Improving the measurement of dielectric function by TEM-EELS: avoiding the retardation effect

We investigated an improved Kramers–Kronig analysis (KKA) routine for measuring the dielectric function of α-Al2O3, avoiding the retardation effect arising in electron energy-loss spectroscopy (EELS). The EELS data differed from the optical data in the energy range of 10–20 eV due to the retardation effect, even though Cerenkov loss was thoroughly suppressed. The calculated differential cross-section indicates that the influence of the retardation appears at scattering angles less than 0.2 mrad in the loss energy range of 10–15 eV. Using the improved KKA routine, we obtained the correct dielectric function that agreed with the optical data. The present technique is especially useful in measuring the dielectric function by EELS with a small collection semi-angle.