Limitations of step profile models in describing the space-charge distribution near semiconductor surfaces

High-resolution electron energy-loss (HREEL) spectra have been analysed using local dielectric theory in a study of the depletion layer formed at the InSb(100) surface. Two-, three- and four-layer models were used to simulate a series of low-incidence-energy HREEL spectra (1.25 - 10 eV). An abrupt charge profile (the two-layer model) provided good agreement with experimental data when spatial dispersion and wavevector-dependent plasmon damping were included in the local dielectric model. This was in spite of the fact that the two-layer model does not accurately reflect the charge distribution, which was calculated using the modified Thomas - Fermi approximation (MTFA). Smoothing of the step profile by the inclusion of an intermediate layer (the three-layer model) introduced `plasmaron' modes, unless the plasma damping in the middle layer was set to a very high level. These modes were not observed experimentally, indicating that the abrupt charge profile in fact produced more accurate simulations. A four-layer model more closely approximating the calculated charge profile produced superior fits to the experimental spectra, but only when the plasma damping in each layer was carefully controlled. The limitations of step profile approximations and the local dielectric theory approach in describing regions of highly non-uniform charge density are discussed. In particular, the spatial and wavevector dependence of the plasmon damping is considered.