Excitation of phonons in medium-energy electron diffraction.

Abstract

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 medium-energy regime, in which the diffraction pattern is similar to those observed in x-ray photoemission diffraction (XPD) and Auger electron diffraction (AED) experiments. We present a model for the electron scattering which, including the vibrational degrees of freedom of the crystal, contains both regimes and explains the passage from one regime to the other. Our model is based on a separation of the electron and atomic motions (adiabatic approximation) and on a cluster-type formulation of the multiple scattering of the electron. The inelastic scattering events (excitation and/or absorption of phonons) are treated as coherent processes and no break of the phase relation between the incident and the exit paths of the electron is assumed. The LEED and the medium-energy electron diffraction regimes appear naturally in this model as the limit cases of completely elastic scattering and of inelastic scattering with excitation and/or absorption of multiple phonons. Intensity patterns calculated with this model are in very good agreement with recent experiments of electron scattering on Cu(001) at low and medium energies. We show that there is a correspondence between the type of intensity pattern and the mean number of phonons excited and/or absorbed during the scattering: a LEED-like pattern is observed when this mean number is less than 2, LEED-like and XPD/AED-like features coexist when this number is 3--4, and a XPD/AED-like pattern is observed when this number is greater than 5--6. \textcopyright{} 1996 The American Physical Society.