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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 24300–24308
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Non-poissonian formation of multiple excitons in photoexcited CdTe colloidal quantum qots by femtosecond nonresonant two-photon absorption

Andrey Gandman, Michal Bronstein-Tojen, Viki Kloper, Merav Muallem, Diana Yanover, Efrat Lifshitz, and Zohar Amitay  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 24300-24308 (2013)
http://dx.doi.org/10.1364/OE.21.024300


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Abstract

Using direct multiexcitonic spectroscopy, we experimentally observe for the first time the non-Poissonian formation of multiple excitons by femtosecond nonresonant two-photon absorption process in semiconductor colloidal quantum dots (QDs). Each of the multiple excitons is individually generated via the absorption of a pair of photons during the femtosecond pulse irradiation. The non-Poissonian distribution of the generated excitons is reflected as a non-quadratic dependence on the pulse intensity of the average number of excitons per QD. This is the main observation of the present work. It is explained by a multiexcitonic formation model that is based on the phenomenon of intrapulse state filling of the few quantum electronic states accessed by the two-photon transitions. The experiments are conducted with 3.9-nm CdTe QDs in room-temperature hexane solution using the femtosecond pump-probe transient absorption technique, where an intense pump pulse generates the excitons and a weak probe pulse measures their number via intraband one-photon absorption.

© 2013 OSA

1. Introduction

When a semiconductor colloidal quantum dot (QD) [1

1. V. I. Klimov, Nanocrystal Quantum Dots (CRC, 2010). [CrossRef]

] is irradiated by photons that their energy is much smaller than the full bandgap energy but larger than its half, one-photon absorption is not possible and the dominant absorption process is the nonresonant two-photon absorption. It is a process of both fundamental and technological importance and, hence, it has previously been investigated in many QDs studies [2

2. E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kartner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74, 3927 (1999). [CrossRef]

17

17. Y. Qu, W. Ji, Y. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007). [CrossRef]

]. Possible novel applications include ultrafast optical switching for optical communications, data storage and optical limiting applications [2

2. E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kartner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74, 3927 (1999). [CrossRef]

] as well as in-vivo biological imaging [3

3. D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003). [CrossRef] [PubMed]

].

However, these past two-photon studies have been mostly limited to the single-excitonic regime, where no more than one exciton is generated in a single QD. So, one of the unique optical properties of QDs of highly efficient multiple exciton formation (MEF) within a single QD [18

18. V. I. Klimov, “Spectral and Dynamical Properties of Multiexcitons in Semiconductor Nanocrystals,” Annu. Rev. Phys. Chem. 58, 635 (2007). [CrossRef]

] has not been fully addressed in the context of two-photon absorption. In the corresponding MEF process each of the multiple excitons is individually generated via the non-resonant absorption of a pair of photons and, consequently, the whole set of multiple excitons is formed by the absorption of several pairs of photons during the pulse irradiation. For the sake of clear terminology, we emphasize that by MEF we do not refer to what is usually referred to as multiple exciton generation (MEG) [19

19. A. J. Nozik, “Multiple exciton generation in semiconductor quantum dots,” Chem. Phys. Lett. 457, 3–11 (2009). [CrossRef]

], that is, the carrier multiplication (CM) [20

20. J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41, 1810 (2008).

] process in which the absorption of a single high-energy photon results in creation of several excitons.

Here, we investigate with direct multiexcitonic spectroscopy the corresponding MEF process generated via the nonresonant two-photon absorption. Most importantly, our study extends beyond the MEF regime that is described by Poisson statistics into a regime of non-Poissonian MEF. This is the main innovation of our work.

2. Experiment

The present experiments are conducted at room temperature with CdTe QDs having a mean diameter of 3.9 nm (2.06 eV bandgap energy corresponding to the 1Se-1S3/2,h state) and 5% size distribution. CdTe QDs are chosen as the model system for the study due to the applicable band gap for their nonresonant two-photon absorption, excellent stability, good quantum yield, very simple crystal structure, and low degeneracy of the exciton states. The QDs are prepared according to the synthesis procedure given in [21

21. V. Kloper, R. Osovsky, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The growth of CdTe nanocrystals using in situ formed Cd0 crystalline particles,” J. Phys. Chem. C 111, 10336 (2007). [CrossRef]

]. The linear optical properties of the QDs are discussed in detail in [22

22. R. Osovsky, V. Kloper, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The Influience of small deviation from a spherical shape on the electronic and optical properties of CdTe nanocrystal quantum dots,” J. Phys. Chem. C 111, 10841 (2007). [CrossRef]

]. After the synthesis, the oleic acid/trioctylphosphine capped CdTe QDs are isolated as a clean powder of high-quality, with nearly spherical shape. Then they are dissolved again in n-hexane and placed into a thin quartz cuvette. Determination of the QDs size and its distribution is performed by the analysis of both the HR-TEM spectrographs and the static one-photon absorption measurements [21

21. V. Kloper, R. Osovsky, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The growth of CdTe nanocrystals using in situ formed Cd0 crystalline particles,” J. Phys. Chem. C 111, 10336 (2007). [CrossRef]

, 22

22. R. Osovsky, V. Kloper, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The Influience of small deviation from a spherical shape on the electronic and optical properties of CdTe nanocrystal quantum dots,” J. Phys. Chem. C 111, 10841 (2007). [CrossRef]

].

3. Experimental and Theoretical-Model Results and Discussion

The intraTA probe signal, Δα(τ), measured at a pump-probe delay time τ is proportional to the average number of excitons per QD, 〈N(τ)〉, at the time of probing. Hence, 〈N(τ)〉 = Δα(τ)/Ksig_exc, with Ksig_exc being the corresponding proportionality constant. This is true as long as our near-infrared one-photon intraband absorption cross-section per exciton is independent of the number of excitons residing in the QD. Since the one-photon intraband transition induced by the near-infrared probe pulse (photon energy of about 1.53 eV) excites the QD far above the band-edge into a region of very high density of hole states, this situation indeed holds in our case. Figure 1 presents several examples of the experimental results of 〈N(τ)〉 as a function of τ, up to τ =50 ps, for different pump pulse energies, together with the corresponding values obtained for 〈N0〉. The results clearly show the increase in 〈N0〉 with the increase in the pulse intensity, and the corresponding evolution from the single-excitonic [〈N0〉=0.35 in Fig. 1(a)] to the multi-excitonic [〈N0〉=3.80 in Fig. 1(f)] two-photon absorption regime.

Fig. 1 Examples of experimental results for the average number of excitons per QD as a function of the pump-probe delay measured with different pump pulse energies. Each panel indicates the corresponding pump pulse energy and the value obtained for the average number of excitons per QD generated by the femtosecond pump pulse via nonresonant two-photon absorption, 〈N0〉. Note the different scale of the vertical axis in the different panels.

The experimental value of Ksig_exc is obtained using the saturation behavior of the asymptotic probe signal, Δαasympα (τ =45–50ps), that occurs with the increase in pump pulse energy. As explained below, Δαasymp is measured at pump-probe delays when each excited QD contains a single exciton, which is left after the cascaded decay of the multiple excitons initially generated in the QD. Thus, Δαasymp is a measure of the total number of excited QDs that increases with the pump-pulse energy, until it reaches saturation when all the QDs in the interaction region are excited. At saturation, Δαasymp_sat corresponds to 〈Nasymp=1. Hence, one obtains that Ksig_excαasym_sat and 〈N(τ)〉=Δα (τ)/Δαasymp_sat. Such a saturation behavior of the asymptotic signal is indeed seen in our results of Fig. 1.

The decay behavior of the measured 〈N(τ)〉 traces reflects a non-radiative cascaded mul-tiexcitonic decay of the generated excitons that proceeds as long as there is more than one exciton in the QD. In each step, for m>1, m excitons in the QD decay into m−1 excitons. It is commonly interpreted to result from non-radiative Auger recombination of the charge carriers in the QD [24

24. V. I. Klimov, A. A. Mikhailovsky, D. W. McBranch, C. A. Leatherdale, and M. G. Bawendi, “Quantization of multiparticle Auger rates in semiconductor quantum dots,” Science 287, 1011–1013 (2000). [CrossRef] [PubMed]

]. Initially, during approximately the first 2 ps after the excitation, the multiple (hot) excitons generated by the two-photon process undergo a fast intraband relaxation to their lowest multiexcitonic energy level. The end of this relaxation correlates well with the delays at which the measured traces have their highest values. Then, multiexcitonic decay is measured on a timescale of 35–40 ps, after which each excited QD is left with only a single exciton that decays radiatively on nanosecond timescale [22

22. R. Osovsky, V. Kloper, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The Influience of small deviation from a spherical shape on the electronic and optical properties of CdTe nanocrystal quantum dots,” J. Phys. Chem. C 111, 10841 (2007). [CrossRef]

]. Overall, the measured traces of 〈N(τ)〉 exhibit a multi-exponential picosecond decay behavior, where the decay constants of the various components correspond to the various lifetimes of multi-excitons of a different order m. By analyzing the total sum over all the 〈N(τ)〉 data, we have extracted the bi-excitonic (m=2) and tri-excitonic (m=3) lifetimes as τ2=12.2±2 ps and τ3=4.5±1.5 ps, respectively. For each trace, the value of 〈N0〉 and its error are obtained by extrapolating the 〈N(τ)〉 results to time zero. It is done by averaging over the results obtained by numerically extrapolating the measured data up to 10 ps using 2nd-, 3rd-, and 4th-order polynomials.

Based on the presented traces, we conclude that, within the experimental noise and error bars, the transient absorption results are not affected by surface trapping of electrons and/or holes. The signal effect of surface trapping of (cold) carriers residing at the bottom of their band can be ruled out due the time independence of the measured signal at larger delay times (25–50 ps) for low excitation regimes (see Figs. 1(a) and 1(b)). The signal effect of trapping of excited (hot) carriers can be ruled out due to the expected saturation behavior that is observed for the measured asymptotic signal as a function of the pump pulse energy.

Figure 2 presents the full set of the experimental values of 〈N0〉 as a function of the pump pulse energy Epump (circles) together with several analysis lines. One is a line of quadratic dependence on the pulse energy and intensity (black line) corresponding to N0quad_intensity_dep=K˜TPACdTe×Epump2=KTPACdTe×I0,pump2, where I0,pump is the peak intensity of the pump pulse with energy Epump. The presented line corresponds to KTPACdTe=2.094×105 cm4/W2 that, based on our experimental parameters, corresponds to the theoretical value of the single-excitonic two-photon absorption cross-section, σTPA,theoCdTe,3.9nm=11500 GM (Goeppert-Mayer), calculated in [11

11. Y. Qu and W. Ji, “Two-photon absorption of quantum dots in the regime of very strong confinement: size and wavelength dependence,” J. Opt. Soc. Am. B 26, 1897 (2009).

] for 3.9-nm CdTe QDs sample. This theoretical cross-section value is in excellent agreement with our experimental value of σTPA,expCdTe,3.9nm=12222±1633 GM that is obtained from fitting our 〈N0〉 results at the three lower pulse energies to a quadratic intensity dependence. As seen, the full set of experimental results of 〈N0〉 significantly deviates from a quadratic dependence on I0,pump and Epump; the results fit this dependence only at the region of the lower 〈N0〉 values. As we explain, the meaning of this observed non-quadratic intensity dependence is the non-Poissonian formation of multiple excitons via nonresonant two-photon absorption.

The instantaneous probability at time t for an intrapulse exciton generation in a given QD via two-photon absorption is pTPA(t) ∝ sTPA(t) × [Ipump(t)]2, where sTPA(t) is the instantaneous effective two-photon absorption cross-section and Ipump(t) = g(t) × I0,pump is the instantaneous pump pulse intensity with g(t) as the pulse shape (here, 87-fs Gaussian). The total exciton generation probability is then obtained from integration over the full pulse as PTPA=pTPA(t)dtsTPA(t)[g(t)]2I0,pump2dt. Hence, for a given pulse shape, PTPA exhibits a quadratic dependence on I0,pump only if sTPA(t) is time-independent with a constant value along the entire pulse irradiation. This constant value is by definition equal to the two-photon absorption cross-section for generating the first exciton in the QD, σTPA. When an ensemble of QDs is considered, since 〈N0〉 ∝ PTPA, the same conclusion also holds for the resulting values of 〈N0〉. In the single-excitonic regime, sTPA(t) = σTPA always holds since no more than one exciton is generated in a QD, so the corresponding 〈N0〉 values always exhibit a quadratic intensity dependence [4

4. K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement-induced valence-band mixing in CdS quantum dots observed by two-photon spectroscopy,” Phys. Rev. B 45, 3465–3468 (1992). [CrossRef]

15

15. G. Xing, W. Ji, Y. Zheng, and J. Y. Ying, “Two- and three-photon absorption of semiconductor quantum dots in the vicinity of half of lowest exciton energy,” Appl. Phys. Lett. 93, 241114 (2008). [CrossRef]

]. However, in the multiexcitonic regime, the occurrence of sTPA(t) = σTPA and quadratic intensity dependence happens only if the generation of a new exciton is unaffected by the presence of other excitons in the QD i.e., it is effectively independent of the number of excitons already existing in the QD. Physically, such independence among different events of exciton generation in the same QD also implies that the multiple excitons generated by a given pulse in a QD’s ensemble follow the Poisson distribution, with PPoisson(m)=N0mm!exp(N0) being the probability of generating m excitons in a QD when 〈N0〉 = ∑mm × PPoisson(m) is the corresponding mean. Hence, the non-quadratic intensity dependence of 〈N0〉 measured here reflects multiexcitonic formation by femtosecond nonresonant two-photon absorption with a distribution that significantly deviates from the Poisson distribution. This is the main observation of this research.

Fig. 2 Results for the average number of excitons per QD generated by the femtosecond pump pulse, 〈N0〉, as a function of the pump pulse energy. Shown are: (i) the experimental results (circles), (ii) a line of quadratic intensity dependence corresponding to Poissonian multiexcitonic formation (MEF) (black line), and (iii–iv) the results calculated for the full model of non-Poissonian MEF based on intrapulse electronic state filling (red line) and for this model without the inclusion of multiexcitonic transition shift (blue line). See text for details.

Another multiexcitonic effect that potentially might also lead to the attenuation of the effective two-photon absorption cross-section is the shift to lower energies that the excitonic transitions experience due to the exciton-exciton interactions in the QD [18

18. V. I. Klimov, “Spectral and Dynamical Properties of Multiexcitons in Semiconductor Nanocrystals,” Annu. Rev. Phys. Chem. 58, 635 (2007). [CrossRef]

, 25

25. R. Osovsky, D. Cheskis, V. Kloper, A. Sashchiuk, M. Kroner, and E. Lifshitz, “Continuous-Wave Pumping of Multiexciton Bands in the Photoluminescence Spectrum of a Single CdTe-CdSe Core-Shell Colloidal Quantum Dot,” Phys. Rev. Lett. 102, 197401 (2009). [CrossRef] [PubMed]

, 26

26. S. L. Sewall, R. R. Cooney, E. A. Dias, P. Tyagi, and P. Kambhampati, “State-resolved observation in real time of the structural dynamics of multiexcitons in semiconductor nanocrystals,” Phys. Rev. B 84, 235304 (2011). [CrossRef]

]. At each point along the multiexcitonic formation process, such a shift might increase or decrease the (partial) cross-section associated with a given two-photon transition, since it changes the relative position and overlap of the corresponding absorption line and pump pulse spectrum. The corresponding changes in the various partial cross-sections and total cross-section depend, both in sign and magnitude, on the specifics of the QD system and pump pulse. For our case, the results show that the dominant phenomenon for explaining our observation of non-Poissonian multiexcitonic formation is the state-filling effect and not the transition-shifting effect. This is seen in Fig. 2, which presents our model results for the case of zero transition shift (blue line) and for the representative model case with a transition-shift-per-exciton of Δper_exc = −15 meV [25

25. R. Osovsky, D. Cheskis, V. Kloper, A. Sashchiuk, M. Kroner, and E. Lifshitz, “Continuous-Wave Pumping of Multiexciton Bands in the Photoluminescence Spectrum of a Single CdTe-CdSe Core-Shell Colloidal Quantum Dot,” Phys. Rev. Lett. 102, 197401 (2009). [CrossRef] [PubMed]

, 26

26. S. L. Sewall, R. R. Cooney, E. A. Dias, P. Tyagi, and P. Kambhampati, “State-resolved observation in real time of the structural dynamics of multiexcitons in semiconductor nanocrystals,” Phys. Rev. B 84, 235304 (2011). [CrossRef]

] (red line). The latter means that with (m − 1) excitons in the QD, i.e., for the generation of the mth exciton, all the two-photon transition energies are different by an amount of (m − 1)×Δper_exc from their values with zero excitons in the QD. As seen, the difference between the shifting and no-shifting cases is not significant for the deviation of our measured 〈N0〉 values (circles) from the values of the Poissonian multiexcitonic formation (black line).

The CdTe information used in our model calculations is taken from the detailed theoretical study of Qu and Ji [11

11. Y. Qu and W. Ji, “Two-photon absorption of quantum dots in the regime of very strong confinement: size and wavelength dependence,” J. Opt. Soc. Am. B 26, 1897 (2009).

] conducted for the single-excitonic nonresonant two-photon absorption in CdTe QDs. Based on this study, the various single-excitonic quantum states that are resonantly accessed here via two-photon transitions by our pump pulse are 1Se–2P3/2,h, 1P1/2,e– 2S3/2,h and 1P3/2,e–2S3/2,h having electronic degeneracy of DG=2, 2 and 4, respectively. The state-specific information that depends on the QD diameter includes here the transition (excitation) energy and partial single-excitonic two-photon absorption cross-section ( σk,TPACdTe,Dnm) corresponding to each of these excitonic states (k). Summing up all the partial cross-sections gives the total single-excitonic two-photon absorption cross-section σTPACdTe,Dnm=kσk,TPACdTe,Dnm. For 3.9-nm CdTe QD, the transition energies are 2.92, 2.98 and 3.00 eV, respectively. The corresponding total single-excitonic cross-section for the present excitation is σTPACdTe,3.9nm=11500 GM (as supported also by our experimental results; see above), with a ratio of 0.07 : 0.07 : 0.86 between the partial cross sections σk,TPACdTe,3.9nm of the various excitonic states, respectively. It is worth mentioning that the cross-sections have been calculated in [11

11. Y. Qu and W. Ji, “Two-photon absorption of quantum dots in the regime of very strong confinement: size and wavelength dependence,” J. Opt. Soc. Am. B 26, 1897 (2009).

] by considering all the possible two-photon transition pathways to each of the final excitonic states, with their corresponding transition energies, dipole-moment matrix elements and intermediate-state detunings. In addition to all these theoretical characteristics, the homogeneous broadening of our room-temperature experiment is accounted for by applying a homogeneous linewidth of 0.1 eV [21

21. V. Kloper, R. Osovsky, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The growth of CdTe nanocrystals using in situ formed Cd0 crystalline particles,” J. Phys. Chem. C 111, 10336 (2007). [CrossRef]

, 22

22. R. Osovsky, V. Kloper, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The Influience of small deviation from a spherical shape on the electronic and optical properties of CdTe nanocrystal quantum dots,” J. Phys. Chem. C 111, 10841 (2007). [CrossRef]

, 27

27. M. R. Salvador, M. A. Hines, and G. D. Scholes, “Exciton-bath coupling and inhomogeneous broadening in the optical spectroscopy of semiconductor quantum dots,” J. Chem. Phys. 118, 9380–9388 (2003). [CrossRef]

] for each two-photon transition.

Based on the above model and information, the dynamics of the intrapulse multiexcitonic formation in a given CdTe QD of diameter D, which experiences a temporal pump pulse intensity Ipump(t), is numerically calculated over a time grid using the Monte Carlo method by following the time-dependent population of each of the electronic states corresponding to the different excitonic states accessed by the two-photon excitation. The probability pk,TPA(t) of generating a new exciton at state k at the time interval between t and t+dt is determined by sk,TPACdTe,Dnm(t)[Ipump(t)]2, where sk,TPACdTe,Dnm(t) is the corresponding effective partial two-photon absorption cross-section at time t. Based on our model, it is given by sk,TPACdTe,Dnm(t)=[DGkmk(e)(t)DGk]×Tk(m(t);Δper_exc)×σk,TPACdTe,Dnm, where DGk and mk(e)(t) are, respectively, the degeneracy and instantaneous population of the electronic state corresponding to the excitonic state k. As defined above, σk,TPACdTe,Dnm is the partial single-excitonic two-photon cross-section of state k. The factor Tk originates from the multiexcitonic change in the transition energy of state k that amounts to m(t) × Δper_exc, where m(t) is the total number of excitons in the QD at time t(m(t)=kmk(e)(t)) ; It is equal to the ratio between the values of the overlap integral of the pump pulse spectrum and absorption line of state k in the shifted-line case and unshifted-line case.

For a given pump pulse energy, such calculations are conducted for an array of CdTe QDs of a given diameter that are uniformly distributed over the radial spatial intensity profile of the pump laser beam, Ipump(t; r) = I0,pump(r) × g(t) where r is the radial distance from the pump laser beam axis. After the pump pulse ending, the probed 〈N0〉 value for this array is obtained by averaging over the final number of excitons in the different QDs of the array according to the spatial profile of the probe laser beam, i.e., the contribution from each QD is weighted by the relative intensity of the probe laser beam at the position of the QD. The final 〈N0〉 value calculated for our experiment with a given pump pulse energy is obtained by applying a proper (weighted) averaging over the results calculated for several representative QD diameters within the size distribution of our sample. The model results in Fig. 2 present such calculated 〈N0〉 values for different pump pulse energies. Their excellent quantitative agreement with the experimental results strongly supports the identification of the intrapulse electronic state filling as the key element behind the observed non-Poissonian multiexcitonic formation.

4. Conclusion

In conclusion, using direct multiexcitonic spectroscopy, we have experimentally observed for the first time the phenomenon of non-Poissonian formation of multiple excitons by femtosecond nonresonant two-photon absorption process in QDs. The non-Poissonian nature of the process is reflected as a non-quadratic dependence on the exciting pulse intensity of the average number of generated excitons per QD. The corresponding near-infrared pump-probe transient absorption experiments have been conducted with a room-temperature ensemble of 3.9-nm CdTe QDs. The experimental observation is explained by a multiexcitonic formation model that its main ingredient is the phenomenon of intrapulse state filling of the few quantum electronic states accessed by the two-photon transitions. The present study is not limited to a specific system and can be extended to other semiconductor nanocrystals and other excitation wavelengths for further fundamental studies and application development.

Acknowledgments

This research was supported by The Israel Science Foundation (Grant No. 1450/10) and by The James Franck Program in Laser Matter Interaction.

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S. A. Blanton, A. Dehestani, P. C. Lin, and P. Guyot-Sionnest, “Photoluminescence of single semiconductor nanocrystallites by two-photon excitation microscopy,” Chem. Phys. Lett. 229, 317–322 (1994). [CrossRef]

15.

G. Xing, W. Ji, Y. Zheng, and J. Y. Ying, “Two- and three-photon absorption of semiconductor quantum dots in the vicinity of half of lowest exciton energy,” Appl. Phys. Lett. 93, 241114 (2008). [CrossRef]

16.

J. He, J. Mi, H. Li, and W. Ji, “Observation of Interband Two-Photon Absorption Saturation in CdS Nanocrystals,” J. Phys. Chem. B 109, 19184–19187 (2005). [CrossRef]

17.

Y. Qu, W. Ji, Y. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007). [CrossRef]

18.

V. I. Klimov, “Spectral and Dynamical Properties of Multiexcitons in Semiconductor Nanocrystals,” Annu. Rev. Phys. Chem. 58, 635 (2007). [CrossRef]

19.

A. J. Nozik, “Multiple exciton generation in semiconductor quantum dots,” Chem. Phys. Lett. 457, 3–11 (2009). [CrossRef]

20.

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41, 1810 (2008).

21.

V. Kloper, R. Osovsky, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The growth of CdTe nanocrystals using in situ formed Cd0 crystalline particles,” J. Phys. Chem. C 111, 10336 (2007). [CrossRef]

22.

R. Osovsky, V. Kloper, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The Influience of small deviation from a spherical shape on the electronic and optical properties of CdTe nanocrystal quantum dots,” J. Phys. Chem. C 111, 10841 (2007). [CrossRef]

23.

H. Zhu, N Song, W. Rodriguez-Cordoba, and T. Lian, “Wave Function Engineering for Efficient Extraction of up to Nineteen Electrons from One CdSe/CdS Quasi-Type II Quantum Dot,” J. Am. Chem. Soc. 134, 4250–4257 (2012). [CrossRef] [PubMed]

24.

V. I. Klimov, A. A. Mikhailovsky, D. W. McBranch, C. A. Leatherdale, and M. G. Bawendi, “Quantization of multiparticle Auger rates in semiconductor quantum dots,” Science 287, 1011–1013 (2000). [CrossRef] [PubMed]

25.

R. Osovsky, D. Cheskis, V. Kloper, A. Sashchiuk, M. Kroner, and E. Lifshitz, “Continuous-Wave Pumping of Multiexciton Bands in the Photoluminescence Spectrum of a Single CdTe-CdSe Core-Shell Colloidal Quantum Dot,” Phys. Rev. Lett. 102, 197401 (2009). [CrossRef] [PubMed]

26.

S. L. Sewall, R. R. Cooney, E. A. Dias, P. Tyagi, and P. Kambhampati, “State-resolved observation in real time of the structural dynamics of multiexcitons in semiconductor nanocrystals,” Phys. Rev. B 84, 235304 (2011). [CrossRef]

27.

M. R. Salvador, M. A. Hines, and G. D. Scholes, “Exciton-bath coupling and inhomogeneous broadening in the optical spectroscopy of semiconductor quantum dots,” J. Chem. Phys. 118, 9380–9388 (2003). [CrossRef]

OCIS Codes
(190.4180) Nonlinear optics : Multiphoton processes
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(320.7100) Ultrafast optics : Ultrafast measurements
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors

ToC Category:
Nonlinear Optics

History
Original Manuscript: July 31, 2013
Manuscript Accepted: September 3, 2013
Published: October 3, 2013

Citation
Andrey Gandman, Michal Bronstein-Tojen, Viki Kloper, Merav Muallem, Diana Yanover, Efrat Lifshitz, and Zohar Amitay, "Non-poissonian formation of multiple excitons in photoexcited CdTe colloidal quantum qots by femtosecond nonresonant two-photon absorption," Opt. Express 21, 24300-24308 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-24300


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References

  1. V. I. Klimov, Nanocrystal Quantum Dots (CRC, 2010). [CrossRef]
  2. E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kartner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett.74, 3927 (1999). [CrossRef]
  3. D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science300, 1434 (2003). [CrossRef] [PubMed]
  4. K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement-induced valence-band mixing in CdS quantum dots observed by two-photon spectroscopy,” Phys. Rev. B45, 3465–3468 (1992). [CrossRef]
  5. R. Tommasi, M. Lepore, M. Ferrara, and I. M. Catalano, “Observation of high-index states in CdS1−x Sex semi-conductor microcrystallites by two-photon spectroscopy,” Phys. Rev. B46, 12261–12265 (1992). [CrossRef]
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  7. L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B75, 075325 (2007). [CrossRef]
  8. G. S. He, K. -T. Yong, Q. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, “Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range,” Opt. Express15, 12818 (2007). [CrossRef] [PubMed]
  9. S. -C. Pu, M. -J. Yang, C. -C. Hsu, C. -W. Lai, C. -C. Hsieh, S. H. Lin, Y. -M. Cheng, and P. -T. Chou, “The Empirical Correlation Between Size and Two-Photon Absorption Cross Section of CdSe and CdTe Quantum Dots.” Small2, 1308 (2006). [CrossRef] [PubMed]
  10. L. Pan, N. Tamai, K. Kamada, and S. Deki, “Nonlinear optical properties of thiol-capped CdTe quantum dots in nonresonant region,” Appl. Phys. Lett.91, 051902 (2007). [CrossRef]
  11. Y. Qu and W. Ji, “Two-photon absorption of quantum dots in the regime of very strong confinement: size and wavelength dependence,” J. Opt. Soc. Am. B26, 1897 (2009).
  12. J. Khatei, C. S. Suchand Sandeep, R. Philip, and K. S. R. Koteswara Rao, “Near-resonant two-photon absorption in luminescent CdTe quantum dots,” Appl. Phys. Lett.100, 081901 (2012). [CrossRef]
  13. A. D. Lad, P. P. Kiran, D. More, G. Ravindra Kumar, and S. Mahamuni, “Two-photon absorption in ZnSe and ZnSe/ZnS core/shell quantum structures,” Appl. Phys. Lett.92, 043126 (2008). [CrossRef]
  14. S. A. Blanton, A. Dehestani, P. C. Lin, and P. Guyot-Sionnest, “Photoluminescence of single semiconductor nanocrystallites by two-photon excitation microscopy,” Chem. Phys. Lett.229, 317–322 (1994). [CrossRef]
  15. G. Xing, W. Ji, Y. Zheng, and J. Y. Ying, “Two- and three-photon absorption of semiconductor quantum dots in the vicinity of half of lowest exciton energy,” Appl. Phys. Lett.93, 241114 (2008). [CrossRef]
  16. J. He, J. Mi, H. Li, and W. Ji, “Observation of Interband Two-Photon Absorption Saturation in CdS Nanocrystals,” J. Phys. Chem. B109, 19184–19187 (2005). [CrossRef]
  17. Y. Qu, W. Ji, Y. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett.90, 133112 (2007). [CrossRef]
  18. V. I. Klimov, “Spectral and Dynamical Properties of Multiexcitons in Semiconductor Nanocrystals,” Annu. Rev. Phys. Chem.58, 635 (2007). [CrossRef]
  19. A. J. Nozik, “Multiple exciton generation in semiconductor quantum dots,” Chem. Phys. Lett.457, 3–11 (2009). [CrossRef]
  20. J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res.41, 1810 (2008).
  21. V. Kloper, R. Osovsky, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The growth of CdTe nanocrystals using in situ formed Cd0 crystalline particles,” J. Phys. Chem. C111, 10336 (2007). [CrossRef]
  22. R. Osovsky, V. Kloper, J. Kolny-Olesiak, A. Sashchiuk, and E. Lifshitz, “The Influience of small deviation from a spherical shape on the electronic and optical properties of CdTe nanocrystal quantum dots,” J. Phys. Chem. C111, 10841 (2007). [CrossRef]
  23. H. Zhu, N Song, W. Rodriguez-Cordoba, and T. Lian, “Wave Function Engineering for Efficient Extraction of up to Nineteen Electrons from One CdSe/CdS Quasi-Type II Quantum Dot,” J. Am. Chem. Soc.134, 4250–4257 (2012). [CrossRef] [PubMed]
  24. V. I. Klimov, A. A. Mikhailovsky, D. W. McBranch, C. A. Leatherdale, and M. G. Bawendi, “Quantization of multiparticle Auger rates in semiconductor quantum dots,” Science287, 1011–1013 (2000). [CrossRef] [PubMed]
  25. R. Osovsky, D. Cheskis, V. Kloper, A. Sashchiuk, M. Kroner, and E. Lifshitz, “Continuous-Wave Pumping of Multiexciton Bands in the Photoluminescence Spectrum of a Single CdTe-CdSe Core-Shell Colloidal Quantum Dot,” Phys. Rev. Lett.102, 197401 (2009). [CrossRef] [PubMed]
  26. S. L. Sewall, R. R. Cooney, E. A. Dias, P. Tyagi, and P. Kambhampati, “State-resolved observation in real time of the structural dynamics of multiexcitons in semiconductor nanocrystals,” Phys. Rev. B84, 235304 (2011). [CrossRef]
  27. M. R. Salvador, M. A. Hines, and G. D. Scholes, “Exciton-bath coupling and inhomogeneous broadening in the optical spectroscopy of semiconductor quantum dots,” J. Chem. Phys.118, 9380–9388 (2003). [CrossRef]

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