Sterile neutrinos are a minimal extension of the Standard Model of Particle Physics. A promising model-independent way to search for sterile neutrinos is via high-precision beta spectroscopy. The Karlsruhe Tritium Neutrino (KATRIN) experiment, equipped with a novel multi-pixel silicon drift detector focal plane array and read-out system, named the TRISTAN detector, has the potential to supersede the sensitivity of previous laboratory-based searches. In this work we present the characterization of the first silicon drift detector prototypes with electrons and we investigate the impact of uncertainties of the detectors response to electrons on the final sterile neutrino sensitivity.