A simple structure with high breakdown voltage and a low leakage current of a vertical GaN p-n diode on a GaN free-standing substrate is demonstrated. We describe a vertical p-n diode with a simple edge termination that has a drift layer etched deeply and vertically. A device simulation revealed that the electric field was more relaxed at the device edge and applied uniformly in the entire device with increasing etching depth. We fabricated the simulated structure and succeeded in reducing the leakage current and improving the breakdown voltage. With this structure, a stable avalanche breakdown can be observed. (C) 2019 The Japan Society of Applied Physics