Hole Band Mixing in CdS and CdSe Quantum Dots and Quantum

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J. Phys. Chem. C 2010, 114, 8337–8342

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Hole Band Mixing in CdS and CdSe Quantum Dots and Quantum Rods J. Planelles, F. Rajadell, and J. I. Climente* Departament de Quimica Fisica i Analitica, UniVersitat Jaume I, E-12080, Castello, Spain ReceiVed: March 8, 2010; ReVised Manuscript ReceiVed: March 30, 2010

Using a six-band k · p Hamiltonian for wurtzite lattice, we study the hole ground state symmetry and composition in spherical quantum dots and elongated quantum rods made of CdS and CdSe. The ground state crossovers which occur when changing the nanocrystal size and shape are well understood in terms of hole band mixing. Contrary to previous belief, the quantum rod ground state crossover with increasing length is shown not to occur at a fixed aspect ratio. The geometry and composition that maximize the spin purity and the intensity of linearly polarized light emission are elucidated. The six-band wurtzite Hamiltonian results for CdSe are compared to those obtained with quasi-cubic four-band and one-band Hamiltonians, and the performance of these simplified Hamiltonians is discussed. Introduction Wurtzite nanocrystals made of different sizes, shapes, and compositions are currently under intense investigation, mainly motivated by their potential applications in optics, biology, solar energy conversion, and spintronics.1-7 While the behavior of electrons in these structures can be easily understood from the quantum confinement, holes display less intuitive phenomena which follow from the mixing of valence bands. In spherical quantum dots (QDs) made of CdS and CdSe, the hole ground state changes from S-like to P-like orbital symmetry with decreasing radius, which gives rise to dark excitons for small nanocrystals.8-12 In CdSe quantum rods (QRs), the hole ground state symmetry changes with increasing aspect ratio, which is responsible for a transition from circular to linearly polarized light emission.13-15 Both these phenomena have profound implications in the optical activity of nanocrystals. So far, theoretical understanding of the hole behavior has mainly relied on atomistic models13,16 and multiband effective mass models in the quasi-cubic approximation.7,8,15,17-20 A few works have used multiband k · p Hamiltonians for wurtzite lattice,9,11,21 which combines the physical insight of effective mass theory with a complete inclusion of crystal anisotropy effects. These works focused on the electronic structure and symmetry of the hole states in CdSe and CdS QDs,9,11 but they provided little insight into the composition of the spinorial hole states, which is necessary to understand the origin of the trends in the spectrum as well as the ground-state properties. They also described the electronic structure of CdSe QRs,21 even though no ground state crossover was found with increasing rod length, contrary to experimental, atomistic, and quasi-cubic model results.13,15,22 No simulations were carried out for CdS QRs, which are now routinely synthesized.4,23 In this paper we study energy spectrum and composition of low-lying hole states in CdS and CdSe QDs and QRs with different sizes and aspect ratios. We observe a strong dependence of the coupling between valence bands on the strength and the shape of the quantum confinement. This dependence allows us to rationalize the origin of the ground state transitions reported in the literature and to determine the physical regimes * To whom correspondence should be addressed, josep.planelles@ qfa.uji.es. (http://quimicaquantica.uji.es/)

minimizing or maximizing hole band coupling. Likewise, we determine the regimes of maximum spin purity, which is desirable for applications in spintronics and magnetic doping.5,7 We test the validity of the widely used quasi-cubic approximation for CdSe nanocrystals by comparing with the wurtzite Hamiltonian results. It is shown that the quasi-cubic approximation provides qualitatively correct predictions for the ground state transitions and symmetries. The theoretical prediction of Voon et al.,15 stating that the ground state crossover in QRs depends on the aspect ratio alone,15 is shown to fail in wurtzite structures due to the intrinsic anisotropy of the crystal. Theoretical Method The valence-band spectrum near the Γ point in wurtzite crystals is formed by three (doubly degenerate) bands, which we refer to as A, B and C. We label accordingly the corresponding Bloch functions, given in ref 24: |Av〉 ) -1/2|(X + iY)v〉, |AV〉 ) 1/2|(X - iY)V〉, |Bv〉 ) 1/2|(X - iY)v〉, |BV〉 ) -1/2|(X + iY)V〉, |Cv〉 ) |Zv〉, |CV〉 ) |ZV〉, where the arrow represents the spin projection. These functions have Bloch angular momenta Jz ) +3/2, -3/2, -1/2, +1/2, +1/2, -1/2, respectively. A, B, and C bands are split in energy by the joint action of spin-orbit interaction (∆so) and the hexagonal component of the crystal field (∆c). Their energy order depends on relative strength of these two factors. For CdS, ∆c J ∆so, and the energy order that follows is that in Figure 1a. For CdSe, ∆c , ∆so, and the energy order is that in Figure 1b. For simplicity, in both illustrations we have neglected the second-order spin-orbit coupling between B and C bands. To consider the coupling between all A, B, and C bands, we use the Rashba-Sheba-Pikus Hamiltonian projected on the above-mentioned Bloch functions.24 We model QDs as spheres of radius R surrounded by a numerically infinite potential. Similarly, QRs are modeled as two hemispheres of radius R separated by a cylinder of length L (see Figure 1c). The potential is set to zero within the entire nanostructure. Since the structures are axially symmetric, it is convenient to write the Hamiltonian in cylindrical coordinates as done in ref 25. The eigenstates can then be classified by their total angular momentum Fz ) mz + Jz, which is the sum of the envelope (mz) plus Bloch (Jz) angular momenta. The Hamilto-

10.1021/jp102086q  2010 American Chemical Society Published on Web 04/15/2010

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Planelles et al. TABLE 1: Crystal Field Splitting, Spin-Orbit Splitting, and Mass Factors for A (also B) and C Valence Bands CdS CdSe

∆c (meV)

∆so (meV)

mzA

mA⊥

mzC

mC⊥

27 39

21.7 138.6

1.96 1.78

0.22 0.29

0.22 0.20

2.56 2.32

Results and Discussion

Figure 1. Valence band structure at the Γ point for wurtzite (a) CdS and (b) CdSe. (c) Geometry of the nanostructures under study.

CdS Nanocrystals. In this section we study CdS nanocrystals. For this material the spin-orbit constant is moderately small and one has to consider all six valence bands necessarily.18 First, we study the lowest energy states in spherical QDs with increasing radius. Li and Xia11 reported a ground state crossover, from P-like symmetry to S-like symmetry, with increasing size, which was consistent with later experimental findings in refs 12 and 20. The same crossover is observed in Figure 2a: the ground state is of Fz ) 1/2 symmetry for small radii and changes to Fz ) 3/2 after R ∼ 45 Å. The composition of the Fz ) 1/2 state, which is depicted in Figure 2b, reveals that the Fz ) 1/2 is mainly an admixture of |Av〉 and |Bv〉. As can be seen in eq 1, these components have mz ) (1; i.e., they are of P-like orbital symmetry. Similarly, the Fz ) 3/2 state (Figure 2c) at large radii is mainly composed of |Av〉, which has mz ) 0 (i.e., S-like symmetry). The ground-state crossover can be explained from the competition between band mixing and single band effects. In

nian is integrated numerically using a finite diferences scheme. The eigenstates are spinorial wave functions expanded on the six Bloch functions given above. For all the structures we investigate, the ground state symmetry may be either Fz ) (3/2 or Fz ) (1/2. (Fz states are Kramers degenerate, so we shall only consider the positive instance. The lowest eigenstates with Fz ) 3/2 and Fz ) 1/2 are of the form:

|Fz ) 3/2〉 )

() () f0A(r)|Av〉

A f-1 (r)|Av〉

f2B(r)|Bv〉 f1C(r)|Cv〉 f3A(r)|AV〉 f1B(r)|BV〉 f2C(r)|CV〉

f1B(r)|Bv〉

,

|Fz ) 1/2〉 )

f1C(r)|Cv〉 f2A(r)|AV〉

f0B(r)|BV〉

f1C(r)|CV〉

(1)

where f mX z(r) is a three-dimensional envelope function with angular momentum mz corresponding to the valence band X ) A, B, C. We use the set of wurtzite material parameters derived in ref 26. When inserted into our Hamiltonian,25 these imply highly anisotropic mass factors for both CdS and CdSe. By mass factor we refer to the mass coefficients appearing in front of the radial (m⊥) and longitudinal (mz) derivatives in the diagonal terms of the Hamiltonian. Note that the concept of mass factor differs from the concept of effective masses given in ref 26, which implicitly account for band mixing effects. Arguing in terms of diagonal mass factors allows us to disentangle singleband and band mixing effects in the discussion of the results. We summarize the mass factors (hereafter masses), crystal field splitting, and spin-orbit splitting constants in Table 1, since they will be useful for later analysis. For simplicity we only show the masses of A-type and C-type holes. The masses of B-type holes are the same as those of A-type holes. Unless otherwise stated, the reference energy in all the calculations is the top of the C-band.

Figure 2. (a) Energy of the lowest hole state with Fz ) 1/2 (solid line) and Fz ) 3/2 (dashed line) in CdS QDs of different radii. (b) and (c) Compositions of the Fz ) 1/2 and Fz ) 3/2 spinors, respectively.

Hole Band Mixing

Figure 3. (a) Energy of the lowest hole state with Fz ) 1/2 and Fz ) 3/2 in CdS QRs of different length and R ) 15 Å. Inset: same for R ) 60 Å. (b) and (c) Composition of the ground state for QRs of R ) 15 Å and R ) 60 Å, respectively.

QDs with large R the ground state is |Fz ) 3/2〉, with dominant component |Av〉. This corresponds to the weak band coupling regime. In this regime, the ground state is mainly formed by A-type holes, which are the lowest in energy due to crystal field and spin-orbit effects (recall Figure 1a). The ground-state symmetry is Fz ) 3/2 because quantum confinement renders |Fz ) 3/2〉 (whose |Av〉 component has mz ) 0) more stable than |Fz ) 1/2〉 (whose |Av〉 component has mz ) -1, see eq 1). In QDs with small R, however, band mixing effects start dominating because the mixing terms (off-diagonal terms of the Hamiltonian) scale up with the confinement. The mixing is particularly strong for |Fz ) 1/2〉, because the initially dominant |Av〉 component is susceptible to strong coupling with |Bv〉. The two components have identical diagonal contributions to the kinetic energy (|mz| ) 1, same mass), so that they are only split by ∆so. Since the spin-orbit constant does not scale with the confinement, in the small R limit its influence becomes negligible as compared to that of the mixing terms. The strong band mixing between these two components provides a source of energy stabilization. It then follows that the ground state for small QDs is formed by |Fz ) 1/2〉, which is roughly a 50% admixture of |Av〉 and |Bv〉 (see Figure 2b). Next, we investigate the energy spectrum and state composition in CdS QRs. Figure 3 illustrates the results for QRs with R ) 15 Å (panel a) and R ) 60 Å (inset), as a function of L. One can see that the rods do not exhibit a ground-state crossover

J. Phys. Chem. C, Vol. 114, No. 18, 2010 8339 with increasing aspect ratio, in sharp contrast to CdSe QRs (see, e.g. refs 13, 14, 21, and 22 and next section). Instead, the symmetry of the ground state is always that of the spherical QD: Fz ) 1/2 for rods with small R and Fz ) 3/2 for rods with large R. This result is relevant to the production of linearly polarized light using CdS QRs, which is of interest for a variety of applications.13 Linearly polarized light is associated to hole states in which the optically active component (the one with mz ) 0) corresponds to the C band, for its Bloch orbital symmetry is |Z〉. As can be seen in eq 1, this requirement is met by states with Fz ) 1/2. In CdS QRs, |Fz ) 1/2〉 ground states are only feasible if R is small enough. A closer inspection into the composition of the |Fz ) 1/2〉 ground state for the QR with R ) 15 Å (Figure 3b) reveals that for short QRs the |Cv〉 component is negligible, so that the ground state is optically inactive. At L ∼ 45 Å, however, an anticrossing between the ground and first excited states with Fz ) 1/2 leads to a sharp increase of the |Cv〉 component. At this point the CdS QR ground state becomes suitable for linearly polarized light emission. The rise of the |Cv〉 component of the ground state with increasing length can be understood as follows. As the longitudinal confinement is weakened, the coupling of the C band with A and B bands is reduced. In this context, anisotropic confinement clearly favors C-type hole states because only radial confinement matters, and the radial mass (m⊥) of C-type holes is heavier than that of A-type and B-type holes (Table 1). For nanocrystals where the radial confinement is also weak (e.g., R ) 60 Å example in Figure 3), the situation is different because quantum confinement effects can no longer compete against ∆c and ∆so. As a result, A-type holes are favored and the ground state is always |Fz ) 3/2〉, with a dominant |Av〉 component (Figure 3c). The results reported so far allow us to draw some general observations about the spin purity of the hole ground state in CdS nanocrystals. Figure 2 and Figure 3 reveal that the groundstate spin purity is over 90% for most CdS geometries (i.e., the spin down components-dashed lines in the figures-rarely exceed a weight of 0.1). Only in QRs with small R and L, where the ground state is of P-like symmetry, this value reduces to about 75%. Maximum purities (over 95%) can be achieved in small spherical QDs and long QRs with small radius. Note that the latter geometry is precisely the optimal regime for linearly polarized light emission. CdSe Nanocrystals. In this section we study CdSe nanocrystals. Despite the large spin-orbit constant of this material (∆so ) 138 meV), which pushes the B band far in energy (Figure 1b), its influence cannot be generally neglected.18 Thus we keep using the six-band Hamiltonian. First, we study the lowest energy states in spherical QDs with increasing radius, shown in Figure 4. As opposed to the CdS case, no ground state crossover is observed for the entire range of R under study. The ground state is always |Fz ) 3/2〉 (S-like symmetry). What is more, the composition of the ground state is almost exclusively given by |Av〉. This is because band mixing effects are much weaker than those for CdS. In particular, the coupling of A with B and C bands is severely weakend by the strong spin-orbit splitting. In trying to explain the dark exciton ground state observed in CdSe QDs,27 some authors have proposed a similar crossover to that of CdS QDs (Figure 2a), which would lead to P-like symmetry states for small CdSe crystals.8,9 Indeed, this can be reproduced by the six-band k · p Hamiltonian for wurtzite lattice if instead of the set of parameters we use here one employs another set, as that in ref 9, enhancing band mixing effects.

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Figure 4. Same as Figure 2 but for CdSe QDs.

Note however that the dark exciton may also be originated by the electron-hole exchange interaction,27 i.e., by considering spin-forbidden optical transitions rather than orbital-forbidden ones. We have tested that the set of parameters employed in ref 9 give results somewhat closer to those of CdS. As a matter of fact, they predict no crossover of the hole ground state for QRs with increasing aspect ratio,21 which is contradiction to atomistic calculations for CdSe.13 Instead, the set of parameters employed here does predict the crossover, as shown in Figure 5a, where we illustrate the energy of the lowest hole states for QRs with R ) 15 Å. The different behavior of CdSe QRs as compared to CdS ones (compare Figure 5a and Figure 3a) can be ascribed to the weaker band mixing. Indeed, the behavior in CdSe can be interpreted disregarding band mixing effects. Thus, for nearly spherical CdSe QRs one expects a ground state with dominant A-type component due to the influence of crystal field and spin-orbit terms. The ground-state symmetry is Fz ) 3/2 because its |Av〉 component has the lowest possible angular momentum, mz ) 0 (see eq 1). With increasing length, however, C-type holes become increasingly stable due to their heavy radial mass (Table 1). This in turn favors |Fz ) 1/2〉, which has a |Cv〉 component with mz ) 0. Note that these reasonings are consistent with the composition of |Fz ) 1/2〉 and |Fz ) 3/2〉 states, which are plotted in parts b and c of Figure 5. If the QR radius is larger (see the R ) 60 Å case in the insets of Figure 5), quantum confinement can no longer compete against the energy stabilization provided by ∆c and ∆so. As a result, the ground state is always |Fz ) 3/2〉 with a high-purity |Av〉 composition.

Planelles et al.

Figure 5. (a) Energy of the lowest hole state with Fz ) 1/2 and Fz ) 3/2 in CdSe QRs of different length and R ) 15 Å. (b) and (c) Composition of the Fz ) 1/2 and Fz ) 3/2 states. Insets: same as the main panel but for R ) 40 Å.

Figure 6. Energy spectrum of (a) CdSe QDs, (b) CdSe QR with R ) 1.5 nm, and ((b) inset) CdSe QR with R ) 4 nm. The spectra are calculated with a quasi-cubic four-band k · p Hamiltonian. The reference energy is the top of the valence band.

Hole Band Mixing

J. Phys. Chem. C, Vol. 114, No. 18, 2010 8341 ratio. As a matter of fact, the crossovers do not take place at all if the QR radius is large enough (see insets), just like for CdS QRs (Figure 3). This contradicts the results of ref 15, which claimed that the crossover occurred for constant aspect ratio alone, so that it should always appear provided the QR is long enough. The discrepancy arises from their use of a purely cubic Hamiltonian, which applies to InAs QRs but cannot be extrapolated to CdSe. In cubic lattices, the eigenvalues of the Hamiltonian for the same QR but at two different length scales can be related to each other,15 but this is no longer possible in hexagonal lattices due to the intrinsic anisotropy. Note that a quasi-cubic description, including the effective crystal field splitting, already captures the correct behavior (Figure 6 and Figure 7). Conclusions

Figure 7. Same as Figure 6 but calculated with a single-band Hamiltonian for decoupled heavy and light holes.

Regarding the spin purity of hole states in CdSe nanocrystals, Figure 4 and Figure 5 reveal that it is generally larger than that of CdS structures (>95%). The exceptions are long QRs with small radius, where the ground state is |Fz ) 1/2〉. In this case, the spin purity reduces to about 70%. The high spin purity of CdSe may seem surprising for a material with such a strong spin-orbit interaction. The reason is that the spin-orbit interaction couples spin up and down components of B and C bands only. For the A band, the spin admixture is indirect, through mixing with B and C. Since the ground state of CdSe nanocrystals is often a nearly decoupled A-band, the spin purity is high. Next, we compare the results for CdSe nanocrystals with those obtained upon inclusion of usual simplifications. First, we employ the quasi-cubic approximation, i.e., a zinc blende Hamiltonian where hexagonal lattice effects are included via an effective crystal field splitting heavy and light holes bands (see eq 14 in ref 24). Second, we disregard the split-off band due to the large value of ∆so, thus reducing the Hamiltonian to four bands. The CdSe Luttinger parameters are taken from ref,28 and the effective crystal field splitting is set to ∆c ) 16.5 meV. The resulting energy spectrum for spherical QDs is represented in Figure 6a, while those for elongated QRs with R ) 1.5 nm and R ) 4 nm are represented in Figure 6b and its inset, respectively. One can see that the spectra are qualitatively consistent with those of the fully hexagonal Hamiltonian. The presence or absence of ground state crossovers are properly reproduced. Indeed, the Fz ) 3/2 (Fz ) 1/2) hole state in this description is a nearly pure heavy hole (light hole). It then turns out that a single-band description also gives a qualitatively correct description. This is shown in Figure 7, which is the same as Figure 6 but decoupling the hole bands in the Hamiltonian. Therefore, the single-band quasi-cubic approximation suffices to provide a qualitatively correct description of the hole ground state crossovers and symmetry in CdSe nanocrystals. At this point it is worth noting that the QR ground state crossover from |Fz ) 3/2〉 to |Fz ) 1/2〉, observed in Figure 5a, Figure 6b, and Figure 7b, does not occur at a constant aspect

We have investigated the hole ground state in wurtzite QDs and QRs made of CdS and CdSe. Significant differences appear between the two materials owing to the different strength of the valence band mixing, which is far more important in CdS. Thus, in spherical QDs made of CdS the ground state changes from S-like to P-like symmetry with decreasing size, which we have successfully interpreted from the interplay between band mixing (favoring P-like states) and quantum confinement (favoring S-like states). No such crossing is however observed in CdSe QDs. The ground state behavior in QRs is also different. As previously noted by other authors,13-15,21,22 in CdSe nanocrystals with increasing aspect ratio the hole ground state changes from one that emits circularly polarized light to one that emits linearly polarized light. We have shown that this change does not occur at a constant aspect ratio, which is due to the intrinsic anisotropy of the wurtzite crystal. Actually, the change is only possible for narrow QRs. In CdS QRs the hole ground state is also liable of emitting linearly polarized light, provided the rod is narrow enough. In view of the interest of hole spin states for magnetic and spintronic applications of nanocrystals, we have also analyzed the spin purity as a function of the geometry and composition. We have found the highest spin purity in CdSe QDs (>95%). In narrow CdSe QRs, however, the spin admixture becomes significant and CdS QRs are preferred (>90% spin purity). We have finally shown that, owing to the weak band coupling, the ground state symmetry and crossovers of wurtzite CdSe QDs and QRs are qualitatively captured by a quasi-cubic approximation including in an effective way the hexagonal component of the crystal field. In this approximation the states are nearly decoupled heavy holes and light holes, so that the usual fourband k · p description8,14,15 provides little advantadge as compared to simpler one-band models.22,29 Acknowledgment. We thank B. Lassen for testing his wurtzite Hamiltonian code against ours. Support from MCINN project CTQ2008-03344, UJI-Bancaixa project P1-1A2009-03 and the Ramon y Cajal program (JIC) is acknowledged. References and Notes (1) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. ReV. 2005, 105, 1025. (2) Peng, X.; Manna, L.; Yang, W.; Wickham, J.; Scher, E.; Kadavanich, A.; Alivisatos, A. P. Nature 2000, 404, 59. (3) Manna, L.; Scher, E. C.; Alivisatos, A. P. J. Am. Chem. Soc. 2000, 122, 12700. (4) Shieh, F.; Saunders, A. E.; Korgel, B. A. J. Phys. Chem. B 2005, 109, 8538. (5) Norris, D. J.; Efros, A. L.; Erwin, S. C. Science 2008, 319, 776.

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(6) Wang, X.; Ren, X.; Kahen, K.; Hahn, M. A.; Rajeswaran, M.; Maccagnano-Zacher, S.; Silcox, J.; Cragg, G. E.; Efros, A. L.; Krauss, T. D. Nature 2009, 459, 686. (7) Naha´lkova, P.; Sprinzl, D.; Maly´, P.; Nemec, P.; Gladilin, V. N.; Devreese, J. T. Phys. ReV. B 2007, 75, 113306. (8) Efros, Al. L.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D. J.; Bawendi, M. Phys. ReV. B 1996, 54, 4843. (9) Xia, J. B.; Li, J. Phys. ReV. B 1999, 60, 11540. (10) Kuno, M.; Lee, J. K.; Dabbousi, B. O.; Mikulec, F. V.; Bawendi, M. G. J. Chem. Phys. 1997, 106, 9869. (11) Li, J.; Xia, J. B. Phys. ReV. B 2000, 62, 12613. (12) Yang, B.; Schneeloch, J. E.; Pan, Z.; Furis, M.; Achermann, M. Phys. ReV. B 2010, 81, 073401. (13) Hu, J.; Li, L. S.; Yang, W.; Manna, L.; Wang, L. W.; Alivisatos, A. P. Science 2001, 292, 2060. (14) Katz, D.; Wizansky, T.; Millo, O.; Rothenberg, E.; Mokari, T.; Banin, U. Phys. ReV. Lett. 2002, 89, 086801. (15) Lew Yan Voon, L. C.; Melnik, R.; Lassen, B.; Willatzen, M. Nano Lett. 2004, 4, 289. (16) Zhao, Q.; Graf, P. A.; Jones, W. B.; Franceschetti, A.; Li, J.; Wang, L. W.; Kwiseon, K. Nano Lett. 2007, 7, 3274. (17) Shabaev, A.; Efros, Al. L. Nano Lett. 2004, 4, 1821.

Planelles et al. (18) Richard, T.; Lefebvre, P.; Mathieu, H.; Allegre, J. Phys. ReV. B 1996, 53, 7287. (19) Fonoberov, V. A.; Pokatilov, E. P.; Balandin, A. A. Phys. ReV. B 2002, 66, 085310. (20) Yu, Z.; Li, J.; O’Connor, D. B.; Wang, L. W.; Barbara, P. F. J. Phys. Chem. B 2003, 107, 5670. (21) Li, X. Z.; Xia, J. B. Phys. ReV. B 2002, 66, 115316. (22) Rajadell, F.; Climente, J. I.; Planelles, J.; Bertoni, A. J. Phys. Chem. C 2009, 113, 11268. (23) Zhang, H.; Delikanli, S.; Qin, Y.; He, S.; Swihart, M.; Zeng, H. Nano Res. 2008, 1, 314, and references therein. (24) Chuang, S. L.; Chang, C. S. Phys. ReV. B 1996, 54, 2491. (25) Lew Yan Voon, L. C.; Galeriu, C.; Lassen, B.; Willatzen, M.; Melnik, R. Appl. Phys. Lett. 2005, 87, 041906 (See also arxiv:cond-mat/ 0509621v1). (26) Jeon, J. B.; Sirenko, Y. M.; Kim, K. W.; Littlejohn, M. A.; Stroscio, M. A. Solid State Commun. 1996, 99, 423. (27) Nirmal, M.; Norris, D. J.; Kuno, M.; Bawendi, M. G. Phys. ReV. Lett. 1995, 75, 3728. (28) Laheld, U. E. H.; Einevoll, G. T. Phys. ReV. B 1997, 55, 5184. (29) Climente, J. I.; Planelles, J.; Rajadell, F. Phys. ReV. B 2009, 80, 205312.

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