Vibration modes of a resonant silicon tube density sensor

We present an investigation of the resonance parameters for a new sensor for on-line measurements of fluid density. The sensor consists of a tube system made of single crystalline silicon. The tube system is excited electrostatically into mechanical resonance and the vibration is detected optically. Using a simplified theoretical analysis, the resonance frequency can be shown to be proportional to 1/spl radic//spl rho/, where /spl rho/ is the density of the silicon and the fluid weighted according to their areas in a cross section of the tube. Thus, a change in fluid density results in a change in the resonance frequency. This dependence is demonstrated by measurements for four different vibrations modes. The quality of the vibration is also investigated through measurements of the Q-values of the vibration modes. The tubes are made using anisotropic silicon KOH etching and silicon-to-silicon fusion bonding micromachining techniques. The dimensions of the tube system are 8.6/spl times/17.7 mm with an outer tube thickness of 1 mm and a wall thickness of 100 /spl mu/m. Total tube length is 61 mm, and the sample volume is 0.035 ml. The sensor has a very good density sensitivity of the order of -200 ppm/(kgm/sup -3/) and a high Q of the order of 3000 for air in the tube.