Sep 1, 2008
Electrostatic 3D finite element analysis for electric and Kelvin force microscopy
The study of a surface’s electrical properties at very small scales with scanning probe microscopy is of great interest in many theoretical and applicative science fields. For instance, electric and Kelvin probe force microscopy can provide direct information about local polarization, charge distribution, and electrostatic properties of materials surfaces. In semiconductor devices and biological samples, the knowledge of the local electric potential distribution is of significant interest because it helps in linking the specimen’s observed function with its local structure and composition. The understanding of electrostatic forces is, in general, of fundamental importance for the development of nanotechnology, since these forces govern many physical processes on which a large number of technological applications are based.
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.
About the author
Giovanni Valdrè obtained his “Laurea” in physics from The University of Bologna and his MPhil and PhD in physics from the University of Cambridge, UK. He is MInstP and obtained the Chartered Engineering degree from The Engineering Council, London. Currently he is researcher and aggregate professor (Faculty of Sciences and Biomedical Engineering) and chair of the Laboratory of Biomaterials and Applied Crystallography of the University of Bologna c/o the Department of Earth and Geo-Environmental Science. His areas of academic interest include mineral nanotechnology, development of SPM techniques and finite element analysis. Daniele Moro is a graduate in biomedical engineering at the University of Bologna under prof Valdre’s supervision. Presently he is a postgraduate researcher at the Laboratory of Biomaterials and Applied Crystallography of the University of Bologna. His current research activity includes development of SPM techniques, finite element analysis and surface characterization.