Numerical Path Following as an Analysis Method for Electrostatic MEMS

Stulemeijer, J.; Bielen, J.A.; Steeneken, Peter G.; Berg, Jan Bouwe van den

doi:10.1109/jmems.2008.2011111

Cited by 12 publications

(13 citation statements)

References 19 publications

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“…The results correspond well to the analytical results in [5]. More details and examples of FEM numerical path following can be found in [10]. Although this example is still relatively simple, the FEM path following method can theoretically be applied to analyze any non-linear system of which the Hamiltonian H can be written in terms of the analytic volume integrals (1-10).…”

Section: Finite Element Methods Path Following Simulationssupporting

confidence: 72%

“…Recently it has been shown that path following techniques can be very useful for the analysis of electrostatic MEMS devices with non-linear contact forces [10]. The technique can in fact be applied to almost any non-linear electromechanical system described by equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10). In MEMS and NEMS devices, the system is usually controlled by a single external parameter F , which can for example be the voltage or current from an external source for electromechanical actuators, but can also be an acceleration or gas pressure force in sensor systems.…”

Section: Path Following and Numerical Continuation Methodsmentioning

confidence: 99%

“…At an equilibrium point at coordinate (x eq , Q eq ,V ext,eq ) equations (25) and (26) provide the tangent vector to the solution curve ( dx dQ dQ, dQ, dV ext,eq dQ dQ). In figure 3 1 The method presented here is slightly different from the method which we presented in [10]. In [10] the electrical generalized force equation V ext = Q/C was eliminated before taking the Jacobian of the force vector.…”

Section: Example Of Path Following Methodsmentioning

confidence: 99%

“…Interactions between the electric and magnetic fields can usually be neglected in MEMS and NEMS devices, because the system dimensions are small compared to the electromagnetic wavelength and are large enough to neglect quantum effects. In these approximations the total internal energy of the system U tot = ∑U and total work done by external sources W tot = ∑W can be expressed as a sum over different types of energy and work, given by equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10):…”

Section: Energy and Work In Electromechanical Systemsmentioning

confidence: 99%

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Path Following and Numerical Continuation Methods for Non-Linear MEMS and NEMS

Steeneken

Stulemeijer²

2010

NATO Science for Peace and Security Series B: Physics and Biophysics

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Non-linearities play an important role in micro-and nano-electromechanical system (MEMS and NEMS) design. In common electrostatic and magnetic actuators, the forces and voltages can depend in a non-linear way on position, charge, current and magnetic flux. Mechanical spring structures can cause additional nonlinearities via material, geometrical and contact effects. For the design and operation of non-linear MEMS devices it is essential to be able to model and simulate such non-linearities. However, when there are many degrees of freedom, it becomes difficult to find all equilibrium solutions of the non-linear equations and to determine their stability. In these cases path following methods can be a powerful mathematical tool. In this paper we will show how path following methods can be used to determine the equilibria and stability of electromechanical devices. Based on the energy, work and the Hamiltonian of electromechanical systems (section 1), the equations of motion (section 2), the equilibrium (section 3) and stability conditions (section 6) are derived. Examples of path following simulations (section 4) in Mathematica (section 5), MATCONT (section 7) and using FEM methods in COMSOL (section 8) are given to illustrate the methods.

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Section: Finite Element Methods Path Following Simulationssupporting

confidence: 72%

Section: Path Following and Numerical Continuation Methodsmentioning

confidence: 99%

Section: Example Of Path Following Methodsmentioning

confidence: 99%

Section: Energy and Work In Electromechanical Systemsmentioning

confidence: 99%

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Path Following and Numerical Continuation Methods for Non-Linear MEMS and NEMS

Steeneken

Stulemeijer²

2010

NATO Science for Peace and Security Series B: Physics and Biophysics

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“…amplitude is observed during the retraction of the piezo and the orbit having the lower oscillation amplitude is observed during the approaching of the piezo. This phenomenon is called "hysteresis" and it is also observed in many other MEMS applications [125].…”

Section: Hysteresismentioning

confidence: 90%

High performance nano-scale measurements by advanced atomic force estimation

Ci¹

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Atomic force microscopy (AFM) was invented by G. Binnig and his collaborators in 1986 after the invention of scanning tunnelling microscopy (STM) in the early 1980s. The AFM system deploys a tiny probe to interact with the sample such that topography information of the sample can be obtained. The resolutions of the AFM topography images are in the nanometer scale and they are limited only by the probe diameters. Besides, in AFM imaging, there is no requirement on sample preparation and conductivity. Thus, the AFM provides an easy platform to observe, measure and manipulate atomic interactions. Since its invention, AFM has become an indispensable tool in the research areas of material sciences and biological sciences. The AFM is also widely used in many industry applications in microelectronics and data storage. Although many research areas and industry applications have benefited from the success of AFM, there is still an urgent need to improve the measurement resolution and accuracy of the AFM in order to further exploit the atomic characteristics at the scales of atoms or even smaller. In addition, AFM has been modified as a Casimir oscillator to study quantum fluctuations where highly accurate and precise measurement is also desired. Driven by this motivation, this thesis will focus on the improvement of accuracy ix and resolution of the AFM and its modified system, the Casimir oscillator. Our approach to accuracy and resolution enhancement of the AFM system is by tackling the measurement errors that arise from its components such as the position sensitive detector (PSD) and the sensing principle in the AFM sensing system. In our work, we have proposed a new concept of linearity indices to quantitatively measure the measurement inaccuracies of various PSDs. Based on these linearity indices, new design formulae are proposed for 2-D tetra-lateral PSD and quadrant detector. Their measurement accuracy are significantly improved via our new formulae as well as robustness to the incident beam size and parameter variation. Besides the AFM sensing system, inaccuracies also come from the probe-sample separation estimation. To address this issue, a novel estimation algorithm has been proposed and accurate estimates can be obtained regardless of different nonlinear dynamics. Several methods have also been derived to improve the separation gap estimation in Casimir oscillator which is a modified AFM system. x

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An analysis of electrostatically actuated micro vibrating structures incorporating squeezed film damping effect using an electrical equivalent circuit

Kavitha

Madhan

2016

J Braz. Soc. Mech. Sci. Eng.

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This paper investigates the response of microcantilever and microbridge actuators, under alternating current (AC) and direct current (DC) excitations. The analysis is carried out by simulating the electrical equivalent circuit of the actuators. An analogous circuit model for evaluation of velocity and acceleration in the microstructure is incorporated to the basic circuit model. The influence of squeeze film on the vibrating structure is also investigated. The effect of DC bias voltage on displacement, capacitance and electrostatic force are investigated. The transient response predicts a minimal change due to the pressure variation in the damping medium owing to the geometrical dimensions of the elements in the actuator. The frequency dependence of velocity and acceleration are also evaluated in this study.

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Numerical Path Following as an Analysis Method for Electrostatic MEMS

Cited by 12 publications

References 19 publications

Path Following and Numerical Continuation Methods for Non-Linear MEMS and NEMS

Path Following and Numerical Continuation Methods for Non-Linear MEMS and NEMS

High performance nano-scale measurements by advanced atomic force estimation

An analysis of electrostatically actuated micro vibrating structures incorporating squeezed film damping effect using an electrical equivalent circuit

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