## 3 Results and Discussion
Since the actual physical phenomena occurring in the device were not known, the results only represented the tendency of the gate leakage current depending on the device. Figure 8: Comparison of transfer I–V characteristics of MIS-HEMTs (samples A, B, and C) with respect to V\({}_{\rm{GS}}\) at (**a**) V\({}_{\rm{DS}}\) = 1 V, (**b**) V\({}_{\rm{DS}}\) = 5 V, (**c**) V\({}_{\rm{DS}}\) = 10 V, and (**d**) V\({}_{\rm{DS}}\) = 30 V (drain current (filled dot), transconductance (empty dot)). Figure 7: (**a**) Lattice temperature, and (**b**) electric field distributions across the 2-DEG channel layer with and without the Si\({}_{3}\)N\({}_{4}\) dielectric layer at V\({}_{\rm{GS}}\) = 0 V and V\({}_{\rm{DS}}\) = 30 V.  
the dielectric layer composition and thickness. Sample C's gate leakage current exceeded sample B's. Thus, Al\({}_{2}\)O\({}_{3}\) deposition on Si\({}_{3}\)N\({}_{4}\) effectively reduced the gate leakage current, but the gate leakage current increased with thicker Al\({}_{2}\)O\({}_{3}\) on Si\({}_{3}\)N\({}_{4}\). Figure 9(a) shows that sample C's lattice temperature across the 2-DEG channel layer was the highest, with samples A and B exhibiting similar values when V\({}_{\text{GS}}\) = 0 V and V\({}_{\text{DS}}\) = 30 V. The highest peaks occurred at the drain-side gate head edges with 441.94, 406.64, and 406.38 K for samples C, A, and B, respectively. However, the electric field distributions for the three structures were different. Sample A was the highest, followed by samples B and C at the drain-side gate head edge. As shown in Figure 5; Figure 7, sample C's lattice temperature across the 2-DEG channel layer was higher than sample B because sample C's effective current density was also higher, as shown in Figure 8. Figure 9(b) shows that sample C exhibited an even lower electric field at the drain-side gate edge, which resulted in an increasing gate leakage current, as shown in Figure 9. As the thickness of the insulator increased, the current due to the tunneling effect decreased. However, when the thickness of the insulator increased, the threshold voltage, stress, and heat transfer must be considered. In the case of samples B and C, the dielectric layer composition was a combination of Al\({}_{2}\)O\({}_{3}\) and Si\({}_{3}\)N\({}_{4}\). Since the barrier height in samples B and C were larger than for A, the gate leakage current by FN tunneling was reduced. For sample C, the electric field was the lowest, but the current density was the highest at V\({}_{\text{GS}}\) = 0 V and V\({}_{\text{DS}}\) = 30 V, resulting in generating more heat. In addition, the thermal conductivity of the materials must be taken into account in the heat transfer. The thermal conductivity of Al\({}_{2}\)O\({}_{3}\) was lower than that of Si\({}_{3}\)N\({}_{4}\). The induced heat confined in the Al\({}_{2}\)O\({}_{3}\) further lowered the barrier height and increased the gate leakage current. Figure 11 shows the MIS-HEMT breakdown voltage characteristics. Depositing the Al\({}_{2}\)O\({}_{3}\) on the Si\({}_{3}\)N\({}_{4}\) dielectric layer improved the breakdown voltage. We set the breakdown voltage for the drain current = 1 mA/mm as a reference, and achieved breakdown voltage values that were about 94, 194, and 300 V at pinch-off voltages = \(-\)14, \(-\)12, and \(-\)12.6 V, respectively, considering each threshold voltage. Although the gate leakage current in sample C was larger than for sample B, it showed higher breakdown characteristics. Figure 9: Gate leakage current for MIS-HEMTs (samples A, B, and C) with respect to V\({}_{\text{GS}}\) at (a) V\({}_{\text{DS}}\) = 10 V and (b) V\({}_{\text{DS}}\) = 30 V.  
Figure 12 shows the MIS-HEMT saturation current characteristics with and without SHE for V\({}_{\rm GS}\) = \(-\)2 to 0 V. SHE decreased the drain current for all three structures and made the current unstable. Sample C was more affected by SHE and sample B was less affected. Table 3 shows the calculated level of drain current degradation for all three structures.