# Improvement of Electrical Performance in Heterostructure Junctions TFET Based on Dual Material Gate
## 3 Results and Discussion
### Performance Comparison in Terms of Analog/RF Figure of Merits  
As we know, the frequency characteristics of the integrated circuits is profoundly affected by parasitic capacitances of devices, so it is very necessary to research the capacitance of DMMG-HJLTFET. Apparently, the characteristics of Cgg (gate capacitance), Cgs (capacitance of gate to source), and  
Figure 10: (**a**) Simulated log scale and linear scale transfer characteristics of DMMG-HJLTFET with different thickness of silicon (T\({}_{\text{S}}\)) in sandwich stack structure (GaAs/Si/GaAs); (**b**) the distribution of electric field at the surface with different thickness of silicon (T\({}_{\text{S}}\)) in sandwich stack structure (GaAs/Si/GaAs).  
Figure 9: (**a**) Simulated log scale and linear scale transfer characteristics of DMMG-HJLTFET with different auxiliary gate work function (\(\Phi_{\text{MI}}\)); (**b**) the potential distribution at the surface with different auxiliary gate work function (\(\Phi_{\text{MI}}\)); (**c**) the distribution of electric field at the surface with different auxiliary gate work function (\(\Phi_{\text{MI}}\)); (**d**) the variation of ON-state energy band with different auxiliary gate work function (\(\Phi_{\text{MI}}\)).  
Cgd (capacitance of gate to drain) are of great significance to evaluate the frequency characteristics and analog application ability of devices. Figure 11a-c show the capacitance of JLTFET, HJLTFET and DMM-HJLTFET versus Vgs under Vds = 1 V. In Figure 11a-c, the trend of the capacitance curve versus Vgs is similar, Cgs is very small in three devices due to the existence of polar gate which separates control gate electrode far from source electrode and, as a result, the coupling of control gate electrode and source electrode is relatively slight, so the curve of Cgg and Cgd is highly coincident, and Cgg is mainly determined by Cgd. Figure 11d shows the comparison of Cgg of JLTFET, HJLTFET and DMMG-HJLTFET, Cgg of JLTFET and HJLTFET remain at a small value when Vgs \(<\) Vds and increase rapidly with the increasing Vgs when Vgs \(>\) Vds, as shown in Figure 11d, while Cgg of DMMG-HJLTFET remains at a small value when Vgs \(<\) 0.5 Vds and increases rapidly with the increasing Vgs when Vgs \(>\) 0.5 Vds on account of divided gate electrode, moreover, Cgg of DMMG-HJLTFET is much less than that of JLTFET and HJLTFET due to the hetero dielectric adopted under the control gate.  
Based on the above capacitance changes, we discuss the cut-off frequency(f\({}_{\rm T}\)) and gain bandwidth (GBW). Both of them are the important evaluation indicators for RF performance, and as shown in Equation (4), cut-off frequency(f\({}_{\rm T}\)) can be expressed as ratio of gm to Cgg [36]:  
\[f_{\rm T}=\frac{\rm g_{m}}{2\pi\rm C_{gs}\sqrt{1+2\frac{C_{gd}}{C_{gs}}}}\approx \frac{\rm g_{m}}{2\pi(\rm C_{gs}+C_{gd})}=\frac{\rm g_{m}}{2\pi\rm C_{gg}} \tag{4}\]  
The GBW can be expressed as a ratio of g\({}_{\rm m}\) to C\({}_{\rm gd}\) for the DC gain value equal to 10, as shown in Equation (5) [37; 38]:  
\[\rm GBW=\frac{\rm g_{m}}{2\pi 10\rm C_{gd}} \tag{5}\]  
Figure 11: (**a**) Capacitance of JLTFET versus Vgs; (**b**) capacitance of HJLTFET versus Vgs; (**c**) capacitance of DMMG-HJLTFET versus Vgs; (**d**) comparison of Cgg (gate capacitance) of JLTFET, HJLTFET and DMMG-HJLTFET versus Vgs under Vds = 1.0 V.  
Figure 12a,b shows the characteristic curves of the f\({}_{\rm T}\) and GBW of JLTFET, HJLTFET and DMMG-HJLTFET. Further, benefiting from large transconductance induced by structural innovation, the DMMG-HJLTFET could achieve a maximum f\({}_{\rm T}\) of 9.17 GHz at Vgs = 1.4 V, and a maximum GBW of 0.17 GHz at Vgs = 1.2 V, respectively. However, maximum f\({}_{\rm T}\) of JLTFET and HJLTFET are only 1.01 GHz at Vgs = 2.0 V and 3.74 GHz at Vgs = 1.6 V, and maximum GBW of JLTFET and HJLTFET are only 0.005 GHz and 0.09 GHz at Vgs = 1.1 V.