Insulated-gate AlGaN/GaN heterostructure field-effect transistors (HFETs), i.e., GaN-based metal-insulator-semiconductor (MIS) HFETs, have been fabricated that exhibited excellent DC and RF characteristics together with the reduced gate leakage current (Ig). The Al2O3/ Si 3N4 bilayer gate insulator was used to simultaneously utilize (i) the high-quality interface between Si3N4 and AlGaN, and (ii) the high resistivity and high dielectric constant of Al 2O3. The Ig was less than 10-4 A/mm even at a gate voltage of +3 V. In a device with a gate length of 0.1 μm, the drain current was 1.30 A/mm, and the cut-off frequency (fT) and maximum oscillation frequency (fmax) were 70 and 90 GHz, respectively. Moreover, the deposition effect of insulators on the electrical properties in AlGaN/GaN heterostructures has been examined and theoretically analyzed for Si- and Al-based insulators (Si3N4, SiO 2, AlN, and Al2O3), because insulators are commonly used for surface passivation as well as the gate insulator, and hence, clarifying the insulator deposition effect is a fundamental issue in GaN-based HFETs. The increase in the two-dimensional electron gas (2DEG) was observed for all the insulators, and the effect was found to vary among insulators. One result is that Al2O3 was most effective to increase N s. The results were explained in terms of the change in the potential profile. The band engineering including insulators is proposed to be indispensable for interpreting and designing the device performance, because, through the potential profile change, the essential device parameters are altered such as the source resistance, the channel resistance under the insulated-gate, and its threshold voltage.