequency of 442 kHz and phase noise of -84.75 dBc/Hz at 1 kHz offset was obtained. DC biasing of the MEMS oscillator was modulated with neural signal so that the output RF waveform carries the neural signal information. Third, high-efficiency RF coil link for power and data communications was designed and realized. Based on the coupled mode theory (CMT), intermediate resonance coil was introduced and increased voltage transfer efficiency by up to 5 times. Finally, a complete neural interfacing system was demonstrated with board-level integration. The system consists of both internal and external systems, with wireless powering, wireless data transfer, artificial neuron signal generation, neural signal modulation and demodulation, and computer interface displaying restored neuron signal

Delayed pull-in transitions in overdamped MEMS devices

We consider the dynamics of overdamped MEMS devices undergoing the pull-in instability. Numerous previous experiments and numerical simulations have shown a significant increase in the pull-in time under DC voltages close to the pull-in voltage. Here the transient dynamics slow down as the device passes through a meta-stable or bottleneck phase, but this slowing down is not well understood quantitatively. Using a lumped parallel-plate model, we perform a detailed analysis of the pull-in dynamics in this regime. We show that the bottleneck phenomenon is a type of critical slowing down arising from the pull-in transition. This allows us to show that the pull-in time obeys an inverse square-root scaling law as the transition is approached; moreover we determine an analytical expression for this pull-in time. We then compare our prediction to a wide range of pull-in time data reported in the literature, showing that the observed slowing down is well captured by our scaling law, which appears to be generic for overdamped pull-in under DC loads. This realization provides a useful design rule with which to tune dynamic response in applications, including state-of-the-art accelerometers and pressure sensors that use pull-in time as a sensing mechanism. We also propose a method to estimate the pull-in voltage based only on data of the pull-in times.Comment: 17 page

Large amplitude dynamics of micro/nanomechanical resonators actuated with electrostatic pulses

International audienceIn the field of resonant NEMS design, it is a common misconception that large-amplitude motion, and thus large signal-to-noise ratio, can only be achieved at the risk of oscillator instability. In the present paper, we show that very simple closed-loop control schemes can be used to achieve stable largeamplitude motion of a resonant structure, even when jump resonance (caused by electrostatic softening or Duffing hardening) is present in its frequency response. We focus on the case of a resonant accelerometer sensing cell, consisting in a nonlinear clamped-clamped beam with electrostatic actuation and detection, maintained in an oscillation state with pulses of electrostatic force that are delivered whenever the detected signal (the position of the beam) crosses zero. We show that the proposed feedback scheme ensures the stability of the motion of the beam much beyond the critical Duffing amplitude and that, if the parameters of the beam are correctly chosen, one can achieve almost full-gap travel range without incurring electrostatic pull-in. These results are illustrated and validated with transient simulations of the nonlinear closed-loop system

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

Probing complex RNA structures by mechanical force

RNA secondary structures of increasing complexity are probed combining single molecule stretching experiments and stochastic unfolding/refolding simulations. We find that force-induced unfolding pathways cannot usually be interpretated by solely invoking successive openings of native helices. Indeed, typical force-extension responses of complex RNA molecules are largely shaped by stretching-induced, long-lived intermediates including non-native helices. This is first shown for a set of generic structural motifs found in larger RNA structures, and then for Escherichia coli's 1540-base long 16S ribosomal RNA, which exhibits a surprisingly well-structured and reproducible unfolding pathway under mechanical stretching. Using out-of-equilibrium stochastic simulations, we demonstrate that these experimental results reflect the slow relaxation of RNA structural rearrangements. Hence, micromanipulations of single RNA molecules probe both their native structures and long-lived intermediates, so-called "kinetic traps", thereby capturing -at the single molecular level- the hallmark of RNA folding/unfolding dynamics.Comment: 9 pages, 9 figure