Field Electron Emission - Terminology and Conventions

Terminology and Conventions

Field electron emission, field-induced electron emission, field emission and electron field emission are general names for this experimental phenomenon and its theory. The first name is used here.

Fowler–Nordheim tunneling is the wave-mechanical tunneling of electrons through a rounded triangular barrier created at the surface of an electron conductor by applying a very high electric field. Individual electrons can escape by Fowler-Nordheim tunneling from many materials in various different circumstances.

Cold field electron emission (CFE) is the name given to a particular statistical emission regime, in which the electrons in the emitter are initially in internal thermodynamic equilibrium, and in which most emitted electrons escape by Fowler-Nordheim tunneling from electron states close to the emitter Fermi level. Many solid and liquid materials can emit electrons in a CFE regime if an electric field of an appropriate size is applied.

Fowler–Nordheim-type equations are a family of approximate equations derived to describe CFE from the internal electron states in bulk metals. The different members of the family represent different degrees of approximation to reality. Approximate equations are necessary because, for physically realistic models of the tunneling barrier, it is mathematically impossible in principle to solve the Schrödinger equation exactly in any simple way. There is no theoretical reason to believe that Fowler-Nordheim-type equations validly describe field emission from materials other than bulk crystalline solids.

For metals, the CFE regime extends to well above room temperature. There are other electron emission regimes (such as "thermal electron emission" and "Schottky emission") that require significant external heating of the emitter. There are also emission regimes where the internal electrons are not in thermodynamic equilibrium and the emission current is, partly or completely, determined by the supply of electrons to the emitting region. A non-equilibrium emission process of this kind may be called field (electron) emission if most of the electrons escape by tunneling, but strictly it is not CFE, and is not accurately described by a Fowler-Nordheim-type equation.

Care is necessary because in some contexts (e.g. spacecraft engineering), the name "field emission" is applied to the field-induced emission of ions (field ion emission), rather than electrons, and because in some theoretical contexts "field emission" is used as a general name covering both field electron emission and field ion emission.

Historically, the phenomenon of field electron emission has been known by a variety of names, including "the aeona effect", "autoelectronic emission", "cold emission", "cold cathode emission", "field emission", "field electron emission" and "electron field emission".

Equations in this article are written using the International System of Quantities (ISQ). This is the modern (post-1970s) international system, based around the rationalized-meter-kilogram-second (rmks) system of equations, which is used to define SI units. Older field emission literature (and papers that directly copy equations from old literature) often write some equations using an older equation system that does not use the quantity ε₀. In this article, all such equations have been converted to modern international form. For clarity, this should always be done.

Since work function is normally given in electronvolts (eV), and it is often convenient to measure fields in volts per nanometer (V/nm), values of most universal constants are given here in units involving the eV, V and nm. Increasingly, this is normal practice in field emission research. However, all equations here are ISQ-compatible equations and remain dimensionally consistent, as is required by the modern international system. To indicate their status, numerical values of universal constants are given to seven significant figures. Values are derived using the 2006 values of the fundamental constants.