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Modeling-Simulation and Analysis of MEMS microsensing membrane

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Introduction

Electrostatic actuation, commonly used in MEMS, is based on the electrostatic fields and the forces they generate on the structures.
The deformation of electrodes, caused by the electrostatic forces, is the main concern in electromechanical actuators such as RF micro-switches, comb-drives and Pressure sensors.

In fact, an electric field is created between two electrodes by applying a potential difference which generates electrostatic forces that will be main cause of deflection.

This technology has been used in many industries, such as automotive and bio-medical, due to its light weight, compact size, low-power consumption, and durability.

EMS Simulation software from EMWorks [1]; has been used to study a resultant deflection of a membrane under an applied dc voltage; the Electrostatic analysis type with coupling to structural has been used to achieve such goal.
In the carried out analysis, the electric force has been considered and the gravity acceleration has been ignored.

The Model Geometry

Figure 1 and figure 2 show the geometry of the analyzed model. It consist of two 40 mu m au carré square membranes, one is fixed at the bottom and a movable one at the top, controlled with two serpentine springs.
The thickness of the device is equal to 1 mu m au carré, along z axis.

The geometry of the analyzed model

Figure 1 - The geometry of the analyzed model

The geometry of the serpentine spring

Figure 2 - The geometry of the serpentine spring

All the units are given in micrometer.

Simulation Setup

The Electrostatic module of EMS, coupled to structural analysis, has been used to compute and visualize the electric results and the mechanical deformation of the moving membrane. 

To perform an analysis using EMS, the following important steps have been performed:

  1. Select an appropriate material for all solid bodies.
  2. Define the necessary electromagnetic inputs.
  3. Apply the structural boundary conditions.
  4. Mesh the entire model and run the solver. 

Materials Properties

Table 1 given below summarizes the required material properties for the simulation.

  Table 1 - Properties of materials assigned to the model

Material Name Relative permittivity Density (kg/m au cube) Elastic Modulus (Pa) Poissons Ratio
Platinum 1 2145 170e+09 0.26
Air 1 0 Not required Not required

Boundary conditions

Electrical boundary condition

1. Fixed voltage 1(0V)

The top membrane is grounded, as shown in figure 3. The arrows show the symbols of the boundary condition given to it.

Fixed voltage applied to the top membrane

Figure 3 - Fixed voltage applied to the top membrane

2. Fixed voltage 2 ( positive voltage)

The fixed electrode is assigned a positive voltage. Figure 4 shows where the voltage is applied.

Fixed voltage applied to the bottom membrane

Figure 4 - Fixed voltage applied to the bottom membrane

Structural boundary condition

Fixed boundary conditions are applied to the bottom membrane and to the anchors of the two serpentine springs, as shown in the figure 5:

Fixed constraint applied on the bottom membrane

Figure 5 - Fixed constraint applied on the bottom membrane

Meshing

The model geometry doesn’t contain very complicated shapes. A mesh control has been applied to all solid bodies of the mode; this would be sufficient to get accurate electrical and structural results. Figure 6 shows the generated mesh.

The meshed model

Figure 6 - The meshed model

Simulation Results

Different voltages have been applied to the bottom membrane. The generated electrostatic force is the origin of the top membrane deflection.
The figure 7, shows the resultant displacement as a function of the applied voltage computed by EMS compared with the reference results.

displacement as function of voltage for EMS and reference

 Figure 7 - displacement as function of voltage for EMS and reference

Visualization of the Results for 33v applied Voltage:

EMS offers the possibility to find out the resultant electric rigid body force acting on the structure parts. In our case, we are interested in finding the electric force acting on the top membrane
Table 2 shows the components of the electric force vector acting on the membrane. The force is given in Newtons.

Electric force (Results table)

Table 2 - The components of the electric force vector

The components of the electric force vector
 
The Analytical formula
simple F indice e l fin d'indice égal à 1 demi numérateur de la fraction dérivée partielle simple C au-dessus du dénominateur dérivée partielle simple z fin de la fraction V puissance italique sur 2
C: the capacitance
V: the voltage applied to bottom membrane

Correlation between EMS and the reference result:

Table 3 - Comparison between EMS and the reference results

  EMS Result Reference Result
Resultant Displacement under 33V (in mu m) 0.202591 0.201708
 

Resultant Displacement plot:

Resultant displacement distribution on the top membrane
Figure 8 - Resultant displacement distribution on the top membrane
 

Figure 8 shows that the maximum displacement occurs at the square membrane

Conclusion

The structural behavior of the microsensing membrane with two serpentine springs has been investigated using EMS simulation software. The computed displacement found in a good agreement with the reference results [2].

This numerical analysis helped to get an idea of how the MEMS device responds to different DC voltage inputs; in the studied case, the displacement of the bottom membrane kept increasing with the increase of the applied voltage.

References

[1]: https://www.emworks.com/
[2]: P. A. Manoharan and D. Nedumaran, 2010, “Modeling-Simulation and Analysis of MEMS Capacitive Millibar Pressure Sensor,” J. Nanotechnol. Eng. Med 1(4)