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Electronic states at the surfaces of crystals

I. The approximation of nearly free electrons

Published online by Cambridge University Press:  24 October 2008

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

It is shown that in a crystal there exist states in which the electron is bound to a surface of the crystal and has an energy lying within a forbidden band. The wave functions and energies of these states are calculated, on the nearly free electron approximation, in terms of the constants of the crystalline potential field, which is represented by a triple Fourier series having the periodicity of the lattice. The method is shown to be applicable to a general crystal having a surface parallel to any one of the crystal planes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 35 , Issue 2 , April 1939 , pp. 205 - 220
Copyright
Copyright © Cambridge Philosophical Society 1939

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References

† See, for example, Mott, and Jones, , The theory of the properties of metals and alloys (Oxford, 1936),Google Scholar chap. ii. For convenience, future references to this work are written in the form “M.J.”

‡ Tamm, , Phys. Z. Sowjet. 1 (1932), 732.Google Scholar

§ Rijanow, , Z. Phys. 89 (1934), 806.CrossRefGoogle Scholar

∥ Maue, , Z. Phys. 94 (1935), 717.CrossRefGoogle Scholar

† See, for example, M.J. pp. 59 et seq.

† N.B. Thus V l here replaces − V l in Maue's work.

† In conformity with this expression we could have written (1) without the lattice constant c appearing in the denominator of the exponent. The methods here adopted, however, are so chosen to be as closely as possible in agreement with the notation of M.J.

† Cf. M.J. p. 154.