The ab initio pseudopotential method within the local density functional th
eory and virtual-crystal approximation is used to study the band gap of the
Si1-x-yGexCy (y less than or equal to 0.09) alloys on a Ge(001) substrate.
The heterojunction discontinuities are also investigated in the framework
of the average bond energy theory in conjunction with the deformation poten
tial method. The calculated results show that the energy gap still remains
indirect and only a small amount of C could cause the energy gap to be shru
nk significantly. The top of the valence bands of the strained Si1-x-yGexCy
alloys on Ge(001) is significantly lifted and even could be greatly higher
than that of Ge by the addition of small amounts of carbon. The trends of
our results are consistent with other theoretical data.