Use the following data. L = 200 um; w = 5 um; thickness = 3 um; l = 20 um; b = 3 um; g = 2 um; and p = 4 um. Young's modulus and Poisson's ratio are 150 GPa and 0.25, respectively.
Compute the voltage required to get a displacement of 2 um of the central shuttle using the lumped model analysis for mechanical and electrostatic behavior. The figure shows only five moving combs on each side. If more combs are used to fill the entire length, how much voltage is needed?
Perform a coupled analysis in FEMALB using planar (2-D) model and obtain the voltage required for 2 um displacement. First use only five moving combs. Explain any discrepancy between the results obtained with the lumped model and the finite element analysis. Then, try the maximum number of combs possible along the length. Observe how the computation time increases as you add more combs and make the device more complex.
Perform 3-D analysis of the above problem in FEMLAB. Next, include a ground plane (much larger in size than the footprint of the comb-drive's suspension and combs) with a gap of 2 um below the plane of the comb-drive. Do you see any upward curving of the combs? Note that 3-D analysis can take quite a while in FEMLAB.
A micro-cantilever beam is separated by a gap of 3 um from an electrode underneath. The beam has the dimensions: 250 x 15 x 2 um. Its Young's modulus is 160 GPA and Poisson's ratio is 0.23. Compute the maximum deflection for 10 V applied betweent the beam and the electrode using (a) lumped model calculations with fringing field corrections and (b) finite element analysis using FEMLAB.