Extending continuum models for atom probe simulation

Abstract

This work describes extensions to existing level-set algorithms developed for application within the field of Atom Probe Tomography (APT). We present a new simulation tool for the simulation of 3D tomographic volumes, using advanced level set methods. By combining narrow-band, B-Tree and particle-tracing approaches from level-set methods, we demonstrate a practical tool for simulating shape changes to APT samples under applied electrostatic fields, in three dimensions. This work builds upon our previous studies by allowing for non-axially symmetric solutions, with minimal loss in computational speed, whilst retaining numerical accuracy.

Fast modelling of field evaporation in atom probe tomography using level set methods

“…Previous atom probe simulation approaches using level sets either employed a curvature approximation [16,17] or a finite difference solution for the electric field [33]. The curvature approximation is a well understood problem and it is straightforward to define an extension velocity as a function of φ.…”

“…For the purposes of this work however, the results show that the implementation is correctly following the analytical model, and that the accuracy can be improved with a higher computational cost during the level set integration. This is sufficient to model tip evaporation with higher accuracy and correctness than our prior APT level set works [16,17]. All following simulations use a CFL fraction of δ = 0.1 and reinitialize the level set field every 50 iterations.…”

“…The time per iteration for the major algorithms are given in Figure 18 This data reveals that the current bottleneck is the extension velocity construction. However, multiple options exist for accelerating this component including a narrowband grid implementation [63,64,17] and a fast marching based extension velocity construction [28,29]. Combining both of these methods would reduce the theoretical time complexity to O(N log(N )) and memory complexity to O(N 3 ) in 2D.…”

A Mesoscopic Field Evaporation Model

“…mesoscopic scale), such as level set methods [6]. Even if, these models show qualitative agreement with experimental data in 2D simulation [7], it is no completely the case in 3D, where some improvements remain to be performed [8]. In this paper, a new field evaporation simulation in 3D at the mesoscopic scale is presented.…”

Fast Continuum Models for Atom Probe Simulation and Reconstruction

“…Our model uses the level set method to track the sample geometry and extends previous curvature flow approximations for field evaporation [8,9] by coupling with an electrostatic solver: either through a Boundary Element Method (BEM), or a FEM-BEM coupling depending on whether semiconductors and insulators are also being modeled (see Figure 1). Such methods also allow for ion trajectory integration without the requirement of an external mesh spanning up to the detector: increasing the efficiency of the solution and reducing the physical memory required.…”