Nonconductive polymer microresonators actuated by the Kelvin polarization force

Schmid, Silvan; Wendlandt, Michael; Junker, David; Hierold, Christofer

doi:10.1063/1.2362590

Cited by 43 publications

(41 citation statements)

References 12 publications

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“…4.6 Examples of applications of dielectric polarization forces for transduction of (a) a micromechanical polymeric resonators (Reprinted from [20], with the permission from AIP Publishing), and (b) a silicon nitride membrane resonator (schematic drawing) (Reprinted from [12], with permission from AIP Publishing. )…”

Section: Normal Force Between a Coplanar Electrode Pair And A Floatinmentioning

confidence: 99%

Transduction

Schmid¹,

Villanueva²,

Roukes³

2016

Fundamentals of Nanomechanical Resonators

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The efficient transduction of nanomechanical resonators is quintessential for any practical application. In the context of this book, transduction refers to the translation of mechanical motion to an electrical signal and vice versa for detection and actuation, respectively. In this chapter the most common underlying physical transducing mechanisms are quickly introduced. Most of these mechanisms are of an electrical nature, such as electrodynamic, electrostatic, thermoelastic, piezoresistive, or piezoelectric transduction. Nanomechanical resonators transduced with one of these techniques are therefore known as nanoelectromechanical systems (NEMS). But it is also common practice to transduce nanomechanical resonators by optic means. The full optic transduction and control of nanomechanical resonators is, e.g., employed in the field of cavity optomechanics.

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Section: Normal Force Between a Coplanar Electrode Pair And A Floatinmentioning

confidence: 99%

Transduction

Schmid¹,

Villanueva²,

Roukes³

2016

Fundamentals of Nanomechanical Resonators

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“…This force is called Kelvin polarization force or dielectric force. Based on this actuation scheme, dielectric microresonators made from polymeric materials have been successfully actuated in vacuum 22 and in air and water. 23 Lately, the dielectric force has also been applied in nanomechanical systems actuating silicon nitride strings.…”

Section: Introductionmentioning

confidence: 99%

“…An analytical model for the dielectric slab moving parallel in between the electrodes of a parallel plate capacitor has been derived and tested by means of the finite element method ͑FEM͒. 22 In this work, the force acting on a dielectric that is placed over two coplanar electrodes ͑Fig. 1͒ is modeled.…”

Section: Introductionmentioning

confidence: 99%

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Modeling the Kelvin polarization force actuation of micro- and nanomechanical systems

Schmid

Hierold

Boisen

2010

Journal of Applied Physics

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Polarization forces have become of high interest in micro-and nanomechanical systems. In this paper, an analytical model for a transduction scheme based on the Kelvin polarization force is presented. A dielectric beam is actuated by placing it over the gap of two coplanar electrodes. Finite element method simulations are used to characterize the scheme and to evaluate a field correction factor, which results from simplifying the form of the electric field. The model has been shown to be valid for dielectrics with different permittivities. The presented model facilitates the design of microresonators and nanoresonators with dielectric actuation, which offers a great freedom in the choice of structural material.

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“…In addition, a microwave bypass capacitor is used in the ground connection of one electrode which allows application of additional DC bias and RF voltages to the electrodes. This is used to actuate the mechanical resonator via the dielectric driving mechanism [14,27]. At the same time, the dielectric coupling provides a way to tune the resonance frequency of the two mechanical modes: The static electric field between the electrodes polarizes the dielectric resonator material which is then attracted to high electric fields, thereby changing the spring constant of the modes via the resulting force gradient [14].…”

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Nonadiabatic Dynamics of Two Strongly Coupled Nanomechanical Resonator Modes

et al. 2012

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The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here we present a classical mechanical model system exhibiting analogous behaviour using two inversely tuneable, strongly coupled modes of the same nanomechanical beam resonator. In the adiabatic limit, the anticrossing between the two modes is observed and the coupling strength extracted. Sweeping an initialized mode across the coupling region allows mapping of the progression from diabatic to adiabatic transitions as a function of the sweep rate.PACS numbers: 85.85.+j,62.25.Fg,05.45.Xt The time dynamics of two strongly coupled harmonic oscillators follows the Landau-Zener model [1][2][3][4], which is used to describe the quantum mechanical mode tunneling in a non-adiabatic transition. This phenomenon is observed and utilized in many areas of physics, e. g. atomic resonances [5], quantum dots [6], superconducting qubits [7] and nitrogen-vacancy centers in diamond [8]. It is also possible to create classical model systems exhibiting the same time evolution, which until now have been restricted to optical configurations [9,10]. Such systems are well suited for the study of diabatic behaviour over a wide parameter space; for example nonlinearities could be readily introduced, potentially leading to chaotic behaviour [9,11].Nanomechanical resonators with frequencies in the MHz range can be realized with high mechanical quality factors [12,13] and easily tuned [14] in frequency. This makes them particularly well-suited for exploration of their coupling to other mechanical, optical or electrical microwave resonators. Strong cavity coupling in the optical or microwave regime has been widely studied as it enables both cooling and self-oscillation of the mechanical modes [15][16][17][18]. In addition, the time-resolved Rabi oscillations between a strongly coupled two-level system and a micromechanical resonator have been observed [19].Purely mechanical, static coupling between different resonators [20][21][22][23] and between different harmonic modes of the same resonator [24] has also been demonstrated. Here, we explore the coupling between the two fundamental flexural modes [25] of a single nanomechanical beam vibrating in plane and out of plane, respectively. We study the adiabatic to non-adiabatic transitions between the two strongly coupled classical mechanical modes in time-dependent experiments, in correspondence to the Landau-Zener transition.The nanomechanical high stress silicon nitride string used in this work is shown in Fig. 1. Two parallel gold electrodes vertically offset to the beam are used to dielectrically couple the beam oscillation to an external microwave cavity with a quality factor of ≈ 70 at a resonance frequency of 3.44 GHz [26]. Displacement of the out of plane • also depicts the two adjacent gold electrodes (yellow) used to dielectrically drive, tune and read out the resonator motion. The arrows denote the two mechanical modes, one oscillating parallel and ...

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Nonconductive polymer microresonators actuated by the Kelvin polarization force

Cited by 43 publications

References 12 publications

Transduction

Transduction

Modeling the Kelvin polarization force actuation of micro- and nanomechanical systems

Nonadiabatic Dynamics of Two Strongly Coupled Nanomechanical Resonator Modes

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