Piezoresistive Sensing in Micromechanical Resonators

Microresonators can be used both for sensor and actuator applications and produce a frequency-shift output. These frequency outputs can be very accurately measured and have an advantage over conventional analog sensors in that their outputs can be measured directly in digital systems by pulse counting. Digital systems also offer added advantages over analog systems including higher reliability, lower error rates, lower susceptibility to degradation of transmitted signals by electrical interference, and lower dependence on change in electrical characteristics with time. Microresonator systems have a high sensitivity to physical or chemical parameters that affects the potential or kinetic energy of the system and can be used to sense physical parameters such as pressure[6], acceleration[7,8], and vapor concentration[9]. It is advantageous to have microresonator sensors with high mechanical quality factors(Q) since the mechanical properties have more of an effect on the resonant frequency of the sensor. High quality factors and resonant frequencies can be obtamed in microresonators by using hollow beams[14] which essentially reduce the mass of the microresonator structure. Applications of microresonators include electrostatic voltmetersC9-111 and filters[l2]. There is a need for a convenient, cost-effective method to sense the relevant mechanical and electrical parameters of the microresonator system. In general the parameters of interest are the resonant frequency or, the quality factor Q, and the change in dC capacitance per unit displacement of the electrostatically driven comb-drive fingers. The resonant frequency of the microresonators can be determined theoretically from mechanical parameters. The quality factor and the capacitance gradient are generally speaking, difficult to determine theoretically since they depend on second-order effects. The quality factor is inversely proportional to the viscous and structural damping present in the microresonator system and depends on energy-dissipation mechanisms. Energy-dissipation mechanisms include internal molecular friction and fluid resistance. The quality factor determines the sharpness of the resonance and its magnitude. The capacitance gradient is difficult to determine theoretically since it depends on fringing electric fields and levitation of the comb-drive fingers. These microresonator parameters are easier to determine if the instantaneous position of the microresonator is known with respect to a reference point (usually the anchor points on the substrate). There are various methods of position sensing including inductive[l3], capacitive[l6] and piezoresistive methods[l7].