ARTICLE pubs.acs.org/JPCA
Biexcitonic Fine Structure of CdSe Nanocrystals Probed by Polarization-Dependent Two-Dimensional Photon Echo Spectroscopy Cathy Y. Wong and Gregory D. Scholes* Department of Chemistry, 80 St. George Street, Institute for Optical Sciences, and Centre for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario, M5S 3H6 Canada ABSTRACT: The spectroscopy of colloidal CdSe nanocrystals is investigated using two-dimensional photon echo (2DPE) spectroscopy with copolarized and cross-polarized pulse sequences. Clearly resolved excited state absorption features are observed to beat at the frequency of the longitudinal-optical phonon, and the phase of this beating is found to be polarization-dependent. A simulation is performed using the excitonic and biexcitionic fine structure states predicted by theory, and the polarization-dependent beating allows each feature to be assigned to a particular excited state absorption pathway. Owing to their circularly polarized selection rules, the polarization-dependent 2DPE technique provides valuable insights into the spectroscopy of quantum dots. In particular, transient absorption features observed in pump-probe studies of CdSe quantum dots can now be assigned to specific fine structure transitions to the ground state biexciton.
1. INTRODUCTION CdSe nanocrystals (NCs) are well-known and well-studied1-7 owing to the tunability of their bandgap through the visible wavelength region by synthetically changing NC size. This changes the quantum confinement of the excited electron in the conduction band and the hole left by the electron in the valence band, which influences the energy of the nanoscale exciton. The properties and dynamics of these excitonic species can be probed by spectroscopy. Furthermore, pump-probe spectroscopy can examine photoexcitation of an exciton to a higher electronic state. At probe frequencies similar to the ground state-to-exciton transition frequency, the probe beam is absorbed to form biexciton states that correspond approximately to excitation of a second electron from the valence band to the conduction band. Studies of these manifolds of states reveal how electronic states of nanoscale systems differ from excitons in bulk semiconductors, where electron-hole interactions are weak.8,9 Such studies, in turn, help researchers to understand how to employ nanoscale systems in applications that include laser gain media,10,11 photovoltaics,12 and photodetectors.13,14 In the present report, we investigate the ground state biexcitonic fine structure using polarization co\ntrolled two-dimensional photon echo spectroscopy. 1.1. Excitons and Their Fine Structure. In a molecular orbital picture, the valence and conduction bands consist of HOMOs (highest occupied molecular orbitals) and LUMOs (lowest unoccupied molecular orbitals) constructed from the hundreds of individual unit cells within the NC. The atoms in CdSe are sp3 hybridized, and when an electron is excited from the HOMO, formed by the basis of three 4p orbitals from an Se atom, to the LUMO, defined in terms of the 5s orbitals from a Cd r 2010 American Chemical Society
atom, the electron and the remaining hole form a ground state exciton.5 In the literature,1 this band-edge exciton is termed 1S3/21Se, where S refers to the shape of the envelope function, and this exciton is the origin of the tunable, discrete maximum observed at the red-most edge of their absorption spectra.15-18 This zeroth-order picture defines the orbitals, but spectroscopy probes the electronic states. The electronic states of nanocrystals have a fine structure, somewhat analogous to the singlet and triplet manifolds of organic molecules,8 that is often obscured in frequency domain spectroscopy. Both the ground state exciton and biexciton in CdSe NCs have a complex fine structure that originates from a combination of the strong spin-orbit coupling that modifies the orbitals, the energy lowering provided by the exchange interaction19-22 for singlet and triplet states, the effect of the intrinsic crystal field23 in wurtzite structures, and shape anisotropy24 in NCs that are not perfectly spherical. Owing to the heavy elements which comprise CdSe NCs, the effect of spin-orbit coupling is large, and the fine structure states in these materials become eigenstates of the total angular momentum, as opposed to either the spin or orbital angular momentum alone. The fine structure eigenstates are linear combinations of the various electron and hole configurations; that is, the different combinations of spin and orbital angular momenta possible for the electron and the hole within the orbitals described above. The contribution of each configuration and the energy of each resulting fine structure eigenstate of the Special Issue: Graham R. Fleming Festschrift Received: August 20, 2010 Revised: October 24, 2010 Published: November 11, 2010 3797
dx.doi.org/10.1021/jp1079197 | J. Phys. Chem. A 2011, 115, 3797–3806
The Journal of Physical Chemistry A
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Table 1. Energies (eV) and Squared Transition Dipole Moments, μ2, between Ground State Exciton and Biexciton Fine Structure States exciton μgfe
þ2
-2
-1L
þ1L
0L
þ1U
-1U
0U
0.00
0.00
0.16
0.16
0.00
0.49
0.49
0.61
Energya
2.425
2.425
2.433
2.433
2.441
2.449
2.449
2.456
0A
4.853
0.000
0.000
0.763
0.763
0.000
0.236
0.236
0.000
-1A
4.870
0.000
0.361
0.000
0.488
0.500
0.000
0.151
0.499
þ1A
4.870
0.361
0.000
0.488
0.000
0.500
0.151
0.000
0.499
-2A
4.870
0.000
0.640
0.000
0.300
0.000
0.000
0.022
0.000
þ2A
4.870
0.640
0.000
0.300
0.000
0.000
0.022
0.000
0.000
0B
4.886
0.000
0.000
0.005
0.005
0.000
0.026
0.026
0.006
Biexciton
a
2
Biexciton energies are calculated assuming a 20 meV binding energy.
Figure 1. (a) Optically allowed transitions from the ground state to the first excitonic fine structure states (black) and from these states to the fine structure of the ground state biexciton (gray). The total angular momentum (F) of the state is shown by its horizontal position. Green/ red/blue arrows are transitions originating from a state with F = (2/ (1/0. Solid/dashed/dotted arrows are transitions that are strong/ medium/weak. (b) Three types of transitions within the fine structure. Each solid arrow is a light-matter interaction. Dashed blue arrows show transitions that occur during the population time delay. Of these three types, only the second scenario will produce an oppositely signed signal when using a VHVH polarization sequence (see text).
ground excitonic or biexcitonic state can be determined by diagonalizing a Hamiltonian. We recently reviewed25 the process by which optically allowed ground state exciton-to-biexciton transitions could be identified and their energies and relative transition dipole moments calculated. Table 1 includes these values for the fine structure states relevant to this work. Figure 1a shows a schematic of the fine structure of the ground state exciton and biexciton that result from this type of analysis as well as the strength of optically allowed transitions, calculated using representative parameters for CdSe NCs: spin orbit coupling, Δ = 418 meV; exchange, Kps = 12 meV; crystal field splitting, Δxf = 25 meV. The states can be identified by their total angular momentum, which is shown in the schematic by horizontal position. The fine structure of the ground state exciton has been investigated using both theory1,23,24,26 and experiment.17,19,27-33 Inquiry has largely been driven by practical questions regarding the dark states within the fine structure, which result in an observed Stokes shift and long-lived photoluminescence.31,32
Measurements of the fine structure are made more difficult by the inhomogeneous broadening caused by the size distribution of prepared samples.34 A number of techniques have been used to minimize the effect of inhomogeneous broadening to study the fine structure of the ground state exciton, such as fluorescence line-narrowing.30-32 In our previous work,35-37 we used crosspolarized pulses in a third-order transient grating technique, taking advantage of the circularly polarized selection rules in NCs. In this work, we will again use cross-polarized pulses, this time with two-dimensional photon echo (2DPE) spectroscopy, to investigate the fine structure of the ground state biexciton. In comparison with the ground state exciton, measurement of biexcitonic fine structure is further complicated by the presence of higher excitonic states that can overlap with the biexcitonic states in energy. As such, few studies of biexcitonic fine structure have been performed thus far. Recent studies have focused on the measurement of biexcitonic binding energies, lifetimes, and Stokes shifts using transient absorption techniques to determine their size-dependent properties.4,6,27,38-47 A greater understanding of these states may be of significance for the use of NCs in emerging technologies, such as for multiple exciton generation in photovoltaics,12,48,49 or as the gain material in lasers.10,11,40 1.2. Polarization Controlled Two-Dimensional Photon Echo Spectroscopy. The 2DPE technique50-54 is particularly suitable for the measurement of NCs since inhomogeneous broadening is minimized in the antidiagonal direction. The horizontal axis in each 2DPE spectrum is pωτ, which can be thought of as the “excitation energy”, although this is a simplification; it is the energy of the optical coherence formed by the first pump pulse interaction with the sample. The vertical axis is pωt, which can be considered the “emission energy”, the energy of the signal radiated in the ksignal direction as a result of the three preceding wave-matter interactions. The diagonal line highlights the case where pωτ = pωt, when the excitation and emission energies are the same, generally indicating that state-to-state population relaxation has not occurred. The width of the signal along the diagonal compared with that along the antidiagonal direction shows the degree of inhomogeneous broadening in the excited sample. Signal which appears off the diagonal is the result of homogeneous broadening, population relaxation, or the formation of a coherence during the population time, where the two pump pulses excite a superposition of states within the system. The elimination of inhomogeneous broadening in the antidiagonal direction can allow for the resolution of spectral features that are obscured in one-dimensional spectroscopies. The technique has been used to study many types of sample with complex electronic structure, such as conjugated polymers,55,56 3798
dx.doi.org/10.1021/jp1079197 |J. Phys. Chem. A 2011, 115, 3797–3806
The Journal of Physical Chemistry A photosynthetic proteins,57-61 and various other molecular excitons.62-65 The study of the fine structure of colloidal semiconductor NCs has been hampered by the large amount of inhomogeneous broadening, making these systems ideal candidates for study with 2DPE spectroscopy. Despite the reduced effect of static inhomogeneity in 2DPE spectra, a significant amount of line-broadening can still obscure spectral features. This has led to the use of polarization techniques to isolate the signals of interest. The use of different polarization sequences was pioneered in 2D infrared spectroscopy by Hochstrasser et al.66,67 and has proven to be of great utility. For example, cross-polarized pulse sequences can be used to minimize the diagonal features, allowing for greater resolution of cross-peaks, which are often the features of interest.67 This technique has been extended to electronic spectroscopy, where again, diagonal peaks can be suppressed by the use of cross-polarized pulse sequences.68 It has been used in the study of the photosynthetic “FMO” complex to elucidate the pathways and rates of transfer between specific chromophores.68,69 Zhang et al.70 used collinear, cross-, and circularly polarized pulses to study GaAs quantum wells, determining that specific polarization sequences emphasize the cross-peaks that originate from biexcitonic states. Aside from the clear material differences, the major distinction between quantum wells and the NCs studied in this work is in the isotropic nature of colloidal NC ensembles. Like NCs, quantum wells have circularly polarized selection rules for one-photon absorption,71,72 but unlike quantum wells, irradiating an ensemble of colloidal NCs with circularly polarized light cannot control the spin of the resulting excitonic states.73,74 The resulting excited state would depend on the orientation of the individual NCs relative to the incident circularly polarized light, and in these isotropic samples, an equal number of NCs would be excited to a spin up state as a spin down. The problem is thus less straightforward in an isotropic ensemble of NCs, and the rotational average of the NCs must be considered, as detailed in our previous work73,74 and summarized in Appendix A. The result of this analysis is that when cross-polarized pulse sequences are used, the sign of a signal generated by an exciton in a colloidal NC will depend on the history of the exciton; specifically, whether the sign of the total angular momentum imparted by the pump pulse is the same as that imparted by the probe pulse. Three examples are shown in Figure 1b, where each red arrow represents the transition resulting from the interaction of the sample with a pump or probe pulse, the green arrow is the resulting emitted signal, and blue dashed arrows represent transitions that occur during the population delay time. In the first case, the exciton is initially created by the two pump pulses in a spin up state, that is, a state with a positive total angular momentum (F) value, thus Fpump = þ1. When the probe pulse arrives, the exciton is still in a spin up state, so Fprobe = þ1. In this case, since both the pump and probe pulses cause transitions with a state with a positive F, both VVVV and VHVH polarization sequences will generate a positive signal. In the second case, the two pump pulses again create a population in a spin up state, but during the population delay time, the population is transferred to a spin down state, where F is negative. The probe pulse then interacts with this state, causing stimulated emission back to the ground state. Thus, Fpump = þ1 and Fprobe = -1, so in this case, although a VVVV experiment will produce positive signal, a VHVH sequence will generate negative signal. The third case in Figure 1b shows another type of transition during the population time, from the initially excited spin up state
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Figure 2. (a) Pulse ordering in the 2DPE experiment. (b) Schematic of the 2DPE experiment, in which the detected signal is the interferogram produced by the signal and the local oscillator. (c) Absorption spectrum of the CdSe QD sample (black) and the laser pulse spectrum (red). (d) Interferograms collected in the 2DPE experiment. (e) 2D spectrum in time produced when the frequency axis of the interferograms are Fourier transformed to time. (f) When the 2D signal in time is integrated over t (black), the maximum is the peak shift (red line). (g) Peak shift values extracted from 2DPE measurements using VVVV (blue) and VHVH (red) polarization sequences.
to a linearly polarized state with F = 0. Zero is not opposite in sign to either spin up or spin down states, so this sort of pathway would generate positive signal using either a VVVV or VHVH polarization sequence. In this way, the sign of the signal indicates the exciton’s history, determining relative sign of the total angular momentum imparted by the pump and probe. Although the three cases of Figure 1b show stimulated emission (SE) pathways, two other types of transitions are possible: ground state bleach (GSB) and excited state absorption (ESA). In this work, we will focus on ESA from the ground state exciton to the ground state biexciton. The polarization rules remain the same: analogous to the second case, if the transition to fine structure of the ground state exciton induced by the pump pulses has oppositely signed total angular momentum as the subsequent ESA transition to the fine structure of the ground state biexciton, a VHVH polarization sequence will produce a negative signal, whereas a VVVV sequence will generate a positive signal. If both of the transitions involve changes in F of the same sign, or if either transition does not change the total angular momentum, analogous to the first and last case from Figure 1b, respectively, both VVVV and VHVH measurements will yield a positive signal. In this way, measurements using both collinear and cross-polarized pulse sequences can help identify ESA features. When applied with the 2DPE technique discussed above, the improved resolution of features, both by separation of features in two dimensions and the differentiation of pathways involving a change in the sign 3799
dx.doi.org/10.1021/jp1079197 |J. Phys. Chem. A 2011, 115, 3797–3806
The Journal of Physical Chemistry A of F, allows for the direct inspection of ESA pathways to the biexcitonic fine structure that were previously unresolvable. In this work, we apply the 2DPE technique using collinear and cross-polarized pulse sequences to study the biexcitonic fine structure of a sample of CdSe NCs. The experimental details will be outlined in section 2, and the results of our measurements are presented in section 3. These results are simulated with a physical model, as discussed in section 4.
2. EXPERIMENTAL METHODS CdSe NCs with wurtzite crystal structure and passivated by trioctylphosphine oxide ligands were synthesized using wellestablished methods.75 The absorption maximum for the first excitonic state was found at 507 nm (see Figure 2c), which corresponds to a NC radius of 24 Å.18 In a 1 mm path length cuvette, the optical density of the sample was 0.3, corresponding to a 1.7 10-5 volume fraction.18 Two-dimensional photon echo (2DPE) spectroscopy was used to examine this sample at room temperature. During the measurement, the sample was periodically moved, and to ensure that the sample did not degrade during the measurement, linear absorption spectra were collected before and after the scan. In this third-order nonlinear spectroscopy, the sample interacts with three 25 fs pulses in a specific pulse order (Figure 2a) and with a specific wavevector geometry (Figure 2b). The sample was initially excited by two pump pulses with wavevectors k1 and k2 and separated in time by a small delay, termed the coherence time (τ). After another time delay, termed the population time (T), the system was probed with a pulse with wavevector k3, producing a signal that radiates in a phase-matched direction, ksignal = -k1 þ k2 þ k3. The signal pulse was directed to a charge-coupled device (CCD) camera and was overlapped with a local oscillator pulse for heterodyne detection. The polarization of each pulse was controlled using a waveplate in each beam path before the sample and an analyzer polarizer in the signal direction after the sample. Two polarization sequences were used: either all vertically polarized pulses (VVVV), or cross-polarized pump pulses and probe/local oscillator pulses (VHVH). The laser pulse spectrum (centered at 510 nm, intensity
