J. Phys. Chem. C 2010, 114, 3743–3747
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Impact Ionization and Auger Recombination Rates in Semiconductor Quantum Dots Y. Fu,†,‡ Y.-H. Zhou,† Haibin Su,† F. Y. C. Boey,† and H. Ågren†,‡ DiVision of Materials Science, Nanyang Technological UniVersity, Singapore and Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden ReceiVed: August 26, 2009; ReVised Manuscript ReceiVed: December 13, 2009
Impact ionization and Auger recombination in nanoscale spherical quantum dots (QDs) have been studied theoretically. It is shown that due to the strong quantum confinement of both electrons in the conduction band and holes in the valence band, impact ionization and Auger recombination energies in these QDs can be on the order of a few millielectronvolts when various selection rules are fulfilled, which are much higher than spontaneous radiative emission energies. This explains the experimentally reported high occurrence rates of the multiple exciton generation (MEG) effect in QDs. However, due to quantum confinement, the energy states are discrete in QDs, especially for low-energy states where the densities of states are low. This implies that only a limited number of high-energy electron states can interact with (i.e., impact ionize) low-energy hole states in QDs having certain values of radii due to the energy conservation requirement. This explains the vastly scattered experimental data and difficulties in utilizing the MEG effect in practice. I. Introduction Theoretically, the maximum achievable efficiency of lightmatter interaction is limited by the principle of detailed balance, i.e., the Shockely-Queissar limit.1 One scheme for exceeding the Shockely-Queissar limit is the so-called multiple exciton generation (MEG), which, in theory, can maximize utilization of the energy from solar photons by generating multiple charge carrier pairs from the absorption of one photon. Nozik proposed that impact ionization might be enhanced in semiconductor quantum dots (QDs) to increase the efficiency of solar cells up to about 66%.2 This was later verified experimentally by Schaller and Klimov.3 Impact ionization was reported to produce MEG per photon in a particular QD that results in a very high quantum yield (up to 300% when the photon energy reaches 4 times the QD band gap) in QD solar cells.4 Multiple carrier extraction (>100%) was observed at photon energies greater than 2.8 times the PbSe QD band gap with about 210% measured at 4.4 times the band gap.5 In a recent communication in Nano Letters, Trinh et al.6 showed compelling support for carrier multiplication in PbSe QDs while at the same time the obtained MEG efficiency was very close to that in bulk material. Several sophisticated approaches such as the pseudopotential method,7 sp3d5s* tight binding,8 and the atomistic semiempirical pseudopotential method9 were applied to study MEG effects in QDs. In particular, the atomistic pseudopotential calculations have shown that a conventional impact ionization mechanism can explain the experimentally observed MEG effect.7 However, the diameters of QDs in these studies were less than 3 nm. Therefore, we concentrate in this work on investigating impact ionization and Auger recombination in QDs with larger diameters as studied in experiments for realistic applications, such as CdSe QDs with a diameter larger than 6 nm and luminescence wavelengths longer than 600 nm for MEG by UV radiation from the sun. Solid-state-based quantum mechanical description of impact ionization and Auger recombination will be presented * To whom correspondence should be addressed. E-mail:
[email protected]. † Nanyang Technological University. ‡ Royal Institute of Technology.
in section II followed by numerical analysis, discussions, and conclusions in section III. A brief summary will be given in section IV. II. Theoretical Considerations A. Electron and Hole in a Single QD. We consider first electrons (re) and holes (rh) in spherical nanoscale semiconductor quantum dots (QDs) in vacuum. In order to describe the impact ionization and Auger recombination processes, we adopt the following single-particle pictures
[ [
-
p2∇2e 2m/e
p ∇2h 2m/h
] ]
+ Vc(re) + Vi(re) ψi(re) ) Eiψi(re)
2
(1)
+ Vv(rh) + Vj(rh) φj(rh) ) Ejφj(rh)
where m*e and m*h are the effective masses of electrons and holes, Vc(re) and Vv(rh) are confinement potentials for the electrons and holes, and Vi(re) is the Coulomb potential experienced by electrons occupying ψi
∇2Vi(r) ) -
e ε
[∑
m*i
fm|ψm(r)|2 -
∑ fj|φj(r)|2]
(2)
j
where fm is the occupation probability of ψm. Other parameters such as Vj(rh) and fj are similarly defined. An exciton, composed of en electron in the conduction-band (CB) state ψi and a hole in the valence-band (VB) state φj, is thus denoted by its envelope wave function ψi(re)φj(rh) and its energy Ei + Ej. To estimate the Coulomb potential of eq 2, we make the following analysis. Assume that the electron distributes uniformly over the QD volume so that its Coulomb potential is analytically expressed as
10.1021/jp9082486 2010 American Chemical Society Published on Web 02/16/2010
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{(
Fu et al.
2 , r>a e r 2 8πε 1 3 - r , r e a a a2
)
(3)
where a is the radius of the QD. If also the hole is assumed to distribute uniformly in the same QD volume, the Coulomb interaction energy between this electron-hole pair is 3e2/10πεa, which is about 29 meV when a ) 5 nm and ε ) 12 (common semiconductors). It can be deduced similarly that the Coulomb interaction between one electron (hole) and an exciton is much less. On the other hand, the electron affinities of many colloidal QD materials such as CdS, CdSe, CdTe, ZnS, and ZnO are on the order of 4-5 eV.10 For spherical QDs under investigations, we thus approximate that the total potential energy for the conduction-band electron, i.e., the confinement potential Vc(re), which is spherically symmetric since the QD itself is spherical, plus the Coulomb potential Vi, which is not necessary to be spherically symmetric but is very small as compared with Vc(re), is still spherically symmetric so that the wave function φi(re) of eq 1 can be expressed by a radial component Rnl(re) and a spherical harmonics Ylm(θe, φe). A similar approximation is made for valence-band hole states. We can then utilize the addition theorem for spherical harmonics, and numerical integrations over r1 and r2 become integrations over r1 and r2 in calculating the Coulomb interaction between two charges, denoted by r1 and r2, and the impact ionization interaction and Auger recombination energy (see below). More specifically, the wave function of the conduction-band electron is expressed by ψnlm, e(r, θ, φ) ) Rnl, e(r)Ylm, e(θ, φ), where Ylm,e(θ, φ) is the spherical harmonics. The radial component Rnl,e(r) ) unl,e(r)/r is determined by 2
d unl,e(r) dr2
+
2m/e 2 p
[
En - Vc(r) - Vnl,e(r) -
]
l(l + 1)p2 unl,e(r) ) 0 2m/e r2
(4)
This looks very much like a one-dimensional Schro¨dinger equation and is easy to solve. The one-dimensional Coulomb energy Vnl,e(r) is then given by
∇2Vnl,e(r) ) -
e ε
[∑
nl*nl
fnl,e|Rnl,e(r)|2 -
]
∑ fn l ,h|Rn l ,h(r)|2
nl
(5)
Note that since the amplitudes of spherical harmonics with high values of l and m depend less on θ, the errors induced by neglect of the θ dependence in the above equation will be small for high-energy states with large l and m, On the other hand, highenergy states are directly relevant to impact ionization and Auger recombination processes (see more discussions below); we can therefore expect that the approximation will not affect the numerical results for the impact ionization and Auger recombination processes. Note, however, that the Coulomb interaction energies (exciton bindings) will be accounted for in the singleparticle energy levels. Possible numerical errors due to the spherical symmetry approximation will cancel out in the impact ionization and Auger interactions; see eq 8 below. B. Impact Ionization and Auger Recombination. We now study the impact ionization and its reverse process the Auger
Figure 1. Schematic depiction of impact ionization of a high-energy electron-hole pair. (1) Electron-hole pair (e1 and h1) is generated, e.g., by a photon. (2) e2 gets excited from a valence-band state to a conduction-band state via Coulomb interaction with e2, leaving hole h2 behind. CB/VB ) conduction/valence band. The reverse process is referred to be Auger recombination.
recombination in nanoscale QDs. As shown in Figure 1, a highly photoexcited electron and hole pair can evolve into a multipleexciton state through impact ionization. The carrier-carrier interaction is expressed by the Coulomb potential in the form of
V)
e2 4πε|r1 - r2 |
(6)
to account for the two-body interaction of two electrons from an initial state φj(r1)ψi(r2)exp[-i(Ej + Ei)t/p] to a final state
|
|
1 ψn(r1)ψm(r1) exp[-i(En + Em)t/p] √2 ψn(r2)ψm(r2)
(7)
Notice that the two electrons in the final state are not distinguishable, so that we use a Slater determinant. Other ionization pathways exist, such as one electron occupying a low-energy VB state falling into h1 and the released energy excites another electron from the VB to the CB. Auger recombination can be expressed similarly. By the scattering theory and generalized Golden rule11 and denoting 〈φjψi|Tˆ(t)|φjψi〉 ≈ e-wjit/2 as the temporal development Tˆ(t) of state ji, it is easy to obtain
wji )
∑
2π |〈φ ψ |V|ψnψm〉|2δ(Ej + Ei - En - Em) p nm*ji j i
(8) where Γji ) pwji/2 is the relaxation energy and 1/wji the decaying time. In numerical calculations the δ functions in the above equation are replaced by Γji/[Γ2ji+ (Ej + Ei - En - Em)2] and Γji is to be calculated by the above equation in a self-consistent way that the left and right sides of eq 8 are equal after knowing the interaction values of 〈φjψi|V|ψnψm〉|2. We can use eq 3 to estimate the impact ionization relaxation energy. We then consider the best configuration for eq 6 that the four wave functions involved in the impact ionization are all uniformly distributed within the QD volume. The impact ionization energy will be 28.8 meV for a ) 5 nm and ε ) 12 when we neglect the energy conservation requirement, i.e., we neglect the δ function in eq 8. This is very large compared with the value in bulk because of the quantum confinement (electrons and holes are now confined within a spherical volume with a radius of a). Such an interaction energy is much larger compared with the light-matter interaction, which is normally less than
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0.1 meV in similar QDs.12 Large impact ionization and Auger recombination are thus expected in colloidal QDs. III. Numerical Analysis and Discussions Numerical calculation of Coulomb interaction eq 6 is not trivial. It was simplified in ref 8 by using a screened Coulomb potential involving one-electron wave functions, which was derived for bulk semiconductor materials.13 To calculate the impact ionization interaction from an initial state of Rl1(r1)Yl1m1(θ1, φ1)Rl2(r2)Yl2m2(θ2, φ2) to a final state Rl3(r1)Yl3m3(θ1, φ1)Rl4(r2)Yl4m4(θ2, φ2) (the first term one in eq 7), we notice
1 ) 4π|r1 - r2 | ∞
l
∑ ∑
1 2l + m)-l
l)0
r
(9)
where r< ) min{|r1|,|r2|} and r> ) max{|r1|,|r2|}, so that the impact ionization energy consists of
rl+1
Rl1(r1)Rl2(r2)Rl3(r1)Rl4(r2) / (θ2, φ2) × Yl/1m1(θ1, φ1)Yl/2m2(θ2, φ2)Ylm × Ylm(θ1, φ1)Yl3m3(θ1, φ1)Yl4m4(θ2, φ2)
(10) for which we utilize the addition theorem for spherical harmonics14 l1+l2
Yl1m1Yl2m2 )
∑
l)|l1-l2|
(2l1 + 1)(2l2 + 1) × 4π(2l + 1)
C(l0|l10;l20)C(lm1 + m2 |l1m1 ;l2m2)Ylm1+m2
(11)
where C(lm1 + m2|l1m1; l2m2) is the CG coefficient. A more detailed analysis shows a few selection rules for l’s and m’s such as m4 - m2 ) m1 - m3. However, these selection rules can be easily fulfilled in nanoscale QDs because of the large number of available states confined in the QDs (see further discussion below). The most important qualitative selection rules refer to the radial functions
r
1
2
3
[
∫0a Rl (r1)Rl (r1) ∫0r 1
3
+
∫r
a
1
)
4
rl1
rl+1 2
1
rl2 rl+1 1
Rl2(r2)Rl4(r2)r22 dr2
]
Rl2(r2)Rl4(r2)r22 dr2 r21 dr1
(12)
which shows that a direct spatial overlap between Rl2(r2) (VB hole state) and Rl4(r4) (CB electron sate) will result in a large impact ionization. Impact ionization in type-II QDs is thus negligible since the electron-hole wave function overlap is small. Furthermore, to ensure energy conservation, Rl1(r) is
Figure 2. (a) Conduction-band (CB) electron states and (b) valenceband (VB) hole states confined in a spherical CdSe QD with a radius of 4 nm as a function of the angular momentum quantum number l .
normally a high-energy CB state while both Rl3(r) and Rl4(r) are low-energy CB states. Impact ionization in many core-shellstructured QDs (e.g.,15) could be small since the high-energy wave functions are much more extended (extended into shells) than the ground-state wave function (deeply confined in the core region). We now consider a spherical CdSe QD in vacuum with a radius of a. The energy band gap of bulk CdSe material is 1.74 eV (room temperature), and the exciton Bohr radius is 4.9 nm; the quantum confinement energies for the conduction-band electron are 4.95 and 2.5 eV for the valence-band holes, and the electron and hole effective masses are m*c ) 0.14m0 and mV ) 0.46m0, respectively, where m0 is the electron rest mass.10 In numerical calculations we also include a shell of vacuum with a thickness of 20 nm to account for penetration of wave functions of high-energy states from the QD volume to the vacuum (the results are compared with the ones when a shell of a 10 nm thick vacuum shell is included and no significant differences are observed). We include all the confined energy states in the QD (i.e., energy levels below the vacuum state) of all possible combinations of CB electron states and VB hole states that form the initial state of the impact ionization and then all possible combinations of the two final CB electron states. Each single-particle state is denoted by its energy, R(r), l, and m. Spherical harmonics (i.e., l and m) is calculated using the addition theorem, while the radial integration is to be performed numerically. Measures are properly taken in order to guarantee necessary numerical precision. For the exact analytical model of eq 3, our numerical result is 28.7 meV when a ) 5 nm, while eq 3 results in 28.8 meV analytically. Figure 2 shows the CB electron states and VB hole states confined in a spherical CdSe QD with a radius of 4 nm as a function of the angular momentum quantum number l. Note that states with l * 0 are (2l + 1)-fold degenerate. We pick one of the CB states from Figure 2a and one VB state from Figure 2b to calculate the total impact ionization energy to all possible combinations of the two final CB states in Figure 2a, which is shown in Figure 3a. Figure 3a conforms with what can be expected intuitively that the initial CB state has to be high while the VB state low in order to fulfill the energy conservation requirement. Furthermore, as mentioned before, high-energy states can be highly degenerate because of large l, so Γ can be also high. For the case of Figure 3 where a ) 4 nm, we observe a maximal Γ of about 7 meV. We further observe tens of Γ over 4 meV, while majorities are about 1 meV. These are very high as compared with the light-matter interaction of only 0.065 meV in a similar CdSe QD;12 thus, we can be very optimistic about MEG processes in colloidal QDs, as has been much reported and also anticipated for significant solar cell applications (see Introduc-
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Figure 3. (a) Impact ionization energy between initial CB state(s) and initial VB state(s). (Inset) Band structure of the CdSe QD in vacuum. (b) Auger recombination. The QD radius a ) 4 nm.
Figure 5. Auger recombination rate vs one of the two initial CB states as a function of the QD radius a.
Figure 4. Impact ionization rate vs initial CB states as a function of the QD radius a.
tion). This is more clearly reflected in Figure 4 by the relationship between the impact ionization and initial CB state(s). For the CdSe QDs under investigation, the MEG effect can be expected when the excitation radiation energy exceeds a threshold of about 2Eg (note that Eg is the energy of the ground exciton state, i.e., nanocrystal energy gap in ref 16) when the QD radius a ) 4.8 nm, while the threshold energy will be 2.8Eg when a ) 4.0 nm and 3.5Eg for a ) 3.0 nm. Note however that the relationship between the threshold energy of MEG and the QD size is not linear. It is small when the QD size is around 4.2 and 3.8 nm; it is rather large at 3.6 and 4.4 nm in Figure 4. Furthermore, CdSe QDs with r ) 4.8 nm actually reach the commonly referred to weak confinement limit, i.e., a ≈ aBr, where aBr ) 4.9 nm is the exciton Bohr radius in CdSe bulk material, whereas it is not proper to discuss the impact ionization in bulk CdSe by using the data of r ) 4.8 nm in Figure 4 since high-energy states that are relevant for the impact ionization are still strongly confined in our QDs. Most importantly, however, is the fact that the number of the nonzero Γ (g0.05 meV) in Figures 3 and 4 is very limited, only 354 among the 347 CB and 758 VB states listed in Figure 2. This imposes a serious restriction to the eventual occurrence of the MEG effect. When the high-energy initial CB and VB states are generated directly, e.g., resonantly photoexcited by an external optical excitation source, we can expect a very high rate of MEG occurrence because of the large impact ionization energy shown in Figure 4. However, if the initial CB and VB
states listed in Figures 3 and 4 become occupied via other energy relaxation processes including electron-phonon interactions from other excited states, the electron-phonon interaction, known to be the major energy relaxation processes in semiconductors whose relaxation energies are also in the range of a few millielectronvolts, will simply overrun the impact ionization. Furthermore, the phonon density of states can be very high as well as continuous in a large phonon energy range which can easily fulfill the energy conservation requirement for the electron-phonon interactions.12 We can thus envisage that unless two discrete CB and VB states (as listed in Figures 3 and 4) can be resonantly generated simultaneously (e.g., become photoexcited by an external optical source), the occurrence rate of the MEG effect will be low. We see this as a possible reason for the vastly scattered experimental data on the MEG occurrence rates and on quantum yields in various QDs. One can notice here the exceptional case of a ) 3.2 nm that there is only a single CB state that can result in significant impact ionization. This is surely due to the ideal assumption of a single QD, whereas the radii of QD assemblies are widely distributed. The Auger recombination (reverse processes of the impact ionizations) shown in Figure 3b can be similarly analyzed. Similar to the impact ionization in Figure 4, Figure 5 shows the relationship between the Auger recombination and one of the two initial CB states. Note that the energy range of the initial CB states in the Auger recombination processes is much wider than the impact ionization, especially for small QDs. This is due to the large density of states at high energy so that there are more available final CB states for two initial CB states to interact via the Auger recombination process. Figures 4 and 5 show that both the impact ionization and the Auger recombination rates decrease in general following the increase of the QD size, as can be theoretically expected. This also agrees with the experimental report about the Auger recombination in ref 17. However, the detail change of rates is not monotonic for a certain region of QDs in size. In Figure 4 we observed small rates when a ) 4.2 and 3.8 nm and large rates for 3.6 and 4.4 nm. Quantum confinement for low-energy states in our QDs is weak so that resonance conditions of wave
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functions become more important for large QDs, resulting in fluctuations in the rates of impact ionization and Auger recombination as functions of QD size in Figures 4 and 5. Furthermore, when a ) 4.8 nm, we are actually approaching the commonly referred to weak confinement limit. We might here expect weak quantum confinement effects, which is only true for low-energy CB and VB states (thus low-energy exciton states). High-energy states are still strongly confined, so the quantum confinement effect contributes significantly to the large impact ionization and Auger recombination rates in nanoscale QDs. A direct comparison between the impact ionization and Auger recombination spectra indicates that the experimental observation of the MEG effect can be difficult if the resulting two electrons from the impact ionization cannot be extracted before the Auger recombination occurs. We have thus far demonstrated that the yields of multiple electron-hole pairs in a single QD may vary due to the resonance conditions in the experiment. The conclusion can be directly applied to such a QD assembly where the radii of the QDs are very well controlled, whereas in real nanocrystal systems the sizes of QDs are much distributed depending on the QD materials as well as the growth methods. Solid-statebased III-V QDs are normally rather distributed ranging a few nanometers;18 see more explicitly Figure 2 in ref 19. The bandwidths of the fluorescence from chemically synthesized II-VI colloidal QDs are generally very narrow, indicating quite uniform QD sizes within a few monolayers (approximately 1 nm).15,20 Note that the modification in the QD radius in Figures 4 and 5 corresponds to one monolayer, so that the resonance conditions for real nanocrystal systems will be significantly relaxed. For example, CdSe nanocrystals with radii of 3.2 nm were reported to show a significant carrier multiplication effect,16 while only a single CB state in the CdSe QD with a radius of 3.2 nm is found to have a nonzero impact ionization energy in Figure 4. Auger recombination rates on the order of 50 ps-1 were reported experimentally,17,21 whereas Figure 5 shows similar rates related to the lowest energy states. Another important factor is the occupation of the initial two excitons. Our calculation shows that the Auger recombination can be very fast when the two excitons occupy the right states (resonance conditions) at the same time. The requirement of “simultaneous occupation of the two exciton states” is difficult in real systems since the occupation of different exciton states depends on many factors such as electron-photon and electron-phonon interactions. Therefore, the experimentally observed rate can be slow since the Auger recombination depends on the occupations of the exciton states (they are assumed to be 1 in eq 8). We can further envisage that this is the most possible reason for the fact that the impact ionization process was experimentally shown to be faster, while the comparison between Figures 4 and 5 indicates a faster Auger recombination process.
the MEG effect for efficient QD solar cell applications. It was shown that due to the strong quantum confinement of both electrons in the conduction band and holes in the valence band, impact ionization and Auger recombination energies in QDs can be on the order of a few millielectronvolts when various selection rules are fulfilled, which are much higher than spontaneous radiative emission energies. This results in a large occurrence rate of the multiple exciton generation (MEG) effect in QDs, as extensively reported experimentally for potential solar cell applications. However, due to quantum confinement, the energy states are discrete in QDs; in particular, for low-energy states where the densities of states are low, impact ionization only occurs in a limited number of high-energy electron states in QDs having certain values of radii. This explains the vastly scattered experimental data and difficulties in applying MEG effects in practice.
IV. Summary We theoretically studied the impact ionization and Auger recombination effects in QDs with a large range of sizes, which have been investigated experimentally, by applying solid-statebased quantum theory, thus finding guidelines for understanding
Acknowledgment. Computing resources were provided by the Swedish National Infrastructure for Computing (SNIC 00109-52). Work at the Royal Institute of Technology was supported by the Swedish Energy Agency (project number 32076-1). Work at NTU was supported in part by a MOE AcRF Tier-1 grant (grant no. M52070060). References and Notes (1) Shockley, W.; Queisser, H. A. J. Appl. Phys. 1961, 32, 510. (2) Nozik, A. J. Physica E 2002, 14, 115–20. (3) Schaller, R. D.; Klimov, V. I. Phys. ReV. Lett. 2004, 92 (4), 186601. (4) Hanna, M.; Ellingson, R. J.; Beard, M.; Yu, P.; Nozik, A. J. 2004 DOE Solar Energy Technologies Program ReView Meeting, Denver, CO, Oct 25-28, 2004. (5) Kim, S. J.; Kim, W. J.; Sahoo, Y.; Cartwright, A. N.; Prasad, P. N. Appl. Phys. Lett. 2008, 92 (3), 31107. (6) Trinh, M. T.; Houtepen, A. J.; Schins, J. M.; Hanrath, T.; Piris, J.; Knulst, W.; Goossens, A. P. L. M.; Siebbeles, L. D. A. Nano Lett. 2008, 8, 1713–8. (7) Franceschetti, A.; An, J. M.; Zunger, A. Nano Lett. 2006, 6, 2191– 5. (8) Allan, G.; Delerue, C. Phys. ReV. B 2008, 77 (10), 125340. (9) Rabani, E.; Baer, R. Nano Lett. 2008, 8, 4488–92. (10) In Data in Science and Technology: Semiconductors other than Group IV Elements and III-V Compounds; Madelung O., Ed.; Springer: Boston, 1992. (11) Landau L. D.; Lifshitz, E. M. Quantum Mechanics, 2nd ed.; Pergamon Press: Oxford, 1965; p 129. (12) Fu, Y.; Ågren, H.; Kowalewski, J. M.; Brismar, H.; Wu, J.; Yue, Y.; Dai, N.; Thyle´n, L. EuroPhys. Lett. 2009, 86 (6), 37003. (13) Landsberg, P. T. Recombination in Semiconductors; Cambridge University Press: London, 1991. (14) Cohen-Tannoudji, C.; Diu, B.; Laloe, F. Quantum Mechanics; Wiley-Interscience: New York, 1991; Vol. 2; p 1046. (15) Fu, Y.; Han, T.-T.; Ågren, H.; Lin, L.; Chen, P.; Liu, Y.; Tang, G.-Q.; Wu, J.; Yue, Y.; Dai, N. Appl. Phys. Lett. 2007, 90 (3), 173102. (16) Schaller, R. D.; Agranovich, V. M.; Klimov, V. I. Nat. Phys. 2005, 1, 189–94. (17) Klimov, V. I.; Mikhailovsky, A. A.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Science 2000, 287, 1011–3. (18) Ho¨glund, L.; Petrini, E.; Asplund, C.; Malm, H.; Andersson, J. Y.; Holtz, P. O. Appl. Surf. Sci. 2006, 252, 5525–9. (19) Fu, Y.; Ferdos, F.; Sadeghi, M.; Wang, S. M.; Larsson, A. J. Appl. Phys. 2002, 92, 3089–92. (20) Li, J. J.; Wang, Y. A.; Guo, W.; Keay, J. C.; Mishima, T. D.; Johnson, M. B.; Peng, X. J. Am. Chem. Soc. 2003, 125, 12567–75. (21) Kim, J. H.; Kyhm, K.; Kim, S. M.; Yang, H.-S. J. Appl. Phys. 2007, 101 (4), 103108.
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