Numerical and finite element simulations of nanotips for fim/fem

Due to their crucial applications in nanotechnology, several methods have been developed for fabricating nanotips. Such nanotips can be fabricated and characterized in the field ion microscope (FIM), and can be tapered down to a single atom apex. As only a top view of the tip apex can be captured and analyzed in the FIM the overall nanotip shape is still undefined. The FIM images or field emission microscope (FEM) images of single-atom tips (SATs) made by different methods have been found to span a wide range of applied voltages for the respective mode. Here we present theoretical and numerical methods to analyze the distribution of the electric field in the vicinity of the nanotip apex that holds the topmost single atom. We use two different geometries for the nanotip apex, spherical and ellipsoidal shapes, to analyze its electric field. We demonstrate that the electric field at the center of the nano-protrusion is still significantly dominated by the nanotip base and enhanced further at the center of the apex by the nanotip protrusion. The analyses explicitly show that nanotips with broad bases produce even less field than some regular tips, at the same applied voltage. This pronounced effect of the tip base accounts for the relatively high voltages needed for imaging some nanotips in FIM or FEM. In addition, the overall nanotip shape can be estimated based on the radius-voltage relationship. This approach helps in the selection of nanotips for particular applications in ion and electron microscopy, nano lithography, nano characterization and other aspects of nanotechnology.