A 2D TCAD-based approach is proposed to investigate the leakage current and breakdown regime of GaN/AlGaN/Si structures at different ambient temperatures. Deep-level traps originated by Carbon doping, impact-ionization generation and thermally activated Poole-Frenkel conduction have been modeled to assess the role of such physical mechanisms on the forward-bias leakage current. A good agreement with experimental data has been obtained by implementing conduction and valence mini-bands within the deeper transition layer created by conductive dislocation defects or by superlattice structures. A 2D isolation device has been investigated up to breakdown and, for the first time to our knowledge, we prove with 2D TCAD simulation that in GaN based devices both impact-ionization and Poole-Frenkel conduction effects must be taken into account to correctly match experimental data.