This work demonstrates quasi-vertical GaN Schottky barrier diodes (SBDs) on 6-inch Si substrate with a breakdown voltage (BV) over 1 kV, the highest BV reported in vertical GaN-on-Si SBDs to date. The deep mesa inherently in quasi-vertical devices is leveraged to form a self-aligned edge termination, and the mesa sidewall is covered by the p-type nickel oxide (NiO) as a reduced surface field (RESURF) structure. This novel termination enables a parallel-plane junction electric field of 2.8 MV/cm. The device also shows low turn-on voltage of 0.5 V, and low specific on-resistance of 1.1 mΩ⋅ cm 2 . Moreover, the device exhibits excellent overvoltage robustness under the continuous 800 V stress in the unclamped inductive switching test. These results show the good promise of the low-cost vertical GaN-on-Si power diodes.