Extracting the shape of nanometric field emitters

The high resolution nanoanalysis by atom probe tomography is based on needle-shaped samples that represent nanometric field emitters with typical curvature radii of 50 nm. After field desorption and detection of a large set of atoms, the sample volume has to be numerically reconstructed. Conventionally, this reconstruction is performed with the assumption of a hemispherical apex. This established practice can lead to serious distortions of the tomography. In this work, we demonstrate how the real shape of the emitter can be extracted from the event density on the 2D detector setup. Except for convexity, no other restriction is imposed on the shape. The required mathematics is derived and the method is demonstrated with numerically simulated and experimental data sets of complex tip shapes. The computational effort of the method is also suitable to handle data sets of a few hundred million atoms.