Dynamic behavior of thin silicon plate: Application to silicon sensors
Abstract
The small amplitude deflection of thin silicon plates are modeled by means of a Lagrange/Newton's equation. An approximated polynomial solution is obtained from the virtual displacement theorem, for rectangular plates fully clamped on their edges. For free vibration, the expression of the first fifteen natural modes of vibration are given. The responses to uniform harmonic, step and pulse type excitations are computed. Validation of the model is achieved with the help of capacitive structures realized using micro electronic and micro machining of silicon. The twenty to forty micron thick silicon membrane and a rigid metallic plate are assembled to obtain a variable capacitor. Using these devices as mixer and modulator, the first for natural modes of vibration are characterized. The application of the model to the analysis of the dynamic behavior of the piezoresistive and capacitive pressure sensors shows that they can be assimilated to second order systems when submitted to uniform pressure steps. The response time of pressure sensors is minimized by increasing the rectangularity ratio of the membranes and by realizing the latter in silicon rather than steel.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- August 1990
- Bibcode:
- 1990PhDT........21P
- Keywords:
-
- Displacement;
- Dynamic Characteristics;
- Euler Equations Of Motion;
- Pressure Sensors;
- Soi (Semiconductors);
- Vibrational Spectra;
- Proving;
- Remote Sensors;
- Silicon Films;
- Silicon Transistors;
- Instrumentation and Photography