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This study investigated the electrical properties of AlGaN/GaN high-electron-mobility transistors (HEMTs) with varied recess depths under the gate electrode. We demonstrated a recess depth of approximately 6 nm, which was achieved through neutral beam etching (NBE) technique with a low etch rate of 1.8 nm/min, resulting in device enhancement-mode (E-mode) behavior with threshold voltage (V_th) of 0.49 V. The effects of post-metallization annealing (PMA) on the device performance were also examined. The results revealed that PMA treatment improves the DC characteristics of the devices, including maximum drain current (I_DMAX), transconductance (g_m), subthreshold swing (SS), on-off ratio, and off-state leakage current, with maximum enhancement percentage of 18.3% for I_DMAX, 3758% for on-off ratio, and 54.3% for SS. Moreover, this study compared the recess depths of metal-insulator-semiconductor high-electron-mobility transistors (MIS-HEMTs) with the SiN dielectric layer. The results showed that MIS-HEMTs exhibit more negative V_th values, which can be attributed to the controlled surface states achieved through passivation.