A Coupled Microresonator Array for Mass Detection
This work describes a method of mass detection based on coupled arrays of nominally identical resonators. Coupled arrays of this type can be used for a variety of applications, however this work primarily focuses on ultrasensitive mass detection, in which resonator surfaces are functionalized to selectively adsorb one or more target analytes (e.g., chemical or biological agents). The measurement of a system resonant frequency and resonator amplitudes describing the corresponding system mode shape provides the basis for the determination of resonator masses, which are increased by the presence of the target analyte(s). A weighted average of results from measurements of multiple system modes is used to improve the robustness of the approach. The first part of this work describes numerical investigation of the sensitivity of this mass detection approach to measurement noise. System mode shapes are perturbed to simulate measurement noise, and resulting errors in identifying system masses are quantified as a function of array size, coupling strength, and level of mass variation. Sensitivity to measurement noise is low for lightly coupled arrays of nearly identical elements and increases when mass variation causes significant mode localization. For any mass variation level, an optimal combination of array size and coupling strength minimizes noise sensitivity.The second part of this work is an experimental investigation using arrays of nearest-neighbor coupled silicon cantilevers. Designs with a range of coupling strengths are fabricated. The results support the findings of the numerical simulations. Below a transition value in the ratio of mass disorder to coupling strength, responses are spatially extended and the sensitivity of the mass calculation to noise is independent of disorder. Above the transition, mode localization becomes significant and the error in mass identification increases with increasing mass disorder. Experimental results show that in the regime with extended responses, the sensor is linear and highly repeatable when detecting mass up to approximately 15% of the mass of a single cantilever. When used in a regime with localized responses, standard deviation of mass calculations increases dramatically. A threshold of detection for the method is experimentally found to be 0.2% of the cantilever mass (α=0.01).
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