LETTER pubs.acs.org/NanoLett
Enhanced Multiple Exciton Generation in Quasi-One-Dimensional Semiconductors Paul D. Cunningham,*,† Janice E. Boercker,† Edward E. Foos,† Matthew P. Lumb,†,‡ Anthony R. Smith,† Joseph G. Tischler,† and Joseph S. Melinger† † ‡
U.S. Naval Research Laboratory, 4555 Overlook Avenue SW, Washington, D.C. 20375, United States School of Engineering and Applied Science, The George Washington University, 725 23rd Street NW, Washington, D.C. 20052, United States
bS Supporting Information ABSTRACT: The creation of a single electronhole pair (i.e., exciton) per incident photon is a fundamental limitation for current optoelectronic devices including photodetectors and photovoltaic cells. The prospect of multiple exciton generation per incident photon is of great interest to fundamental science and the improvement of solar cell technology. Multiple exciton generation is known to occur in semiconductor nanostructures with increased efficiency and reduced threshold energy compared to their bulk counterparts. Here we report a significant enhancement of multiple exciton generation in PbSe quasi-one-dimensional semiconductors (nanorods) over zero-dimensional nanostructures (nanocrystals), characterized by a 2-fold increase in efficiency and reduction of the threshold energy to (2.23 ( 0.03)Eg, which approaches the theoretical limit of 2Eg. Photovoltaic cells based on PbSe nanorods are capable of improved power conversion efficiencies, in particular when operated in conjunction with solar concentrators. KEYWORDS: Multiple exciton generation, carrier multiplication, nanorods, nanocrystals, photovoltaic
T
ypically, the absorption of a single photon by a semiconductor results in the creation of a single electronhole pair, or exciton. A high-energy photon creates a hot exciton with excess energy above the band edge. This excess energy is typically dissipated as heat through sequential phonon emission, i.e., lattice vibration, resulting in a single exciton at the band edge. Multiple exciton generation (MEG) occurs when the absorption of a single high-energy photon instead results in the creation of two or more excitons. In this case, the excess energy of the hot exciton is used to excite a second electron across the band gap. MEG is of interest for sensitive photodetectors,1 high-speed electronics, photoelectrolytic devices, lasers,2 and photovoltaic cells.3,4 In particular, MEG may allow for the efficient use of the excess energy given to excitons by high-energy photons in the solar spectrum, which could alleviate solar cell losses due to hot exciton relaxation. MEG has been reported to be more efficient in semiconductor nanocrystals than in the bulk due to a relaxation of momentum conservation, slowed carrier cooling, and enhanced Coulomb interaction.57 In small nanocrystals where the physical radius is on the order of or smaller than the exciton Bohr radius, quantum confinement leads to discrete excitonic energy levels. The larger energy spacing between levels can slow phonon-assisted relaxation processes through an effect known as the phonon bottleneck.8 Unlike a bulk material, where the size of the exciton is defined by the Bohr radius, the dimensions of nanocrystals determine the spatial extent of excitons.4 Such confined states show enhanced interparticle interaction9 from increased wave function overlap and reduced dielectric screening,10 as the electric fields associated with the electron and hole extend outside of the nanocrystal. These strong Coulomb interactions r 2011 American Chemical Society
increase the probability that a hot exciton can transfer its excess energy to excite a second exciton in a collision-like Coulomb mediated process, which competes favorably with other cooling channels.7,11,12 In addition to enhanced MEG, size-tunable optical properties and solution processability make nanocrystals desirable for photovoltaic applications.4,13 To that end, MEG has been investigated in CdSe,14,15 PbSe,5 PbS,16,17 PbTe,18 Si,19 InP20 and InAs nanocrystals.21,22 However, this rapidly evolving field of study is filled with controversy over how to properly compare MEG in bulk materials and nanocrystals,5,23 the magnitude of MEG quantum yields,24 and whether MEG occurs at all in certain materials.25,26 Pb chalcogenide nanocrystals have attracted much attention due to their large exciton Bohr radii in bulk, high degeneracy of the first excited state, and mirror-like symmetry of the conduction and valence bands.27,28 Though early reports showed large MEG yields in PbSe,29 these observations were overestimated by the effects of photoionization and trapping.30 Improved experimental practices have revealed that the quantum yields are more modest.6,31,32 The discovery of ultrafast charge transfer from nanocrystals demonstrates that multiple excitons can be extracted and utilized in devices.33 Recently, there have been reports of quantum yields larger than 100% in photodetectors1,34 and photovoltaic cells3 based on Pb chalcogenide nanocrystals. However, detailed balance calculations show that photovoltaic cells exploiting MEG in PbSe nanocrystals are theoretically capable of only small improvements over the ShockleyQueisser limit.5 Received: June 15, 2011 Revised: July 12, 2011 Published: July 18, 2011 3476
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Figure 1. Comparison of size, shape, and optical absorption in nanorods and nanocrystals. Transmission electron microscope images of PbSe (a) nanorods and (b) nanocrystals. (c) First excitonic absorption feature of the 4.4 nm in diameter by 16.1 nm in length PbSe nanorods, which has nearly the same center wavelength as (d) the first excitonic absorption feature of the 4.7 nm in diameter PbSe nanocrystals. The arrows denote the probe wavelengths used during transient absorption measurements.
The road to improving photovoltaic cells therefore involves identifying materials systems with lower MEG threshold energy (hνth/Eg) and higher MEG efficiency. While the optoelectronic properties of nanocrystalline semiconductors have been extensively examined, there have been few studies of quasi-one-dimensional nanorods.28,35 Unlike zerodimensional nanocrystals, in nanorods there is strong confinement in two dimensions due to the small radius, while the third dimension is only weakly confined along the length of the rod. In PbSe nanorods, the electronhole separation is expected to be approximately the radius of the nanorod, enhancing the oscillator strength of the ground state absorption and decreasing the singlet exciton lifetime.28 It has been suggested that increased Coulombic interaction in nanorods could increase the rate of Auger-like processes, including MEG.7,28 As confinement is mainly determined by the radius, but Auger recombination depends on the nanostructure volume, nanorods can also allow for reduction of Auger recombination of multiple excitons necessary for lasing.35 In this Letter, we report the first measurement demonstrating MEG is enhanced in quasi-one-dimensional semiconductors as compared to zero-dimensional semiconductors. We accomplished this by directly comparing MEG in PbSe nanorods and nanocrystals through transient absorption measurements of exciton dynamics. For a given relative photon energy (hν/Eg), we observed larger exciton quantum yields in nanorods than in nanocrystals. Pump wavelength dependent measurements revealed that the source of this observation is the reduction of the MEG threshold energy and a corresponding increase in the MEG efficiency. These results show that nanorods may be a more promising class of materials for thin film photovoltaic cells owing to their increased absorption cross sections and enhanced MEG.
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The presence of efficient MEG is particularly valuable to photovoltaic cells under solar concentration. Further, one-dimensional semiconductors could offer both improved charge transport and enhanced MEG when compared to zero-dimensional semiconductors. Oleic acid capped PbSe nanorods were synthesized using standard Schlenk line techniques under an inert atmosphere, Figure 1a. Nanorods that were 4.4 nm in diameter by 16.1 nm in length had a first excitonic absorption peak at 1412 nm (878 meV), Figure 1c. (See the Supporting Information for details.) As the exciton Bohr radius in bulk PbSe is 46 nm, these nanorods are in the strong confinement regime. Though the electronic transitions are primarily diameter dependent,28 the weaker confinement along the length of the rod also affects the transition energies. As expected from their quasi-onedimensionality, the first excitonic transition in nanorods is at a lower energy than observed in nanocrystals28,36,37 and a higher energy than observed in nanowires37 of similar diameter. Further studies are needed to determine the aspect ratio dependence of the electronic properties of nanorods. Nanocrystals with 4.7 nm diameters and a first excitonic absorption peak at 1416 nm (876 meV), panels b and d of Figure 1, were synthesized to have similar absorption spectra to the nanorods. Multiple excitons are identified by exploiting the large difference in single-exciton and multiexciton decay dynamics resulting from the orders-of-magnitude shorter multiexciton lifetime. Multiexcitons decay through Auger recombination, where an electron and hole recombine and transfer their energy to another exciton present in the material instead of being released by photon emission, in 10200 ps.9 Single excitons are much longer lived, with photoluminescence lifetimes between 0.1 and 1 μs.28,38 The multiexciton quantum yield is quantified by determining the ratio of multiexcitons to excitons, where the exciton quantum yield is assumed to be 1. This is typically accomplished through optical spectroscopy by either time-resolved photoluminescence or transient absorption experiments. MEG quantum yields based on time-resolved photoluminescence experiments depend on the ratio of biexciton to exciton emission rates, which are not precisely known.6,30 Transient absorption instead measures the dynamics of the ground state bleach due to state filling after photoexcitation9 or intraband transitions of the excited exciton.39 Delay-dependent changes in absorption due to excitation with a short pulse are measured by a second, low-intensity, probe pulse yielding energy relaxation and recombination dynamics information. The photoinduced change in absorption is proportional to the number of excited excitons. The ratio of the ground state bleach soon after excitation to that at long delays constitutes the ratio of the multiexciton to single exciton population (Rpop).9,19 The exciton quantum yield is experimentally determined by measuring the fluence dependence of Rpop. In the absence of MEG, the exciton population exhibits a Poisson distribution, where the probability of exciting an exciton in a given nanostructure is independent of the number of excitons already present. The average number of excitons per photoexcited nanostructure is proportional to the pump fluence. At high fluences, where the average number of absorbed photons per nanostructure (ÆNæ) is g1, sequential absorption leads to the creation of multiexcitons that decay via Auger recombination. At low fluences, in the absence of MEG, this fast decay disappears leaving only the longlived decay of singlet excitons. When ÆNæ , 1 the average number of excitons per photoexcited nanostructure is approximately 1 and the photoinduced bleach is proportional to the 3477
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Figure 2. Determination of the MEG quantum yield in PbSe nanorods and nanocrystals. Transient absorption dynamics in PbSe nanorods (a) without and (b) with MEG for 775 nm (1.8Eg) and 499 nm (2.8Eg) wavelength pump excitation, respectively. ÆNæ was estimated based on values of σ determined through fits to eq 1. (c) The ratio of multiexciton to exciton population for both pump wavelengths, where the solid lines are fits to eq 1. Similar transient absorption dynamics in PbSe nanocrystals for (d) 775 nm (1.8Eg) and (e) 489 nm (2.9Eg) wavelength pump excitation. Thick lines are biexponential fits to the data. (f) The ratio of multiexciton to exciton population for both pump wavelengths, where the solid lines are fits to eq 1. Fit parameters are listed on the graph.
fraction of photoexcited nanostructures. At photon energies where MEG occurs, multiexcitons are created even at low fluences and the Auger component to the bleach relaxation persists. In this case, Rpop no longer follows a Poisson distribution with ÆNæ, which instead must be modified to Rpop ¼
ΔTðt1 Þ=T0 Jσϕδ ¼ 1 eJσ ΔTðt2 Þ=T0
ð1Þ
which accommodates nonunity multiplicity.19 Here ÆNæ = Jσ, where J is the pump fluence and σ is the absorption cross section at the pump wavelength, and ϕ is the exciton quantum yield. Depletion of singlet excitons over the scanned temporal window is corrected by the term δ = e(t2t1)/τX, where t1 is a delay just following photoexcitation, t2 is the longest delay in the measured temporal window, and τX is the singlet exciton lifetime. In the presence of MEG, the average number of excitons per nanostructure does not depend on the pump fluence but instead depends on the pump photon energy. According to conservation of energy, for MEG to occur the amount of excess energy given to an exciton must exceed the electronhole pair creation energy, εEHP. Ideally, if no energy is lost, then εEHP is equal to the band gap energy, Eg. Thus the MEG threshold energy, hνth, would be equal to 2Eg. As each additional exciton requires an additional Eg of energy, then the
exciton quantum yield will have a staircase-like energy dependence. Such ideal energy dependence has recently been measured in photoconductors based on single-walled carbon nanotubes.40 For nonideal cases, the exciton quantum yield has the energy dependence ! hν 1 ηMEG ð2Þ ϕ¼ Eg where the MEG efficiency (ηMEG) is related to the electronhole pair creation energy by ηMEG = Eg/εEHP.5 In bulk materials, conservation of momentum forces the energy threshold to be higher than the energy conservation limit. The lack of translational symmetry relaxes momentum conservation in nanostructures, lowering this activation barrier to MEG.4 The photoinduced bleach dynamics in PbSe nanorod solutions were measured as a function of fluence, Figure 2a,b. (See the Supporting Information for details.) At each fluence, Rpop was calculated from the measured change in transmission, Figure 2c. The fluence dependence of Rpop was then fit with eq 1. For pump photon energies hν < 2Eg, where MEG is forbidden by conservation of energy, the exciton quantum yield was assumed to be 1 and at low fluences Rpop reaches a fluenceindependent value of δ. Consequently, δ allows for estimation of the single exciton lifetime. For pump photon energies hν > 2Eg, 3478
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Figure 3. Comparison of MEG in nanorods and nanocrystals. The MEG quantum yield vs relative photon energy of 985 meV (red 9), 908 meV (blue (), and 878 meV (green b) PbSe nanorods compared to PbSe nanocrystals (black 2). Literature values were taken from Beard, et al.5 Solid lines are fits to eq 2 with fit parameters listed in the graph.
where MEG is possible, δ was assumed to maintain its low energy value and fits to eq 1 yield the exciton quantum yield. MEG is clearly observed in Figure 2b for photon energies below 3Eg, which is the approximate MEG threshold energy in PbSe nanocrystals.5,30 The fast Auger recombination of multiexcitons can be observed at early delays, Figure 2b, which is absent for low photon energies, Figure 2a. At low fluences, Rpop remains significantly larger than δ, its value for low photon energies, indicating nonunity exciton multiplicity. Applying eq 1 to the fluence dependence of Rpop yields exciton quantum yields larger than 1. Similar transient absorption measurements of nanocrystals show little MEG for these photon energies, Figure 2df. There is little Auger recombination visible in the bleach dynamics, and Rpop is seen to reach nearly the same value for both photon energies at low fluences. This is consistent with observations in the literature, where photon energies g3Eg are required for MEG in PbSe nanocrystals.5 For low photon energies, the fast Auger recombination of multiple excitons in both PbSe nanorods and nanocrystals occurs with a time constant of 4050 ps, similar to decay times previously measured for PbSe nanocrystals in solution.19 This decay time monotonically decreases with increasing pump photon energy for nanorods. This is similar to observations made of PbSe nanocrystals above their MEG threshold energy.16 The observed decay time is a combination of the Auger recombination times of all the different order (bi-, tri-, etc.) multiexcitons generated in the sample. At higher photon energies, a larger fraction of the photoexcited nanostructures generate higher order multiexcitons, which undergo more rapid Auger recombination. The decay time appears relatively constant in the nanocrystal samples measured here as the photon energies used are below the MEG threshold energy and multiple excitons are generated by sequential absorption only. Due to their larger volume and high exciton binding energy, nanorods possess larger absorption cross sections than nanocrystals,28,41 making the high fluence measurements used for nanocrystals unnecessary. The absorption cross sections of nanorods determined through fits to eq 1 reflect this increase, Figure 2c,f. This property may allow thin film photovoltaic cells made from nanorods to have thinner active layers than similar devices made from nanocrystals. Unfortunately, this same property also prevents fluence-independent values of Rpop from being reached for nanorods within the experimental signal-to-noise ratio. Similar difficulties have been encountered with MEG measurements of PbSe nanocrystalline solid films.19 However,
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fitting eq 1 to the fluence dependence of Rpop allows for accurate determination of the MEG quantum yield. This fluenceindependent regime can be reached for nanocrystals, providing a highly accurate measurement of the MEG quantum yield.32 The values of δ determined from the fits to eq 1 deviate significantly from 1 for both nanocrystals and nanorods, indicating that the single exciton lifetimes here are on the order of nanoseconds, orders of magnitude shorter than the microsecond values measured via time-resolved photoluminescence.27,28,38,42 These lifetimes are similar to those estimated from MEG measurements for solid films of PbSe nanocrystals.19 Measurements of ϕ as a function of pump photon energy allow for the determination of the MEG threshold energy and electron hole pair creation energy using eq 2, as shown in Figure 3. MEG is clearly observed in PbSe nanorods for photon energies larger than 2.3Eg. MEG is absent or insignificant in nanocrystals for photon energies less than 3Eg. On comparison of literature values of the MEG quantum yield for PbSe nanocrystals,5 it is clear that the onset of MEG is lower and the slope of ϕ vs hν/Eg is higher in nanorods than in nanocrystals. Fits to eq 2 yield a MEG threshold energy of 2.23Eg ( 0.03Eg, an electronhole pair creation energy of 1.23Eg ( 0.03Eg, and a MEG efficiency of 0.81 ( 0.02 for nanorods. The MEG threshold energy and efficiency are approaching the energy conservation limit. Ideally, this limit is a staircase function, where each exciton requires Eg of energy. If the multiexciton quantum efficiency instead possessed a slope, as is commonly observed for nanocrystals, then conservation of energy would limit the MEG efficiency to values e1. The MEG measurements shown here only include photon energies up to 2.9Eg, restricted by the wavelength range of the visible optical parametric amplifier used to excite the solutions. Measurements at higher photon energies would be useful in determining the ultimate efficiency of MEG in nanorods, which given the high degeneracy of the first excited state should stay constant until the 1S state is filled and further increases in the exciton quantum yield require occupation of the 1P state. Enhanced MEG in nanorods may seem counterintuitive, as elongation of the nanocrystal is expected to reduce confinement and restore momentum conservation along that axis.35 However, excitons in nanorods are tightly bound28 and enhanced Coulomb interactions may cause the observed increase in MEG efficiency.7 If this is the case, the observed enhancement of MEG in nanorods may be preserved in one-dimensional nanowires. This could lead to a material that combines efficient MEG and improved conductivity, as charge transport should be efficient down the length of the wire compared to hopping or tunneling between nanostructures. Precisely varying the aspect ratio of the nanorods to explore the effects of systematically weakening confinement along the length of the rod may add insight as to the effects transitioning from zero- to one-dimensions has on MEG. We do not observe an accompanying increase in the Auger recombination rates in nanorods compared to nanocrystals. Auger recombination requires that two excitons be in close proximity, on the order of an exciton radius, in order to recombine. In nanorods, elongation allows excitons to be further apart, contributing to suppressed Auger recombination.35,43 As MEG occurs over the volume of the optically excited exciton, elongation of the nanostructure does not lead to a similar suppression. In the absence of Auger recombination, the radiative biexciton lifetime is expected to be shorter in nanorods due to the smaller exciton radius, incomplete charge screening, and increased oscillator strength.43 3479
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Figure 4. Effect of MEG on maximum photovoltaic power conversion efficiency. The power conversion efficiency vs band gap energy under (a) AM1.5 and (b) 500 solar concentration for PbSe nanocrystals (red) and nanorods (blue). The ShockleyQueissier limit (black) is included for reference.
We conducted detailed balance calculations4446 to assess whether enhanced MEG in PbSe nanorods could further improve the power conversion efficiencies (PCE) of photovoltaic cells. The ShockleyQueisser limit represents the maximum efficiency from a photovoltaic cell where all photons with energy above the band gap are absorbed, one electronhole pair is created per absorbed photon, the carrier mobilities are infinite, and only radiative recombination limits the efficiency. To accommodate MEG, we allow the internal quantum yield to be dependent on the incident photon energy and assume values larger than 100% in accordance with eq 2 and our measurements in Figure 3. We also must account for the increase in chemical potential associated with multiexcitons,4446 which serves to increase radiative recombination dark current and thus decrease the total current. The presence of MEG is expected to increase the PCE and shift the optimal band gap to lower energies, as the increase in the photocurrent due to MEG outweighs the increase in dark current. Intuitively, this improvement is expected due to reduced carrier thermalization. Given the MEG threshold energy and electronhole pair creation energy of PbSe nanocrystals, little improvement over the 33% ShockleyQueisser limit is possible, Figure 4a. The PCE was calculated using the ASTM G173-03 AM1.5d terrestrial spectrum, normalized to 1000 W/m2, for a photovoltaic cell at 300 K. The reduced MEG threshold energy and electronhole pair creation energy in PbSe nanorods allow the PCE to be increased to 34.5%, a 3% relative increase. For band gap energies greater than 1.4 eV, MEG has no effect due to the small number of solar photons with energies >2.8 eV. The PCE is strongly dependent on the MEG threshold energy, as more of the solar spectrum can be utilized for the generation of multiexcitons. Though such an increase in PCE is meaningful to the photovoltaic industry, the improvement may seem modest given that MEG in PbSe nanorods is approaching the theoretical limit for both the energy threshold and the MEG efficiency. The potential of MEG based photovoltaic cells becomes more apparent when used in conjunction with solar concentrators. Solar concentrators, typically lenses, are used to concentrate the
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photon count from a large area onto a relatively small area photovoltaic cell, enhancing the PCE. Under 500 concentration, nanorods can yield PCE up to 47%, a 17% relative increase, while nanocrystals still show minimal improvement over the ShockleyQueisser limit, which increases to 40%, Figure 4b. The increased solar flux leads to correspondingly larger increases in photocurrent than in radiative recombination. This allows the optimum band gap to decrease further to take advantage of a larger number of photons energetically capable of producing multiexcitons. The reduced MEG threshold energy makes PbSe nanorods more suitable to take advantage of the increased solar flux. Clearly photovoltaic cells based on PbSe nanorods show more promise for improving PCE via MEG than nanocrystals. As there is some debate in literature as to whether the MEG efficiency varies with nanocrystal diameter,5,47 studies should be conducted to confirm that MEG remains enhanced for larger nanorods with narrower bandgaps capable of exploiting the enhanced PCE possible with solar concentration. In summary, we have reported the observation of MEG in PbSe nanorods, which is enhanced as compared to MEG in PbSe nanocrystals. This improvement is characterized by a decrease in the MEG threshold energy and an increase in MEG efficiency, which we attribute to the increased Coulomb interaction in nanorods. Detailed balance models of photovoltaic cells based on PbSe nanorods show enhanced PCE over both nanocrystals and the ShockleyQueisser limit. Use of nanorod solar cells in conjunction with solar concentrators has the potential to yield large improvements in the PCE. The increased absorption cross section of nanorods implies that thinner active layers in thin-film solar cells can be used, decreasing recombination losses. These observations also suggest that one-dimensional nanowires may be a promising class of materials for photovoltaics, as they could combine the enhanced MEG observed here in quasi-one-dimensional nanorods with improved charge transport properties.
’ ASSOCIATED CONTENT
bS
Supporting Information. Materials, synthesis, sample preparation, characterization, and transient absorption experimental details. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This research was performed while P. D. Cunningham and A. R. Smith held National Research Council Research Associateship Awards at the U.S. Naval Research Laboratory. We thank Sasha Efros for helpful discussions of MEG and Auger recombination. ’ REFERENCES (1) Sukhovatkin, V.; Hinds, S.; Brzozowski, L.; Sargent, E. H. Science 2009, 324, 1542. (2) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H.-J.; Bawendi, M. G. Science 2000, 290, 314. (3) Sambur, J. B.; Novet, T.; Parkinson, B. A. Science 2010, 330, 63. 3480
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Nano Letters (4) Nozik, A. J.; Beard, M. C.; Luther, J. M.; Law, M.; Ellingson, R. J.; Johnson, J. C. Chem. Rev. 2010, 110, 6873. (5) Beard, M. C.; Midgett, A. G.; Hanna, M. C.; Luther, J. M.; Hughes, B. K.; Nozik, A. J. Nano Lett. 2010, 10, 3019. (6) McGuire, J. A.; Sykora, M.; Joo, J.; Pietryga, J. M.; Klimov, V. I. Nano Lett. 2010, 10, 2049. (7) Witzel, W. M.; Shabaev, A.; Hellberg, C. S.; Jacobs, V. L.; Efros, A. L. Phys. Rev. Lett. 2010, 105, 137401. (8) Nozik, A. J. Phys. E (Amsterdam, Neth.) 2002, 14, 115. (9) Schaller, R. D.; Klimov, V. I. Phys. Rev. Lett. 2004, 92, 186601. (10) Achermann, M.; Hollingsworth, J. A.; Klimov, V. I. Phys. Rev. B 2003, 68, 245302. (11) Efros, A. L.; Kharchenko, V. A.; Rosen, M. Solid State Commun. 1995, 93, 281. (12) Klimov, V. I. Annu. Rev. Phys. Chem. 2007, 58, 635. (13) Sargent, E. H. Nat. Photonics 2009, 3, 325. (14) Schaller, R. D.; Petruska, M. A.; Klimov, V. I. Appl. Phys. Lett. 2005, 87, 253102. (15) Schaller, R. D.; Sykora, M.; Jeong, S.; Klimov, V. I. J. Phys. Chem. B 2006, 110, 25332. (16) Schaller, R. D.; Sykora, M.; Pietryga, J. M.; Klimov, V. I. Nano Lett. 2006, 6, 424. (17) Ellingson, R. J.; Beard, M. C.; Johnson, J. C.; Yu, P.; Micic, O. L.; Nozik, A. J.; Shabaev, A.; Efros, A. L. Nano Lett. 2005, 5, 865. (18) Murphy, J. E.; Beard, M. C.; Nozik, A. J. J. Phys. Chem. B 2006, 110, 25455. (19) Luther, J. M.; Beard, M. C.; Song, q.; Law, M.; Ellingson, R. J.; Nozik, A. J. Nano Lett. 2007, 7, 1779. (20) Stubbs, S. K.; Hardman, S. J. O.; Graham, D. M.; Spencer, B. F.; Flavell, W. R.; Glarvey, P.; Masala, O.; Picket, N. L. Phys. Rev. B 2010, 81, 081303(R). (21) Klimov, V. I.; Mcguire, J. A.; Schaller, R. D.; Rupasov, V. I. Phys. Rev. B 2008, 71, 195324. (22) Pijpers, J. J. H.; Milder, M. T. W.; Delerue, C.; Bonn, M. J. Phys. Chem. C 2010, 114, 6318. (23) Pijpers, J. J. H.; Ulbricht, R.; Tielrooij, K. J.; Osherov, A.; Golan, Y.; Delerue, C.; Allan, G.; Bonn, M. Nat. Phys. 2009, 5, 811. (24) Nair, G.; Geyer, S. M.; Chang, L.-Y.; Bawendi, M. G. Phys. Rev. B 2008, 78, 125325. (25) Ben-Lulu, M.; Mocatta, D.; Bonn, M.; Banin, U.; Ruhman, S. Nano Lett. 2008, 8, 1207. (26) Nair, G.; Bawendi, M. G. Phys. Rev. B 2007, 76, 081304. (27) Tischler, J. G.; Kennedy, T. A.; Glaser, E. R.; Efros, A. L.; Foos, E. E.; Boercker, J. E.; Zega, T. J.; Stroud, R. M.; Erwin, S. C. Phys. Rev. B 2010, 82, 245303. (28) Bartnik, A. C.; Efros, A. L.; Koh, W.-K.; Murray, C. B.; Wise, F. W. Phys. Rev. B 2010, 82, 195313. (29) Schaller, R. D.; Agranovich, V. M.; Klimov, V. I. Nat. Phys. 2005, 1, 189. (30) McGuire, J. A.; Joo, J.; Pietryga, J. M.; Schaller, R. D.; Klimov, V. I. Acc. Chem. Res. 2008, 41, 1810. (31) Midgett, A. G.; Hillhouse, H. W.; Hughes, B. K.; Nozik, A. J.; Beard, M. C. J. Phys. Chem. C 2010, 114, 17486. (32) 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. (33) Tisdale, W. A.; Williams, K. J.; Timp, B. A.; Norris, D. J.; Aydil, E. S.; Zhu, X.-Y. Science 2010, 328, 1543. (34) Kim, S. J.; Kim, W. J.; Sahoo, Y.; Cartwright, A. N.; Prasad, P. N. Appl. Phys. Lett. 2008, 92, 031107. (35) Htoon, H.; Hollingsworth, J. A.; Dickerson, R.; Klimov, V. I. Phys. Rev. Lett. 2003, 91, 227401. (36) Dai, Q.; Wang, Y.; Li, X.; Zhang, Y.; Pellegrino, D. J.; Zhao, M.; Zou, B.; Seo, J. T.; Wang, Y.; Yu, W. W. ACS Nano 2009, 3, 1518. (37) Boercker, J. E.; Clifton, E. M.; Tischler, J. G.; Foos, E. E.; Zega, T. J.; Twigg, M. E.; Stroud, R. M. J. Phys. Chem. Lett. 2011, 2, 527. (38) Kigel, A.; Brumer, M.; Maikov, G. I.; Sashchiuk, A.; Lifshitz, E. Small 2009, 5, 1675.
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(39) Ji, M.; Park, S.; Conner, S. T.; Mokari, T.; Cui, Y.; Gaffney, K. J. Nano Lett. 2009, 9, 1217. (40) Gabor, N. M.; Zhong, Z.; Bosnick, K.; Park, J.; McEuen, P. L. Science 2009, 325, 1367. (41) Giblin, J.; Kuno, M. J. Phys. Chem. Lett. 2010, 1, 3340. (42) Schaller, R. D.; Crooker, S. A.; Bussian, D. A.; Pietryga, J. M.; Joo, J.; Klimov, V. I. Phys. Rev. Lett. 2010, 105, 067403. (43) Shabaev, A.; Efros, A. L. Nano Lett. 2004, 4, 1821–1825. (44) Hanna, M. C.; Nozik, A. J. J. Appl. Phys. 2006, 100, 074510. (45) Takeda, Y.; Motohiro, T. Sol. Energy Mater. Sol. Cells 2010, 94, 1399. (46) Brendel, R.; Werner, J. H.; Queisser, H. J. Sol. Energy Mater. Sol. Cells 1996, 41/42, 419. (47) Delerue, C.; Allan, G.; Pijpers, J. J. H.; Bonn, M. Phys. Rev. B 2010, 81, 125306.
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