Effect of added mass distribution on the dynamic PI and frequency shifting in MEMS and NEMS biosensors

Resonance nano biosensors are electrostatically actuated sensors that recognize an analyte which is defined as the objective substance. These sensors take advantage of the vibrational characteristics such as the effect of analyte inertia on the natural frequency. In most of the previous studies, the analyte is modeled as a point-mass. This study focuses on more realistic distributions on the surface of micro/nano transducers. Gaussian function (normal distribution), as well as a uniform mass distribution, are inspected and compared with the point-mass model. A non-dimensionalized (ND) form of Euler–Bernoulli beam theory is employed whilst an electrostatic field acts on the biosensor. Two FEM algorithms and a dynamic solution are presented for the added mass to cantilevered nano-wire biosensors. Also, the effect of mass quantity and the length of distribution for Gaussian and uniform mass distributions are examined and compared with the point-mass model. Results signify the importance of analyte distribution shapes due to the resonance frequency shift.