Characterization and modeling of 3-D vibration modes of a micromachined U-shaped cantilever

The present work explores the potential applicability of the Lorentz force actuation of a micromachined U-shaped cantilever device for 3-D vector magnetic field measurements in a broad range of frequencies. The structures simulated are made entirely from aluminum and designed using CMOS fabrication technology and bulk micromachining in CoventorWare simulation environment. Analytical models describing 3-D cantilever vibration modes that are actuated by the Lorentz force and their verification by simulation is discussed. Results show that the resonant frequencies for mode 1 and 2 increase with increasing thickness of the cantilever while it is independent of the thickness for mode 3. On the other hand the resonant frequency for mode 3 increases with increasing width of the cantilever while it is independent of width for mode 1 and 2. It is also observed that the displacement of the cantilever for identical applied Lorentz force is highest, indicated highest sensitivity, for mode 1 and lowest for mode 3.