## 2 Simulation Conditions and Parameterization of the Transistor  
The advanced TCAD tool Sentaurus is used to numerically simulate the device. Since 2D MoS\({}_{2}\) is not included in the standard version of Sentaurus, the parameters and simulation methods proposed in [2,13] are implemented. The main idea of the method for simulating 2D material-based MOSFETs proposed in [2,13] consists of the following steps: (1) the compilation of data for the material and transport parameters needed for the simulation of 2D material-based MOSFET; (2) the elaboration of a suitable approach to correctly describe the density of states (DOS) and the quantum capacitance in 2D material-based MOS structures; and (3) the implementation of these features in TCAD. It has been shown that carrier transport in 2D MoS\({}_{2}\) MOSFETs with channels of dimensions 10 nm and even sub 10 nm are still far from ballistic but dissipative and scattering dominated channels [14, 15, 16]. The drift-diffusion approach is also considered a reasonable guide in the presence of transient and quasi-ballistic transport in short-channel MOSFETs as it correctly accounts for both device geometry and electrostatics [17]. In order to account for thermal effects, the thermodynamic transport model is used in conjunction with the drift-diffusion transport model in our simulation. To calibrate the model used, simulation results of the Id-Vg characteristics are compared with the results in [2]. The comparison for different gate lengths of the transistor (see Figure 1) has led to a good agreement. The channel of the simulated transistor consists of a MoS\({}_{2}\) monolayer with a thickness of 0.65 nm, and the total length of the device varies between 60 nm and 300 nm depending on the gate length. For all considered transistors, the channel length is three times longer than the gate length. The aluminum gate has a thickness of 2 nm and lengths of 20 nm, 30 nm, 50 nm and 100 nm. The charge carrier mobility in the channel depends on the gate oxide material, so we used a mobility of 125 cm\({}^{2}\)/(V\(\cdot\)s) for Al\({}_{2}\)O\({}_{3}\)[2] and 320 cm\({}^{2}\)/(V\(\cdot\)s) for HfO\({}_{2}\) gate oxide (see ref. [18]). In order to define the optimal structure of the transistor to increase the immunity against degradation effects, the SHE and DIBL effects for a MOSFET with 2D MoS2 as transistor channel are simulated in two cases (see Figure 2). In the first case, the length of the gate oxide is equal to the length of the MoS2 channel (Figure 2a), and in the second case, the length of the gate oxide is equal to the length of the gate (Figure 2b). The simulation is performed considering the four combinations of gate oxide and back oxide materials (see Table 1). An equivalent gate oxide thickness of 1 nm is chosen for all combinations. Therefore, SiO2-based gate oxide is not considered to likely rule out possible gate leakage current at such thicknesses. Since Al2O3 is practically not used as a back oxide material in MOSFETs, Al2O3 is not considered as a back oxide material in this work. The thickness of the BOX material has a high impact on the temperature of the transistor channel [19]. The temperature in the channel is increased with increasing thickness of the BOX. In our simulation, we have chosen a thickness of BOX 80 nm. This thickness is in the range of BOX thicknesses of the field effect transistors considered in many works, for example in [20] which was devoted to the investigation SHE in hybrid FinFET [20]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Combination** & **Gate Oxide Material** & **Back Oxide Material** \\ \hline \(1\) & Al2O3 & SiO2 \\ \hline \(2\) & HfO2 & SiO2 \\ \hline \(3\) & Al2O3 & HfO2 \\ \hline \(4\) & HfO2 & HfO2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Combination of the gate and back oxide materials considered in the work. Figure 1: Ig-Vd characteristics of the considered 2D MoS2-based MOSFETs with different gate lengths. The gate oxide material is Al2O3 and the BOX material is SiO2 with a thickness of 1020 nm.