= Direct-gap semiconductor gain condition
{title2=$E_g<\hbar\omega<F_c-F_v$}
For a vertical optical transition between parabolic <energy bands> with common carrier <temperature>, net <stimulated emission> has occupation factor $f_c(E_c)-f_v(E_v)$. The monotonic <Fermi-Dirac distribution> makes this positive exactly when the <quasi-Fermi-level splitting> exceeds the transition <photon energy>. An allowed transition must also lie above the <band gap>. Broadening, band degeneracy and a zero-temperature occupation window require their own qualifications; this condition alone does not establish <laser threshold>.
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