  A technique to measure the band gap of dielectric materials with high
refractive index by means of energy electron loss spectroscopy (EELS) is
presented. The technique relies on the use of a circular (Bessel) aperture and
suppresses Cherenkov losses and surface-guided light modes by enforcing a
momentum transfer selection. The technique also strongly suppresses the elastic
zero loss peak, making the acquisition, interpretation and signal to noise
ratio of low loss spectra considerably better, especially for excitations in
the first few eV of the EELS spectrum. Simulations of the low loss inelastic
electron scattering probabilities demonstrate the beneficial influence of the
Bessel aperture in this setup even for high accelerating voltages. The
importance of selecting the optimal experimental convergence and collection
angles is highlighted. The effect of the created off-axis acquisition
conditions on the selection of the transitions from valence to conduction bands
is discussed in detail on a simplified isotropic two band model. This opens the
opportunity for deliberately selecting certain transitions by carefully tuning
the microscope parameters. The suggested approach is experimentally
demonstrated and provides good signal to noise ratio and interpretable band gap
signals on reference samples of diamond, GaN and AlN while offering spatial
resolution in the nm range.
