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Electronic states at the surfaces of crystals

II. The approximation of tight binding: finite linear chain of atoms

Published online by Cambridge University Press:  24 October 2008

E. T. Goodwin
E. T. Goodwin
Affiliation:
The UniversitySheffield
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Extract

The wave functions and energies of both the normal and surface electronic states of a finite linear chain are determined in terms of the overlap integrals by the approximation of tight binding, it being assumed that the interaction of atomic s-states with p-states can be neglected. It is shown that the existence of surface states depends on the ratio of two overlap integrals being greater than unity, and reasons are given for expecting this to be so.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 35 , Issue 2 , April 1939 , pp. 221 - 231
Copyright
Copyright © Cambridge Philosophical Society 1939

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References

† See, e.g., M.J. pp. 65 et seq. (cf. paper I, reference on p. 205.)

‡ Loc. cit. (paper I), p. 725.

§ The extension to a three-dimensional crystal is considered in the next paper.

† The factor (−)n is included for convenience since we have found that the subsequent results then take a simpler form.

† N.B. (21a) corresponds to (20a) if N is even but to (20b) if N is odd.

† M.J. pp. 59 and 70.

‡ M.J. p. 71.

† Slater, , Phys. Rev. 36 (1930), 57.CrossRefGoogle Scholar

‡ Rosen, , Phys. Rev. 38 (1931), 255.CrossRefGoogle Scholar