# Characteristics of Resonant Tunneling in Nanostructures with Spacer Layers
## 3 Results and Discussion
For Structure #1, the transition times to a new stationary state are approximately 1.3 ps, while for Structures #2 and #3, the transition times are approximately 0.9 ps. The difference in the transition times between Structure #1 and Structures #2 and #3 is because Structures #2 and #3 have smaller values of the  
Figure 5: The dependence of current (left \(y\)-axis) and voltage (right \(y\)-axis) on time for Nanostructure #1 at \(L_{SE}=4\) nm. thickness of the barrier layers, which leads to a greater value of the width of the resonance level, and consequently to a decrease in the transition time. Let us consider the behavior of the peak current dependences on the thickness of the emitter spacer in the simplified model from [11; 12], i.e., without taking into account the effects of charge accumulation (the self-consistent potential simulating interelectronic interaction is zero), as well as without taking into account the highly doped contact areas. The calculation results for the three resonant tunneling nanostructures are shown in Figure 6. For Structures #1 and #3, the peak current maximum is observed at a certain value of the emitter spacer thickness (for Structure #1, it is 6.8 nm; for Structure #3, it is 5.5 nm). The increase in the peak current due to the optimization of the thickness of the emitter spacer compared to small spacer thicknesses for Structure #1 is approximately 2.4-times, and for Structure #3, it is 2-times. For Structure #2, the peak current decreases with the increasing thickness of the emitter spacer. The difference between Structures #2 and #3 is the use of the material with a smaller band gap in Structure #2 for a quantum well. This leads to a decrease in the energy of the resonance level in Structure #2, which makes it possible to reach peak current values at significantly lower values of the applied voltage. Thus, in the simplified model, without taking into account the effects of charge accumulation and heavily doped contact areas, the applied voltages at which the peak current value is reached are of the order of 0.15 eV for Structure #2 and the order of 0.7 eV for Structure #3. At the same time, in the considered range of changes in the thickness of the emitter spacer of 2-8 nm, Structure #2 has at least 2-times lower peak current values compared to Structure #3. The current-voltage characteristics were calculated in our model at different values of the emitter spacer thickness in the range of 2-8 nm and the collector spacer thickness in the range of 3-18 nm for Structure #1 and in the range of 5-25 nm for Structures #2 and #3. The values of the peak current \(l_{p}\), the valley current \(l_{v}\), and the corresponding applied voltages \(V_{p}\) and \(V_{v}\) were determined from the obtained current-voltage characteristics. The results are presented in Table 2 for Structure #1 and Table 3 for Structures #2 and #3. The convergence problems of the numerical solution observed when solving the stationary Schrodinger-Poisson model were absent in our model in the considered range of the emitter spacer thickness. Figure 6: The dependence of the peak current on the thickness of the emitter spacer calculated in the simplified model (without the accumulation charge effect and highly doped contact layers) for the considered resonant tunneling nanostructures. Figure 7 shows the dependence of the peak current on the thickness of the emitter spacer for the considered resonant tunneling nanostructures. Taking into account the effects of charge accumulation and heavily doped contact areas in the Schrodinger-Poisson model led to a radical change in the nature of the dependence of the peak current on the thickness of the emitter spacer for Structures #1 and #3. For these structures, an increase in the thickness of the emitter spacer was accompanied by a decrease in the peak current.