Angular distribution of backscattered electrons with excitation of phonons and plasmons

Abstract

The ''elastic'' backscattering of electrons from crystalline surfaces has two regimes: at low energies the angular distribution has the narrow peaks characteristic of the Bragg diffraction, but at medium energies the angular distribution changes and becomes similar to that observed in Auger and x-ray photoelectron diffraction. We have presented recently a model that explains this change of the angular distribution in terms of the excitation/absorption of phonons during the scattering. In this paper we apply the model to the case of the electron backscattering from Al͑111͒, finding good agreement between calculated and measured angular distributions. In addition to this, we present a decomposition of the calculated intensity into the contributions of the scattering events with excitation and/or absorption of n phonons (0рnр8), and we compare these contributions with the angular distributions of electrons reflected having excited n plasmons (0рnр8). All these results are used to elucidate the nature of the change of the angular pattern in passing from low to medium energies.

Diffraction effects in the incident and exit paths of electrons backscattered from Cu(001) at medium energies

“…Therefore, these latter are the ones that control the long-range coherence of the scattering waves, and are ultimately responsible for the passage from one regime to the other. 15 To understand the physical origin of the LEED ↔ MEED transition, it is convenient to decompose Eq. ͑1͒ into the contributions of the scattering events with excitation and/or absorption of 0, 1, 2, etc., phonons.…”

“…͑1͒ into the contributions of the scattering events with excitation and/or absorption of 0, 1, 2, etc., phonons. Then, it can be shown 14,15 that the low phonon terms (nр2), which have a long-range coherence and give rise to LEED-like angular patterns, dominate at low energies, whereas the high phonon terms (nу5), which have only a short-range coherence and give rise to XPD-like angular patterns, dominate at medium energies. Therefore, the low and high phonon terms can be viewed as the coherent and incoherent parts of the scattering, respectively.…”

“…In all the previous works this symmetry remained un-observed because either k i was kept fixed 6,13 or it was scanned outside the observation plane. 11,14,15 .…”

“…As the energy is increased, the intensities of these beams first pass a succession of maxima and minima and then gradually fade away. When the diffracted beams disappear, several experiments have shown that the electrons are reflected in all directions with broad intensity maxima at directions that can be associated with crystal chains of atoms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . Because of this drastic change in the angular pattern, a LEED experiment extended into this energy region is often referred to as medium-energy electron diffraction ͑MEED͒.…”

“…According to the model, it is the excitation and/or absorption of phonons, whose probability increases with the energy, what causes the transition. It has been demonstrated 14,15 that the LEED-like angular pattern corresponds to a low (Շ2) mean number of phonons exchanged with the lattice, in which case there is a pseudoconservation of the electron wave vector parallel to the surface, and that the MEED-like angular pattern corresponds to a high (տ5) mean number of phonons exchanged with the lattice, in which case there is a complete relaxation of the wave vector conservation rule.…”