Comparative Apex Electrostatics of Atom Probe Tomography Specimens

Area of Science:

• Materials Science
• Physics
• Computational Modeling

Background:

• Accurate electrostatic modeling is crucial for understanding atom probe tomography (APT) processes and data analysis.
• The traditional k-factor approximation for apex electric field is widely used but its applicability across material types is not fully understood.

Purpose of the Study:

• To develop and validate a simulation tool for rigorous electrostatic modeling of APT specimen-electrode environments.
• To investigate the validity of the k-factor approximation for metallic, semiconductor, and dielectric APT tips.

Main Methods:

• Developed a simulation tool that self-consistently solves the nonlinear electrostatic Poisson equation and mobile charge carrier concentrations.
• Applied the simulation to model the electrostatic environment of metal, semiconductor, and dielectric specimen tips under APT conditions.
• Compared simulation results with the traditional k-factor approximation ($E_{apex}=SV/\left(kr\right)$).

Main Results:

• The simulation tool accurately captures the electrostatic environment of APT tips for various materials.
• The k-factor approximation shows good agreement for metallic and semiconductor tips, even with varying semiconductor doping levels.
• For dielectric tips, the k-factor approximation yields significantly higher k values than typically observed for metallic conductors.

Conclusions:

• The developed simulation tool provides a detailed and accurate picture of the electrostatic landscape in APT specimens.
• The k-factor approximation is reliable for metals and semiconductors due to surface inversion layer effects mimicking metallic behavior.
• The k-factor approximation is not suitable for dielectric materials in APT, necessitating more sophisticated modeling.