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Confinamiento dieléctrico 249THEORY OF DIELECTRICALLY INDUCED SURFACE…dielectric mismatch effects, that will help to analyze the obtainedresults.Figures 1c1–1c3 show sudden changes of e-h overlap2S e-hthat parallel the transition from volume to surface excitonstates, as can be seen in the corresponding insets. Thistransition is also reflected as a change of sign of the slope inthe excitonic energy vs QD profile Figs. 1a1–1a3, whileit is not reflected in the binding energy plots Figs. 1b1–1b3, whose profile vs QD is very smooth. Differencesbetween polarized and unpolarized excitonic energies seeFigs. 1a1–1a3 basically reflect self-polarization effects,while differences between polarized and unpolarized bindingenergies see Figs. 1b1–1b3 essentially show the influenceof the polarization of the Coulomb interaction, as wehave verified in a series of calculations not shown. Ourresults are an extreme example denying the cancellation ofsingle- and two-particle polarization contributions to the excitonicenergy. Also, they lead to the conclusion that themain effect of single-particle self-polarization is the productionof a redshift in the optical band gap, while the polarizationof the Coulomb interaction basically enhances the excitonbinding energy. Figure 1 additionally reveals that theconditions for the QD materials to yield exciton surfacestates when the QD is in air or a vacuum are rather severe,namely, quite low electroaffinity and not very light electroneffective mass m * e . Not many semiconductors can fulfillthis requirement. We may mention SiO 2 as a possible candidatem * e =0.5, =0.9 eV, =4, and m * h =10, see Refs.27–30.Next, we study the same QD doped with a hydrogenicdonor impurity at its center. This impurity exerts the mostrelevant influence for low values of the dielectric constant bybinding the electron while repelling the hole, thus leading toa drop in excitonic binding energy 31 and brightness see panelsd1–d3 and e1–e3 in Fig. 1. Our calculations alsoreveal that the heavier the electron effective mass is, thecloser its density distribution bound to the impurity site is.Accordingly, an acceptor impurity attracts the heavier holevery close to the QD center and creates an effective neutralentity that leads the electron to behave as an almost independentparticle in the QD.Case (ii): QD embedded in a medium with a larger dielectricconstant. We consider, as above, a spherical 5 nmradius QD defined by the following parameters: m e,QD =0.5, QD =4, V e =1 eV, and V h =0.5 eV, the ratio V e /V h simulatingtypical alignments of different materials. Two differenteffective masses for holes have been considered, namely,*m h,QD=1 and 10, slightly and much heavier than m e,QD , respectively.This QD is embedded in a fictitious medium witha dielectric constant ranging from out = QD up to out =50.The effective masses in this medium are assumed to be thesame as in the QD since we have no criterion to assign them.The key difference with respect to the previous case i ofa QD in air is that now, the self-polarization potential has theattractive well located on the inner side of the QD border.Then, both particles can be confined in it, the heavier particlebeing more strongly attracted by this well due to its smallerkinetic energy. This is in contrast with the above case iwhere the hole the heavier particle was unable to overcomeits large confining potential barrier, while the electron the**E (eV)E (eV)2e−hSS 2 e−h−0.2−0.4−0.6−0.80.30.20.1010.80.60.40.2010.80.60.40.20515PHYSICAL REVIEW B 76, 115312 2007(a1)(b1)(c1)(d1)25 35 45 5 15 25 35 45ε outε outFIG. 2. Same as Fig. 1 but for a R=5 nm, QD =4 QD with V e*=1 eV, V h =0.5 eV, and m e,QD =0.5, and two different hole effective**masses, namely, m h,QD =10 a1, b1, and c1 and m h,QD =1a2, b2, and c2, as a function of the dielectric constant of theenvironment out . Panels d1 and d2 correspond to c1 and c2when a hydrogenic donor impurity is located at the QD center.lighter particle, confined by a shorter wall, could jump tothe self-polarization potential well. Indeed, in case ii, ourexploratory single-particle calculations vs out showed agradual localization of the carriers in the self-polarizationwell, facing three different phases: namely, phase 1 low out corresponding to volumetrically distributed electron andhole, phase 2 intermediate out where the electronic densitydistribution is still volumetric while the hole forms a surfacestate, and phase 3 large out in which both electron and holeare located in the surface well. However, as the strong e-hattraction QD =4 is incorporated into the CI calculation,phase 2 drops out. 32 Thus, only two phases are encountered,in which both particles show volumetric or facial distributionssimultaneously. This is shown in Fig. 2, which showsthe overlap S 2 e-h , excitonic E, and binding E b energies of the*considered QD with m h,QD =1 and 10 vs out ranging from out = QD up to out =50. The quantitative differences in excitonicand binding energies in either case are a direct consequenceof the quite different kinetic energy of the hole.Both cases show, however, similar qualitative trends increasingband gap redshift and decreasing E b vs an increasingdielectric mismatch, which is in turn similar to the behavioralready shown for a QD in air see Fig. 1. A relevantdifference arises in the overlap vs out profile. While Fig.*2c1 m h,QD =10 resembles Figs. 1c1–1c3, in which thetransition from volume to surface excitonic states involves a2sudden S e-h drop and therefore a sudden reduction in the(a2)(b2)(c2)(d2)115312-3