ABSTRACT
Field emission (FE) (also known as field electron emission or electron field emission) is the emission of electrons from a solid surface into vacuum induced by an electrostatic field. FE was first explained by quantum tunneling of electrons in the late 1920s [1], and the theory of FE from bulk metals was proposed by Fowler and Nordheim [2]. A family of approximate equations, called Fowler–Nordheim equations (F–N equations), are named in their honor and have been shown in terms of experimentally measured quantities as https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315371795/61f23981-4f37-4614-a3a6-1f5751b07853/content/math9_1.jpg"/> ln ( I V 2 ) = 1 V ( α φ 3 2 d β ) + offset where φ is the work function (WF) of the emitter, d is the interelectrode distance, β is the field amplification factor (field enhancement factor) determined by the geometry of the emission region, and α is a constant [3]. The hypothesis of this model includes
Electrons are fermions, and their distribution meets Fermi–Dirac statistics.
The surface of the metal is a smooth plane, and its atomic-scale irregularities can be ignored.
The influence of the classic mirror-image force is taken into consideration.
The distribution of work functions is uniform.
