Cancellation of environmental effects in resonant mass sensors based on resonance mode and effective mass

A novel technique is developed to cancel the effect of environmental parameters, e.g., temperature and humidity, in resonant mass sensing. Utilizing a single resonator, the environmental cancellation is achieved by monitoring a pair of resonant overtones and the effective sensed mass in those overtones. As an eminent advantage, especially compared to dual-mode temperature compensation techniques, the presented technique eliminates any need for previously measured look-up tables or fitting the measurement data. We show that a resonant cantilever beam is an appropriate platform for applying this technique, and derive an analytical expression to relate the actual and effective sensed masses on a cantilever beam. Thereby, it is shown that in applying the presented technique successfully, the effective sensed masses must not be the same in the investigated pair of resonance overtones. To prove the feasibility of the proposed technique, flexural resonance frequencies of a silicon cantilever are measured before and after loading with a strip of photoresist. Applying the presented technique shows significant reductions in influence of environmental parameters, with the temperature and humidity coefficients of frequency being improved from -19.5 to 0.2 ppm degrees C(-1) and from 0.7 to -0.03 ppm %RH(-1), respectively.