1. EE 5323 – Nonlinear Systems, Spring 2012 MEMS Actuation Basics: Electrostatic Actuation Two basic actuator types: Out of Plane(parallel plate) In Plane (lateral rezonator) Vz k V=0-150V V=0 F N=15 D gap =4µm

2. EE 5323 – Nonlinear Systems, Spring 2012 MEMS Actuation Basics: Electrostatic Actuation Out of plane actuator VZo-Z k Z V Zo 0.33 Zo V snap Unstable Stable Hard Stops Problem: Snap-down occurs in 2/3 of the travel range.

3. EE 5323 – Nonlinear Systems, Spring 2012 MEMS Actuation Basics: Electrostatic Actuation Out of plane actuator VZo-Z k Solutions: Use hard stops: reduced range of motion Use charge control: requires on-chip circuitry Stiffening mechanical spring: increases required voltage

4. EE 5323 – Nonlinear Systems, Spring 2012 MEMS Actuation Basics: Electrostatic Actuation Out of plane actuator VZo-Z k Solutions: Use hard stops: reduced range of motion Use charge control: requires on-chip circuitry Stiffening mechanical spring: increases required voltage

5. EE 5323 – Nonlinear Systems, Spring 2012 MEMS Actuation Basics: Electrostatic Actuation In plane MUMPS or DRIE comb drive Linearized comb model V=0 V=0-150V V=0 F N=15 D gap =4µm Damping is given by a Couette flow Model. High K => High Q, high force. Low K => High displacement.

6. EE 5323 – Nonlinear Systems, Spring 2012 MEMS Actuation Basics: Electrostatic Actuation General Formula T – actuator thickness X o – finger engagement L – finger length H(x)=g(x)-f(x+L-x o ) – gap function Only if the fingers are sufficiently Parallel to one another. stationary movable xoxo g(x) f(x+L-x o ) L x

7. EE 5323 – Nonlinear Systems, Spring 2012

11. MEMS Actuation Basics: Electrostatic Actuation Example

12. EE 5323 – Nonlinear Systems, Spring 2012

16. MEMS Actuation Basics: Electrothermal Principle: Electrical current  Joule Heating  Thermal expansion  Deflection and Force Thermal governing equation: Fourier (Heat) Equation: E - Thermal energy stored W - Power Generated by Joule Heat H - Heat Transferred to surroundings C- volumetric specific heat - thermal conductivity K – convection coefficient

17. EE 5323 – Nonlinear Systems, Spring 2012 Electrothermal MEMS bimorph If the driving input is voltage applied: “cold” arm “ hot” arm Elements n-1, n, n+1 FEA Approximation Model: In which Rn is the resistance of the n-th element which depends on temperature +V-

18. EE 5323 – Nonlinear Systems, Spring 2012 Thermal Bimorph: Electro-Thermal-Mechanical Model The full linearized model is expressed by: In this equation and are vectors containing positions and temperature of the elements, while M, B, K, N, and  are tri-diagonal matrices. The governing equations are non-linear. An FEA package will simply integrate the equations using many elements to provide a solution.

19. EE 5323 – Nonlinear Systems, Spring 2012 Electrothermal MicroActuators Rotary stage, tooth gap – 6 µm [Skidmore00] Translation stage, scanning mirror 30 µm [Sin04] Precision guided MEMS flexure stage And microgrippers using flexible hinges

20. EE 5323 – Nonlinear Systems, Spring 2012 Silicon MEMS devices: Linear Stage Electro-thermal actuation Back-bent for power-off engagement 0.6mm / second operation speed

21. EE 5323 – Nonlinear Systems, Spring 2012 Micro Optical Bench Assembly

22. EE 5323 – Nonlinear Systems, Spring 2012 Fiber Alignment – “Pigtailing” 1XN V-Groove array Pigtailing with Ferrules

23. EE 5323 – Nonlinear Systems, Spring 2012 Nonlinearities during Fiber Alignment Light transmission loss is parabolic with d and  Alignment Algorithms: Model Based Alignment Conical/circular scanning Gradient Based Methods MBA decreased search time by a factor of 10 [Sin03]

24. EE 5323 – Nonlinear Systems, Spring 2012 Fiber Alignment Algorithms Model-based alignment method  Gradient-based search  Conical scanning search 

25. EE 5323 – Nonlinear Systems, Spring 2012 Optical Fiber Insertion Into Ceramic Ferrule Experimental setup Connector hole with fiber

26. EE 5323 – Nonlinear Systems, Spring 2012 Optical Fiber Insertion Into Ceramic Ferrule Measured Computed Laser intensity around the hole of connector Laser intensity during insertion

27. EE 5323 – Nonlinear Systems, Spring 2012 Textbook Readings for Week 2 Chapter 2 from Slotine & Li text Chapters 1,2 from F. Verlhurst Chapters 1,2 from M. Vidyasagar