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The carrier transport mechanisms of Ni/Ag/Pt contacts to moderately Mg-doped p-GaN (sample A) and highly Mg-doped p-GaN (sample B) were investigated. Depending on the Mg doping concentration, the dominant carrier transport mechanism could be categorized as thermionic field emission for sample A and carrier transport through the deep-level defect (DLD) band for sample B, resulting in different specific contact resistances of 7.1 × 10-2 and 7.0 × 10-4 Ωcm2 for samples A and B, respectively. For sample A, the contact parameters, including a Schottky barrier height of 0.94 eV and a tunneling parameter of 0.045 eV, could be observed, yielding the substantial interfacial carriers of 4.5 ×1019 cm-3 and, hence, field emission through a thin barrier. For sample B, the effective barrier height associated with the DLD band was suggested to be an important parameter since the carrier transport predominantly occurred through the DLD band rather than the valence band. Accordingly, the effective barrier height was calculated to be 0.12 eV, which was low enough to explain the excellent ohmic contact.