  Conduction and valence band states for the highly mismatched alloy (HMA) Ge:C
are projected onto Ge crystal states, Ge vacancy states, and Ge/C atomic
orbitals, revealing that substitutional carbon not only creates a direct
bandgap, but the new conduction band is optically active. Overlap integrals of
the new Ge:C conduction band with bands of pure Ge shows the new band has
almost no Ge band character. C sites structurally mimic uncharged vacancies in
the Ge lattice, similar to Hjalmarson's model for other HMAs. C perturbs the
entire Ge band structure even at the deepest crystal core energy levels.
Projection onto atomic sites shows relatively weak localization compared with
other HMAs, but does show a strong anisotropy in probability distribution.
L-valley conduction band states in Ge are ruled out as major contributors to
the carbon state in Ge:C, both by weak inner products between these states and
by a negligible effect on optical transition strength when adding C.
