Theoretical comparison of electron energy-loss and x-ray absorption near-edge fine structure of the Si L_2,3 edge

Various approximations in the calculations of electron energy-loss cross section and x-ray absorption coefficient have been evaluated using the Si L _2,3 edge as an example. It was found that the random phase approximation, for which the cross terms are neglected in the expressions of electron energy-loss cross section and x-ray absorption coefficient, is a very good approximation. The dipole approximation in the calculation of the electron energy-loss cross section was found to begin to break down even at small acceptance half angles, such as 12.5 mrad. For energy losses larger than that of the Si L_2,3 edge the dipole approximation will break down faster. This approximation also fails for a large scattering angle even at a small energy loss. The electron energy-loss cross section and x-ray absorption coefficient of the Si L_2,3 edge has been calculated and compared. The large difference in relative intensity reported experimentally between the two spectra is not confirmed in this study. More experimental comparisons between electron energy loss and x-ray absorption spectra are recommended for Si and other compounds.