# Compact Trap-Assisted-Tunneling Model for Line Tunneling Field-Effect-Transistor Devices
## 2 Model Presentation  
Figure 1a shows the schematic of the LTFET [12]. The channel is sandwiched between the gate and source. The source with height \(H_{\text{source}}\) = 70 nm is heavily p\({}^{+}\) (10\({}^{19}\) cm\({}^{-3}\)) doped with \(H_{\text{source}}\) in the \(y\) direction, and the channel is n\({}^{-}\) (10\({}^{15}\) cm\({}^{-3}\)) doped. A part of the channel is also found underneath the source and does not overlap between the gate and source. This is termed as \(R_{\text{nonoverlap}}\). The part of the channel that overlaps between the source and gate is termed as \(R_{\text{overlap}}\) and has a thickness \(T_{\text{j}}\) = 10 nm in the \(x\) direction and height (\(H_{\text{overlap}}\) = \(H_{\text{source}}\) = 70 nm [12, 13]) in the \(y\) direction. The HfO\({}_{2}\) gate dielectric is 2 nm thick (\(t_{\text{ox}}\)). The drain is heavily n\({}^{+}\) doped (10\({}^{19}\) cm\({}^{-3}\)).  
Before delving into the details of the model, it is important to illustrate the different current mechanisms in line tunneling TFETs. There are three different current mechanisms including (1) 2D BTBT, (2) 1D BTBT, and (3) TAT. 2D BTBTs originate from the corner-effect present in line tunneling TFETs. Because of the corner shape present in line tunneling TFETs, where the source and channel meet, the electric field converges around the sharp source corner, and increases the potential in the area surrounding the corner region [14]. This increased potential causes a 2D BTBT. The threshold voltage of 2D BTBT is lower than that of a 1D BTBT. However, the threshold voltage of the TAT is lower than that of the 2D BTBT and, as a consequence, the TAT current is generated at a lower \(V_{\text{gs}}\) than both the 2D and 1D BTBT currents. This is summarized in Table 1. Details of the 1D and 2D BTBT mechanisms can be found in [15, 16]. Depending on the number of traps, their energy level, density and whether the traps  
Figure 1: (**a**). Schematic of the L-shaped tunneling field-effect-transistor (LTFET). (**b**) Black: \(I_{\text{ds}}\)–\(V_{\text{gs}}\) characteristics of experimental LTFET [12], blue: trap-assisted-tunneling (TAT) current calculated using the trap distribution and method in [13], and red: Band-to-band tunneling (BTBT) current fitted using dynamic nonlocal BTBT current [10].  
are bulk or interface traps, the TAT generated drain current can vary. In most cases, the TAT current dominates the low \(V_{\text{gs}}\) bias subthreshold-BTBT current of TFETs [5; 6], but in some cases such as the one reported in [13], the TAT current can dominate over the BTBT current for the entire \(V_{\text{gs}}\) range. This is explained with the help of Figure 1b. Figure 1b shows the \(I_{\text{ds}}\)-\(V_{\text{gs}}\) characteristics of the experimental LTFET [12]. It was first fitted using a dynamic nonlocal BTBT model [10] with theoretically determined, material-dependent \(A_{\text{k}}=3.9\times 10^{15}\) cm\({}^{3}\)/s, and \(B_{\text{k}}=23.8\) MV/cm parameters. However, the BTBT-\(I_{\text{ds}}\) was found to be too low. With the BTBT current failing to match the experimental device's \(I_{\text{ds}}\), it was determined that it is instead the TAT-generated current that dominates for the entire \(V_{\text{gs}}\) range [13], as shown in Figure 1b.  
For simplicity, only the 1D potential model is considered [15], and any 2D effects [16] are ignored. The model is divided into two parts. The first part deals with the potential model which has already been reported in detail in [16] and is only briefly described here. Next is the standard Schenk model itself, which has been taken from [10] followed by its compact implementation using the Gaussian distribution function.