Development of a Silicon Drift Detector Array to Search for keV-scale Sterile Neutrinos with the KATRIN Experiment

Sterile neutrinos in the keV mass range present a viable candidate for dark matter. They can be detected through single $\beta$ decay, where they cause small spectral distortions. The Karlsruhe Tritium Neutrino (KATRIN) experiment aims to search for keV-scale sterile neutrinos with high sensitivity. To achieve this, the KATRIN beamline will be equipped with a novel multi-pixel silicon drift detector focal plane array named TRISTAN. In this study, we present the performance of a TRISTAN detector module, a component of the eventual 9-module system. Our investigation encompasses spectroscopic aspects such as noise performance, energy resolution, linearity, and stability.