  The performance of many superconducting devices is degraded in presence of
non-equilibrium quasiparticles in the superconducting part. One promising
approach towards their evacuation is the use of normal-metal quasiparticle
traps, where normal metal is brought into good metallic contact with the
superconductor. A voltage biased normal-metal--insulator--superconductor
junction equipped with such a trap is used to investigate on the trapping
performance and the part played by the superconducting proximity effect
therein. This involves an appropriate one-dimensional model of the junction and
the numerical solution of Usadel equations describing the non-equilibrium state
of the superconductor. The functionality of the trap is determined by the
density of states (DOS) at the tunnel barrier. Herein, the proximity effect
leads to two antagonistic characteristics affecting the trapping performance:
the beneficial reduction of the DOS at an energy $|E| = \Delta_{\text{BCS}}$
versus the contraction of the spectral energy gap causing quasiparticle
poisoning. For both effects the trap position is decisive, which needs to be
taken into account for optimizing the trapping performance. In addition, the
conversion between dissipative normal and supercurrent inside the
superconducting part with its impact on the quasiparticle density is studied.
