Electron-hole liquid in heavily doped n-type ge and si

The ground-state energy of an electron-hole liquid in n-type doped si and ge at high dopant concentrations is computed. The impurities are taken to be randomly distributed, linearly screened point charges and their effect on the energy calculated to second order in the impurity potential. The band structure is treated in the effective-mass approximation with the anisotropic conduction-electron effective masses and coupled light and heavy hole bands. The correlation energy is computed in the random-phase approximation with a spherically averaged conduction-electron polarizability. The binding energy per charge carrier increases in magnitude with impurity concentration, but is weaker than in the intrinsic case except for densities much higher than the mott density. Good agreement is found with experimental results for the shift in the optical band gap with doping and the shift in the luminescence edge when droplets are formed.