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Multiple-analyte mass detection in a coupled microresonator array

Resonant sensors using coupled micro-cantilever arrays have found wide applications in the ultrasensitive mass detection of biomolecules and chemical analytes. Experimental observations indicate that a target mass deposited on one of the cantilevers can be detected by measuring the change in resonant frequencies or in eigenmodes. Analytical works have studied eigenvalue and eigenmode sensitivities, but for a single analyte only. Since a resonator array consists of several cantilevers, it offers an opportunity for the simultaneous detection of multiple analytes. However, multiple-analyte mass detection has not been investigated so far. In this paper, an analytical foundation for the detection of multiple analytes, through the measurement of eigenvalue shifts, is developed using matrix perturbation theory. The formulation presents a system of over-determined linear equations in terms of unknown analyte masses. A novel approach based on solving the equations in a least square sense is proposed and it is shown that it gives far better estimation accuracy than using a subset of equations for direct solution. The approach is demonstrated through numerical simulation for a typical three-cantilever array for the detection of two analyte masses. Estimation errors are studied for a range of analyte masses and presented in the form of an error surface. The effect of interconnection stiffness and array size on estimation error is also investigated. The robustness of the method is further tested against manufacturing variations and it is shown that an envelope guideline of maximum estimation error can be constructed for the user.