# Characteristics of Resonant Tunneling in Nanostructures with Spacer Layers
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(L_{SE}\), **nm** & \(L_{SC}\), **nm** & \(I_{p}\), \(10^{9}\)**A/m\({}^{2}\)** & \(I_{p}\), \(10^{9}\)**A/m\({}^{2}\)** & \(V_{p}\), \(\mathbf{V}\) & \(V_{p}\), \(\mathbf{V}\) \\ \hline  & 3 & 5.30 & 1.29 & 0.30 & 0.31 \\
2 & 8 & 5.55 & 1.32 & 0.36 & 0.37 \\  & 13 & 5.56 & 1.32 & 0.44 & 0.46 \\  & 18 & 5.41 & 1.31 & 0.50 & 0.53 \\ \hline  & 3 & 3.78 & 0.89 & 0.26 & 0.28 \\
4 & 8 & 3.79 & 0.89 & 0.34 & 0.35 \\  & 13 & 3.78 & 0.89 & 0.40 & 0.42 \\  & 18 & 3.79 & 0.90 & 0.47 & 0.49 \\ \hline  & 3 & 2.81 & 0.70 & 0.23 & 0.275 \\
6 & 8 & 2.81 & 0.70 & 0.29 & 0.34 \\  & 13 & 2.81 & 0.70 & 0.36 & 0.40 \\  & 18 & 2.81 & 0.70 & 0.42 & 0.47 \\ \hline  & 3 & 2.41 & 0.57 & 0.20 & 0.27 \\
8 & 8 & 2.42 & 0.57 & 0.26 & 0.33 \\  & 13 & 2.42 & 0.57 & 0.32 & 0.39 \\  & 18 & 2.39 & 0.56 & 0.38 & 0.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The values of peak current \(I_{p}\), valley current \(I_{p}\), peak voltage \(V_{p}\), and valley voltage \(V_{v}\) for different thicknesses of spacer emitter and spacer collector. The results are presented for the resonant tunneling Structure #1. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(L_{SE}\), **nm**} & \multirow{2}{*}{\(L_{SC}\), **nm**} & \multirow{2}{*}{\(I_{p}\), \(10^{9}\)} & \multirow{2}{*}{\(I_{p}\), \(10^{9}\)} & \multirow{2}{*}{\(I_{p}\), \(10^{9}\)} & \multirow{2}{*}{\(V_{p}\), \(\mathbf{V}\)} & \multirow{2}{*}{\(V_{p}\), \(\mathbf{V}\)} & \multirow{2}{*}{\(V_{p}\), \(\mathbf{V}\)} & \multirow{2}{*}{\(V_{p}\), \(\mathbf{V}\)} \\  & & & & & & & & \(\mathbf{A/m^{2}}\  
For Structure #2, the peak current also decreased with increasing the thickness of the emitter spacer, i.e., a similar behavior was observed as in the calculations in the simplified model. Thus, there was a discrepancy with the results of similar studies from [11; 12]. The latter study predicted the existence of the optimal thickness of the emitter spacer at which the peak current of resonant tunneling nanostructures reaches the maximum value \(I_{p_{max}}\). Moreover, the value of \(I_{p_{max}}\) significantly exceeded the value of the peak current at small thicknesses of the emitter spacer. When a voltage was applied to the structure, an additional triangular quantum well was formed in the region of the emitter spacer. The peak current increased significantly at such sizes of the additional quantum well, when the energy of the quasi-level in this well coincided with the energy of the resonant level in the main quantum well [11; 12]. The calculations in [11; 12] were carried out in the simplified formulation of the problem, which does not take into account the effects of charge accumulation and the presence of heavily doped contact regions. The consideration of these factors led to a significant modification of the triangular quantum well that occurs in the region of the emitter spacer in the presence of the applied voltage (see Figure 8). With an increase in the emitter spacer thickness, the size of the additional quantum well decreased, which led to a decrease in the peak current. As can be seen from Tables 2 and 3, with an increase in the thickness of the emitter spacer, the values of \(I_{v}\), \(V_{p}\), and \(V_{v}\), as well as the value of \(I_{p}\) decreased for all the resonant tunneling nanostructures considered. The values of the applied voltage at which the current reached peak value \(V_{p}\) were significantly increased compared to the results obtained within the simplified model. Figure 9 shows the current-voltage characteristics for different values of the thicknesses of the emitter and collector spacer, obtained by the calculations for the resonant tunneling Nanostructure #2. It can be seen from the results presented in Figure 9 and Tables 2 and 3 that the peak current and valley current values were generally preserved when the collector spacer thickness was varied, regardless of the chosen value of the emitter spacer thickness and the features of the RTD layer structure.