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Title: Theory of low energy electron diffraction
Author: Gibbons, Alan M.
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1969
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An understanding of Low Energy Electron Diffraction has been sought using an energy band structure formalism. The approach, which matches wavefunctions at the vacuum/crystal intertace, is similar to that first used by Sommerfeld and Bethe (5). However,following Heine (8), we have included complete sets of matching functions at the crystal boundary and on this basis derived formal expressions for the reflected intensities. Previous theories have tended to ignore the inner potential as a source ot internal reflections. Not accepting the usual rationale that the inner potential merely requires us to apply an energy' correction to the observed peak positions. we have shown that its inclusion in the formalism leads to a modification ot the relative intensities of the diffraction spots and to additional scattering mechanisms. In particular it has been shown that the presence of the inner potential leads to a particularly simple mechanism for the production of pronounced secondary Bragg peaks. On the grounds that the inelastic scattering would damp out processes of high order in the multiple scattering this particular mechanism has been assumed to be the most dominant. Some justitication has been found in a discussion of Taylor's (28) results for Cu (111). This discussion demonstrates that the mechanism for secondary Bragg peaks proposed by Boudreaux and Heine (14) predicts too many peaks in practice. It has also been shown that their mechanism is inappropriate in a large number of cases where the inner potential does not even approximately allow a single Bloch function to describe the total wavefunction in the crystal. A calculation has been performed which demonstrates that the particular surface resonance mechanism of Boudreaux and Heine (14) is likely to be important in practice. This is of course in accordance with the emphasis of these authors. The work of Duke and Tucker (4) has shown that, in any case, the surface resonances should be damped out by the inelastic scattering. We have tentatively suggested an alternative mechanism for the peaks observed by McRae and Caldwell (16) which they interpret as resonance peaks. Our qualitative and quantitative results obtained by using our formalism and by taking the Bloch states in the crystal to zero order have led us to develop a simple theory for predicting the positions of intensity peaks in the specular reflectivity. This theory is closely related to that of Marcus/Jona and Jepsen (20) but specifically incorporates our ideas on which secondary Bragg peaks will be appreciably intense. The theory has been used in an attempt to interpret the experimental results of McRae and Caldwell for lithium fluoride (9) and sodium fluoride (16). From the misfit in this comparison between theory and experiment we have suggested that our initial assumption (that the NFE approximation maybe a reasonable first approach at the energies of LEED) is not correct. Finally, although we believe that the band-structure approach gives a good 'physical feel' for the LEED problem, we give reasons which suggest that ultimately it will not provide the best means of calculating LEED intensities with any accuracy. The most important of these is that we believe the elastic and inelastic scattering should be treated on an equal basis, and, as Dukeand Tucker (4) have indicated, the inelastic scattering makes a Bloch wavedescription inappropriate at the energies in LEED.
Supervisor: Not available Sponsor: Science Research Council (Great Britain)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QC Physics