Spectral and Dynamical Properties of Single Excitons, Biexcitons, and

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Spectral and dynamical properties of single excitons, biexcitons, and trions in cesium-lead-halide perovskite quantum dots Nikolay S. Makarov, Shaojun Guo, Oleksandr Isaienko, Wenyong Liu, Istvan Robel, and Victor I. Klimov Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b05077 • Publication Date (Web): 16 Feb 2016 Downloaded from http://pubs.acs.org on February 20, 2016

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Spectral and dynamical properties of single excitons, biexcitons, and trions in cesium-lead-halide perovskite quantum dots Nikolay S. Makarov, Shaojun Guo, Oleksandr Isaienko, Wenyong Liu, István Robel, Victor I. Klimov* Center for Advanced Solar Photophysics, Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA * Address correspondence to [email protected]

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ABSTRACT Organic-inorganic lead-halide perovskites have been the subject of recent intense interest due to their unusually strong photovoltaic performance. A new addition to the perovskite family is all-inorganic Cs-Pb-halide perovskite nanocrystals, or quantum dots, fabricated via a moderate-temperature colloidal synthesis. While being only recently introduced to the research community, these nanomaterials have already shown promise for a range of applications from color-converting phosphors and light-emitting diodes to lasers, and even room-temperature single-photon sources. Knowledge of the optical properties of perovskite quantum dots still remains vastly incomplete. Here we apply various time-resolved spectroscopic techniques to conduct a comprehensive study of spectral and dynamical characteristics of single- and multiexciton states in CsPbX3 nanocrystals with X being either Br, I, or their mixture. Specifically, we measure exciton radiative lifetimes, absorption cross-sections, and derive the degeneracies of the band-edge electron and hole states. We also characterize the rates of intraband cooling and nonradiative Auger recombination and evaluate the strength of excitonexciton coupling. The overall conclusion of this work is that spectroscopic properties of Cs-Pbhalide quantum dots are largely similar to those of quantum dots of more traditional semiconductors such as CdSe and PbSe. At the same time, we observe some distinctions including, for example, an appreciable effect of the halide identity on radiative lifetimes, considerably shorter biexciton Auger lifetimes, and apparent deviation of their size dependence from the “universal volume scaling” previously observed for many traditional nanocrystal systems. The high efficiency of Auger decay in perovskite quantum dots is detrimental to their prospective applications in light-emitting devices and lasers. This points towards the need for the development of approaches for effective suppression of Auger recombination in these nanomaterials, using perhaps insights gained from previous studies of II-VI nanocrystals. TOC GRAPHICS

CsPbX3

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Keywords: Cs-Pb-halide perovskites, nanocrystal, quantum dot, radiative recombination, Auger recombination, absorption cross-section, band-edge-state degeneracy, intraband cooling, excitonexciton interaction.


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Introduction. Hybrid organic-inorganic perovskites CH3NH3MX3 (M is a metal, typically Pb, and X is a halide, typically Cl, Br, or I) exhibit large absorption coefficients, high emission efficiencies and excellent charge transport characteristics.1-4 These properties make them attractive materials for applications across a range of technologies from solar energy conversion1, 2, 5

to light emitting diodes (LEDs)6 and lasers.7 Especially impressive have been recent advances

in the efficiency of perovskite solar cells that surged from 3.8%8 to 20.1% over the past several years.5, 9, 10 Recently, hybrid perovskites have been also synthesized as nanocrystal quantum dots (QDs) and studied in the context of their applications as color-tunable down-converting phosphors.11 The newest addition to the family of perovskite QDs is all-inorganic nanocrystals introduced by Kovalenko and co-workers.12 In these nanostructures, the organic CH3NH3 cations are replaced with Cs+, which results in the composition CsPbX3, where X is one of the three halides (Cl, Br, or I) or their binary mixture. The particles reported in ref [12] were cubically shaped with a side length ranging from 4 to 15 nm. The emission was color tunable across the entire range of visible wavelengths (400 - 700 nm) by combining size and composition control. More recent works demonstrated a highly effective post-synthetic anion exchange, which resulted in the partial or complete replacement of ions of one halide with another.13,

14

This

interesting approach allowed for facile manipulation of emission color without modifying the QD dimensions. The initial reports on Cs-based QDs primarily focused on the chemistry of these novel materials and their basic spectroscopic properties such as absorption and photoluminescence (PL) spectra as well as PL efficiencies and lifetimes.12-14 These earlier measurements found surprisingly high emission efficiencies (~50% and higher) for as-fabricated QDs suggesting their


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potential usability as, for example, color-converting phosphors or active elements in LEDs. A demonstration of low-threshold, color-tunable amplified spontaneous emission (ASE) also suggested that this type of QDs could be explored in the context of lasing applications.15 Furthermore, recent single-dot measurements indicated the feasibility of using individual perovskite QDs as room-temperature sources of single photons.16 While the conducted studies indicate considerable promise of these novel QDs for applications that rely on light emission, their practical utilization in light-emitting devices would benefit from a more complete understanding of spectral and dynamical properties of electronic excitations in these materials. More studies are also required to assess whether perovskite QDs can compete, and potentially outperform, more traditional visible-light-emitting II-VI and III-V nanocrystals that have been successfully exploited in a range of applications including a commercialized display technology. The purpose of the present study is to conduct a comprehensive spectroscopic characterization of Cs-based perovskite QDs with focus on energy relaxation and recombination processes. Specifically, using time-resolved PL and transient absorption (TA) spectroscopies, we evaluate the degeneracies of the band-edge states and quantify spectroscopic characteristics such as absorption cross-sections, radiative lifetimes, time constants of nonradiative Auger decay, exciton-exciton interaction energies, and intraband cooling rates. Our overall assessment is that the properties of perovskite QDs are in general similar to those of well-studied CdSe and PbSe QDs. Specifically, we observe extremely fast intraband relaxation, which occurs on subpicosecond-to-picosecond time scales, similar to those reported for CdSe17 and PbSe18 QDs. Our measurements also indicate fairly large exciton-exciton interaction energies of the order of 10 meV, again comparable to those in large-size CdSe QDs.19, 20 Further, we find that multiexciton


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recombination is dominated not by radiative processes but by very fast Auger recombination, which is in direct analogy to other nanocrystalline systems.21, 22 In fact, the biexciton lifetimes measured for perovskite QDs are even shorter than those in CdSe and PbSe QDs of similar sizes, suggesting that Auger decay will represent a serious obstacle to the realization of practical lasing and LED devices, as in the case of other QD systems. This points towards the importance of developing effective approaches for suppressing Auger decay in novel perovskite QDs, perhaps, by taking advantage of a large amount of theoretical23 and experimental24-26 studies devoted to controlling Auger decay in II-VI nanocrystals. Quantum dot samples. Perovskite QDs of three compositions, CsPbBr3, CsPbI3 and CsPbBr1.5I1.5 (referred to as Br-QDs, I-QDs, and Br1.5I1.5-QDs, respectively) were synthesized following a procedure from ref [12] with some modifications (see Methods). The synthesized QDs are cubically shaped single crystals with a mean side length (L) of 6.3 to 11.2 nm and size dispersion of ~10% (see Figure 1a and Figure S1 of Supporting Information, SI). High-resolution transmission electron microscopy (TEM) images (Figure 1a, inset) indicate that QD sides are parallel to the {100} lattice planes. The spacing between these planes is 0.62 nm for the I-QDs (Figure S1b of SI), which is consistent with the cubic perovskite crystal structure of CsPbI3.12-14 According to calculations of ref [12], the Bohr exciton diameters (2a0) in bulk CsPbBr3 and CsPbI3 are 7 and 12 nm, respectively. On the basis of these values, in a mixed-halide sample, 2a0 is approximately 9.4 nm. For the QD sizes studied in the present work, the L/2a0 ratio is from ~0.9 to ~1.3. This situation corresponds to the regime of so-called “intermediate confinement” when the QD size is comparable to that of a bulk exciton. A similar regime is realized, for example, in large-size (8-10 nm diameter) CdSe QDs where the Bohr exciton diameter (2a0 = 9.6 nm) is close to that in Pb-halide perovskites.


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Optical spectra, photoluminescence dynamics, and radiative lifetimes. In all optical measurements described in this work, perovskite QDs were dissolved in hexane, and loaded into airtight optical cuvettes under argon atmoshere. All spectroscopic studies were conducted at room temperature. Figure 1b shows the absorption (α), PL, and PL excitation (PLE) spectra of the studied QD samples. We observe that the PLE spectra closely match the absorption spectra up to energies of ~4 eV (instrument limit in these measurements), indicating that photoinjected “hot” carriers are efficiently funneled into the “emitting” band-edge states independent of excitation energy. The absorption spectra exhibit a relatively sharp step-like onset and a fairly narrow PL band (~90 meV; determined in terms of a full width at half maximum, FWHM). Since the absorption spectra lack a pronounced band-edge peak, to quantify the position of the lowestenergy “absorbing” transition, we analyze the second-derivative of α(hv), α”(hv), an approach used previously for visualizing poorly resolved spectral features in QD samples (hv is the photon energy).27 Based on the position of the first minimum in the α”(hv) spectrum (black lines in the Figure 1c) versus the PL peak, we infer that the apparent Stokes shift (ΔS) is of the order of 20 to 30 meV, which is comparable to that in large-size CdSe QDs.28 As was reported previously,12 as-synthesized QDs exhibit high PL quantum yields (QYs) that are in the 40 - 50% range (see Table S1 of SI). Such high QYs are remarkable given that these QDs are synthesized at relatively low temperatures (130 - 160° C) and are not overcoated with a shell of a wider-band-gap semiconductor usually required for obtaining high emission efficiencies in II-VI or III-V QDs. We also do not detect any signatures of intra-gap emission, which is often present in core-only CdSe QDs. These observations suggest a considerably lower abundance of intra-gap states in perovskite QDs compared to other studied QDs.


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Figure 2a shows PL dynamics for the perovskite QDs measured with a superconducting nanowire single-photon detector (SNSPD; temporal resolution Δtres = 50 ps)29 using pulsed excitation (220 fs pulse duration) at 3.6 eV, with a per-pulse fluence of 3.5×1011 photons/cm2, which corresponds to the average QD excitonic occupancy, τm) ∝ (1 − p0) = (1 – 11 ACS Paragon Plus Environment

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e−) = (1 – e−σjp), where τm is the lifetime of the initial fast decay of multiexcitons. Thus, the long-time PL intensity saturates with increasing pump fluence, and since the onset of this saturation is directly controlled by the QD absorption cross-section, it can be used to quantify σ. In Figure 3b, we display the fluence dependence of the late-time PL signal for perovskite QDs of different compositions (symbols) (additional measurements using a streak camera, uPL, and saturation data for time-integrated PL are shown in Figure S2a of SI). We observe that all of the measured dependences can be accurately fit to the Poisson expression (lines in Figure 3b), confirming that the short-lived, early-time PL component is due to multiexcitons. As a result of the fitting procedure, we also obtain QD absorption cross-sections. Based on the fits in Figure 3b and additional measurements in Figure S2a of SI, the average values of the 3.1-eV cross-sections are 1.3±0.6×10−14 cm2, 1.5±0.5×10−14 cm2, and 1.3±0.6×10−14 cm2 for the Br-QD, Br1.5I1.5-QD, and I-QD samples respectively. We plot the derived values in Figure 3c as a function of QD volume (VQD) along with absorption cross-sections of two more Br-QD samples of smaller sizes. All of these data are also included in Table S1 of SI. We observe that for Br-QDs of varied sizes σ scales linearly with the QD volume, which is a trend commonly seen for other colloidal nanocrystals excited well above the band edge.39 Further, we find that the measured absorption cross-sections are considerably smaller (by almost an order of magnitude) than those of CdSe QDs of the same volume. This conclusion is confirmed by side-by-side pump-intensity-dependent measurements of saturation of the latetime-PL signal in samples of CdSe and Br-QDs (Figure S2b of SI). Despite a large difference in QD volumes for these two samples (250 versus 47.7 nm3 for the perovskite and the CdSe QDs, respectively) both samples show essentially identical absorption cross-sections of 3.5×10−15 cm2 at 3.1 eV. 12 ACS Paragon Plus Environment

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The above results suggest that the absorption coefficient of bulk CsPbX3 perovskites is smaller than that of bulk CdSe. Indeed, the absorption cross-section of the QDs can be related to the bulk absorption coefficient by the following expression: σ = ( nm ns ) f αVQD , where ns and nm 2

!

are refractive indices of the semiconductor material and the surrounding medium, respectively (all spectroscopic parameters are taken at the excitation wavelength). Based on this expression and the difference in the dielectric-screening factors, we estimate that at 3.1 eV the absorption coefficient of bulk CsPbBr3 is approximately an order of magnitude smaller than that of bulk CdSe. It would be interesting to see if this assessment is confirmed by direct measurements of absorption coefficients of bulk CsPbX3 crystals. Such data, however, are not readily available in the literature, as the majority of previous optical studies of perovskites have focused on hybrid organic-inorganic versions of these materials.36, 40 Biexciton and trion Auger lifetimes. The pump-intensity dependent dynamics in Figure 3a can also be used to quantify the lifetime of doubly excited QDs, which is usually referred to as a biexciton lifetime (τ2X). For this purpose, we first normalize the PL traces in such a way as to match their late-time components (Figure 4a). In this representation the long-time dynamics appear to be self-similar, as expected for the single-exciton recombination regime, which establishes following the multiexciton decay. Next, we subtract the contribution from singleexcitons obtained based on traces measured for τcool

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References: (1)

Liu, M.; Johnston, M. B.; Snaith, H. J. Nature 2013, 501, 395-398.

(2)

Nie, W.; Tsai, H.; Asadpour, R.; Blancon, J.-C.; Neukirch, A. J.; Gupta, G.; Crochet, J. J.;

Chhowalla, M.; Tretiak, S.; Alam, M. A.; Wang, H.-L.; Mohite, A. D. Science 2015, 347, 522525. (3)

Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J. P.; Leijtens, T.;

Herz, L. M.; Petrozza, A.; Snaith, H. J. Science 2013, 342, 341-344. (4)

Kagan, C. R.; Mitzi, D. B.; Dimitrakopoulos, C. D. Science 1999, 286, 945-947.

(5)

Jeon, N. J.; Noh, J. H.; Yang, W. S.; Kim, Y. C.; Ryu, S.; Seo, J.; Seok, S. I. Nature

2015, 517, 476-480. (6)

Tan, Z.-K.; Moghaddam, R. S.; Lai, M. L.; Docampo, P.; Higler, R.; Deschler, F.; Price,

M.; Sadhanala, A.; Pazos, L. M.; Credgington, D.; Hanusch, F.; Bein, T.; Snaith, H. J.; Friend, R. H. Nat. Nano. 2014, 9, 687-692. (7)

Xing, G.; Mathews, N.; Lim, S. S.; Yantara, N.; Liu, X.; Sabba, D.; Grätzel, M.;

Mhaisalkar, S.; Sum, T. C. Nat. Mater. 2014, 13, 476-480. (8)

Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. J. Am. Chem. Soc. 2009, 131, 6050-

6051. (9)

Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Science 2012,

338, 643-647. (10)

Zhou, H.; Chen, Q.; Li, G.; Luo, S.; Song, T.-b.; Duan, H.-S.; Hong, Z.; You, J.; Liu, Y.;

Yang, Y. Science 2014, 345, 542-546.


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(11)

Page 46 of 50

Pathak, S.; Sakai, N.; Wisnivesky Rocca Rivarola, F.; Stranks, S. D.; Liu, J.; Eperon, G.

E.; Ducati, C.; Wojciechowski, K.; Griffiths, J. T.; Haghighirad, A. A.; Pellaroque, A.; Friend, R. H.; Snaith, H. J. Chem. Mater. 2015, 27, 8066-8075. (12)

Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.;

Yang, R. X.; Walsh, A.; Kovalenko, M. V. Nano Lett. 2015, 15, 3692-3696. (13)

Nedelcu, G.; Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Grotevent, M. J.;

Kovalenko, M. V. Nano Lett. 2015, 15, 5635-5640. (14)

Akkerman, Q. A.; D’Innocenzo, V.; Accornero, S.; Scarpellini, A.; Petrozza, A.; Prato,

M.; Manna, L. J. Am. Chem. Soc. 2015, 137, 10276-10281. (15)

Yakunin, S.; Protesescu, L.; Krieg, F.; Bodnarchuk, M. I.; Nedelcu, G.; Humer, M.; De

Luca, G.; Fiebig, M.; Heiss, W.; Kovalenko, M. V. Nat. Commun. 2015, 6. (16)

Park, Y.-S.; Guo, S.; Makarov, N. S.; Klimov, V. I. ACS Nano 2015, 9, 10386-10393.

(17)

Klimov, V. I.; McBranch, D. W. Phys. Rev. Lett. 1998, 80, 4028-4031.

(18)

Schaller, R. D.; Pietryga, J. M.; Goupalov, S. V.; Petruska, M. A.; Ivanov, S. A.; Klimov,

V. I. Phys. Rev. Lett. 2005, 95, 196401. (19)

Klimov, V.; Hunsche, S.; Kurz, H. Phys. Rev. B 1994, 50, 8110-8113.

(20)

Achermann, M.; Hollingsworth, J. A.; Klimov, V. I. Phys. Rev. B 2003, 68, 245302.

(21)

Klimov, V. I.; Mikhailovsky, A. A.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M.

G. Science 2000, 287, 1011-1013. (22)

Robel, I.; Gresback, R.; Kortshagen, U.; Schaller, R. D.; Klimov, V. I. Phys. Rev. Lett.

2009, 102, 177404. (23)

Cragg, G. E.; Efros, A. L. Nano Lett. 2010, 10, 313-317.


Page 47 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(24)

García-Santamaría, F.; Brovelli, S.; Viswanatha, R.; Hollingsworth, J. A.; Htoon, H.;

Crooker, S. A.; Klimov, V. I. Nano Lett. 2011, 11, 687-693. (25)

Bae, W. K.; Padilha, L. A.; Park, Y.-S.; McDaniel, H.; Robel, I.; Pietryga, J. M.; Klimov,

V. I. ACS Nano 2013, 7, 3411-3419. (26)

Park, Y.-S.; Bae, W. K.; Baker, T.; Lim, J.; Klimov, V. I. Nano Lett. 2015, 15, 7319-

7328. (27)

Ekimov, A. I.; Kudryavtsev, I. A.; Efros, A. L.; Yazeva, T. V.; Hache, F.; Schanne-Klein,

M. C.; Rodina, A. V.; Ricard, D.; Flytzanis, C. J. Opt. Soc. Am. B 1993, 10, 100-107. (28)

Kuno, M.; Lee, J. K.; Dabbousi, B. O.; Mikulec, F. V.; Bawendi, M. G. J. Chem. Phys.

1997, 106, 9869-9882. (29)

Sandberg, R. L.; Padilha, L. A.; Qazilbash, M. M.; Bae, W. K.; Schaller, R. D.; Pietryga,

J. M.; Stevens, M. J.; Baek, B.; Nam, S. W.; Klimov, V. I. ACS Nano 2012, 6, 9532-9540. (30)

Kane, E. O. J. Phys. Chem. Solids 1956, 1, 82-99.

(31)


(32)


(33)

Kane, E. O., The K.P Method. In Semiconductors and Semimetals, Vol. 1. Physics of Iii-V

Compounds, Willardson, R. K.; Beer, A. C., Eds. Academic: New York, 1966; pp 75-100. (34)

Cardona, M. J. Phys. Chem. Solids 1963, 24, 1543-1555.

(35)

Look, D. C.; Manthuruthil, J. C. J. Phys. Chem. Solids 1976, 37, 173-180.

(36)

Brivio, F.; Butler, K. T.; Walsh, A.; van Schilfgaarde, M. Phys. Rev. B 2014, 89, 155204.

(37)

Even, J.; Pedesseau, L.; Dupertuis, M. A.; Jancu, J. M.; Katan, C. Phys. Rev. B 2012, 86,

205301.


Nano Letters

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(38)

Page 48 of 50

Even, J.; Pedesseau, L.; Katan, C.; Kepenekian, M.; Lauret, J.-S.; Sapori, D.; Deleporte,

E. J. Phys. Chem. C 2015, 119, 10161-10177. (39)

Klimov, V. I. J. Phys. Chem. B 2000, 104, 6112-6123.

(40)

De Wolf, S.; Holovsky, J.; Moon, S.-J.; Löper, P.; Niesen, B.; Ledinsky, M.; Haug, F.-J.;

Yum, J.-H.; Ballif, C. J. Phys. Chem. Lett. 2014, 5, 1035-1039. (41)

Klimov, V. I. Annu. Rev. Cond. Matt. Phys. 2014, 5, 285-316.

(42)

McGuire, J. A.; Joo, J.; Pietryga, J. M.; Schaller, R. D.; Klimov, V. I. Acc. Chem. Res.

2008, 41, 1810-1819. (43)

Stewart, J. T.; Padilha, L. A.; Bae, W. K.; Koh, W.-K.; Pietryga, J. M.; Klimov, V. I. J.

Phys. Chem. Lett. 2013, 4, 2061-2068. (44)

Padilha, L. A.; Stewart, J. T.; Sandberg, R. L.; Bae, W. K.; Koh, W.-K.; Pietryga, J. M.;

Klimov, V. I. Acc. Chem. Res. 2013, 46, 1261-1269. (45)

Htoon, H.; Hollingsworth, J. A.; Dickerson, R.; Klimov, V. I. Phys. Rev. Lett. 2003, 91,

227401. (46)

Klimov, V. I.; McGuire, J. A.; Schaller, R. D.; Rupasov, V. I. Phys. Rev. B 2008, 77,

195324. (47)

Piatkowski, P.; Cohen, B.; Javier Ramos, F.; Di Nunzio, M.; Nazeeruddin, M. K.;

Gratzel, M.; Ahmad, S.; Douhal, A. PCCP 2015, 17, 14674-14684. (48)

McGuire, J. A.; Sykora, M.; Robel, I.; Padilha, L. A.; Joo, J.; Pietryga, J. M.; Klimov, V.

I. ACS Nano 2010, 4, 6087-6097. (49)

Padilha, L. A.; Robel, I.; Lee, D. C.; Nagpal, P.; Pietryga, J. M.; Klimov, V. I. ACS Nano

2011, 5, 5045-5055.


Page 49 of 50

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(50)

Galland, C.; Ghosh, Y.; Steinbrück, A.; Hollingsworth, J. A.; Htoon, H.; Klimov, V. I.

Nat. Commun. 2012, 3, 908. (51)

McGuire, J. A.; Sykora, M.; Joo, J.; Pietryga, J. M.; Klimov, V. I. Nano Lett. 2010, 10,

2049-2057. (52)

Midgett, A. G.; Hillhouse, H. W.; Hughes, B. K.; Nozik, A. J.; Beard, M. C. J. Phys.

Chem. C 2010, 114, 17486-17500. (53)

Park, Y.-S.; Bae, W. K.; Pietryga, J. M.; Klimov, V. I. ACS Nano 2014, 8, 7288-7296.

(54)

Schaller, R. D.; Klimov, V. I. Phys. Rev. Lett. 2004, 92, 186601.

(55)

Ellingson, R. J.; Beard, M. C.; Johnson, J. C.; Yu, P.; Micic, O. I.; Nozik, A. J.; Shabaev,

A.; Efros, A. L. Nano Lett. 2005, 5, 865-871. (56)

Hanna, M. C.; Nozik, A. J. J. Appl. Phys. 2006, 100, 074510.

(57)

Schaller, R. D.; Petruska, M. A.; Klimov, V. I. Appl. Phys. Lett. 2005, 87, 253102.

(58)

Schaller, R. D.; Petruska, M. A.; Klimov, V. I. J. Phys. Chem. B 2003, 107, 13765-

13768. (59)

Efros, A. L.; Rosen, M. Phys. Rev. B 1998, 58, 7120-7135.

(60)

Kang, I.; Wise, F. W. J. Opt. Soc. Am. B 1997, 14, 1632-1646.

(61)

Nirmal, M.; Norris, D. J.; Kuno, M.; Bawendi, M. G.; Efros, A. L.; Rosen, M. Phys. Rev.

Lett. 1995, 75, 3728-3731. (62)

Norris, D. J.; Efros, A. L.; Rosen, M.; Bawendi, M. G. Phys. Rev. B 1996, 53, 16347-

16354. (63)

Ahmed, T.; La-o-vorakiat, C.; Salim, T.; Lam, Y. M.; Chia, E. E. M.; Zhu, J.-X. EPL

(Europhysics Letters) 2014, 108, 67015. (64)

Bockelmann, U.; Bastard, G. Phys. Rev. B 1990, 42, 8947-8951.


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(65)

Page 50 of 50

Benisty, H.; Sotomayor-Torrès, C. M.; Weisbuch, C. Phys. Rev. B 1991, 44, 10945-

10948. (66)

Efros, A. L.; Kharchenko, V. A.; Rosen, M. Solid State Commun. 1995, 93, 281-284.

(67)

Wehrenberg, B. L.; Wang, C.; Guyot-Sionnest, P. J. Phys. Chem. B 2002, 106, 10634-

10640. (68)

Guyot-Sionnest, P.; Shim, M.; Matranga, C.; Hines, M. Phys. Rev. B 1999, 60, R2181-

R2184. (69)

Yang, Y.; Ostrowski, D. P.; France, R. M.; Zhu, K.; van de Lagemaat, J.; Luther, J. M.;

Beard, M. C. Nat. Photon. 2016, 10, 53-59. (70)

Zhu, X. Y.; Podzorov, V. J. Phys. Chem. Lett. 2015, 6, 4758-4761.

(71)

Klimov, V. I. Annu. Rev. Phys. Chem. 2007, 58, 635-673.

(72)

Kawai, H.; Giorgi, G.; Marini, A.; Yamashita, K. Nano Lett. 2015, 15, 3103-3108.

(73)

Huang, L.-y.; Lambrecht, W. R. L. Phys. Rev. B 2014, 90, 195201.

(74)

Huang, L.-y.; Lambrecht, W. R. L. Phys. Rev. B 2013, 88, 165203.

(75)

Shah, J. IEEE J. Quant. Electron. 1988, 24, 276-288.


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