Optical properties of Quantum Disks: Real density matrix approach

• Authors: Gerard Czajkowski , Leonardo Silvestri
• Languages of publication: EN

Abstracts

EN

We show how to compute the optical response of a Quantum Disk (QDisk) to an electromagnetic wave as a function of the incident wave polarization, in the energetic region of interband transitions. Both the TM and TE polarization in guided-wave geometry are analyzed. The method uses the microscopic calculation of Quantum Disk eigenfunctions and the macroscopic real density matrix approach to compute the effective QDisk susceptibility, taking into account the valence band structure of the QDisk material and the Coulomb interaction between the electron and the hole. Analytical expressions for the QDisk susceptibility are obtained for a certain model electron - hole potential. Using these expressions, all optical functions can be computed. Results for the absorption coefficient are computed for InAs/GaAs QDisks. Fair agreement with experiments is obtained.

Keywords

EN

Quantum Disks; optical properties; excitons; size effect; optical absorption anisotropy; 71.35.-y; 71.35.Cc; 73.20.Mf; 78.67.Hc

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2006
• Volume: 4
• Issue: 2
• Pages: 254-269

Dates

published

1 - 6 - 2006

online

1 - 6 - 2006

Contributors

author

Gerard Czajkowski

author

Leonardo Silvestri

• Scuola Normale Superiore, I-56126, Pisa, Italy

References

• [1] C. Weisbuch and B. Vinter: Quantum Semiconductor Structures: Fundamentals and Applications, Academic Press, New York, 1991.
• [2] L. Banyai and S.W. Koch: Semiconductor Quantum Dots, World Scientific, Singapure, 1993.
• [3] E.L. Ivchenko and G.E. Pikus: Superlattices and Other Heterostructures. Symmetry and Optical Phenomena, Springer Verlag, Berlin, 1995.
• [4] L. Woggon: Optical Properties of Semiconductor Quantum Dots, Springer Verlag, Berlin, 1997.
• [5] L. Jacak, P. Hawrylak and A. Wojs: Quantum Dots, Springer Verlag, Berlin, 1998.
• [6] D. Bimberg, M. Grundmann and N.N. Ledentsov: Quantum Dot Heterostructures, Wiley, New York, 1998.
• [7] T. Chakraborty: Quantum Dots, Elsevier, Amsterdam, 1999.
• [8] V.M. Ustinov, A.E. Zhukov, A.Yu. Egorov and N.A. Maleev: Quantum Dot Lasers, Oxford University Press, Oxford, 2003.
• [9] J. Song and S.E. Ulloa: “Geometrical-confinement effects on excitons in quantum disks”, Phys. Rev. B, Vol. 52, (1995), pp. 9015–9022. http://dx.doi.org/10.1103/PhysRevB.52.9015[Crossref]
• [10] P.D Wang et al.: “Magnetoluminescence studies on InyAl1−y As self-assembled quantum dots in AlxGa1−x As matrices”, Phys. Rev. B, Vol. 53, (1996), pp. 16458–16461. http://dx.doi.org/10.1103/PhysRevB.53.16458
• [11] P. Hawrylak et al.: “Light scattering from self-assembled quantum disks”, Physica E, Vol. 2, (1998), pp. 652–656. http://dx.doi.org/10.1016/S1386-9477(98)00133-7[Crossref]
• [12] C. Trallero-Giner, E. Menéndez-Proupin and S.E. Ulloa: “Resonant Raman scattering in asymmetric quantum disks”, Phys. Stat. Sol. (b), Vol. 215, (1999), pp. 459–463. http://dx.doi.org/10.1002/(SICI)1521-3951(199909)215:1<459::AID-PSSB459>3.0.CO;2-X[Crossref]
• [13] T. Takagahara: “Theory of exciton dephasing in semiconductor quantum dots”, Phys. Rev. B, Vol. 60, (1999), pp. 2638–2652. http://dx.doi.org/10.1103/PhysRevB.60.2638[Crossref]
• [14] M. Korkusiński and P. Hawrylak: “Electronic structure of vertically stacked self-assembled quantum disks”, Phys. Rev. B, Vol. 63, (2001), art. 195311.
• [15] K.L Janssens, F.M. Peeters and V.A. Schweigert: “Magnetic-field dependence of the exciton energy in a quantum disk”, Phys. Rev. B, Vol. 63, (2001), art. 205311.
• [16] K.L. Janssens, F.M. Peeters, V.A. Schweigert and B. Partoens: “Magnetic field dependence of the exciton energy in type I and type II quantum disks”, Physica B, Vol. 298, (2001), pp. 277–281. http://dx.doi.org/10.1016/S0921-4526(01)00316-7[Crossref]
• [17] C. Trallero-Giner: “Optical phonons and resonant Raman scattering in II-VI spheroidal quantum dots”, Phys. Stat. Sol. (b), Vol. 241, (2004), pp. 572–578. http://dx.doi.org/10.1002/pssb.200304307[Crossref]
• [18] Z.R. Wasilewski, S. Fafard and J.P. McCaffrey: “Size and shape engineering of vertically stacked self-assembled quantum dots”, J. Cryst. Growth, Vol. 201, (1999), pp. 1131–1135. http://dx.doi.org/10.1016/S0022-0248(98)01539-5[Crossref]
• [19] M.V. Maximov et al.: “High-power continuous-wave operation of a InGaAs/AlGaAs quantum dot laser”, J. Appl. Phys., Vol. 83, (1998), pp. 5561–5563. http://dx.doi.org/10.1063/1.367390[Crossref]
• [20] S. Fafard, Z.R. Wasilewski, C.Ni. Allen, K. Hinzer, J.P. McCaffrey and Y. Feng: “Lasing in quantum-dot ensembles with sharp adjustable electronic shells”, Appl. Phys. Lett., Vol. 75, (1999), pp. 986–988. http://dx.doi.org/10.1063/1.124253[Crossref]
• [21] T. Lundstrom, W. Schoenfeld, H. Lee and P.M. Petroff: “Exciton storage in semiconductor self-assembled quantum dots”, Science, Vol. 286, (1999), pp. 2312–2314. http://dx.doi.org/10.1126/science.286.5448.2312[Crossref]
• [22] P. Hawrylak, S. Fafard and Z.R. Wasilewski: “Engineering quantum states in self-assembled quantum dots for quantum information processing”, Condens. Matter News, Vol. 7, (1999), pp. 16–25.
• [23] M. Bayer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusiński, Z.R. Wasilewski, O. Stern and A. Forchel: “Coupling and entangling of quantum states in quantum dot molecules”, Science, Vol. 291, (2001), pp. 451–453. http://dx.doi.org/10.1126/science.291.5503.451[Crossref]
• [24] A. Stahl and I. Balslev: Electrodynamics of the Semiconductor Band Edge, Springer-Verlag, Berlin, 1987.
• [25] I. Balslev, R. Zimmermann and A. Stahl: “Two-band density-matrix approach to nonlinear optics of excitons”, Phys. Rev. B, Vol. 40, (1989), pp. 4095–4104. http://dx.doi.org/10.1103/PhysRevB.40.4095[Crossref]
• [26] G. Czajkowski, F. Bassani and A. Tredicucci: “Polaritonic effects in superlattices” Phys. Rev. B, Vol. 54, (1996), pp. 2035–2043. http://dx.doi.org/10.1103/PhysRevB.54.2035[Crossref]
• [27] G. Czajkowski, F. Bassani and L. Silvestri: “Excitonic optical properties of nanostructures: real density matrix approach”, Rivista del Nuovo Cimento, Vol. 26(5–6), (2003), pp. 1–150.
• [28] S. Cortez, O. Krebs, P. Voisin and J.M. Gérard: “Polarization of the interband optical dipole in InAs/GaAs self-organized quantum dots”, Phys. Rev. B, Vol. 63, (2001), art. 233306.
• [29] D.S. Chuu, C.M. Hsiao and W.N. Mei: “Hydrogenic impurity states in quantum dots and quantum wires”, Phys. Rev. B, Vol. 46, (1992), pp. 3898–3905. http://dx.doi.org/10.1103/PhysRevB.46.3898[Crossref]
• [30] R. Atanasov, F. Bassani and V.M. Agranovich: “Mean-field polariton theory for asymmetric quantum wells”, Phys. Rev. B, Vol. 49, (1994), pp. 2658–2666. http://dx.doi.org/10.1103/PhysRevB.49.2658[Crossref]
• [31] N. Tomassini, A. D’Andrea, G. Martino, R. Girlanda and R. Atanasov: “Zn(S,Se)-based superlattices and quantum wells: band offsets, excitons, linear and nonlinear optical properties”, Phys. Rev. B, Vol. 52, (1995), pp. 11113–11119. http://dx.doi.org/10.1103/PhysRevB.52.11113[Crossref]
• [32] J. Schlösser, A. Stahl and I. Balslev: “Polarisation effects of the dynamical Stark effect of excitons in quantum wells”, J. Phys.: Condens. Matter, Vol. 2, (1990), pp. 5979–5989. http://dx.doi.org/10.1088/0953-8984/2/27/005[Crossref]
• [33] L. Silvestri, G. Czajkowski and F. Bassani: “Optical properties of excitons in quantum dots: diffraction of an electromagnetic plane wave by a spherical quantum dot”, Journ. Phys. Chem. Sol., Vol. 61, (2000), pp. 2043–2053. http://dx.doi.org/10.1016/S0022-3697(00)00206-7[Crossref]
• [34] R. Zimmermann: “On the dynamical Stark effect of excitons: the low field limit”, Phys. Stat. Sol. (b), Vol. 150, (1988), pp. 545–554.
• [35] A. Abramowitz and I. Stegun (Eds.): Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, US GPO, Washington, D. C., 1964.
• [36] G. Bastard: Wave Mechanics Applied to Semiconductor Heterostructures, Les Editions de Physique, Paris, 1989.
• [37] G. Czajkowski, K.-H. Pantke, K. Ziebegk and P. Schillak: “Energy transfer between electromagnetic modes near the isotropic point in CdS”, J. Cryst. Growth, Vol. 101, (1990), pp. 379–384. http://dx.doi.org/10.1016/0022-0248(90)91001-7[Crossref]
• [38] G. Czajkowski and P. Schillak: “Higher order isotropic points in CdS”, Nuovo Cimento D, Vol. 13, (1991), pp. 1199–1202. [Crossref]
• [39] P. Schillak and G. Czajkowski: “Optical properties of wurtzite-type semiconducting crystals near the isotropic point”, Nuovo Cimento D, Vol. 14, (1992), pp. 563–574. [Crossref]
• [40] J.A. Barker and E.P. O’Reilly: “Theoretical analysis of electron-hole alignment in InAs-GaAs quantum dots”, Phys. Rev. B, Vol. 61, (2000), pp. 13840–13851. http://dx.doi.org/10.1103/PhysRevB.61.13840[Crossref]

Identifiers

DOI

10.2478/s11534-006-0011-4