Advances in Materials Science and Engineering

Volume 2017 (2017), Article ID 2031631, 7 pages

https://doi.org/10.1155/2017/2031631

## Theoretical Study of High-Frequency Response of InGaAs/AlAs Double-Barrier Nanostructures

^{1}Department of Condensed Matter Physics, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe Sh. 31, Moscow 115409, Russia^{2}Laboratory of Computational Design of Nanostructures, Nanodevices and Nanotechnologies, Research Institute for the Development of Scientific and Educational Potential of Youth, Aviatorov Str. 14/55, Moscow 119620, Russia

Correspondence should be addressed to Mikhail M. Maslov; moc.liamg@volsam.ekim

Received 2 May 2017; Accepted 5 June 2017; Published 6 July 2017

Academic Editor: Francesco Ruffino

Copyright © 2017 Konstantin S. Grishakov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The presented article contains the numerical calculations of the InGaAs/AlAs resonant tunneling diode’s (RTD) response to the AC electric field of a wide range of amplitudes and frequencies. These calculations have been performed within the coherent quantum-mechanical model that is based on the solution of the time-dependent Schrödinger equation with exact open boundary conditions. It is shown that as the field amplitude increases, at high frequencies, where (Γ is the width of the resonant energy level), the active current can reach high values comparable to the direct current value in resonance. This indicates the implementation of the quantum regime for RTD when radiative transitions are between quasi-energetic levels and the resonant energy level. Moreover, there is an excitement of higher quasi-energetic levels in AC electric fields, which in particular results in a slow droop of the active current as the field amplitude increases. It also results in potentially abrupt changes of the operating point position by the value. This makes it possible to achieve relatively high output powers of InGaAs/AlAs RTD having an order of 10^{5} W/cm^{2} at high frequencies.

#### 1. Introduction

The resonant tunneling diode is a two-barrier nanostructure. It operates on the principle of electron transport through resonant energy levels. These energy levels are formed in a quantum well due to the interference of electrons. Such electron transport leads to the appearance of the negative differential conductivity (NDC) area at the current-voltage characteristic (*I-V* curve) of RTD. This* I-V* curve enables the generation of an electromagnetic field. The fact that the resonant tunneling diode has NDC area was experimentally demonstrated at liquid nitrogen temperatures (77 К) in [1] and the same at room temperature in [2].

A resonant tunneling diode is a compact solid electronic device operated at room temperature and is a possible candidate to be a source of terahertz radiation. The generation of electromagnetic waves within an RTD was obtained at about 200 K in 1984 [3], wherein the frequency and output power were low 18 GHz and some microwatts, respectively. In recent years, through the reduction of the thickness of the quantum well and barriers [4], the optimisation of the collector spacer layer thickness [5], and the size of the slot antenna [6], a significant growth of frequency has been achieved. Currently, the oscillation frequency of GaAs-based RTD equal to 1.92 THz has been achieved [7]. It is the highest one ever recorded for electronic devices operating at room temperature. The output power in the latter case was about 0.4 *µ*W.

Despite the obvious recent progress in the frequency characteristics of InGaAs/AlAs resonant tunneling diodes, the output powers within a terahertz range are still low (some microwatts). Also, there is still a pending problem of RTD’s high-frequency features. This results in the growing importance of theoretical studies aimed at researching the behaviour of a resonant tunneling diode in a high-frequency electromagnetic field.

Since an RTD works based upon quantum effects, the most consistent model for the theoretical description thereof is the so-called coherent model based upon the solution of the time-dependent Schrödinger equation with open boundary conditions. For the first time, RTD was described using this model in [8, 9] that used numerical calculations. Furthermore, it is also necessary to note analytical work [10] that developed an effective method to research RTDs in strong electromagnetic fields.

An important result obtained within the coherent model is the assumption that there does exist a quantum regime for RTD [11] associated with photon emission through resonant transitions between quasi-energetic levels appearing in an AC electric field [12] and resonant energy level in a quantum well. In this case, active current reaches its maximum at the finite frequency when the condition is complied with, that is, beyond the area of the maximum NDC. Here, is the energy of the emitter’s electrons, and are the energy and the width of the resonant level, respectively, and is the frequency of the AC electric field. However, in a “classical” regime (as defined in [11]), where the operating point position is selected in the maximum NDC, is at its highest within the low-frequency limits, whereas its value drops as the frequency increases as . Thus, at high frequencies, active current in quantum regime is much higher than the active current in “classical” regime. Subsequently, the results of [11] obtained for a weak field having the field potential amplitude were confirmed by numerical calculations of [13] and summarised in [14] for a wider range of field amplitudes limited by the condition . The latter condition is always complied with RTD. It resulted that, in quantum regime, the dependence of the active current on the amplitude of the AC electric field coincides with the intensity distribution at the Fraunhofer diffraction, which indicates the interference of electrons absorbing and emitting photons. Moreover, current reaches a high value approximately equal to half of the maximum direct current of the RTD. The results of [11, 13, 14] were obtained in a simplified model with -functional barriers and monoenergetic electrons (i.e., it was believed that the structure was bombarded by a flow of electrons having the assigned density with a fixed value of the energy) and in the absence of the DC voltage.

Subsequently, [15, 16] using computer simulation studied the behaviour of InGaAs/AlAs RTD in an AC electric field in the model that more accurately coincides with the experiment with square barriers of the finite width and height, with the Fermi distribution of electrons over the energy states as well as in the presence of the DC voltage. They used a numerical solution of the time-dependent Schrödinger equation based upon the expansion of the wave function under the Floquet modes. However, in these studies, much attention is paid to double-well structures of RTDs and the opportunities to detect the alternating current signal using these double-well structures.

The purpose of this work is to calculate, using computer simulation, the InGaAs/AlAs RTD response to an AC electric field within a wide range of frequency and field amplitudes, taking into consideration the Fermi distribution of electrons over the energy states and in the presence of the DC voltage.

#### 2. The Model

We consider a one-dimensional two-barrier nanostructure schematically depicted in Figure 1. From the left of the emitter and from the right of the collector, the structure is bombarded by a flow of electrons. The RTD is exposed to the direct current and alternating current electric fields. The electron wave function matches the time-dependent Schrödinger equation: