Mechanically stable nanostructures with desirable characteristic field enhancement factors: a response from scale invariance in electrostatics

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

This review of the quantitative electrostatics of field emitters, covering analytical, numerical and 'fitted formula' approaches, is thought the first of its kind in the 100 years of the subject. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is 'polarity independent', so that the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors-which exhibit the 'electrostatic lightning-rod effect', but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than fields) becomes apparent. Space and time limitations have meant that the review cannot be comprehensive in both detail and scope. Rather, it focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called 'screening' or 'shielding'). Core to the review are discussions of the 'minimum domain dimensions' method for implementing effective finite-element-method electrostatic simulations, and of the variant of this that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001% in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many 'related considerations' that are relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

Properties of blade-like field emitters

Blade-Like Field Emitters (BFE), as defined here, are emitters expanded in one direction, forming a sharp emitting edge instead of a sharp tip. These structures have four main advantages compared to their needle counterparts, i.e., they are mechanically firmer, are better electrical and thermal conductors, and provide a larger emission area. We focus on the optimization of the last of these. We evaluate the emission properties of three types of BFEs, which we short-named hSoC-blade, HCP-blade and Elli-blade. Each is built from the expansion of a hemisphere-on-a-cone (hSoC), hemisphere-on-a-cylindrical-post (HCP) and an ellipsoidal (Elli) emitter, respectively. The characteristics of the field enhancement factor, the local electrostatic field distribution on each blades' edges and their notional area (An) of emission as a function of the expansion length are described. Finally, we point out how to improve the edge of the HCP-blade to obtain the optimal profile, which yield the largest An.