C245 Homework 4

Due 3/9/05

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  1. Calculate the deflection vs. applied voltage for a Comtois-style "heatuator".  You'll be making a lot of bad approximations, which ultimately balance out reasonably well and give a reasonable approximation to the measured deflection.  Lhot=240u, Lcold=40um, Whot=Wcold=2um, tfilm=2um, rhosi=4e-3ohm-cm, TCEsi=2.3e-6/K, Esi=150GPa, kappaSi=160W/m*K, kappa_air=0.03W/m*K.  You may find Rob Conant's paper on thermal actuators to be a useful reference for this problem.
    1. Calculate the resistance of the hot arm. (resistance actually varies as a function of temperature and strain)
    2. Calculate the power dissipated in the hot arm as a function of the applied voltage.
    3. Estimate the thermal conductance along the length of the hot arm.
    4. Estimate the thermal conductance to the substrate
    5. Assuming all of the power dissipated in the hot arm enters at the tip (bad assumption) and flows through the two conductances above in parallel to thermal ground (bad assumption), calculate the temperature rise at the tip of the beam.
    6. Assuming that the whole beam heats up uniformly to the temperature calculated above (bad assumption), calculate the strain and resulting axial force in the beam due to thermal expansion if the hot beam is not allowed to expand.
    7. Calculate the moment applied to the end of the short/cool beam.
    8. Calculate Kqq for the short beam, and the resulting angular deflection, ignoring the other spring constants in the problem (not such a bad assumption, but assuming that E is constant is a bad assumption).
    9. Write down the lateral tip deflection as a function of applied voltage.
    10. Which of your assumptions do you think is the most bogus?
  2. You have a 1mm square parallel plate capacitor with a 1 micron air gap.  With 150V across the gap, what is the force closing the gap?  What thickness of silicon (1mm square) would generate the same force (weight) in a 1 g field?  What is the "electrostatic pressure" (force per area) in Pascals?  Atmospheres? 
  3. You have a gap closing actuator of length Lc on the end of a cantilever of length Lb, both etched into a 40 micron thick SOI film.  Assume that the actuator beams are rigid, and that the beam width and the initial electrostatic gap are 2 microns.  Calculate the pull-in voltage when:
      1. Lb=1000 microns, Lc=100 microns
      2. Lb = 100 microns, Lc=1000 microns
      3. Lb=Lc=100microns
  4. Same problem, but use sugar.  Compare your hand analysis and sugar answers.
  5. Design and lay out a large-displacement electrically driven actuator with the following properties:
    1. Your design must fit inside a square one millimeter on a side
    2. The process used is Matt Last's single-mask SOI with all of the design rules he gave in his lecture.
    3. You may use as many different electrical contacts as you wish, but to win the contest you must be able to run your design in air with no more than 6 electrical contacts
    4. Displacement must be static and repeatable, i.e. you must be able to apply a sequence of voltages/currents and measure a deflection for at least 5 seconds, then apply a sequence of voltages/currents and return to the original position, and repeat this three times.  The "official" deflection will be the *minimum* of the 3 sequential deflections measured.


(Kris Pister)