## 3 Results and Discussion
### Effect of Device Parameters on the Transfer Characteristics
The ON-state current of the DMGE-HJLTFET decreased with the increase of \(\Phi_{\rm M2}\) and the OFF-state current of the DMGE-HJLTFET decreased with the increase of \(\Phi_{\rm M2}\) when \(\Phi_{\rm M2}\)\(\leq\) 4.4 eV. In addition, the ambipolar current occurred when \(\Phi_{\rm M2}\)\(\geq\) 4.5 eV which led to very poor transfer characteristic curves in the DMGE-HJLTFET as shown in Figure 8a. In Figure 8b, it is very clear that the value of electric field under M3 decreased with the increase of \(\Phi_{\rm M2}\) while the value of the electric field under M1 and M2 decreased with the increase of \(\Phi_{\rm M2}\) when \(\Phi_{\rm M2}\)\(\leq\) 4.4 eV and increased with the increase of \(\Phi_{\rm M2}\) when \(\Phi_{\rm M2}\)\(\geq\) 4.5 eV, which further explains the variation of the ON-state current in Figure 8a and made the energy band bend severely in this region, as shown in Figure 8c,d. Figure 8c,d depict the energy band diagram in ON-state and OFF-state, where it was observed that the tunneling barrier height increased with the increase of \(\Phi_{\rm M2}\) and height of barrier in OFF-state was much higher than that of ON-state. Hence, the overall performance of the DMGE-HJLTFET was significantly affected by \(\Phi_{\rm M2}\), considering all the factors, the optimal value of control gate workfunction was chosen as 4.4 eV. Figure 8: _Cont._  
Figure 7: (a) Transfer characteristics of the DMGE-HJLTFET with different polar gate workfunction (\(\Phi_{\rm PG}\)); (b) the variation of energy band diagram with different polar gate workfunction (\(\Phi_{\rm PG}\)). Figure 9a-d illustrate the impact of the auxiliary gate workfunction (\(\Phi_{\text{M1}}\)) and tunnel gate workfunction (\(\Phi_{\text{M3}}\)) on transfer characteristics, surface potential, electric field and band diagram with keeping \(\Phi_{\text{M2}}\) = 4.4 eV and keeping \(\Phi_{\text{PG}}\) = 5.9 eV. The transfer characteristics of the DMGE-HJLTFET at different values of \(\Phi_{\text{M1}}\) is shown in Figure 9a, where \(\Phi_{\text{M1}}\) was varied from 3.7 eV to 4.4 eV in a step of 0.1 eV. It could be found through the observation of Figure 9a that the ON-state current and the OFF-state current of the DMGE-HJLTFET decreased with the increase of \(\Phi_{\text{M1}}\), that is to say, appropriate selection of \(\Phi_{\text{M1}}\) was required to achieve higher Ion/Ioff ratio and lower Ssave, therefore, \(\Phi_{\text{M1}}\) = 4.1 eV was selected as the optimal value for auxiliary gate workfunction. In fact, the variation of transfer characteristics depended on the changes of surface potential and electric field. Figure 9b,c show the distribution of surface potential and electric field at the device surface. It can be noticed that both of them were markedly influenced by \(\Phi_{\text{M1}}\) and the DMGE-HJLTFET exhibited higher surface potential and electric field at the position of M1 and M3 under small \(\Phi_{\text{M1}}\), in which M1 suppressed the ambipolar leakage current and reduced hot carrier effects (HCEs) by diminishing the lateral electric field at the drain-channel interface. M3 improved the ON-state current by increasing the tunneling probability at the source-channel interface. A higher tunneling rate at the source-channel interface and higher barrier height at drain-channel interface were introduced simultaneously, as shown in Figure 9d. Therefore, \(\Phi_{\text{M1}}\) should be small in terms of ON-state current and OFF-state current, and \(\Phi_{\text{M1}}\) should not be small in terms of barrier height at the drain-channel interface. All things considered, the optimal value of \(\Phi_{\text{M1}}\) was chosen as 4.1 eV. Figure 8: (**a**) Transfer characteristics of the DMGE-HJLTFET with different control gate workfunction (\(\Phi_{\text{M2}}\)); (**b**) the distribution of electric field with different \(\Phi_{\text{M2}}\); (**c**) the ON-state energy band diagram with different \(\Phi_{\text{M2}}\); (**d**) the OFF-state energy band diagram with different \(\Phi_{\text{M2}}\). Figure 9: _Cont._