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.
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