8570
J. Phys. Chem. C 2008, 112, 8570–8574
Efficient Auger Electron Cooling in Seemingly Unfavorable Configurations: Hole Traps and Electrochemical Charging Marco Califano Institute of MicrowaVes and Photonics, School of Electronic and Electrical Engineering, UniVersity of Leeds, Leeds LS2 9JT, United Kingdom ReceiVed: October 30, 2007; ReVised Manuscript ReceiVed: March 17, 2008
The absence of a phonon bottleneck in the intraband relaxation between p-like and s-like electron states in CdSe nanocrystals is generally ascribed to efficient inelastic scattering with the photogenerated hole (Auger cooling). However, the fast relaxation of electrons observed in the absence of a hole or in the presence of a hole trapped in a surface state has raised serious questions about the suitability of this model. The semiempirical pseudopotential calculations reported here show that electron-electron scattering in chemically reduced or electrochemically charged (i.e., holeless) CdSe nanocrystals leads to short p electron lifetimes comparable to those calculated in the presence of a photogenerated hole delocalized in the dot core. Furthermore, it is shown that efficient energy transfer can also be achieved between a delocalized electron and a surface-trapped hole, leading to short p electron lifetimes in the (sub-) picosecond range. These results are in quantitative agreement with experiment and are consistent with the Auger interpretation of the electron relaxation. The fast subpicosecond electron relaxation times calculated in the presence of a hole localized in a shallow surface trap raise the intriguing question of whether in earlier measurements in TOPO-capped nanocrystals the hole was indeed delocalized within the dot core, as it was believed at the time, or whether it could have been in a trap state. I. Introduction Auger electron cooling (AC) is a nonradiative decay process whereby an excited electron relaxes to the ground-state by transferring its excess energy to a hole (usually photogenerated with the electron), which is excited to deep valence levels. The hole then undergoes a fast relaxation (with typical times e1 ps) to the band edge through the denser valence band energy ladder, via inelastic energy transfer to the lattice. Despite increasing evidence1–3 in favor of this hypothesis4,5 for the explanation of the observed fast intraband electron decay in semiconductor nanocrystals (NCs), culminated very recently with the direct observation of electron-to-hole energy transfer by Hendry and co-workers,3 there are still unresolved issues regarding the origin of fast electron decays observed in electronic configurations seemingly unfavorable for, if not totally preclusive of, the Auger process: (i) when the hole effective mass and density of states are similar to those of the electron, as it is believed to be the case in PbSe NCs;7,8 (ii) when the hole is trapped in a surface state;1,2,8 or (iii) when the hole is altogether missing (as in the case of electrochemically charged8,9 or chemically reduced10 NCs). It has already been shown11 that the assumptions (i) leading to the expectation of long lifetimes for excited electrons in PbSe NCs were unfounded, and our recently calculated12 Auger relaxation times for that system agree with experiment in both magnitude and trend with size. This paper will address the remaining two issues, (ii) and (iii). The use of different types of surface passivation has led to the observation of a large spread of sometimes contrasting 1P electron lifetimes: the short, sub-picosecond, relaxation times reported for well (ZnS) passivated NCs by Klimov et al.2 showed an almost 10-fold increase (to 3 ps) in dots passivated with the hole-accepting pyridine capping group. Decay times of about 1 ps in NCs capped with trioctylphos-
phine oxide (TOPO), increasing by a factor of 2 in thiocresolterminated dots and exceeding 200 ps in pyridine-capped samples (the latter exhibiting a difference of 2 orders of magnitude compared to the lifetimes reported in ref 2 for the same capping group) were instead observed by GuyotSionnest and co-workers.1 Further surface modifications added more intermediate values for the relaxation times: Guyot-Sionnest et al.8 measured relaxation times varying from 3.8 ps, for a tetradecylphosphonic acid-treated sample, up to 27 ps, for n-dodecanethiol-treated NCs of the same size. The first observations1,2 of such surface-termination-dependent lifetimes were considered direct evidence for the electron-hole energy transfer (i.e., the AC) hypothesis.1,2 The increasingly longer lifetimes observed in ref 1 for different surface terminations were rationalized in terms of decreasing electron-hole coupling originating from the different kind of hole trap states created by different capping groups: shallow Se traps for TOPO, deeper S traps for thiocresol, and charge-separated complexes for pyridine. In the work reported by Klimov et al.,2 in small (R ∼ 11.5 Å) CdSe/ZnS dots, the electron dynamics was found to be independent of the delay (∆t) between visible photoexcitation and infrared (IR) re-excitation pulses. In pyridine-terminated NCs of the same size, instead, the electron dynamics was shown2 to depend on ∆t, exhibiting fast decay times of 250 fs at short (70 fs) delays, which increased to 3 ps for delays comparable to (and larger than) the hole-transfer time to the capping molecule. Again, this was considered qualitatiVely consistent with the AC model: shortly after the excitation the hole is in a delocalized state where it has a large overlap with the electron wave function yielding short electron decay times; when, after a time on the order of the transfer time to the capping molecule (∼400 fs), it becomes trapped in a surface state, the reduced overlap between electron and hole
10.1021/jp7104743 CCC: $40.75 2008 American Chemical Society Published on Web 05/15/2008
Efficient Auger Electron Cooling
J. Phys. Chem. C, Vol. 112, No. 23, 2008 8571
Figure 1. Schematics of the two types of Auger electron cooling considered in this work: (a) in the presence of a hole trapped in a surface state ti (see Figure 2), in an overall neutral NC; (b) in the presence of another electrochemically injected electron also excited to the p state, in an overall doubly negatively charged NC.
wave functions is expected to lead to longer lifetimes. The fact that a relatively fast decay persisted even in the case of a significant spatial separation between electron and hole was qualitatiVely explained2 as arising from the long-range of Coulomb interactions, which do not require a direct overlap between the wave functions to yield strong coupling. All the above evidence shows that the electron relaxation is influenced by the location of the hole, with short lifetimes for delocalized states and progressively longer lifetimes for increasingly deeper trap states (in this respect, the 2 orders of magnitude difference between the observed1,2 electron decay times in pyridine-capped NCs remains difficult to reconcile). However the quantitatiVe aspect of this effect has been questioned recently in ref 8, where a much larger decrease of the electron-hole coupling is hypothesized for holes in surface-trapped states with a consequently larger increase in the expected electron lifetime. Another observation that is used as evidence for the need for a new mechanism to explain electron decay in NCs is the fast electron relaxation in electrochemically charged (i.e., holeless) NCs,8 where lifetimes ∆sp and the denominator in eq 1 is .0 for all values of the screening. As evidenced in Figure 4, where positive (negative) values on the x-axis indicate energy-(non)-conserving transitions,24 for εout ) 1 no transition conserves energy. For higher values of the dielectric constants at the surface instead, energy-conserving transitions are available only if the hole is in shallow traps (t1 or t2), but never if it is in deep traps (t3 or t4). Therefore, the counterintuitive behavior of the lifetime as a function of the surface screening for shallow traps is explained by the dominant role of the energy conservation constraint (denominator of eq 1) compared to the strength of the Auger coupling between initial and final states. Nevertheless, the astonishingly fast decay times calculated here for shallow traps and εout ) 2.5 may have important implications: if the assumption of a value of 2.5 for the dielectric screening at the surface is considered reasonable (and this assumption is supported by the fact that, as discussed above, such value represents a good approximation for the dielectric constant of routinely used solvents, such as toluene, and capping groups, such as TOPO), then the fact that such fast lifetimes fall within the experimental range of the electron decay times measured in refs 22 and 23 (relative to transitions in TOPO-capped NCs occurring at early times ( 17 Å) considered in refs 22 and 23, the transfer from this state to a shallow trap could be as energetically favorable (i.e., it could involve a similar reduction of the hole energy) as the transfer to a deep trap from the 1s state, and therefore could have as high a rate. Also, the wave function of an excited hole, due to the larger kinetic energy associated with it, would sample regions of the NC closer to the surface, increasing the probability of capture from the unsaturated dangling bonds of the surface Se atoms. Finally, the fact that no optical gain was observed in any of the samples considered in ref 22 may also be considered to be a further indication of hole trapping, as previously suggested.27 In the case of a surface-trapped hole, the observed size dependence of the electron lifetime would then be given by the different extent of the delocalized electron wave function, which depends on the NC size, similarly to what happens in inverted core/shell heteronanostructures.28 As we have seen, therefore, the presence of a surface-localized hole during the electron relaxation in CdSe NCs cannot be ruled out based on the available experimental observations.22,23 What is probably as intriguing as the hypothesis just discussed is the prediction of a super fast subpicosecond decay of a p electron in the absence of a hole (see Figure 5): if two electrons, instead of one, are injected in the s state and they are consequently both excited to the p state by the IR pump, one of them can decay in less than 1 ps by transferring its excess energy to the other electron, which, acting as the hole in a conventional AC decay mechanism, is excited to high conduction band states. Such a fast decay is due to the combination of a strong Auger coupling and the availability of energy-matched final states. The hypothesis of the presence of a second electron is not too far fetched, as the exact number of electrons injected in the NC is not mentioned in ref 8. The process described here would leave the second electron in an excited state, which should be evidenced by the failure to achieve complete bleaching, in agreement with the experimental observation.8 This failure is also experienced, however, in photoexcited samples (i.e., when there is a hole present), even in the strong saturation regime.1 Figure 5 presents the lifetimes calculated here for three NC sizes. This result shows, therefore, that in holeless NCs an excited electron can decay in less than 6 ps, which makes its lifetime
8574 J. Phys. Chem. C, Vol. 112, No. 23, 2008
Figure 5. Auger lifetimes of a p electron in the presence of a second electron in the p state are displayed (a) as a function of NC radius, calculated as an average over a range of sp splitting energies εep - εse corresponding to a 10% (filled squares) and 0% (empty squares) size dispersion [the latter value corresponds to τ(0) in panels b-d]; as a e function of the difference (εep - εse) - ∆sp for NCs with R ) 10.3 (b), e 14.6 (c), and 19.2 Å (d), where ∆sp is the value of the sp splitting for a 0% size dispersion, and the energy range displayed corresponds to a 10% size dispersion. Auger lifetimes where the second electron is replaced by a hole delocalized in the dot are also shown (dashed lines) for comparison.
indistinguishable from that of an electron decaying in the presence of a S-trapped hole, on the time scale of the abovementioned experimental resolution.8 IV. Conclusions In conclusion, is has been shown that although alternative models for electron relaxation in CdSe NCs8 may be consistent with the observed lifetimes, AC cannot be ruled out based on the present experimental evidence. Moreover, the results presented here suggest a possible alternative interpretation of the dynamics behind the electron decay times observed in refs22 and.23 Acknowledgment. I’d like to thank A. Franceschetti and A. Zunger for providing the latest version of most of the codes used here. The Royal Society is gratefully acknowledged for financial support. References and Notes (1) Guyot-Sionnest, P.; Shim, M.; Matranga, C.; Hines, M. Phys. ReV. B 1999, 60, R2181.
Califano (2) Klimov, V. I.; Mikhailovsky, A. A.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Phys. ReV. B 2000, 61, R13349. (3) Hendry, E.; Koeberg, M.; Wang, F.; Zhang, H.; de Mello Donega, C.; Vanmaekelbergh, D.; Bonn, M. Phys. ReV. Lett. 2006, 96, 057408. (4) Efros, Al. L.; Kharchenko, V. A.; Rosen, M. Solid State Commun. 1995, 93, 281. (5) Wang, L.-W.; Califano, M.; Zunger, A.; Franceschetti, A. Phys. ReV. Lett. 2003, 91, 056404. (6) Norris, D. J.; Nirmal, M.; Murray, C. B.; Sacra, A.; Bawendi, M. G. Z. Phys. D 1993, 26, 355. (7) (a) Kang, I.; Wise, F. W. J. Opt. Soc. Am. B 1997, 14, 1632. (b) 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. (c) Schaller, R. D.; Pietryga, J. M.; Goupalov, S. V.; Petruska, M. A.; Ivanov, S. A.; Klimov, V. I. Phys. ReV. Lett. 2005, 95, 196401. (8) Guyot-Sionnest, P.; Wehrenberg, B.; Yu, D. J. Chem. Phys. 2005, 123, 074709. (9) Wang, C. J.; Shim, M.; Guyot-Sionnest, P. Appl. Phys. Lett. 2002, 80, 4. (10) Shim, M.; Guyot-Sionnest, P. Nature 2001, 407, 981. (11) An, J. M.; Franceschetti, A.; Dudiy, S. V.; Zunger, A. Nano Lett. 2006, 6, 2728. (12) An, J. M.; Califano, M.; Franceschetti, A.; Zunger, A. J. Chem. Phys., in press. (13) Wang, L.-W.; Zunger, A. Phys. ReV. B 1995, 51, 17–398. (14) Franceschetti, A.; Fu, H.; Wang, L.-W.; Zunger, A. Phys. ReV. B 1999, 60, 1819. (15) Wang, L.-W.; Zunger, A. Phys. ReV. B 1996, 53, 9579. (16) Hill, N. A.; Whaley, K. B. J. Chem. Phys. 1994, 100, 2831. (17) Califano, M.; Franceschetti, A.; Zunger, A. Nano Lett. 2005, 5, 2360. (18) Leung, K.; Whaley, K. B. J. Chem. Phys. 1999, 110, 11012. (19) Puzder, A.; Williamson, A. J.; Zaitseva, N.; Galli, G.; Manna, L.; Alivisatos, A. P. Nano Lett. 2004, 4, 2361. (20) Manna, L.; Wang, L.-W.; Cingolani, R.; Alivisatos, A. P. J. Phys. Chem. B 2005, 109, 6183. (21) Cartoixa, X.; Wang, L.-W. Phys. ReV. Lett. 2005, 94, 236804. (22) Klimov, V. I. J. Phys. Chem. B 2000, 104, 6112. (23) Klimov, V. I.; McBranch, D. W Phys. ReV. Lett. 1998, 80, 4028. (24) Whilst negative values always identify energy nonconservation, positive values only indicate overlap of the initial state energy with the range of final state energies and, although being a necessary condition for it, are not sufficient to ensure energy conservation. (25) Klimov, V. I.; Schwarz, C. J.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Phys. ReV. B 1999, 60, R2177. (26) I calculated that in a R ) 14.3 Å NC, a pump pulse at 3.1 eV that excites the electron above the three nearly degenerate P levels would only populate the ground hole state (VBM). A pump at the same energy is therefore expected to populate deeper hole levels in larger dots where the band gaps are smaller due to the reduced confinement. (27) Bawendi, M. G.; Wilson, W. L.; Rothberg, L.; Carroll, P. J.; Jedju, T. M.; Steigerwald, M. L.; Brus, L. E. Phys. ReV. Lett. 1990, 65, 1623. (28) (a) Ivanov, S. A.; Nanda, J.; Piryatinski, A.; Achermann, M.; Balet, L. P.; Bezel, I. V.; Anikeeva, P. O.; Tretiak, S.; Klimov, V. I. J. Phys. Chem. B 2004, 108, 10625. (b) Nanda, J.; Ivanov, S. A.; Htoon, H.; Bezel, I. V.; Piryatinski, A.; Tretiak, S.; Klimov, V. I. J. Appl. Phys. 2006, 99, 034309. (29) Schroeter, D. F.; Griffiths, D. J.; Sercel, P. C. Phys. ReV. B 1996, 54, 1486.
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