The Electron—Hole Plasma at Finite Temperatures. Calculation of Exchange‐Correlation Energies and Padeé Approximants

The thermodynamics of an electron—hole plasma is investigated with special emphasis on the temperature dependence of exchange (x) and correlation (c). The basic quantity of the RPA approach used, is the free energy as a function of density and temperature. In a wide density range a remarkable compensation is found of the temperature dependence between x and c which is exemplified for the chemical potential. Numerical results are presented with parameters modelling Ge and GaAs. For the phase diagram minor changes result compared with the usual approach taking xc at zero temperature. For practical purposes Padé approximants are constructed.