Homework #4
Assigned: Jan. 25th, 2005
Due: Feb. 1st, 2005
Points: 20

Please look at practice4.pdf before you begin to work on this homework.

1. 10 points
   Problem 3.4 in the textbook. (Reproduced below for your convenience.)
   When KOH etching is used on 500 um thick (100) oriented silicon wafer,
   • what mask feature size is required to produce a 400 um squarediaphragm of thickness 20 um?
   • what is the edge-length variation for the diaphragm if the actual wafer thicknness for different wafers varies between 490 and 510 um?
   • assuming that the sensitivity of a pressure sensor varies as the inverse fourth power of the diaphragm edge-length, what percentage variation in sensitivity can be attributed to variations in wafer thickness?
   The last sub-question above tells us how an analytical model is model useful in assessing the model performance than the simulaion results from 3-D analysis. That is, knowing the inverse fourth power relationship is more useful here than being able to simulate the sensitivity using the 3-D geometry using a software program.
2. 10 points
   Sandia lab's SUMMiT V process helps make very sophisticated micromechanisms consisting of gears and linkages. Central to this process is a nice in-plane revolute (pin) joint that has very little play (clearance) in radial as well as axial directions. The layer thicknesses in this process and the approximate desired cross-section of the revolute joint are shown below. Draw the masks and process flow with cross-section. Note that SUMMiT V uses two planarization steps, which are indicated with CMP in the figure below.