Effects of intense laser field and position dependent effective mass in Razavy quantum wells and quantum dots
Introduction
Low dimensional systems (LDSs) in which the motion of the carriers is confined in one, two, and three dimensions known as quantum wells (QW), quantum-well wires, and quantum dots (QD), respectively, have attracted a great deal of attention due to their wide applications in technology. The electronic and also optical properties of these structures can be adjustable according to purpose by proper choice of the sample geometry, material parameters, and applied external fields, which will cause new applications in optoelectronic devices. Thus, these structures have been extensively researched under the external fields like electric, magnetic, and intense laser fields (ILF) [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]] and are still being investigated. The main purpose of the convenient choice of the confinement potential profile for any structure mentioned above is to manipulate the electronic properties so that the best reflect the atomic structure of the material and to provide the design of the new optoelectronic devices. It should be noted that the physics of the QWs with different confinement potential offers the opportunity to explore new applications by realizing them in lower dimensions. Thanks to recent advances in material growth techniques that permit the growth of semiconductor QWs with different confinement potentials, symmetric or asymmetric single, double, triple, or multiple QWs have been produced and extensively studied. The realistic structure of the confinement potential profile is essential to a better understanding of the electronic properties of QWs and is essential for the manufacture of advanced devices. In this context, investigation of the electronic and optical properties of the QWs created by using of interatomic interaction potential functions like Lennard-Jones, Morse and Tietz-Hua [[12], [13], [14], [15]] which are widely used in molecular and material physics, is rather realistic, and this results in QW systems with more useful geometries and typical features than those studied in the literature so far. Furthermore, some potential energy functions have been used to obtain information about diatomic molecules. Some of them are quartic [16], sextic [17], Razavy [18], and Manning [19] double-well potentials, which are called as quasi-exactly solvable (QES) potentials and provide a useful approximation for the potential energy of a diatomic molecule.
The more the effect of the applied external fields on the electronic and optical properties of LDSs is important, the more the effect of the spatially varying effective mass approach is important. When investigating the electronic and optical properties of the structures in question, generally, the constant effective mass (CM) approach is used, but the CM approach is not valid for any non-periodic material [20]. This is because CM of the carriers in layered heterostructures differs in the place that is close to the interface due to the faulty inter-layer surfaces. Thus, in order to adjust the energy spectrum of the carriers in the LDSs, one has to use suitable models with the realistic potential profile and position-dependent effective mass (PDM). To better determine the physical properties of these systems, the Schrödinger equation with PDM is solved by using different approaches. Quantum mechanical systems with a spatially varying effective mass or position-dependent effective mass (PDM) have attracted attention in recent years and intensively been researched [[21], [22], [23], [24], [25], [26], [27], [28]]. Sari et al. have studied the PDM effects on the electronic structure of a Gaussian QW under ILF [21]. Herling et al. have calculated the PDM effects on the optical properties of parabolic QWs [22]. Yu et al. have realized the solutions with PDM of the Schrödinger equation for the Morse potential [23]. PDM effect on the bound states energies and intersubband optical transitions in the Tietz–Hua QW has been investigated by Sari and collaborators [24]. Panda et al. have considered the effects of ILF and PDM on the confinement potential of a QW [25,26]. Khlevniuk et al. have investigated the motion of a classical particle with PDM in 1D and 2D subjected to harmonic potential [27]. Saha et al. have investigated the influences of geometrical anisotropy and PDM on the electro-optic effect of doped QD with Gaussian white noise [28]. The other studies that show the importance of the PDM effect in low dimensional semiconductor systems are given in the Refs. [[29], [30], [31], [32], [33], [34]].
We have investigated the electronic and optical properties of QW and QD, which has Razavy potential under the non-resonant high-frequency ILF by taking into account the effects of PDM and structure parameters. In the case of QWs, it should be noted that the polarization of the incident radiation and the confining potential are oriented in the z-direction corresponding to the growth direction of the heterostructure. The method used to calculate the wave functions and energy levels of the system we have studied has been used in many studies before [38,39,46], and the degree of accuracy is quite sufficient. In order to test the convergence of the obtained results, also the Finite Elements Method (FEM) has been implemented to solve the eigenvalues differential equations. The organization of the paper is the following: Section II contains the presentation of the theoretical framework, in Section III, we discuss the obtained results, and in Section IV the conclusions are given.
Section snippets
Theoretical framework
Within the framework of the effective mass approximation, the PDM Schrödinger equation can be given by [40,41].where m(z) is the electron PDM and V(z) is the QW Razavy potential which is defined as follows:Here z represents the growth direction, V0 is the barrier height, A and M are t he constant structure parameters, and the QW has different shapes depending on the values of these parameters. For A > M, A = M, and A < M
Results and discussion
As commented above, in this work the effects of the ILF and PDM on the electronic structure in the Razavy-like QW and QD are investigated. The used parameters are V0 = 0.228eV and m* = 0.067 m0 (m0 is the free electron mass). These parameters correspond to Al0.3Ga0.7As QWs and QDs [44].
Conclusions
In the present study, we have investigated the absorption and relative changes of the refraction index coefficients for the intersubband transition between the two lower-lying electronic levels of the symmetric Razavy-like quantum wells. The study has been extended to the calculation of the electronic structure of spherical quantum dots with Razavy-like confinement potential. We have included the effects of a position-dependent effective mass, and the system has been exposed to the effects of
Author contributions statement
The contributions of the authors are as follows: E. Kasapoglu: proposed the problem and was responsible of the numerical calculations and writing of the manuscript. H. Sari: was responsible of the optical properties discussion. I. Sökmen: was responsible of the electronic structure discussion. J. A. Vinasco: was responsible of the Razavy-like QW DFT calculations. D. Laroze: was responsible of the Razavy-like QD DFT calculations. C. A. Duque: was responsible of the numerical calculations and
Data availability statement
All the files with tables, figures, and codes are available. The corresponding author will provide all the files in case they are requested.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
JAV acknowledges financial support from UTA fellowship. DL acknowledges partial financial support from FONDECYT 1180905 and Centers of excellence with BASAL/CONICYT financing, Grant AFB180001, CEDENNA. CAD is grateful to the Colombian Agencies: CODI-Universidad de Antioquia (Estrategia de Sostenibilidad de la Universidad de Antioquia and projects ”Efectos de capas delta dopadas en pozos cuánticos como fotodetectores en el infrarrojo”, ”Propiedades magneto-ópticas y óptica no lineal en
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