  The electronic band structure of complex nanostructured semiconductors has a
considerable effect on the final electronic and optical properties of the
material and, ultimately, on the functionality of the devices incorporating
them. Valence electron energy-loss spectroscopy (VEELS) in the transmission
electron microscope (TEM) provides the possibility of measuring this property
of semiconductors with high spatial resolution. However, it still represents a
challenge for narrow-bandgap semiconductors, since an electron beam with low
energy spread is required. Here we demonstrate that by means of monochromated
VEELS we can study the electronic band structure of narrow-gap materials GaSb
and InAs in the form of heterostructured nanowires, with bandgap values down to
0.5 eV, especially important for newly developed structures with unknown
bandgaps. Using complex heterostructured InAs-GaSb nanowires, we determine a
bandgap value of 0.54 eV for wurtzite InAs. Moreover, we directly compare the
bandgaps of wurtzite and zinc-blende polytypes of GaSb in a single
nanostructure, measured here as 0.84 and 0.75 eV, respectively. This allows us
to solve an existing controversy in the band alignment between these structures
arising from theoretical predictions. The findings demonstrate the potential of
monochromated VEELS to provide a better understanding of the band alignment at
the heterointerfaces of narrow-bandgap complex nanostructured materials with
high spatial resolution. This is especially important for semiconductor device
applications where even the slightest variations of the electronic band
structure at the nanoscale can play a crucial role in their functionality.
