1. Project #3: Design of a MEMS Vertical Actuator Jianwei Heng Alvin Tai ME128 Spring 2005

2. Introduction The MEMS vertical actuator described in this project consists of a center mass with a flat surface and is supported by simple flexures arranged symmetrically around the center mass. The device uses electrostatic comb structures to displace the flat surface.

3. Introduction Design constraints Active Constraints  Minimum width of structure  5  m  Minimum gap  5  m  Thickness of the device  50  m  Minimum diameter of center mass  200  m  E =160 GPa   =2.33 gm/cm 3  Maximum DC input voltage = 30 V  Maximum die area, A d  10mm 2 

4. Introduction Design Constraints Inactive Constraints  Minimum displacement under max voltage: 20  m  Maximum DC acceleration survival, a max  2,000g  Maximum stress in suspension,  max  1.6 GPa  Bandwidth of the device  1 kHz (resonance frequency)

5. Approach to Problem Observations To fully maximize mass displacement, it is desirable to design a system with:  Minimum spring constant, k By using a circular center mass, we can maximize the spring length/constant  Maximum amount of combs, N  Maximum overlapping comb distance, t

6. Approach to Problem From the force equation, We can easily observe that it is a function of N and t: F = f(N,t) With our area constraint active, there is a direct effect on one variable when the other is modified (as t is decreased, N can be increased and vice versa). Therefore, a compromise must be realized.

7. Approach to Problem If t is designed too large, the combs may deflect. Conversely, if t is too small, the gaps between the combs become significant and limits the number of combs in our system. t  200  m >> 5  m t>>5  m t  5  m

8. Approach to Problem 1. Used MATLAB to get a preliminary analysis of the design  Calculated k using Euler-Bernoulli Beam Theory (guided/fixed beam)  Optimized comb overlap, t  Calculated displacement 2. Built the model in Solidworks to verify that it satisfies all constraints  Used static and frequency analysis to check constraints

9. Approach to Problem Formation of final design We initially set the thickness = 50  m as an active constraint, but that resulted either in deflections that are too small, or resonant frequencies that are too small. Since actuating a maximum of 20  m requires the thickness to be 30  m (to allow for significant comb overlap when fully displaced), we changed the thickness constraint from active to inactive! Then we redesigned the actuator with thickness = 30  m

10. Final Design Final Design of the Actuator

11. Final Design Final Design of the Substrate

12. Final Design Spring and Center massCombs design

13. Final Design Deflection when 30V force applied >20um Min DC displacement under Max DC voltage SATISFIED

14. Final Design Max Stress when 30V force applied >150MPa <1.6GPa Max Stress in suspension Min Deformation stress (Part B) SATISFIED

15. Final Design Max Stress points

16. Final Design Max Stress when 30V force applied Max DC acceleration survival SATISFIED <1.6GPa

17. Final Design Resonant Frequencies for Modes I to V

18. Approach to Problem  Although the resonant frequency requirement fails in Mode I, the actuator is unlikely to exhibit this characteristic motion due to the forces applied.  Hence we can rule out Mode I.

19. Approach to Problem  More importantly, Mode II resonant frequency = 1244.2Hz > 1kHz.  Since the motion in Mode II is the most likely one, we can conclude that the actuator will fulfill the resonant frequency requirement stipulated. Resonant Frequency Requirement SATISFIED

20. Final Design FEM constraints Displacement (satisfied) Maximum acceleration shock test (satisfied) Maximum Stress (satisfied) Minimum Deformation Stress, Part B (satisfied) Resonant Frequency (satisfied) Concerns Base structure analysis: instability issues involving comb contact