A mechanistic model for adsorption-induced change in resonance response of submicron cantilevers

Submicron cantilever structures have been demonstrated to be extremely versatile sensors and have potential applications in physics, chemistry and biology. The basic principle in submicron cantilever sensors is the measurement of the resonance frequency shift due to the added mass of the molecules bound to the cantilever surface. This paper presents a theoretical model to predict the resonance frequency shift due to molecular adsorption on submicron cantilevers. The influence of the mechanical properties of the adsorbed molecules bound to the upper and lower surface on the resonance frequency has been studied. For various materials, the ratio between the thicknesses of the adsorbed layer and the cantilever where either stiffness or added mass is dominant will be determined. The critical ratio (which contribution of effect cancel each others) between the thickness of the adsorbed layer and the cantilever and ratio between stiffness and density of adsorbed layer and cantilever have been determined. The calculations show the added mass and stiffness how contribute to the resonant behavior. This model gives insight into the decoupling of both opposite effects and is expected to be useful for the optimal design of resonators with high sensitivity to molecular adsorption based on either stiffness or mass effects.