[en] The density of states in heavily doped strongly compensated semiconductors is calculated by using Feynman's path-integral method. The case is considered when correlation exists in the impurity positions due to the Coulomb interactions between the ionised donors and acceptors and the intrinsic carriers in the plasma prior to the freeze-out of the impurity diffusion during the growth of the crystal. The density of states in the tail is calculated and numerical results for n-GaAs are compared with previous calculations. At positive energies corresponding to the conduction band the density of states is found to agree in the first approximation with the semiclassical formula derived by Bonch-Bruevich (1962) and Kane (1963). Corrections to it due to the correlation and the short-range fluctuations in the impurity potential are obtained. (author)