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Surface Micromachined Accelerometer
Introduction
This example shows how to model a surface micromachined accelerometer in COMSOL, using the electromechanics interface. The example is based on the case study in Ref. 1. The model also demonstrates the use of linked subsequences. A collection of geometric building blocks can be stored in a source model file as subsequences. Thereafter, other model files can reuse the same building blocks by linking to the subsequences in the source model file. Each subsequence can take arguments to generate a building block with specific dimensions or number of features. In this model, a surface micromachined accelerometer is created from three building blocks, two of which are used multiple times by calling the corresponding subsequence with different arguments.
Model Definition
The surface micromachined accelerometer is composed of a released proof mass supported by anchored springs at its two ends, together with sensing and self test electrodes extending to the sides. When the device is subject to an acceleration, the restoring force from the springs gives a displacement of the proof mass in proportion to the acceleration. The displacement causes a change in the capacitance between the fixed and moving electrodes. This change in capacitance can be measured with a number of standard circuits.
For acceleration along the axis of the accelerometer, symmetry allows modeling only half of the geometry for faster computation. The three geometric building blocks are the proof mass with attached electrodes (Figure 1), the folded spring (Figure 2), and the fixed electrode array (Figure 3). These building blocks are implemented as Subsequences that take arguments to specify dimensions, orientation, position, and number of features. For example, the proof mass shown in Figure 1 has 7 sense electrodes at the center and 3 self test electrodes at each end. The actual model on the other hand is built with 21 sense electrodes, by calling the same Subsequence with the corresponding argument 21. As another example, Figure 4 shows an electrode array built from the same Subsequence as in Figure 3, with a different set of arguments, resulting in different number of electrodes, dimensions, and orientation of the anchor pads.
Figure 1: Building block for the proof mass with attached electrodes. Grid scales are in micrometers.
Figure 2: Building block for the folded spring. Grid scales are in micrometers.
Figure 3: Building block for the fixed electrode array. Grid scales are in micrometers.
Figure 4: Example of an electrode array built from the same Subsequence as in Figure 3, with a different set of arguments. Grid scales are in micrometers.
The geometry sequence begins by calling the proof mass Subsequence, followed by calling the folded spring Subsequence twice to attach a spring at each end of the proof mass. Subsequently 6 calls to the fixed electrode array Subsequence are made to construct the sense and self test fixed electrodes.
Each Subsequence call contributes to a domain and a boundary selection. This allows easy assignment of domain physics and boundary conditions in the physics interface.
The model uses polysilicon for the building material and includes a rectangular air domain surrounding the polysilicon. The Electromechanics multiphysics interface models the electric field within the deforming gaps between the electrodes, and applies the appropriate electrostatic forces to the solids, which creates a corresponding structural deformation. The deformation of the gaps between electrodes results in nonlinear geometrical effects, which are included in the Electromechanics multiphysics interface by default.
The entire polysilicon solid is subject to an acceleration using the Body Load domain physics feature. The (mechanically) fixed electrodes are set at constant potentials, and the proof mass (and its attached electrodes) is at a floating potential whose value will be determined by the position-dependent capacitance (and the applied voltages on the fixed sense electrodes).
Results and Discussion
The first study illustrates the normal operation of the accelerometer by sweeping the applied acceleration from -50 to +50 g and computing the resulting displacement of the proof mass. Figure 5 shows the displacement of the polysilicon domains when the applied acceleration is 50 g. The proof mass (and the attached moving electrodes) moves by about 0.07 micrometer. The anchored spring bases and the fixed electrodes have very little movement. The folded springs have varying displacement along its length as expected.
Figure 5: Displacement of the polysilicon domains when the applied acceleration is 50 g. The proof mass moves by about 0.07 micrometer. The anchored spring bases and the fixed electrodes have very little movement. The springs have varying displacement along its length as expected.
Figure 6: Displacement vs acceleration.
Figure 6 shows the linear relationship between the displacement and the applied acceleration. The displacement is measured via the capacitive coupling between the moving and the fixed sense electrodes. In the real device, during normal operation, the proof mass with its attached moving electrodes is floating at a potential close to one half of the supply voltage, and a high frequency square wave swinging between zero and the full supply voltage is applied with opposite phase to the fixed sense electrodes on each side of the moving electrodes. The fixed self test electrodes are biased at one half of the supply voltage. When the proof mass moves as a result of the acceleration, an alternating voltage in proportion to the displacement is induced due to the capacitive coupling between the fixed and moving electrodes. This arrangement nulls the average electrostatic force between the fixed and moving sense electrodes, and facilitates easier signal processing in the attached circuitry. In this example the stationary part of the square wave is modeled using a stationary study, so that the problem solves relatively quickly. The bias is shifted to zero for convenience, and the amplitude of the square wave is divided by an artificial factor of 1000 to reduce the electrostatic force between the fixed and moving sense electrodes (in practice the time average of the force will be zero due to the high frequency excitation). For a 5 V supply in the physical device, this corresponds to applying a +/-2.5 mV on the right-side and left-side fixed sense electrodes in the model. In postprocessing, the artificial factor of 1000 is multiplied back to the sensed voltage of the proof mass. Figure 7 shows the linear relationship between the sense voltage and the acceleration. This signal is fed into an amplifier that in the real device was built on the same substrate as the mechanical structure.
Figure 7: Sensed voltage vs. applied acceleration.
The accelerometer in the model was designed with self test electrodes that could be employed to calibrate the device in the factory. The second study illustrates the self testing by applying a bias of 2 V on the fixed self test electrodes, which are at the side of the moving electrodes attached to the proof mass. The electric field between the fixed and the moving electrodes exerts an electrostatic force that causes the proof mass to move. Figure 8 shows the displacement of the polysilicon domains when 0 V is applied to the fixed self test electrodes on the left-hand side of the moving electrodes attached to the proof mass, and 2 V to those on the right-hand side. The proof mass moves by about 0.02 μm, which is large enough in magnitude for the self test purpose (compared to the 0.07 μm of full range displacement shown in Figure 5 and Figure 6).
Figure 8: Displacement of the polysilicon domains when 0 V is applied to the fixed self test electrodes on the left side of the moving electrodes attached to the proof mass, and 2 V to those on the right side. The proof mass moved by about 0.02 μm, which is large enough in magnitude for the self test purpose (compared to the 0.07 μm of full range displacement shown in Figure 5 and Figure 6).
Figure 9 compares the displacement obtained from applying the self test voltage to each side of the fixed electrodes. The displacement values have the same magnitude with opposite signs, as expected from symmetry.
Figure 9: Displacement vs. applied self test voltage.
Reference
1. S.D. Senturia, Microsystem Design 5th ed., Kluwer Academic Publishers, pp. 513–525, 2003.
Application Library path: MEMS_Module/Sensors/surface_micromachined_accelerometer
Modeling Instructions
Root
Load the geometry file.
1
From the File menu, choose Open.
2
Browse to the model’s Application Libraries folder and double-click the file surface_micromachined_accelerometer_geom_sequence.mph.
The model geometry has been set up using parts in a linked file. It is easier to visualize with wireframe rendering.
Component 1 (comp1)
1
Click the  Wireframe Rendering button in the Graphics toolbar.
2
Click the  Zoom Extents button in the Graphics toolbar.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Air.
4
Click  Add to Component 1 (comp1).
5
In the tree, select MEMS>Semiconductors>Si - Polycrystalline silicon.
6
Click  Add to Component 1 (comp1).
7
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Si - Polycrystalline silicon (mat2)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Polysilicon.
Definitions
All domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type All domains in the Label text field.
3
Locate the Input Entities section. Select the All domains check box.
Air
1
In the Definitions toolbar, click  Difference.
2
In the Settings window for Difference, type Air in the Label text field.
3
Locate the Input Entities section. Under Selections to add, click  Add.
4
In the Add dialog box, select All domains in the Selections to add list.
5
Click OK.
6
In the Settings window for Difference, locate the Input Entities section.
7
Under Selections to subtract, click  Add.
8
In the Add dialog box, select Polysilicon in the Selections to subtract list.
9
Click OK.
Deforming Domain 1
1
In the Model Builder window, expand the Component 1 (comp1)>Definitions>Moving Mesh node, then click Deforming Domain 1.
2
In the Settings window for Deforming Domain, locate the Domain Selection section.
3
From the Selection list, choose Air.
Solid Mechanics (solid)
1
In the Model Builder window, under Component 1 (comp1) click Solid Mechanics (solid).
2
In the Settings window for Solid Mechanics, locate the Domain Selection section.
3
From the Selection list, choose Polysilicon.
Body Load 1
1
In the Physics toolbar, click  Domains and choose Body Load.
2
In the Settings window for Body Load, locate the Force section.
3
Specify the FV vector as
acceleration*solid.rho*g_const
x
0
y
0
z
4
Locate the Domain Selection section. From the Selection list, choose Polysilicon.
Fixed Constraint 1
1
In the Physics toolbar, click  Boundaries and choose Fixed Constraint.
2
In the Settings window for Fixed Constraint, locate the Boundary Selection section.
3
From the Selection list, choose Anchor plane.
Symmetry 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
In the Settings window for Symmetry, locate the Boundary Selection section.
3
From the Selection list, choose Symmetry plane.
Definitions
Symmetry/Roller 1
1
In the Model Builder window, under Component 1 (comp1)>Definitions>Moving Mesh click Symmetry/Roller 1.
2
In the Settings window for Symmetry/Roller, locate the Boundary Selection section.
3
From the Selection list, choose Symmetry plane.
Electrostatics (es)
In the Model Builder window, under Component 1 (comp1) click Electrostatics (es).
Charge Conservation, Air
1
In the Physics toolbar, click  Domains and choose Charge Conservation.
2
In the Settings window for Charge Conservation, type Charge Conservation, Air in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Air.
Ground 1
1
In the Physics toolbar, click  Boundaries and choose Ground.
2
Select Boundary 45 only.
Sense Terminal L
1
In the Physics toolbar, click  Boundaries and choose Terminal.
2
In the Settings window for Terminal, type Sense Terminal L in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Sense left boundaries.
4
Locate the Terminal section. From the Terminal type list, choose Voltage.
5
In the V0 text field, type -2.5[mV].
Sense Terminal R
1
In the Physics toolbar, click  Boundaries and choose Terminal.
2
In the Settings window for Terminal, type Sense Terminal R in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Sense right boundaries.
4
Locate the Terminal section. From the Terminal type list, choose Voltage.
5
In the V0 text field, type 2.5[mV].
Floating Potential 1
1
In the Physics toolbar, click  Boundaries and choose Floating Potential.
2
In the Settings window for Floating Potential, locate the Boundary Selection section.
3
From the Selection list, choose Proof mass boundaries.
Self Test Terminal L
1
In the Physics toolbar, click  Boundaries and choose Terminal.
2
In the Settings window for Terminal, type Self Test Terminal L in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Self test left boundaries.
4
Locate the Terminal section. From the Terminal type list, choose Voltage.
5
In the V0 text field, type VtestL.
Self Test Terminal R
1
In the Physics toolbar, click  Boundaries and choose Terminal.
2
In the Settings window for Terminal, type Self Test Terminal R in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Self test right boundaries.
4
Locate the Terminal section. From the Terminal type list, choose Voltage.
5
In the V0 text field, type VtestR.
Mesh 1
Free Triangular 1
1
In the Mesh toolbar, click  Boundary and choose Free Triangular.
2
In the Settings window for Free Triangular, locate the Boundary Selection section.
3
From the Selection list, choose Meshing plane.
4
Click  Build Selected.
Swept 1
In the Mesh toolbar, click  Swept.
Distribution 1
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Domain Selection section.
3
Click  Clear Selection.
4
Select Domain 3 only.
5
Locate the Distribution section. In the Number of elements text field, type 1.
6
Click  Build All.
Study 1: Normal Operation
1
In the Model Builder window, right-click Study 1 and choose Rename.
2
In the Rename Study dialog box, type Study 1: Normal Operation in the New label text field.
3
Click OK.
Step 1: Stationary
1
In the Model Builder window, expand the Study 1: Normal Operation node, then click Step 1: Stationary.
2
In the Settings window for Stationary, click to expand the Results While Solving section.
3
Select the Plot check box.
4
From the Update at list, choose Steps taken by solver.
5
Click to expand the Study Extensions section. Select the Auxiliary sweep check box.
6
Click  Add.
7
Click  Range.
8
In the Range dialog box, type -50 in the Start text field.
9
In the Step text field, type 25.
10
In the Stop text field, type 50.
11
Click Add.
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: Normal Operation>Solver Configurations>Solution 1 (sol1)>Dependent Variables 1 node, then click Spatial mesh displacement (comp1.spatial.disp).
4
In the Settings window for Field, locate the Scaling section.
5
In the Scale text field, type 1e-7.
6
In the Model Builder window, click Displacement field (comp1.u).
7
In the Settings window for Field, locate the Scaling section.
8
In the Scale text field, type 1e-7.
9
In the Model Builder window, click Electric potential (comp1.V).
10
In the Settings window for Field, locate the Scaling section.
11
From the Method list, choose Manual.
12
In the Scale text field, type 1e-3.
13
In the Model Builder window, click Floating potential (comp1.es.fp1.V0_ode).
14
In the Settings window for State, locate the Scaling section.
15
From the Method list, choose Manual.
16
In the Scale text field, type 5e-5.
17
In the Model Builder window, expand the Study 1: Normal Operation>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1>Segregated 1 node.
18
Right-click Electric potential and choose Move Down.
19
Right-click Electric potential and choose Move Down.
20
In the Study toolbar, click  Compute.
Results
Surface 1
1
In the Model Builder window, expand the Displacement (solid) node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type u.
4
In the Displacement (solid) toolbar, click  Plot.
Multislice 1
1
In the Model Builder window, expand the Electric Potential (es) node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Expression section.
3
From the Unit list, choose mV.
4
Locate the Multiplane Data section. Find the x-planes subsection. In the Planes text field, type 0.
5
Find the y-planes subsection. In the Planes text field, type 0.
6
In the Electric Potential (es) toolbar, click  Plot.
1D Plot Group 4
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
Point Graph 1
1
Right-click 1D Plot Group 4 and choose Point Graph.
2
Select Point 65 only.
3
In the Settings window for Point Graph, locate the y-Axis Data section.
4
In the Expression text field, type u.
Displacement vs. Acceleration
1
In the Model Builder window, right-click 1D Plot Group 4 and choose Rename.
2
In the Rename 1D Plot Group dialog box, type Displacement vs. Acceleration in the New label text field.
3
Click OK.
4
In the Settings window for 1D Plot Group, locate the Plot Settings section.
5
Select the x-axis label check box.
6
In the associated text field, type Acceleration (g).
7
In the Displacement vs. Acceleration toolbar, click  Plot.
1D Plot Group 5
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
Global 1
1
Right-click 1D Plot Group 5 and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
es.fp1.V0*1000
mV
Raw sense voltage
4
Click to expand the Legends section. Clear the Show legends check box.
5
In the 1D Plot Group 5 toolbar, click  Plot.
Sense V vs. Acceleration
1
In the Model Builder window, right-click 1D Plot Group 5 and choose Rename.
2
In the Rename 1D Plot Group dialog box, type Sense V vs. Acceleration in the New label text field.
3
Click OK.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies>Stationary.
4
Click  Add Study.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2
Step 1: Stationary
1
In the Settings window for Stationary, locate the Study Extensions section.
2
Select the Auxiliary sweep check box.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
VtestL (Test voltage, left side)
2 0
V
5
Click  Add.
6
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
VtestR (Test voltage, right side)
0 2
V
7
From the Run continuation for list, choose No parameter.
8
In the Model Builder window, right-click Study 2 and choose Rename.
9
In the Rename Study dialog box, type Study 2: Self Test in the New label text field.
10
Click OK.
Solution 2 (sol2)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 2 (sol2) node.
3
In the Model Builder window, expand the Study 2: Self Test>Solver Configurations>Solution 2 (sol2)>Dependent Variables 1 node, then click Spatial mesh displacement (comp1.spatial.disp).
4
In the Settings window for Field, locate the Scaling section.
5
In the Scale text field, type 1e-8.
6
In the Model Builder window, click Displacement field (comp1.u).
7
In the Settings window for Field, locate the Scaling section.
8
In the Scale text field, type 1e-8.
9
In the Model Builder window, click Electric potential (comp1.V).
10
In the Settings window for Field, locate the Scaling section.
11
From the Method list, choose Manual.
12
In the Scale text field, type 1.
13
In the Model Builder window, click Floating potential (comp1.es.fp1.V0_ode).
14
In the Settings window for State, locate the Scaling section.
15
From the Method list, choose Manual.
16
In the Scale text field, type 0.1.
17
In the Study toolbar, click  Compute.
Results
Surface 1
1
In the Model Builder window, expand the Displacement (solid) 1 node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type u.
4
In the Displacement (solid) 1 toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Multislice 1
1
In the Model Builder window, expand the Electric Potential (es) 1 node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Multiplane Data section.
3
Find the x-planes subsection. In the Planes text field, type 0.
4
Find the y-planes subsection. In the Planes text field, type 0.
5
In the Electric Potential (es) 1 toolbar, click  Plot.
1D Plot Group 9
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Dataset list, choose Study 2: Self Test/Solution 2 (sol2).
Point Graph 1
1
Right-click 1D Plot Group 9 and choose Point Graph.
2
Select Point 65 only.
3
In the Settings window for Point Graph, locate the y-Axis Data section.
4
In the Expression text field, type u.
5
Locate the x-Axis Data section. From the Parameter list, choose Expression.
6
In the Expression text field, type VtestR.
7
In the 1D Plot Group 9 toolbar, click  Plot.
Displacement vs. Self Test V
1
In the Model Builder window, right-click 1D Plot Group 9 and choose Rename.
2
In the Rename 1D Plot Group dialog box, type Displacement vs. Self Test V in the New label text field.
3
Click OK.
Appendix — Geometry 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>Electromagnetics-Structure Interaction>Electromechanics>Electromechanics.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Geometry 1
1
In the Geometry toolbar, click  Parts and choose Load Part.
2
Browse to the model’s Application Libraries folder and double-click the file surface_micromachined_accelerometer_geom_subsequence.mph.
3
In the Load Part dialog box, in the Select parts list, choose Proof mass with fingers, Spring and anchor, and Electrode array.
4
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
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file surface_micromachined_accelerometer_parameters.txt.
Geometry 1
Part Link: Proof mass
1
In the Geometry toolbar, click  Parts and choose Proof mass with fingers.
2
In the Settings window for Part Instance, type Part Link: Proof mass in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
l_PM
l_PM
4.48E-4 m
Proof mass length
w_PM
w_PM
1E-4 m
Proof mass full width
t_PM
tSi
2E-6 m
Proof mass thickness
l_f
l_f
1.14E-4 m
Length of finger
w_f
w_f
4E-6 m
Width of finger
n_st
n_st
3
Number of self test fingers
n_f
n_f
21
Number of sense fingers
g_f
g_f
1E-6 m
Gap between sense fingers
g_st
g_st
3E-6 m
Gap between self test fingers
x_st
x_st
1E-5 m
Starting position of self test fingers
x_f
x_f
7.2E-5 m
Starting position of sense fingers
w_eh
w_eh
4E-6 m
Etch hole size
p_eh
p_eh
1.8E-5 m
Etch hole period
4
Click  Build All Objects.
5
Click the  Zoom Extents button in the Graphics toolbar.
Part Link: Spring 1
1
In the Geometry toolbar, click  Parts and choose Spring and anchor.
2
In the Settings window for Part Instance, type Part Link: Spring 1 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
l_sp
l_sp
2.8E-4 m
Spring length
w_sp
w_sp
2E-6 m
Spring width
g_sp
g_sp
1E-6 m
Spring gap
w_sp_conn
w_sp_conn
4E-6 m
Spring connection width
w_f
w_f
4E-6 m
Guard finger width
l_anch_base
l_anch_base
1.7E-5 m
Anchor base length
w_anch_base
w_anch_base
1.7E-5 m
Anchor base width
r_anch
r_anch
3E-6 m
Anchor radius
x_anch
x_anch
1.2E-5 m
Anchor position
t_sp
tSi
2E-6 m
Spring thickness
t_anch
tOx
1.6E-6 m
Anchor thickness
x_sp
l_PM
4.48E-4 m
Position
4
Click  Build All Objects.
Part Link: Spring 2
1
Right-click Part Link: Spring 1 and choose Duplicate.
2
In the Settings window for Part Instance, type Part Link: Spring 2 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
mirror
0
0
0: no mirror. 1: mirror
l_sp
l_sp+10[um]
2.9E-4 m
Spring length
w_anch_base
w_anch_base+10[um]
2.7E-5 m
Anchor base width
x_sp
0[um]
0 m
Position
4
Click  Build All Objects.
Part Link: Sense Electrodes L
1
In the Geometry toolbar, click  Parts and choose Electrode array.
2
In the Settings window for Part Instance, locate the Input Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
LH
0
0
0: RH, 1: LH
l_e
l_e_l
1.4E-4 m
Electrode length
w_e
w_f
4E-6 m
Electrode width
l_p
l_p
1.6E-5 m
Pad length
w_p
w_p
8E-6 m
Pad width
r_an
r_an
3E-6 m
Anchor radius
t_e
tSi
2E-6 m
Electrode thickness
t_an
tOx
1.6E-6 m
Anchor thickness
n_e
n_f+1
22
Number of electrodes
p_e
3*(w_f+g_f)
1.5E-5 m
Periodicity
x_e
x_f-w_f-g_f
6.7E-5 m
x position
y_e
w_PM/2+l_f-l_ovrlp
6E-5 m
y position
4
In the Label text field, type Part Link: Sense Electrodes L.
5
Click  Build All Objects.
6
Click the  Wireframe Rendering button in the Graphics toolbar.
Part Link: Sense Electrodes R
1
Right-click Part Link: Sense Electrodes L and choose Duplicate.
2
In the Settings window for Part Instance, type Part Link: Sense Electrodes R in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
LH
1
1
0: RH, 1: LH
l_e
l_e_s
1.2E-4 m
Electrode length
x_e
x_f-2*(w_f+g_f)
6.2E-5 m
x position
4
Click  Build All Objects.
Part Link: Self Test Electrodes L 1
1
Right-click Part Link: Sense Electrodes R and choose Duplicate.
2
In the Settings window for Part Instance, type Part Link: Self Test Electrodes L 1 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
LH
0
0
0: RH, 1: LH
n_e
n_st
3
Number of electrodes
p_e
3*w_f+2*g_f+g_st
1.7E-5 m
Periodicity
x_e
x_f-2*(w_f+g_f)
6.2E-5 m
x position
4
Click  Build All Objects.
5
In the table, enter the following settings:
Name
Expression
Value
Description
x_e
x_st-w_f-g_f
5E-6 m
x position
6
Click  Build All Objects.
Part Link: Self Test Electrodes L 2
1
Right-click Part Link: Self Test Electrodes L 1 and choose Duplicate.
2
In the Settings window for Part Instance, type Part Link: Self Test Electrodes L 2 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
l_e
l_e_l
1.4E-4 m
Electrode length
x_e
l_PM-(x_st+w_f+g_f)-(n_st-1)*(3*w_f+2*g_f+g_st)-w_f
3.95E-4 m
x position
4
Click  Build All Objects.
Part Link: Self Test Electrodes R 1
1
Right-click Part Link: Self Test Electrodes L 2 and choose Duplicate.
2
In the Settings window for Part Instance, type Part Link: Self Test Electrodes R 1 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
LH
1
1
0: RH, 1: LH
x_e
x_st-w_f-g_f+2*(w_f+g_f)
1.5E-5 m
x position
4
Click  Build All Objects.
Part Link: Self Test Electrodes R 2
1
Right-click Part Link: Self Test Electrodes R 1 and choose Duplicate.
2
In the Settings window for Part Instance, type Part Link: Self Test Electrodes R 2 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
l_e
l_e_s
1.2E-4 m
Electrode length
x_e
l_PM-(x_st+w_f+g_f)-(n_st-1)*(3*w_f+2*g_f+g_st)-w_f+2*(w_f+g_f)
4.05E-4 m
x position
4
Click  Build All Objects.
5
Click the  Go to Default View button in the Graphics toolbar.
Air box
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, type Air box in the Label text field.
3
Locate the Size and Shape section. In the Width text field, type l_polySi+40[um].
4
In the Depth text field, type hw_polySi+20[um].
5
In the Height text field, type 10[um].
6
Locate the Position section. In the x text field, type -l_spAssm-20[um].
7
In the z text field, type -tOx.
8
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (m)
Layer 1
tOx
Layer 2
tSi
9
Click  Build All Objects.
10
In the Model Builder window, click Geometry 1.
11
In the Settings window for Geometry, locate the Units section.
12
From the Length unit list, choose µm.
13
In the Model Builder window, click Air box (blk1).
14
In the Settings window for Block, click  Build All Objects.
15
Click the  Go to Default View button in the Graphics toolbar.
Ground plane
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, type Ground plane in the Label text field.
3
Locate the Plane Definition section. In the z-coordinate text field, type -tOx.
Ground plane (wp1)>Plane Geometry
1
In the Model Builder window, click Plane Geometry.
2
Click the  Zoom Extents button in the Graphics toolbar.
Ground plane (wp1)>Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type l_PM.
4
In the Height text field, type w_PM/2+l_f.
5
Click  Build Selected.
Extrude 1 (ext1)
1
In the Model Builder window, right-click Geometry 1 and choose Extrude.
2
In the Settings window for Extrude, locate the Distances section.
3
In the table, enter the following settings:
Distances (µm)
tOx
4
Click  Build Selected.
Part Link: Proof mass (pi1)
1
In the Model Builder window, click Part Link: Proof mass (pi1).
2
In the Settings window for Part Instance, click to expand the Domain Selections section.
3
Click to select row number 1 in the table.
4
Click New Cumulative Selection.
5
In the New Cumulative Selection dialog box, type Polysilicon in the Name text field.
6
Click OK.
7
In the Settings window for Part Instance, click to expand the Boundary Selections section.
8
Click New Cumulative Selection.
9
In the New Cumulative Selection dialog box, type Proof mass boundaries in the Name text field.
10
Click OK.
11
In the Settings window for Part Instance, locate the Boundary Selections section.
12
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Proof Mass + Fingers Seq
 
√
Proof mass boundaries
Part Link: Spring 1 (pi2)
1
In the Model Builder window, click Part Link: Spring 1 (pi2).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Spring + anchor
 
√
Polysilicon
4
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Spring + anchor
 
√
Proof mass boundaries
Part Link: Spring 2 (pi3)
1
In the Model Builder window, click Part Link: Spring 2 (pi3).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Spring + anchor
 
√
Polysilicon
4
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Spring + anchor
 
√
Proof mass boundaries
Part Link: Sense Electrodes L (pi4)
1
In the Model Builder window, click Part Link: Sense Electrodes L (pi4).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Polysilicon
4
Locate the Boundary Selections section. Click to select row number 1 in the table.
5
Click New Cumulative Selection.
6
In the New Cumulative Selection dialog box, type Sense left boundaries in the Name text field.
7
Click OK.
Part Link: Sense Electrodes R (pi5)
1
In the Model Builder window, click Part Link: Sense Electrodes R (pi5).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Polysilicon
4
Locate the Boundary Selections section. Click to select row number 1 in the table.
5
Click New Cumulative Selection.
6
In the New Cumulative Selection dialog box, type Sense right boundaries in the Name text field.
7
Click OK.
Part Link: Self Test Electrodes L 1 (pi6)
1
In the Model Builder window, click Part Link: Self Test Electrodes L 1 (pi6).
2
In the Settings window for Part Instance, locate the Boundary Selections section.
3
Click New Cumulative Selection.
4
In the New Cumulative Selection dialog box, type Self test left boundaries in the Name text field.
5
Click OK.
6
In the Settings window for Part Instance, locate the Boundary Selections section.
7
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Self test left boundaries
Part Link: Self Test Electrodes L 2 (pi7)
1
In the Model Builder window, expand the Component 1 (comp1)>Geometry 1>Cumulative Selections node, then click Component 1 (comp1)>Geometry 1>Part Link: Self Test Electrodes L 2 (pi7).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Polysilicon
4
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Self test left boundaries
Part Link: Self Test Electrodes R 1 (pi8)
1
In the Model Builder window, click Part Link: Self Test Electrodes R 1 (pi8).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Polysilicon
4
Click to select row number 1 in the table.
5
Locate the Boundary Selections section. Click New Cumulative Selection.
6
In the New Cumulative Selection dialog box, type Self test right boundaries in the Name text field.
7
Click OK.
8
In the Settings window for Part Instance, locate the Boundary Selections section.
9
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Self test right boundaries
Part Link: Self Test Electrodes R 2 (pi9)
1
In the Model Builder window, click Part Link: Self Test Electrodes R 2 (pi9).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Polysilicon
4
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Self test right boundaries
Part Link: Self Test Electrodes L 1 (pi6)
1
In the Model Builder window, click Part Link: Self Test Electrodes L 1 (pi6).
2
In the Settings window for Part Instance, locate the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Electrode array
 
√
Polysilicon
Ground plane (wp1)
In the Model Builder window, collapse the Component 1 (comp1)>Geometry 1>Ground plane (wp1) node.
Cumulative Selections
1
In the Model Builder window, collapse the Component 1 (comp1)>Geometry 1>Cumulative Selections node.
2
In the Model Builder window, collapse the Geometry 1 node.
Definitions
Symmetry plane
1
In the Definitions toolbar, click  Box.
2
In the Settings window for Box, locate the Geometric Entity Level section.
3
From the Level list, choose Boundary.
4
Locate the Box Limits section. In the y minimum text field, type -0.1.
5
In the y maximum text field, type 0.1.
6
Locate the Output Entities section. From the Include entity if list, choose Entity inside box.
7
In the Label text field, type Symmetry plane.
Anchor plane
1
In the Definitions toolbar, click  Box.
2
In the Settings window for Box, type Anchor plane in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Box Limits section. In the z minimum text field, type -tOx*1.01.
5
In the z maximum text field, type -tOx*0.99.
6
Locate the Output Entities section. From the Include entity if list, choose Entity inside box.
Meshing plane
1
In the Definitions toolbar, click  Box.
2
In the Settings window for Box, type Meshing plane in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Box Limits section. In the z minimum text field, type -tOx*0.01.
5
In the z maximum text field, type tOx*0.01.
6
Locate the Output Entities section. From the Include entity if list, choose Entity inside box.