In this paper, the electrical properties of different metal/p-GaN contacts (Ti/Al, TiN/Ti/Al and Ni/Au) have been investigated to get a deeper understanding of the behavior of p-GaN/AlGaN/GaN heterostructures for normally-off HEMTs. In particular, the study of the temperature dependent current-voltage characteristics allowed to identify the dominant carrier transport mechanism at the metal/p-GaN interface (Thermionic Field Emission). From the fit of the experimental current-voltage data it was possible to determine the Schottky barrier height values for the three systems, 2.08 eV (Ti/Al), 1.57 eV (TiN/Ti/Al) and 1.89 eV (Ni/Au). Hence, choosing the highest barrier height contact (Ti/Al) as gate electrode on a p-GaN/AlGaN/GaN heterostructure, optimized based on simulations, allowed to obtain devices with a normally-off behavior and a positive V th of+ 1.3 V.