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This letter describes a new two-step electrode process on p-GaN and characteristics of GaN p-n junction diodes on free-standing GaN substrates with low specific ON-resistance Rοn and high breakdown voltage VB. We develop a two-step process for anode electrodes in order to avoid plasma damage to the p+-GaN contact layer during the sputtering process. The specific ON-resistance is further improved due to a new low-damage process. The breakdown voltage of the diodes with the field-plate (FP) structure is over 1100 V, and the leakage current was low, i.e., in the range of 10-9 A. The specific ON-resistance of the diodes of 50 μm in diameter with the FP structure was 0.4 mΩ · cm2. Baliga's figure of merit (VB2/Ron) of 3.0 GW/cm2 is obtained. These are the best values ever reported among those achieved by GaN p-n junction diodes on free-standing GaN substrates.