# Characteristics of Resonant Tunneling in Nanostructures with Spacer Layers
## 1 Introduction
In [19], the data for three values of the thickness of spacer layers \(L_{SE}=L_{SC}=15\), 30, 60 nm for an AlGaAs/GaAs structure was demonstrated, and it was shown that the peak current remains constant. However, the results of [19] did not address the important region of small spacer layer thicknesses <15 nm, and the spacer thickness step was also rather large, which does not allow one to correctly identify the possible features of the dependence of the peak current on the spacer thickness. In [20], it was demonstrated  
Figure 1: Scheme of the potential profile of the two-barrier resonant tunneling nanostructure and the characteristic dependence of the current on the applied voltage for such a structure. Strongly doped contact layers with donor concentration \(n_{D}\) and thickness \(L_{c}\) are indicated in green; \(I_{p}\) and \(V_{p}\) are the peak current and peak voltage; \(I_{v}\) and \(V_{V}\) are the valley current and valley voltage. \(L_{SE}\)—thickness of emitter spacer layer; \(L_{SC}\)—thickness of collector spacer layer; \(L_{b}\)—thickness of barrier layer; \(L_{QW}\)—thickness of quantum well; \(\Delta E_{c}\) and \(\Delta E_{c}^{QW}\)—conduction band discontinuities between layers with different band gaps. for the AlGaAs/GaAs structure that a change in the emitter spacer thickness leads to a decrease in the peak current and valley current, while a change in the collector spacer thickness keeps these static characteristics constant. In [21] for a AlGaAs/GaAs resonant tunneling nanostructure, the peak current dependence was obtained for large thicknesses of the emitter spacer (\(<\)20 nm). The maximum value of the peak current was reached at the smallest considered thickness of the emitter spacer \(L_{SE}\) = 20 nm, then the peak current decreased and remained constant with a further increase in the thickness of the emitter spacer. Thus, experimental works usually consider a limited set of several spacer layer thicknesses for the chosen configuration of the RTD active region. Moreover, a number of studies considered simultaneous changes in the thickness of the emitter spacer and the collector spacer [18; 19]. Often, studies are carried out for sufficiently large thicknesses of spacer layers \(>\)15 nm with a large thickness step (\(>\)15 nm) [19; 20]. This does not allow one to establish the influence of each of the spacers separately and draw some generalized conclusions about the functional dependences of important static characteristics (peak current, valley current, etc.) on the thickness of the spacer layers. In [11; 12], using a numerical solution of the Schrodinger equation with open boundary conditions, it was shown that the dependence of the peak current on the emitter spacer thickness has an oscillating character. Moreover, the peak current takes the smallest value at small spacer thicknesses. The peak current reaches its maximum value at the emitter spacer thicknesses at which the resonant level in the quantum well overlaps with the energy level that occurs in the triangular well of the emitter spacer, which is formed when a constant voltage is applied [11; 12]. For the RTD structure considered in [11; 12], due to the correct choice of the emitter spacer thickness, it was possible to achieve peak current amplification by about six-times compared to the case of the absence of a spacer. However, the results in [11; 12] were obtained in a simplified formulation of the problem, which did not take into account the effects of charge accumulation (i.e., the approximation of non-interacting electrons was used), as well as the presence of highly doped contact regions. In this study, the effect of the emitter and collector spacer thickness on the main static characteristics, such as the peak current (\(I_{p}\)), valley current (\(I_{v}\)), and corresponding applied voltages (\(V_{p}\) and \(V_{v}\)), of resonant tunneling nanostructures, was studied, taking into account the effects of charge accumulation and the presence of highly doped contact regions.