## Design, Simulation and Modeling of a Micromachined U-shaped Cantilever Device for Application in Magnetic Field Detection
Talha Mohammed, Waddah Abdelbagi
(2009)
## AbstractThe research explores the potential applicability of the Lorentz force actuation of a MEMS based U-shaped cantilever which is made entirely of aluminum. The main objective of the study is to design, simulate and derive mathematical models for the behavior of the cantilever. The design is based on CMOS fabrication technology and bulk micromachining implemented in CoventorWare simulation environment using a Si substrate and SiO2 insulating layer supporting the Al U-shaped cantilever. Analytical models describing 3-D vibration modes (mode 1, 2 and 3) of the cantilever and their verification by simulation are discussed based on the direction of the current through the cantilever and the direction of the orthogonal external magnetic field. The response of the cantilever is discussed in two situations: static and dynamic. The static motion is obtained w hen a constant force, representing the Lorentz force due to a direct current through the cantilever placed in a static magnetic field, is applied. On the other hand, the dynamic vibration is realized when a periodic force is applied representing the Lorentz force due to a static external magnetic field acting on an alternating current through the cantilever. Results show that the displacement of the cantilever is significantly large indicating that high sensitivity can be achieved when it is driven at its resonant frequency. Three resonant frequencies were obtained for the three modes of vibration of 3, 8 and 86.6 kHz for mode 1, 2 and 3 respectively when the thickness is 5 µm, width is 20 µm, length of the base is 760 µm and length of the arm is 1000 µm. Results show the resonant frequency and sensitivity of mode 1 depend on the thickness and length of the arms only, mode 2 depends on the length of the base, length of the arms and thickness. While the resonant frequency and sensitivity of mode 3 are depend on the length of the base, length of the arms and width. The displacement as a function of the applied force is shown to be perfectly linear. The quality factors (Q-factor) of the system for the three modes were determined to be the same at the same damping coefficient. The systems response is found to decrease exponentially with increasing damping. Finally polysilicon piezoresistors in Wheatstone’s bridge configuration is used to convert the response of the cantilever to electrical measurements at various voltages for different dimensions of the cantilever. The highest sensitivity of about 64 V/T without amplification is obtained for a thin beam of 0.6 m polysilicon embedded in 2 µm thick silicon cantilever beam.
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