Numerical model for the calculation of the electrostatic force in non-parallel electrodes for MEMS applications

Ouakad, Hassen M.

doi:10.1016/j.elstat.2015.06.001

Cited by 15 publications

(10 citation statements)

References 38 publications

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“…This particular force acting on the moving electrode is a function of the actuator geometrical properties ( w e , t e , R , g , and d ) and the air permittivity ε 0 = 8.8542 × 10 −12 F/m . The electrostatic field distribution as well as the electrostatic force acting on the movable electrode of Figure A, is solution of a Laplace equation obtained from the Maxwell‐Laplace equation of electromagnetism:

\frac{\partial^{2} φ}{\partial x^{2}} + \frac{\partial^{2} φ}{\partial y^{2}} + \frac{\partial^{2} φ}{\partial z^{2}} = - \frac{ρ}{ε_{0}},

where the function φ in Equation symbolizes here the electric potential between the 2 stationary rectangular electrodes and the movable electrode (the CNT) of Figure and ρ represents electric charge density. As for the boundary conditions for the electrostatic potential used to solve the above Maxwell‐Laplace equation, Equation , mixed boundary conditions are considered: A nonhomogeneous potential φ = 1 in the neighborhood of the movable electrode (the CNT) and a homogeneous condition φ = 0 are assumed far from the nanoactuator, ie, for ( x , y , z )→∞.…”

Section: Problem Formulation: Electrical Modelmentioning

confidence: 99%

“…While numerous appropriate functions can be used in this regards, in this investigation, we consider the following expression which showed small error values and more rationality in reproducing the FEM numerical results:

F_{elec} ((), d) = \frac{c_{1} d^{c_{2}}}{1 + c_{3} d^{c_{4}}} .

…”

Section: Appropriate Fitting Function For the Electric Forcementioning

confidence: 99%

“…This particular force acting on the moving electrode is a function of the actuator geometrical properties (w e , t e , R, g, and d) and the air permittivity ε 0 = 8.8542 × 10 −12 F/m. The electrostatic field distribution as well as the electrostatic force acting on the movable electrode of Figure 4A, is solution of a Laplace equation obtained from the Maxwell-Laplace equation of electromagnetism 22 :…”

Section: Problem Formulation: Electrical Modelmentioning

confidence: 99%

“…Therefore, since the stroke is considered to be an important characteristic parameter in any design of any kind of microactuator and nanoactuator, few previous works were reported to be successful in extending the range of travel of electrostatically actuated microsystem and nanosystem. [14][15][16][17][18][19][20][21][22] These reported designs presented excellent success in amplifying the displacements of the electromechanical microdevice and nanodevice, however revealed practical limits on the amplification factor, as well as penalties on the overall actuator performance. Therefore, there is a need for smart design of nanoactuator that simultaneously provide actuation and larger strain amplification as compared with conventional mechanical amplifiers.…”

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confidence: 99%

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A numerical‐analytical methodology for acquiring the electrical force of carbon nanotube–based nanoactuator assuming an out‐of‐plane electrodes arrangement

Ouakad

2017

Int J Numerical Modelling

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In this paper, we develop a simple expression to evaluate the electric force acting on a carbon nanotube–(CNT) based nanoactuator assuming a nonparallel actuating plates (out‐of‐plane) arrangement. The actuating force is initiated by the asymmetry of the resultant electric fringing fields caused mainly due to the nonparallel electrodes arrangement. The nanoactuator is designed based on a CNT flexible electrode (nonstationary) and 2 symmetrically located actuating stationary rectangular shaped out‐of‐plane plates. The resultant electric force is mathematically approximated from the outcomes of a planar (2‐D) numerical solution of the electric problem via a finite element–based numerical analysis. The influence of the design geometrical parameters on the resultant electric force are examined. Several key design parameters were inspected: the width and thickness of the stationary actuating electrodes, the radius of the flexible electrode (the CNT), and the lateral and vertical separation distances between the movable and grounded electrodes. Through several simulations, we show the effect of the lateral and vertical offsets as well as the electrodes thickness in the optimization of the performance of the nanoactuator assuming such nonparallel plates actuating configuration. We also simulate the effect on the resultant actuating force level with the electrode thickness as well as the electrodes lateral separation distance.

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\frac{\partial^{2} φ}{\partial x^{2}} + \frac{\partial^{2} φ}{\partial y^{2}} + \frac{\partial^{2} φ}{\partial z^{2}} = - \frac{ρ}{ε_{0}},

Section: Problem Formulation: Electrical Modelmentioning

confidence: 99%

F_{elec} ((), d) = \frac{c_{1} d^{c_{2}}}{1 + c_{3} d^{c_{4}}} .

…”

Section: Appropriate Fitting Function For the Electric Forcementioning

confidence: 99%

“…This particular force acting on the moving electrode is a function of the actuator geometrical properties (w e , t e , R, g, and d) and the air permittivity ε 0 = 8.8542 × 10 −12 F/m. The electrostatic field distribution as well as the electrostatic force acting on the movable electrode of Figure 4A, is solution of a Laplace equation obtained from the Maxwell-Laplace equation of electromagnetism 22 :…”

Section: Problem Formulation: Electrical Modelmentioning

confidence: 99%

mentioning

confidence: 99%

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A numerical‐analytical methodology for acquiring the electrical force of carbon nanotube–based nanoactuator assuming an out‐of‐plane electrodes arrangement

Ouakad

2017

Int J Numerical Modelling

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“…The main reason of this collapse is the restoring force that can no longer overcome the electrostatic attractive force. This phenomenon is called as pull-in instability and to avoid it, many presented studies have used techniques such as comb-drive fingers, fringing-field based configurations [30][31][32][33] and repulsive force (out-of plane) designs [13,34].…”

Section: Model Description and Operation Principle Electrostatic Actumentioning

confidence: 99%

A MEMS Microphone Using Repulsive Force Sensors

Ozdogan

Towfighian

2016

Volume 4: 21st Design for Manufacturing and the Life Cycle Conference; 10th International Conference on Micro- And Nanosystems

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We present a MEMS microphone that converts the mechanical motion of a diaphragm, generated by acoustic waves, to an electrical output voltage by capacitive fingers. The sensitivity of a microphone is one of the most important properties of its design. The sensitivity is proportional to the applied bias voltage. However, it is limited by the pull-in voltage, which causes the parallel plates to collapse and prevents the device from functioning properly. The presented MEMS microphone is biased by repulsive force instead of attractive force to avoid pull-in instability. A unit module of the repulsive force sensor consists of a grounded moving finger directly above a grounded fixed finger placed between two horizontally seperated voltage fixed fingers. The moving finger experiences an asymmetric electrostatic field that generates repulsive force that pushes it away from the substrate. Because of the repulsive nature of the force, the applied voltage can be increased for better sensitivity without the risk of pull-in failure. To date, the repulsive force has been used to engage a MEMS actuator such as a micro-mirror, but we now apply it for a capacitive sensor. Using the repulsive force can revolutionize capacitive sensors in many applications because they will achieve better sensitivity. Our simulations show that the repulsive force allows us to improve the sensitivity by increasing the bias voltage. The applied voltage and the back volume of a standard microphone have stiffening effects that significantly reduce its sensitivity. We find that proper design of the back volume and capacitive fingers yield promising results without pull-in instability.

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Bi-stability behavior in electrostatically actuated non-contact based micro-actuator

Ouakad

Bahadur

2020

Microsyst Technol

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Numerical model for the calculation of the electrostatic force in non-parallel electrodes for MEMS applications

Cited by 15 publications

References 38 publications

A numerical‐analytical methodology for acquiring the electrical force of carbon nanotube–based nanoactuator assuming an out‐of‐plane electrodes arrangement

A numerical‐analytical methodology for acquiring the electrical force of carbon nanotube–based nanoactuator assuming an out‐of‐plane electrodes arrangement

A MEMS Microphone Using Repulsive Force Sensors

Bi-stability behavior in electrostatically actuated non-contact based micro-actuator

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