CONFINAMIENTO NANOSC´OPICO EN ESTRUCTURAS ... - It works!

Confinamiento dieléctrico 205150 J.L. Movilla, J. Planelles / Computer Physics Communications 170 (2005) 144–152Fig. 2. Coulombic potential, excluding φ A , ρ = 0 cross section (Eqs. (5), (6)) for on-center (z I = 0, dotted line) and off-centered (z I = 0.7,full line) impurity in a R = 3nm,ǫ i = 4 spherical QD in air or vacuum (ǫ o = 1).Fig. 3. Self-polarization potential φ s corresponding to a R = 3 nm spherical QD in vacuum (ǫ o = 1) for two different internal dielectricconstants, namely ǫ i = 4 (dashed lines) and ǫ i = 8 (full lines).The contribution of the self-polarization potential to the energy can be either stabilizing or destabilizing, dependingon the real charge located in the region with lower or higher dielectric constant, respectively [24]: Asisshown in Fig. 3 this potential (self-polarization) is destabilizing inside the QD and very stabilizing outside, by theQD edge. This figure also reveals that the stabilizing well grows up faster vs. ǫ i than the destabilizing barrier, sothat we may say that as ǫ i increases the ratio stabilizing well/destabilizing barrier of self-potential also increases,its net contribution to the energy being strongly dependent on the amount of electronic density that spreads overoutside. For low ǫ i values, the electron wave function is highly localized near the impurity inside the QD, so thatthe self-energy contribution is destabilizing. However, for large ǫ i values the situation is reversed, and both theincreased spread of the wave function and the higher attracting capability of the self-polarization potential wellproduce a large energy stabilization (see Fig. 1).An even more relevant result obtained is that self-polarization enhances the energy differences between oncenterand off-center impurities (see Fig. 1), due to the fact that as we push the impurity from the center towardsthe QD edge, a larger amount of electron density comes into the deep, stabilizing well of the self-polarizationpotential. These differences can be further increased by tuning the appropriate mass mismatch. Fig. 4(a) displaysthe enhancement produced by the use of an outside effective mass m o = 1. We can understand this effect asfollows: the closer the impurity to the dot boundary, the larger the charge spread in the surrounding medium, andthe smaller the kinetic contribution to the total energy. However, these effects can be drastically reduced by thespatial confining potential, as it prevents the wave-function from leaking outside the QD (see Fig. 5). In other