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微機電分析 MEMS Actuator Cantilever Beam

微機電分析 MEMS Actuator Cantilever Beam. 報告人：劉俊昇. Reference Introduction. 1-Dimensional Model. Pull-in voltage. The system will be unstable when a moving plate is displaced g 0 /3. 2-Dimensional Model. Bernoulli-Euler beam bending theory

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微機電分析 MEMS Actuator Cantilever Beam

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  1. 微機電分析MEMS Actuator Cantilever Beam 報告人：劉俊昇

  2. Reference Introduction

  3. 1-Dimensional Model • Pull-in voltage

  4. The system will be unstable when a moving plate is displaced g0/3

  5. 2-Dimensional Model • Bernoulli-Euler beam bending theory (1)small deflection for which the radius of curvature equals the inverse of the second-derivative of deflection (2)no shear deformation from the transverse loading (3)no in-plane curvature adjustment due to transverse extension or compression of the thickness

  6. (4)the supports are ideally fixed (5)membrane effects from stress-stiffening are negligible (6)anticlastic curvature along a beam’s width w is geometrically insignificant • The coupled electromechanical equation where the fringing-field correction ff = 0.65g/w for cantilevers (stress-free) for beams

  7. Algebra equation B : bending parameter S : stress parameter • Simulation methods (1)finite-difference MATLAB scripts (2)Rayleigh-Ritz energy methods

  8. Table 1. Closed-form M-TEST models for ideal test structures

  9. Table 2. Numerical constants used in Table 1

  10. 3-Dimensional Model • The effects which should be considered id 3D model (1)Plate Effect (2)Support Compliance (3)Stress-Gradients Through Film Thickness • Plate effect (2D Bernoulli-Euler mechanics)

  11. Support Compliance • Built-in support found in conformal deposition processes of MEMS fabrication • Built-in residual stress (1)Increase structure compliance (2)Increase rotate in the presence of external moments

  12. Stress-Gradients Through Film Thickness • Nonuniform stresses in the film thickness create built-in moments, which is released cantilevers cause them to curl out of plane.

  13. Because the stress-gradients is assumed to be uniform in-plane • Due to linearity for small deflections • Modified coefficient for VPI

  14. Modeling Using the Graphical User Interface 2D Version

  15. Model Navigator • 2D Multiphysics： • MEMS Module>Structural Mechanics>Plane Strain • COMSOL Multiphysics>Deformed Mesh>Moving Mesh (ALE) • Frame (ale) MEMS Module>Electrostatics> Electrostatics

  16. Geometry Modeling • Options>Axes/Grid Settings Clear Axis equal check box • Draw Rectangle/Square(holding shift and click)

  17. Physics Settings for Electrostatics • Multiphysics>Electrostatics (emes) • Subdomain Settings Physics>Subdomain Settings (1)Subdomains 1, 3, and 4 default settings εr = 1(for air) (2)Subdomain 2  εr = 4.5(for polysilicon) Force tab>enter variable Fes

  18. Boundary Conditions Physics>Boundary Settings (1)select the Interior boundaries check box (2)enter boundary conditions in the table below

  19. Physics Settings for Moving Mesh • Multiphysics>Moving Mesh (ale) • Subdomain Settings (1)Subdomains 1, 3, and 4 Keep the default Free displacement setting (2)Subdomain 2 use Physics induced displacement enter variable dx=u, dy=v

  20. Boundary Conditions (1)Enter themesh displacements, dx and dy (2)Do not assign any settings for interior boundaries, which appear dimmed

  21. Physics Settings for Plane Strain • Multiphysics>Plane Strain (smpn) • Physics>Properties Large deformation select On • Subdomain Settings (1)Subdomain 2enter the following settings pull-in voltageuse nonlinear parametric solver (2)Subdomains 1, 3, and 4clear the Active in this domain check box

  22. Boundary Conditions (1)verifythe Interior boundaries check box is cleared (2)Constraint tab Boundary 3Constraint conditionFixed (3)Load tab Boundary 3,6,8Value/expression FX=0, FY=0 (4) Boundary 4Value/expression FX=Fes_nTx_emes , FY=Fes_nTy_emes

  23. Mesh Generation • Mesh>Mapped Mesh Parameters • Boundary tab Select boundaries and click Constrained edge element distribution check box • Enter the value of Number of edge elements (1)Boundaries 1, 3, and 5 5 (2)Boundary 660 (3)Boundary 104 • Click Remesh and then OK

  24. Computing the Solution • Solver>Solver Parameters • Solver list>Parametric>General tab (1)Name of parameterenter Vin (2)List of parameter valuesenter 1:6, 6.1:0.1:6.3 • Click OK and then click Solve on the Main toolbar

  25. Postprocessing and Visualization • Postprocessing>Plot Parameters • To see deformations inside the cantilever beam： • General tabselect the Surface check box and clear other check boxes of plot types • Surface tabPredefined quantities listselect Plane Strain (smps)>Total displacement

  26. To visualize the deformed mesh in the air domain • General tab (1)clear the Element refinement: Auto check box and type 1 in the associated edit field (2)Only the Surface and Geometry edges check boxes are selected (3)Frame listselect Frame (ale) • Surface tab (1)Predefined quantities listselect Electrostatics (emes)>Electric potential (2)Fill style listselect Wireframe

  27. To find the displacement of the cantilever beam’s tip over voltage • Postprocessing>Domain Plot Parameters • Point tab (1)Point selection listselect Point 5 (2)Predefined quantities listselect Plane Strain (smpn)>Y-displacement (smps)

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