Local versus nonlocal description of the energy loss of electrons via plasmon excitation backscattering from solid surfaces

The differences between the local and nonlocal descriptions of the energy loss of electrons backscattered from a Si surface, focusing on surface and bulk plasmon excitations, are studied quantitatively in the present work. Beyond the usually applied "V-shape" electron trajectories, calculations have done for realistic electron trajectories derived by Monte Carlo simulation even in the case of nonlocal description of the electron-energyloss process. It allowed to perform the detailed investigation of the effects of the interference (i.e., the interaction of the electron with the electric field induced at the earlier stage of its trajectory) in case of real electron trajectories. It is clearly shown that significant interference effects occur only in the case of surface plasmon excitations, however, these are less pronounced than predicted by the simple V-shape trajectory approximation. Furthermore, it is pointed out that the error caused by neglecting interference effects in the case of the local description of electron energy losses through collective excitations in the near-surface region of the solid is less than 6.2% when the primary electron energy is higher than 500 eV. As a consequence, the application of Monte Carlo simulation techniques based on a local description of the electron-energy-loss process is possible at these primary electron energies in order to the fast modeling of the complete near-surface electron-transport process (including inelastic and elastic electron scattering) without significant errors due to the neglect of the interference effects.