Generally, in this kind of investigation, the cantilever contribution operates as large additional capacitance and gives rise to a background force on top of which the tip-sample interaction has to be detected. For this reason, its effect on the total force gradient must be taken into account for a thorough understanding of the experimental data. Numerical calculations performed on real experimental set-ups can give a more precise and accurate value of the electromechanical force acting on the cantilever than simple analytical models.

In a study recently published in Nanotechnology, the authors reported on a 3D finite element analysis (FEA), by using the Maxwell stress tensor, of the electrostatic deflection of the cantilever-probe system. FEA is applied to commercial and FIB-modified conductive probes above a conductive sample when a potential difference Delta;V is applied between them to work out the force/distance relationship for different parts of the probe, resolution and sensitivity. It is emphasized that the calculations have been made considering the actual shapes and dimensions of the cantilevers, probes, specimen features and experimental set-up. The results obtained for the deflection resulted in good agreement with the corresponding experimental data.

The authors show that the simulation provides practical hints for optimizing the performances of the probes and allow the estimation of important physical and engineering parameters, namely: (i) the regime where a single component between tip-apex, lateral surface of the pyramid and cantilever dominates; (ii) an estimate of the spatial resolution and of the electrical force sensitivity of EFM; (iii) the optimum working condition of the EFM (e.g. tip-to-specimen distance, voltage); (iv) the design of FIB customised probes and cantilevers for EFM and MEMS; (v) the design of active shields to minimize parasitic capacitive effects.

Finally, it is possible to calculate the probe spread function and its distance dependence in view of understanding the image formation mechanisms in Kelvin probe force microscopy and other SPM methodologies.