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Confinamiento dieléctrico 277Dielectric confinement in quantum dots 9own induced charge, and È (Eq. (12)) represents the interaction of one carrier with theimage charges induced by the other one. It is easy to prove that in the absence of dielectricmismatch the latter two terms become zero, thus reducing Eq. (10) to the bulk Coulombinteraction. If the two real charges have opposite signs, the - sign in Eq. (10) holds; thesign + holds if the charges have equal signs.In the excitonic case (interaction between a conduction band electron and a valenceband hole), one can notice that È and Î × terms have opposite signs, and that the Ð=0term (the most important one) of È is exactly cancelled out with the Ð=0 terms of Î ×´Ö½µand Î ×´Ö¾µ. Furthermore, the residual terms (Ð ½) ofÈ and those of Î ×´Ö½µ·Î ×´Ö¾µ℄have, on average, close absolute values [2, 19, 22]. This fact almost totally cancels out theinfluence of the dielectric mismatch on the electron-hole Coulomb interaction, therebyreducing the excitonic energy to the bare electron-hole attraction. This characteristic is notonly restricted to spherical geometries. Indeed, Bolcatto and Proetto [23] showed that thiscancellation was also effective for cubic quantum dots.Although the excitonic energy spectrum is not altered by polarization effects, otherexcitonic properties can be profoundly affected. Thus, Fonoberov et al. [22] predictedan enhancement of the exciton binding energy by a factor of 2 when CdS nanocrystalsare immersed in a =1.78 dielectric medium, and Bolcatto and Proetto [24] showed thatthe enhancement of the exciton binding energy was even more pronounced in the case ofinhomogeneous quantum dots.More involved is the case of charges of the same sign, due mainly to the followingreasons: (i) The polarization (Eq. (12)) and self-polarization (Eq. (11)) potentials do notoffset each other since they have the same sign, thus leading to the enhancement of theCoulomb interaction in the (most frequent) case of ÓØ ÓÙØ , and (ii) The bare Coulombrepulsion (first term on the right hand side in Eq. (10)) pushes the carriers toward the QDsurface, thereby enhancing the image charge effects.Under these circumstances (carriers of the same sign) the QD energy spectrum mayvary markedly as the QD dielectric environment is changed [2]. Indeed, at the limitof strong dielectric mismatch, the interaction among carriers is dominated by surfacepolarization effects [25], which are even capable of yielding reconstructions of excitedmany-body states [26]. Optical and transport related properties are also affected bypolarization. For instance, Franceschetti et al. [25] and Orlandi et al. [26] reported a largeenhancement of addition energies when the QDs are embedded in a medium with a lowdielectric constant.It is worth stressing that all the calculations referenced in this section deal with perfectconfinement. In the next section we will show that this assumption is frequently too strongto accurately describe the physics of quantum dots, so that a more realistic model of the