Macroscopic electrical field distribution and field-induced surface stresses of needle-shaped field emitters

One major concern since the development of the field ion microscope is the mechanical strength of the specimens. The macroscopic shape of the imaging tip greatly influences field-induced stresses and there is merit in further study of this phenomenon from a classical perspective. Understanding the geometrical, as opposed to localized electronic, factors that affect the stress might improve the quality and success rate of atom probe experiments. This study uses macroscopic electrostatic principles and finite element modelling to investigate field-induced stresses in relation to the shape of the tip. Three two-dimensional idealized models are considered, namely hyperbolic, parabolic and sphere-on-orthogonal-cone; the shapes of which are compared to experimental tips prepared by electro-polishing. Three dimensional morphologies of both a nano-porous and single-crystal aluminium tip are measured using electron tomography to quantitatively test the assumption of cylindrical symmetry for electro-polished tips. The porous tip was prepared and studied to demonstrate a fragile specimen for which such finite element studies could determine potential mechanical failure, prior to any exhaustive atom probe investigation.