1. Slide 5.1 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Lecture 5 Analysis and design of electro- thermally actuated MEMS Solving three sets of coupled partial differential equations and its implications in design.

2. Slide 5.2 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Contents Overview of thermal actuators Principle of electro-thermal-compliant (ETC) actuation Analysis issues –Thermal modeling Design issues Examples

3. Slide 5.3 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Bimorph effect is used widely… Benecke, W. and Riethmuller, W, 1989, “Applications of Silicon Microactuators Based on Bimorph Structures,” Proceedings of the IEEE MEMS Workshop, Salt Lake City, Utah, Feb. 1989, pp. 116-120. Takeshima, N. and Fujita, H, 1990, “Polyimide Bimorph Actuators for a Ciliary Motion system,” Micromechanical Sensors, Actuators, and Systems, 1991, pp. 203- 209. Chu, W.-H. and Mehregany, M., 1994, “MicrofabricatedTweezers with a Large Griping Force and a Large Range of Motion,” Technical Digest of Solid State Sensors and Actuators Workshop, Hilton Head Island, SC, June 1994, pp. 107-100. Mismatched thermal expansion coefficients of two materials make a bi-material structure bend. Heating is easily achieved in MEMS with Joule heating. The earliest analysis of this goes back to Timoshenko: Timoshenko, S., “Analysis of Bi-metal Thermostats,” J. of the Optical Society of America, Vol. 11, 1925, pp. 233-255.

4. Slide 5.4 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Electro-thermal actuation using a single material structure Guckel, H., Klein, J., Christenson, T., Skrobis, K., Laudon, M., and Lovell, E.G., 1992, ‘Thermomagnetic Metal Flexure Actuators,” Technical Digest of Solid State Sensors and Actuators Workshop, Hilton-Head Island, SC, 1992, p 73. Comtois, J. and Bright, V, 1996, “Surface Micromachined Polysilicon Thermal Actuator Arrays and Applications,” Technical Digest of Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, June 1996, pp. 174-177. Lerch, P, Slimane, C.K., Romanwicz, B., and Renaud, P, 1996, “Modelization and characterization of asymmetrical thermal micro-actuators,” J. Micromechanics and Microengineering, Vol. 6, 1996, pp. 134-137 Moulton, T., 1997, “Analysis and design of Electro-Thermal-Compliant micro devices” Center for Sensor Technologies at the university of Pennsylvania technical report #TR-CST31DEC97, pp.13-26. Keller, C.G. and Howe, R.T., 1997, “Hexsil Tweezers for Teleoperated Micro-Assembly,” Proc. 10th Annual International Workshop on Micro-Electro-Mechanical Systems (MEMS '97), Nagoya, Japan, January 26-30, 1997, pp. 72-77. Pan, C. S. and Hsu, W., 1997, “An electro-thermally and laterally driven polysilicon microactuator,” J. Micromechanics and Microengineering, 7 (1997), pp. 7-13. Sigmund, O., “Topology Optimization in Multiphysics Problems,” Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium, Vol. 3, St Louis, August 1998, pp. 1492-1500. Cragun, R. and Howell, L.L., “A Constrained Thermal Expansion Micro-Actuator,” Proceedings of the Micro-Electro- Mechanical Systems (MEMS) Symposium at the International Mechanical Engineering Congress and Exhibition, DSC- Vol. 66, pp. 365-371. Huang, Q. and Lee, N., “Analysis and Design of Polysilicon Thermal Flexure Actuator,” J. Micromechics and Microengineering., Vol. 9, 1998, pp. 64-70. Comtois, J. H., Michalicek, M.A., and Barron, C.C., “ Electrothermal actuators fabricated in four-level planarized surface micromachined polycrystalline silicon.” Sensors and Actuators A Physical, Vol. 70, 1998, pp 23-31.

5. Slide 5.5 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Electrical actuation by applying an voltage. Joule heating causes thermal loads. The structure is flexible. They are small. Electro-Thermal-Compliant MEMS

6. Slide 5.6 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Actuator and mechanism are together. Moulton, T. and Ananthasuresh, G.K., “Design and Manufacture of Electro-Thermal-Compliant Micro Devices,” Sensors and Actuators, Physical, 90 (2001), pp. 38-48. Temperature Embedded ETC actuation

7. Slide 5.7 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh V Bends up (Guckel et al., 1992; Comtois and Bright, 1996) Temperature In series connection

8. Slide 5.8 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh V Bends down (Moulton and Ananthasuresh, 1997) Temperature In parallel connection

9. Slide 5.9 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Prototype in the series mode

10. Slide 5.10 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh 25 um diameter gold wire Prototype in the parallel mode

11. Slide 5.11 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Changing electrical resistivity with doping (if made with silicon)

12. Slide 5.12 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Changing the length of the flexure Bends downwards

13. Slide 5.13 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh ETC expansion building block

14. Slide 5.14 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh With three degrees of freedom; Made using MUMPs, polysilcon. Parallel micro manipulator

15. Slide 5.15 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh V Analysis of ETC devices Fixed Traction force Specified temperature Thermal flux Specified voltage

16. Slide 5.16 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Three analyses ElectricalVoltage and current Thermal Joule heating term Temperature Thermo-elastic Deformation, stresses, and strains. Temperature The equations are coupled because… -- almost all properties are temperature-dependent -- deformation can effect thermal boundary conditions (e.g., convection and radiation)

17. Slide 5.17 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Electrical analysis: steady-state equilibrium equations Strong form Weak form = voltage = electrical conductivity = “virtual” voltage

18. Slide 5.18 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Thermal analysis: Steady-state equilibrium equations Joule heating  Convection and radiation  Fixed temperature = Temperature = thermal conductivity = “virtual” temperature Strong form Weak form

19. Slide 5.19 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Thermo-elastic analysis: static equilibrium equations = stress = elastic constitutive properties = deformation = stress = virtual deformation = thermal strain = thermal expansion coefficient = ambient temperature Strong form Weak form

20. Slide 5.20 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Convection –Temperature dependence of heat transfer properties. –Size dependence of heat transfer properties. Radiation –View / Shape factors. –Radiation heat transfer between parts of the same device which are at different temperatures. Boundary Conditions –Essential Boundary conditions at the device anchor. –Natural Boundary conditions at the device anchor. Conduction through trapped air volume –Conduction between parts of the same device at different temperature with an intervening trapped air volume. –Conduction from the underside of the device to the substrate through the air trapped between them. Temperature dependence of thermo-physical Properties Issues in thermal modeling

21. Slide 5.21 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Thermal Expansion Device (TED), Cragun & Howell (1998) Without convection or radiation With convection and radiation Why is convection so important?

22. Slide 5.22 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Essential vs. natural boundray conditions Silicon Device SiO 2 Silicon Handle Glass Ground Essential boundary conditions Thermally Grounded Natural boundary conditions Not Thermally Grounded Having one or the other makes a big difference.

23. Slide 5.23 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh 20 node, 3-D Continuum finite elements in ABAQUS Fully Coupled Electro-Thermal Analysis Sequentially Coupled Thermo-Elastic Analysis With temperature dependent material properties and heat transfer coefficients. Scaling effects are quite significant Mankame, N. and Ananthasuresh, G. K., “Comprehensive Thermal Modelling and Characterization of an Electro-Thermal- Compliant Microactuator,” J. Micromechanics and Microengineering, Vol. 11, 2001, pp. 452-462. Meso Micro For the same maximum temperature, meso (up to a cm) scale device provides more deflection.

24. Slide 5.24 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Experimental validation of temperature distribution

25. Slide 5.25 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Dealing with more complicated geometry…”line element” modeling R1R1 R4R4 R3R3 R2R2 Electrical Model Narrow arm, seg. 1 End connection, seg. 2 Wide arm, seg. 3 Flexure, seg. 4 T in T out Thermal Model Beam 1 Beam 2 Beam 4 Beam 3 Encastre supports Thermo-elastic Model

26. Slide 5.26 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Thermal insulation Mechanical constraint Desired displacement Thermal insulation Mechanical constraint Desired displacement V Heat flux Thermal insulation Mechanical constraint Desired displacement Uniform temperature rise Non-uniform temperature with external heating Non-uniform heating with voltage (Joule heating) Objective Output disp. Outdisp & temp. Outdisp., temp. & current Three types of problems Electro-thermal-compliant design

27. Slide 5.27 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Output displacement V M1M1 M2M2 MnMn With multiple materials

28. Slide 5.28 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Convection Material properties Design parameterization

29. Slide 5.29 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Weak form of the thermal equilibrium equation: h convection heat transfer coefficient Output displacement Hole created during optimization fixed Heat flux convection e Convection through element surfaces only if the neighboring elements are empty Interpolation of convection

30. Slide 5.30 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Minimize Optimization problem

31. Slide 5.31 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh First Variation of the Lagrangian = 0  Adjoint temp.: Adjoint disp.: Optimality criteria Adjoint volt.: Solve from bottom to top

32. Slide 5.32 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Lagrangian multiplier for volume constraint: k is iteration number Step lengthMove limit Variable update scheme Solved in an inner loop

33. Slide 5.33 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Intuitive Non- intuitive Uniform heating with one material

34. Slide 5.34 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Red color stiffer material Blue color flexible material only the top portion of the square design domain is utilized Since the objective is to maximize the downward displacement, it helps if the middle bar expands less Uniform heating with two materials

35. Slide 5.35 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Intermediate material to prevent heat flow to the output port specifications Optimal topology Initial temp. profilefinal temp. profile Non-uniform heating with heat flux input

36. Slide 5.36 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Side convection has two effects on the topology optimization: to make boundary smoother to preserve heat; to make boundary rougher to dissipate heat. Only top and bottom convectionNo convection Temperature profiles Side surface as well as top and bottom convection Effect of convection

37. Slide 5.37 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh ETC design example 1 Single material

38. Slide 5.38 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh ETC design example 2 Single material Two materials

39. Slide 5.39 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh ETC design example 3

40. Slide 5.40 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Penalty to be added to the objective to run optimization again… Eliminating the “intermediate” material

41. Slide 5.41 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Single material Two materials ETC design example 4

42. Slide 5.42 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Subtrate silicon Thin deposited metal (seed layer) Electroplated metal After shallow maskless etching of metal and deep etching of the substrate from underneath Micro-structure with in-plane heterogeneity Side viewsFirst trial with Si and gold Silicon Gold Microfabrication of structures with in-plane heterogeneity

43. Slide 5.43 Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Main points Three analyses need to be done to simulate ETC devices Thermal modeling is not trivial Ideas from design in single energy domain easily extend to multiple energy domains –Adjoint method is powerful