Bifurcation-based MEMS mass sensors

Linear mass or gas micro-sensors are based on detecting a shift in the response frequency as associated with the deposited mass. To enhance the sensitivity of these sensors, it has been suggested to relate the deposited mass to a change in the response amplitude over a specified hysteretic range where multiple solutions coexist. We expand on this notion and show that the sensitivity of micro electromechanical sensors can be enhanced further by exploiting specific qualitative changes induced by deposited masses to yield a binary response. Specifically, rather than depending on small quantitative shifts in response frequency, in the jump frequency or in the amplitude of a response that may require a change in the excitation frequency and may be hard to evaluate, we propose two binary sensing approaches based on a change in the type of bifurcation or a finite amplitude response that would be associated with a deposited mass under specified and fixed excitation conditions. Both approaches are based on the capability to establish a relation between the target mass and the required detuning to result in the binary response. We derive the governing equations from first principles and implement the method of multiple scales to quantify this relation for two sensors and show that such sensors can be designed to meet enhanced and specified mass sensing requirements.