Tunable MEMS Capacitor

In an electrostatically tunable parallel plate capacitor you can modify the distance between the two plates when the applied voltage changes. For tuning of the distance between the plates the capacitor includes a spring that attaches to one of the plates. If you know the characteristics of the spring and the voltage between the plates, you can compute the distance between the plates. This application shows an electrostatic simulation for a given distance. A postprocessing step then computes the capacitance.

The capacitor in this example is a typical component in various microelectromechanical systems (MEMS) for electromagnetic fields in the radio frequency range 300 MHz to 300 GHz.

Figure 1: The tunable MEMS capacitor consists of two metal plates. The distance between the plates is tuned via a spring connected to one of the plates.

Model Definition

To solve the problem, use the 3D interface in the AC/DC Module. The capacitance is available directly as a variable for postprocessing.

The electric scalar potential, V, satisfies Poisson’s equation,

where ε0 is the permittivity of free space, εr is the relative permittivity, and ρ is the space charge density. The electric field and the displacement are obtained from the gradient of V:

The capacitor plates and bars are assumed to be conductive and therefore have a uniform electric potential under electrostatic conditions.

In the interface, this phenomenon can be modeled by applying a condition to the external boundaries of the conductive regions. The boundaries will then behave like an equipotential. As the potential inside the conductors will have a uniform, predefined value, the model will only have to solve for the Infinite void surrounding the conductors.

Results and Discussion

Figure 2 shows the computed electric potential distribution near the capacitor plates. The potential on each capacitor plate is constant, as dictated by the applied conditions.

Figure 2: The electric potential distribution near the capacitor plates.

The capacitance, C, obtained from the simulation is approximately 0.1 pF.

ACDC_Module/Capacitive_Devices/capacitor_tunable

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

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In the tree, select .

Click .

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In the tree, select .

Click

Geometry 1

Insert the geometry sequence from the capacitor_tunable_geom_sequence.mph file.

In the toolbar, click

Browse to the model’s Application Libraries folder and double-click the file capacitor_tunable_geom_sequence.mph.

In the toolbar, click

Click the

button in the toolbar.

Definitions

Ground Plane

In the toolbar, click

In the window for , type Ground Plane in the text field.

Select Domain 2 only.

Locate the section. From the list, choose .

Terminal

In the toolbar, click

In the window for , type Terminal in the text field.

Select Domain 1 only.

Locate the section. From the list, choose .

Materials

Dielectric

In the window, under right-click and choose .

In the window for , type Dielectric in the text field.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	4.2	1	Basic

Electrostatics, Boundary Elements (esbe)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Ground 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Terminal 1

The condition allows for feeding the system more easily. It automatically computes the systems lumped parameters. In this model the capacitance is determined.

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