R. Erni,* N. D. Browning**, P. Specht***, and C. Kisielowski**** * EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium ** Materials Science and Technology Division, Lawrence Livermore National Laboratory, P.O. Box 808, L-356, Livermore, CA 94550, and Department of Chemical Engineering and Materials Science, University of California Davis, One Shields Ave., Davis, CA 95616 *** Materials Sciences Division, Lawrence Berkeley National Laboratory (LBNL), One Cyclotron Road, Berkeley, CA 94720 **** National Center for Electron Microscopy, LBNL, One Cyclotron Road, Berkeley, CA 9420 Valence electron energy-loss spectroscopy (VEELS) in (scanning) transmission electron microscopy (STEM) offers the possibility to measure band-structure information and in particular band-gap and band-transition energies of semiconductor materials with (sub-)nanometer spatial resolution. Using an electron monochromator implemented in the gun area of a (scanning) transmission electron microscope, VEEL spectra can be recorded that reveal in an unprecedented way the spectral fine structure of the low-loss area. Down to an energy loss of about 1.0 eV the signal is hardly affected by the low-energy tail of the zero-loss peak. For the case that electrons are detected that are inelastically scattered at very small angles, VEELS approaches the optical limit providing information about the complex dielectric function e(