Homework #3

Assigned: Jan. 29, 2004
Due: Feb. 5, 2004
Points: 40

The figure below shows the suspension of the electrostatic comb-drive. Except the shaded gray region, the rest of the structure is free to move above the substrate separated by a gap.

1. Points: 10
   Obtain the linear stiffness of the suspension in terms of the length L, width w, and the Young's modulus E, and the thickness t, in the vertical direction (i.e., along the axis of symmetry shown in the figure). Obtain the expression for the maximum stress as well.
2. Points: 20
   Use FEMLAB software to check the validity of the above formula via linear finite element analysis. Use E = 150 GPA, nu = 0.25, L = 200 um, w = 5 um, and t = 3 um.
3. Points: 10
   If the failure stress of the material (polysilicon) is 900 MPa, what is the maximum vertical deflection of the central mass before the failre state is reached? Once again, do a calculation and then verify with FEMLAB's results.