Dependence of threshold voltage (VTh) on oxide thickness (tox) for GaN-based metal-insulator-semiconductor high-electron-mobility transistors (MIS-HEMTs) using sputter-deposited Al2O3 as gate dielectric is studied in detail. Different III-nitride (III-N) heterostructures (AlGaN/GaN and AlInN/GaN) with/without GaN cap layer were used for fabricating these MIS devices. Interestingly, for all the sets of devices, a positive shift in VTh was observed initially with a increase in tox, followed by a negative shift of the same. A comprehensive analytical model has been proposed to explain the variation of VTh with tox and has been shown to match the experimental data for MIS-HEMTs fabricated on different heterostructures and with different values of tox. This model allows the extraction of different charge components in the oxide or at oxide/III-N interface. Normally OFF AlInN/GaN MIS-HEMTs with VTh of +0.67 V have been demonstrated with the optimized tox of sputtered Al2O3. © 2016 IEEE.