Effect of Shape and Size on Electron Transition Energies of InAs Semiconductor Quantum Dots

Li, Yiming; Voskoboynikov, O.; Lee, Chien-Ping; Sze, Simon M.; Tretyak, O. V.

doi:10.1143/jjap.41.2698

Cited by 11 publications

(23 citation statements)

References 13 publications

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“…The energy band gap [10][11][12][13][14] is a summation of the lowest state energies of the electrons and holes. The energy band gaps of the DI-, EL-, and CO-shaped QDs are shown in Figs.…”

Section: Resultsmentioning

confidence: 99%

Transition Energies of Vertically Coupled Multilayer Nanoscale InAs/GaAs Semiconductor Quantum Dots of Different Shapes

Li¹

2005

Jpn. J. Appl. Phys.

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The energy spectra of vertically coupled multilayer nanoscale semiconductor quantum dots (QDs) are theoretically studied using a unified three-dimensional (3D) model. The model formulation includes (1) the position-dependent effective mass Hamiltonian in a nonparabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in a parabolic approximation for holes, (3) the finite hard wall confinement potential, and (4) Ben Daniel-Duke boundary conditions. To solve a nonlinear problem, a nonlinear iterative method is further improved in our developed 3D QD simulator. At an applied magnetic field (B), we explore the transition energy and the energy band gap of disk (DI)-, ellipsoid (EL)-and cone (CO)-shaped vertically coupled multilayer nanoscale semiconductor quantum dots. We find that the electron transition energy of vertically coupled multilayer InAs/GaAs QDs depends on their shape and is strongly dominated by the number of stacked layers (N). The interdistance (d) among InAs QDs plays a crucial role in the tunable states of these QDs. In DI-shaped vertically coupled 10-layer QDs at B ¼ 0 T and d ¼ 1:0 nm, we find approximately 40% variation in electron ground state energy, which is larger than that ($20% variation) in CO-shaped QDs. In QDs at a nonzero magnetic field, the electron transition energy decreases with increasing N. In QDs with d ¼ 1 nm, the rate of decrease is low when N > 6. This results in QDs with energy band gaps having similar dependences on N. This study implies different applications in magnetooptical phenomena and quantum optical structures.

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“…The energy band gap [10][11][12][13][14] is a summation of the lowest state energies of the electrons and holes. The energy band gaps of the DI-, EL-, and CO-shaped QDs are shown in Figs.…”

Section: Resultsmentioning

confidence: 99%

Transition Energies of Vertically Coupled Multilayer Nanoscale InAs/GaAs Semiconductor Quantum Dots of Different Shapes

Li¹

2005

Jpn. J. Appl. Phys.

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“…The decrease of energy gap flats off when N > 6 due to the stable localization effect (weak coupling effect). For N ¼ 1 the coupled system becomes a single InAs/GaAs QD and the energy gap variation is mainly from diamagnetic shift [16]. For the system with each N > 2 the shift of energy gap is weakened.…”

Section: Resultsmentioning

confidence: 99%

“…1, we apply the nonlinear iterative method to calculate the self-consistent solution of the multilayer QDs structure. This computer simulation method has been developed for QDs and quantum ring simulation in our recent works [15][16][17]. Our calculation experiences show this method converges monotonically; it takes only 12-15 feedback iterative loops to meet a given convergence criterion (the maximum norm error <10 À12 eV) for all energies.…”

Section: D Quantum Dot Model and Simulation Methodsmentioning

confidence: 94%

“…We consider the vertically stacked QDs with the hard-wall confinement potential [12][13][14][15][16][17]. In a magnetic field the effective mass Hamiltonian for electrons (k ¼ e) and for holes (…”

Section: D Quantum Dot Model and Simulation Methodsmentioning

confidence: 99%

“…Our model considers: (1) the position-dependent effective mass Hamiltonian in non-parabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in parabolic approximation for holes, (3) the finite hard-wall confinement potential, and (4) the Ben Daniel-Duke boundary conditions [12][13][14][15][16][17]. The problem is solved numerically with a generalized nonlinear iterative method [15][16][17]. This iterative method enables us to compute the vertically coupled multilayer QDs electronic structure efficiently [15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Vertical coupling effects and transition energies in multilayer InAs/GaAs quantum dots

2004

Surface Science

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Electronic structure of three‐dimensional triangular torus‐shaped quantum rings under external magnetic fields

2003

phys. stat. sol. (c)

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In this paper, we calculate the electron -hole energy states and the magnetization for InAs/GaAs triangular torus-shaped (TTS) quantum rings in a magnetic field. Our three-dimensional (3D) model considers (i) the effective one-band Hamiltonian approximation, (ii) the position-and energy-dependent quasi-particle effective mass approximation, (iii) the finite hard wall confinement potential, and (iv) the Ben DanielDuke boundary conditions. This model is solved numerically with the nonlinear iterative method to obtain the "self-consistent" solutions. We investigate the electron-hole energy spectra versus magnetic field for two different ring widths: R 0 = 20 and 50 nm, and find that they strongly depend on the ring shape and size. Since the magnetic field penetrates into the inside region of the nonsimply connected ring, the electron (hole) transition energy between the lowest states versus magnetic field oscillates nonperiodically and is different from that of quantum dots. We find the magnetization at zero temperature is a negative function, saturates, and oscillates nonperiodically when the magnetic field increases.1 Introduction Based on the advanced semiconductor technology, nanoscale systems including quantum rings can be fabricated with a wide range of geometries. The ring shape can be viewed as a triangular cross section with the typical ring widths: 20 and 50 nm. The TTS ring height is about 2 nm and inner radius varies in the 10 nm regime, respectively (see [1] and references therein). For semiconductor nanoscale rings, it is necessary to explore their magnetic properties for device and spintronics applications [2]. Various models for studying electronic structures of rings have been proposed; unfortunately, these models did not systematically consider the ring (inner and outer) radius effect, the finite hard wall confinement potential, and nonparabolic band approximation for electron effective mass. To the best of our knowledge, the study of magnetization for 3D nanoscale rings has never been done yet.In this paper, we study the electron and hole energy states and magnetization for 3D nanoscale quantum rings. Figure 1 shows the studied TTS ring that is from an experimental formation of quantum rings [1]. The calculations are performed for 3D models of InAs/GaAs quantum rings with the finite hard wall confinement potential. We use the effective 3D one-band Hamiltonian, the energy-(non-parabolic approximation) and position-dependent quasi-particle effective mass approximation, and the Ben DanielDuke boundary conditions. The simulation of the above 3D model applies the nonlinear iterative method [3] to compute the self-consistent solutions. In the 1D approach, varying the magnetic field strength B only changes the phase of the electronic wave function, resulting in periodic oscillations in the magnetization (the Aharonov-Bohm effect). In the 2D confinement parabolic potential approach, the effects of

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Effect of Shape and Size on Electron Transition Energies of InAs Semiconductor Quantum Dots

Cited by 11 publications

References 13 publications

Transition Energies of Vertically Coupled Multilayer Nanoscale InAs/GaAs Semiconductor Quantum Dots of Different Shapes

Transition Energies of Vertically Coupled Multilayer Nanoscale InAs/GaAs Semiconductor Quantum Dots of Different Shapes

Vertical coupling effects and transition energies in multilayer InAs/GaAs quantum dots

Electronic structure of three‐dimensional triangular torus‐shaped quantum rings under external magnetic fields

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