# Characteristics of Resonant Tunneling in Nanostructures with Spacer Layers
## 4 Conclusions  
A method for calculating the static characteristics of resonant tunneling nanostructures based on the numerical solution of a non-stationary open Schrodinger-Poisson system of equations with a stepwise dependence of the applied voltage on time was developed. In the presented technique, the electroneutrality condition was performed with a high degree of accuracy, in contrast to the stationary numerical formulation, in which the associated divergences of the solution are observed at certain values of the emitter spacer thickness. The developed calculation method makes it possible to study the static characteristics of resonant tunneling nanostructures taking into account the features characteristic of the experiment, such as the presence of charge accumulation effects and the presence of heavily doped contact layers in the nanostructure. The use of exact discrete open boundary conditions, which require taking into account the entire prehistory, leads to a slowdown in the calculations over long periods. One possible way to improve the efficiency of the developed technique is to use perfectly matched layers (PMLs) [33], instead of discrete open boundary conditions. In the present study, we considered three different resonant tunneling nanostructures with a symmetric active region consisting of two barriers and a quantum well. The calculation method developed in this study was applied to the analysis of the effect of the emitter and collector spacers' thickness on the most-important static characteristics of resonant tunneling nanostructures: peak current, valley current, and the corresponding values of the applied voltage. As a result of the numerical simulation, it was found that taking into account heavily doped contact layers and the effects of charge accumulation is extremely important. Taking into account these effects leads to a significant modification of the potential of the resonant tunneling nanostructure, which, in turn, is reflected in electronic transport. In this regard, the results of [11; 12], obtained without taking into account these effects, undergo significant changes. The calculations in the work were carried out for three different resonant tunneling nanostructures, which suggests some generality of the results obtained. The numerical simulations showed that the peak current and valley current  
Figure 10: Dependences of \(\Delta I=I_{p}-I_{v}\) (red line, left \(Y\)-axis) and \(\Delta V=V_{v}-V_{p}\) (blue line, right \(Y\)-axis) on the thickness of the emitter spacer for RTD Structure #1 at \(L_{SC}=3\) nm. monotonically decrease with the increasing thickness of the emitter spacer. Thus, to obtain the maximum values of the peak current and peak-to-valley-current ratio, it is necessary to create the nanostructures with small values of the emitter spacer. The collector spacer weakly affects the values of the peak current and valley current, while having a strong influence on the values of the peak and valley voltage, so the collector spacer can have a strong influence on the output power of resonant tunneling nanostructures, as evidenced by the experimental results of [6]. The observed peculiarities of the peak and valley current behavior from the thickness of the emitter spacer and collector spacer agreed well with the experimental data of [18; 19; 20; 21; 22]. InGaAs-based structures with thin barriers (similar to Structure #3) give the highest peak current values and PVCR, while the operating voltages for this type of structures are quite large (\(\sim\)1 V). The use of a quantum well material with a smaller band gap (as in Structure #2) makes it possible to significantly reduce the operating voltages (by about 3-4-times), but at the same time, the peak current value is also significantly reduced (by about 3-times).