It was investigated the possibility of creating NbN superconducting single-photon detectors with saturated dependence of quantum efficiency versus normalized bias current. It was shown that the saturation increases for the detectors based on finer films with a lower value of Rs300/Rs20. The decreasing of Rs300/Rs20 related to increasing influence of quantum corrections to conductivity of superconductors and, in its turn, to decreasing electron diffusion coefficient. The best samples has constant value of system quantum effi-ciency 94% at Ib/Ic~0.8 and wavelength 1.31 mkm.