Cooling and Auger Recombination of Charges in PbSe Nanorods

Aug 22, 2013 - The cooling and Auger recombination of electron–hole pairs in PbSe quantum dots (QDs) and a series of nanorods (NRs) with similar dia...
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Cooling and Auger Recombination of Charges in PbSe Nanorods: Crossover from Cubic to Bimolecular Decay Michiel Aerts, Frank C. M. Spoor, Ferdinand C. Grozema, Arjan J. Houtepen, Juleon M. Schins,* and Laurens D. A. Siebbeles* Optoelectronic Materials Section, Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands S Supporting Information *

ABSTRACT: The cooling and Auger recombination of electron−hole pairs in PbSe quantum dots (QDs) and a series of nanorods (NRs) with similar diameter and varying length was studied by ultrafast pump−probe laser spectroscopy. Hot exciton cooling rates are found to be independent of nanocrystal shape. The energy relaxation rate decreases during cooling of charges, due to reduction of the density of electronic states. Auger recombination occurs via cubic third-order kinetics of uncorrelated charges in the QDs and NRs with length up to 29 nm. On increasing the NR length to 52 nm, a crossover to bimolecular exciton decay is found. This suggests a spatial extent of the one-dimensional exciton of 30−50 nm, which is significantly smaller than the value of 92 nm for the three-dimensional exciton diameter in bulk PbSe. The Auger decay time increases with NR length, which is beneficial for applications in nanocrystal lasers as well as for generation of free charges in photovoltaics. KEYWORDS: PbSe, nanorods, quantum dots, Auger recombination, charge cooling

T

Coulomb interactions and relaxes momentum conservation conditions. Auger decay has a negative effect on lasing applications, since it limits the accumulation of e-h pairs, which is necessary for gain to occur. In photovoltaic devices, Auger decay can limit the photocurrent, since it competes with formation of free charges. In the case that electrons and holes act as uncorrelated particles, Auger recombination follows cubic third-order kinetics. A situation of uncorrelated charges arises when the Coulomb interaction is small compared with the kinetic energy, or in the case of strong quantum confinement so that charges are delocalized over the entire nanocrystal. Bimolecular secondorder Auger recombination occurs when electrons and holes are Coulombically bound in the form of excitons with a spatial extent that is smaller than the dimension of the nanocrystal in one or more directions. In the latter situation, excitons diffuse within the nanocrystal and undergo Auger recombination on close encounter. A transition from cubic to bimolecular Auger decay has been observed on-going from zero-dimensional CdSe QDs to one-dimensional NRs with aspect ratio exceeding 8.13 The transition to bimolecular decay of excitons in longer NRs is not surprising, since the exciton Bohr radius in bulk CdSe is only 5.4 nm. Interestingly, bimolecular exciton decay kinetics has been reported for PbSe nanorods with a length of 20−30 nm,14 which is well below the PbSe bulk Bohr radius of 46 nm.

he optical and electronic properties of colloidal semiconductor nanocrystals are of fundamental interest and offer promising prospects for development of devices, such as light-emitting diodes, lasers, and photovoltaics.1,2 The interest in nanocrystals results largely from the possibility to tune their optoelectronic properties by variation of composition, size, and shape.3 Using colloidal synthesis it is possible to obtain zerodimensional spherical quantum dots (QDs) and nanocubes, one-dimensional nanorods (NRs) and nanowires, and twodimensional nanoplatelets and nanosheets.3−6 As a result of the large optical absorption cross section it is readily possible to photoexcite multiple electrons in a nanocrystal by using common (laser) light sources. Multiexcitons play a central role in lasing applications of nanocrystals.7,8 Multiexcitons can also result from photoexcitation of a nanocrystal with a single photon of sufficient energy. In this case, photoexcitation initially leads to formation of a hot electron−hole (e-h) pair that relaxes by Coulomb scattering on other electrons, leading to formation of a multiexciton. This process of multiple exciton generation (MEG, also known as carrier multiplication) receives a great deal of attention due to prospects for development of highly efficient nanocrystal photovoltaics.9−11 Multiexcitons can decay via an Auger process in which an electron and hole recombine and transfer their energy by reexciting a third particle, either an electron or a hole.12 In general, Auger recombination can be considered as the inverse of MEG. Auger decay is more efficient in nanocrystals than in bulk, because confinement of charges in a nanocrystal enhances © 2013 American Chemical Society

Received: June 18, 2013 Revised: August 16, 2013 Published: August 22, 2013 4380

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Excitons in longer NRs may be much more localized than in bulk, because the e-h Coulomb attraction acts predominantly through the low dielectric host medium.15,16 As already noted in ref 14, studies on a wider range of PbSe NR aspect ratios are needed to further establish the threshold for the crossover from cubic to bimolecular Auger recombination. Such studies are also important in view of applications, since the near-infrared band gap of PbSe nanocrystals is of interest for development of lasers at these wavelengths and is optimal for exploitation of MEG in solar cells.9,10 It has been shown that the efficiency of MEG is enhanced in PbSe nanorods compared to PbSe quantum dots,17−19 leading to discussion about the nature of the photoexcited electron−hole pair in a nanorod, and the consequences for the MEG efficiency.20,21 The current work involves ultrafast optical pump−probe laser spectroscopic studies on the effect of the aspect ratio of PbSe nanocrystals on the cooling of hot charges and the nature of the kinetics of Auger recombination. Near-infrared broadband detection of the transient change in optical absorption is essential to distinguish the biexcitonic spectral shift induced by Coulomb interactions22,23 from population dynamics of the band-edge states due the cooling of hot charges. The relaxation rate of hot charges was found to be similar for QDs and NRs. We found a transition from third-order to second-order Auger decay kinetics on increasing the length of the NRs from 29 to 52 nm. The biexciton lifetime was found to scale linearly with the length (or volume) of the NRs. This volume scaling of the biexciton lifetime does no longer hold for QDs with similar diameter. Sample Preparation and Spectroscopic Characterization. Spherical PbSe QDs were synthesized according to the recipe of Murray et al.24 PbSe NRs were synthesized according to the method of Koh et al.25 This method uses tris(diethylamino)phosphine (TDP) to create the selenium precursor, leading to anisotropic growth in the reaction with the lead precursor. Details of the synthesis are given in the Supporting Information. To study the effect of rod length we prepared QDs and four NR samples with similar diameter and varying length: QDs with diameter d = 4.6 (±0.3) nm, short NRs with length L = 11.5 (±1.0) nm and d = 4.3 (±0.3) nm, medium-sized NRs with L = 27 (±5) nm and d = 4.3 (±0.3) nm or L = 29 (±5) nm and d = 4.5 (±0.4) nm, and long NRs with L = 52 (±8) nm and d = 4.2 (±0.4) nm. The length and diameter were determined from transmission electron microscopy (TEM) images (Figure 1b−e) taken using a FEI monochromated Tecnai 200STEM-FEG microscope equipped with a Gatan US1000 CCD camera. TEM pictures show monodisperse QDs and short NRs, though for the longer NRs (27, 29, 52 nm) a significant fraction (20−40%) of branched (T- and L-shaped) structures was found. The optical absorption spectrum of the QDs in Figure 1a exhibits a pronounced peak at 1420 nm due to the 1Sh−1Se electronic transition. The corresponding optical transition at the band gap of the NRs is red-shifted due to reduced quantum confinement along the axis direction. Additional transitions can be observed in the QD spectrum at shorter wavelengths, including the 1Ph−1Pe transition at 1120 nm,23,26 transitions involving heavily mixed P- and D-states at 820 nm27 and the Σpoint transition at 650 nm.26 For the NRs the Σ-point transition (near 650 nm, not shown) is discernible, while other individual transitions cannot be distinguished due to the increased density of states resulting from charge delocalization along the NR axis.

Figure 1. (a) Optical absorption spectra of colloidal dispersions of PbSe QDs and NRs in toluene. The similar position of the first absorption peak reflects the similar diameter of the samples. (b−e) TEM pictures of the nanocrystal samples: (b) 4.6 nm QDs, (c) 11.5 nm × 4.3 nm NRs, (d) 27 nm × 4.3 nm NRs and (e) 52 nm × 4.2 nm NRs.

We studied the dynamics of excitons by using ultrafast pump−probe laser spectroscopy with near-infrared broad band detection. The nanocrystal samples were dispersed in toluene in a 2 mm stirred cuvette at a typical optical density of 0.05 at the band gap. The samples were excited with a ∼200 fs laser pulse (Light Conversion Pharos-SP combined with Orpheus OPA) of 800, 500, or 400 nm and probed using multichannel detection of near-infrared (1080−1630 nm) probe pulses (Ultrafast Systems Helios). The broad band probe pulses were generated in a sapphire crystal using 1030 nm pump light. We determine the pump-induced transient change of the optical density of the sample according to ΔA = log10(Ioff/Ion), with Ioff (Ion) the transmitted probe fluence with pump laser off (on). Hence, negative signals (ΔA < 0) correspond with a bleach and positive signals (ΔA > 0) correspond with induced absorption. The pump laser fluence was kept low enough to prevent features due to multiexcitons, unless stated otherwise (i.e., in the studies of multiexciton Auger decay). Figure 2 shows spectra of the transient change in optical density for the PbSe QDs (left) and 11.5 nm PbSe NRs (right) after excitation by a 800 nm pump pulse. The response of the QDs is dominated by a large bleach of the 1Sh−1Se transition, 4381

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Figure 2. Spectra of transient change in absorption, ΔA, after 800 nm photoexcitation of PbSe QDs with diameter of 4.6 nm (left) and PbSe NRs with length of 11.5 nm (right). Optical bleach corresponds with ΔA < 0 and induced absorption gives ΔA > 0. The upper panels show the magnitude of ΔA in color code as a function of probe wavelength and pump−probe delay time. The lower panels show the wavelength dependence of ΔA at specific pump−probe delay times (data have been corrected for time-dispersion of the probe light).

Figure 3. Upper panels: Rise of the band-edge bleach for QDs and NRs after excitation at (a) 800 and (b) 400 nm. Lower panels: Bleach integrated over wavelength near the band gap (see text) versus time for excitation at (c) 800 and (d) 400 nm.

entire 3 ns pump−probe delay time, due to the long exciton lifetime (0.1−1 μs).14 The initial transient absorption on the red side of the QD band gap (>1450 nm) is due to the

caused by reduced ground state absorption and stimulated emission from the band-edge excitons. The 1Sh−1Se bleach shows a fast subpicosecond rise and does not decay over the 4382

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Figure 4. Spectrally integrated transient absorption (left axis, data points) for different excitation densities for the (a,b) 4.6 nm QDs, (c,d) 11.5 nm NRs, (e,f) 29 nm NRs, and (g,h) 52 nm NRs. Right axis, solid lines: curves obtained by fitting the cascade model for cubic third-order Auger decay of uncorrelated charges (left panels), or bimolecular decay of excitons (right panels).

biexciton shift,22 induced by the presence of the exciton generated by the pump pulse.4,19 The biexciton shift is more pronounced on short time before cooling of hot charges has completed, in agreement with previous findings.19 The transient absorption in the range 1200−1300 nm at short times is caused by hot charges and disappears on longer times after cooling. The undulating feature consisting of bleach/ absorption at wavelengths below/above 1120 nm is due to a biexcitonic redshift of the 1Ph−1Pe transition.23 The transient absorption spectrum of the NR only exhibits a bleach of the first optical transition and features due to higher transitions are absent, in agreement with the steady-state

absorption spectrum in Figure 1a. A biexcitonic redshift of the band-edge transition is observed at early times when hot charges are still present. Cooling Dynamics of Hot Charges. The cooling of hot excitons to the band-edge was studied by measurements of the rise of the optical bleach in the wavelength range of the bandedge transition. Figure 3a,b shows the absolute value of the bleach at a single probe wavelength corresponding with the maximum of the band-edge transition for QDs and NRs, measured after excitation with a 800 nm (1.55 eV) or 400 nm (3.1 eV) pump pulse. The bleach immediately increases during the ∼200 fs pump pulse and becomes constant on longer times. 4383

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extents to somewhat longer wavelengths than the maximum attainable probe wavelength of 1630 nm in the transient absorption measurements. For these samples, we integrated the transient absorption over a symmetric wavelength interval around the maximum in the bleach up to 1630 nm. The signal at 2−3 ps after the pump laser pulse obtained in this way was found to be proportional with the pump laser fluence, or equivalently, the population of band-edge states. To realize higher values of Navg we used shorter pump wavelengths at which the absorption cross section of the nanocrystals is larger. The photon energy was in all cases kept sufficiently low to prevent MEG, as inferred from the absence of a fast Auger decay component at low pump fluence for which Navg ≪ 1. The results for the generation and decay of (multi)excitons in the QDs and NRs with different length are shown in Figure 4. The initial rise of the integrated transient absorption is due to cooling of hot excitons to the band-edge. The transients exhibit a fast and slow decaying component. The amplitude and decay rate of the fast component increase with Navg and therefore this component is attributed to Auger decay of multiexcitons. The long-lived tail is due to single excitons that remain after Auger decay is complete. To determine if Auger decay occurs via third-order kinetics of uncorrelated charges, or via bimolecular decay of bound excitons, we analyzed the data in Figure 4 by a stochastic cascade model of multiexciton decay.31 The time-dependent probability ρn(t) that a nanocrystal contains n e-h pairs is obtained from the kinetic equation

The bleach at a single probe wavelength can be affected by the biexcitonic redshift and does not necessarily provide an accurate measure of the population of cold band-edge states.22 In case only a biexcitonic shift occurs, without population of a band edge state the transient absorption integrated over wavelength becomes zero. In case the band edge state is populated, integration over the negative and positive undulations near the band gap results in a nonzero value and represents the band edge population. The absolute values of the integrated transient absorption signals obtained in this way are shown in Figure 3c,d. Immediately after the pump pulse the integrated transient absorption is zero, reflecting that hot charges have not yet relaxed to the band-edge. The integrated transient absorption in Figure 3d for excitation at 400 nm is close to zero during one picosecond after the pump pulse, while the bleach measured at a single wavelength in Figure 3b has almost reached its maximum value after this time duration. The data in Figure 3 demonstrate that spectral integration is essential to determine the population of band-edge excitons. Interestingly, the cooling dynamics of charges for the QDs and NRs is similar, in agreement with previous experimental results.14 Figure 3c,d shows that it takes ∼300 fs before the first charges arrive at the band-edge after 800 nm excitation, while it takes ∼1 ps for excitation at 400 nm. There is no immediate population of band-edge states and it is not necessary to invoke an energy level that is common to the pump and probe pulses, as was done previously to explain the ultrafast bleach at a single probe wavelength.14 The average relaxation time, defined as the time after which the integrated bleach has reached half of its maximum, is 0.7 ps for excitation at 800 nm and 1.7 ps for excitation at 400 nm. Because of the similar effective mass of electrons and holes in PbSe the photon energy in excess of the band gap is divided close to equally over the two types of charges. The band gap of the nanocrystals is about 0.85 eV, so that a charge initially has 0.35 or 1.1 eV excess energy for excitation at 800 and 400 nm, respectively. From the relaxation times determined above it can be inferred that it takes 1 ps to cool from 1.1 eV down to 0.35 eV (rate 0.75 eV/ps) and 0.7 ps to cool from 0.35 eV to the band-edge (rate 0.50 eV/ps). The latter rate is similar to that for PbSe QDs reported in ref 28. For the nanocrystals studied, we found that MEG occurs after excitation at 400 nm with an efficiency of 30−40%. Hence, the initial cooling of a charge with 1.1 eV excess energy to the nanocrystal band gap is due to both MEG and phonon emission, while at lower energy only the latter process occurs. Taking the effect of MEG into account, our results show that the relaxation rate by phonon emission decreases at lower energy when the levels become sparser, in agreement with previous measurements.29 Taking this energy dependence of the cooling rate into account will improve theoretical modeling studies on the efficiency of MEG, such as those reported in ref 30. Auger Decay of Multiexcitons. Multiexcitons were generated by pumping with sufficient fluence to absorb more than one photon per nanocrystal on average, that is, Navg exceeds one. Note that Navg = jσ, with j the pump fluence (number of incident photons per unit area) and σ the absorption cross section of the nanocrystal at the pump wavelength. The time-dependent multiexciton population was determined from the integrated transient absorption near the band gap, similar to the studies on cooling dynamics described above. For the two longest NRs the absorption (Figure 1)

d ρ (t ) = −knρn (t ) + kn + 1ρn + 1(t ) dt n

(1)

with kn the rate of decay from n to n − 1 excitons. First-order (non)radiative decay was taken into account for single excitons (n = 1), while it was neglected for n ≥ 2 since Auger recombination of multiexcitons is orders of magnitude faster. The initial multiexciton distribution is given by Poisson statistics, according to ρn (t = 0) =

(Navg)n n!

e−Navg

(2)

The integrated transition absorption near the band gap on a time scale after cooling and prior to Auger recombination scales linearly with the number of excitons as long as saturation due to state-filling does not occur. For the excitation densities in Figure 4 nonlinear effects due to saturation were always less than 10%, in agreement with previous results,14,23 and in that case ∞

|

∫

ΔA(t )dλ| ∝ =

∑ nρn (t ) n=1

(3)

The rate constant of third-order Auger recombination of uncorrelated charges scales with the number of possibilities to select an electron from n electrons and a hole from n holes, and a third charge from the remaining (n − 1) electrons and holes, so that kneh =

1 2 n (n − 1)k 2eh 4

(4)

for n ≥ 2. The rate constant of bimolecular exciton decay scales with the number of possibilities to select two excitons from a population of n excitons; that is 32,33

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1 n(n − 1)k 2ex 2

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(5)

for n ≥ 2.32,33 The model outlined above was used to describe the experimental data in Figure 4 and the values of the rate of ex single exciton decay k1, as well as keh 2 or k2 , and Navg were treated as fitting parameters. For each nanocrystal sample, the ex rate constants k1, keh 2 , and k2 were kept constant, while Navg scales linearly with pump fluence. The results obtained from fitting ⟨n(t)⟩ to the experimental data are plotted against the right-axis in Figure 4 for cubic decay (eq 4, left panels) or bimolecular decay (eq 5, right panels). The relatively small absorption cross section at the 800 nm pump wavelength used for the QD sample restricted the maximum attainable value of Navg to 3. At the maximum excitation density of 3.0, the difference between the cubic and bimolecular fits is small. However, cubic decay gives a better fit (χ2 = 0.096) than bimolecular decay (χ2 = 0.148). Cubic decay is expected, since the bulk exciton Bohr radius of 46 nm largely exceeds the QD radius, so that the charges are uncorrelated. The cubic Auger decay rate constant for two e-h pairs found −2 ps−1. Comparison of Figure 4c,e from the fits is keh 2 = 1.4 × 10 with Figure 4d,f, respectively, shows that cubic Auger decay describes the experimental data for the 11.5 and 29 nm NRs very well, while bimolecular decay does not reproduce the measurements at higher initial exciton population. The cubic −3 ps−1 decay constants obtained from the fits are keh 2 = 3.1 × 10 eh −3 −1 for L = 11.5 nm and k2 = 1.6 × 10 ps for L = 29 nm. As can be seen in Figure 4g, the experimental data for the long NRs with L = 52 nm cannot be reproduced by cubic decay, while the bimolecular Auger decay of excitons in Figure 4h −3 describes the data very well with kex ps−1. Hence, 2 = 1.4 × 10 for a NR length between 29 and 52 nm the nature of e-h pairs changes from that of uncorrelated particles to that of bound excitons. Our finding of cubic Auger decay in NRs with lengths of 29 nm differs from that of Yang et al.,14 who inferred bimolecular exciton decay for PbSe NRs with length of 20−30 nm and diameter similar to that in the present work. The discrepancy could be due to restriction of Navg to values of 2 and 3 only, and single wavelength probing by Yang et al.14 According to the results in Figure 4 the crossover from uncorrelated charges to bound excitons takes place for NRs with lengths between 29 and 52 nm. In case the bound excitons do initially not exhibit significant spatial overlap, the spatial extent of an exciton along the NR axis is in the range 30−50 nm. Although care should be taken to compare the spatial extent of one- and three-dimensional excitons, we consider it of interest that the one-dimensional spatial extent is smaller than the bulk exciton Bohr diameter of 92 nm. The smaller spatial extent of an exciton in a NR can result from reduced dielectric e-h screening, and possibly a change of effective mass of charges, on going from bulk to a one-dimensional system, see ref 34. The significance of these factors could be determined in studies by theorists. Figure 5 shows the Auger decay time of biexcitons ex (τ2 = 1/keh 2 or 1/k2 ) as a function of nanocrystal volume. Since the NRs have similar diameter, it can be inferred that the biexciton lifetime scales linearly with NR length, in agreement with previous results on PbSe NRs.19 The increase of the biexciton lifetime with length reflects the lower charge density along a NR, which reduces the Coulomb interaction matrix element. The biexciton lifetime for the QD does not follow the

Figure 5. Biexciton Auger recombination time τ2 as a function of nanocrystal volume. The solid line is a fit of a linear dependence of τ2 on volume.

linear trend of the NRs, despite the similar diameter. This suggests an effect of nanocrystal shape on the biexciton lifetime, which was not observed in earlier measurements.14,19 An explanation of the influence of nanocrystal shape on the biexciton lifetime is still lacking. Conclusions. We used ultrafast pump−probe laser spectroscopy to measure hot exciton cooling and Auger recombination in a series of PbSe QDs and NRs with similar diameter (4.2−4.6 nm) and increasing length (4.6−52 nm). For these samples, the cooling rate of hot charges was found to be similar. Auger recombination occurs via cubic decay of uncorrelated charges in QDs and NRs with a length up to 29 nm. Bimolecular exciton decay is found to occur in NRs of 52 nm length. From this observation, we infer that the spatial extent of the one-dimensional exciton is 30−50 nm. The biexciton lifetime increases linearly with the NR length as a result of charge delocalization and consequently decreased Coulomb interaction. The increase of the Auger decay time of multiexcitons in longer NRs is beneficial to achieving optical gain in nanocrystal lasers and can lead to enhanced photocurrent in photovoltaics.

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ASSOCIATED CONTENT

S Supporting Information *

Materials and synthesis details. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.A. acknowledges financial support for this research from ADEM, A green Deal in Energy Materials of the Ministry of Economic Affairs of The Netherlands (www.ademinnovationlab.nl).

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REFERENCES

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