Article pubs.acs.org/JPCC
Spectral Isolation and Measurement of Surface-Trapped State Multidimensional Nonlinear Susceptibility in Colloidal Quantum Dots Lena A. Yurs, Stephen B. Block, Andrei V. Pakoulev, Rachel S. Selinsky, Song Jin, and John Wright* Department of Chemistry, University of WisconsinMadison, Madison, Wisconsin 53706, United States S Supporting Information *
ABSTRACT: Multiresonant coherent multidimensional spectroscopy (CMDS) is a powerful new method for probing the coupling between vibrational modes and their dynamics. The line narrowing that occurs because of the multidimensional nature of CMDS allows the separation of homogeneous and inhomogeneous broadening and enhances spectral resolution. Recent work has extended multiresonant CMDS to electronic resonances in quantum confined nanostructures. Vibrational modes of the solvent also appear in the CMDS spectra. The phase oscillations of the vibrational and electronic coherences interfere and change the line shapes. Since the form of the vibrational thirdorder susceptibility and hyperpolarizability are well-known and since they can be measured against known standards, it becomes possible to use the interference effects as a probe of the absolute magnitude and phase of the electronic resonances. This approach is demonstrated using PbSe quantum dots where incomplete capping causes ultrafast relaxation to a new electronic state that appears directly in the CMDS spectra. The new state is believed to be a mixed core/surface exciton. Closed-form expressions for the electronic nonlinearities are used to analyze the frequency dependence of the fully resonant complex hyperpolarizability of the 1S exciton and the surface-trapped state. The ability of mixed frequency/time domain multiresonant CMDS methods to spectrally resolve surface states promises to be an important new way to characterize the interface states in complex heterostructures and the surface states that define the stability of nanostructures resulting from different synthetic strategies.
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INTRODUCTION The electronic properties of quantum confined nanostructures form the basis for many of the promising applications of nanotechnology including photocatalytic production of solar fuels, photovoltaic devices, light emitting diodes, electronic devices, and biological probes.1−9 These nanostructures can be optimized for specific functions such as solar energy harvesting, charge separation, charge transport, and photocatalysis, and they can be used as building blocks for complex nanoscale heterostructures.5−7 Quantum confinement and surface chemistry can provide tools for optimizing the efficiency of the substructures within heterostructures and the transport between them. The successful development of these new technologies requires molecular level information that can guide synthetic methodologies to optimize device efficiency. Since nanostructures have high surface/volume ratios, surface states play an important role in controlling the efficiency in many applications. Multiresonant coherent multidimensional spectroscopy (CMDS) is a new approach that provides quantum state resolved measurement of excitonic dynamics. In this paper, we show that CMDS can resolve the spectrum of the surfacetrapped excitonic states in colloidal PbSe quantum dot samples and that vibrational resonances can be used to measure the absolute real and imaginary parts of the fully resonant thirdorder susceptibility.10−12 Therefore, CMDS provides a new characterization method that is sensitive to the surface and interface states that control the efficiency in nanostructure applications and the stability of nanostructures created by different synthetic strategies. © 2012 American Chemical Society
The fundamental strategies for applying multiresonant CMDS to quantum confined nanostructures have been developed in a recent publication.13 Multiresonant CMDS is a frequency domain spectroscopy that is not constrained by the spectral width of the excitation pulses.14−16 The experiments use three excitation pulses to excite a series of coherences and populations. Pairs of states in the resulting multiple quantum coherences reemit directional output beams at frequencies defined by the phase-matching conditions. Multidimensional spectra result from monitoring the intensity of a specific output beam as a function of the excitation frequencies. Cross peaks in the multidimensional spectra reflect the coupling between individual quantum states. Observing the output intensity while changing the time delay between the excitation pulses measures the coherent and incoherent dynamics of specific quantum states. A closed-form theoretical model was developed to simulate the multidimensional CMDS spectra.13 It was shown that detailed fitting of the multidimensional spectra could extract the frequencies, dephasing rates, population relaxation rates, relative transition moments, Coulombic coupling energies, and inhomogeneous broadening parameters for the individual excitonic states. The success of the fitting depended on spectral signatures from each parameter. Direct integration of the Liouville equation using the methods developed by Domcke extracts the coherent and incoherent dynamics from the temporal data.17−19 Received: February 12, 2012 Published: February 15, 2012 5546
dx.doi.org/10.1021/jp3014139 | J. Phys. Chem. C 2012, 116, 5546−5553
The Journal of Physical Chemistry C
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Article
THEORY The nth order susceptibility is defined in the Maker−Terhune convention37 by the Taylor series expansion of the polarization, P, in terms of the electromagnetic field, E.16,38−42
In this paper, we demonstrate that vibrational resonances provide a direct way to resolve the real and imaginary phase of electronic coherences. The approach is based on a method developed by Levenson and Bloembergen who showed that the quantum mechanical interference between two different coherences created phase-sensitive line shapes that defined the relative size of the real and imaginary parts of the system’s response function.20,21 Detailed fitting of the line shapes then provides a direct measure of the real and imaginary parts of the relative nonlinearities from the two coherences. Knowing the absolute value and phase of one nonlinearity then provides the absolute value and phase of the second nonlinearity. We have used this effect to probe the 1S excitonic resonance in PbSe quantum dots using the vibrational states of the carbon tetrachloride solvent in which the quantum dots are dispersed. The third-order susceptibility (χ(3)) of the vibrational modes was determined by fitting the vibrational line shapes using nonlinear Raman spectroscopy of neat carbon tetrachloride. Since the nonresonant χ(3) of carbon tetrachloride had been measured by Levenson and Bloembergen,20,21 the χ(3) of the vibrational modes could be readily determined by fitting the resonant line shapes. These experiments were performed on PbSe quantum dot samples that had aged and been exposed to high light intensities.10,22−25 It was previously shown that aging and phototreatment can cause loss of capping ligands and result in surface-trapped excitonic states formed by charge trapping and/ or photoionization.10,11 Typically, colloidal PbSe quantum dots are less stable than other quantum dot materials such as CdS. Sample characterization by transmission electron microscopy (TEM) and absorption spectroscopy are often not sensitive to these changes in the sample, but these changes become important in fluorescence and ultrafast pump−probe measurements of the excitonic dynamics, particularly in experiments that involve multiple exciton generation.26−36 Since surface states can control the exciton dynamics that underlies many of the intended applications of nanomaterials,2−4,8,9 it is important to develop an understanding of these states.1,10,11 TEM and absorption spectroscopy did not reveal any significant changes between the initial and aged PbSe quantum dot sample used in this work, but multiresonant CMDS experiments showed clear changes, not only in the excitonic dynamics but also in the multidimensional spectra. Two-dimensional CMDS of the initially prepared sample contained only the 1S excitonic diagonal peak. The diagonal peak disappeared after the sample aged and was replaced by a cross peak between the initially excited 1S state and the frequency-shifted surfacetrapped excitonic peak. Detailed spectral fitting of the vibrational and excitonic line shapes extracted the Coulombic coupling, coherence dephasing rates, coherence frequencies, population relaxation rates, relative transition moments, and inhomogeneous broadening parameters for the 1S and surfacetrapped excitonic states. These results show that excitation of the 1S population results in a rapid transfer to a new excitonic state attributed to surface states and that multiresonant CMDS provides a way to directly access and measure the characteristics of this important state. Our work suggests that multiresonant CMDS can provide a new measurement capability for obtaining detailed information that can guide synthetic efforts in understanding the states that define the quality and efficiency of nanostructures.
P=
∑ χ(n)En (1)
n
where
∑
E=
i = 1,2,2 ′
Ei° i(k i⃗ ·z −ωit ) ⃗ (e + e−i(k i·z −ωit )) 2
(2)
and E°, k, and ω are the electric field amplitude, wave vector, and angular frequency of the nth excitation pulse. The thirdorder susceptibility of a sample is related to the hyperpolarizability, γ, of all of the individual sample components by χ(3) =
∑ i = all components
χ(3) i =
∑
NiF γi
i = all components (3)
where N is the concentration and F is the local field enhancement given by ⎛ n2 + F = ⎜⎜ ⎝ 3
2⎞ ⎟⎟ ⎠
4 (4)
where n is the index of refraction of the sample. The output intensity created by the nonlinear polarization is proportional to (3) (3) 2 |χ(3)|2 = |χ(3) QD + χ Raman + χ NR |
(5)
where the χ values are complex numbers describing the quantum dots and the carbon tetrachloride Raman resonance and nonresonant background. We define the frequency dependence of the quantum dot resonances by the Liouville equation in steady state since the excitation pulse width is long compared to the quantum dot dephasing times. Quantum mechanically, there are 16 coherence pathways that we considered when three excitation pulses are temporally overlapped.15,43 The pathways used for this work are defined by the kout = k1 − k2 + k2′ phase matching condition and are shown in Figure 1. They assume the initially (3)
Figure 1. Liouville pathways that trace the evolution of the quantum states from the initial gg ground state population (yellow box) to the ket and bra states of the eg and e′g output coherence (enclosed in boxes). The numbers above each solid arrow designate the excitation pulse responsible for the transition. The dotted arrows define population transfer events between the initially excited 1S exciton and the surface-trapped exciton states, e and e′, respectively. 5547
dx.doi.org/10.1021/jp3014139 | J. Phys. Chem. C 2012, 116, 5546−5553
The Journal of Physical Chemistry C
Article
ωba, and Γba are the transition moment, frequency, and dephasing rate of the ba coherences. The equation contains both linenarrowed terms whose spectral width depends only on the homogeneous broadening and terms that are not line-narrowed and depend on both the homogeneous and inhomogeneous broadening.13 Similarly, the Raman third-order susceptibility is
excited state labeled e relaxes to another state labeled e′. States e and e′ are assigned to the 1S exciton and a surface-trapped exciton, respectively. The ki wave-vectors correspond to beams with frequencies ω1 and ω2. The ω2 beam is split to create a third beam labeled ω2′. In Figure 1, the ba symbols represent the ρba density matrix elements of coherences between the b and a states; the arrows represent the transitions induced by ω1, ω2, and ω2′; and the dotted arrows represent rapid population relaxation. We neglect the four pathways where the first two interactions create double quantum coherences (e.g., |2e>
