260 PublicacionesJ. L. MOVILLA AND J. PLANELLES PHYSICAL REVIEW B 74, 125322 2006tion induced by the dielectric discontinuity strongly affectsinterparticle correlations and interaction energies. In addition,the study also demonstrates how the combination ofsingle- and two-particle Coulombic effects may give rise, inweakly confined D − systems, to the appearance of differentphases. Strong, Wigner-like localizations of the electronicdensity and important reconstructions of the two-electronground state are found.The main conclusions of the paper are itemized as follows.i Surface states in QDs surrounded by air or a vacuummay localize the electronic density in the external medium,and, then, electrons undergo a strong angular correlation.This correlation is gradually reduced as the QD dielectricconstant increases, due to the influence of the polarizationcharges induced at the dielectric interface.ii In the case of surface states in air-filled nanocavitiesof semiconductor matrices, polarization charges reduce theelectronic correlation to a greater extent than in the QD case.iii A transition phase from volume to surface states accompaniedby a strong radial Wigner-like localization of theelectronic density is produced when a quantum dot is dopedwith a central shallow donor impurity in the weak confinementregime. Within this phase, the D − center presents zerobinding energy, providing a situation in which the systembehaves as a twofold electron reservoir. We show that theimpurity is able to attach the first excess electron strongly.However, this electron totally blocks the effect of the impurity,and the system now behaves as an undoped and emptyQD for the second excess electron.iv The radial-Wigner phase vanishes as we approach thestrong confinement regime. However, it is stable within awide range of QD sizes, thus making its experimental searchand characterization feasible.ACKNOWLEDGM<strong>EN</strong>TSFinancial support from MEC-DGI Project No. CTQ2004-02315/BQU and UJI-Bancaixa Project No. P1-B2002-01Spain is gratefully acknowledged. A Spanish MECD FPUgrant is also acknowledged J.L.M..*Electronic address: planelle@exp.uji.es1 L. Bányai and S. W. Koch, Semiconductor Quantum Dots WorldScientific, Singapore, 1993.2 L. E. Brus, J. Chem. Phys. 80, 4403 1984.3 V. A. Fonoberov, E. P. Pokatilov, and A. A. Balandin, Phys. Rev.B 66, 085310 2002.4 L. Bányai, I. Galbraith, C. Ell, and H. Haug, Phys. Rev. B 36,6099 1987.5 T. Takagahara, Phys. Rev. B 47, 4569 1993.6 P. G. Bolcatto and C. R. Proetto, J. Phys.: Condens. Matter 13,319 2001.7 F. Stern, Phys. Rev. B 17, 5009 1978.8 M. Iwamatsu, M. Fujiwara, N. Happo, and K. Horii, J. Phys.:Condens. Matter 9, 9881 1997.9 G. Goldoni, F. Rossi, and E. Molinari, Phys. Rev. Lett. 80, 49951998.10 A. Franceschetti, A. Williamson, and A. Zunger, J. Phys. Chem.B 104, 3398 2000.11 R. Tsu and D. Babić, Appl. Phys. Lett. 64, 1806 1994.12 Z. Y. Deng, J. K. Guo, and T. R. Lai, J. Phys.: Condens. Matter 6,5949 1994.13 A. Mews, A. Eychmüller, M. Giersig, D. Schoos, and H. Weller,J. Chem. Phys. 98, 934 1994.14 A. P. Alivistatos, Nature London 271, 933 1996.15 A. Mews, A. V. Kadavanich, U. Banin, and A. P. Alivisatos, Phys.Rev. B 53, R13242 1996.16 R. B. Little, M. A. El-Sayed, G. W. Bryant, and S. Burke, J.Chem. Phys. 114, 1813 2001.17 D. J. Norris and M. G. Bawendi, Phys. Rev. B 53, 16338 1996.18 Special Issue on Spectroscopy of Isolated and Assembled SemiconductorNanocrystals, J. Lumin. 70 1-6 1996.19 G. Bastard, Wave Mechanics Applied to Semiconductor HeterostructuresLes Éditions de Physique, Les Ulis, 1988.20 J. P. Loehr, Physics of Strained Quantum Well Lasers KluwerAcademic, Boston, 1998.21 G. W. Bryant and W. Jaskólski, Phys. Rev. B 67, 205320 2003.22 J. J. Shi, Chin. Phys. 11, 1286 2002.23 J. D. Jackson, Classical Electrodynamics Wiley, New York,1962.24 L. E. Brus, J. Chem. Phys. 79, 5566 1983.25 M. Lannoo, C. Delerue, and G. Allan, Phys. Rev. Lett. 74, 34151995.26 P. G. Bolcatto and C. R. Proetto, Phys. Rev. B 59, 12487 1999.27 L. Bányai, P. Gilliot, Y. Z. Hu, and S. W. Koch, Phys. Rev. B 45,14136 1992.28 A. Orlandi, G. Goldoni, F. Mangui, and E. Molinari, Semicond.Sci. Technol. 17, 1302 2002.29 J. L. Movilla, J. Planelles, and W. Jaskólski, Phys. Rev. B 73,035305 2006.30 J. Planelles and J. L. Movilla, Phys. Rev. B 73, 235350 2006.31 L. W. Wang and A. Zunger, Phys. Rev. Lett. 73, 1039 1994.32 D. BenDaniel and C. B. Duke, Phys. Rev. 152, 683 1966.33 P. Harrison, Quantum Wells, Wires and Dots Wiley, Chichester,2001.34 J. L. Movilla and J. Planelles, Comput. Phys. Commun. 170, 1442005.35 Once a prominent role of the bare Coulomb term between theelectrons located in the crown on the vacuum side is assumed,pushing either electron to an opposite site in this outside crown.36 In these volume states, carriers are almost completely confinedinside the QD border. Then, the dielectric constant coming intothe bare Coulomb term is QD .37 Care should be taken when talking about splitting the electronelectroninteraction energy into a sum of bare Coulomb andpolarization. Indeed, the so-called bare Coulomb term may includedielectric polarization. For example, the interaction betweentwo electrons in a completely uniform medium so that nopolarization terms coming from dielectric mismatches arisewith permittivity 1 is given by the bare Coulomb term e 2 /r.125322-8
Confinamiento dieléctrico 261DIELECTRIC MISMATCH EFFECTS IN TWO-ELECTRON…<strong>It</strong> still includes the polarization of the dielectric medium, screeningthe vacuum bare Coulomb e 2 /r term. In this sense, pleasenote that there is no contradiction between the limit values thatthe bare Coulomb term may reach for very large values of QDin the case of a high/low V 0 confining QD barrier, which doesnot allow/allows the formation of surface states. In the first instance,the bare Coulomb term goes to zero as the dividingscreening factor QD increases greatly. In the second case, wefind a value of 1/R a.u. which corresponds to the work requiredto bring an electron from infinity up to the border of a radius RQD when a unit charge is uniformly distributed in an outsidespherical crown by this border.PHYSICAL REVIEW B 74, 125322 200638 Note that the radial pair density Pr 1 ,r 2 , Eq. 5, includes thedifferential surfaces dS i =r i 2 sin i d i d i in its definition. <strong>It</strong> istherefore necessarily zero at the origin, r 1 =r 2 =0. However, thisdoes not mean at all that the wave function has a node at theorigin.39 Within the radial-Wigner phase, the electron-electron Coulombrepulsion is nearly independent of QD and can be accuratelyestimated by 1/ 0 r max . This same value, but with opposite sign,corresponds to the attractive interaction of the unit negativecharge located in the outside crown and the central hydrogenicimpurity. Both interactions lead, then, the second electron to feelnearly free, within the region where it is confined.125322-9
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CONFINAMIENTO NANOSCÓPICO ENESTRUC
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AgradecimientosDecía Albert Einste
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A mi madreA la memoria de mi padre
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viiihigh-correlation electronic reg
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xric) resolution method proves the
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xii14. F. Rajadell, J.L. Movilla, M
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xivcen para moldear a voluntad su e
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xvideterminar las características
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Capítulo 1Fundamentos teóricosEl
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1.1 Modelo k · p 3donde p = −i¯
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1.1 Modelo k · p 5inversa de la ma
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1.2 Heteroestructuras. Aproximació
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1.3 Masa efectiva dependiente de la
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1.7 Transiciones intrabanda 17Tras
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Capítulo 2Confinamientos espacial
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23esta aproximación asume implíci
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Capítulo 3Confinamiento periódico
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Capítulo 4Confinamiento magnético
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51donde m ∗ es la masa efectiva d
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Capítulo 5Confinamiento dieléctri
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69Más complicado pero también ana
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5.1 Validez de la electrodinámica
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Capítulo 6ConclusionesEn esta Tesi
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155entre los anillos como la orient
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157fuerte decaimiento de la intensi
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Publicaciones
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Confinamientos espacial y másico
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Confinamientos espacial y másico 1
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Confinamiento periódico
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Confinamiento periódico 171J. Phys
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Confinamiento magnético
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Confinamiento magnético 179Symmetr
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Confinamiento magnético 185Aharono
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Confinamiento magnético 187PHYSICA
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Confinamiento magnético 193938Mean
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Confinamiento magnético 195940QRs
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Confinamiento dieléctrico
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Confinamiento dieléctrico 199Compu
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BIBLIOGRAFÍA 311[220] J.L. Zhu y X
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