Post-field ionization

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


This chapter provides a simple explanation of post-field ionization and the probability of its occurrence.

Post-field ionization (PFI) (also called “post-ionization”) is the field-induced ionization of an ion from charge state j (1) into the charge state j+1. The PFI theory used in the context of field evaporation was developed, mainly by Kingham (see [82K]), from earlier theory relating to the field ionization of noble gases, as occurs in field ion microscopy. In principle, this PFI theory needs: (a) an expression for the field ionization rate-constant Pe(n,x,F(x)) of an ion in charge-state j that has its nucleus situated at distance x from the emitter’s electrical surface, with F(x) denoting the relevant ionizing field for this position; and (b) an expression for the speed v(x) of the ionic nucleus at position x. It is implicitly assumed that, at any position x, this field F(x) scales with the local field FL in the electrical surface. The total probability, Πet(FL), that PFI from j+ to (j+1) + occurs is given formally by
$$ {\varPi}_{\mathrm{e}\mathrm{t}}\left({F}_{\mathrm{L}}\right)=1-\exp \left[-\underset{0}{\overset{\infty }{\int }}\left\{{P}_{\mathrm{e}}/v\right\}\mathrm{dx}\right] $$

In practice, the lower limit of the integral is determined by the critical distance xjcr at which the topmost occupied orbital in the j+ ion rises above the emitter Fermi level, thereby allowing PFI to take place into an empty emitter electron state above the Fermi level. Details of the various approximations used by Kingham are given in [82K].

For a large number of elements, Kingham [82K] plotted curves showing charge-state abundances as a function of field, for all relevant charge states. Parameters of interest are the local field values Fj,j+1 at which the probable abundances of both j+ and (j+1)+ ions are 50%. These equal-abundance fields have been extracted from the Kingham diagrams and are shown above in Table 159.2.

There is some reason to believe [92L, 14F] that Kingham’s approximations are less satisfactory than he thought, but it is currently not clear what effect any corrections would have. However, there is no doubt that PFI occurs, and there is no empirical evidence that his PFI predictions are seriously incorrect.

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post-field ionization


  1. [82K]
    Kingham, D.R.: Surf. Sci. 116, 273 (1982)ADSCrossRefGoogle Scholar
  2. [92L]
    Lam, S.C., Needs, R.J.: Surf. Sci. 277, 359 (1992)ADSCrossRefGoogle Scholar
  3. [14F]
    Forbes, R.G.: Unpublished work (2014)Google Scholar

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© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Advanced Technology InstituteUniversity of SurreyGuildfordUK

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