  Contrary to the conventional empirical law, band gap of dilute nitride
semiconductors decreases with nitrogen concentration.
  In spite of a number of investigations, origin of this "large band gap
bowing", is still under debate. In order to elucidate this phenomenon, we
investigate change of band edge energies of GaN$_x$As$_{1-x}$ due to nitrogen
by using the perturbation theory. It is found that energy shift of conduction
band edge is arising from mixing between $\Gamma$- and L-states and/or
$\Gamma$- and X-states induced by displacement of Ga atoms around N. We also
found that the valence band edge state shows upward shift in spite of negative
potential of nitrogen. These results are well understood from character of the
wavefunctions and symmetry of the perturbation potential.
