Theory of Atom-Metal Interactions. I. Application of Quantum-Mechanical Collision Theory to Field-Ionization Processes

D. S. Boudreaux; P. H. Cutler

doi:10.1103/PhysRev.149.170

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Theory of Atom-Metal Interactions. I. Application of Quantum-Mechanical Collision Theory to Field-Ionization Processes

D. S. Boudreaux^* and P. H. Cutler

Department of Physics, The Pennsylvania State University, University Park, Pennsylvania

^*This paper is based on part of a dissertation submitted by D. S. Boudreaux in partial fulfillment of the requirements for the Ph.D. degree in Physics at the Pennsylvania State University. Present address: Cavendish Laboratory, Cambridge University, Cambridge, England.

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Phys. Rev. 149, 170 – Published 9 September, 1966

DOI: https://doi.org/10.1103/PhysRev.149.170

Abstract

The principles of the field-ion microscope have been qualitatively well described by one-dimensional models in which the WKB approximation is used to calculate the probability of an atomic electron penetrating the potential barrier into the metal. It was concluded from such models that field ionization cannot occur once the atoms come closer to the tip than a certain critical distance. Recent experiments have shown that the ions are produced in a very narrow region of space just outside the critical distance, this region being called the ionization zone. The one-dimensional calculations give a value for the half-width of this zone which is about twice the experimental value. In the present treatment, the width of the ionization zone and a relative ionization probability have been calculated quantum-mechanically in a three-dimensional model. This is done by considering the process of field ionization as a rearrangement-type collision of an atom with a metal surface and applying the formalism of quantum-mechanical scattering theory. The calculated results are found to be in better agreement with experiment than previous one-dimensional theories.

References (11)

E. W. Müller, Advan. Electron. Electron Phys. 13, 83 (1960) M. Inghram and R. Gomer, Z. Naturforsch. 10a, 864 (1955)
T. Tsong and E. W. Müller, J. Chem. Phys. 41, 3279 (1964)
M. H. Rice and R. H. Good, J. Opt. Soc. Am. 52, 239 (1962)
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N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, London, 1949), p. 142
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S. Raimes, Wave Mechanics of Electrons in Metals (North-Holland Publishing Company, Amsterdam, 1961), p. 156
Omitted endnote
S. RaimesSurface Sci. 5, 20 (1966)
M. L. Goldberger and K. M. Watson, Collision Theory (John Wiley & Sons, Inc., New York, 1964), Secs. 3.2-3.3

[c1] E. W. Müller, Advan. Electron. Electron Phys. 13, 83 (1960) M. Inghram and R. Gomer, Z. Naturforsch. 10a, 864 (1955)

[c2] T. Tsong and E. W. Müller, J. Chem. Phys. 41, 3279 (1964)

[c3] M. H. Rice and R. H. Good, J. Opt. Soc. Am. 52, 239 (1962)

[c4] L. Pauling and E. B. Wilson, Introductory Quantum Mechanics (McGraw-Hill Book Publishing Company, Inc., New York, 1935), p. 185

[c5] K. Huang and G. Wyllie, Proc. Phys. Soc. (London) A62, 180 (1949)

[c6] N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, London, 1949), p. 142

[c7] T. Wu and T. Ohmura, Quantum Theory of Scattering (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1962), p. 2

[c8] S. Raimes, Wave Mechanics of Electrons in Metals (North-Holland Publishing Company, Amsterdam, 1961), p. 156

[c9] Omitted endnote

[c10] S. RaimesSurface Sci. 5, 20 (1966)

[c11] M. L. Goldberger and K. M. Watson, Collision Theory (John Wiley & Sons, Inc., New York, 1964), Secs. 3.2-3.3

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Theory of Atom-Metal Interactions. I. Application of Quantum-Mechanical Collision Theory to Field-Ionization Processes

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