Two-dimensional boundary conditions and finite-size effects in angle-resolved photoelectron emission spectroscopy, low-energy electron diffraction, and high-resolution electron-energy-loss spectroscopy

The plane-wave and spherical-wave boundary conditions across a vacuum-solid interface are derived for electron emission and diffraction spectroscopies. The proper boundary condition to be chosen across a realistic interface is determined. We also compare the exact form of inelastic electron damping with those of phenomenological models. We determine the errors in the latter. Finite-size effects in low-energy electron diffraction and high-resolution electron-energy-loss spectroscopy are determined.