In this work, the breakdown characteristics of AlGaN/GaN planar Schottky barrier diodes (SBDs) fabricated on the silicon substrate are investigated. The breakdown voltage (BV) of the SBDs first increases as a function of the anodeto-cathode distance and then tends to saturate at larger inter-electrode spacing. The saturation behavior of the BV is likely caused by the vertical breakdown through the intrinsic GaN buffer layer on silicon, which is supported by the post-breakdown primary leakage path analysis with the emission microscopy. Surface passivation and field plate termination are found effective to suppress the leakage current and enhance the BV of the SBDs. A high BV of 601 V is obtained with a low on-resistance of 3.15 mΩ·cm^2.