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# Multi physics FEM simulation of MEMS thermal actuator using EMS

Used Tools:

## Introduction:

Micro-electro-mechanical systems (MEMS) make it possible to reduce the size of complex engineering devices to a micrometer scale,for various applications: micro positioning, micro fixturing, micromanipulation etc. Micro-thermal actuators convert thermal energy into force and motion. Here, we study a low voltage micro-thermalactuator that develops relatively large thermally-induceddeflections.

Figure1 - Electron microscope image of thermal actuator [1]

## Problem description:

The U-shaped actuator analysed in this study consists of two parallel arms: cold and hot arm. They are connected to the pads substrate at one side and to each other at the other side, like in Figure 2.

EMS simulation coupled to thermo-structural analysis is used to compute the mechanical displacement of the micro-device caused by temperature expansion effect.

Figure 2 - The basic design of the U-shaped thermal actuator.

Table 1: Model dimensions [2]

 Part Dimension (µm) Hot arm length 495 Hot arm width 2 Cold arm length 470 Cold arm width 30 Arms separation 10 Connecting bar width 10 Pad length 40 Pad width 30

### Simulation Setup:

In order tocompute and visualize the mechanical displacement of the studied thermal actuator device,the Magnetostatic module is used along withthe steady state thermal and structural analysis.

The simulation setup consists of the following steps:
1. Selectan appropriate material.
2. Define the necessary electromagnetic inputs.
3. Define the necessary thermal inputs.
4. Apply the structural boundary conditions.
5. Mesh the entire model and run the solver.

In our case study, the following properties of material are used (Table 2):

Table 2:Polysilicon material properties

 Property Electrical conductivity (S/m) thermal conductivity (W/m. K) Thermal expansion coefficient (/K) Elastic Modulus (GPa) Poisson’s ratio Polysilicon 43.5 E+03 150 2.9 E-06 169 0.22

The micro actuator is defined as a solid coil, carrying a voltage of 5V, with the hot-armconnected pad serving as the entry port. Theinitial temperature applied to both anchored pads is0 °C. The thermal convection is defined on the ambient air body, by setting theinitial (ambient) temperature to 273.15 K, and the convection coefficient to 10 W/ . A “Fixed” constraint structural boundary condition is applied to both sides of the anchored pads, as shown in the figure 3:

Figure 3 - Applied mechanical boundary conditions.

The whole model uses a fine mesh control for a better results accuracy (Figure 4).

Figure 4 - Meshed model.

## Results:

The final simulation results for the thermal distribution are shown in figure 5. The voltage difference across the pads causes a temperature difference between the two arms, therefore achieves a maximum value of 864°C at the most critical zone of the thin arm.

Figure 5 - Temperature distribution across the actuator.

The mechanical displacement caused by the thermal expansion effect reaches 16.99 µm. The actuator is moving mostly in the area connecting the two arms.

Figure 6 - Resultant displacement plot.

The comparison between EMS andthe reference [2] resultsfor the actuator deflection can be found in Table 3.

Table 3:Comparative table between EMS and the reference [2] results.

 EMS Reference [2] Deflection (µm) 16.99 17

## Conclusion:

EMS tool enables the validation and prediction of the micro-machined thermal actuators performance. It successfully evaluated and validated its capacityto produce large deflection under low supply voltages.