NANO LETTERS
Nature of the Second Optical Transition in PbSe Nanocrystals
2008 Vol. 8, No. 7 2112-2117
M. Tuan Trinh,† Arjan J. Houtepen,*,† Juleon M. Schins,* Jorge Piris, and Laurens D. A. Siebbeles Optoelectronic Materials, Faculty of Applied Sciences, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received April 17, 2008; Revised Manuscript Received May 19, 2008
ABSTRACT The second peak in the optical absorption spectrum of PbSe nanocrystals is arguably the most discussed optical transition in semiconductor nanocrystals. Ten years of scientific debate have produced many theoretical and experimental claims for the assignment of this feature as the 1Pe1Ph as well as the 1Sh,e1Pe,h transitions. We studied the nature of this absorption feature by pump-probe spectroscopy, exactly controlling the occupation of the states involved, and present conclusive evidence that the optical transition involves neither 1Se nor 1Sh states. This suggests that it is the 1Ph1Pe transition that gives rise to the second peak in the absorption spectrum of PbSe nanocrystals.
Colloidal semiconductor nanocrystals (NCs) are often praised for their sharp, size-tunable optical transitions. These make them important candidates for technological applications such as light-emitting diodes, solid state lasers, and solar cells.1–3 Consequently, the understanding of the optical transitions in NCs is of both fundamental and technological interest. The optical absorption spectrum of the prototypical CdSe NCs has been explained satisfactorily. Norris et al. studied the optical transitions in 1995 by size-narrowing excitation spectroscopy and explained their results successfully describing the energy levels by quantum numbers of the angular momentum of the envelope wave function and, for hole states, the total spin-orbit coupled momentum (e.g., 1S3/21Se).4 In contrast, a similar assignment of the peaks in the optical absorption spectrum of PbSe NCs, one of the most studied NC materials in the past five years, has proven significantly more difficult.5–13 The exciton Bohr radius in bulk PbSe is particularly large: 46 nm. As a result, quantum confinement is stronger in PbSe NCs than in most other materials, which results in sharp, well-separated peaks in the optical absorption spectrum, shown in Figure 1. The first absorption feature (of the lowest energy) corresponds to an interband transition with both electrons and holes having a 1S envelope function: 1Sh1Se. However, the assignment of the second peak has generated an intense debate. Comparing the energy of this transition to results from 4-band k·p calculations, Du et al. attributed it to 1Sh1Pe and 1Ph1Se transitions12,14 (in short notation: 1Sh,e1Pe,h). This assignment is controversial since the * Corresponding author. E-mail:
[email protected] (A.J.H.) and
[email protected] (J.M.S.). † A.J.H. and M.T.T. have contributed equally to this work. 10.1021/nl8010963 CCC: $40.75 Published on Web 05/30/2008
2008 American Chemical Society
Figure 1. Optical absorption spectrum of 6.8 nm PbSe nanocrystals.
1Sh,e1Pe,h transitions are optically forbidden.15–17 Despite the controversy about the 1Sh,e1Pe,h transition strength, this assignment was also obtained by tight binding calculations,18 and experimental evidence in apparent agreement with this assignment was presented in refs 6, 7, 10, and 11. These experiments are discussed in detail below. However, Liljeroth et al. measured the single particle energy levels in PbSe NCs using scanning tunneling spectroscopy and observed from their measurements that the energy of the second optical transition matches the energy difference between the second hole and the second electron resonances.8 They consequently concluded that this feature results from the 1Ph1Pe transition. Pseudopotential calculations by An et al. have supported the assignment of the
second absorption feature as a 1Ph1Pe transition.9 According to these calculations, the hole levels are more closely spaced than the electron levels, as a result of coupling between multiple valence band maxima in the band structure. This is not the case in the effective mass12,14 and tight-binding calculations18 mentioned above, which predict symmetric electron and hole energy levels. The more closely spaced hole manifold leads to a calculated 1Ph1Pe transition energy that matches the energy of the second peak in the absorption spectrum. Thus, there are experimental and theoretical claims for both the 1Sh,e1Pe,h and the 1Ph1Pe assignments. Deciding this debate is important to test the validity of the pseudopotential9 and tight-binding18 models and thereby to improve the understanding of the optical properties of semiconductor NCs. In the experiments presented here, we carefully controlled the occupation of the 1Sh and 1Se levels, which are 8-fold degenerate, using time- and energy-resolved pump-probe spectroscopy. The second transition in the absorption spectrum is not bleached, even if four electrons and four holes are introduced into the 1S levels. This shows beyond doubt that the 1S levels are not involved in the second optical transition and suggests that it is the 1Ph1Pe transition that is responsible for the second peak in the absorption spectrum of PbSe NCs. The experimental results of refs 6, 7, 10, and 11, which are apparently in support of the 1Sh,e1Pe,h assignment, are discussed in light of our new experimental evidence. PbSe nanocrystals were prepared following the recipe of Talapin and Murray.19 Lead(II) oleate was prepared from 2.16 g of lead(II) acetate trihydrate and 7.3 mL of oleic acid by heating a mixture of these chemicals in 40 mL of squalane under vacuum. A 14.2 mL sample of the resulting Pb-oleate stock solution was heated to 150 °C at which point 5.4 mL of 1.0 M selenium in trioctyl phosphine was injected employing 1 bar overpressure in a Schlenk-line. The NCs were allowed to grow for 5 min resulting in monodisperse, quasi-spherical NCs with a diameter of 6.8 nm, determined from the energy of the first exciton absorption (0.65 eV) and the calibration provided in ref 5. The full width at halfmaximum of the first absorption feature is only 43 meV, showing that these NCs are very monodisperse. The NCs were precipitated twice by the addition of a butanol-methanol mixture (2:1 v/v) and collected by centrifugation. Finally, the NCs were dispersed in tetrachloroethylene for the measurements. The sample is carefully kept free from oxygen and water contamination, both during its preparation and during the measurement. The occupation of the 1S electron and hole levels was controlled and monitored by femtosecond optical pulses from a chirped-pulse amplified Ti:sapphire laser system (MiraLegend USP, Coherent Inc.), which runs at 1 kHz and delivers pulses of 60 fs, 2.2 mJ, at 795 nm wavelength. Tunable infrared and visible pulses (10 meV), then the oscillatory behavior in the transient absorption spectrum is large and may dominate over an eventual bleach. This would complicate the analysis of the change in oscillator strength. To circumvent this problem, we have performed a second experiment, in which on average four 1Sh1Se excitons were created per NC. In this case, the relative bleach of an eventual 1Sh,e1Pe,h transition would be four times larger than that for occupation of a single 1Sh1Se state and would easily be detected. To obtain these four excitons per NC, we have increased the fluence of the pump pulse, which was again resonant with the 1Sh1Se transition in the absorption spectrum. At high fluence, more than one photon is absorbed per NC, which results in the characteristic transient signals shown in Figure 3A. Multiple 1Sh1Se excitons are created, which decay on a picosecond time scale, presumable by Auger recombination,25 although this assignment has recently been challenged.26 The Nano Lett., Vol. 8, No. 7, 2008
of the 1S electron and hole levels) the rate of stimulated emission is equal to the rate of absorption. The initial average number of excitons per excited NC (the exciton multiplicity, Nx) can be obtained from the ratio A/B of the transient absorption at short time (“A”, cf. Figure 3A) to the transient absorption at long time (“B”, where the number of excitons per photoexcited NC equals 1),25 provided one spectrally integrates the first absorption feature to correct for shifts in the energy of the transition.21 This is illustrated in Figure 3A. The ratio A/B at the maximum of the first peak in the absorption spectrum (0.646 eV) reaches a value of ∼6. However, when integrated from 0.57 to 0.71 eV, the value of the multiplicity obtained at the highest fluence is 3.9, in full agreement with the expected exciton multiplicity of four at saturation. This confirms the 8-fold degeneracy of the 1S levels in PbSe and shows that, to obtain the correct multiplicity, the transient absorption has to be integrated over the entire transition. Since the optical transition is close to saturation, the average number of excitons per NC is four throughout the sample. The integrated A/B ratio of ∼4 suggests that the bleach of the first optical transition is indeed linear with the number of excitons, as stated by eq 1. This is in contrast to recent calculations by Franceschetti and Zhang20 who predict a more complex dependence (at least for CdSe NCs) that results from changes in the matrix elements of the optical transitions upon photoexcitation.
Figure 3. (A) Relaxation dynamics for exciting and probing at the first exciton maximum at increasing laser fluence. At the lowest fluences, a step function is observed (cf. Figure 2A). At higher fluences, multiphoton absorption creates multiple excitons, which decay in tens of picoseconds. Also shown are transient absorption spectra at 0.5 ps (B) and 1.0 ns (C) delay time. The solid circles are experimental data points. The solids lines are fits of a model that assumes the second exciton is a 1Ph1Pe transition; the dashed lines are fits of a 1Sh,e1Pe,h model (see text). The insets show the region around the second optical transition in more detail.
number of excitons per NC that can be created this way is four, since at this value (which equals half the degeneracy Nano Lett., Vol. 8, No. 7, 2008
The transient absorption spectrum is shown in Figure 3B,C at short and long delay times, respectively. It is immediately clear from these figures that there is no significant bleach of the second transition, since the signature produced by the red shift of this transition is antisymmetric. If the second peak is due to the 1Sh,e1Pe,h transitions, the relative bleach (-∆R/R0) should be 0.5 upon the addition of four electrons or holes to the 1S levels. For comparison, the 1Sh1Se should be fully bleached (-∆R/R0 ) 1). In the linear absorption spectrum (Figure 1), the area of the second peak is 56% of that of the first peak.27 In case the nature of the second peak is 1Sh,e1Pe,h, we can deduce that ∆Rsecond peak ) 0.28∆Rfirst peak. In case the nature of that peak is 1Ph1Pe, one should of course find ∆Rsecond peak ) 0. We have integrated the transient absorption over the first transition as well as over the second transition and found that the bleach of the second transition is (0.02 ( 0.03)·∆Rfirst peak. This shows that the bleach of the second absorption is zero within the noise of the measurement. We conclude that the oscillator strength of the second transition in the optical absorption spectrum is not affected by the presence of as many as four 1S excitons per NC. A quantitative description of the transient absorption spectrum can be obtained by a simple model that assumes a bleach of optical transitions according to eq 1, and a shift ∆ in the energy of those transitions as a result of the presence of excitons in the NCs. Both bleach and shift are a function of the exciton multiplicity Nx: 2115
Npeak
∆R(E, Nx) )
∑ R (N )e
-(E-E0,i+∆i[Nx])2/2wi2
i
x
-
i)1
Npeak
∑ R (0)e
-(E-E0,i)2/2wi2
i
(2)
i)1
The peak energies (Ei,0), amplitudes (Ri,0), and widths (wi) of the optical transitions in the ground-state are obtained by fitting the low energy part of the absorption spectrum (below 1.0 eV, cf. Figure 1) to three Gaussian functions, after subtraction of an increasing background.5 The amplitudes Ri(Nx) are obtained from eq 1 using the known exciton multiplicities of 4 (0.5 ps delay time) and 1 (1 ns delay time), while the biexciton shifts ∆i(Nx) of the transitions in excited nanocrystals are free fitting parameters. Two models can be formulated: one that assumes the second feature to be due to the 1Sh,e1Pe,h transitions, and one that assumes it is due to the 1Ph1Pe transition. The models differ only in the value of the bleach of the second transition. The experimental transient absorption spectra in Figure 3B,C were fitted with both models; the fits are included as the solid (1Ph1Pe) and dashed (1Sh,e1Pe,h) lines. The biexciton shift of the first exciton that we obtained from these fits is 6 meV at Nx ) 4 and 3 meV at Nx ) 1, while the biexciton shift of the second exciton is 15 and 6 meV at Nx ) 4 and Nx ) 1, respectively (see Tables S1 and S2 in the Supporting Information for all parameters). While the 1Ph1Pe model gives an excellent description of the data, the 1Sh,e1Pe,h model deviates strongly in the spectral region around the second optical transition; the bleach of this feature, which is predicted by the 1Sh,e1Pe,h model is clearly not present in the experimental data. The data presented here represent a single size of nanocrystals dispersed in tetrachloroethylene that were excited at the first exciton. However, we have also investigated different NC sizes, different solvents, and different excitation energies (i.e., exciting the NCs at higher pump photon energy after which the hot carriers quickly relax to the 1S electron and hole levels) with the same result: the second transition is not bleached. The evidence is conclusive: neither the initial nor the final state of the second transition in the absorption spectrum of PbSe NCs involves a 1S electron or hole state. A natural conclusion is that the second absorption feature corresponds to the optically allowed 1Ph1Pe transition. Apparent experimental support for the 1Sh,e1Pe,h assignment has been presented in several papers. We will now discuss the experimental findings of those papers in light of the current conclusive evidence against the 1Sh,e1Pe,h nature of the second optical transition. Wehrenberg et al.6 measured an infrared absorption feature that appeared upon optical excitation of the PbSe NCs and assigned this feature to the 1Se1Pe and 1Sh1Ph intraband transitions, which they assumed to be degenerate. They further noted a strong similarity between the energy of this absorption feature and the energy difference between the first and the second interband absorption peaks. Since they expected that the difference between the 1Ph1Pe and the 1Sh1Se interband transitions should correspond to two times the 1S-1P single particle level splitting and should be twice the energy of the 1Se1Pe and 1Sh1Ph intraband transitions, they assigned the second 2116
absorption peak to the 1Sh,e1Pe,h transitions. This assignment is tacitly based on several assumptions: (i) electron-hole symmetry (i.e., the hole level splittings and the electron level splittings are the same) and (ii) the electron and hole polarization energies and (iii) their Coulomb and exchange interactions28,29 depend weakly on the specific level that is excited (i.e., a 1S or a 1P level). Assumption (i) is not valid, since it has been shown by Liljeroth et al.8 that the hole SP splitting is smaller than the electron SP splitting. This asymmetry is supported by pseudopotential calculations and may be as large as ESP(electron):ESP(hole) ) 2.9,28 However, this electron-hole asymmetry is not large enough to explain the energy spacing between the 1Sh1Se and the 1Ph1Pe transitions. Thus, the results of Wehrenberg et al. do not agree with our experimental results. We wish to stress, however, that our results leave no room for interpretation: the second interband transition does not contain 1S states. Therefore, we speculate that the assumptions (ii) and (iii) mentioned above may not be valid. Little is known about the polarization energies and electron-hole interactions of the 1P levels. The simultaneous bleaching of the first and second peaks was reported upon electrochemical charging of films of PbSe NCs with either electrons or holes.7 On the basis of this, it was concluded that the second peak must involve 1S states and must be due to the 1Sh,e1Pe,h transitions. However, in Figure 3 of ref 7, there is an induced absorption of similar intensity to the low energy side of the “bleach” of the second transition. This resembles the antisymmetric signatures shown in Figures 2 and 3. We, therefore, conclude that the change in absorption that was reported is in fact not a bleach but a red shift of the second peak as a result of the introduction of spectator charges. It is apparent from Figure 3 in ref 7 that this antisymmetric signature only evolves into a net bleach at high oxidation or reduction potentials, where carriers are also injected into states other than the 1Sh and 1Se levels, namely, 1Ph and 1Pe levels. Consequently, the experimental data presented in ref 7 are in line with the 1Ph1Pe assignment of the second optical transition. Harbold et al. performed pump-probe studies on PbSe NCs.11 They excited them at the second absorption feature with a pump pulse and monitored the time-resolved bleach of the first (1Sh1Se) feature. The transient absorption showed a fast component and a slower component, which they assigned to a bleach resulting from a 1S electron/hole directly excited by the pump and a 1P electron/hole that cooled to a 1S state in several picoseconds, respectively. Thus, they concluded that this composite signal is evidence for the 1Sh,e1Pe,h character of the second transition. However, it follows from the present work that the fast component is actually due to a red shift induced instantaneously by the exciton created by the pump pulse. We have observed identical transient signals when exciting the second exciton and probing at the maximum or at the blue side of the maximum of the first peak. Similar signals were reported by Schaller et al.30 and were correctly assigned to the biexciton effect. Probing at the red side of the maximum, we find that the transient is composed of an instantaneous induced absorption (caused by the biexciton effect) and a Nano Lett., Vol. 8, No. 7, 2008
slower bleach that results from cooling of 1P carriers to the 1S levels. This will be elaborately discussed in a forthcoming publication. When it is spectrally integrated over the first absorption feature, we find that the net bleach goes to zero at short times, which again illustrates that 1S levels are not involved in the second optical transition. Finally, Peterson et al. recently presented two-photon photoluminescence excitation spectra of PbSe NCs and showed that there is a two-photon absorption close to the second peak in the single-photon absorption spectrum.10 According to tight-binding calculations by these authors, the selection rules for two-photon transitions are complementary to those for one-photon transitions; that is, the 1Sh,e1Pe,h twophoton transitions should theoretically be dipole-allowed. Therefore, Peterson et al. concluded that their measurement confirmed the 1Sh,e1Pe,h nature of the second peak in the absorption spectrum. However, the two-photon spectrum is only shown in a very limited energy range, and it is not clear what the strength of the observed two-photon absorption is relative to other two-photon transitions. Moreover, the conclusion by Peterson et al. is based on two-photon selection rules but violates single-photon selection rules. They could equivalently have concluded that their observed absorption is a two-photon 1Ph1Pe transition, violating the two-photon but obeying the one-photon selection rules. In any case, either the one- or the two-photon selection rules are violated. In conclusion, we have shown that the strength of the second optical transition in the absorption spectrum of PbSe NCs is not affected by the presence of 1Sh1Se excitons, even if four of those excitons are introduced. The second optical transition exhibits a red shift due to the presence of other excitons, which results in an antisymmetric signature in the transient absorption spectrum. However, integration of this oscillation shows that the transition is not bleached. This clearly shows that the 1S levels are not involved in the second optical transition, in contrast to previous assignments of this feature as a arising from the 1Sh,e1Pe,h transitions. We conclude that it is very likely the 1Ph1Pe transition that gives rise to the second optical transition in PbSe NCs. This confirms pseudopotential calculations by An et al.,9 but it disagrees with calculations using the effective mass14 or tightbinding18 approximations. Acknowledgment. This work is part of the Joint Solar Programme (JSP) of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is supported financially by Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). JSP is cofinanced by “Gebied Chemische Wetenschappen” of NWO and by Stichting Shell Research. In The Netherlands, the three Universities of Technology have formed the 3TU.Federation. This article is the result of joint research in the 3TU.Centre for Sustainable Energy Technologies. This work was financially supported by The
Nano Lett., Vol. 8, No. 7, 2008
Netherlands Organisation for Scientific Research (NWO), Division of Chemical Sciences (VICI Award No. 700.53.443). Supporting Information Available: Mathematical derivation of eq 1 and parameters used to model the transient absorption spectra in Figure 3B,C. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Coe, S.; Woo, W. K.; Bawendi, M.; Bulovic, V. Nature 2002, 420 (6917), 800–803. (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 (5490), 314–317. (3) Nozik, A. J. Annu. ReV. Phys. Chem. 2001, 52, 193–231. (4) Norris, D. J.; Bawendi, M. G. Phys. ReV. B 1996, 53 (24), 16338– 16346. (5) Koole, R.; Allan, G.; Delerue, C.; Meijerink, A.; Vanmaekelbergh, D.; Houtepen, A. J. Small 2008, 4 (1), 127–133. (6) Wehrenberg, B. L.; Wang, C. J.; Guyot-Sionnest, P. J. Phys. Chem. B 2002, 106 (41), 10634–10640. (7) Wehrenberg, B. L.; Guyot-Sionnest, P. J. Am. Chem. Soc. 2003, 125 (26), 7806. (8) Liljeroth, P.; van Emmichoven, P. A. Z.; Hickey, S. G.; Weller, H.; Grandidier, B.; Allan, G.; Vanmaekelbergh, D. Phys. ReV. Lett. 2005, 95 (8), 86801. (9) An, J. M.; Franceschetti, A.; Dudiy, S. V.; Zunger, A. Nano Lett. 2006, 6 (12), 2728–2735. (10) Peterson, J. J.; Huang, L.; Delerue, C.; Allan, G.; Krauss, T. D. Nano Lett. 2007, 7, 3827–3831. (11) Harbold, J. M.; Du, H.; Krauss, T. D.; Cho, K. S.; Murray, C. B.; Wise, F. W. Phys. ReV. B 2005, 72 (19), 195312. (12) Du, H.; Chen, C. L.; Krishnan, R.; Krauss, T. D.; Harbold, J. M.; Wise, F. W.; Thomas, M. G.; Silcox, J. Nano Lett. 2002, 2 (11), 1321– 1324. (13) An, J. M.; Franceschetti, A.; Zunger, A. Phys. ReV. B 2007, 76 (16), 161310. (14) Kang, I.; Wise, F. W. J. Opt. Soc. Am. B: Opt. Phys. 1997, 14 (7), 1632–1646. (15) Gaponenko, S. V. Optical properties of Semiconductor Nanocrystals; Cambridge University Press: Cambridge, 1998; p 245. (16) Norris, D. J., Electronic Structure in Semiconductor Nanocrystals. In Semiconductor and Metal Nanocrystals; Klimov, V. I., Ed.; Marcel Dekker, Inc.: New York, 2004; pp 65-102. (17) Delerue, C.; Lannoo, M., Nanostructures: Theory and Modelling; Springer-Verlag: Berlin, 2004. (18) Allan, G.; Delerue, C. Phys. ReV. B 2004, 70 (24), 245321. (19) Talapin, D. V.; Murray, C. B. Science 2005, 310 (5745), 86–89. (20) Franceschetti, A.; Zhang, Y. Phys. ReV. Lett. 2008, 100 (13), 136805– 4. (21) 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, DOI: 10.1021/nl0807225. (22) Zhang, J.; Jiang, X. App. Phys. Lett. 2008, 92, 141108. (23) Houtepen, A. J.; Vanmaekelbergh, D. J. Phys. Chem. B 2005, 109 (42), 19634–19642. (24) Klimov, V. I. Annu. ReV. Phys. Chem. 2007, 58, 635–673. (25) Schaller, R. D.; Klimov, V. I. Phys. ReV. Lett. 2004, 92 (18), 186601. (26) Pandey, A.; Guyot-Sionnest, P. J. Chem. Phys. 2007, 127 (11), 111104. (27) The ratio of the areas of peaks 1 and 2 was obtained by fitting a Gaussian function to each. (28) An, J. M.; Franceschetti, A.; Zunger, A. Phys. ReV. B 2007, 76 (4), (29) Franceschetti, A.; Williamson, A.; Zunger, A. J. Phys. Chem. B 2000, 104 (15), 3398–3401. (30) Schaller, R. D.; Pietryga, J. M.; Goupalov, S. V.; Petruska, M. A.; Ivanov, S. A.; Klimov, V. I. Phys. ReV. Lett. 2005, 95 (19), 196401.
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