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Thermal Actuator
Introduction
For a description of this model, see Thermal Actuator — Parameterized, which describes a version of the same model (called thermal_actuator_tem_parameterized) that only differs in the way the geometry is created; while the modeling instructions below describe how you can import the finished geometry from an MPHBIN-file, the instructions in the above referenced model detail the steps required to create the geometry in the COMSOL Desktop.
Reference
1. D.M. Burns and V.M. Bright, “Design and performance of a double hot arm polysilicon thermal actuator,” Proc. SPIE 3224, Micromachined Devices and Components III, 1997; doi: 10.1117/12.284528.
Application Library path: MEMS_Module/Actuators/thermal_actuator_tem
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Structural Mechanics > Thermal–Structure Interaction > Joule Heating and Thermal Expansion.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies > Stationary.
6
Click  Done.
Thermal Actuator
1
In the Model Builder window, right-click Component 1 (comp1) and choose Rename.
2
In the Rename Component dialog, type Thermal Actuator in the New label text field.
3
Click OK.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
htc_s
0.04[W/(m*K)]/2[um]
20000 W/(m²·K)
Heat transfer coefficient
htc_us
0.04[W/(m*K)]/100[um]
400 W/(m²·K)
Heat transfer coefficient, upper surface
DV
5[V]
5 V
Applied voltage
Geometry 1
Import 1 (imp1)
1
In the Geometry toolbar, click  Import.
2
In the Settings window for Import, locate the Source section.
3
Click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file thermal_actuator.mphbin.
5
Click  Build All Objects.
6
Click the  Go to Default View button in the Graphics toolbar.
Definitions
substrate contact
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, locate the Input Entities section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 10, 30, 50, 70, 76, and 82 only.
5
In the Label text field, type substrate contact.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select MEMS > Semiconductors > Si - Polycrystalline silicon.
4
Click the Add to Component button in the window toolbar.
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Si - Polycrystalline silicon (mat1)
By default, the first material you add applies on all domains so you can keep the Geometric Entity Selection settings.
1
In the Settings window for Material, locate the Material Contents section.
2
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
5e4
S/m
Basic
Solid Mechanics (solid)
Fixed Constraint 1
1
In the Physics toolbar, click  Boundaries and choose Fixed Constraint.
2
Select Boundaries 10, 30, and 50 only.
Roller 1
1
In the Physics toolbar, click  Boundaries and choose Roller.
2
Select Boundaries 70, 76, and 82 only.
Heat Transfer in Solids (ht)
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose 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 contact boundaries 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 Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose All boundaries.
4
In the Graphics window, click on the top surface to remove it from the selection.
A convective heat flux is used to model the heat flux through a thin air layer. The heat transfer coefficient, htc_s is defined as the ratio of the air thermal conductivity to the gap thickness.
5
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
6
In the h text field, type htc_s.
Heat Flux 2
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
Select Boundary 4 only.
A convective heat flux is used to model the heat flux through a thin air layer. The heat transfer coefficient, htc_us is defined as the ratio of the air thermal conductivity to the gap thickness.
3
In the Settings window for Heat Flux, locate the Heat Flux section.
4
From the Flux type list, choose Convective heat flux.
5
In the h text field, type htc_us.
Temperature 1
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
In the Settings window for Temperature, locate the Boundary Selection section.
3
From the Selection list, choose substrate contact.
Electric Currents (ec)
Ground 1
1
In the Physics toolbar, click  Boundaries and choose Ground.
2
Select Boundary 10 only.
Electric Potential 1
1
In the Physics toolbar, click  Boundaries and choose Electric Potential.
2
Select Boundary 30 only.
3
In the Settings window for Electric Potential, locate the Electric Potential section.
4
In the V0 text field, type DV.
Mesh 1
1
In the Model Builder window, under Thermal Actuator (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
From the Element size list, choose Extra fine.
4
Click  Build All.
Study 1
Step 1: Stationary
1
In the Model Builder window, under Study 1 click Step 1: Stationary.
2
In the Settings window for Stationary, locate the Study Settings section.
3
Select the Include geometric nonlinearity checkbox.
The default solver sequence is not optimal for this problem. The only deviation from linearity comes from the geometric nonlinearity. Both the Electric Currents and Temperature groups in the segregated solver contain damping intended to make solution of nonlinear problems more stable, but slower. Removing that damping gives a significant speed up. Also, if iterations are performed for the Solid Mechanics group where the actual nonlinearity is present, there will be fewer iterations over the whole set of segregated groups.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, expand the Study 1 > Solver Configurations > Solution 1 (sol1) > Stationary Solver 1 > Segregated 1 node, then click Electric Currents.
4
In the Settings window for Segregated Step, click to expand the Method and Termination section.
5
In the Damping factor text field, type 1.
6
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Stationary Solver 1 > Segregated 1 click Temperature.
7
In the Settings window for Segregated Step, locate the Method and Termination section.
8
In the Damping factor text field, type 1.
9
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Stationary Solver 1 > Segregated 1 click Solid Mechanics.
10
In the Settings window for Segregated Step, locate the Method and Termination section.
11
From the Termination technique list, choose Tolerance.
12
Locate the General section. From the Linear solver list, choose Suggested Iterative Solver solid (te1).
13
In the Study toolbar, click  Compute.
Results
Stress (solid)
The first default plot show the von Mises stress.
Volume 1
1
In the Model Builder window, expand the Stress (solid) node, then click Volume 1.
2
In the Settings window for Volume, locate the Expression section.
3
From the Unit list, choose MPa.
4
In the Stress (solid) toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Temperature (ht)
1
Click the  Go to Default View button in the Graphics toolbar.
The second default plot shows the temperature field.
Create a new plot for displacement.
Displacement
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type Displacement in the Label text field.
Surface 1
1
Right-click Displacement and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
From the Unit list, choose µm.
4
Locate the Coloring and Style section. From the Color table list, choose SpectrumLight.
Deformation 1
1
Right-click Surface 1 and choose Deformation.
2
In the Displacement toolbar, click  Plot.