3D finite element analysis of electrostatic deflection of commercial and FIB-modified cantilevers for electric and Kelvin force microscopy: I. Triangular shaped cantilevers with symmetric pyramidal tips.

The investigation of the nanoscale distribution of electrostatic forces on material surfaces is of paramount importance for the development of nanotechnology, since these confined forces govern many physical processes on which a large number of technological applications are based. For instance, electric force microscopy (EFM) and micro-electro-mechanical-systems (MEMS) are technologies based on an electrostatic interaction between a cantilever and a specimen. In the present work we report on a 3D finite element analysis of the electrostatic deflection of cantilevers for electric and Kelvin force microscopy. A commercial triangular shaped cantilever with a symmetric pyramidal tip was modelled. In addition, the cantilever was modified by a focused ion beam (FIB) in order to reduce its parasitic electrostatic force, and its behaviour was studied by computation analysis. 3D modelling of the electrostatic deflection was realized by using a multiphysics finite element analysis software and it was applied to the real geometry of the cantilevers and probes obtained by using basic CAD tools. The results of the modelling are in good agreement with experimental data.