Universal behavior of exchange-correlation energy in electron-hole liquid

Abstract

Exchange-correlation energy of electron-hole liquid (EHL) is shown to be independent of different band characteristics of semiconductors. A simple expression of ${\ensuremath{\epsilon}}_{\mathrm{xc}}$ for EHL in all semiconductors is given. In units of excitonic rydberg, ${\ensuremath{\epsilon}}_{\mathrm{xc}}=\frac{(a+{\mathrm{br}}_{s})}{(c+{\mathrm{dr}}_{s}+{r}_{s}^{2})}$, where $a=\ensuremath{-}4.8316$, $b=\ensuremath{-}5.0879$, $c=0.0152$, and $d=3.0426$. Ground-state and thermodynamic properties calculated with this expression are in good agreement with earlier theoretical calculations and experimental results.