Multiresonant Multidimensional Spectroscopy of Surface-Trapped

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Multiresonant Multidimensional Spectroscopy of Surface-Trapped Excitons in PbSe Quantum Dots Stephen B. Block, Lena A. Yurs, Andrei V. Pakoulev, Rachel S. Selinsky, Song Jin, and John C. Wright* Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States S Supporting Information *

ABSTRACT: Recent work spectrally isolated and measured the quantum states associated with ultrafast relaxation from an initially excited 1S excitonic state to a lower energy state that is present in an inadequately capped PbSe quantum dot sample. The relaxed state was attributed to a surface-trapped exciton (STE). This letter reports the line-narrowed, multiresonant, two-dimensional spectrum of this sample. The multidimensional spectrum is unusual because diagonal peaks are absent, but there is a strong cross-peak between the 1S and STE transitions. Theoretical modeling provided values for the coherent and incoherent dynamics, the relative exciton and biexciton transition moments, the Coulombic coupling, and the homogeneous and inhomogeneous broadening. This work demonstrates the feasibility of using multiresonant methods to probe the quantum state dynamics of interface states in nanostructures. SECTION: Physical Processes in Nanomaterials and Nanostructures

T

inadequate capping of the QD sample due to impurities in the oleic acid (OA) ligand reagent used during QD synthesis. The cross-peak has been attributed to ultrafast relaxation of the initially excited 1S exciton to a surface-trapped excitonic (STE) state,6 which is similar to that observed by Kambhampati et al. in CdSe QDs.7−9 The CMDS spectra show this state has a different dependence on the size distribution within the inhomogeneously broadened excitonic line profile and no appreciable coupling to the 1S excitonic state. Modeling the CMDS spectrum provides a detailed characterization of the 1S and STE states. The cross-peak is different from the cross-peak between the (1Se−1S3/2) and (1Se−2S3/2) excitonic states observed by Turner et al. in CdSe QDs.10 That cross-peak was red-shifted by ∼810 cm−1, and it was an intrinsic state of CdSe. The multiresonant CMDS experiments on the unstable PbSe colloidal QDs contrast with the earlier experiments on stable PbSe colloidal QDs that demonstrated the feasibility of multiresonant CMDS.5 The excitation pulse frequencies were ⃗ = k1⃗ − k2⃗ ω1 and ω2, and the phase matching condition was kout + k2′⃗ where the subscripts label the frequencies and the k2⃗ and k2′⃗ beams were formed by splitting the ω2 beam. Fitting the line-shapes provided a state-resolved measurement of the dephasing and population relaxation rates, relative transition moments, biexciton Coulombic coupling, and the inhomogeneous broadening of the excitonic states.5 In multiresonant CMDS experiments, the initial spectra of the 1S exciton diagonal peak in the incompletely capped QD

he creation of stable donor−acceptor nanostructures with high solar collection efficiencies requires balancing efficient donor−acceptor coupling across heterojunctions and the passivation of surface states. Engineering nanostructure synthesis can be facilitated by surface and interface characterization methodologies that can guide the synthetic strategies. Multiresonant coherent multidimensional spectroscopy (CMDS) provides a new approach for probing excitonic dynamics and surface states with quantum state resolution.1−3 The technique is a mixed frequency- and time-domain method that selectively excites individual, energetically disparate quantum states and measures their dynamics. Three tunable picosecond excitation pulses create a nonlinear polarization by four wave mixing (FWM). Scanning their frequencies while measuring the resonance enhancements of the FWM output beam creates multidimensional spectra. The multiple resonances of CMDS can resolve features beneath the inhomogeneously broadened excitonic resonances by multiplicatively enhancing transitions arising from a fully resonant subensemble of QDs within the inhomogeneous ensemble. They also provide strong discrimination between the quantum-confined excitonic states and the strong and broad background from delocalized excitonic states4 that obscures the quantum confined states.5 In this work, we show it is capable of isolating other quantum states involved in excitonic relaxation and defining the correlations between them. Typical CMDS spectra contain diagonal peaks where the multiple excitation frequencies excite the same quantum states and cross-peaks between quantum states that are coupled.3 This paper reports an unusual multiresonant CMDS spectrum for a PbSe colloidal quantum dot (QD) sample that exhibits only a cross-peak after aging. The cross-peak is believed to result from © 2012 American Chemical Society

Received: May 11, 2012 Accepted: September 6, 2012 Published: September 6, 2012 2707

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standard deviation for the intensity was typically 7% (see Supporting Information). A recent paper developed closed form equations for the resonance enhancements in the steady state that include the multiple coherence pathways and the inhomogeneous broadening.5 The steady state is an appropriate limit since the picosecond excitation pulse width is much longer than the short excitonic dephasing times. Earlier work13 demonstrated that it was possible to obtain closed form expressions for the resonance enhancements in multiresonant CMDS if the inhomogeneous broadening was described by a Lorentzian distribution that approximates the more appropriate Gaussian distribution. It is particularly advantageous in having efficient algorithms that model multidimensional spectra. This approximation results in differences between simulations and experiment in the wings of spectral features, but it works well elsewhere. Figure 1 shows only the coherence pathways where

sample were the same as those seen in the stable PbSe QD sample.6 However, the spectra changed as the sample aged over a 2 month period. The diagonal 1S exciton peak disappeared and was replaced by a cross-peak that was red-shifted by ∼500 cm−1. In order to measure the optical properties of this crosspeak, a one-dimensional FWM spectrum was obtained by temporally overlapping the three excitation pulses, fixing the ω1 frequency to probe the lower frequency relaxed peak, and scanning the ω2 frequency across the entire region of the 1S exciton while monitoring the output beam intensity. The resulting spectrum contained enhancements from the PbSe excitonic and biexcitonic resonances, but it also contained vibrational resonances of the solvent at ω2−ω1 difference frequency from coherent anti-Stokes Raman scattering (CARS). The interference between the PbSe and solvent output coherences created complex line-shapes that allowed the determination of the magnitude and phase of the underlying excitonic and biexcitonic states. Since the frequency dependence of vibrational resonances is well-known and the third order susceptibility and hyperpolarizability can be calibrated against standards, it was possible to extract absolute values for the frequency dependence of the magnitude and phase of the excitonic and biexcitonic resonances as well as the dephasing and population relaxation rates, relative transition moments, biexciton Coulombic coupling, and the inhomogeneous broadening of the excitonic states. These values and those obtained from the stable PbSe QD sample were used to model the spectra of this unstable sample. Details of the preparation of the OA-capped PbSe QD sample used in this study were described previously.5,6 The sample was dispersed in anhydrous carbon tetrachloride solvent in a 1 mm thick cuvette under an inert nitrogen atmosphere. It was stored in this cuvette at room temperature in the normal laboratory environment over the 2.5 month period leading to these experiments. Transmission electron microscopy (TEM) imaging showed that unlike previously synthesized samples, the QDs in this sample had asymmetric shapes and diverse morphologies. Many self-aligned into wire-like structures.11 TEM imaging of the samples after 2.5 months of aging showed no significant changes in size, shape, or morphology. Representative TEM images appear in the Supporting Information. We discovered that impurities in the OA reagent used during QD synthesis resulted in inadequate capping and the diverse morphologies in the QD sample. No further samples were synthesized with this specific batch of OA reagent. Subsequent QD samples synthesized using fresh OA were stable and lacked the cross-peak. The multiresonant CMDS experiments used two optical parametric amplifiers’ (OPAs) pulses with ∼1 ps temporal width, ∼20 cm−1 spectral width (fwhm), ∼1 μJ pulse energies, and ω1 and ω2 frequencies that were tunable from ∼7000 cm−1 ⃗ = k1⃗ − k2⃗ + k2′⃗ . to 9000 cm−1. The phase-matching was kout Details appear elsewhere.5 The ω2 and ω2′ beams interact first and create a population in the 1S exciton state. The ω1 beam appeared last and created the output coherences. The beams’ fluence and intensity were 200 μJ/cm2 and 2 × 108 W/cm2, respectively. Since the absorption cross-section for our sample is 5 × 10−16 cm2,12 the fluence of these beams excites ∼0.7 excitons on an individual QD. The corresponding excitation rate is 8 × 1012 s−1. Saturation and higher order effects are therefore present but are not likely to change the spectral features. The output beam was spatially isolated and spectrally resolved with a monochromator at the frequency ωm. The

Figure 1. Relevant Liouville coherent pathways. The arrows designate transitions between states. The numbers designate the excitation ⃗ = k1⃗ − frequencies (ω1 and ω2 with the phase matching condition kout k2⃗ + k2′⃗ ) the dotted arrow represents population transfer, the letters designate states for each coherence and population. g, e, and e′ designate the ground, 1S, and STE states, respectively. The boxes designate the initial ground state and the emitting coherences.

the ω1 pulse occurs last. Interaction with temporally overlapped k2⃗ and k2′⃗ beams creates a 1S state population indicated by ee. The dotted arrow designates population relaxation to the STE e′e′ state population. Figure 1 also includes pathways involving the intermediate ee population that were neglected in the earlier work.5 They are necessary in this work to understand the absence of the diagonal peak. As a specific example, we consider the Liouville pathway gg 2′

−2

PT

1

⇒ e′e′ → 2e′,e′, where the letters represent the ba → ge → ee = states of the ρba density matrix elements: g, e, e′, 2e, 2e′, and e + e′ represent the ground state, the 1S, and the STE excitonic and biexcitonic states; the numbered arrows represent the interactions with the ωi beam, and the double arrow represents the rapid population relaxation of state e to e′. In the absence of inhomogeneous broadening and in the steady state, the frequency dependence of the 2e′,e′ biexciton−exciton coherence output is proportional to −

μeg2 μ2e2 ′ ,e ′ (2,2 ′) (1,2,2 ′) Δ(2) ge Δee Δ2e ′ ,e ′

⎞ ⎡ ⎛ ≡ −⎜⎜μeg2 μ2e2 ′ ,e ′⎟⎟ /⎢(ωge + ω2 − i Γeg)(ωee − ω2 + ω2 ′ ⎢ ⎠ ⎣ ⎝ ⎤ − i Γee)(ω2e ′ ,e ′ − ω1 + ω2 − ω2 ′ − i Γ2e ′ ,e ′)⎥ ⎥⎦ (1) 2708

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where Γba and μba are the dephasing rate and transition moment of the ba transition. Averaging over a Lorentzian inhomogeneous profile gives −

⎞ ⎡

⎛

∫ ⎜⎝μeg2 μ2e2 ′,e′⎟⎠/⎢⎣(ωge − ξ + ω2 − i Γeg)(ωee − ω1 + ω2 ⎤ − i Γee)(ω2e ′ ,e ′ + κξ − ω1 + ω2 − ω2 ′ − i Γ2e ′ ,e ′)⎥ ⎦ σ2 dξ π (ξ + σ 2 ) 2

=

2πμeg2 μ2e2 ′ ,e ′ 2 2 (2) (1,2,2 ) Γee((Δ(2) ge ) + σ )(Δ2e ′ ,e ′′ + κ Δge )

−

πμeg2 μ2e2 ′ ,e ′ (1,2,2 ) Γee(Δ(2) ge + iσ )(Δ2e ′ ,e ′′ + iκσ )

(2)

where σ is the half-width-half-maximum of the Lorentzian distribution, ξ is the inhomogeneous broadening shift, and κ is the ratio of the energy shift of e′ relative to e caused by perturbation ξ. The first term describes the line-narrowed ) (2) feature in CMDS spectra since the (Δ(1,2,2 2e′,e′ ′ + κΔge ) factor 2 does not involve inhomogeneous broadening. The ((Δ(2) ge ) + 2 σ ) factor describes the intensity of the inhomogeneous envelope of the line-narrowed feature.1 All the resonance factors in the second term contain the inhomogeneous broadening effects, so this term represents the inhomogeneous background lying beneath the line-narrowed feature. Similar expressions are available for all other coherence pathways (see Supporting Information). Together, they are proportional to the output field. Figure 2 illustrates the change in the multiresonant spectrum between the initial sample and the sample after 2.5 months. The solid lines denote spectral scans where ω2 was tuned to the center of the 1S excitonic resonance at ω2 = 7360 cm−1 and 7800 cm−1 for Figure 2a,b, respectively. The change in the 1S frequency reflects sample aging. The dashed lines in Figure 2a,b denote scans where ω2 was detuned to lower frequencies by 160 cm−1 and 300 cm−1, respectively. The monochromator was tuned so that ωm = ω1. The spectra of the initial sample (Figure 2a) have only the diagonal 1S excitonic peak that is centered at the same ω1, ω2, and ωm frequencies. It is line-narrowed because the ω2 excitation preferentially excites the resonant PbSe QDs within the inhomogeneously broadened line shape. It appears at the center of the inhomogeneously broadened 1S exciton transition when ω2 = 7360 cm−1 and it shifts when ω2 is detuned as the excitation frequency preferentially excites a different set of resonant PbSe QDs. The shift of the peak matches the detuning of ω2. Figure 2b shows the new crosspeak where ω2 is offset by ∼500 cm−1 from ω1 and the center of the 1S excitonic peak. The position of the cross-peak shifts as ω2 is detuned, but the shift is less than the detuning of ω2. The Figure 2b inset shows a logarithmic plot of the spectrum that confirms the absence of a diagonal feature. Figure 3a shows the two-dimensional CMDS dependence of the normalized intensity on the ω1 and ω2 frequencies for the aged sample. For this data, τ21 = τ2′1 = −1.5 ps so the ω2 and ω2′ pulses were temporally overlapped and the ω1 pulse followed by 1.5 ps. Even when the excitation pulses were temporally overlapped, the same shifted peak appeared and there was still no observable intensity at frequencies along the

Figure 2. Spectra of (a) the initial unstable PbSe QD sample and (b) the same sample 49 days later. The ω1 excitation frequency was scanned together with the monochromator frequency while ω2 was set at (a) 7360 (solid) and 7200 (dashed) cm−1 or (b) 7800 (solid) and 7500 (dashed) cm−1. The ω1 excitation pulse was delayed by (a) 2.0 ps and (b) 1.0 ps. The inset shows a logarithmic scale for the intensity so the absence of the diagonal feature is clearer.

diagonal. The cross-peak is narrower than the absorption transition, and it shifts as a function of ω2. The shifting and narrowing occurs because the ω2 resonance with the 1S state of a subset of QDs within the inhomogeneously broadened transition selectively enhances ω1 resonances with the STE state of the same subset. In order to analyze the spectral shape of the CMDS crosspeak, the pathways denoted by Figure 1 were modeled using the steady state and the Lorentzian inhomogeneous broadening approximations described earlier. In order to reduce the number of fitting parameters, the fitting uses many of the same values measured earlier.5,6 We used the dephasing and population relaxation rates, Coulombic coupling, and relative transition moments for the STE excitonic and biexcitonic states in the earlier work6 since that work directly measured the crosspeak with the 1S exciton. We used the dephasing rates, Coulombic coupling, and relative transition moments of the 1S exciton measured for the stable sample5 since only the 1S exciton appeared in this work. The 1S and STE state frequencies (ωeg and ωe′g), the 1S exciton population relaxation rate (Γee), and the relative transition moment of the STE exciton to 1S-STE biexciton transition (μe+e′,e′) were the remaining fitting parameters. The 1S exciton population relaxation rate affects the 1S dephasing rate through the relationship Γeg = (Γee + Γgg)/2 + Γ*eg, where Γ*eg is the pure dephasing rate. Since the dephasing rate is much faster than the population relaxation rate in stable QD samples,5 the measured dephasing rates are the pure dephasing rates. We further 2709

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Table 1

assume that the STE population decays directly to the ground state so Γe′e′=Γgg. Figure 3b shows the results of the simulation, and Table 1 summarizes the fitting parameter values. The average intensity difference between the model and data is 6%. The dephasing rates, Coulombic coupling, and relative transition moments of the excitons and biexcitonic states for the 1S and STE states are similar. The 0.45 value for κ shows that the QD size distribution that controls the inhomogeneous broadening has less effect on the STE state than on the 1S exciton. The absence of the diagonal feature results from two factors. 2′

−2

1

2′

The diagonal pathways are gg → ge → gg → eg, gg → ge → ee 1

−2

2′

1

−2

2′

PT

values 7754 cm−1 7284 cm−1 179 cm−1 151 cm−1 198 cm−1 174 cm−1 179 cm−1 5.1 cm−1 167 cm−1 5.1 cm−1 124 cm−1 117 cm−1 0 cm−1 678 cm−1 0.45 1 1.4 1.56 0.87

important, and their nonlinear polarizations have opposite phases. They cancel when the Coulombic coupling is negligible, Γee= Γ(e+e′),e′, and μeg = μe+e′,e′. Although the model provides the connection between the loss of the diagonal peak and the appearance of the cross-peak, it does not provide information about the nature of the STE state. TEM and visible absorption spectroscopy measurements did not reveal any significant changes in the morphology or size distribution between the initial and aged samples (see Supporting Information), so there is no indication that noticeable physical changes occurred. Surface states are often attributed to charge separated states where the excitonic electron and hole are separated so one is trapped at a surface defect and the other remains in the core.8,14−22 They also control QD blinking where the hole is localized on a surface defect and the electron is ionized.15,18,23−27 The QD fluorescence is quenched when the electron remains nearby in a reservoir state and returns when the electron recombines. The behavior of the PbSe QD sample in this work is similar to the STE state of the CdSe QDs observed by Kambhampati et al.7−9 The STE appeared as an A1 excited state absorption feature in the transient absorption spectrum of the CdSe QDs. The absorption includes transitions to an excitonic continuum that become allowed because the perturbations caused by the STE lower the symmetry of the system. The STE feature appeared in the CdSe QD samples that were phototreated to remove capping ligands, but it did not appear in well-passivated samples. The trapping rate was fast compared to the intraband relaxation rate. The CdSe wurtzite crystal structure allows an impulsive piezoelectric response from the internal electric field of the STE exciton. It launches an acoustical phonon that modulates the transient absorption. The measurements reported in this work provide new information about QD surface states that is not available by other methods. It shows that CMDS isolates and measures the spectral characteristics of surface states and observes changes in a QD sample that are not reflected in TEM imaging or absorption spectroscopy experiments. Although the CMDS measurements may be specific for the STE state in this particular sample, the measurements can still provide a point of

Figure 3. (a) Multiresonant CMDS spectra of the PbSe QD sample 49 days after synthesis (top) and (b) theoretical simulation (bottom). The color bar indicates the output signal intensity. The ω2 and ω2′ pulses are temporally overlapped, and the ω1 pulse is delayed by 1.5 ps.

−2

parameter ωeg ωe′g Γeg Γe′g Γ2e,e Γ2e′,e′ Γ(e+e′),e′ Γgg Γee Γe′e′ ω2e,e − ωeg ω2e′e′ − ωe′g ω(e+e′),e′ − ωeg σ κ μe′g/μeg μ2e,e/μeg μ2e′,e′/μe′g μ(e+e′),e′/μeg

1

⇒ e′e′ → e + e′,e′ → eg, gg → ge → ee → 2e, e, gg → ge → ee = for the 2′ pulse following pulse 2. There are four additional pathways with opposite time ordering. The second and third pathways depend on the Γee/Γe′e′ ratio. The measured ratio is 0.03 (Table 1). The value of Γee corresponds to a 1S state lifetime of 32 fs so the ultrafast relaxation makes these pathways unimportant. The first and last pathways, however, remain 2710

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comparison for future systematic studies28−32 that explore the role of different ligand impurities in creating surface states. Such studies are also important for characterizing the reproducibility of samples28−36 and understanding the factors that control the reproducibility. In addition, the presence of a cross-peak involving the STE state and the absence of a diagonal peak in CMDS is a striking and potentially important observation. It may well represent the signature of ultrafast charge transfer in donor−acceptor nanostructures in general where charge separation occurs efficiently. This work also demonstrates an important advantage of multiresonant CMDS. The STE peak appears as a small change in the probe intensity at the position of the A1 transient absorption feature in the previously reported phototreated CdSe QDs, and it is inhomogeneously broadened.7−9 The corresponding peak in our work appears as a strong, spectrally resolved, and line-narrowed cross-peak. The difference arises because multiresonant CMDS measures the appearance of a new phase-matched beam that depends on the contrast of the grating created by the crossing of the first two excitation beams. The grating contrast isolates the spectral changes created by the first two excitation beams. This capability is particularly important in extending this work to measurements of charge transfer in donor−acceptor structures such as epitaxial heterostructures of PbSe QDs on Fe2O3 nanowires.37

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information includes TEM images, a table and histograms of the size distribution, absorption spectra of the initial and aged colloidal PbSe QDs, example spectra that define the reproducibility of multiresonant CMDS scans, a comparison of representative experimental and simulated spectra, a two-dimensional display of the difference between the experimental and simulated spectra, the intensity dependence of the signal on the excitation pulse energies, and closed form expressions for the resonance enhancements of the relevant coherence pathways in the presence of a Lorentzian inhomogeneous distribution. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation under Grant DMR-0906525. Yanghai Yu synthesized and Rachel Selinsky characterized the QD samples used for this work. They were supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award # DE-FG02-09ER46664.

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REFERENCES

(1) Wright, J. C.; Carlson, R. J.; Hurst, G. B.; Steehler, J. K.; Riebe, M. T.; Price, B. B.; Nguyen, D. C.; Lee, S. H. Molecular, Multiresonant Coherent Four Wave Mixing Spectroscopy. Int. Rev. Phys. Chem. 1991, 10, 349−390. (2) Wright, J. C. Coherent Multidimensional Vibrational Spectroscopy. Int. Rev. Phys. Chem. 2002, 21, 185−255. (3) Pakoulev, A. V.; Block, S. B.; Yurs, L. A.; Mathew, N. A.; Kornau, K. M.; Wright, J. C. Multiply Resonant Coherent Multidimensional 2711

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The Journal of Physical Chemistry Letters

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