Parallel plate actuator

Motion is generated by electrostatic attraction force between electrically charged surfaces. Examples of electrostatic MEMS actuators are in-plane comb drives (Fig. la) and out-of-plane parallel plate actuators (Fig. lb) [4]. Both types of actuators require large driving voltages... 

Electrostatic actuators are commonly used in MEMS devices because they scale well in the micro domain, use very little power, and are straightforward to fabricate in a number of different processes. Two common forms are parallel plate actuators and comb-drive actuators. The parallel plate actuator is a parallel plate capacitor with one of the plates released so that it is able to move, as shown in Figure 3.1. The relationship between the capacitance C, voltage V, and charge Q for a parallel plate capacitor is given by... 

Since the plate area /I scales as the second power of its dimensions and the gap scales as one of the second powers of its dimensions, the electrostatic force in a parallel plate actuator does not scale down with decreasing dimension. For a gap of 1 pm and a voltage of 10 V, the electrostatic force would be 0.44 nN for each square micron of capacitor plate area. 

In contrast to the parallel plate actuator, the comb-drive actuator varies capacitance through a change in the overlap area between a set of interpenetrating comb fingers, as shown in Figure 3.2 [1]. 

As an example, we consider a parallel plate actuator that is fabricated in the Poly MUMPS process using the first released polysilicon layer. Poly 1, as the structural layer and the first oxide. Oxide 1, as the sacrificial layer. We consider two configurations for the springs an X-beam configuration, as shown in Figure 3.5, and a Z-beam configuration, as shown in Figure 3.6. 

Figure 3.5 X-beam parallel plate actuator fabricated in the PolyMUMPS process.

Explain in words why a parallel plate actuator such as the one shown in Figure 3.3 exhibits a pull-in instability. 

You may also assume that each of these structures can be approximated as an ideal parallel plate actuator, and that there is a uniform electrostatic load on each of them, as shown in Figure 3.10. You can also ignore the length of the beam taken up by the anchors in your calculations, and any fringing effects of the fields. The displacements would then be given by Cantilever beam ... 

If we would like to eliminate pull-in completely, what capacitance value (measured in terms of the capacitance value of the parallel plate actuator) should we use ... 

Find the size of the gap z at pull-in relative to the initial gap 0 for an electrostatic parallel plate actuator with a nonlinear spring that follows Snook s Law ... 

Since the mirror is supported by two torsion rods, the total mechanical restoring torque x would be x = 2x. The tilt angle 0q as a function of voltage can be found from equating the electrostatic torque to the total mechanical restoring torque x. The pull-in voltage can be found from setting the torques and the slopes of the torques equal, as was done for the parallel plate actuator ... 

Since, in most cases, the nominal overlap Xo is much larger than the displacement x, parallel-plate interfaces have considerably larger sensitivity. Lateral combs are most often used for actuation where large range is required or in electromechanical oscillators, where the position-dependence of the negative spring of parallel-plate interfaces introduces nonlinearity [13]. Parallel-plate structures are usually preferred for maximum displacement resolution. 

Electrowetting-on-dielectric (EWD) microfluidics is based on the actuation of droplet volumes up to several microliters using the principle of modulating the interfacial tension between a liquid and an electrode coated with a dielectric layer [1]. An electric field established in the dielectric layer creates an imbalance of interfacial tension if the electric field is applied to only one portion of the droplet, which forces the droplet to move [2]. Droplets are usually sandwiched between two parallel plates - the bottom... 

The actuation of DEs can be approximated as the lateral electrostatic compression and planar expansion of an incompressible Unearly elastic material where the electrical component is treated as a parallel plate capacitor [141], The incompressibility constraint can be expressed as ... 

To analyze the fundamentals of a droplet motion actuated by ctMitmuous electrowetting principles, for illustration, one may consider two infinite parallel plates separated by a distance H, with an intervening liquid. For a steady, fully developed incompressible flow along the x-direction, the Navier-Stokes equation assumes the following simplified form ... 

Fig. 2 Schematic illustration of the principal types of membrane actuations in micropump, (a) Thin-film piezoelectric actuation, (b) stack piezoelectric actuator, (c) parallel plate electrodes for electrostatic actuation, (d) thermopneumatic actuation using thermal expansion of a secondary working fluid...

Two basic actuator types Out of Plane(parallel plate)... 

Microactuators, Fig. 1 Diagrams of (a) in-plane electrostatic comb-drive actuator and actuation force and (b) out-ofplane parallel plate electrostatic actuator... 

Chen NC et al (2014) Single-cell trapping and impedance measurement utilizing dielectrophoresis in a parallel-plate microfluidic device. Sens Actuator B 190 570-577... 

Fig. 2 (a) Reference left) and current right) configurations of a planar soft dielectric actuator. Symbol w represents the current charge density (b) parallel-plate capacitor in vacuum... 

Figure 3.3 Parallel plate electrostatic actuator with a mechanical spring that provides a restoring force F in opposition to the attractive electrostatic force The initial gap is go-...

When one-third of the initial gap has been closed, the plates snap together or pull in. This pull-in instability limits the useful range of parallel plate electrostatic actuators with linear springs. For parallel plate electrostatic actuators formed in surface micromachining processes, the initial gap is defined by the sacrificial layer thickness, which is practically limited to a few microns, so that the useful actuation range is typically less than a micron. To find the pull-in voltage, the gap at pull-in, go/3, can be substituted into equation (3.22) and solved for the voltage ... 

Figure 3.12 Parallel plate electrostatic actuator with a feedback capacitor.

A parallel plate electrostatic actuator with a variable capacitance Cl is in series with a fixed feedback capacitance C2, as shown in Figure 3.12 [7]. 

J.I. Seeger and B.E. Boser, Charge control of parallel-plate, electrostatic actuators and the tip-in instability, J. Microelectromechanical Systems... 

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