Cerenkov losses: a limit for bandgap determination and Kramers-Kronig analysis.

Measuring low energy losses in semiconductors and insulators with high spatial resolution becomes attractive with the increasing availability of modern transmission electron microscopes (TEMs) equipped with monochromators, C(s) correctors and energy filters. In this paper, we demonstrate that Cerenkov losses pose a limit for the interpretation of low energy loss spectra (EELS) in terms of interband transistions and bandgap determination for many materials. If the velocity of a charged particle in a medium exceeds the velocity of light, photons are emitted leading to a corresponding energy loss of a few electronvolt. Since these losses are strong for energies below the onset of interband transitions, they change the apparent loss function of semiconductors and insulators, with the risk of erroneous interpretation of spectra. We measured low energy losses of Si and GaAs with a monochromated TEM demonstrating the effect of sample thickness on Cerenkov losses. Angle resolved EELS and energy filtered diffraction patterns (taken without a monochromator) show the extremely narrow angular distribution of Cerenkov losses. The latter experiment provides a method that allows to decide whether Cerenkov radiation masks the very low loss signal in EELS.