Superconducting tunnel junctions X-ray detectors Ti/Nb/Al,AlO x /Al/ Nb(2)/NbN with killed Ti/Nb electrode was studied as a function of bias voltage, energy of the absorbed quantum, and thickness of the Nb(2) layer. The data was compared with a simple diffusion model including the losses of excess quasiparticles due to self-recombination. It was shown that increasing of the electrode thickness reduces the self-recombination contribution and improves the linearity of the detector response.