Models.mems.Thermal Actuator Tem Parameterized

7/24/2019 Models.mems.Thermal Actuator Tem Parameterized

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Solved with COMSOL Multiphysics 4.3

2 0 1 2 C O M S O L 1 | T H E R M A L M I C R O A C T U A T O R

T h e rma l M i c r o a c t u a t o r

Introduction

This example model consists of a two-hot-arm thermal actuator made of polysilicon.

The actuator is activated through thermal expansion. The temperature increase

required to deform the two hot arms, and thus displace the actuator, is obtained

through Joule heating (resistive heating). The greater expansion of the hot-arms,

compared to the cold arm, causes a bending of the actuator.

The material properties of polysilicon are temperature dependent, which means that

the involved physics phenomena are fully coupled. The electric current through the

hot arms increases the temperature in the actuator, which in turn causes thermal

expansion and changes the electrical conductivity of the material.

The actuators operation thus involves three coupled physics phenomena: electric

current conduction, heat conduction with heat generation, and structural stresses and

strains due to thermal expansion.


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2 | T H E R M A L M I C R O A C T U A T O R 2 0 1 2 C O M S O L

Model Definition

Figure 1shows the actuators parts and dimensions as well as its position on top of asubstrate surface.

Anchors

Hot arms

Cold armDimple

2 m

3 m

Substrate

Upper surface

240 m

Figure 1: The thermal microactuator.

B O U N D A R Y C O N D I T I O N S A N D C O N S T R A I N T S

An electric potential is applied between the bases of the hot arms anchors. The cold

arm anchor and all other surfaces are electrically insulated.

Applied voltage

Ground

Figure 2: Electrical boundary conditions.

The temperature of the base of the three anchors and the three dimples is fixed to that

of the substrates constant temperature. Because the structure is sandwiched, all other


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Results

Figure 5shows the surface temperature distribution for the actuator. It also illustratesthe displacement field through a deformation plot.

Figure 5: Temperature (surface) and displacement (deformation).

Model Library path: MEMS_Module/Actuators/

thermal_actuator_tem_parameterized

Modeling Instructions

M O D E L W I Z A R D

1 Go to the Model Wizardwindow.

2 Click Next.

3 In the Add physicstree, select Structural Mechanics>Joule Heating and Thermal

Expansion (tem).

4 Click Next.


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5 Find the Studiessubsection. In the tree, select Preset Studies>Stationary.

6 Click Finish.

M O D E L 1

1 In the Model Builderwindow, right-click Model 1and choose Rename.

2 Go to the Rename Modeldialog box and type Thermal Actuatorin the New name

edit field.

3 Click OK.

G L O B A L D E F I N I T I O N S

Parameters

1 In the Model Builderwindow, right-click Global Definitionsand choose Parameters.

2 In the Parameterssettings window, locate the Parameterssection.

3 In the table, enter the following settings:

G E O M E T R Y 1

Work Plane 1

1 In the Model Builderwindow, under Thermal Actuatorright-click Geometry 1and

choose Work Plane.

NAME EXPRESSION DESCRIPTION

d 3[um]

dw 15[um]

gap 3[um]

wb 10[um]

wv 25[um]

L 240[um] Actuator length

L1 L-wbL2 L-wb-wv

L3 L-2*wb-wv-L/48-L/6

L4 L/6

L5 L/48

htc_s 0.04[W/(m*K)]/2[um] Heat transfer coefficient

htc_us 0.04[W/(m*K)]/

100[um]

Heat transfer coefficient,

upper surfaceDV 5[V] Applied voltage


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2 Right-click Work Plane 1and choose Build Selected.

3 Click the Show Work Planebutton.

Rectangle 1

1 In the Model Builderwindow, under Thermal Actuator>Geometry 1>Work Plane 1

right-click Plane Geometryand choose Rectangle.

2 In the Rectanglesettings window, locate the Sizesection.

3 In the Widthedit field, type L3.

4 In the Heightedit field, type dw.

5 Locate the Positionsection. In the xwedit field, type L-L3.

6 Click the Build Selectedbutton.

Rectangle 2





4 In the Heightedit field, type d.

5 Locate the Positionsection. In the xwedit field, type L-L3-L4.

6 In the ywedit field, type dw-d.


8 Click the Zoom Extentsbutton on the Graphics toolbar.

Rectangle 3




3 In the Widthedit field, type wb.

4 In the Heightedit field, type dw.

5 Locate the Positionsection. In the xwedit field, type L-L3-L4-wb.



Rectangle 4




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6 In the ywedit field, type dw+gap.


Rectangle 5





4 In the Heightedit field, type dw+gap+d.

5 Locate the Positionsection. In the xwedit field, type L-L2-wb.



Rectangle 6







6 In the ywedit field, type dw+d+2*gap.



Rectangle 7





4 In the Heightedit field, type dw+gap+d.

5 Locate the Positionsection. In the ywedit field, type dw+d+2*gap.


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Rectangle 8




3 In the Widthedit field, type d.

4 In the Heightedit field, type gap.

5 Locate the Positionsection. In the xwedit field, type L-d.

6 In the ywedit field, type dw+gap+d.


Rectangle 9




3 In the Widthedit field, type d.

4 In the Heightedit field, type gap.

5 Locate the Positionsection. In the xwedit field, type L-d.

6 In the ywedit field, type dw.


Union 1


right-click Plane Geometryand choose Boolean Operations>Union.

2 Click in the Graphicswindow, press Ctrl+A to highlight all 9 rectangles, then

right-click to confirm the selection.

3 In the Unionsettings window, locate the Unionsection.

4 Clear the Keep interior boundariescheck box.


Fillet 1


right-click Plane Geometryand choose Fillet.

2 In the Filletsettings window, locate the Radiussection.


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3 In the Radiusedit field, type d/3.

4 On the object uni1, select Points 1, 2, 49, 1114, 16, 17, 1923, and 28 only.


Extrude 1

1 In the Model Builderwindow, under Thermal Actuator>Geometry 1right-click Work

Plane 1and choose Extrude.

2 In the Extrudesettings window, locate the Distances from Planesection.



5 Click the Go to Default 3D Viewbutton on the Graphics toolbar.

Work Plane 2

1 In the Model Builderwindow, right-click Geometry 1and choose Work Plane.2 Right-click Work Plane 2and choose Build Selected.

3 Click the Show Work Planebutton.

Plane Geometry

Click the Zoom Extentsbutton on the Graphics toolbar.

Rectangle 1

1 In the Model Builderwindow, under Thermal Actuator>Geometry 1>Work Plane 2right-click Plane Geometryand choose Rectangle.


3 In the Widthedit field, type wb-2*d.

4 In the Heightedit field, type 2.5*(wb-2*d).

5 Locate the Positionsection. In the xwedit field, type d.

6 In the ywedit field, type (dw+d+2*gap)+(dw+gap+d)-2.5*(wb-2*d)-d .


Rectangle 2




DISTANCES (M)

2e-6


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5 Locate the Positionsection. In the xwedit field, type L-L2-wb+d.

6 In the ywedit field, type d.


Rectangle 3






5 Locate the Positionsection. In the xwedit field, type L-L3-L4-wb+d.

6 In the ywedit field, type d.


Fillet 1


right-click Plane Geometryand choose Fillet.

2 In the Filletsettings window, locate the Radiussection.



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4 Click the Select Boxbutton on the Graphics toolbar.

5 In the Graphicswindow, draw a box encompassing the three rectangles you just

created, then right-click to confirm the selection.


Circle 1


right-click Plane Geometryand choose Circle.

2 In the Circlesettings window, locate the Size and Shapesection.


4 Locate the Positionsection. In the xwedit field, type L-L3/4.

5 In the ywedit field, type dw/2.


Circle 2





4 Locate the Positionsection. In the xwedit field, type L-L3/2.



Circle 3





4 Locate the Positionsection. In the xwedit field, type L-3*L3/4.



Extrude 2

1 In the Model Builderwindow, under Thermal Actuator>Geometry 1right-click Work

Plane 2and choose Extrude.

2 In the Extrudesettings window, locate the Distances from Planesection.


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4 Select the Reverse directioncheck box.


Union 1

1 In the Model Builderwindow, right-click Geometry 1and choose Boolean

Operations>Union.


3 Click in the Graphicswindow, press Ctrl+A to highlight all objects, then right-click

to confirm the selection.

4 Click the Build Allbutton.

D E F I N I T I O N S

Explicit 1

1 In the Model Builderwindow, under Thermal Actuatorright-click Definitionsand

choose Selections>Explicit.

2 In the Explicitsettings window, locate the Input Entitiessection.

3 From the Geometric entity levellist, choose Boundary.

4 Select Boundaries 10, 30, 50, 70, 76, and 82 only.

5 Right-click Thermal Actuator>Definitions>Explicit 1and choose Rename.

6 Go to the Rename Explicitdialog box and type substrate contactin the New name

edit field.

7 Click OK.

M A T E R I A L S

1 In the Model Builderwindow, under Thermal Actuatorright-click Materialsand

choose Open Material Browser.

2 In the Material Browserwindow, locate the Materialssection.

3 In the tree, select MEMS>Semiconductors>Poly-Si.

4 Right-click and choose Add Material to Modelfrom the menu.

DISTANCES (M)

2e-6


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Poly-Si

By default, the first material you add applies on all domains so you can keep the

Geometric Scope settings.

1 In the Model Builderwindow, under Thermal Actuator>Materialsclick Poly-Si.

2 In the Materialsettings window, locate the Material Contentssection.


J O U L E H E A T I N G A N D T H E R M A L E X P A N S I O N

Fixed Constraint 1

1 In the Model Builderwindow, right-click Thermal Actuator>Joule Heating and Thermal

Expansionand choose the boundary condition Solid Mechanics>Fixed Constraint.

2 Select Boundaries 10, 30, and 50 only.

Roller 1

1 In the Model Builderwindow, right-clickJoule Heating and Thermal Expansionand

choose the boundary condition Solid Mechanics>Roller.

2 Select Boundaries 70, 76, and 82 only.

Heat Flux 1


choose the boundary condition Heat Transfer>Heat Flux.This boundary condition applies to all boundaries except the top-surface boundary

and those in contact with the substrate. A Temperature condition on the

substrate_contactboundaries will override this Heat Flux condition so you do not

explicitly need to exclude those boundaries. In contrast, because the Heat Flux

boundary condition is additive, you must explicitly exclude the top-surface

boundary from the selection. Implement this selection as follows.

2 In the Heat Fluxsettings window, locate the Boundary Selectionsection.3 From the Selectionlist, choose All boundaries.

4 In the Graphicswindow, click on the top surface and then right-click to remove it

from the selection.

5 Locate the Heat Fluxsection. Click the Inward heat fluxbutton.

6 In the hedit field, type htc_s.

PROPERTY NAME VALUE

Electric conductivity sigma 5e4


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Heat Flux 2


choose the boundary condition Heat Transfer>Heat Flux.2 Select Boundary 4 only.

3 In the Heat Fluxsettings window, locate the Heat Fluxsection.

4 Click the Inward heat fluxbutton.

5 In the hedit field, type htc_us.

Temperature 1

1 In the Model Builderwindow, right-clickJoule Heating and Thermal Expansionandchoose the boundary condition Heat Transfer>Temperature.

2 In the Temperaturesettings window, locate the Boundary Selectionsection.

3 From the Selectionlist, choose substrate contact.

Ground 1


choose the boundary condition Electric Currents>Ground.2 Select Boundary 10 only.

Electric Potential 1


choose the boundary condition Electric Currents>Electric Potential.

2 Select Boundary 30 only.

3 In the Electric Potentialsettings window, locate the Electric Potentialsection.4 In the V0edit field, type DV.

M E S H 1

In the Model Builderwindow, under Thermal Actuatorright-click Mesh 1and choose Free

Tetrahedral.

Size

1 In the Model Builderwindow, under Thermal Actuator>Mesh 1click Size.

2 In the Sizesettings window, locate the Element Sizesection.

3 From the Predefinedlist, choose Fine.

4 Click the Custombutton.


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5 Locate the Element Size Parameterssection. In the Maximum element growth rateedit

field, type 1.2.

This setting makes the mesh more robust for parametric sweeps over the geometrylength parameter L.

Size 1

1 In the Model Builderwindow, under Thermal Actuator>Mesh 1right-click Free

Tetrahedral 1and choose Size.

2 In the Sizesettings window, locate the Element Sizesection.

3 From the Predefinedlist, choose Finer.4 Locate the Geometric Entity Selectionsection. From the Geometric entity levellist,

choose Boundary.

5 Select Boundaries 8691 only.

6 Click the Build Allbutton.

S T U D Y 1

Step 1: Stationary

1 In the Model Builderwindow, under Study 1click Step 1: Stationary.

2 In the Stationarysettings window, locate the Study Settingssection.

3 Select the Include geometric nonlinearitycheck box.

4 In the Model Builderwindow, right-click Study 1and choose Compute.

R E S U L T S

Temperature (tem)

Click the Go to Default 3D Viewbutton on the Graphics toolbar.

The third default plot shows the combined temperature field and deformation,

compare it to that shown in Figure 5.


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Documents

Models.mems.Thermal Actuator Tem Parameterized