Dynamic response of microcantilever-based sensors in a fluidic chamber

The dynamic response of a microcantilever beam used as a transducer in a biomechanical sensor for molecule detection is analyzed. The cantilever motion is modeled using the classical Euler-Bernoulli beam theory coupled to the Reynolds equation of lubrication accounting for the hydrodynamic interactions. The beam is oscillated by an electrostatic harmonic force in close proximity to a rigid wall in an analysis chamber. It is shown that the dynamic response of the beam can be accurately predicted by a simple equivalent damped harmonic oscillator whose quality factor has been estimated as a function of the beam-wall gap. As the gap is reduced the quality factor is reduced and damping becomes more and more important. A transduction relationship between the frequency shift and the mass of molecules adherent on the beam is proposed which accounts for the beam-fluid-substrate interactions.