  The group-IV diamond-structure elements are known to host a variety of planar
defects, including {001} planar defects in C and {001}, {111} and {113} planar
defects in Si and Ge. Among the {001} planar defects, the Humble defect, known
for some time to occur in Ge, has recently also been observed in Si/Ge alloys,
but the details of its electronic structure remain poorly understood. Here we
perform first-principles density functional calculations to study Humble
defects in both Ge and Ge$_{0.8}$Si$_{0.2}$. We also measure the Si
L$_{2,3}$-edge electron energy loss spectra both at the defect and in a
bulk-like region far from the defect, and compare with theoretical calculations
on corresponding Si sites in our first-principles calculations. We find that
inclusion of core-hole effects in the theory is essential for reproducing the
observed L$_{2,3}$ edge spectra, and that once they are included, the results
provide a set of fingerprints for different types of local atomic bonding
environments in Ge$_{0.8}$Si$_{0.2}$. Our first-principles calculations reveal
that the Humble defects have a tendency to enlarge the electronic band gap,
which may have potential uses in band engineering. The use of hybrid
functionals for an improved description of the band gap in these systems is
also discussed.
