  Nowadays, silicon micro-cantilevers with different geometrical shapes are
widely used as micro-electro-mechanical systems and, more recently, as force
sensor probes in atomic force microscopy (AFM). During the last ten years,
several applications, which include these AFM micrometer-sized cantilevers as
mass probes in microbalances or as chemical sensors in chemical micro-system
devices, were developed. In the case of complex shapes of cantilevers, where
the cross-section is not constant along the cantilever length (case of
?V-shaped? micro-cantilevers), their resonant frequencies can not be
analytically calculated. Firstly, in order to validate the accuracy of our FEM
approach, we carried out a comparison between analytical, experimental and
FEM-computed values of the resonant frequencies for homogenous rectangular
shaped micro-cantilevers. Then, we performed a modeling of silicon beams coated
with a thin sensitive layer (50 nm of Gold). To precisely calculate the
resonant frequencies of these multilayer-cantilevers, the influence of the mesh
parameters on the calculated frequencies was strongly investigated. Secondly,
the sensitivity of different ?V-shaped? silicon cantilevers was estimated, as a
function of their geometrical dimensions and of their mechanical parameters
(Young modulus, density). The resonant frequencies of uncoated cantilevers were
calculated and compared with the values experimentally determined. Then, a
similar approach was employed to predict the sensitivities of such cantilevers
recovered with a sensitive layer.
