Keywords: boundary conditioning, AFM cantilevers, micromechanical structures, microfabrication, MEMS, vibrations, boundary characteristic orthogonal polynomials, Rayleigh-Ritz, nanotechnology
An improved method for predicting microfabrication influence in atomic force microscopy performances
This paper presents the application of the concept of boundary conditioning to the prediction of spring constant of atomic force microscope (AFM) cantilevers after considering the inherent microfabrication limitations. The boundary support conditions of micromechanical structures such as AFM probes are non-classical in nature, and they influence the modal response and natural frequencies of the cantilever that cannot be modelled on purely classical boundary conditions. In this paper, an AFM cantilever end support is modelled with artificial translational and rotational springs in order to capture the deviation from classical boundary conditions. The dynamic and static behaviour of the beam is investigated by the Rayleigh-Ritz energy method using boundary characteristic orthogonal polynomials and compared with published theoretical and experimental results. The comparison shows a close agreement and presents an insight into the inherent limitation associated with AFM probe fabrication processes that would affect the stiffness of the probe.