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Nb-based superconducting tunnel junctions are being developed as high energy resolution X-ray detectors. Unfortunately, loss of excess quasiparticles at the edges, combined with lateral diffusion, results in an inhomogeneous response. To study this degradation of energy resolution, we manufactured detectors with a Ta trap in the top or bottom electrode away from the tunneling barrier. Excess quasiparticles in this so-called killed electrode will be trapped effectively and thus removed from the tunneling process. The X-ray spectra of the active electrode can be fitted with a model based on classical diffusion of quasiparticles. On junctions with a killed bottom electrode also Low Temperature Scanning Electron Microscopy (LTSEM) measurements have been performed. The X-ray spectra and the LTSEM scans are consistent with each other and with the model. The energy resolution of the junctions presented here is limited by loss of quasiparticles at the edges.