Comparative Apex Electrostatics of Atom Probe Tomography Specimens.
JOURNAL OF ELECTRONIC MATERIALS 2021;
50:10.1007/s11664-021-08932-6. [PMID:
37732102 PMCID:
PMC10510675 DOI:
10.1007/s11664-021-08932-6]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 04/05/2021] [Indexed: 09/22/2023]
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 a p e x has been approximated by the relation E a p e x = S V / ( k r ) , which was originally derived for sharp, metallic conductors; we refer to this equation as the "k-factor approximation". Here, S V 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 S V 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 applied to a purely dielectric tip results in k values far greater than the typical range for metallic tips. We put our numerical results into further context with a brief discussion of our own, separate, experimental work and the results of other publications.
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