×
Doğan, Ü.; Sakiğlu, S.; Yildiz, A.; Akgüngör, K.; Epik, H.; Sökmen, İ.; Sari, H.; Ergün, Y.

Exciton states in a quantum dot with parabolic confinement. (English) Zbl 1247.81141

Int. J. Mod. Phys. B 25, No. 32, 4489-4497 (2011).
Summary: In this study the electronic eigenstructure of an exciton in a parabolic quantum dot (QD) has been calculated with a high accuracy by using finite element method (FEM). We have converted the coordinates of electron-light-hole system to relative and center of mass coordinate, then placed the spherical harmonics into Schrödinger equation analytically and obtained the Schrödinger equation which depends only on the radial variable. Finally we used FEM with only radial variable in order to get the accurate numerical results. We also showed first 21 energy level spectra of exciton depending on confinement and Coulomb interaction parameters.

MSC:

81Q37 Quantum dots, waveguides, ratchets, etc.
81V65 Quantum dots as quasi particles
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

exciton; parabolic confinement; finite element method
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1088/0256-307X/21/1/048 · doi:10.1088/0256-307X/21/1/048
[2] DOI: 10.1142/9789814354417 · doi:10.1142/9789814354417
[3] Woggon U., Optical Properties of Semiconductor Quantum Dots (1997)
[4] Thao T. T., Commun. Phys. 14 pp 2–
[5] DOI: 10.1103/PhysRevB.73.125321 · doi:10.1103/PhysRevB.73.125321
[6] DOI: 10.1103/PhysRevA.57.120 · doi:10.1103/PhysRevA.57.120
[7] DOI: 10.1051/jp3:1995210 · doi:10.1051/jp3:1995210
[8] DOI: 10.1103/PhysRevLett.67.1157 · doi:10.1103/PhysRevLett.67.1157
[9] Hutton D. V., Fundamentals of Finite Element Analysis (2004)
[10] DOI: 10.1088/0268-1242/9/3/006 · doi:10.1088/0268-1242/9/3/006
[11] DOI: 10.1088/0268-1242/9/3/001 · doi:10.1088/0268-1242/9/3/001
[12] DOI: 10.5488/CMP.10.1.23 · doi:10.5488/CMP.10.1.23
[13] Xie W. F., Chin. Phys. 15 pp 203–
[14] DOI: 10.1103/PhysRevB.44.13085 · doi:10.1103/PhysRevB.44.13085
[15] Şakiroğlu S., Chin. Phys. B 18 pp 1–
[16] DOI: 10.1103/PhysRevB.42.1713 · doi:10.1103/PhysRevB.42.1713
[17] DOI: 10.1103/PhysRevB.42.11708 · doi:10.1103/PhysRevB.42.11708
[18] DOI: 10.1103/PhysRevLett.62.2164 · doi:10.1103/PhysRevLett.62.2164
[19] Ram-Mohan L. R., Finite Element and Boundary Element Applications in Quantum Mechanics (2002) · Zbl 1054.81001
[20] Nakamura K., IEEE J. Quantum Electron. 25 pp 5–
[21] Li Z., Chin. J. Lumin. 27 pp 641–
[22] DOI: 10.1088/0953-8984/8/31/006 · doi:10.1088/0953-8984/8/31/006
[23] Kwon Y. W., The Finite Element Method using MATLAB (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.