# Compact Model for L-Shaped Tunnel Field-Effect Transistor Including the 2D Region
## 3 Results  
Figure 7a-c shows \(I_{\rm ds}\)-\(V_{\rm gs}\) characteristics of LTFET with \(T_{\rm j}\) = 4, 5, and 6 nm, respectively. Symbols and lines denote the simulation results of TCAD and the proposed model, respectively. Blue, red, and black colors denote \(V_{\rm ds}\) = 0.25, 0.5, and 0.7 V, respectively. A kink is observed in Figure 7a-c, at the transition point where the 1D model takes over the 2D model. This is observed because the 1D and 2D models are independent of each other and don't produce the same and continuous \(G_{\rm tun}\) at the transition point. There is no noticeable change observed in the subthreshold behavior as \(T_{\rm j}\) is changed from 4 nm to 6 nm. However, the on-current (\(I_{\rm ON}\)) is observed to decrease as \(T_{\rm j}\) is increased. \(I_{\rm ON}\) at \(V_{\rm gs}\) = 0.8 V and \(V_{\rm ds}\) = 0.7 V is 0.48, 0.22, and 0.09 uA for \(T_{\rm j}\) = 4, 5, and 6 nm, respectively. This is because \(W_{\rm t}\) and \(G_{\rm tun}\) are inversely proportional, as can be observed from (13); the longer \(W_{\rm t}\) in \(T_{\rm j}\) = 5 and 6 nm results in lower \(G_{\rm tun}\), and consequently, lower \(I_{\rm ds}\). This effect is captured by the model reasonably well. This suggests that shorter \(T_{\rm j}\) is more desirable for getting higher \(I_{\rm ON}\). Figure 7d-f shows \(I_{\rm ds}\)-\(V_{\rm ds}\) characteristics of the LTFET for \(T_{\rm j}\) = 4, 5, and 6 nm, respectively. Symbols denote TCAD simulation results, and lines denote model results. Black, red, blue, and magenta denote \(V_{\rm gs}\) = 0.2, 0.4, 0.6, and 0.8 V, respectively. As shown in Figure 7d-f, the saturation characteristics of the LTFET are predicted reasonably well by the model. Figure 7: **(a–c)**\(I_{\rm ds}\)–\(V_{\rm gs}\) characteristics of LTFET with \(T_{\rm j}\) = 4, 5, and 6 nm, respectively, at \(V_{\rm ds}\) = 0.25 (blue), 0.5 (red), and 0.7 V (black). **(d–f)**\(I_{\rm ds}\)–\(V_{\rm ds}\) characteristics of LTFET with \(T_{\rm j}\) = 4, 5, and 6 nm, respectively, at \(V_{\rm gs}\) = 0.2 (black), 0.4 (red), 0.6 (blue), and 0.8 V (magenta). Error bar: 10%. Lines: Model. Symbols: TCAD. Figure 8 shows \(I_{\text{ds}}\)-\(V_{\text{gs}}\) characteristics of LTFET with \(T_{\text{j}}\) = 4 nm and \(H_{\text{overlap}}\) = \(H_{\text{s}}\) varied at \(V_{\text{ds}}\) = 0.5 V. Symbols denote TCAD simulation results and lines denote model results. Blue, red, and black represent \(H_{\text{overlap}}\) = 40, 50, and 60 nm, respectively. It is shown in Figure 8 that, as \(H_{\text{overlap}}\) = \(H_{\text{s}}\) is increased, the \(I_{\text{ds}}\) increases. This is because, with an increase in \(H_{\text{overlap}}\), the BTBT area increases. This results in an increase in \(I_{\text{ds}}\). Once again, the model captures this effect reasonably well. Compared to the planar TFET, the LTFET offers better SS and \(I_{\text{ON}}\) performance. This can be gauged from the fact that while in planar TFET, the dominant BTBT generation area comprises the surface source/channel depletion regions. In the LTFET, however, because of the gate-source overlap, this area is significantly amplified by the height of the source and \(C_{\text{overlap}}\) regions. Furthermore, because of this overlap, the electrostatic coupling between gate and source is stronger in LTFET. In other words, the electric field is stronger in the LTFET as compared to the planar TFET, which also results in higher \(I_{\text{ON}}\) and lower inverse subthreshold slope in LTFET, as was demonstrated even in the case of the experimental LTFET and planar TFET in [4]. For a compact model, the simulation results of the model agree reasonably well with those of TCAD within a maximum error of 10%. However, it is not entirely accurate. The inaccuracy results from the simplified integral expression in (14). Numerical integration of \(G_{\text{tun}}\) with respect to \(x\) will significantly improve the result. Another source of error is the use of the smoothing function to model electron inversion.