Details

Autor(en) / Beteiligte

• Forbes, Richard G
• Deane, Jonathan H.B

Titel

Reformulation of the standard theory of Fowler–Nordheim tunnelling and cold field electron emission

Ist Teil von

• Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2007-11, Vol.463 (2087), p.2907-2927

Ort / Verlag

London: The Royal Society

Erscheinungsjahr

2007

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• This paper presents a major reformulation of the standard theory of Fowler–Nordheim (FN) tunnelling and cold field electron emission (CFE). Mathematical analysis and physical interpretation become easier if the principal field emission elliptic function
• . The new formulation is designed so that it can easily be generalized; thus, our treatment of the SN barrier is a paradigm for other barrier shapes. We urge widespread consideration of this approach.
• is the Nordheim parameter. For the Schottky–Nordheim (SN) barrier used in standard CFE theory,
• ′. The previously reported formula
• ′ and
• ′ is a good low-order approximation, with |
• ). This paper separates mathematical and physical descriptions of standard CFE theory, reformulates derivations to be in terms of
• ′) is found to satisfy the ordinary differential equation
• |<0.0025. With
• rather than
• and gives a fuller account of SN barrier mathematics.
• ′ is equal to the ‘scaled barrier field’
• and d
• which is the ratio of the electric field that defines a tunnelling barrier to the critical field needed to reduce barrier height to zero. The tunnelling exponent correction factor
• this has been used to create good approximate formulae for the other special CFE elliptic functions, and to investigate a more universal, ‘scaled’, form of FN plot. This yields additional insights and a clearer answer to the question: ‘what does linearity of an experimental FN plot mean?’ FN plot curvature is predicted by a new function
• is expressed as a function
• where
• ′) of the mathematical variable
• ; an exact series solution, defined by recurrence formulae, is reported. Numerical approximation formulae, with absolute error |
• are given for