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Lecture 1b Analysis

Lecture 1b Analysis . …of MEMS and of structures and compliant mechanisms undergoing small and large deformations. Contents. Analysis and simulation of MEMS Deformation and stress analysis of deformable structures

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Lecture 1b Analysis

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  1. Lecture 1bAnalysis …of MEMS and of structures and compliant mechanisms undergoing small and large deformations. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  2. Contents • Analysis and simulation of MEMS • Deformation and stress analysis of deformable structures • Pseudo rigid-body model-based analysis of elastic structures undergoing large deformations Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  3. Hierarchical view of MEMS Ref: Microsystems Design—S. D. Senturia Lab on a chip Digital readout Specimen collector Signal amplifier and processor Plumbing system Reaction chamber Signal transduction Pump Valve Process Flow channel Masks System Device 3 Device 1 …Device nD Device 2 Component 1 Device 1 Process Component 1 Mask 1 Component 2 Mask 2 …Mask nM …Component nC Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  4. Modeling challenges Integration of sensor, actuator, mechanism, processor, power, and communication makes system level tasks challenging -- common representation for multiple energy domains is needed. Device level too has multiple energy domains -- “macromodels” are necessary. Component (physical) level -- coupled energy domain equations need to be solved. Mask level -- geometric modeling has its own difficulties. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  5. Modeling at four levels Ref: Microsystems Design—S. D. Senturia System Representing as block diagrams of multi-domain subsystems Device Redcuced order “macro models” of the components Component (physical) Multiple, coupled energy behavioral simulations Artwork of masks and process Defining mask geometry for the process steps Each level involves design There is “analysis” (forward) problem and “synthesis” (inverse) problem. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  6. Structural analysis of MEMS • Roark’s formulas • Energy methods • Finite element and boundary element analyses • Commercial packaged software are now available exclusively for MEMS • Intellisuite • CoventorWare • Memscap • Etc. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  7. Roark’s formulas Roark’s formulas for stress and strain, Raymond J. Roark, Richard G. Budynas, Warren C. Young, McGraw-Hill, 2001. • These are widely used by MEMS designers • They are very accessible to people with any engineering/science background • Reasonably accurate • Well suited for back-of-the-envelope calculations, which most situations demand in the initial stages • Disadvantage: Large deformations and residual stresses require special attention Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  8. Example: compliant ortho-planar platform Encastered-guided beam d d d The platform moves up and down without rotation. Doing FEA for this is an overkill. Instead, think of simple beam analysis. F Stiffness = Maximum stress: For details, see: Compliant Mechanisms, Howell, L. L., Wiley, 2003. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  9. Approximate solutions using energy methods Mostly Rayleigh-Ritz and Castiglianos methods. Assume a polynomial deflection profile for the beam and obtain coefficients by minimizing the potential energy. Axial stretching is also accounted for. Residual stress effect is also considered. q r The membrane of a pressure sensor Even the spherical approximation is used for large deflection analysis because it is simple and suits capacitance calculation. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  10. Support boundary conditions can be tricky The compliance of the support is to be modeled properly. • Most processes do not give perfect supports as in encastered beams • Especially true of surface micromachined structures It is an artifact of the fabrication process. B B A A B A Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  11. Finite/boundary element analysis of MEMS structures • Several energy domains are coupled and self-consistent solutions need to be obtained. • Aspect ratios (thickness to lateral dimensions) poses problems in meshing. • What commercial MEMS-CAD software do: • Enable model construction from mask layouts and process description to get realistic geometry • Hide FEA related details from the user (e.g., type of elements, imposing boundary conditions, etc.) • Include “wrappers” that communicate between different solvers and the user’s model • Finally, they show cool animations • Lately, some also provide “macromodeling” capability and circuit simulation • Automatic extraction of reduced order models • Simulation of dynamic behavior with equivalent circuit models Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  12. Equivalent circuit modeling of electrostatic MEMS structures (Gary Fedder and Tamal Mukherjee, CMU) Components: Combs, suspension, shuttle mass, anchor, electrodes E.g., electrostatic linear actuator Layout schematic 3-D model (of a portion) Nodas, CMU. SUGAR, Berkeley Circuit schematic Behavioral schematic Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  13. Electro-thermally actuated MEMS Electrical analysis Jy Jx J = current density T = Temperature T Thermal analysis Elastic analysis Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  14. How to handle more complicated geometries? Heavy computational load if FEA is used. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  15. One-dimensional approximation of electro-thermal micro structures Narrow arm, seg. 1 End connection, seg. 2 Flexure, seg. 4 Wide arm, seg. 3 NA Beam1 Encastre supports Beam2 Beam4 Beam3 R1 Tin R2 Tout R4 R3 Electrical Model Thermal Model Elastic Model Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  16. Maizel’s theorem: energy method for thermo-elastic deformations Deformation at a point of interest in a desired direction due to temperature loading Maizel’s theorem = stress tensor due to unit load applied at point of interest in the desired direction Maizel’s theorem is similar to the unit dummy load method used for computing deflection at a point (in a given direction) due to mechanical loads: Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  17. Advantages of equivalent circuit models • Can be embedded into system-level simulators (SPICE-like) • Parameterize the model for design refinement or optimization Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  18. Pseudo rigid-body (PRB) modeling • Approximating an elastic structure using rigid bodies connected with joints and springs. • Reasonable accuracy over large deformations. • Can use the simpler analysis and synthesis techniques of rigid bodies. • Good reduced order models can be obtained. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  19. PRB for a prismatic cantilever beam with a vertical tip load L g L KQ Q F Burns and Crossley, 1968: Burns, R.H. and Crossley, F.R.E., 1968, “Kinetostatic Synthesis of Flexible Link Mechanisms,” ASME Paper No. 66-Mech-5. Accurate up to… Kinematics: Kinetostatics: Howell and Midha, 1995: Howell, L.L., and Midha, A., 1995, "Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms," ASME Journal of Mechanical Design, Vol. 117, No. 1, pp. 156-165. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  20. Example: Fully compliant bistable switch (thermally-actuated) N. Masters and L. L. Howell, JMEMS, Vol. 12, No. 3, 2003, pp. 273-280 d Shuttle Compression beam Switch Thermal actuator Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  21. Principle of bistability and design issues PE = potential energy PE F = actuating force d Design objective: Achieve suitable PE curve with the available actuating force. Unstable Stable 2 Stable 1 Adjusting geometry with FEA is very time-consuming. F d Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  22. Modeling using PRB approach Determining suitable spring constants and lengths (and hence the geometry) using kinematic analysis is much easier! Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  23. Main points • Hierarchical view of analyzing MEMS • System level • Circuit simulation at device level • Detailed domain level simulation • Methods of analysis • Roark’s formulas • Energy methods • Finite element analysis • Pseudo rigid-body analysis Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

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