The aim of this work is to investigate the breakdown mechanisms of the layers constituting the vertical buffer of GaN-on-Si HEMTs; in addition, for the first time we demonstrate that the breakdown field of the AlN nucleation layer grown on a silicon substrate is equal to 3.2 MV/cm and evaluate its temperature dependence. To this aim, three samples, obtained by stopping the epitaxial growth of a GaN on Silicon stack at different steps, are studied and compared: Si/AlN, Si/AlN/ AlGaN, full vertical stack up to the Carbon doped buffer layer. The current-voltage (IV) characterizations performed at both room temperature and high temperature show that: (i) the defectiveness of the AlN nucleation layer is the root cause of the leakage through an AlN/Silicon junction, and causes the vertical I-V characteristics to have a high device-to-device variability; (ii) the first AlGaN layer grown over the AlN, beside improving the breakdown voltage of the whole structure, causes the leakage current to be more stable and uniform across the sample area; (iii) a thick strain-relief stack and a carbon-doped GaN buffer enhance the breakdown voltage up to more than 750 V at 170°C, and guarantee a remarkably low device-to-device variability. Furthermore, a set of constant voltage stress on the Si/AlN sample demonstrate that the aluminum nitride layer shows a time dependent breakdown, with Weibull-distributed failures and a shape factor greater than 1, in line with the percolation model.