Level Set Methods for Modelling Field Evaporation in Atom Probe

Abstract

Atom probe is a nanoscale technique for creating three-dimensional spatially and chemically resolved point datasets, primarily of metallic or semiconductor materials. While atom probe can achieve local high-level resolution, the spatial coherence of the technique is highly dependent upon the evaporative physics in the material and can often result in large geometric distortions in experimental results. The distortions originate from uncertainties in the projection function between the field evaporating specimen and the ion detector. Here we explore the possibility of continuum numerical approximations to the evaporative behavior during an atom probe experiment, and the subsequent propagation of ions to the detector, with particular emphasis placed on the solution of axisymmetric systems, such as isolated particles and multilayer systems. Ultimately, this method may prove critical in rapid modeling of tip shape evolution in atom probe tomography, which itself is a key factor in the rapid generation of spatially accurate reconstructions in atom probe datasets.

Extending continuum models for atom probe simulation

“…Scale is identical in all frames, settings are as per the sphere simulation. Note how the truncated end of the tip is shrinking, which is a nonphysical result observable in our previous work[8].…”

“…In a previous work, we described the use of so-called "level set" algorithms, and the relationship between the problem of field evaporation and the mathematics of level set methods [8]. In this prior work, a simple proof-of-concept method was demonstrated for rapid simulation of the field evaporation of atom probe needles incorporating different material phases.…”

“…High run-times (Circa 12 atoms/min, for a 28 M atom tip [14], 1 month for complete evaporation) for these applications mean that performing numerous trial-and-error calculations can be daunting for day-to-day use -however these provide valuable insight into specific effects that can occur within atom probe specimens, such as upon encountering grain boundaries and voids. Earlier attempts to implement 3D simulations were incomplete [8], and had a high computational cost, which scaled poorly with respect to real specimen volumes, rendering the approach of limited utility. The insight gained from rapid feedback in simulations can help atom probe users to better understand and avoid misinterpretation of artefacts within their datasets.…”

An analytical model accounting for tip shape evolution during atom probe analysis of heterogeneous materials

“…However, and as expected, the present analytical model exhibits a smoother surface for the field emitter and the shape computation is much faster than simulation. On these points this model appears in the same vein as the level-set method approach [30], but it goes one step further. Indeed, one of the main advantages of this model is that the analytical formulation allows for a direct understanding of the sample parameters impact on the tomographic reconstruction.…”

Simulation tools for atom probe tomography: A path for diagnosis and treatment of image degradation

“…Ad-hoc simulation tools have been developed for years to first understand the analyzing process, and to find usable solutions to improve metrological parameters. Different simulation tools were built up for the purpose of understanding different issues and shortcomings [5,6,7,8,9,10,11,12,13,14,15,16]. We will focus this paper on three different kinds of modelling approaches used to…”