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We propose an AlN/GaN/InGaN/GaN double-heterojunction high electron mobility transistor (DH-HEMT) structure with a 4 nm thin AlN barrier layer. The performance of the DH-HEMT device is investigated by using two-dimensional numerical simulation. The conduction band profile is obtained by using the Poisson’s equation and Fermi–Dirac statistics in combination with the polarization charges. Due to large conduction-band offset of the AlN/GaN interface and strong polarization of AlN, the minor channel at GaN/InGaN interface can be eliminated. Further, the hot electron and self-heating effects on the transport properties of this DH-HEMT are investigated by using hydrodynamic model. In comparison with the AlGaN barrier DH-HEMT and conventional HEMT, this kind of DH-HEMT can effectively reduce the hot electron effect under high voltage. The reason is that the maximum field strength is far below the critical value for the existence of the hot electron effect in the AlGaN barrier DH-HEMTs and conventional HEMTs with the same voltage 6 V. The simulation results also show that the ultrathin AlN barrier layer can significantly reduce thermal impedance, and then lower the self-heating effect. Furthermore, the passivation layer has significant role in the self-heating effect of the ultrathin barrier DH-HEMTs.