Electro-structural analysis of a MEMS Comb Drive Actuator

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Introduction

Electrostatic comb-drive actuators feature easy design, fabrication and implementation. They are used in for different applications, such as optical communication, biomedical engineering, wireless communication and nanotechnology. Increase in traveling distance and force output are two major concerns in developing comb-drive actuators.

The actuator consists of two interdigitated structures; one is fixed and the other is connected to a compliant suspension.The moving part consists of four fingers, whereas the fixed one is formed by five fingers.
The driving voltage between the comb structures causes the displacement of the movable fingers towards the fixed fingers by an attractive electrostatic force.

EMS electro-structural module aims at finding the resultant deflection of the moving finger under an applied dc voltage.
In our analysis, we are not accounting for forces other than the electric force; gravity acceleration is ignored.

The model geometry

Figure 1 presents the geometry of the analyzed model. The thickness of the device is equal to 2um, along z axis.
All the units are given in micrometer.

Figure 1 - The geometry of the analyzed actuator

Materials properties

Table1 given below summarizes material properties required for the simulation.

Material Name	Relative permittivity	Electrical conductivity (Mho/m)	Elastic modulus (N/m2)	Poisson’s Ratio
PolySilicon	4.5	Not required	160e+09	0.22
Air	1	0	Not required	Not required

Table1 - Properties of materials assigned to the model

Boundary conditions

Electrical boundary condition

Fixed voltage 1(0V)

The finger colored in blue is grounded, as shown in figure 2. The arrows show the symbols of the boundary condition given to it.

Figure 2 - Fixed voltage applied on the upper finger

Fixed voltage 2 (30V)

The movable part of the actuator is assigned a positive voltage. Figure 3 shows the where the voltage is applied.

Figure 3 - Fixed voltage applied on the lower finger

Structural boundary condition

Fixed boundary condition

Figure 4 - Fixed constraint applied on the fingers

Meshing

The model geometry doesn’t contain very complicated shapes. A mesh control to refine the lower finger would be sufficient to get accurate electrical and structural results.
As given in figure 4, the mesh is quite fine in the movable part compared to the other parts. The beam connecting the lower finger to its anchor does not need a fine mesh.

The upper finger (the body colored in blue in figure 5) is coarsely meshed as it will not experience any deflection.

The meshed model

Figure 5 - The meshed model

Simulation Results

Once the simulation is done, EMS creates a table giving the resultant electric rigid body force acting on the model parts. In our case, we are interested in finding the electric force acting on the lower finger (the movable part of the actuator).
Figure 6 shows the components of the electric force vector acting on the plate. The force is given in Newtons.

Electric force (Results table)

The Analytical formula

F e l equals 1 half fraction numerator partial differential c over denominator partial differential y end fraction space V squared space equals fraction numerator n epsilon subscript 0 space t over denominator g end fraction V squared

C: the capacitance of the actuator
V: the voltage applied to the moving finger
n: the number of moving fingers
t: The thickness of the actuator
g: the gap between the upper and lower fingers

epsilon subscript 0

: absolute electrical permittivity

Correlation between EMS and the reference result

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	EMS Result	Simulation Result
Resultant Displacement under 30V (in meters)	4.16e-08	5e-08

Table 2. Comparison between EMS and the reference results

Reaction force (Spring restoring force)

Resultant Displacement plot

Figure 6 - The deformed geometry of the actuator

Conclusion

Electro-structural analysis of a comb drive actuator is done inside EMS. EMS results have shown to be in good agreement with numerical (given in [1]) and analytical results.

References

[1]: S. Gupta, T Pahwa, R Narwal, B.Prasad and D. Kumar. Optimizing the Performance of MEMS Electrostatic Comb Drive actuator with different Flexure Springs.