Confined states in lens-shaped quantum dots
TL;DR: In this paper, the problem of infinite-barrier lens-shaped quantum dots (QDs) in parabolic rotational coordinates was solved using the Frobenius method and also by first transforming the separated differential equations into the Whittaker equation.
Abstract: We solve the problem of infinite-barrier lens-shaped quantum dots (QDs) in parabolic rotational coordinates exactly. The solutions are obtained directly using the Frobenius method and also by first transforming the separated differential equations into the Whittaker equation. We have obtained a new relation connecting the Bessel wavefunctions to the Whittaker functions. Results are given for both symmetrical and asymmetrical QDs. Studies of the energy spectra at constant volume were also performed; it is found that the shape dependence is very different from those found in previous studies of QDs with ellipsoidal and elliptic shapes.
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TL;DR: In this article, the lower lying states of a hydrogenic impurity, located at the centre of an infinite barrier lens-shaped quantum dot (LSQD), are calculated analytically in parabolic rotational coordinates.
Abstract: The lower-lying states of a hydrogenic impurity, located at the centre of an infinite barrier lens-shaped quantum dot (LSQD), are calculated analytically in parabolic rotational coordinates. The solutions are obtained directly using the Frobenius method and by transforming the separated differential equations into the Whittaker equation. Results are given for both symmetric and asymmetric LSQDs. It is found that the energy states of the system are positive for a very small LSQD and decrease as the size of the dot increases. They become negative as the size increases, and approach the energy states of a free hydrogen atom. Also symmetric and antisymmetric eigenfunctions have been constructed for a hydrogenic impurity in a symmetric LSQD. Antisymmetric eigenfunctions can be used as eigenfunctions of a hydrogenic impurity located at the surface of a semi-LSQD.
44 citations
TL;DR: In this article, a comprehensive study of anisotropic quantum rings, subject to axial and in-plane magnetic field, both aligned and transverse to the anisotropy direction, is carried out.
Abstract: A comprehensive study of anisotropic quantum rings, QRs, subject to axial and in-plane magnetic field, both aligned and transverse to the anisotropy direction, is carried out. Elliptical QRs for a wide range of eccentricity values and also perfectly circular QRs including one or more barriers disturbing the QR current are considered. These models mimic anisotropic geometry deformations and mass diffusion occurring in the QR fabrication process. Symmetry considerations and simplified analytical models supply physical insight into the obtained numerical results. Our study demonstrates that, except for unusual extremely large eccentricities, QR geometry deformations only appreciably influence a few low-lying states, while the effect of barriers disturbing the QR current is stronger and affects all studied states to a similar extent. We also show that the response of the electron states to in-plane magnetic fields provides accurate information on the structural anisotropy.
43 citations
TL;DR: In this paper, the authors have studied optical properties of spherical quantum dots by using Rosen-Morse potential and obtained energy levels and wave functions by applying Nikiforov-Uvarov (NU) method.
Abstract: In this paper, we have studied optical properties of spherical quantum dots by using Rosen-Morse potential. In this regard, we have first solved the Schrodinger equation and obtained energy levels and wave functions by applying Nikiforov-Uvarov (NU) method. Then, by using density matrix method, we have applied analytical expressions for the linear and third-order nonlinear absorption coefficient and refractive index changes. The results show that the total refractive index changes and the absorption coefficients increase and shift towards higher by enhancing height potential.
37 citations
Posted Content•
TL;DR: In this paper, the energy level structure and direct light absorption in a cylindrical quantum dot, having thin falciform cross section, are studied under the framework of the adiabatic approximation.
Abstract: Energy level structure and direct light absorption in a cylindrical quantum dot, having thin falciform cross section, are studied within the framework of the adiabatic approximation. An analytical expression for the energy spectrum of the particle is obtained. For the one-dimensional fast subsystem, an oscillatory dependence of the wave function amplitude on the cross section parameters is revealed. For treatment of the slow subsystem, parabolic and modified Poschl-Teller effective potentials are used. It is shown that the low-energy levels of the spectrum are equidistant. In the strong quantization regime, the absorption coefficient and edge frequencies are calculated. Selection rules for the corresponding quantum transitions are obtained.
24 citations
TL;DR: In this article, a GaAs/Ga1−xAlxAs V-shaped quantum wire with a hydrogenic donor impurity at the center was considered and the binding energy and spin-orbit interaction was investigated.
24 citations
References
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01 Jan 1944
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Abstract: 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices.
9,584 citations
TL;DR: In this paper, the strain distribution in and around pyramidal InAs/GaAs quantum dots (QD's) on a thin wetting layer fabricated recently with molecular-beam epitaxy, is simulated numerically.
Abstract: The strain distribution in and around pyramidal InAs/GaAs quantum dots (QD's) on a thin wetting layer fabricated recently with molecular-beam epitaxy, is simulated numerically. For comparison analytical solutions for the strain distribution in and around a pseudomorphic slab, cylinder, and sphere are given for isotropic materials, representing a guideline for the understanding of strain distribution in two-, one-, and zero-dimensional pseudomorphic nanostructures. For the pyramidal dots we find that the hydrostatic strain is mostly confined in the QD; in contrast part of the anisotropic strain is transferred from the QD into the barrier. The optical-phonon energies in the QD are estimated and agree perfectly with recent experimental findings. From the variation of the strain tensor the local band-gap modification is calculated. Piezoelectric effects are additionally taken into account. The three-dimensional effective-mass single-particle Schr\"odinger equation is solved for electrons and holes using the realistic confinement potentials. Since the QD's are in the strong confinement regime, the Coulomb interaction can be treated as a perturbation. The thus obtained electronic structure agrees with luminescence data. Additionally AlAs barriers are considered.
1,056 citations
TL;DR: The effective mass approximation is used to study the dependence of energy levels of lens-shaped SAD on size, depth of confining potential, and the magnetic field and relate the electron and hole energy levels to the magneto-optical properties of the SAD.
Abstract: The electronic structure of lens-shaped self-assembled quantum dots is studied as a function of the dot size, the confining potential, and the magnetic field. The parabolic confining potential and its corresponding energy spectrum are shown to be an excellent approximation. The magnetoexciton spectrum is calculated and compared with recent experiments. \textcopyright{} 1996 The American Physical Society.
285 citations
TL;DR: In this paper, a detailed effective mass calculation of the energy levels in InAs quantum dots embedded in GaAs is presented, and the results of a separable approximate treatment with a more complete numerical approach are compared.
166 citations