Dependence of threshold voltage ( $V_{\mathrm{ Th}}$ ) on oxide thickness ( $t_{\mathrm{ ox}}$ ) 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 $V_{\mathrm{ Th}}$ was observed initially with a increase in $t_{\mathrm{ ox}}$ , followed by a negative shift of the same. A comprehensive analytical model has been proposed to explain the variation of $V_{\mathrm{ Th}}$ with $t_{\mathrm{ ox}}$ and has been shown to match the experimental data for MIS-HEMTs fabricated on different heterostructures and with different values of $t_{\mathrm{ ox}}$ . 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 $V_{\mathrm{ Th}}$ of +0.67 V have been demonstrated with the optimized $t_{\mathrm{ ox}}$ of sputtered Al2O3.