Frequency softening of an electrostatically actuated beam

#### Author

Parmeshwar Prasad

#### Date

Nov 29, 2014 2:53:53 AM

#### Company

CeNSE

#### Version

3

### Summary

Frequency softening of an electrostatically actuated fixed-fixed Silicon

Nitride beam structure is studied.

Contents

1. |  | Global Definitions
1.1. |  |  | Parameters 1
2. |  | Component 1 (comp1)
2.1. |  |  | Definitions
2.2. |  |  | Geometry 1
2.3. |  |  | Materials
2.4. |  |  | Electromechanics (emi)
2.5. |  |  | Mesh 1
3. |  | bias
3.1. |  |  | Parametric Sweep
3.2. |  |  | Stationary
3.3. |  |  | Eigenfrequency
4. |  | Results
4.1. |  |  | Data Sets
4.2. |  |  | Derived Values
4.3. |  |  | Tables
4.4. |  |  | Plot Groups

## 1. Global Definitions

### 1.1. Parameters 1

Parameters
Name | Expression | Description
--- | --- | ---
W1 | 1[um] | width
L1 | 10[um] | length of the beam
L2 | 40[um] | length of the pads
W2 | 1[um] | width of the pads
T1 | 1[um] | thickenss of the beam and substrate
T2 | 2[um] | thickness of the pads
Vdc | 200[V] | DC Voltage appliead

## 2. Component 1 (Comp1)

### 2.1. Definitions

#### 2.1.1. Selections

##### OuterContactPads

Selection type
Explicit

Selection
Domains 3, 14

##### InnerContactPads

Selection type
Explicit

Selection
Domains 6, 11

##### BoundaryInnerContactPads

Selection type
Adjacent

Selection
Boundaries 23–26, 35, 38, 52–55, 66, 69

##### BoundaryouterContactPads

Selection type
Adjacent

Selection
Boundaries 9–12, 14, 16, 74–77, 79, 81

##### SiN

Selection type
Explicit

Selection
Domains 2, 4–5, 7–10, 12–13

##### PolySi

Selection type
Explicit

Selection
Domains 3, 6, 11, 14

##### Air

Selection type
Explicit

Selection
Domain 1

#### 2.1.2. Coordinate Systems

##### Boundary System 1

Coordinate system type | Boundary system
Identifier | sys1

### 2.2. Geometry 1

Geometry 1

Units
Length unit | µm
Angular unit | deg

### 2.3. Materials

#### 2.3.1. Air

Air

Selection
Geometric entity level | Domain
Selection | Domain 1

#### 2.3.2. Poly-Si

Poly-Si

Selection
Geometric entity level | Domain
Selection | Domains 3, 6, 11, 14

#### 2.3.3. Si3N4

Si3N4

Selection
Geometric entity level | Domain
Selection | Domains 2, 4–5, 7–10, 12–13

### 2.4. Electromechanics (Emi)

Electromechanics

Features
Free Deformation 1
Electrical Material Model 1
Zero Charge 1
Free 2
Electromechanical Interface 1
Prescribed Mesh Displacement 1
Linear Elastic Dielectric 1
Initial Values 1
Linear Elastic Material 1
Fixed Constraint 1
Fixed Mesh 2
Electric Potential 1
Electric Potential 2

### 2.5. Mesh 1

Mesh 1

## 3. Bias

### 3.1. Parametric Sweep

Parameter name: Vdc

Parameters:

### 3.2. Stationary

Study settings
Property | Value
--- | ---
Include geometric nonlinearity | On

Mesh selection
Geometry | Mesh
--- | ---
Geometry 1 (geom1) | mesh1

Physics selection
Physics | Discretization
--- | ---
Electromechanics (emi) | physics

### 3.3. Eigenfrequency

Study settings
Property | Value
--- | ---
Include geometric nonlinearity | On

Mesh selection
Geometry | Mesh
--- | ---
Geometry 1 (geom1) | mesh1

Physics selection
Physics | Discretization
--- | ---
Electromechanics (emi) | physics

## 4. Results

### 4.1. Data Sets

#### 4.1.1. Solution 1

Solution
Name | Value
--- | ---
Solution | Solver 1
Component | Save Point Geometry 1

Data set: Solution 1

#### 4.1.2. Solution 2

Solution
Name | Value
--- | ---
Solution | Store Solution 2
Component | Save Point Geometry 1

Data set: Solution 2

#### 4.1.3. Solution 3

Solution
Name | Value
--- | ---
Solution | Parametric 3
Component | Save Point Geometry 1

Data set: Solution 3

### 4.2. Derived Values

#### 4.2.1. Global Evaluation 1

Data
Name | Value
--- | ---
Data set | Solution 3

Expression
Name | Value
--- | ---
Expression | emi.freq
Unit | Hz
Description | Frequency

### 4.3. Tables

#### 4.3.1. Evaluation 3D

Interactive 3D values

Evaluation 3D
x | y | z | Value
--- | --- | --- | ---
6 | 1.09769 | 2.07095 | 1.91234e-20

#### 4.3.2. Table 1

Global Evaluation 1 (emi.freq)

Table 1
Vdc | Frequency (Hz)
--- | ---
0 | 5.279e6
50 | 5.26937e6
100 | 5.24075e6
150 | 5.19399e6
200 | 5.13047e6
250 | 5.05203e6
300 | 4.96082e6
350 | 4.85899e6
400 | 4.74816e6

### 4.4. Plot Groups

#### 4.4.1. Displacement (Emi)

Vdc(4)=150 Eigenfrequency=5.193995e6 Surface: Total displacement (µm)

#### 4.4.2. Potential (Emi)

Vdc(4)=150 Eigenfrequency=5.193995e6 Slice: Electric potential (V) Streamline: Displacement field (Material) Contour: Electric potential (V)

#### 4.4.3. 1D Plot Group 9