Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots

doi:10.1016/j.physb.2011.08.105

Physica B: Condensed Matter

Volume 406, Issue 23, 1 December 2011, Pages 4423-4428

https://doi.org/10.1016/j.physb.2011.08.105 Get rights and content

Abstract

In this work, influences of external electric and magnetic fields on the optical rectification coefficient, the linear and the third-order nonlinear optical absorption coefficients as well as refractive index changes of finite semi-parabolic quantum dots are investigated. In this regard, energy eigenvalues and eigenfunctions of the system are calculated numerically, and optical properties are obtained using the compact density matrix approach. The results show that external electric and magnetic fields have a great influence on these optical quantities.

Introduction

With the immense technological progress in the field of nanoprocessing, it is possible to fabricate high precision semiconductor nanostructures with three-dimensional confinement of electrons, called quantum dots (QDs). The reduction in dimensionality, produced by confining electrons (or holes) to thin semiconductor layers, leads to drastic changes in their behaviors and dramatically affect their electronic structures and optical properties.

One of the most interesting properties of QDs is that the optical transitions between the size quantized levels (subbands) in the valence or conduction bands are feasible. Therefore, investigation of the linear and nonlinear optical properties of QDs has been widely made in the literature [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. These studies demonstrate that quantum confinement of carriers in QDs has improved physical properties, as compared with semiconductor quantum wells and wires, for high-performance optoelectronic devices [12], [13].

Furthermore, external electric and magnetic fields have become an effective tool for studying the physical properties of low-dimensional systems, both from the theoretical and the practical point of views. Investigation of the effects of external electric and magnetic fields on the linear and nonlinear optical properties of semiconductor nanostructures have been reported in several papers [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]. All of the studies mentioned above have shown that the linear and nonlinear optical properties sensitivity depend on the applied fields.

Recently, especial attention had been paid to a semi-parabolic confinement potential as an asymmetrical quantum system, which can be more pronounced when an electric field is applied to this quantum system too [24], [25], [26], [27], [28], [29], [30]. To our knowledge, in all of the investigations the dot is held at infinite parabolic potential and the emphasis is put upon the dependence of physical properties of the enclosed particles on the confinement frequency. It should be noted that the infinite potential wells are not physically feasible. The reason is that the maximum barrier height obtained in GaAs/Al_xGa_1−xAs system is 350 meV [31]. However, progress in computational physics with high accuracy permits us to investigate semi-parabolic finite potentials, which are important theoretically and experimentally. To this end, we consider a finite one-dimensional semi-parabolic quantum dot (SPQD), and investigate the effects of external electric and magnetic fields on the optical rectification coefficient (ORC), the linear and the third-order nonlinear intersubband optical absorption coefficients (ACs) and refractive index changes (RICs).

The paper is organized as follows: in Section 2, we describe the theoretical framework. Our numerical results and a brief summary are presented in 3 Results and discussion, 4 Conclusions, respectively.

Section snippets

Electronic states in SPQDs

In the effective mass approximation, the Hamiltonian of an electron confined in one-dimensional SPQDs, under the influence of external electric and magnetic fields, is given by $H = - \frac{ℏ^{2}}{2 m^{⁎} (z)} \frac{\partial^{2}}{\partial z^{2}} + V (z) + \frac{e^{2} B^{2}}{2 m^{⁎} (z) c^{2}} z^{2} - eFz,$ where $m^{⁎} (z)$ is the position dependent electron effective mass, c is the speed of light, F is the electric field strength, and B is the magnetic field applied perpendicular to the growth direction. As shown in Fig. 1, the confinement potential V(z) is given by $V (z) = \{\begin{matrix} \frac{1}{2} m_{1}^{⁎} ω_{0}^{2} z^{2}, & 0 \leq z \leq L, \\ V_{0} \end{matrix}$

Results and discussion

In the following we will calculate the ORC, the linear and the third-order nonlinear ACs and RI changes of finite SPQDs under the influence of external electric and magnetic fields. We perform our calculations for a typical Al_xGa_1−xAs/GaAs/Al_xGa_1−xAs SPQD. The parameters used in our calculations are as follows [33]: $m_{1}^{⁎} = 0.067 m_{0}$ , $m_{2}^{⁎} = (0.067 + 0.083 x) m_{0}$ (where m₀ is the free electron mass and x=0.4 is the aluminum concentration), $σ_{v} = 5.0 \times 10^{22} m^{- 3}$ , n_r=3.2, $Γ_{0} = 1 / T_{0}$ where $T_{0} = 0.14 ps$ , $μ = 4 π \times 10^{- 7} H m^{- 1}$ , n_r

Conclusions

In conclusion, we have presented the optical properties of a finite SPQD, using compact density matrix approach. Numerical calculations are performed to solve the Schrödinger equation in order to find energy eigenvalues and eigenfunctions of an electron confined in a finite SPQD, in the presence of external electric and magnetic fields. Results are employed to investigate the influence of external electric and magnetic fields on the ORC, optical ACs and RI changes of the system.

It is found that

Acknowledgements

This work is partially supported by the Shiraz University of Technology and Yasouj University.

References (33)

W. Xie
J. Lumin.
(2011)
M.R.K. Vahdani et al.
Phys. Lett. A
(2010)
W. Xie
Phys. Lett. A
(2011)
Y. Yakar et al.
Opt. Commun.
(2010)
M.R.K. Vahdani et al.
Phys. Lett. A
(2009)
W. Xie
Solid State Commun.
(2011)
D. Heiss et al.
Solid State Commun.
(2005)
İ. Karabulut et al.
J. Lumin.
(2011)
B. Li et al.
Phys. Lett. A
(2008)
C.M. Duque et al.
Superlattices Microstruct.
(2011)

E. Ozturk et al.

Superlattices Microstruct.

(2010)

R. Khordad

Solid State Sci.

(2010)

G. Rezaei et al.

Superlattices Microstruct.

(2010)

L. He et al.

Superlattices Microstruct.

(2010)

Y.-B. Yu et al.

Physica E

(2003)

C.-J. Zhang et al.

Physica E

(2007)

Cited by (97)

Exploring Shannon entropy and heat capacity of doped GaAs quantum dot under the influence of noise
2024, Physica B: Condensed Matter
Present enquiry explores the Shannon entropy and the corresponding heat capacity of $G a A s$ quantum dot (QD) which is doped with Gaussian impurity and under the aegis of Gaussian white noise (GWHN). GWHN may take additive and multiplicative routes for its entrance to the doped QDs. The enquiry analyzes the features of temperature-dependence of above thermodynamic properties and also the effect of various physical parameters on them at a given temperature. The study reveals some kind of complex interplay involving the temperature zone, presence/absence of GWHN, mode of application of GWHN and the particular physical parameter concerned which ultimately shapes the profiles of entropy and heat capacity. Often, the study reveals competitive behavior between thermal disorder and spatial disorder which noticeably affects the said thermal properties. Moreover, the study also highlights some unusual behavior in the entropy profiles only under multiplicative noise of high noise strength.
Tuning the magnetocaloric effect in GaAs quantum dot under the aegis of noise-anharmonicity interplay
2024, Physica B: Condensed Matter
Present study rigorously scrutinizes the magnetocaloric effect (MCE) of $G a A s$ quantum dot (QD) under the simultaneous influence of anharmonicity and Gaussian white noise (GWHN). The parity of the anharmonic potential, the route of introduction of GWHN and the QD confinement interplay delicately to fine-tune the MCE. Anharmonicity of odd (even) parity diminishes (augments) the confinement of the system with respect to the anharmonicity-free state. Generally, multiplicative noise brings in larger deviation of MCE (from the noise-free state) than additive noise. Additionally, additive (multiplicative) noise depletes (enhances) the magnitude of MCE in comparison with the noise-free values.
Magneto-optical absorption in an asymmetric finite quantum well
2023, Micro and Nanostructures
We examine the influence of internal (confinement frequency, Al-doped concentration, β parameter) and extrinsic (magnetic field, temperature) parameters on the energy differences and magneto-optical absorption properties of a finite semi-parabolic plus semi-inverse squared (FSPSISP) quantum well. Our results demonstrated that the energy difference between the ground and excited states is substantially dependent on the amount of Al-doped in the system, the confinement frequency, and the magnetic field, and slightly dependent on parameter characterizing the inverse squared part of the confinement potential, but not temperature. The magneto-optical absorption coefficient (MOAC) increases with confinement frequency, Al-doped concentration, magnetic field, and temperature, but decreases with β. The full width at half maximum (FWHM) increases with all parameters. By optimizing these parameters, we can enhance the MOAC. Our results provide deeper insight into the optical properties of low-dimensional systems with finite confinement potential.
Pulsed field induced excitation in impurity doped quantum dot: Interplay with Gaussian white noise
2022, Physica B: Condensed Matter
Citation Excerpt :
Consequently, a great deal of research has been done that deciphers the importance of impurity doping in LDSS [1–8]. The interaction of LDSS with incident electromagnetic radiation produces linear and nonlinear optical (NLO) responses [9–29] which unravel their tremendous potential towards quantum computation and laser technology [30–32]. Furthermore, above interaction also highlights new prospects of electronic transport, designing of novel opto-electronic devices and lasers and several other important engineering applications like optical encoding, multiplexing, photovoltaic and light emitting devices [32–37].
Current study strives to realizing the role of Gaussian white noise (GWN) and external pulsed field (PF) on the time-average excitation rate (TAER) of impurity doped quantum dot (QD). The PF is characterized by a pulse shape function which may be continuous or discontinuous with time. In the present study we invoke sinusoidal and triangular shape functions as continuous ones and regular telegraphic and random telegraphic shape functions as discontinuous ones. GWN links with the system additively and multiplicatively. The study emphasizes on analyzing the role of various physical parameters, application of noise, pathway of application of noise and the attributes of the PF (amplitude, phase, shape and the number of pulses) in designing the TAER profiles. The TAER profiles come out to be comprising of features like persistent rise, persistent fall, maximization (useful for attaining large nonlinear optical response), minimization and saturation (the dynamic freezing).
Linear and nonlinear optical properties in wurtzite MgZnO/ZnO double quantum wells: Roles of external electric and magnetic fields
2022, Micro and Nanostructures
In this work, the modulation effects of external magnetic and electric fields on the inter-subband optical absorption coefficients and refractive index changes in asymmetric wurtzite MgZnO/ZnO double quantum wells are investigated considerably. The linear and nonlinear characteristics among the three lowest confined states are calculated here. The obtained results show that the optical properties of the structure are very sensitive to the external field. The optical characteristics related to higher energy levels which have been ignored in past works are as important as the transition related to the ground state. The transition from the ground state to the second excited state is the most sensitive to the external fields. The optical parameters can be risen by two orders of magnitude through the manipulation of the applied electric and magnetic fields.
Role of anharmonicity binding energy on the transition dynamics of GaAs quantum dot in presence of noise
2024, Indian Journal of Physics

View all citing articles on Scopus

View full text

Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots

Abstract

Introduction

Section snippets

Electronic states in SPQDs

Results and discussion

Conclusions

Acknowledgements

J. Lumin.

Phys. Lett. A

Phys. Lett. A

Opt. Commun.

Phys. Lett. A

Solid State Commun.

Solid State Commun.

J. Lumin.

Phys. Lett. A

Superlattices Microstruct.

Superlattices Microstruct.

Solid State Sci.

Superlattices Microstruct.

Superlattices Microstruct.

Physica E

Physica E