Characterization of MEMS Resonator Nonlinearities Using the Ringdown Response

Polunin, Pavel M.; Yang, Yushi; Dykman, M. I.; Kenny, Thomas W.; Shaw, Steven W.

doi:10.1109/jmems.2016.2529296

Cited by 75 publications

(67 citation statements)

References 30 publications

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“…This model has been broadly used in science and engineering. Recently, there has been renewed interest in positive nonlinear friction following its observations in various passive (rather than self-oscillating) nanomicro-and optomechanical systems [4][5][6][7][8][9][10]. Furthermore, such friction has also been engineered in microwave cavities in order to create long-lived coherent quantum states [11,12].…”

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confidence: 99%

Strong negative nonlinear friction from induced two-phonon processes in vibrational systems

Dong¹,

Dykman²,

Chan³

2018

Nat Commun

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Self-sustained vibrations in systems ranging from lasers to clocks to biological systems are often associated with the coefficient of linear friction, which relates the friction force to the velocity, becoming negative. The runaway of the vibration amplitude is prevented by positive nonlinear friction that increases rapidly with the amplitude. Here we use a modulated electromechanical resonator to show that nonlinear friction can be made negative and sufficiently strong to overcome positive linear friction at large vibration amplitudes. The experiment involves applying a drive that simultaneously excites two phonons of the studied mode and a phonon of a faster decaying high-frequency mode. We study generic features of the oscillator dynamics with negative nonlinear friction. Remarkably, self-sustained vibrations of the oscillator require activation in this case. When, in addition, a resonant force is applied, a branch of large-amplitude forced vibrations can emerge, isolated from the branch of the ordinary small-amplitude response.

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confidence: 99%

Strong negative nonlinear friction from induced two-phonon processes in vibrational systems

Dong¹,

Dykman²,

Chan³

2018

Nat Commun

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“…We find excitations larger than 100 µV are enough to drive the resonator into the nonlinear regime. When the resonator is excited with an even larger force, it displays the signature of nonlinear damping [20,23,27,28].…”

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confidence: 99%

Self-Sustained Micromechanical Oscillator with Linear Feedback

et al. 2016

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Autonomous oscillators, such as clocks and lasers, produce periodic signals without any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, nonlinearity is provided by the sustaining feedback mechanism, which also supplies energy, whereas the constituent resonator that determines the output frequency stays linear. Here we propose a new self-sustaining scheme that relies on the nonlinearity originating from the resonator itself to limit the oscillation amplitude, while the feedback remains linear. We introduce a model to describe the working principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical (MEMS) based oscillator.Autonomous oscillators are systems that can spontaneously commence and maintain stable periodic signals in a self-sustained manner without external frequency references. They are abundant both in Nature and in manmade devices. In Nature made systems, the self-sustained oscillators are the fundamental piece that describes systems as diverse as neurons, cardiac tissue, and predator-prey relationships [1]. In manmade devices, self-sustained autonomous oscillators are overwhelmingly used for communications, timing, computation, and sensing [2], with examples such as quartz watches [3] and laser sources [4]. A typical oscillator consists of a resonating component and a sustaining feedback element: the constituent resonator determines the oscillation frequency, whereas the feedback system draws power from an external source to compensate the energy loss due to damping during each oscillation of the resonator [5]. In order to initiate the oscillations, the initial gain of the feedback must be larger than unity, so that energy accumulates to build up oscillation amplitude [6]. However, to avoid ever increasing oscillations, some limiting mechanism must act to ensure that, eventually, the vibrational amplitude no longer grows.In the conventional designs of oscillators, the resonating element is operated in the linear regime, where its resonant frequency is independent of the excitation levels, and the necessary amplitude limiting mechanism is enacted in the feedback loop by introducing a nonlinear element (Fig. 1a). However, maintaining the resonating element in the linear regime has been challenging for a variety of applications requiring self-sustained oscillators made from micro-/nanoelectromechanical (M/NEMS) resonators [7][8][9], mostly because these resonators exhibit significantly reduced linear dynamic range. To limit the amplitude, common mechanisms include impulsive energy replenishment [5], saturated gain medium [4,10] or amplifiers [11,12], automatic level control [13,14], phase locked loops [15,16], nonlinear signal transduction [17], and dedicated nonlinear components [18]. These mechanisms to incorporate nonlinear elements into the electronic feedback circuitry introduce tec...

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“…Apart from the coupling Table 2) can be directly measured using standard MEMS characterization tests. The Duffing coefficient β 0 is obtained by performing closed-loop measurements of a single device below the critical point and tracking the frequency shift as the amplitude of the actuation force is increased [21], [24]. Once the frequency and Duffing parameter of the drive mode in addition to the quality factors and frequencies of the parasitic modes are measured for the single chip the three-wave coupling α can be deduced from the measurement of the critical point and equation (5) [1].…”

Section: Measurementsmentioning

confidence: 99%

Validating the Critical Point of Spontaneous Parametric Downconversion for Over 600 Scanning MEMS Micromirrors on Wafer Level

et al. 2020

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Sensors and actuators based on resonant micro-electro-mechanical systems (MEMS), such as scanning micro mirrors, are well-established in automotive and consumer products. As the areas of application broaden towards highlyautomated driving and augmented reality, the performance requirements for the MEMS are also increasing. Devices outside of the performance specifications have to be rejected which is costly due to the high processing times of MEMS technologies. In particular, nonlinear system behavior is often found to cause unexpected device failure or performance issues. Thus, accurate simulation or rather system models which account for nonlinear sensor dynamics can not only increase process yield, but more importantly, lead to a comprehensive understanding of the underlying physics and consequently to improved MEMS design. In a recent work [1], we have studied the possibility of a rather drastic device failure induced by nonlinearities on the example of a resonant scanning MEMS micro mirror. On the level of a few selected chips, we have carefully measured the complex nonlinear system behavior and modelled it by a nonlinear mode-coupling phenomenon known as spontaneous parametric down-conversion (SPDC). The most intriguing feature of SPDC is the sudden change from a rather linear to a highly nonlinear system behavior at the threshold or rather critical oscillation amplitude of the mirror. However, the threshold only lies within the range of the mirror's operational amplitude, if certain frequency resonance conditions regarding the modes of the mechanical structure are met. As a direct consequence, the critical amplitude strongly depends on the frequency spectrum of the MEMS design which in turn is largely influenced by fabrication imperfections. In this work, we validate the dependence of the critical amplitude on the resonance condition by measuring it for over 600 micro mirrors on wafer-level. Our work does not only validate the theory of SPDC with measurements on such a large scale, but also demonstrates modeling strategies which are essential for MEMS product design.

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Characterization of MEMS Resonator Nonlinearities Using the Ringdown Response

Cited by 75 publications

References 30 publications

Strong negative nonlinear friction from induced two-phonon processes in vibrational systems

Strong negative nonlinear friction from induced two-phonon processes in vibrational systems

Self-Sustained Micromechanical Oscillator with Linear Feedback

Validating the Critical Point of Spontaneous Parametric Downconversion for Over 600 Scanning MEMS Micromirrors on Wafer Level

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