Energy distributions for the Schottky-Nordheim barrier

  • R. G. ForbesEmail author
Part of the Condensed Matter book series (volume 45B)


In this chapter an overview of the different energy distribution for the Schottky-Nordheim barrier is provided.

Particularly in connection with the theory of field electron emission sources and their electron-optical properties, it is useful to have information about the normal energy distribution (NED), parallel energy distribution (PED), and total energy distribution (TED) of emitted electrons, for each of the LECD regimes. In each case what one ideally needs to know is the mathematical form of the distribution, information about its peak value and average value, and information about the width of the distribution, as assessed by one or more appropriate criteria (such as full width at half maximum).

For the cold field electron emission and barrier-top regimes, these values (and analytical formulae for them, where derivable) would depend somewhat on the form assumed for the tunneling barrier and on precisely what other theoretical assumptions are made. In practice, it is only for the Murphy-Good-type theory [56Mur] of emission across the SN barrier that substantial amounts of detailed theory have been developed, and this theory is neither fully complete in its scope nor presently assembled in any one place.

It is beyond the scope of this contribution to complete and assemble detailed information concerning energy distribution theory. Useful introductory material may be found in [73S], more details concerning cold field electron emission in [09S2] and more about barrier-top electron emission in [09S1]. Other relevant material may be found in [73G, 84Mod, 96H, 07J].

Symbols and abbreviations

Short form

Full form


parallel energy distribution


local emission current density


transmission electron diffraction


normal energy distribution


  1. [56Mur]
    Murphy, E.L., Good Jr., E.H.: Phys. Rev. 102, 1464 (1956)ADSCrossRefGoogle Scholar
  2. [73G]
    Gadzuk, J.W., Plummer, E.W.: Rev. Mod. Phys. 45, 487 (1973)ADSCrossRefGoogle Scholar
  3. [73S]
    Swanson, L.W., Bell, A.E.: Adv. Electr. Electron. Phys. 32, 193 (1973)CrossRefGoogle Scholar
  4. [84Mod]
    Modinos, A.: Field, Thermionic and Secondary Electron Emission Spectroscopy. Plenum, New York (1984). Republished as paperback edition by Springer, New York (2013)Google Scholar
  5. [96H]
    Hawkes, P.W., Kasper, E.: Principles of Electron Optics. Applied Geometrical Optics, vol. 2. Academic, London (1996)Google Scholar
  6. [07J]
    Jensen, K.L.: Electron emission physics. Adv. Imaging Electron Phys. 149, 1 (2007)CrossRefGoogle Scholar
  7. [09S1]
    Swanson, L.W., Schwind, G.A.: Chapter 1. In: Orloff, J. (ed) Handbook of Charged Particle Optics (2nd Edition). Boca Raton, CRC Press (2009)Google Scholar
  8. [09S2]
    Swanson, L.W., Schwind, G.A.: Chapter 2. In: Hawkes, P. (ed.) Cold Field Emission and the Scanning Transmission Electron Microscope. Advances in Imaging and Electron Physics, vol. 139, p. 63. Elsevier, Amsterdam (2009)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Advanced Technology InstituteUniversity of SurreyGuildfordUK

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