Homework #5
Assigned: Feb. 13th, 2009
Due: Feb. 19th, 2009
Points: 20

• Problem 1: 10 points
  A 100 um by 100 um square silicon plate of thickness 5 um is suspended over an etched cavity. It is suspended by four beams connected to its corners. The length, width, and the thickness of the beams are 100 um, 5 um, and 5 um. A potential difference of 5 V is applied across the diagonally opposite beams. Use lumped modeling approach to estimate the steady-state temperature of the plate and the time it takes for it to reach that temperature. Do this problem with and without taking convection into account. You may ignore radiation effects. For convection heat transfer coefficients, you need to look up heat transfer book! For that extra effort, you will get extra points!! Please include the sources and your justification for using it.
  Use the following data:
  
  • Electrical conductivity = 1500 Siemens/m
  • Temperature coefficient of resistance = 2500E-6 /K
  • Density = 2330 kg/m³
  • Specific heat = 712 J/(Kg-K)
  • Thermal conductivity = 148 W/(K-m)
• Problem 2: 10 points
  What effect would the heating have on the plate in terms of its mechanical behavior? At what voltage do you expect this plate to buckle out of plane? Lumped modeling is fine as long as you state your assumptions. Use 2.8E-6 /K for the thermal expansion coefficient of silicon.