On the need for a tunneling prefactor in FowlerNordheim tunneling theory
Abstract
This paper argues that a tunneling prefactor should appear in expressions for the tunneling probability D relevant to cold field electron emission (CFE) and in FowlerNordheim (FN) type equations. Except in the case of the "ideally smooth" parabolic barrier, a prefactor is always present for barriers where D can be found by exact solution of the Schrödinger equation. A review of the JeffreysWentzelKramersBrillouin (JWKB) approach to solving the Schrödinger equation shows that tunneling barriers should be classified according to whether they are weak or strong and ideally smooth or not: there are four different JWKBtype formulas, depending on the nature of the barrier. CFE tunneling barriers are not ideally smooth but since the 1950s have usually been analyzed using the JWKB formulas for ideally smooth barriers. These analyses, and the standard MurphyGood FNtype equation, seem mathematically and physically incomplete. The FNtype equations currently used to describe CFE should be revised to explicitly include a tunneling prefactor. Some implications are explored.
 Publication:

Journal of Applied Physics
 Pub Date:
 June 2008
 DOI:
 10.1063/1.2937077
 Bibcode:
 2008JAP...103k4911F
 Keywords:

 73.40.Gk;
 79.70.+q;
 Tunneling;
 Field emission ionization evaporation and desorption