Exciton Recombination Dynamics in CdSe Nanowires: Bimolecular to

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NANO LETTERS

Exciton Recombination Dynamics in CdSe Nanowires: Bimolecular to Three-Carrier Auger Kinetics

2006 Vol. 6, No. 7 1344-1349

Istva´n Robel,†,‡ Bruce A. Bunker,‡ Prashant V. Kamat,*,†,§,| and Masaru Kuno*,†,§ Radiation Laboratory, Department of Chemistry and Biochemistry, Department of Chemical and Biomolecular Engineering, and Department of Physics, UniVersity of Notre Dame, Notre Dame, Indiana 46556 Received January 26, 2006; Revised Manuscript Received April 8, 2006

ABSTRACT Ultrafast relaxation dynamics of charge carriers in CdSe quantum wires with diameters between 6 and 8 nm are studied as a function of carrier density. At high electron−hole pair densities above 1019 cm-3 the dominant process for carrier cooling is the “bimolecular” Auger recombination of one-dimensional (1D) excitons. However, below this excitation level an unexpected transition from a bimolecular (exciton− exciton) to a three-carrier Auger relaxation mechanism occurs. Thus, depending on excitation intensity, electron−hole pair relaxation dynamics in the nanowires exhibit either 1D or 0D (quantum dot) character. This dual nature of the recovery kinetics defines an optimal intensity for achieving optical gain in solution-grown nanowires given the different carrier-density-dependent scaling of relaxation rates in either regime.

In recent years it has become possible to tailor the size, shape, and dimensionality of semiconductor nanostructures with ever-growing precision.1 Studies of the electronic and optical properties of these systems have provided classic examples of quantum-confinement effects in reduced geometries.2,3 Understanding charge carrier dynamics in semiconductors with limited spatial degrees of freedom is therefore of fundamental scientific interest with practical implications in the design of optoelectronic and photovoltaic devices. The ultrafast relaxation of charge carriers in semiconductor quantum dots (QDs) has been extensively studied4 revealing the role of particle size5 and excitation density5-7 in carrier cooling. It has been assumed that due to large confinementinduced energies, both the electron and hole are separately confined within the QD.8 At high excitation densities many carriers are present in each nanocrystal and de-excitation occurs through multicarrier processes.5-7 An example of such an Auger-mediated recombination includes a scenario where one electron-hole (e-h) pair gives up its energy to another carrier. The rate of this three-charge process (also referred to as a CHCC mechanism9) is thus cubic in carrier density. Recent experiments with nanorods10,11 (NRs) have extended these studies showing the effects of shape on the * To whom correspondence may be addressed. E-mail: [email protected]; [email protected]. † Radiation Laboratory. ‡ Department of Physics. § Department of Chemistry and Biochemistry. | Department of Chemical and Biomolecular Engineering. 10.1021/nl060199z CCC: $33.50 Published on Web 06/02/2006

© 2006 American Chemical Society

electronic properties of low-dimensional semiconductors. Rich features in the excitation spectrum as well as differences in carrier cooling dynamics have been observed.10,11 Furthermore, nanorod-specific properties, such as potentially high fluorescence quantum yields, short radiative lifetimes, low thresholds for optical gain,12,13 and linearly polarized emission14 make them especially suitable building blocks for optoelectronic,15 photovoltaic,16 and lasing applications.17 Multicarrier de-excitation rates in NRs suggest the presence of one-dimensional (1D) excitons with a translational degree of freedom along the NR axis.11,12 Such 1D excitons result from increases in the exciton binding energy relative to the bulk due to dielectric contrast effects.18 This is especially relevant in nanowires because of the significantly lower dielectric constant of the surrounding medium relative to the semiconductor. In this respect, binding energies up to 300 meV have been predicted.18 Thus, theoretical calculations suggest that the excited-state properties of nanowires (NWs) and NRs are dominated by 1D exciton dynamics.19 However, previous experimental studies of semiconductor NWs have generally been limited to transport measurements20,21 and to a lesser extent photoluminescence studies.18,22 As a consequence, the role of 1D exciton-exciton annihilation in NW relaxation dynamics has yet to be explored fully. In this Letter we present ultrafast transient differential absorption (TA) studies of carrier cooling kinetics in straight CdSe nanowires with lengths exceeding 1 µm and diameters between 6 and 8 nm. For the specific case described herein,

Figure 1. (A) Linear absorption and band-edge emission of CdSe NWs. Features in the absorption are labeled R, β, and γ. Low- (B, C) and high-resolution (D) TEM micrographs of the CdSe NWs. The NWs are generally viewed down a non-〈110〉 zone.

the average diameter and corresponding size distribution of the NWs is 6.8 (σ ) 1.0) nm. Furthermore, intrawire diameter distributions range from 3 to 6%.23 The wires are highly crystalline as determined through high-resolution transmission electron microscopy (TEM) measurements (Figure 1B-D).23 Their synthesis is described elsewhere.23,24 Briefly, however, ∼2 nm diameter Au-Bi core-shell nanoparticles are used as catalysts for the nucleation and growth of the wires in a reaction mixture consisting of trioctylphosphine oxide, trioctylphosphine selenide, cadmium oxide, and octanoic acid. The resulting NWs are subsequently suspended in toluene after repeated “washing” and centrifugation to remove excess surfactant. The absorption spectra of the resulting NWs show peaks originating from quantization effects due to their radii (3-4 nm), below the bulk Nano Lett., Vol. 6, No. 7, 2006

Figure 2. (A) Transient bleach (5 ps delay) and corresponding Gaussian fits, revealing individual subbands labeled R, β, and γ. Vertical lines on the x-axis denote predicted peak positions obtained from a cylindrical confinement model. (B) Transient absorption spectra of CdSe NWs after 387 nm excitation. The inset shows the initial rise of the band edge state along with the complementary decay of higher excited states.

exciton Bohr radius of CdSe (aB ∼ 5.6 nm). Furthermore, the NWs also exhibit band edge photoluminescence (PL) with no sign of deep trap emission (Figure 1A). Our ultrafast transient absorption spectroscopy measurements are conducted over a wide range of intensities to study as a function of carrier density, the time-dependent charge recombination kinetics of e-h pairs in the NWs. TA measurements were carried out using a Clark-MXR CPA 2010 laser system and an Ultrafast Systems pump-probe detection scheme. The 387 nm (3.2 eV) second harmonic of the fundamental (775 nm, 1.6 eV, 1 kHz repetition rate, 1 mJ/pulse) was used to excite the sample and was followed by a femtosecond white-light probe between 420 and 800 nm (1.5-2.9 eV), generated by passing a fraction of the fundamental through a sapphire plate. Pump fluences were varied between 11 and 120 µJ/cm2. Representative TA spectra (Figure 2) show a series of 1345

broad induced bleaches after initial excitation with the 387 nm (3.2 eV, 150 fs) pulse. These peaks are consistent with features in the solution linear absorption (Figure 1A) and indicate a progression of excited states/subbands toward higher energies. In particular, Figure 2A shows the induced bleach 5 ps after excitation. At least three peaks are resolved and are fit by a series of Gaussians. These states labeled R, β, and γ are seen in this as well as other samples studied. The spacing between states (∆1 ) 0.21 eV and ∆2 ) 0.40 eV) is consistent with that expected from a simple cylindrical confinement model, as indicated by the stick spectrum included in the figure. Such spacings differ from those observed in similarly sized QDs.25 Furthermore, based on angular momentum projections of the electron and hole wave functions onto the NW axis, these states may be labeled Σ, Π, and ∆ analogous to s, p, and d atomic orbitals.22,26 Upon excitation at 3.2 eV, higher excited states in the progression are populated, followed by rapid intraband relaxation toward the band edge state (R) with a ∼3 ps rise time. The time scale for intraband cooling is longer than that for QDs (∼400 fs, 1p to 1s transition)4,10 or even NRs (∼1 ps),4,10 suggesting potential bottleneck effects27,28 or issues associated with the accessibility of surface states that mediate the recovery.29 However, analogous to QDs and NRs, corresponding interband decays are much longer (∼100700 ps). Since quantifying intraband relaxation kinetics at high intensities is made difficult by the wavelength and intensity dependence of the process, we focus on analyzing the dynamics of the band edge recovery. There are several mechanisms that contribute to e-h pair relaxation at R. This includes radiative recombination,30 surface-mediated nonradiative recombination,29,31 Augerassisted ionization,32 and multicarrier Auger recombination.5 Of the above processes, the radiative pathway can be neglected in our TA measurements due to the low intrinsic quantum yield of the NWs (∼0.1%).33 In this respect, the NWs have not been overcoated by a higher band gap material as frequently done with more highly luminescent colloidal QDs. Likewise, surface trap contributions are small at high carrier densities due to the saturation of surface states.6 At lower excitation densities they play an increasingly important role that can be tested through intensity- and surfacedependent measurements.29,34 However, due to the intrinsically large cross section of the NWs (shown below), multicarrier Auger processes are expected to be as significant if not more so than surface contributions. Thus, even at the lowest excitation levels used in our experiments (11 µJ/cm2) hundreds of e-h pairs are generated in a single wire with an average interexciton distance less than aB (a regime where strong exciton-exciton interactions might occur). By way of contrast, the same pump intensity results in less than 0.1 e-h pairs per QD in nanocrystals having similar diameters. This motivates our subsequent analysis of carrier cooling dynamics primarily within the context of multicarrier Auger recombination processes. In this respect, previous studies of the Auger decay mechanism in colloidal QDs and other nanostructures have revealed dominant third-order kinetics with individual carriers 1346

recombining in a three-carrier process.5,9,35 Underlying this model is the assumption that the binding energy of e-h pairs is low compared to corresponding confinement-induced energies.8 In both NRs and NWs, however, enhancements in the exciton binding energy can lead to the formation of a 1D exciton possessing a degree of freedom along the NW length.19 As a consequence, the Auger recombination of such 1D excitons is generally expected to occur through a bimolecular (exciton-exciton) annihilation process36,37 where one exciton recombines nonradiatively, transferring its energy to the other. The overall mechanism is therefore second order in exciton density11 and can be tested explicitly through studies of e-h recombination kinetics at high intensities. In either case, a generic Auger rate equation has the form dn ) -CDnD dt

(1)

with solutions n(t) )

n(0) D-1 1 CDn(0)D-1t 1+ D-1

(

)

(2)

(D > 1) where D ) 3 for e-h pairs characteristic of QDs and D ) 2 for 1D excitons characteristic of NWs.11 CD is the Auger constant, representative of the recombination probability, and n is the time-dependent e-h pair density. Plots of [n(0)/n(t) - 1]D-1 versus time yield linear behavior with a slope m ) CDn(0).11 To analyze the e-h pair decay dynamics of NWs at the band edge (R), a relation between the measured absorbance change and the time-dependent e-h pair density [n(t)] is needed. More specifically, the initial e-h pair density of the wires [n(0)] can be calculated using the expression n(0) ) jσ/V, where j is the pump photon fluence (cm-2), σ is the linear absorption cross section of the NW at the pump wavelength (cm2), and V is its volume (cm3). A major assumption underpinning this model is that sufficiently far from the band edge, the NW density of states (QDs4 as well) becomes bulklike, allowing the use of the above cross section.4 Note that at high excitation intensities this may result in an overestimation of exciton densities. Next, measuring the initial absorption change (∆A) of the band edge state as a function of pump fluence (after a rise due to intraband relaxation) establishes a calibration curve relating the number of excitons to ∆A.5 Applying this relation to the measured TA kinetic profiles subsequently allows us to obtain the time-dependent behavior of n. The measured absorption saturation curve (Figure S1 in Supporting Information) is fit by a phenomenological expression, ∆A/A ) B1n(0)/(B2 + n(0)k), where k, B1, and B2 are fit parameters. This saturation of the band edge state is characteristic of 0D systems4 but is unexpected for NWs where the density of states forms a continuum due to the degree of freedom associated with the wire length. Nano Lett., Vol. 6, No. 7, 2006

Table 1. Auger Constants and Initial Decay Lifetimes Extracted from the Decay Kinetics in Figure 3a pump fluence (µJ/cm2)

n(0) (1018 cm-3)

C2 (10-10 cm3 s-1)

τ0 (ps)

23.3 38.0 73.0 120

13.2 21.7 41.5 68.8

2.11 1.99 1.98 3.13

357 231 121 47

a

The time constant τ0 is defined as τ0 ) -n(0)(dn/dt)-1 ) [C2 n(0)]-1.

Figure 3. Time-dependent e-h pair density at pump fluences of (A) 23.3 µJ/cm2 [n(0) ) 13.2 × 1018 cm-3], (B) 38 µJ/cm2 [n(0) ) 21.7 × 1018 cm-3], (C) 73 µJ/cm2 [n(0) ) 41.5 × 1018 cm-3], and (D) 120 µJ/cm2 [n(0) ) 68.8 × 1018 cm-3]. Solid lines are fits to the data using eq 3 with D ) 2.

The absorption cross section of NWs far from the band edge is estimated using a long dielectric cylinder in a uniform electric field, angle averaged to account for the random orientation of an ensemble in solution.4,33,38 The resulting expression is

| |

4I 2 ω σ (cm ) ) (πr2l) (2nSkS) nIc  I + S 2

(3)

where ω is the angular frequency of the pump photon (4.9 × 1015 s-1), nI is the refractive index of the surrounding medium (toluene, nI ∼ 1.5), r and l are the NW radius and length (r ∼ 3.5 nm, l ∼ 1 µm), nS and kS are the real and imaginary parts of the CdSe refractive index (nS ∼ 2.9, kS ∼ 0.7),39 and I and S are the dielectric constants of the surrounding medium and CdSe with I ∼ 2.2 (S ∼ 7.9 + 4i).40 On the basis of this approximation, we estimate the NW linear cross section to be σ387 nm ) 1.1 × 10-11 cm2, nearly 4 orders of magnitude larger than that for comparable QDs.41 As shown in Figure 3, the decay kinetics of R depend strongly on the excitation intensity, with faster decay rates at higher pump fluences. At excitation levels above 23 µJ/ cm2, the decays are in excellent agreement with the bimolecular recombination of 1D excitons. Specifically, an Auger model based on second-order kinetics accurately describes our experimental data for pump fluences between 23 and 120 µJ/cm2 (n(0) ) 13.2 × 1018 to 68.8 × 1018 cm-3). The agreement between the two therefore provides one of the first experimental indications for the existence of 1D excitons in NWs. In all cases, fits to the data using eq 3 with D ) 2 were performed using a single fitting parameter, the secondorder Auger constant C2. The data and fits are plotted as a function of n(t) versus t, to illustrate both long- and shorttime data equally well. Alternative plots of [n(0)/n(t) - 1]D-1 versus time, yielding linear time-dependence, are included in the Supporting Information. The robustness of the fits is Nano Lett., Vol. 6, No. 7, 2006

Figure 4. Decay of the band edge state (R) modeled by a thirdorder Auger decay mechanism. The solid line is a fit to the data using eq 3 with D ) 3.

apparent from the relative insensitivity of C2 to intensity, which decreases by only 30% when the intensity is reduced by a factor of 5. The slight intensity dependence does, however, indicate stronger interactions between 1D excitons at higher excitation levels. Values of the Auger constant along with corresponding relaxation rates, extracted from our analysis, are summarized in Table 1. In all cases, good fits to an exciton-exciton annihilation model and steady values of C2 over a wide range of intensities, suggest that the bimolecular recombination of 1D excitons is the prevailing carrier-relaxation pathway at high intensities, superseding radiative and surface-mediated recombination. Quite unexpectedly, at lower excitation intensities, below 11 µJ/cm2, the bimolecular recombination mechanism no longer appears consistent with the measured decay kinetics. Instead, systematic deviations occur in the fit with a tendency to underestimate the decay rate at early times (t < 400 ps) and to overestimate it at longer times. Modeling the measured decay at low intensities (11 µJ/cm2) with a three-carrier Auger recombination mechanism (D ) 3 in eq 3) does, however, result in a remarkably good agreement to the data as illustrated by Figure 4. As with the previous bimolecular fits (Figure 3), the only fitting parameter used is the Auger constant C3 whose resulting value (2.5 × 10-28 cm6 s-1) has the same order of magnitude as those previously reported for large CdSe QDs5 (C3 ∼ 10-28 cm6 s-1). This further supports our assignment and suggests a change in the exciton dynamics from a bimolecular (exciton-exciton) annihilation mechanism to a three-carrier Auger relaxation process, characteristic of QDs and bulk materials. An additional example of this intensity-dependent transition of the Auger 1347

Figure 5. (A) High-resolution TEM micrograph of a nanowire segment showing ZB and W phase admixtures. (B) Cartoon scheme of a predicted type II band structure in CdSe NWs arising from band offsets between ZB and W phases.

mechanism is illustrated in Figure S3, Supporting Information. Although the low intensity trace can also be fit to a biexponential, with a fast (slow) time constant of ∼200 ps (∼2.5 ns), the large absorption cross section of the NWs easily yields ∼102 e-h pairs per wire, such that multicarrier Auger processes should still play a leading role in mediating carrier relaxation. To further understand both the transition and origin of the third-order kinetics, a careful analysis of high-resolution TEM micrographs was conducted (Figure 5A). This study reveals phase disorder in the NWs characterized by alternating segments of both zinc blende (ZB) and wurtzite (W), as well as twinning within ZB sections. Such phase disorder is apparent in high-resolution TEM images of 〈110〉 oriented NWs and appears representative of solution-based II-VI NWs.23 Theoretical predictions indicate that both ZB and W phases have different electron affinities, ionization potentials, and even band gaps.42-44 The result is a staggered (type II) potential along the NW length with conduction band offsets of ∆E(CB) ) 75-140 meV and valence band (VB) offsets of ∆E(VB) ) 30-60 meV (Figure 5B). Since the enhanced 1D exciton binding energy in CdSe NWs has a magnitude18 comparable to these offsets, such type II structures will act as trapping or scattering potentials for 1D excitons. Furthermore, the lowest energy state of the conduction band electron occurs within ZB segments while the lowest energy hole state occurs within W sections. In this respect, the separation and localization of e-h pairs by such type II structures was recently cited as a potential source for optical heterogeneity in single CdSe NW photoluminescence experiments.33 To estimate an excitation limit (and corresponding carrier density) where the type II nature of the NWs becomes relevant, we consider a simple model for electron and hole bound states in a potential well formed by ∼3 nm (σ ) 1 nm) long ZB (W) segments of the wire.23 Corresponding 1348

barrier heights are ∆E(CB) and ∆E(VB), respectively. Using bulk values for the electron and hole effective masses, we calculate that at most one (two) electron (hole) bound states are accommodated by each potential well. Beyond this, additional electrons and holes sample extended states of the NW. We estimate a bound state density of ∼300/µm, setting an approximate exciton density below which a three-carrier Auger recombination mechanism dominates. Coincidentally, this value is close to the e-h pair density generated by the 11 µJ/cm2 pump fluence in our experiments, which has already been shown to decay via a three-carrier Auger mechanism (Figure 4). Therefore, depending on excitation density, the e-h pair relaxation dynamics in NWs follows either a third-order process, previously associated with 0D systems, or a second-order process, predicted for NWs with 1D excitons present. In principle, such a transition from bimolecular to three-carrier kinetics should also occur in the tail of our high intensity decays. However, a subsequent reanalysis of these data does not unambiguously distinguish the two due to the suppressed signal-to-noise in this region. At low intensities a more complex treatment of carrier relaxation dynamics at the NW band edge must account for other processes such as carrier trapping by surface states and Auger-assisted ionization.32 This is especially relevant given that the latter process accounts for ∼10% of all relaxation events in CdSe QDs.32 Therefore, more detailed studies, aimed at deconvoluting the role of the surface must be carried out in the future by comparing the relaxation dynamics of overcoated to bare NWs. This can be undertaken once suitable surface modification chemistries have been developed for solution-based wires. Furthermore, such studies must be carried out as a function of excitation intensity given the multicarrier nature of an Auger-assisted ionization process. Despite the current lack of such studies, the robustness of the fits to a three-carrier Auger relaxation at low intensities (Figure 4) would suggest dominant Auger recombination kinetics occurring in the NWs. Motivating our study has been the understanding that learning to suppress and/or control multicarrier Auger processes is integral to achieving both ensemble45 and single wire lasing.46 In this respect, NWs have two major advantages over QDs or NRs. First, the large NW absorption cross section reduces the optical gain threshold by several orders of magnitude since relevant intensity thresholds are inversely proportional to σ. Pump fluences that induce less than 1 e-h pair per QD or NR create hundreds to thousands of e-h pairs per NW within the model discussed herein. Furthermore, another important advantage is the different scaling of exciton lifetimes with n(t). Whereas in QDs, τ is proportional to 1/n2, in NWs it scales as 1/n, resulting in longer optical gain lifetimes.11,12 As an example, our results show that a pump fluence of 23 µJ/cm2 creates approximately 500 1D excitons per NW with a recombination lifetime of ∼350 ps. This is greater than corresponding values for QDs and NRs, both in terms of number (larger by nearly 2 orders of magnitude) and duration (larger by at least a factor of 3), meaning that, in principle, lasing is more readily achieved with NWs.12 Nano Lett., Vol. 6, No. 7, 2006

In conclusion, we have investigated carrier recombination dynamics in CdSe NWs over a wide range of excitation intensities. At pump fluences above 23 µJ/cm2 the decay of the band edge state is dominated by the bimolecular annihilation of 1D excitons with a quadratic Auger constant C2 of ∼2 × 10-10 cm3 s-1. These data provide some of the first evidence for the formation of 1D excitons in NWs. At lower intensities, however, an apparent transition to threecarrier Auger decay kinetics occurs. The corresponding Auger constant C3 is ∼2.5 × 10-28 cm6 s-1, consistent with that previously reported in large CdSe QDs. Contributions to the recovery by a three-carrier Auger process is supported by phase admixtures in the NWs, leading to a type II staggered potential for electrons and holes at the band edge. As a consequence, e-h pair dynamics in solution-based CdSe NWs can exhibit both NW- and QD-like behavior depending on excitation intensity. Acknowledgment. We thank Vladimir Protasenko and Dani Meisel for a critical reading of the manuscript. The research described herein was supported by the Office of Basic Energy Sciences of the US Department of Energy. M.K. thanks the University of Notre Dame, the Notre Dame Faculty Research Program, the ACS Petroleum Research Fund, the NSF CAREER Program, the Notre Dame Radiation Laboratory, and the DOE Office of Basic Energy Sciences for financial support. This is contribution number 4647 from the Notre Dame Radiation Laboratory. Supporting Information Available: Absorption saturation curve of the band edge state and alternative linear plots of Auger fits to the experimental data. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Burda, C.; Chen, X. B.; Narayanan, R.; El-Sayed, M. A., Chem. ReV. 2005, 105, 1025-1102. (2) Brus, L. Appl. Phys. A 1991, 53, 465-474. (3) Alivisatos, A. P. Science 1996, 271, 933-937. (4) Klimov, V. I. J. Phys. Chem. B 2000, 104, 6112-6123. (5) Klimov, V. I.; Mikhailovsky, A. A.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Science 2000, 287, 1011-1013. (6) Ghanassi, M.; Schanneklein, M. C.; Hache, F.; Ekimov, A. I.; Ricard, D.; Flytzanis, C. Appl. Phys. Lett. 1993, 62, 78-80. (7) Roussignol, P.; Kull, M.; Ricard, D.; Derougemont, F.; Frey, R.; Flytzanis, C., Appl. Phys. Lett. 1987, 51, 1882-1884. (8) Efros, A. L.; Efros, A. L. SoV. Phys. Semicond. 1982, 16, 772-775. (9) Abram, R. A.; Kelsall, R. W.; Taylor, R. I. J. Phys. Chem. Solids 1988, 49, 607-613. (10) Mohamed, M. B.; Burda, C.; El-Sayed, M. A. Nano Lett. 2001, 1, 589-593. (11) Htoon, H.; Hollingsworth, J. A.; Dickerson, R.; Klimov, V. I. Phys. ReV. Lett. 2003, 91, 227401. (12) Htoon, H.; Hollingsworth, J. A.; Malko, A. V.; Dickerson, R.; Klimov, V. I. Appl. Phys. Lett. 2003, 82, 4776-4778.

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