Band-gap measurements of direct and indirect semiconductors using monochromated electrons

With the development of monochromators for transmission electron microscopes, valence electron-energy-loss spectroscopy (VEELS) has become a powerful technique to study the band structure of materials with high spatial resolution. However, artifacts such as Cerenkov radiation pose a limit for interpretation of the low-loss spectra. In order to reveal the exact band-gap onset using the VEELS method, semiconductors with direct and indirect band-gap transitions have to be treated differently. For direct semiconductors, spectra acquired at thin regions can efficiently minimize the Cerenkov effects. Examples of hexagonal GaN $(h\text{\ensuremath{-}}\mathrm{Ga}\mathrm{N})$ spectra acquired at different thickness showed that a correct band-gap onset value can be obtained for sample thicknesses up to 0.5 $t∕\ensuremath{\lambda}$. In addition, $\ensuremath{\omega}\text{\ensuremath{-}}q$ maps acquired at different specimen thicknesses confirm the thickness dependency of Cerenkov losses. For indirect semiconductors, the correct band-gap onset can be obtained in the dark-field mode when the required momentum transfer for indirect transition is satisfied. Dark-field VEEL spectroscopy using a star-shaped entrance aperture provides a way of removing Cerenkov effects in diffraction mode. Examples of Si spectra acquired by displacing the objective aperture revealed the exact indirect transition gap ${E}_{g}$ of $1.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.