Microscopic Description of Electron-Solid Interactions at a Surface

A microscopic quantum theory of the scattering of an electron at metal-vacuum interfaces is constructed. The interactions of the electron with the short-range electron-ion core potential, the bulk-density fluctuations (e.g., plasmons), and the induced surface charge all are incorporated into the theory in a systematic fashion. Models of the surface- and bulk-charge-density fluctuations are catalogued as appropriate limiting cases of theory. The structure and predictions of the various models are compared, and the suitability of the models as the basis of a theory of electron-solid scattering is examined. The approximations required to produce from the general theory the usual semiclassical description of bulk- and surface-plasmon emission by keV electron transmission are displayed. Similarly, the theory is applied to "derive" the model Hamiltonian recently used to construct a semiphenomenological quantum-field theory of inelastic low-energy ($10\ensuremath{\lesssim}E\ensuremath{\lesssim}{10}^{3}$ eV) electron diffraction. A distorted-wave-scattering theory of elastic low-energy electron diffraction is proposed in which bulk- and surface-plasmon inelastic processes appear as loss terms in a nonlocal complex optical potential whose nature is examined in detail. In appropriate limits, the optical potential is shown to lead both to the image force and to the empirical local-potential models which have been used in calculating elastic low-energy electron diffraction. The pronounced differences between the empirical models and the predictions of the microscopic theory for the optical potential are explored. Some of the consequences of these differences for the analysis of experimental elastic---low-energy---electron-diffraction data are derived.