Impact ionisation in combination with carrier-carrier scattering in the absence of phonon scattering in an illuminated semiconductor leads to an energy distribution of electrons in the conduction band and of holes in the valence band which is best described by a single Fermi-distribution with no splitting of quasi-Fermi-energies, but with a temperature different from the lattice temperature. To make proper use of this distribution in a solar cell, electrons and holes must be withdrawn through membranes, which are composed of narrow band, large bandgap semiconductors and which allow only electrons or holes in a narrow energy range to be transmitted. Current-voltage characteristics;Ind efficiencies are calculated analytically for maximum concentration of the solar radiation. A maximal efficiency of 85% is found for a vanishing bandgap of the solar cell material.