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Temperature-dependent surface current measurements were performed to analyze the mechanism of surface conductance of AlGaN/GaN channel high-electron-mobility transistors by utilizing process-optimized double gate structures. Different temperatures and electric field dependence have been found in surface current measurements. At low electric field, the mechanism of surface conductance is considered to be two-dimensional variable range hopping. At elevated electric field, the Frenkel-Poole trap assisted emission governs the main surface electrons transportation. The extracted energy barrier height of electrons emitting from trapped state near Fermi energy level into a threading dislocations-related continuum state is 0.38 eV. SiN passivation reduces the surface leakage current by two order of magnitude and nearly 4 orders of magnitude at low and high electric fields, respectively. SiN also suppresses the Frenkel-Poole conductance at high temperature by improving the surface states of AlGaN/GaN. A surface treatment process has been introduced to further suppress the surface leakage current at high temperature and high field, which results in a decrease in surface current of almost 3 orders of magnitude at 476 K. [ABSTRACT FROM AUTHOR]