We study statistical properties of a strongly separated electron-hole plasma in an undoped GaN/ AlGaN quantum well. We use a self-consistent approach, which is based on the proper account of the impact of screening on bound and scattered states. A new mechanism of screening of Coulomb interaction by spatially indirect excitons is proposed and investigated within the framework of the Thomas-Fermi approximation. We calculate the ionization degree as a function of total carrier density for different quantum well widths. The interplay between screening, charge-separation and k-space filling effects is discussed.