Oscillator Strengths of Quantum Transitions in Spherical Quantum Dot GaAs/AlxGa1-xAs/GaAs/AlxGa1-xAs with On-Center Donor Impurity

Holovatsky, V. A.; Bernik, I.; Voіtseкhіvsкa, О. М.

doi:10.12693/aphyspola.125.93

Cited by 23 publications

(8 citation statements)

References 25 publications

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“…During last few decades many theoretical and experimental studies on QDs have been performed within parabolic confinement models as well as beyond this approximation. Both the 2D and 3D QD's have been investigated in a framework of strict quantum-mechanical and semiclassical approaches, including also effects of an external magnetic field [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Semiclassical solutions for a two-electron QD in a magnetic field have been investigated in terms of action-angle variables using the classical adiabatic approximation [19].…”

Section: Introductionmentioning

confidence: 99%

Two-Electron Spherical Quantum Dot in a Magnetic Field

Poszwa

2016

Few-Body Syst

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We investigate three-dimensional, two-electron quantum dots in an external magnetic field B. Due to mixed spherical and cylindrical symmetry the Schrödinger equation is not completely separable. Highly accurate numerical solutions, for a wide range of B, have been obtained by the expansion of wavefunctions in double-power series and by imposing on the radial functions appropriate boundary conditions. The asymptotic limit of a very strong magnetic field and the 2D approach have been considered. Ground state properties of the two-electron semiconductor quantum dots are investigated using both the 3D and 2D models. Theoretical calculations have been compared with recent experimental results. IntroductionThe influence of spatial confinement on properties of quantum systems have been widely studied in the literature and remains subject of continuous interest in both theoretical and experimental fields [1][2][3][4][5]. One of the most interesting confined quantum systems is the two-electron Hooke's-law atom (HA) also known as hookium or harmonium [6]. The HA refers to a model system composed of two electrons interacting by the Coulombic potential and confined in an external harmonic potential. Many applications for this system ensues from some unique properties of the HA. For the parabolic confinement the two-electron Hamiltonian separates. This property significantly simplifies the two-particle Schrödinger equation leading, in fact, to the one-dimensional radial problem. We note that the separability of the Schrödinger equation describing many interacting particles is rather exceptional. In particular, it is possible when interactions between disjoint pairs of particles, interacting by arbitrary two-particle potentials, are harmonic [7,8]. For the HA the Schrödinger equation not only separates exactly but also, for a set of the coupling constants, closed-form analytical solutions exist [9,10]. This is of particular importance for the understanding of the role of electron-electron interaction and correlation effects.When the electron mass is replaced by the relevant effective mass and the e-e interaction coupling constant is supplemented by the dielectric constant of semiconductor, the HA atom may be regarded to as a twoelectron quantum dot (QD). During last few decades many theoretical and experimental studies on QDs have been performed within parabolic confinement models as well as beyond this approximation. Both the 2D and 3D QD's have been investigated in a framework of strict quantum-mechanical and semiclassical approaches, including also effects of an external magnetic field [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Semiclassical solutions for a two-electron QD in a magnetic field have been investigated in terms of action-angle variables using the classical adiabatic approximation [19]. Spin-singlet and spin-triplet transitions have been studied and the magnetic moment and susceptibility have been obtained as functions of the magnetic field [20].A.

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Section: Introductionmentioning

confidence: 99%

Two-Electron Spherical Quantum Dot in a Magnetic Field

Poszwa

2016

Few-Body Syst

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“…The solutions of Eq. (6) are expressed as the products of spherical functions and Coulomb or Whittaker functions [2][3][4]7], and the solutions of Eq. 7are the products of spherical functions and Bessel functions.…”

Section: Formulation Of the Problem The Solution Of The Schrödinger mentioning

confidence: 99%

“…Therefore, the impurities may be in the QD and affect its properties. In this connection, there are a number of theoretical works [1][2][3][4][5][6][7][8][9], in which the energy spectra of donors and acceptors are determined as functions of the nanocrystal parameters.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Shallow Impurities on the Light Absorption by the Nanocrystals CdS

2018

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The energy of quantum transitions of exciton-impurity states in a heterosystem with nanocrystals is calculated. The absorption spectra associated with the indicated transitions are analyzed. It is qualitatively shown that broad luminescence bands in the red region are related to the impurity acceptor states, and the high narrow ones in the violet region to pure excitonic states and excitonic states interacting with the ion of a donor. The satisfactory quantitative agreement of our calculations with experimental data for high energy luminescence bands is obtained.

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“…The authors of [38] used a similar orthonormal WF basis to study the effect of the magnetic field on the optical properties of spherical nanosystems of the core/shell type (MSQD with a single potential well). The use of exact solutions of the Schrödinger equation based on degenerate hypergeometric functions to study the binding energy of an electron and an impurity and the oscillator force of quantum transitions of quasiparticles in MSQD with two potential wells separated by potential barrier was demonstrated in [37,39]. It was shown that the calculated binding energy agrees well with the results obtained by other methods, and that the dipole moment of quantum transitions depends significantly on the ratio of MSQD potential well width as this affects the distribution of the electron density in the nanosystem.…”

Section: Introductionmentioning

confidence: 99%

Impurity photoionization cross-section and intersubband optical absorption coefficient in multilayer spherical quantum dots

Holovatsky

Chubrei

Yurchenko

2021

Phys. Chem. Solid St.

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Energy spectrum, wave functions and binding energies of the electron to the donor impurity ion located in the center of a multilayer spherical quantum dot (MSQD) consisting of a core and two spherical shells were studied within the effective mass approximation. Based on the exact wave functions of the electron expressed in terms of Coulomb functions of the first and second kind, the spectral dependences of the photoionization cross section of the impurity (PCS) and the intersubband optical absorption coefficient (OAC) for various geometric dimensions of the nanostructure were calculated. It is shown that the decrease in the width of the external potential well changes the localization of the electron in the nanosystem which significantly affects the binding energy of the electron with the impurity, photoionization cross section and interband absorption coefficient. The position of the PCS peak associated with the quantum transition of an electron from the ground state to the 1p0 state shifts to the region of higher energies, and its height decreases. At the same time, the height of PCS peaks associated with quantum transitions to higher excited states (2p0, 3p0) increases.The presence of impurities and changes in the MSQD size significantly affect the intersubband absorption coefficient. Decrease of the external potential well width in the absence of impurities leads to a monotonous increase in OAC through the first excited state, and in the presence of a central impurity, absorption through states with higher energy increases.

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Oscillator Strengths of Quantum Transitions in Spherical Quantum Dot GaAs/Al_xGa_1-xAs/GaAs/Al_xGa_1-xAs with On-Center Donor Impurity

Cited by 23 publications

References 25 publications

Two-Electron Spherical Quantum Dot in a Magnetic Field

Two-Electron Spherical Quantum Dot in a Magnetic Field

The Effect of Shallow Impurities on the Light Absorption by the Nanocrystals CdS

Impurity photoionization cross-section and intersubband optical absorption coefficient in multilayer spherical quantum dots

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