## 3 Results and Discussion  
We first compared BG-HEMT and MIS-HEMT (sample A) transfer I-V characteristics for each drain voltage (V\({}_{\text{DS}}\)) = 1, 5, 10, and 30 V. The sample A threshold voltage shifted negatively to reach approximately \(-7.5\) V, and the maximum transconductance decreased compared with BG-HEMT, as shown in Figure 5. The sample A drain current was generally larger than that for BG-HEMT and became much larger as V\({}_{\text{DS}}\) increased. Figure 4: Thermal conductivities for GaN, Al\({}_{2}\)O\({}_{3}\), and Si\({}_{3}\)N\({}_{4}\) with respect to temperature. Figure 6 shows the measured gate leakage current with respect to the gate voltage (V\({}_{\text{GS}}\)) for V\({}_{\text{DS}}\) = 1, 5, 10, and 30 V. In the case of BG-HEMT, the gate leakage current decreased as V\({}_{\text{GS}}\) increased at low V\({}_{\text{DS}}\) = 1 and 5 V. However, at high V\({}_{\text{DS}}\) = 10 and 30 V, the gate leakage current decreased with increasing V\({}_{\text{GS}}\), but increased again. The gate leakage current was affected by heat, and when V\({}_{\text{GS}}\) was above the threshold voltage of about \(-\)3.7 V, the gate leakage current increased because heat was generated by the device operation. In contrast, the gate leakage current was significantly reduced in sample A. Figure 7 shows the lattice temperature and electric field across the 2-DEG channel layer of the BG-HEMT and sample A at V\({}_{\text{GS}}\) = 0 V and V\({}_{\text{DS}}\) = 30 V. Sample A's lattice temperature in the 2-DEG channel layer was significantly higher than that for BG-HEMT, but sample A's electric field was lower than that for BG-HEMT. Since the increase of current density was larger (see Figure 5d) than the decrease of the electric field in sample A, as shown in Figure 7b, the overall lattice temperature of sample A across the 2-DEG channel layer was larger than that of BG-HEMT, as shown in Figure 7a (see Equation (5)). Although the gate leakage current can be affected by temperature, the dielectric layer effectively reduced the gate leakage current [21]. After confirming that sample A's gate leakage current was markedly reduced, the dielectric layer composition was changed, as shown in Figure 1c. We then compared the transfer I-V characteristics for these structures when V\({}_{\text{DS}}\) = 1, 5, 10, and 30 V. Figure 8 shows the threshold voltages, maximum transconductances, and drain currents for samples A, B, and C. Sample B's threshold voltage shifted toward the positive direction as compared with sample A, and sample C shifted toward the negative direction [35]. Sample B and C's threshold voltages were about \(-6.2\) and \(-9.4\) V, respectively. Maximum transconductance was achieved for sample B, then C and A, in descending order. However, the drain current exhibited different tendencies, with sample C obtaining the highest value, then sample B and A, in descending order. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **GaN** & **AlGaN** \\ \hline Bandgap energy (eV) & 3.39 & 3.89 \\ Electron affinity (eV) & 4 & 3.6 \\ Low field mobility (cm\({}^{2}\) V\({}^{-1}\) s\({}^{-1}\)) & 990 & 300 \\ Relative permittivity & 9.5 & 9.38 \\ Thermal conductivity constant (W cm\({}^{-1}\) K\({}^{-1}\)) & 1.3 & 0.4 \\ TC.NPOW & 0.43 & - \\ High field mobility model & GANSAT saturation velocity model \\ Electron Saturation velocity (cm s\({}^{-1}\)) & \(1.9\times 10^{7}\) & \(1.12\times 10^{7}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Material parameters used for simulations at temperature 300 K.  
Figure 6: Gate leakage current for BG-HEMT and MIS-HEMT (sample A) with respect to V\({}_{\text{GS}}\) at (**a**) \(\text{V}_{\text{DS}}\) = 1 V, (**b**) V\({}_{\text{DS}}\) = 5 V, (**c**) V\({}_{\text{DS}}\) = 10 V, and (**d**) V\({}_{\text{DS}}\) = 30 V.  
Samples A, B, and C's gate leakage currents were simulated at high V\({}_{\rm{DS}}\) = 10 and 30 V. Figure 9 shows that sample B's gate leakage current was significantly reduced compared with sample A, even though the values were extremely low.