Analysis of first KATRIN data and searches for keV-scale sterile neutrinos

The phenomenon of neutrino oscillation stands in contradiction with the Standard Model of Particle Physics (SM) where neutrinos are formulated as massless particles. One way to introduce a non-zero neutrino mass to the SM is the so-called see-saw-mechanism. It adds at least one sterile neutrino to the particle framework. A sterile neutrino would not participate in any SM interaction, only interact gravitationally and would be of arbitrary mass-scale. These unique properties make a sterile neutrino an interesting Dark Matter candidate. The Karlsruhe Tritium Neutrino (KATRIN) experiment aims to determine the effective electron anti-neutrino mass with a sensitvity of 0.2 eV/c${}^2$ (90 % C.L.) by observing the tritium β-decay close to its kinematic endpoint. Studies show that the experiment can be additionally extended to search for a sterile neutrino, for example on the keV mass-scale. This thesis specifies how the KATRIN experiment can be operated to search for keV-scale sterile neutrinos without any significant hardware modifications. It presents a first comprehensive overview of all yet known systematic effects that occur in such a measurement. This information is used for a first keV-scale sterile neutrino measurement with KATRIN data. By analyzing 82 KATRIN β-spectrum scans wit a total measurement time of approximately 160 hours, the current laboratory limit on the active-to-sterile mixing angle could be improved by up to a factor of eight on a mass scale of 0.10 keV ≤ m${}_{{\nu }_s}$ ≤ 0.76 keV with a resolution on the mixing amplitude of up to sin${}^2$θ < 2.33⋅10${}^{-3}$.