The harsh radiation environment in present and future high-energy physics experiments, such as the Large Hadron Collider (LHC), is a driving force for the development of high-voltage Si strip detectors. It is well known that mobile surface ions can affect the stability and long-term behaviour of Si detectors. These instabilities can be nearly eliminated and the performance of Si detectors can be improved by implementing suitably passivated metal-overhang structures. This paper presents the influence of the relative permittivity of the passivant on the breakdown performance of the Si detectors using computer simulations. The semi-insulator and the dielectric-passivated metal-overhang structures are compared under optimal conditions. Influence of the salient design parameters such as field oxide thickness, junction depth, metal-overhang width, and the surface charge on the breakdown performance of these structures are systematically analyzed, thus providing a comprehensive picture of the behaviour of metal-overhang structures and helping in the detector optimization task. The results presented in this paper clearly demonstrate the superiority of the metal-overhang structure design employing semi-insulator-passivated structures over dielectric-passivated ones in realizing a given breakdown voltage.