Rigorous nonlinear electrostatic simulation of atom probe tomography

Abstract

Laser-assisted atom probe tomography (L-APT) is a field driven microscopic technique that can provide sub-nm atomic mapping of solid materials at ppm-level sensitivity and has been successfully used to analyze the nano-structures of metals, semiconductors, and dielectrics. In APT, the specimen is biased with voltage just below the threshold with a low-power laser imparting a small thermal transient to trigger the field evaporation process. Activation energy, the energy required for an atom to become ionized thus escape from the specimen, strongly depends on electrostatic environment across the apex surface of the specimen. Therefore, rigorous electrostatic analysis is required to help understand the fundamental processes of APT. Using a simulation tool to solve the nonlinear electrostatic Poisson’s equation self-consistently with electron and hole concentrations, the field- and charge-related behavior of spherical apex-shaped GaN specimens used in atom probe experiments can be calculated. The equation E=V/(kr) has been used to describe the peak electric field magnitude along the central axis of the apex of metallic specimens as a function of standing voltage and the cross-sectional radii of the apex. We have found that this equation is consistent with the results obtained from our Poisson solver for semiconductor specimens, but not insulating specimens. We have observed that the formation of an inversion layer within the apex surface of semiconductor specimen at high biasing voltages is responsible for the semiconductor specimens exhibiting field magnitudes consistent with metallic specimens. Calculated field and charge density results will be presented for a range of tip geometries corresponding to experimental conditions.