Electron Energy in Rectangular and Cylindrical Quantum Wires

Gulyamov, G.; Gulyamov, A. G.; Davlatov, A. B.; Shahobiddinov, B. B.

doi:10.21272/jnep.12(4).04023

Cited by 20 publications

(5 citation statements)

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“…The low-energy subband dispersions of the hole gas in the nanowire are thus apparently distinct from that of the electron gas, where the subband minima of the electron gas are usually located at the center of the k z space, i.e. k z R = 0 [38,39,52].…”

Section: Discussion and Summarymentioning

confidence: 99%

Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger–Kohn Hamiltonian

Li (李睿)

2024

J. Phys.: Condens. Matter

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Based on the Luttinger-Kohn Hamiltonian in the axial approximation, the transcendental equations determining the hole subband dispersions in a cylindrical Ge nanowire are analytically derived. These equations are more general than that derived using the spherical approximation, and are suitable to study the growth direction dependence of the subband dispersions. The axial approximation almost gives rise to the accurate low-energy subband dispersions for high-symmetry nanowire growth directions [001] and [111]. The perturbation correction from the non-axial term is negligible for these two directions. The lowest two subband dispersions can be regarded as two shifted parabolic curves with an energy gap at $k_{z}=0$ for both growth directions [001] and [111]. At the position of the energy gap, the eigenstates for growth direction [111] are inverted in comparison with the normal eigenstates for growth direction [001]. A nanowire growth direction where the energy gap closes at $k_{z}=0$ is predicted to exist between directions [001] and [111].

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Section: Discussion and Summarymentioning

confidence: 99%

Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger–Kohn Hamiltonian

Li (李睿)

2024

J. Phys.: Condens. Matter

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“…We determined that the mesh was sufficiently refined and the chosen value of the parameter r b was sufficiently high to ensure an accuracy better than 5 × 10 −5 for the calculation of the ground state energy. The typical error can be estimated by comparing the FEM result e = 0.154 021 with the exact semi-analytical solution e sa = 0.154 005, in the particular case of a finite-wall cylindrical confinement with v (ξ , η) = H (ρ (ξ , η) − 1), where H denotes the Heaviside step function [49].…”

Section: Two-dimensional Finite Element Calculation and Sample Prepar...mentioning

confidence: 99%

Deep learning neural network for approaching Schrödinger problems with arbitrary two-dimensional confinement

Radu,

Duque

2023

Mach. Learn.: Sci. Technol.

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This article presents an approach to the two-dimensional Schrödinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential, starting from the knowledge of the solutions to a large number of arbitrary sample problems. A network architecture with two hidden layers is proposed to predict the wave function and energy of the ground state. Several accuracy indicators are proposed for validating the estimates provided by the neural network. The testing of the trained network is done by applying it to a large set of confinement potentials different from those used in the learning process. Some particular cases with symmetrical potentials are solved as concrete examples, and a good network prediction accuracy is found.

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“…Recently, cylindrical quantum wires (CQWRs), called also cylindrical nanowires, based on semiconductor can create a one-dimensional (1D) electronic system, due to their small diameter and the possibility of being used as basic elements of nanoscale electronics. Improved methods for their growth, such as molecular (MBE), metal-organic and gas-phase molecular beam epitaxy, have enabled the formation of longitudinal heterostructure nanowires (LOHNs) [1][2][3][4][5][6]. The advantages of axially combined materials allow countless applications, from nanoelectronics to the medical field, and allow a better understanding of the mechanism of one-dimensional transport of electrons.…”

Section: Introductionmentioning

confidence: 99%

Electron Transport in AlGaAs Cylindrical Quantum Wire Sandwiched between Two GaAs Cylindrical Quantum Well Wires

Qasem¹,

Ben-Ali

Falyouni³

et al. 2022

SSP

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In this work, we study theoretically and analytically the electronic transport through a nanowire structure composed of a finite cylindrical quantum wire (CQWR) based on barrier AlGaAs semiconductor, sandwiched between two semi-infinite cylindrical GaAs quantum well wires (CQWWRs). Using the Green function approach to determine the electronic structure of this artificial nanostructure, which is analyzed as a function of the geometrical and physical parameters of nanowires structure. The results show the eigen states (confined states), when they interact with the incoming electronic waves from the first semi-infinite cylindrical GaAs quantum well wire. The decrease of the radius of the system leads to the energy quantization of the electrons and the electronic states move towards high energies until a critical radius Rc=20Å below which no electronic state can exist. In addition, we found that the electronic energy levels of the finite cylindrical quantum wire depend on the mole fraction of aluminum and the ratio between the radius of the cylindrical nanowires and the thickness of the barrier, which are the most important parameters in the optimization of the cylindrical quantum wires nanostructure.Keywords: Cylindrical Quantum Wire, Nanowire, Electronic States, Green Function

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Electron Energy in Rectangular and Cylindrical Quantum Wires

Cited by 20 publications

References 0 publications

Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger–Kohn Hamiltonian

Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger–Kohn Hamiltonian

Deep learning neural network for approaching Schrödinger problems with arbitrary two-dimensional confinement

Electron Transport in AlGaAs Cylindrical Quantum Wire Sandwiched between Two GaAs Cylindrical Quantum Well Wires

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