Fluid Dynamics & Materials Processing |

DOI: 10.32604/fdmp.2022.021759

ARTICLE

Numerical Study of Temperature and Electric Field Effects on the Total Optical Absorption Coefficient in the Presence of Optical Inter-Conduction-Subband Transitions in InGaN/GaN Single Parabolic Quantum Wells

1LPS, Sidi Mohamed Ben Abdullah University, Fez, 30000, Morocco

2ENSAM, Hassan-II University, Casablanca, 20470, Morocco

*Corresponding Author: Redouane En-nadir. Email: redouane.en-nadir@usmba.ac.ma

Received: 02 February 2022; Accepted: 25 February 2022

Abstract: In this paper, we theoretically investigate the total optical coefficient (TOAC) considering 1S-2P and 2S-2P conduction subband transitions in a single parabolic quantum well (SPQW) with an on-center hydrogen-like impurity. Within the framework of the effective-mass approximation, the Schrödinger equation is solved numerically to obtain the eigenvalues and their corresponding eigenvectors using the finite difference method. The calculations are performed for finite confinement potential height, taking into account the dielectric and effective mass mismatches between GaN and InGaN materials under the considered electric field and temperature effects. The temperature dependence of the effective mass, dielectric constant and band gap energy are obtained accordingly. On the one hand, the results show that a significant shift is produced with the variation of both the temperature and the intensity of the electric field. On the other hand, the absorption spectrum is shifted to lower energies with increasing both electric field strength and temperature. Moreover, its amplitude is enhanced with an increase in the intensity of the electric field, and show a slight drop with increasing temperature for the two optical transitions considered. The results show that such parameters can be used to adjust the optical properties of single parabolic Quantum Well for solar cell applications.

Keywords: TOAC; optical transitions; SPQW; electric field intensity; temperature; hydrogenic-impurity

Nomenclature

TOAC | Total optical absorption coefficient |

SPQW | Single parabolic quantum well |

GaN | Gallium-nitride |

InGaN | Indium-gallium-nitride |

| Quantum state |

µ | Effective electric field strength |

Due to their particular thermodynamic and chemical proprieties, III-nitride semiconductor materials alloys such as InN, GaN, AlN, InGaN have gained much interest and have emerged as a very attracted and promising materials for optoelectronic applications. Their direct band gap make them a great candidate for solar cells, Laser, Photo-detectors and so on [1–4]. A variety of nanostructure forms such us quantum well (QW), quantum well wire (QWW), quantum dot (QD) and quantum ring (QR) are experimentally manufactured. Since the revolutionary work of Bastard [5] related to QWs, intense studies have been reported that take into account of different structure forms, with and without the impurity, the well and barrier concentration and the exciton. Among different types of QWs, we can indicate rectangular [6] as a perfect profile, semi-triangular [4], triangular [7], semi-parabolic [8], infinite parabolic corresponding to one type of material extending in infinite space and finite parabolic profile with finite potential confining determined by the band offset between the well and barrier considering two types of materials.

The linear and third order nonlinear optical absorptions in different shapes and different confinement potential profiles (infinite and/or finite) are one of the most important proprieties of nano-structured semiconductor materials. For instance, Ungan et al. [9–13] have investigated the effects of hydrostatic pressure and intense laser field on the linear and nonlinear optical properties for typical square GaAs/AlxGa1−xAs single quantum well system. They have studied the linear and nonlinear optical properties in GaAs/AlxGa1−xAs double inverse parabolic quantum wells under applied electric and magnetic fields. Moreover, the linear and third order nonlinear optical absorptions in typical asymmetric double triangular QWs are investigated theoretically under the applied electric field influences [7]. In addition, Yesilgul et al. have examined theoretically the changes in the refractive index and inter-subband optical absorption coefficients in symmetric double semi-V-shaped QWs under the effects of the incident optical intensity and structure parameters for a finite confinement potential profile [14].

Recently, Aydinoglu et al. have studied the nonlinear optical properties of asymmetric double-graded quantum wells under the effects of the structure parameters such as the central barrier’s thickness and the aluminum concentrations [13]. Additionally, hydrostatic pressure and temperature effects on the nonlinear optical properties in semi-parabolic and semi-inverse squared QW have been investigated by Xu et al. [15]. In our recently published paper [16], we investigated the influence of several types of confinement potential on the photovoltaic conversion properties of a single-intermediate band solar cell based on (In,Ga)N quantum well emerged in the intrinsic area of the typical p-i-n structure in which it is revealed that the performance of solar cells decreases with increasing temperature. Additionally, Ungana et al. [17] have showed that the linear and nonlinear optical properties in a GaAs/Ga0.7Al0.3As parabolic quantum well under the intense laser field can be tuned by changing the hydrostatic pressure and temperature. Xu et al. [15] have examined the hydrostatic pressure and temperature effects on the nonlinear optical properties in semi-parabolic plus semi-inverse squared quantum well. They showed that hydrostatic pressure and temperature have significant impact on the optical properties of semi-parabolic plus semi-inverse squared QWs, and that the energy levels and magnitudes of the resonant peaks of the total OACs vary according to the shape of the limiting potential, the hydrostatic pressure, and the temperature. This promise a new degree of freedom in the tunability of various electro-optical devices.

However, all authors cited above have reported their works without considering the presence of the impurity, which generally alters the electronic and optical properties leading to the degradation of the performance of devices based-on. In the present paper, on the one hand, our aim is to investigate the combined effects of temperature and electrical field on the total optical absorption related to 1S-2P and 2S-2P transitions in

2 Theory and Mathematical Expressions

Within the framework of the effective-mass approximation, the time-independent Schrödinger equation in the effective units describing an electron in the presence of the impurity and electric field is given by the following expression:

where, ℏ is the Planck’s constant, e is the electron charge,

where, L, l are respectively the barrier and the well widths, respectively.

To obtain the ground (1S-state), second-excited state (2P-state) and their associated energy levels of the Hamiltonian (1), the finite element method (FEM) was used taking into account the continuty of electron effective-mass as well as the dielectric constant at the interfaces between the barriers (GaN) and the well (InGaN). The boundary conditions are given by the following equation:

The mesh-grid of 3N + 1 point is considered for both layers (Barriers/wells). We provided A specific discretization step for each layer was provided. For the well, the step is hw (=

The derivatives electron wave functions are given by the following expressions:

3 Optical Absorption Coefficients

Based on the compact density matrix approach and the iterative procedure, the linear, third-order nonlinear and total optical absorption coefficients are given as the same that was described in our previous works [18–20] as follows:

where, the total optical absorption coefficient is defined as the sum of both linear and third order nonlinear contributions. It is given as following:

where,

To ensure the validity of this approach, we have discussed along this paper the electric field and temperature effects on the implied subband transitions for finite parabolic confinement profile.

All parameters related to the ternary

Fig. 2 depicts the variation of the dipole matrix element related to 1S-2P and 2S-2P transitions in

From Eqs. (5) and (6), it is clear that the total absorption coefficient mastering passes through the exact knowledge of the energy difference of all implied transitions. In this sense, Fig. 3 displays the changes of the energy difference related to 1S-2P and 2S-2P transitions vs. the electric field and temperature effects in

It is interesting to notice that the amplitudes of both transitions induced spectra appear to be enhanced as

Finally, TOAC related to 1S-2P and 2S-2P subband transitions in symmetric

Generally, our obtained results related to 1S-2P and 2S-2P transitions induced TOAC in SPQW based on

To sum up, this work is devoted to the theoretical study of the effects of external applied electric field and temperature on total optical absorption coefficients (OACs) of a single parabolic quantum well (QW). The results show that the applied electric field and temperature have significant influences on the optical properties of single parabolic QW. It is obtained that the wave functions, the energy levels and magnitudes of the resonant spectra of the total OACs vary according to the electric field and the temperature. A significant red-shift of the optical spectra is obtained with increasing both the electric field and the temperature. Therefore, it is revealed that the optical characteristics can be adjusted by changing the intensity of electric field and temperature which promise a new degree of freedom in the next generation of eventual GaN/(In,Ga)N based solar cells.

Owing to the importance of the III-nitrides semiconductors, particularly in optoelectronics, we assume that the present work provides a modest contribution to optimizing optical absorption for solar cell applications. In addition, it would induce further theoretical and experimental research works on Gan/InGaN based Multi-QWs for LEDs, lasers, and photo-detector applications.

Acknowledgement: I thank all authors with whom I have had the pleasure to work during this paper and other related project.

Funding Statement: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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