  The bandgap and band bowing parameter of semiconductor alloys are calculated
with a fast and realistic approach. The method is a dielectric scaling
approximation that is based on a scissor approximation. It adds an energy shift
to the bandgap provided by the local density approximation (LDA) of the density
functional theory (DFT). The energy shift consists of a material-independent
constant weighted by the inverse of the high-frequency dielectric constant. The
salient feature of the approach is the fast calculation of the dielectric
constant of alloys via the Green function (GF) of the TB-LMTO (tight-binding
linear muffin-tin orbitals) in the atomic sphere approximation (ASA). When it
is applied to highly mismatched semiconductor alloys (HMAs) like Zn Te$_x$
Se$_{1-x}$, this method provides a band bowing parameter that is different from
the band bowing parameter calculated with the LDA due to the bowing exhibited
also by the high-frequency dielectric constant.
