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

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