MEMS Oscillator Research Articles

Real-Time Temperature Compensation of MEMS Oscillators Using an Integrated Micro-Oven and a Phase-Locked Loop

We present a new temperature compensation system for microresonator-based frequency references. It consists of a phase-locked loop (PLL) whose inputs are derived from two microresonators with different temperature coefficients of frequency. The resonators are suspended within an encapsulated cavity and are heated to a constant temperature by the PLL controller, thereby achieving active temperature compensation. We show repeated real-time measurements of three 1.2-MHz prototypes that achieve a frequency stability of ± 1 ppm from -20°C to +80°C, as well as a technique to reduce steady-state frequency errors to ±0.05 ppm using multipoint calibration.

MNM-P11-1 自己回帰モデルによるMEMS振動子パラメータ抽出法の提案(P11 電気等価回路から考えるMEMS設計手法)

System identification by Auto-regressive Model that based on time series data is widely used for the purpose of estimating a mathematical model of system in various fields. However, this approach needs to estimate according to the individualized theory. In this study, considered whether this technique could be applied in the MEMS oscillator. The AR model method is generally used to estimate the unknown parameter that constitute system. So, MEMS oscillator system parameter changes with packaging before and after, can be expected to analyze. In addition, white noise including using a variety of input frequencies can be expected to establish high-throughput extraction parameters.

2.2 MHz piezoresistive MEMS oscillator operating in air

This paper describes a MEMS oscillator capable of operation at atmospheric pressure, based on a square-extensional mode single crystal silicon resonator. The resonator is actuated by differential capacitive driving and the motion of the structure is transduced piezoresistively. This transduction scheme successfully mitigates the effects of capacitive feedthrough and enhances the motional signal at micron scale transduction gaps. The oscillator demonstrates an Allan deviation of close to 1 ppm at an integration time of 200 seconds for an output power level of 0 dBm.

Silison MEMS Oscillators for high-speed digital systems

Silison MEMS Oscillators for high-speed digital systems

T0302-2-4 MEMS振動子を用いた昇圧素子(マイクロ・ナノ力学とシステム設計論(2))

This paper described a boosting device by MEMS oscillator. Recently, the semiconductor memory such as SRAM proceed rapidly to be installed in the storage medium such as mobile information devices. In the semiconductor memory, the voltage more than the input voltage (1.8〜5V) is necessary for rewriting and erasing the data. Therefore, the boosting circuit with coil and capacitor is used now. However, the boosting circuit is a trouble with energy-saving because the boosting that uses the electrical circuit has the energy loss at the switching. The boosting device by MEMS aims at highly effective conversion. The effect of boost of comb-drive actuator was confirmed by SPICE simulation that used the equivalent circuit. When the input voltage was 1.8V, the output of 14V or more was obtained.

A KICKED OSCILLATOR AS A MODEL OF A PULSED MEMS SYSTEM

In this paper, we study the behavior of a MEMS oscillator by applying methods of nonlinear dynamics. We model the system as a kicked damped oscillator and obtain the iterative maps that describe the MEMS system. The dynamics of the maps are studied numerically: we present a study of limit cycles and their rotation numbers and show how the control parameters and initial conditions may affect the output frequencies.

T1601-1-6 静電型MEMSオシレータの周波数ゆらぎに関する影響の考察(マイクロナノダイナミクスの計測と制御・マイクロナノメカトロニクス(1))

T1601-1-6 静電型MEMSオシレータの周波数ゆらぎに関する影響の考察(マイクロナノダイナミクスの計測と制御・マイクロナノメカトロニクス(1))

Limit Cycles in a MEMS Oscillator

In this paper, we apply methods of nonlinear dynamics to study the behavior of a microelectromechanical oscillator. We show how the analysis predicts the appearance of a devil's staircase-like relationship between frequencies, but also show how the output frequency of the oscillator, and hence the devil's staircase, may not be uniquely determined. Both of these features - the sequence of steps corresponding to different output frequencies and the fact that the output frequency may not be uniquely defined for a given set of parameters - have a direct bearing on the ease with which a designer can produce an useful oscillator of this form.

Monolithic CMOS MEMS Oscillator Circuit for Sensing in the Attogram Range

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This letter presents the design, fabrication, and demonstration of a CMOS/microelectromechanical system (MEMS) electrostatically self-excited resonator based on a submicrometer-scale cantilever with <formula formulatype="inline"> <tex>$\sim$</tex></formula>1 ag/Hz mass sensitivity. The mechanical resonator is the frequency-determining element of an oscillator circuit monolithically integrated and implemented in a commercial 0.35-<formula formulatype="inline"> <tex>$\mu$</tex></formula>m CMOS process. The oscillator is based on a Pierce topology adapted for the MEMS resonator that presents a mechanical resonance frequency of <formula formulatype="inline"><tex>$\sim$</tex></formula>6 MHz, a relative low quality factor of 100, and a large motional resistance of <formula formulatype="inline"><tex>$\sim$</tex> </formula>25 M<formula formulatype="inline"><tex>$\Omega$</tex></formula>. The MEMS oscillator has a frequency stability of <formula formulatype="inline"><tex>$\sim$</tex></formula>1.6 Hz resulting in a mass resolution of <formula formulatype="inline"><tex>$\sim$</tex></formula>1 ag (1 ag <formula formulatype="inline"><tex>$= \hbox{10}^{ - 18}$</tex></formula> g) in air conditions. </para>

Fabrication and characterization of a force coupled sensor–actuator system for adjustable resonant low frequency vibration detection

Micromechanical resonators for vibration sensing are typically limited to frequencies above 1kHz [D. Scheibner, J. Mehner, D. Reuter, T. Gessner, W. Dötzel, A spectral vibration detection system based on tunable micromechanical resonators, Sens. Actuators A 123–124 (2005), 63–72]. A novel method for resonant vibration detection at lower frequencies is introduced in the literature [R. Forke, D. Scheibner, J. Mehner, T. Gessner, W. Dötzel, Electrostatic force coupling of MEMS oscillators for spectral vibration measurements, Sens. Actuators A: Phys. (2007), doi:10.1016/j.sna.2007.04.004]. The micro-electro-mechanical-system (MEMS) operates at standard pressure and utilizes the superheterodyne principle well known from information technologies. By mixing the low frequency vibration with a high frequency carrier, the information of the vibration is transformed into a higher frequency range. A resonant oscillator amplifies and filters the information. This paper reports on the characterization and the silicon technology of the force coupled oscillator system (FCOS).

Squeeze-film damping in the free molecular regime: model validation and measurement on a MEMS

Squeeze-film damping (SFD) is important in MEMS oscillators because it determines the quality factor of the oscillators. Published models for predicting SFD gave widely different results in the free-molecule regime, where the distance traveled by gas molecules between collisions in free space is much larger than the thickness of the squeezed gas film. The work presented here provides new experimental data for validating SFD models in that regime. The case studied here is where a rigid plate oscillates vertically while staying parallel to the substrate. The test device was an almost rectangular microplate supported by beam springs. The structure was excited by shaking the base. The velocities of numerous points on the plate and of the substrate were measured with a laser Doppler vibrometer and a microscope. An experimental modal analysis curve-fit the multiple frequency response functions to give the damping ratios. The test structure was contained in a vacuum chamber with air pressures controlled to provide a five-order-of-magnitude range of Knudsen numbers. The damping ratios from the measurements are compared with predictions from various published models. The measured damping ratios are close to predictions from models that are based on the Reynolds equation and take into account the inertia of the gas.

Nonlinear behavior of SOI free-free micromechanical beam resonator

Measured nonlinear behavior of a capacitively driven free-free micromechanical beam resonator at different driving conditions is presented. The resonator, fabricated in SOIMUMPs process, has a measured resonant frequency of 654 kHz with an average quality factor, Q value of 12,000 operating at a pressure of 37.5 μTorr. The overall nonlinearity (including mechanical and electrical) in the resonator was found to be triggered after critical ac drive voltage amplitude of about 120 mVpp was exceeded. The observed nonlinearity was relatively independent of the proof-mass dc voltage, V P, as long as the critical ac drive voltage is not exceeded. Furthermore, partial compensation of spring hardening effect (arising from mechanical nonlinearity) with spring softening effect (from capacitive force used to actuate the resonator) is observed in this work. This feature is particularly useful for MEMS oscillator applications where frequency tuning can be done by varying V P without inducing nonlinearity in the resonator.

Electrostatic force coupling of MEMS oscillators for spectral vibration measurements

Within this paper we present a new microsystem for frequency selective vibration monitoring in the frequency range below 1 kHz. The novel sensor is based on two force coupled oscillators, operating at standard pressure, which transform the low frequency vibration signal into a high frequency oscillation of a mechanical resonator. The resonator filters the desired spectral line by means of resonance amplification in a very small band. For the transformation we made use of the superheterodyne principle, known from communications engineering.

Linear and Nonlinear Tuning of Parametrically Excited MEMS Oscillators

Microelectromechanical oscillators utilizing noninterdigitated combdrive actuators have the ability to be parametrically excited, which leads to distinct advantages over harmonically driven oscillators. Theory predicts that this type of actuator, when dc voltage is applied, can also be used for tuning the effective linear and nonlinear stiffnesses of an oscillator. For instance, the parametric instability region can be rotated by using a previously developed linear tuning scheme. This can be accomplished by implementing two sets of noninterdigitated combdrives, choosing the correct geometry and alignment for each, and applying ac excitation voltages to one set and proportional dc tuning voltages to the other set. Such an oscillator can also be tuned to display a desired nonlinear behavior: softening, hardening, or mixed nonlinearity. Nonlinear tuning is attained by carefully designing combdrive geometry, flexure geometry, and applying the correct dc voltages to the second set of actuators. Here, two oscillators have been designed, fabricated, and tested to prove these tuning concepts experimentally

Thermomechanical transitions in doubly-clamped micro-oscillators

The small size and low damping of MEMS oscillators give rise to phenomena that are not observed routinely at the macroscopic scale. In this work we document and explain an experimentally observed transition in the response of a doubly clamped micromechanical oscillator with pretension. The transition from softening to hardening is repeatedly observed upon increasing the power of an incident sensing laser beam, a procedure routinely used to improve signal strength during optical detection of resonant motion of microstructures. At intermediate laser power, a novel resonant response that displays characteristics of both softening and hardening in the same sweep, is observed experimentally. Increased laser heating of a structure in tension may be expected to increase softening behavior. Using tools from non-linear dynamics and continuum mechanics, we show that the observed counter-intuitive behavior can be explained by a competition between the opposing responses of linear and non-linear stiffnesses to a change in temperature.

RF MEMS Oscillator with Integrated Resistive Transduction

A method to integrate micromechanical frequency-determining elements along with the corresponding electromechanical transducers into a poly or single-crystal silicon film layer is demonstrated. A resistor dissipating several microwatt of power induces high-frequency resonant mechanical motion in a shallow-shell membrane. Transduction from the mechanical to the electrical domain is performed using implanted piezoresistors, which are sensitive to strain produced by resonant motion. Self-sustained oscillations at 10 MHz are demonstrated when the device is directly coupled to a high-impedance operational amplifier and a positive feedback loop. Finally, this letter discuss how the resonator and transducers may be incorporated into standard integrated-circuit technology

Dynamic Pull-In of Parallel-Plate and Torsional Electrostatic MEMS Actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided

Intrinsically biased, resonant NEMS–MEMS oscillator and the second law of thermodynamics

An experimentally testable NEMS–MEMS resonant cantilever oscillator is examined theoretically for compliance with the second law of thermodynamics. The device consists of a p–n semiconductor parallel-plate capacitor, with one plate fixed (p-doped) and the other (n-doped) mounted on a flexible double cantilever spring. The built-in potential across the n–p depletion region is expressed as an electric field between the capacitor plates, providing negative pressure capable of closing the plates. For matched electrical and mechanical time constants ( τ e ≃ τ m ), the device is predicted to execute steady-state electromechanical oscillation, powered solely by the p–n diodic electric field, thereby challenging the Kelvin–Planck formulation of the second law. Prospects for laboratory tests are discussed.

Tunable Microelectromechanical Filters that Exploit Parametric Resonance

Abstract Background: This paper describes an analytical study of a bandpass filter that is based on the dynamic response of electrostatically-driven MEMS oscillators. Method of Approach: Unlike most mechanical and electrical filters that rely on direct linear resonance for filtering, the MEM filter presented in this work employs parametric resonance. Results: While the use of parametric resonance improves some filtering characteristics, the introduction of parametric instabilities into the system does present some complications with regard to filtering. Conclusions: The aforementioned complications can be largely overcome by implementing a pair of MEM oscillators with tuning schemes and some processing logic to produce a highly effective bandpass filter.

A theory for thermoelastic damping in MEMS and NEMS flexural oscillators

Intrinsic damping is a major roadblock in the drive to smaller high frequency RF oscillators, from the current mm size to MEMS and ultimately NEMS. Recent measurements on silicon MEMS platelike oscillators show that thermoelastic (TE) damping is the limiting damping mechanism. This talk will describe how the classical theory of Zener for TE damping needs to be revised for small thickness NEMS oscillators. A critical plate thickness is identified, separating thermally thick and thin regimes. In thermally thick oscillators the thermal diffusion is across the thickness, whereas in-plane thermal diffusion can dominate in thermally thin plates. Using the Kirchhoff assumption for the elastic deformation, it is shown that the local thermal relaxation loss depends upon the local state of vibrating flexure, specifically, the principal curvatures at a given point on the plate. The thermal loss is zero at points where the principal curvatures are equal and opposite, i.e., saddle shaped deformation. Effective plate equations are derived that incorporate TE loss as a damping term. A new form of the effective damping is obtained for both thermally thick and thin plates, generalizing the single relaxation Zener model. Applications to MEMS and NEMS oscillators will be discussed.