Abstract
Rigorous electrostatic modeling of the specimen electrode environment is required to better understand the fundamental processes of atom probe tomography (APT) and guide the analysis of APT data. We have developed a simulation tool that self-consistently solves the nonlinear electrostatic Poisson equation along with the mobile charge carrier concentrations and provides a detailed picture of the electrostatic environment of APT specimen tips. We consider cases of metals, semiconductors, and dielectrics. Traditionally in APT, and regardless of specimen composition, the apex electric field \(E_\mathrm{apex}\) has been approximated by the relation \(E_\mathrm{apex} = SV / (kr)\), which was originally derived for sharp, metallic conductors; we refer to this equation as the “K-factor approximation”. Here, SV is tip-electrode bias, r is the radius of curvature of the tip apex, and k is a dimensionless fitting parameter with \(1.5< k < 8.5\). As expected, our Poisson solver agrees well with the k-factor approximation for metal tips; it also agrees remarkably well for semiconductor tips-regardless of the semiconductor doping level. We ascribe this finding to the fact that even if a semiconductor tip is fully depleted of majority carriers under the typical SV conditions used in APT, an inversion layer will appear at the apex surface. The inversion forms a thin, conducting layer that screens the interior of the tip, thus mimicking metallic behavior at the apex surface. By contrast, we find that the k-factor approximation yields a very poor representation of the electrostatics of a purely dielectric tip. We put our numerical results into further context with a brief discussion of our own separate work and the results of other publications.
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References
W. Chen, P. Pareige, in Semiconductor Nanowires, ed. by J. Arbiol, Q. Xiong, Woodhead Publishing Series in Electronic and Optical Materials (Woodhead Publishing, 2015), pp. 305–326. https://doi.org/10.1016/B978-1-78242-253-2.00011-6
C. Kong, S. Cheong, R.D. Tilley, in Comprehensive Nanoscience and Nanotechnology (Second Edition), ed. by D.L. Andrews, R.H. Lipson, T. Nann, second edition edn. (Academic Press, Oxford, 2019), pp. 327–356. https://doi.org/10.1016/B978-0-12-803581-8.10432-1
R. Kohli, in Developments in Surface Contamination and Cleaning, ed. by R. Kohli, K. Mittal (William Andrew Publishing, Oxford, 2012), pp. 215–306. https://doi.org/10.1016/B978-1-4377-7883-0.00005-5
X. Wang, C. Hatzoglou, B. Sneed, Z. Fan, W. Guo, K. Jin, D. Chen, H. Bei, Y. Wang, W.J. Weber, Y. Zhang, B. Gault, K.L. More, F. Vurpillot, J.D. Poplawsky, Nat. Commun. 11(1), 1022 (2020). https://doi.org/10.1038/s41467-020-14832-w
M.D. Mulholland, D.N. Seidman, Microsc. Microanal. 17(6), 950 (2011). https://doi.org/10.1017/S1431927611011895
J.H. Bunton, J.D. Olson, D.R. Lenz, T.F. Kelly, Microsc. Microanal. 13(6), 418 (2007). https://doi.org/10.1017/S1431927607070869
G.L. Kellogg, T.T. Tsong, J. Appl. Phys. 51(2), 1184 (1980). https://doi.org/10.1063/1.327686
M. Gilbert, F. Vurpillot, A. Vella, H. Bernas, B. Deconihout, Ultramicroscopy 107(9), 767 (2007). https://doi.org/10.1016/j.ultramic.2007.02.027
M.K. Miller, R.G. Forbes, Field Evaporation and Related Topics (Springer, Boston, 2014), pp. 111–187
P.J. Birdseye, D. Smith, Surface Sci. 23(1), 198 (1970). https://doi.org/10.1016/0039-6028(70)90013-0
T.F. Kelly, Atom-Probe Tomography (Springer, Cham, 2019), p. 2
R. Gomer, Surface Sci. 299–300, 129 (1994)
A. Cerezo, P.H. Clifton, M.J. Galtrey, C.J. Humphreys, T.F. Kelly, D.J. Larson, S. Lozano-Perez, E.A. Marquis, R.A. Oliver, G. Sha, K. Thompson, M. Zandbergen, R.L. Alvis, Mater. Today 10(12), 36 (2007). https://doi.org/10.1016/S1369-7021(07)70306-1
S.M. Reddy, D.W. Saxey, W.D.A. Rickard, D. Fougerouse, S.D. Montalvo, R. Verberne, A. van Riessen, Geostandards Geoanal. Res. 44(1), 5 (2020)
T.F. Kelly, P.P. Camus, D.J. Larson, L.M. Holzman, S.S. Bajikar, Ultramicroscopy 62(1), 29 (1996)
S.T. Loi, B. Gault, S.P. Ringer, D.J. Larson, B.P. Geiser, Ultramicroscopy 132, 107 (2013)
O. Madelung, Physical Data (Springer, Berlin, 1991), pp. 5–159. https://doi.org/10.1007/978-3-642-45681-7_2
E.F. Schubert, Light-Emitting Diodes, 2nd edn. (Cambridge University Press, Cambridge, 2006). https://doi.org/10.1017/CBO9780511790546
B. El-Kareh, Thermal Oxidation and Nitridation (Springer, Boston, 1995), pp. 39–85. https://doi.org/10.1007/978-1-4615-2209-6_2
S.S. Bajikar, T.F. Kelly, P.P. Camus, Proceedings of the 42nd International Field Emission Symposium on Applied Surface Science 94–95, 464 (1996). https://doi.org/10.1016/0169-4332(95)00411-4
J.R. Shewchuk, Computational Geometry 22(1), 21 (2002). 16th ACM Symposium on Computational Geometry. https://doi.org/10.1016/S0925-7721(01)00047-5
J.R. Shewchuk, in Applied Computational Geometry: Towards Geometric Engineering, Lecture Notes in Computer Science, vol. 1148 (Springer-Verlag, 1996), pp. 203–222
Z.C. Li, S. Wang, J. Comput. Appl. Math. 106(1), 21 (1999). https://doi.org/10.1016/S0377-0427(99)00051-5
T. Dence, Math. Gazette 81(492), 403 (1997)
K. Ueno, A. Kobayashi, H. Fujioka, AIP Adv. 9(7), 075123 (2019). https://doi.org/10.1063/1.5103185
N.A. Sanford, P.T. Blanchard, M. Brubaker, K.A. Bertness, A. Roshko, J.B. Schlager, R. Kirchhofer, D.R. Diercks, B. Gorman, Phys. Status Solidi c 11(3–4), 608 (2014). https://doi.org/10.1002/pssc.201300579
J. Ruzyllo, Silicon Dioxide\(SiO_2\) (World Scientific, Singapore, 2016).
B.W. Caplins, P.T. Blanchard, A.N. Chiaramonti, D.R. Diercks, L. Miaja-Avila, N.A. Sanford, Ultramicroscopy 213, 112995 (2020). https://doi.org/10.1016/j.ultramic.2020.112995
E.P. Silaeva, L. Arnoldi, M.L. Karahka, B. Deconihout, A. Menand, H.J. Kreuzer, A. Vella, Nano Lett. 14(11), 6066 (2014). https://doi.org/10.1021/nl502715s
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Zhang, Q., Klein, B., Sanford, N.A. et al. Comparative Apex Electrostatics of Atom Probe Tomography Specimens. J. Electron. Mater. 50, 3022–3029 (2021). https://doi.org/10.1007/s11664-021-08932-6
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DOI: https://doi.org/10.1007/s11664-021-08932-6