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Level Set Methods for Modelling Field Evaporation in Atom Probe

Published online by Cambridge University Press:  28 August 2013

Daniel Haley*
Affiliation:
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK
Michael P. Moody
Affiliation:
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK
George D.W. Smith
Affiliation:
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK
*
*Corresponding author. E-mail: d.haley@mpie.de
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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.

Type
Techniques and Instrumentation Development
Copyright
Copyright © Microscopy Society of America 2013 

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References

Ang, W.T. (2007). A Beginner's Course in Boundary Element Methods. Boca Raton, FL: Universal Publishers. ISBN: 158112974-2.Google Scholar
Bas, P., Bostel, A., Deconihout, B. & Blavette, D (1995). A general protocol for the reconstruction of 3D atom probe data. Appl Surf Sci 87/88, 298304.CrossRefGoogle Scholar
Bovet, E., Chiaia, B. & Preziosi, L. (2010). A new model for snow avalanche dynamics based on non-Newtonian fluids. Meccanica 45, 753765.Google Scholar
Brochu, T. (2012). Dynamic explicit surface meshes and applications. PhD Thesis. University of British Columbia, British Columbia. Google Scholar
Chen, S., Merriman, B., Osher, S. & Smereka, P. (1997). A simple level set method for solving stephan problems. J Comput Phys 135, 829.CrossRefGoogle Scholar
Elmer (2011). Open Source Finite Element Software for Multiphysical Problems, http://www.csc.fi/english/pages/elmer. Accessed August 23, 2011.Google Scholar
Fried, M. (2004). A level set based finite element algorithm for the simulation of dendritic growth. Comput Vis Sci 7, 97110.Google Scholar
Garrido, S., Moreno, L., Blanco, D. & Martin, F. (2006). Log of the inverse of the distance transform and fast marching applied to path planning. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Google Scholar
Geuzaine, C. & Remacle, J. (2009). Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79, 1097. Google Scholar
Gravouil, A., Moes, N. & Belytschko, T. (2002). Non-planar 3D crack growth by the extended finite element and level sets—Part II: Level set update. Int J Numer Methods Eng 53, 25692586.Google Scholar
Haley, D., Petersen, T., Ringer, S.P. & Smith, G.D.W. (2011). Atom probe trajectory mapping using experimental tip shape measurements. J Microsc 244, 170180.Google Scholar
Jeong, J., Goldenfeld, N. & Dantzig, J. (2001). Phase field modelling for three-dimensional dendritic growth with fluid flow, Phys Rev E 64, 041602. Google Scholar
Kelly, F., Larson, D., Thompson, K., Roger, L., Bunton, J., Olson, J. & Gorman, B. (2007). Atom probe tomography of electronic materials. Annu Rev Mater Sci 37, 681727.CrossRefGoogle Scholar
Kleefsman, K.M.T., Fekken, G., Veldman, A.E.P., Iwanowski, B. & Buchner, B. (2005). A volume-of-fluid based simulation method for wave impact problems. J Comput Phys 206, 363393.CrossRefGoogle Scholar
Larson, D.J., Geiser, B.P., Prosa, T.J., Gerstl, S.S.A., Reinhard, D.A. & Kelly, T.F. (2011). Improvements in planar feature reconstructions in atom probe tomography. J Microsc 243(Pt 1), 1530.Google Scholar
Loberg, B. & Norden, H. (1968). Observations of the field-evaporation end form of tungsten. Arkiv For Fysik 39, 383395.Google Scholar
Marquis, E., Geiser, B., Prosa, T. & Larson, D. (2010). Evolution of tip shape during field evaporation of complex multilayer structures. J Microsc 241, 225233.CrossRefGoogle Scholar
Monaghan, J.J. (1994). Simulating free surface flows with SPH. J Comput Phys 110, 399406.CrossRefGoogle Scholar
Moody, M.P., Gault, B., Stephenson, L.T., Marceau, R.K.W., Powles, R.C., Ceguerra, A.V., Breen, A. & Ringer, S.P. (2011). Lattice rectification in atom probe tomography: Toward true three-dimensional atomic microscopy. Microsc Microanal 17, 226239.CrossRefGoogle ScholarPubMed
Niewieczerzal, D., Oleksy, C. & Szczepkowicz, A. (2010). Image deformation in field ion microscopy of faceted crystals. Ultramicroscopy 10(3), 234241.Google Scholar
Oberdorfer, C. & Schmitz, G. (2011). On the field evaporation behavior of dielectric materials in three-dimensional atom probe: A numeric simulation. Microsc Microanal 17(1), 1525.Google Scholar
Osher, S. & Fedkiw, R. (2003). Applied Mathematical Sciences, Volume 153: Level Set Methods and Dynamic Implicit Surfaces. New York: Springer-Verlag.CrossRefGoogle Scholar
Peng, D., Merriman, B., Osher, S., Zhao, H. & Kang, M. (1999). A PDE based fast local level set method. J Comput Phys 155(2), 410438.Google Scholar
Russo, G. & Smereka, P. (2000). A level set method for the evolution of faceted crystals. Siam J Sci Comput 21(6), 20732095.Google Scholar
Scardovelli, R. & Zaleski, S. (1999). Direct numerical simulation of free-surface and interfacial flow. Ann Rev Fluid Mech 34, 567603.Google Scholar
Sethian, J. (2003). Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge, UK: Cambridge University Press.Google Scholar
Sethian, J. & Strain, J. (1992). Crystal growth and dendritic solidification. J Comput Phys 98, 231253.CrossRefGoogle Scholar
Shin, S. & Juric, D. (2002). Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J Comput Phys 180, 427470.Google Scholar
Smith, R. & Walls, J.M. (1978). Ion trajectories in the field-ion microscope. J Appl Phys D 11, 409419.Google Scholar
Thompson, G., Genc, A., Morris, R., Torres, K. & Fraser, H. (2009). Correlation between TEM imaging and microanalysis for atom probe reconstruction verification. Microsc Microanal 15(Suppl 2), 250251.Google Scholar
Toussaint, G. (2011). Course notes: Introduction to pattern recognition via character recognition, chapter 2, grids, connectivity and contour tracing. http://jeff.cs.mcgill.ca/~godfried/teaching/pr-notes/contour.pdf. Accessed August 23, 2011. Google Scholar
Tsong, T. (1990). Atom-Probe Field Ion Microscopy: Field Ion Emission and Surfaces and Interfaces at Atomic Resolution. Cambridge, UK: Cambridge University Press.Google Scholar
Vurpillot, F., Bostel, A. & Blavette, D. (2001). A new approach to the interpretation of atom probe field-ion microscopy images. Ultramicroscopy 89, 137144.Google Scholar
Vurpillot, F., Bostel, A. & Blavette, D. (2004). Modeling image distortions in 3DAP. Microsc Microanal 10, 384390.Google Scholar
Vurpillot, F., Gruber, M., Da Costa, G., Martin, I., Renaud, L. & Bostel, A. (2011). Pragmatic reconstruction methods in atom probe tomography. Ultramicroscopy 111, 12861294.Google Scholar
Zabaras, N. & Tan, L. (2006). A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods. J Comput Phys 211, 3663.Google Scholar