AdAPTS: An Adaptive Atom Probe Tomography Simulation Library

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Abstract:

In atom probe tomography (APT), spatial reconstruction enables volumetric insight into a specimen's nanostructure. To this day, a fast reconstruction method which utilizes the true potential of APT in terms of resolution does not exist. A model of its effective inverse, the field evaporation, which provides a physically accurate description of the ion trajectories, is a crucial component in reconstruction. The simulation of each individual evaporation, such as in TAPSim, while being able to model some cases accurately, has been time inefficient. Novel methods track surface meshes, achieving better time efficiency, although at the cost of spatial accuracy.

We introduce AdAPTS, an adaptive atom probe tomography simulation library. AdAPTS is a modular volumetric finite element simulation and specimen modeling library for APT written in C++. It is capable of generating accurate detector hit maps of various specimens, efficiently representing and simulating the experimental domain from specimen to detector. Using AdAPTS, we are able to accurately simulate the field evaporation of various specimens, revealing realistic poles and zone lines.

AdAPTS utilizes a unique high quality mesh generation strategy, in which each individual atom is represented by a vertex carrying material property information (e.g. atomic mass, relative permittivity). To constitute the surrounding vacuum chamber, additional vertices are generated using efficient variable density Poisson disk sampling. The software library TetGen is used to Delaunay-tetrahedralize all generated vertices. This yields a tetrahedral mesh in which each element inherits its material properties from the material property previously assigned to each vertex. The resulting vacuum vertices constitute less than 2% of the total vertices, effectively allowing for a fast and full-scale simulation without employing the finite element method/boundary element method (FEM/BEM) coupling scheme proposed by Fletcher et al. Simultaneously, this method provides a rigid surface notion that preserves local protrusions due to lattice nanostructure similar to TAPSim by Oberdorfer et al., which in turn preserves zone lines and poles on the hit map.

The modeling of a specimen comprises two steps. In the first step, individual crystal lattices can be defined using Bravais lattice descriptors (e.g. bcc, fcc), the material lattice constant and the Miller indices of the crystallic plane facing the detector. In the second step, the shape of the specimen and dopants contained within are modeled using implicit surfaces and binary set operators (e.g. union, intersection). However, for amorphous materials, the individual atomic positions can also be specified individually or generated by any other means. The height, tip radius and shank angle of an implicit surface (a truncated cone with a quasi-hemispherical tip) that represents the specimen shape can be specified.

The modular finite element methods library MFEM is utilized to determine the electric field by solving Poisson’s equation given an electric potential Dirichlet boundary condition at the base of the specimen. Using an Euler-forward scheme with variable time steps, the trajectory starting at each evaporation site is calculated. The trajectory integration is terminated when the trajectory intersects with the detector plane. To conclude, AdAPTS provides an efficient and accurate framework which combines specimen modeling with realistic field evaporation due to voltage pulses using state-of-the-art mesh generation and numerical simulation tools. A thorough quantitative comparison in terms of simulation time of the different simulators will be provided by the time of the conference.

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