# Compact Trap-Assisted-Tunneling Model for Line Tunneling Field-Effect-Transistor Devices
## 3 Results  
To demonstrate whether the Gaussian approximation of \(G_{\text{TAT}}\) is feasible, Figure 5 compares \(G_{\text{TAT}}\) calculated from the actual SRH-based \(G_{\text{TAT}}\) equation: (9) and \(G_{\text{TAT}}\) approximated by Gaussian approximation: (16) for \(T_{\text{j}}\) = 7 nm. The approximated \(G_{\text{TAT}}\) is reasonably consistent with the calculated \(G_{\text{TAT}}\). It should be emphasized that this is only an approximation for compact modeling purposes. The approximated \(G_{\text{TAT}}\) overestimates the actual \(G_{\text{TAT}}\), particularly at high bias values. The overestimation at higher \(V_{\text{gs}}\) bias is because the linear potential profile assumption does not remain valid at high \(V_{\text{gs}}\) bias. Figure 5b shows two integrated \(G_{\text{TAT}}\). Based on Figure 5a,b, some overestimation of \(I_{\text{ds\_TAT}}\) can be expected at high \(V_{\text{gs}}\) bias. Figure 4: (**a–d**) Illustration of the method used to estimate the width of the Gaussian distribution. \(G_{\text{TAT}}\) is shown, and \(x_{\text{width}}\) is pointed out by arrows, for \(V_{\text{gs}}\) = 0.4, 0.8, 1.2, and 1.6 V, respectively. Figure 6 compares \(I_{\text{ds\_TAT}}\) from the technology computer-aided design (TCAD) (symbol) against \(I_{\text{ds\_TAT}}\) calculated from (24) for different \(T_{\text{j}}\). Considering that this is a compact model, a reasonable agreement on the simulation results between the TCAD and the model is observed. The expected overestimation in \(I_{\text{ds\_TAT}}\) at high \(V_{\text{gs}}\) bias can be seen in Figure 6. Figure 7 compares \(I_{\text{ds\_TAT}}\) from the TCAD (symbols) against \(I_{\text{ds\_TAT}}\) calculated from the model for \(T_{\text{j}}\) = 10 nm and different \(H_{\text{source}}\), at \(V_{\text{ds}}\) = 0.5 V. The slight disagreement at higher bias is due to the linear potential approximation which is not very accurate at higher bias due to strong surface band bending. Figure 5: (**a**) \(G_{\text{TAT}}\) calculated from Equation (9) (symbols) compared against \(G_{\text{TAT}}\) calculated from Equation (16) (lines) for \(V_{\text{gs}}\) = 0.4, 0.8, 1.6, and 2.0 V shown by black, red, green and blue colors respectively, for \(V_{\text{ds}}\) = 0.5 V and \(T_{\text{j}}\) = 7 nm. (**b**) Integrated \(G_{\text{TAT}}\), \(\int_{\Gamma}^{0}G_{TAT}dx\) shown in Figure 5a. Same annotation as Figure 5a except symbols: Integral of Equation (9), and lines: Integral of Equation (16). Figure 6: \(I_{\text{ds\_TAT}}\) from technology computer-aided design (TCAD) (symbols) compared with \(I_{\text{ds\_TAT}}\) calculated from (24) for \(T_{\text{j}}\) = 7 nm (**a**), 8 nm (**b**), 9 nm (**c**) and 10 nm (**d**). Black, blue, and red represent \(V_{\text{ds}}\) = 0.25, 0.5, and 0.95 V, respectively. To truly test the relevancy of the model, the model was used to fit experimental data from [12]. It was found in [13] that \(I_{\text{ds\_TAT}}\) dominates the entire \(V_{\text{gs}}\) range for all \(V_{\text{ds}}\) biases. Therefore, \(I_{\text{ds\_TAT}}\) from the model was compared against the experimental data. The result is shown in Figure 8. The model was calibrated to match the experimental \(I_{\text{ds}}\)-\(V_{\text{gs}}\) characteristics at \(V_{\text{ds}}=0.95\) V by choosing \(\tau_{0}=10^{-11}\) s. The model follows the experimental \(I_{\text{ds}}\) trend very well. However, it is not entirely accurate, especially at low \(V_{\text{ds}}\). The reason for this is that (1) the electrostatic degradation caused by the trap states was not considered in this work. Electrostatic degradation causes the potential to degrade, and this effect becomes more important at high bias. To account for that, the Poisson and trap charge need to be calculated self-consistently. Furthermore, a different potential profile expression other than the linear potential profile given by (6) will be needed. This is because with the traps causing electrostatic degradation, the degraded potential profile changes from being linear to non-linear.