Sub-picosecond polychromatic photoluminescence ...

Invited Paper

Sub-picosecond polychromatic photoluminescence studies of CdSe and PbSe nanodots. Camilla Bonati, Andrea Cannizzo, Frank van Mourik, Majed Chergui* Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratoire de Spectroscopie Ultrarapide, ISIC, Faculté des Sciences de Base, BSP, CH-1015 Lausanne-Dorigny Switzerland

ABSTRACT We present our studies of femtosecond photoluminescence of colloidal solutions of CdSe and PbSe nanocrystals, using polychromatic fluorescence upconversion. Ultrafast relaxation processes are observed in both cases upon excitation at 400 nm and 800 nm respectively. Under moderately high excitation densities we studied the formation and dynamics of biexitons and triexcitons in CdSe nanocrystals. Contrary to earlier reports, all results could be understood without invoking the presence of charged particles. The dynamics of single excitons in PbSe nanocrystals is found to be similar to the case of CdSe, despite the high confinement in the former., The early-time spectra are characterized by emission from several low lying excited states. The kinetics point to a fast sequential cascade process between excited states, governed by energy gaps, and indicate the presence of additional dark states. The first direct measurement of the lowest excited states Huang-Rhys factors excludes that strong electron-phonon coupling mediates the intraband relaxation. Keywords: PbSe, CdSe, polychromatic fluorescence upconversion, bi-exciton, tri-exciton.

INTRODUCTION In semiconductor quantum dots (QD), Coulomb interaction between carriers is greatly enhanced as compared to bulk semiconductors, as a consequence of strong confinement of electronic wavefunctions. Exciton binding energies are an indication of the electron-hole interaction strength; they depend on crystal size and are perhaps one of the most striking features of quantum confinement. However, the exciton is not the only possible type of bound state in a QD: upon creation of several electron-hole pairs in the nanocrystal, these “quasi-particles” interact with each other. The strength of the exciton-exciton interaction provides the binding energy of these multiexciton (or multiparticle) states. The physics of multiparticle states in semiconductor QDs has recently attracted much attention from experimentalists and theoreticians, both for practical and fundamental reasons1,2,3,4,5,6,7. Besides the theoretical interest in studying these effects, the dynamics of multi-particle states is also of practical significance, since light amplification in nanocrystals relies on emission from these states, and amplification lengths of QD-based lasers are directly related to the multiexciton lifetime8. In CdSe, amplified spontaneous emission is known to develop from the lowest bi-exciton transition. In addition, it has recently been shown that amplified spontaneous emission can also occur from a higher excited state, which has been assigned to a triexciton transition, with optical gain twice as high as that of the biexciton9. In this paper, we present time resolved photoluminescence studies of colloidal CdSe quantum dots of different sizes, in the femtosecond-picosecond time range, as a function of excitation fluence. The dynamics of multi-particle states, occurring on (sub-) picosecond time scales will be investigated. The kinetic signature of the different multiexciton states will be used to reconstruct the time-associated spectra of the different contributions and retrieve the binding energies of the excited species. By modelling the early-time power dependence of the spectra, it will be possible to address several fundamental issues related to the formation - relaxation mechanisms of multiexciton states in CdSe QDs. PbSe nanocrystals on the other hand are interesting from a theoretical point of view, since in these crystals strong confinement of both the electron and the hole occurs, whereas in CdSe nanocrystals only the electron is strongly confined. In PbSe, the similarity of electron and hole effective masses is believed to generate mirror-like valence and conduction band states13, with intraband energy spacings that are significantly larger than phonon energies for nanometer size dots19. Therefore, Pbse nanocrystals were expected to display more of the effects associated with a sparse band structure. Especially the phonon-bottle neck for relaxation processes was expected to be more prominent than in the case Ultrafast Phenomena in Semiconductors and Nanostructure Materials XII edited by Jin-Joo Song, Kong-Thon Tsen, Markus Betz, Abdulhakem Y. Elezzabi Proc. of SPIE Vol. 6892, 68920H, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.763813 Proc. of SPIE Vol. 6892 68920H-1 2008 SPIE Digital Library -- Subscriber Archive Copy

of CdSe nanocrystals. Nevertheless, the first single wavelength pump-probe studies on PbSe relaxation kinetics reported rates that are in the same range as what has been found for CdSe nanocrystals. This was explained by postulating strong coupling with phonons. In this work we measured the femtosecond kinetics of the relaxation processes by broadband polychromatic detection of the photoluminescence. This should give us both a better insight in the relaxation dynamics, and an estimate of the strength of the phonon-coupling.

EXPERIMENTAL Spherical CdSe colloidal nanocrystals (size range of 2-4 nm diameter), were prepared by the method of Talapin et al18. This method provides highly monodisperse and fluorescent nanocrystals (size distribution ~ 5%, and quantum yield ~ 35 %). The samples of different size were obtained from the same synthesis at regular time intervals during growth. The dots were dissolved in toluene, and their size was estimated from the position of the first exciton peak according to the calibration tables given by Peng et al.37, and cross-checked by Transmission Electron Microscopy (TEM). Absorption and emission spectra of the samples investigated are shown in the following section The CdSe samples were excited at 400 nm (~3.1 eV) by the frequency-doubled output of an amplified Ti-Sapphire laser (repetition rate 250 kHz). The PbSe samples were excited at 800 nm (~1.55 eV). The time resolved fluorescence signal was detected using the polychromatic PL up-conversion technique described previously10,11 . From the up-converted Raman line of the toluene solvent, time zero was determined in-situ, along with the instrument time response function of 120-150 fs. The colloidal solutions were circulated through a 0.5 mm thick quartz flow cell at a speed of 1 m/s, to ensure constant renewal of the sample. However, considering the repetition rate of the laser and a focal spot size of 50 µm FWHM, we estimate that a particle passing through the focus can be excited 10-15 times. The PbSe colloidal nanoparticles were prepared according to the hot injection method of Yu et al34, and were dissolved in toluene to reach optical densities of ~0.3 at 800 nm, sufficiently low to avoid reabsorption effects. The solution was continuously flown in a 0.5 mm flow cell in order to minimize photodegradation.

RESULTS Figure 1.a shows the time evolution of the fluorescence of 4 nm size CdSe QDs, excited at a pump power of 18 mW (3.7 mJ/cm2 per pulse), corresponding to ~15 absorbed photons per particle. This estimate should be taken as an upper limit, as it has been shown that in as-prepared CdSe colloidal samples, not all the absorbed photons lead to luminescence, due to scattering which is caused by the capping and the chemical environment of the particles12. 1.b shows normalized transient luminescence spectra recorded at different time delays after excitation, along with the steady-state emission spectrum. The early time spectra are significantly broader than the steady-state emission and are composed of two main bands, centred at 2.05 and 2.28 eV. These bands extend on both the high and low energy side of the steady-state luminescence. The transients reveal that the 2.28 eV band dominates the early-time emission; it narrows down and relaxes in a few picoseconds. The 2.05 eV band also narrows down very fast, shifts to the blue and converges to the steady-state band gap emission at longer time delays. Similar spectral features were observed for all dot sizes and transient spectra recorded at 2 ps after excitation are compared with the linear absorption and steady state fluorescence spectra of each sample14. In all cases, the transients exhibit two separated bands: one appears slightly red-shifted and significantly broader with respect to the steady state emission; the other lies on the high energy side and exhibits a faster decay.

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Figure 1. a) two-dimensional false colour scale plot of the time resolved fluorescence signal. The measurements refer to a 4 nm average size QD ensemble, excited with 18 mw (3.7 mJ/cm2). The time axis is linear up to 10 ps, and continues in logarithmic scale. The colour scale corresponds to the signal intensity. b) Normalized transient luminescence spectra at different time delays, along with the steady-state luminescence spectrum.

In order to address the origin of the early time luminescence, we measured the spectral and dynamic evolution of the QDs emission with increasing excitation fluence. The main fluorescence spectral features discussed above exhibit specific power dependence, as their relative amplitudes vary with excitation power. An example is shown in figure 2, which shows normalized transient luminescence spectra of a 3 nm QD ensemble excited with increasing laser fluence: from 0.2 mJ/cm2 to 10 mJ/cm2. This range corresponds to 1-25 average electron-hole pairs excited per dot. With increasing excitation power, the main emission band shifts to lower energies as compared to the steady state emission,


and a low energy wing develops together with a high energy band. This contribution is shifted by 190 - 300 meV (depending on dot size) with respect to the steady state fluorescence; its peak position is not affected by the excitation fluence and depends only on dot size. The presence of this high energy band might seem surprising, since the detection of single exciton emission from highly excited states borders the limits of our time resolution. Indeed, for CdSe QDs it has been shown that the intraband relaxation between neighbouring electronic states occurs on sub-ps time-scales20. This is confirmed by the fast build-up of the transient fluorescence signal, which also occurs in less than 1 ps for all dot sizes investigated. In addition, the heat deposited into the QDs cannot justify population at these emission energies ( T 20 meV). The assignment of band B to the neutral biexciton does not exclude an overlapping contribution of the positive trion, although we do not consider it to be significant. This is justified by the narrow width of the associated band, which is comparable to the steady-state fluorescence inhomogeneous linewidth. Triexciton - XXXp Band D is assigned to triexciton recombination of the lowest P electron and hole states: (1P3/2-1Pe)1(1S3/2-1Se)2→(1S3/21Se)2. This band lies slightly to the red of the 1Se-1S1/2 absorption transition, that has very low oscillator strength27,28, and well below the allowed optical absorption transitions 1Se-2S1/2 and 1Pe-1P3/2 (~150 meV to the red of the latter). Its decay time of several picoseconds excludes it to originate from a high excited state single exciton emission, since intraband relaxation times are typically one order of magnitude shorter. On the other hand, its lifetime is close to the calculated triexciton lifetime29. Its energy position with respect to the band gap, excludes this state to be thermally populated. The assignment of band D as a triexcitonic feature is also given by Caruge et al21, who based it on the power dependence,


which reflects ours. The correlation between the energy of the band and the 1Pe-1P3/2 absorption state, together with its appearance at high laser fluencies, suggest that this multiexcitonic feature originates from a 3 electron-hole pair state: two electrons in the 1Se level, and the third in the 1Pe level. For what concerns the hole states, the 1P3/2 level can be thermally populated at room temperature, since in our range of dot sizes it lies only ~15 meV above the lowest S3/2 hole state30,28. Consequently, the observed band D emission, can originate from the recombination of the P electron and hole states. The recombination of the 1P electron with an S hole state should be parity forbidden. However, a strong mixing of hole and electron states due to increased Coulomb interaction could induce a relaxation of these selection rules31,32,33. In any case, the dominant contribution to the observed emission should be related to the allowed 1Pe-P3/2 recombination, as low temperature measurements show a significant decrease of band D emission21. Based on this assignment of the triexciton, we estimated its binding energy by taking the difference between the energy of band D and the absorption energy of the 1Pe-1P3/2 state. The results are given in table I as a function of dot size. These values should be considered as an upper limit since they do not account for the fluorescence Stokes shift of the 1Pe-1P3/2 transition, which is not known. Triexciton - XXXs Band A typically lies more than 100 meV to the red of the band gap emission. It exhibits a nonlinear behaviour with laser fluence, indicating a multiexcitonic character1,21. Its power dependence is similar to the one retrieved for band D, suggesting an equivalent origin. In addition, their decay rates are very close, and both exhibit large binding energies. Indeed, the energy difference between bands A and D reflects, to some extent, the energy separation between the absorption states 1P3/2,1Pe and 1S3/2,1Se. We attribute band A to triexciton recombination of the S electron and hole states: (1P3/2-1Pe)1(1S3/2-1Se)2→(1P3/2-1Pe)1(1S3/2-1Se)1. The small differences in the decay rates between A and D can be explained by the strong spectral overlap of the former with biexcton and single exciton bands, which eventually affects the outcome of the fit. For this reason, and for the relatively small amplitude of band A, its binding energy should be taken as an upper estimate. Previously35, we proposed that band A could originate from positively charged biexciton recombination. However, this explanation has been excluded by a subsequent theoretical work38, which shows that the positively charged biexciton should rather lie to the high energy side of the single exciton fluorescence line. Within this framework, the authors have already successfully predicted energy and lifetimes of other multiexcitonic/ charged species4, so we preferentially rely on this theoretical interpretation. Burda et al39 reported the observation of a band developing at high pump powers, which appeared as stimulated emission in their transient absorption spectra. Their measurements were performed on 4 nm diameter CdSe nanodots. This band was shifted by ~ 120 meV to the red of the exciton absorption, bearing strong resemblance with the A band in our spectra. They proposed different assignments to it: a Stark shifted exciton band, due to the many e-h pairs formed under high power excitation, absorption by a metastable state, or the formation of a biexciton. Other ultrafast photoluminescence experiments1,21 do not mention the presence of this spectral feature, despite the fact that their early transients exhibit a spectral wing extending at lower energies with respect to the biexciton band. In these works, as already mentioned, the authors did not characterize the fluorescence dynamics over the entire spectral range of interest. The low energy transients were described spectrally by taking into account only the well known single and bi-exciton contribution, eventually overlooking dynamic features of smaller amplitude. The combined spectral and temporal resolution of our polychromatic up-conversion experiment clearly gives us an advantage over single wavelength detection schemes. An additional dimension of the experiment comes from the power dependence of the amplitudes of the bands, which is consistent with the interpretation given above 14. Results PbSe Figure 5.a shows the time evolution of the photoluminescence of 7.2 nm diameter PbSe QDs, excited with a pump fluence of 16 nJ per pulse. Transient spectra at fixed time delays are shown in panel b, and the linear absorption spectrum of the sample is shown in the inset. The transient luminescence is characterized by three main bands: one centred at 0.62 eV, which corresponds to the band gap emission energy, and two bands contributing to the broad high energy side of the emission spectrum, centred at 0.78 eV and 0.92 eV respectively. The high energy components dominate the spectra at early times, but within 2 ps the lowest energy band becomes dominant. The latter does not appreciably shift or broaden during the time evolution of the fluorescence emission. These spectra are representative for all dot sizes investigated14.


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Energy/ eV Figure 5. a) Time- and wavelength-resolved photoluminescence spectra of a 7.2 nm QD sample. The false colour scale represents the emission intensity in arbitrary units. b) Transient luminescence spectra at different time delays (from panel a). Inset: linear absorption spectrum of the sample.

The power dependence of the different spectral contributions is presented in figure 6. At low excitation fluence, it is possible to recognize two spectral features: the band gap emission at 0.62 eV, and a weak high energy band at 0.78 eV. Up to 4 nJ of excitation fluence, the spectra differ only by a partial broadening of this contribution. Above this value, the high energy band begins to extend further towards higher energies, and increases nonlinearly with power. Similar behavior is found in the majority of the samples. Although the band-gap emission does not shift and/or broaden with increasing excitation fluence, its temporal evolution is profoundly altered. By increasing the pump power, a shorter lived component (~26 ps for this dot size) develops in addition to this long term contribution (not shown). In analogy to transient absorption measurements, we assign this short lived feature to biexciton emission41,43.Overall, these results show that (i) in PbSe QDs of different size, relaxation from high lying excited states takes place on very fast timescales, despite the fact that the two lowest transitions are separated by more than 9 LO phonons in the range of sizes investigated (In PbSe, the LO phonon energy is hωLO = 16.7 meV). (ii) The intraband dynamics do not appreciably depend on excitation fluence, showing that for these transitions an alternative relaxation mechanism competes efficiently with multi-particle Auger-type processes. Our results suggest that above a certain excitation threshold, multiexciton states might contribute to the early time emission. For the following analysis the important point is that the position of the lowest two emission bands does not depend on excitation fluence, which means that within our spectral resolution,


the energy of the lower multi-exciton states is identical to the single exciton emission energy. This is explained by the strong dielectric screening in PbSe QDs42, which is related to the high dielectric constant of the material (εPbSe ~ 4.6), which reduces particle-particle interactions. As a consequence, the binding energy of multi-exciton states in PbSe QDs is negligible with respect to the confinement energy of single carriers. Wavelength/ nm 2.6

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Figure 7 Kinetic traces (right panel) at different energies, along with their corresponding biexponential fits (solid lines).The traces are representative, respectively of the dynamics of band I, II, III, (as indicated in the left pannel) and higher energy contributions. Traces are normalized and offset for clarity.


Figure 7 shows representative kinetic traces of the three main bands and of the higher energy contribution observed in emission. These time-traces clearly show a rise (τr) and a decay (τd) component, whose time constants are retrieved performing a biexponential fit. The values of the rise and decay times point to a sequential cascade process among excited states, as the rise time of each spectral component reflects the decay time of the next higher level. The reported values do not depend on the excitation fluence. As already discussed, biexciton states are populated under these excitation conditions and show up as an additional fast decay component at the band gap transition. Our results confirm previous reports of fast relaxation processes. It is difficult to interpret the observed dynamics on the basis of the common assignment of the energy structure of PbSe QDs46, which predicts mirror-like, sparse, electron and hole density of states. In a recent theoretical work, Franceschetti and Zunger45 calculated the electronic structure of PbSe QDs, using an atomistic pseudopotential method. Their calculations show that the valence states constitute a very dense manifold, forming a quasi-continuum of levels near the valence band-edge. Their results contradict the mirror-like symmetry between valence and conduction states predicted by 8 × 8 k·p calculations, associated to a sparse energy structure46. The authors motivate their results by the fact that k·p calculations do not account for the presence of multiple valleys in the Brillouin zone, located along the L-K and K-X directions, which lead to additional valence states. In addition, the existence of a finite potential barrier at the surface of the dot gives rise to a more densely spaced manifold of valence band energy levels, with respect to the case of an infinite potential barrier. These calculations account for the possibility of an additional channel for energy relaxation. The presence of a manifold of hole states suggests the occurrence of electron-hole energy transfer during the intraband relaxation process, in analogy to CdSe QDs where the energy loss rates are comparable to the ones we find in PbSe QDs. Our measurements corroborate this recent theoretical prediction. An additional possible explanation for the observed fast relaxation rates comes from the observation that semiconductor nanocrystals in colloidal solutions generally have a significant ground-state dipole moment48. For PbSe nanocrystals this dipole moment was ascribed the role of coordinating the assembly of particles into nano-wires47. The field of this dipole moment could play a role in mixing electronic states and opening up relaxation pathways. ACKNOWLEDGMENTS This work was supported by the Swiss National Science Foundation via the NCCR: “Quantum Photonics.”

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