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In order to assess possible mechanisms of gate reverse-bias leakage current in AlInN/GaN high electron mobility transistors (HEMTs) grown by metalorganic chemical-vapor deposition on SiC substrates, temperature-dependent current-voltage measurements combined with Fourier transform current deep level transient spectroscopy (FT-CDLTS) are performed in the temperature range of 200–400 K. In this range of temperature reverse-bias leakage current flow is found to be dominated by Poole–Frenkel emission. Based on CDLTS measurements, a model of leakage current transport via a trap state located at the AlInN/metal interface with an activation energy of 0.37 eV is suggested. The trap nature is shown to be an extended trap, most probably associated with dislocations in the AlInN barrier layer.