In this paper, we derive analytically from first principles a generalized Fowler–Nordheim (FN) type equation that takes into account the curvature of a nanoscopic emitter and is generally applicable to any emitter shape provided that the emitter is a good conductor and no field-dependent changes in emitter geometry occur. The traditional FN equation is shown to be a limiting case of our equation in the limit of emitters of large radii of curvature R. Experimental confirmation of the validity of our equation is given by the data of three different groups. Upon applying our equation to experimental FN plots complying with the above limitations, one may deduce (i) R and (ii) standard field emission parameters—e.g. enhancement factor—with better accuracy than by using the FN equation.

When an electron emitting tip is subjected to very high electric fields, plasma forms even under ultra high vacuum conditions. This phenomenon, known as vacuum arc, causes catastrophic surface modifications and constitutes a major limiting factor not only for modern electron sources, but also for many large-scale applications such as particle accelerators, fusion reactors etc. Although vacuum arcs have been studied thoroughly, the physical mechanisms that lead from intense electron emission to plasma ignition are still unclear. In this article, we give insights to the atomic scale processes taking place in metal nanotips under intense field emission conditions. We use multi-scale atomistic simulations that concurrently include field-induced forces, electron emission with finite-size and space-charge effects, Nottingham and Joule heating. We find that when a sufficiently high electric field is applied to the tip, the emission-generated heat partially melts it and the field-induced force elongates and sharpens it. This initiates a positive feedback thermal runaway process, which eventually causes evaporation of large fractions of the tip. The reported mechanism can explain the origin of neutral atoms necessary to initiate plasma, a missing key process required to explain the ignition of a vacuum arc. Our simulations provide a quantitative description of in the conditions leading to runaway, which shall be valuable for both field emission applications and vacuum arc studies.

During the previous decade, Jensen et al. developed a general analytical model that successfully describes electron emission from metals both in the field and thermionic regimes, as well as in the transition region. In that development, the standard image corrected triangular potential barrier was used. This barrier model is valid only for planar surfaces and therefore cannot be used in general for modern nanometric emitters. In a recent publication, the authors showed that the standard Fowler-Nordheim theory can be generalized for highly curved emitters if a quadratic term is included to the potential model. In this paper, we extend this generalization for high temperatures and include both the thermal and intermediate regimes. This is achieved by applying the general method developed by Jensen to the quadratic barrier model of our previous publication. We obtain results that are in good agreement with fully numerical calculations for radii R > 4 nm, while our calculated current density differs by a factor up to 27 from the one predicted by the Jensen's standard General-Thermal-Field (GTF) equation. Our extended GTF equation has application to modern sharp electron sources, beam simulation models, and vacuum breakdown theory.

In models of field emission the needle is usually terminated by a hemispherical cap. Here we choose to terminate it with a hemiellipsoidal cap and use a three-dimensional Wentzel–Kramers–Brillouin method for the computations. This has two important consequences: as the ellipsoid becomes more elongated, (a) the effective emission area is decreased and (b) the quantum mechanically computed electron paths converge toward the needle axis. Both mechanisms produce a self-focusing of the field emitted electrons.

We measure the current vs voltage ($I$-$V$) characteristics of a diodelike tunnel junction consisting of a sharp metallic tip placed at a variable distance $d$ from a planar collector and emitting electrons via electric-field assisted emission. All curves collapse onto one single graph when $I$ is plotted as a function of the single scaling variable $V{d}^{$-${}$\lambda${}}$, $d$ being varied from a few mm to a few nm, i.e., by about six orders of magnitude. We provide an argument that finds the exponent $$\lambda${}$ within the singular behavior inherent to the electrostatics of a sharp tip. A simulation of the tunneling barrier for a realistic tip reproduces both the scaling behavior and the small but significant deviations from scaling observed experimentally.