Nanotips with a single atom end as ideal sources of electron and ion beams: Modeling of the nanotip shape

Nanotips with a single atom end have proven to be ideal sources for self collimated electron and ion beams, which presents them as vital tools for ion and electron microscopy. The sharpness of such nanotips is usually inferred from the highly focused ion and electron single spots in the field ion microscope (FIM) and the field emission microscope (FEM) respectively. However, the wide range of applied voltage needed to generate a threshold field, for electron or ion emission, indicates that such tips are different in geometry at a mesoscopic scale. Here we present numerical models using spherical and hyperbolic geometries to calculate the apex field. The analyses demonstrate the significant effect of the tip base on the nanotip apex field. From the tip radius-voltage relationship we present a new approach for estimating the overall nanotip shape. This approach significantly helps in the selection of nanotips for specific applications, like ion microscopy and lithography or multiple nano probe contacts.