An improved empirical formula for the electric field near the surface of field emitters

Abstract

A combination of numerical and analytical techniques is used to develop an improved empirical formula for the electric field near the surface of field emitters. The new relationship is shown to account accurately for the shank variation and the dependence of the field upon polar angle. Also discussed is the suitability of empirical formulas for ion trajectory calculations.

Impact of laser pulsing on the reconstruction in an atom probe tomography

“…Here, as the facet around the (0 0 2) pole gets flatter, one could assume that this results in a relative decrease of the electric field at the apex, thus in an increase of k f with the radius, conversely to what is effectively observed. The experimental trend was, however, expected from the work of Gipson et al [45,46], where a finite-element method and was used to estimate the electric field in the vicinity of a field-ion microscopy specimen in a realistic microscope geometry. They proposed an advanced description of the field factor that accounts not only for the divergence from sphericity, but also for the far-field geometry and parameters specific to the specimen, such as its length, size, radius of curvature or shank angle.…”

Dynamic reconstruction for atom probe tomography

“…There is a clear relationship between specimen radius and this ratio, where increased radius correlates to a decreasing ratio. The overall specimen shape, in particular the shank angle and the ellipticity (flattening) of the apex, has been previously shown to influence the image compression and field factors [11,16,17]. However, here, we were not able to definitively correlate these parameters to the shank angle of the specimen, which is provided in Table 1, its composition or its orientation, (likely to affect the ellipticity of the specimen) [45].…”

Improvements in planar feature reconstructions in atom probe tomography

“…It has long been known that the shape of field‐evaporated endforms is not hemispherical (Loberg & Norden, 1968; Drechsler & Wolf, 1958; Gomer, 1961; Wilkes et al , 1974; Larson et al , 1999). For the case of relatively simple samples (those not containing multiple phases/features with different evaporation fields), this can be attributed to (1) crystallographic faceting (dependence of evaporation field on work function and/or surface energy), (2) the varying field distribution with polar angle above the specimen surface due to the presence of a shank angle (the specimen is not a perfect sphere, but is in fact a needle shape) (Gipson & Eaton, 1980; Gomer, 1961; Gipson, 1980; Van Eekelen, 1970) and/or (3) the presence of a counter electrode (Kelly & Larson, 2000).…”