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

250 PublicacionesRAJADELL et al.*exciton brightness, this is not the case in Fig. 2c2 m h,QD=1. Since in the present case ii the transition from volumeto surface state holds simultaneously for electron and hole,one may expect profiles like Fig. 2c2, revealing an almostconstant overlap vs out . Then, the plot in Fig. 2c1 lookslike an anomaly that deserves an explanation. Indeed, theparameters m * e =0.5, m * h =10, R=5 nm, and QD =4 yieldquite a small effective Bohr radius, thus revealing that bothelectron and hole are in the weak confinement regime, thevolumetric electron and hole density distributions beingsimilar see insets in Fig. 2c1. However, once the trappingof particles in the narrow, deep self-polarization potentialwell occurs, both particles feel different spatial confinement.The heavier particle becomes strongly localized in the well,whereas the lighter one has a relevant leaking outside it seeinsets in Fig. 2c1, yielding as a result a smaller overlap. Inother words, in contrast to case i where the transition fromvolume to surface states always parallels a sudden decreasein brightness, in case ii, this transition only has relevantbrightness impact for QD materials with large m * h /m * e ratios.Also, the influence of a hydrogenic donor impurity is addressed.As above, it attracts the electron toward the QDcenter and repels the hole see Figs. 2d1 and 2d2, resultingin a negligible binding energy and a strong reduction inoscillator strength.In a last series of calculations, we explore the possibilityof surface exciton formation in QDs built of higher dielectric*constant materials. Now we set, as above, R=5 nm, m e=0.5, m * h =1 and 10, V e =1 eV, and V h =0.5 eV. The permittivityof the external medium is set very high, out =100, and2we calculate the e-h overlap S e-h and binding energy E b vs QD . The results are shown in Fig. 3. As previously discussed,sudden changes in overlap reflecting transition fromvolume to surface exciton states only occur for large m * *h /m eratios. As can be seen in Fig. 3b1 corresponding to a largem * h /m * e ratio, small large QD values yield surface volumeexcitonic states with small large overlaps, in agreementwith previous reasoning. However, intermediate QD valuesare characterized by extremely small overlaps that parallel ananomalous minimum in the binding energy Fig. 3a1. Thisbehavior occurs because, in this range of QD dielectric constants,the electron and hole single-particle densities are distributedas in the above mentioned phase 2, but now the e-hCoulomb attraction is not strong enough to drop phase 2 out,so we get a “broken” exciton in which the hole is localized inthe self-polarization potential well, whereas the electronspreads over the whole QD volume see insets in Fig. 3b1.The small overlap and the decrease in the exciton bindingenergy are a direct consequence of the e-h spatial separationin this phase, which does not exist see Figs. 3a2 and 3b2unless the effective masses of electron and hole are verydissimilar. Finally, Figs. 3c1 and 3c2 show the influenceof a hydrogenic donor impurity located at the QD center. Wesee that the D + ,X exciton can approximately be describedas D 0 +h, i.e., a neutral electron-impurity pair and an almostE b (eV)S 2 e−hS 2 e−h0.040.030.020.01010.80.60.40.2010.80.60.40.2PHYSICAL REVIEW B 76, 115312 2007(a1)(b1)(c1)05 15 25 35 45 4 8 12 16ε QDε QD2FIG. 3. Binding energy E b and e-h overlap S e-h of a R=5 nm*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 and b1 and*m h,QD =1 a2 and b2, as a function of QD for a fixed out=100. Insets: same criterion as in Fig. 1. Panels c1 and c2 correspondto b1 and b2 when a hydrogenic donor impurity is locatedat the QD center.independent hole, as it is revealed by the negligible bindingenergy calculated.IV. CONCLUDING REMARKSWe have shown that the dielectric properties of the QDenvironment can strongly influence the brightness of confinedexcitons, as well as excitonic and binding energies, dueto the formation of surface states. While a sudden decrease inexciton brightness parallels the formation of surface excitonsin the case of a QD in air or a vacuum, only QD materialswith a large m h * /m e * ratio present a considerable reduction inexciton brightness when the QD is buried in a large dielectricconstant medium. Our calculations also reveal 33 that the conditionsto reach surface exciton states in this last case are lesssevere than if the QD is surrounded by air or a vacuum. Ashallow donor impurity located at the QD center leads to analmost total suppression of exciton binding and brightness.ACKNOWLEDGMENTSFinancial support from MEC-DGI Project No. CTQ2004-02315/BQU and UJI-Bancaixa Project No. P1-1B2006-03Spain is gratefully acknowledged. UJI J.L.M. and GeneralitatValenciana FPI M.R. grants are also acknowledged.(a2)(b2)(c2)20115312-4