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Electro-structural analysis of a MEMS Comb Drive Actuator Application


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.

The-geometry-of- the analyzed actuator

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.

Fixed voltage applied on the upper finger

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.

Fixed voltage applied on the lower finger

Figure 3 - Fixed voltage applied on the lower finger 

 

Structural boundary condition

Fixed boundary condition 


Fixed constraint applied on the fingers
 
                                  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)


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 resultlarge blank subscript blank
 
  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) 
 

table2


Resultant Displacement plot


 The deformed geometry of the actuator

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. Excerpt from the Proceedings of the 2012 Comsol Conference in Bangalore.