Energy distribution of elastically scattered electrons from double layer samples

We present a theoretical description of the spectra of electrons elastically scattered from thin double layered Au-C samples. The analysis is based on the Monte Carlo simulation of the recoil and Doppler effects in reflection and transmission geometries of the scattering at a fixed angle of 44.3° and a primary energy of 40 keV. The relativistic correction is taken into account. Besides the experimentally measurable energy distributions the simulations give many partial distributions separately, depending on the number of elastic scatterings (single, and multiple scatterings of different types). Furthermore, we present detailed analytical calculations for the main parameters of the single scattering, taking into account both the ideal scattering geometry, i.e. infinitesimally small angular range, and the effect of the real, finite angular range used in the measurements. We show our results for intensity ratios, peak shifts and broadenings for four cases of measurement geometries and layer thicknesses. While in the peak intensity ratios of gold and carbon for transmission geometries were found to be in good agreement with the results of the single scattering model, especially large deviations were obtained in reflection geometries. The separation of the peaks, depending on the geometry and the thickness, generally smaller, and the peak width generally larger than it can be expected from the nominal values of the primary energy, scattering angle, and mean kinetic energy of the atoms. We also show that the peaks are asymmetric even for the case of the single scattering due to the finite solid angle. Finally, we present a qualitative comparison with the experimental data. We find our resulting energy distribution of elastically scattered electrons to be in good agreement with recent measurements.