EXCITATION OF PHONONS IN MEDIUM-ENERGY ELECTRON-DIFFRACTION

The ''elastic'' backscattering of electrons from crystalline surfaces presents two regimes: a low-energy regime, in which the characteristic low-energy electron diffraction (LEED) pattern is observed, and a med ium-energy regime, in which the diffraction pattern is similar to thos e observed in x-ray photoemission diffraction (XPD and Anger electron diffraction (AED) experiments. We present a model for the electron sca ttering which, including the vibrational degrees of freedom of the cry stal, contains both regimes and explains the passage from one regime t o the other. Our model is based on a separation of the electron and at omic motions (adiabatic approximation) and on a cluster-type formulati on of the multiple scattering of the electron. The inelastic scatterin g events (excitation and/or absorption of phonons) are treated as cohe rent processes and no break of the phase relation between the incident and the exit paths of the electron is assumed. The LEED and the mediu m-energy electron diffraction regimes appear naturally in this model a s the limit cases of completely elastic scattering and of inelastic sc attering with excitation and/or absorption of multiple phonons. Intens ity patterns calculated with this model are in very good agreement wit h recent experiments of electron scattering on Cu(001) at low and medi um energies. We show that there is a correspondence between the type o f intensity pattern and the mean number of phonons excited and/or abso rbed during the scattering: a LEED-like pattern is observed when this mean number is less than 2, LEED-like and XPD/AED-like features coexis t when this number is 3-4, and a XPD/AED-like pattern is observed when this number is greater than 5-6.