Control of Phonons in Semiconductor Nanocrystals via Femtosecond

Article pubs.acs.org/JPCB

Control of Phonons in Semiconductor Nanocrystals via Femtosecond Pulse Chirp-Influenced Wavepacket Dynamics and Polarization Jonathan Mooney,† Jonathan I. Saari,† Anne Myers Kelley,‡ Michael M. Krause,† Brenna R. Walsh,† and Patanjali Kambhampati†,* †

Department of Chemistry, McGill University, Montreal, Quebec, Canada Chemistry and Chemical Biology, University of California at Merced, Merced, California, United States

‡

ABSTRACT: The realistic electronic structure of semiconductor nanocrystals is characterized by excitonic fine structure and atomistic symmetry breakings that are challenging to resolve experimentally. Exciton−phonon coupling is one of the most sensitive measures of the excitonic wave functions of the nanocrystals. Here, we exploit this sensitivity via chirped pulse and polarization resolved femtosecond pump/probe spectroscopy of colloidal CdSe nanocrystals. Pulse chirp measurements and simulations are used to explore the contributions of excited- and ground-state vibrational wavepackets to the observed coherent phonons in the pump/probe signals. Polarization resolved pump/probe spectroscopy is used to explore electronic and vibrational polarization anisotropies. We find no electronic polarization anisotropy, whereas vibrational anisotropy is preserved.

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of the electronic coarse structure and its fine structure, Figure 1. This understanding of the electronic structure of NCs and related materials forms much of the basis for exploring and controlling their dynamics and function for the applications described above.8c,f,13 In contrast to molecular systems, however, the coupling of these excitonic states to vibrational degrees of freedom (phonons) is relatively poorly understood. There has been immense variance in the magnitude of the exciton−phonon couplings in NCs whether obtained by experiment or theory. We have made some progress in accounting for this variation, showing a state-dependence to this coupling and suggesting that measurements that subject stationary samples to high photon fluxes often reflect the coupling to surface states.8f,13,14 In ultrafast coherent phonon experiments, the pump pulses have sufficient bandwidth to span potentially several excitonic levels. Given that the pump pulses already have the bandwidth to span the excitonic fine structure in the EMA picture, and that in the atomistic EPM and TDDFT pictures there is an even greater density of excitonic states, such pulses can interrogate the complex excitonic structure and wavepacket dynamics in nanocrystals. In this article, we report the first experimental study of femtosecond chirped pulse pump/probe and transient absorption anisotropy spectroscopy on colloidal CdSe NCs. These experiments probe the wavepacket dynamics of coherent optical and acoustic phonons when pumped resonant with the

INTRODUCTION AND MOTIVATION Ultrafast pulse “chirp”, or second order phase, has been shown to significantly influence phenomena in molecular systems such as coherent vibrational amplitudes and decay times, excited state populations, and fluorescence signal intensities.1 Indeed, chirp has become one of the key variables employed in coherent control experiments involving molecules,2 while experiments involving chirp have provided insight into vibrational dephasing and wavepacket dynamics in molecular systems.1a In addition, transient absorption anisotropy experiments have been employed in molecular systems to explore both electronic and vibrational coherence.3 However, while there exists a rich literature regarding the effect of the effect of ultrafast pulse chirp and polarization on molecules, no studies have yet examined the effect of pulse chirp on the behavior of nanoscale systems or the influence of pulse polarization on phonons in nanomaterials. Semiconductor nanocrystals (NC) have been under intense investigation due to their potential in key applications such as bioimaging,4 photovoltaics,5 lighting and displays,6 photodetectors,7 laser gain media,8 and photonic devices.9 In addition, NCs have played a role in fundamental science due to their status as a canonical system to explore quantum effects that occur on the nanoscale.8f As mesoscale systems between molecular and bulk sizes, NCs experience quantum confinement effects, wherein physical confinement of the bulk electronic states yields quantized excitonic levels in analogy to molecular orbitals. The electronic structure of NCs has been well investigated by various levels of theories ranging from multiband effective mass (EMA),10 atomistic empirical pseudopotential (EPM),11 and methods such as time dependent density functional theory (TDDFT).12 There is presently reasonably good understanding © XXXX American Chemical Society

Special Issue: Michael D. Fayer Festschrift Received: June 26, 2013 Revised: October 16, 2013

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dx.doi.org/10.1021/jp406323f | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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and its duration was 59 fs in duration as measured by intensity autocorrelation. The optical density of the sample was 177 mOD. The pump pulse energy was maintained at ∼60 nJ throughout the experiment. Spot sizes were 286 μm for the pump pulse and 78 μm for the probe pulse. The average number of excitations ⟨N⟩ per particle was calculated to be 0.22. In this experiment, the phase and amplitude profile of pump pulse was shaped using an acousto-optic programmable dispersive filter. Pump pulse properties were measured using second harmonic generation frequency-resolved optical gating (SHG-FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER). Over the course of the experiment, the linear chirp (second order phase) of the pulse was varied from −5000 to +3000 fs2, leaving all other experimental parameters constant. Simulations. The pump−probe signals (ΔOD as a function of pump−probe delay) were simulated for a simple two-level electronic system possessing two undamped phonon modes, the longitudinal optical phonon and one acoustic phonon, modeled as displaced harmonic oscillators. Inhomogeneous broadening of the purely electronic transition was included as a Gaussian distribution of zero−zero energies, and electronic broadening arising from dynamics in any other material degrees of freedom (solvent reorganization, other phonon modes, etc.) was included as a Brownian oscillator in the overdamped, high temperature limit. Specifically, the signal as a function of probe delay was calculated as17 ∞

S(τ ) = Re

∫−∞ dt ∫0

∞

dt 3

∫0

∞

dt 2

∫0

∞

* (t − τ + t3)Epr(t − τ )Epu * dt1{Epr

(t − t 2)Epu(t − t 2 − t1)exp[iωprt3 + iωput1][R1(t3 , t 2 , t1)

Figure 1. (a) The electronic structure of valence and conduction band states in the effective mass approximation (left). The first several optically allowed transitions, showing electronic coarse structure levels in the exciton picture (center). The electronic coarse structure is split into an electronic fine structure which is spanned by the pump pulse (right). (b) Each excitonic state is coupled to two vibrations, a confined acoustic phonon at low frequency and a longitudinal optical phonon at high frequency. (c) Schematic illustration of one sequence of field-matter interactions that is controlled via pump pulse chirp.

* (t − τ + t3)Epr(t − τ )Epu(t − t 2)Epu * + R 4(t3 , t 2 , t1)]χ (t3 + t1) + {Epr (t − t 2 − t1)exp[iωprt3 − iωput1][R 2(t3 , t 2 , t1) + R3(t3 , t 2 , t1)]χ

(1)

(t3 − t1)}

where Epu and Epr are the pump and probe electric field envelopes with center frequencies ωpu and ωpr, respectively, the response functions are defined as

band edge exciton (X1). Pulse chirp experiments enable an investigation of the excited-state and ground-state wavepacket contributions to the measured signals. These experimental results are then tested against simulations. Finally, polarization anisotropy is measured for electronic and vibrational degrees of freedom. The results are discussed with respect to the role of fine structure levels in depolarization in nanocrystals.

R1(t3 , t 2 , t1) = exp(−iωeg t1 − iωeg t3)exp[−g *(t3) − g (t1) − f+ (t3 , t 2 , t1)]

(2a)

R 2(t3 , t 2 , t1) = exp(iωeg t1 − iωeg t3)exp[−g *(t3) − g *(t1)

■

− f +* (t3 , t 2 , t1)]

MATERIALS AND METHODS Solutions of colloidal CdSe NCs passivated with octadecylamine (ODA) ligands were used as received from NN Laboratories. These NCs possess a band edge exciton feature at 2.12 eV corresponding to a radius of 2.00 nm.15 Spectroscopic measurements were made in the pump/probe configuration, the details of which have been previously described.16 The pump pulse was tuned by an Optical Parametric Amplifier (OPA) to be resonant with the band edge excitonic transition of the sample (2.11 eV). The spectral full width at half-maximum (fwhm) of the pump pulse was 56 meV. The unchirped pump pulse duration was 38 fs in duration as measured by intensity autocorrelation. The probe pulse was tuned to the inflection point of the red rising edge of the electronic transition (2.07 eV). Its spectral fwhm was 30 meV

(2b)

R3(t3 , t 2 , t1) = exp(iωeg t1 − iωeg t3)exp[−g (t3) − g *(t1) + f −* (t3 , t 2 , t1)]

(2c)

R 4(t3 , t 2 , t1) = exp(−iωeg t1 − iωeg t3)exp[−g (t3) − g (t1) − f− (t3 , t 2 , t1)]

(2d)

where ωeg is the purely electronic ground- to excited-state energy difference and f− (t3 , t 2 , t1) = g (t 2) − g (t 2 + t3) − g (t1 + t 2) + g (t1 + t 2 + t3) B

(3a)



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determined from FROG measurements. Specifically, the unchirped pulses were assumed to be transform limited Gaussians with pulse durations of 38 and 59 fs for pump and probe, respectively, and simulations were performed for a range of chirp parameters of the pump spanning the same range as the experimental data. Group delay dispersion for the chirped pulses was incorporated as described in Englert et al.18

f+ (t3 , t 2 , t1) = g *(t 2) − g *(t 2 + t3) − g (t1 + t 2) + g (t1 + t 2 + t3)

(3b)

The quantity g(t) is the sum of the contributions from the phonons, ⎡

g (t ) =

⎛ ℏωj ⎞ ⎟(1 − cos ωjt ) ⎝ 2kBT ⎠

■

∑ Sj⎢coth⎜ j

⎢⎣

⎤ + i(sin ωjt − ωjt )⎥ ⎥⎦

RESULTS AND DISCUSSION Femtosecond Pump Pulse Chirping. The electronic structure of semiconductor nanocrystals has been discussed in detail in many reviews,10a,d as has the manner in which this excitonic structure is probed via pump/probe spectroscopy.8c,f,10d,13 Figure 1a schematically illustrates the electronic structure of NC in the multiband effective mass approximation (EMA) picture. Physical confinement yields quantized levels for the electron states in the conduction band (CB) and the hole states in the valence band (VB). These states are conveniently represented by term symbols within EMA. Shown are the states corresponding to the spherical CdSe NCs that are studied here. The transition energies are represented in the exciton picture. Here, we focus on the lowest level of the electronic coarse structure, the band edge exciton (X1), which is described as 1Se−1S3/2 state in the EMA. If the pump pulse is tuned into resonance with X1, the bandwidth spans the electronic fine structure. Hence multiple excitonic states are necessarily excited by the pump pulse. Even in the simplest of electronic level assignments (a single excitonic level), several fine structure states will be excited with additional inhomogeneous broadening. Moreover an atomistic level of theory yields a much greater density of states.19 The coupling to the vibrational (phonon) degrees of freedom can be represented by displaced harmonic oscillators. The configuration coordinates represent the longitudinal optical (LO) phonon and a confined acoustic (AC) phonon. Each mode may have a distinct coupling to each excitonic state as we discussed in detail elsewhere. In our earlier pump−probe studies,8f,13,14e,f we reported on the couplings in CdSe NCs for the first few coarse electronic states within the confines of EMA. Those experiments were not able to assess further details of the electronic structure. Resonance Raman excitation profile analysis finds considerably stronger coupling of the low-lying excitonic states to the LO phonon than was found from the pump−probe studies.14i In order to further explore the realistic electronic structure of nanocrystals, we exploit femtosecond pulse chirping to control vibrational wavepacket dynamics on the ground and excited excitonic levels. In these pump/probe experiments, one can create vibrational wavepackets via excited-state or ground-state pathways.1a,17,20 In the excited state pathway the two fieldmatter interactions with the pump pulse promote the bra and ket to the excited state, whereas in the ground-state pathway the interactions promote the bra (or ket) to the excited state followed by stimulated emission back to the ground states. This second pathway (Figure 1c) is referred to as resonant impulsive stimulated Raman scattering (RISRS). By controlling the time ordering of the spectral components of the pump pulse, its chirp, one has some capacity to control the relative contributions of each pathway. In these experiments, we exploit this fact to further explore the electronic structure and dynamics of these nanocrystals.

(4)

where Sj is the Huang−Rhys factor for phonon j having frequency ωj, and from the Brownian oscillator, g (t ) = −i

2λkBT ℏΛ2

[exp( −Λt ) + Λt − 1]

λ [exp( −Λt ) + Λt − 1] Λ

(5)

where λ is the classical reorganization energy and the line shape parameter is defined by ⎛ ℏΛ2 ⎞1/2 κ=⎜ ⎟ ⎝ 2λkBT ⎠

(6)

Finally, the inhomogeneous broadening function is χ (t ) = exp( −σ 2t 2)

(7)

where σ is the inhomogeneous width. In this model, both the ground-state bleach and excited-state stimulated emission contribute to the pump−probe signal, though excited-state absorption does not. The effect of a very short excited-state lifetime was modeled by multiplying the two terms in the response function that represent propagation on the excitedstate surface (R1 and R2) by exp(−t2/τ) where t2 is the time during which the system is evolving in the excited state and τ was set to 500 fs. The LO phonon amplitude as a function of chirp parameter was calculated by normalizing the data to constant pump and probe pulse energy and then directly measuring the amplitude of the LO phonon oscillations at a delay time of 2500 fs. Note that since no vibrational damping was included in the simulations, the oscillations persist with constant amplitude for long delay times. The parameters of the material system were taken from directly measurable experimental quantities to the extent possible. These include the absorption maximum (17106 cm−1), the phonon frequencies (longitudinal optical = 208 cm−1, acoustic = 21 cm−1), the temperature (298 K), and the total width of the X1 excitonic transition (800 cm−1 fwhm). This width was assumed to be composed of a 750 cm−1 inhomogeneous component and a 280 cm−1 homogeneous (Brownian oscillator) component as found in a recent resonance Raman intensity analysis study.14i The Huang− Rhys factor for the acoustic phonon was set to 0.33 based on the analysis of ref 13. The only material parameter that was varied in the simulations was the Huang−Rhys factor for the LO phonon, which was adjusted to best fit the amplitude of the LO phonon oscillations as a fraction of the total signal in experiments performed with unchirped pulses. The best fit to experiment was obtained with S = 0.24. The center frequency, pulse duration, and chirp of the pump and probe pulses were C



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Figure 2 shows the linear absorption spectrum of R = 2.00 nm colloidal CdSe NCs. Also shown are representative pump

Figure 2. Linear absorption spectrum of R = 2.00 nm CdSe nanocrystals. Typical pump and probe spectra are shown.

Figure 3. (a) Probe wavelength dependence of pump/probe transients, normalized to the maximum of the larger bleach. (b) Probe wavelength dependence of residual oscillations reveals phase shift.

and probe spectra. The probe spectra may be tuned into resonance with the first absorption feature, the band edge exciton (X1). When the probe spectra are exactly on resonance, one observes primarily the band edge bleach signal (B1). A subresonant probe monitors excited state stimulated emission as well as absorption from the single exciton into the biexciton state. These spectroscopic signals have been discussed in detail elsewhere.16,21 In this experiment, the main difference in the choice of probed region is the phase and amplitude of the observed phonons. If the launching of coherent phonons induces level shifting via electron−phonon coupling, the absorption spectrum will be frequency modulated, resulting in a phase shift based upon probed spectral region. Hence observing phase shifts is an indication that the oscillations arise from a straightforward frequency modulation of the dynamic absorption spectrum.14e,f Figure 3 shows femtosecond pump/probe transients at two probe regions, the peak of the X1 feature, and at its red edge inflection point. The pump pulses produce a mean exciton occupancy of ⟨N⟩ = 0.22. The transients show an instrument response function (IRF) limited bleach (Figure 3a) followed by a slow decay on the 10 ps to 10 ns time scale (data not shown), consistent with our prior works.8f,16,21 Probing at the inflection point also produces an IRF limited bleach. In this case the bleach is nearly proportional to the relative magnitudes of the linear absorption spectrum at the two probed spectral regions. Figure 3b shows the residual oscillations obtained by subtracting a model function from the data representing the purely electronic dynamics of the system. The data shows the phase shift anticipated from frequency modulation of the dynamic absorption spectrum by vibrational wavepacket motion. We and others have found this same phase shift in the oscillations along with the relatively weak coupling of the band edge exciton (X1) to the phonon modes. There are two main observable phonon modes, the longitudinal optical (LO) phonon with a period of 160 fs (208 cm−1) and a confined spheroidal acoustic phonon (AC) with a period of 1590 fs (21 cm−1). In contrast to dissociative systems,22 higher harmonics are not observed in this experiment. In CdSe nanocrystals, the

excited state wavepacket will develop little overlap with higher vibrational levels of the ground state due to the small relative displacement of the 1S excited state, resulting in the absence of strong higher harmonic signals. While coherent phonons are spectroscopically observed, it is not obvious whether the wavepacket motion propagates on the excited or the ground potential energy surfaces. The concepts of these wavepacket dynamics have been discussed in detail elsewhere and have been verified in many molecular systems.20a,23 These ideas developed in molecular systems may in turn be used to assess the real electronic structure of nanocrystals by virtue of the sensitivity of exciton−phonon coupling to the electronic wave functions. Since the effect of pulse chirp is well understood for a simple two electronic state system,20a,c,23a we explore how well that model represents the real electronic structure of the band edge exciton in NCs. Hence we implement pump pulse chirp experiments, focusing upon the simplest electronic transition, the band edge exciton, X1. In order to explore excitonic structure of NCs, we exploit pump chirp concepts to probe the coherent phonon dynamics. Figure 4 shows representative chirped pulses used in these experiments. Shown are second harmonic generation frequency resolved optical gating (SHG FROG) images and power/phase spectra for TL and PC pulses. Figure 5a shows pump/probe transients with different chirp for the pump pulse, positive chirp (PC), transform limited (TL), and negative chirp (NC). In all cases, there is no difference in the electronic response, an IRF limited bleach, followed by a slow decay. Nor is there any measurable chirp dependence to the bleach amplitudes. There is, however, a clear chirp dependence to the coherent phonon amplitudes (Figure 5b). To provide more quantitative insight into the amplitude of oscillations, the residual oscillation data was Fourier transformed (Figure 5c). As is clear from the Fourier transform spectra, a peak is visible at 208 cm−1, the amplitude of which varies as a function of chirp. D



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Figure 6. Relating phonon amplitudes to pulse chirp. The optical phonon varies as a function of chirp, while the acoustic phonon is unaffected. Figure 4. (a) SHG-FROG of TL pulse. (b) Power and phase spectra of TL pulse. (c) FROG of PC pulse. (d) Power and phase spectra of PC pulse. The power spectra are in yellow and the phase spectra are in red.

(formation of a ground-state coherent wavepacket), making it possible to distinguish the contributions of ground-state and excited-state coherent phonon motion to the observed signal.1a,20a While previous works have investigated the effect of pulse shaping on chirp in bulk semiconductors,24 we show here for the first time an enhancement in coherent phonon amplitude in a semiconductor system due to a negatively chirp ultrafast pulse. These results suggest that the RISRS framework can be utilized in understanding to solid state systems, including nanoscale systems. Figure 7 shows the simulation results for the LO phonon amplitude versus chirp. The parameters used in the simulations are given above; the Huang−Rhys factors are 0.24 for the LO phonon and 0.33 for the acoustic phonon. Results are shown for two cases. The purely ground-state (RISRS) contribution to the signal is isolated by assuming a very short excited-state lifetime and measuring the LO phonon amplitude at a time much longer than this lifetime. The resulting phonon amplitude is maximized at a slightly negative pump pulse chirp, slightly less negative than observed experimentally, and the width of the amplitude versus chirp peak is in good agreement with experiment. On the other hand, when a long excited-state lifetime is assumed, the LO phonon amplitude reflects a combination of ground-state (RISRS) and excited-state stimulated emission contributions. This plot shows a secondary maximum at a positive value of the chirp which does not agree with experiment. While similarities between the two simulations prevent any firm conclusions regarding the magnitude of each contribution, ground-state dynamics clearly play a role in the observed signal. The mechanism for the rapid excited-state population decay may be redistribution into the “dark” states of the exciton fine structure, as discussed further below. Electronic and Vibrational Polarization Anisotropies. In order to explore anisotropies, pump/probe experiments were performed with parallel in addition to the usual perpendicular polarization. The anisotropy is defined as r(t) = ((I∥ − I⊥)/(I∥ + 2I⊥)). For molecules in liquid solvents, the time scale for decay of r(t) typically reflects orientational dynamics. For a transition dipole coupling two electronic states, r(t = 0) has a theoretical maximum value of 0.4, while r(t = infinity) = 0. However, in transient absorption measurements, the situation is complicated by the possibility of excited-state absorption and stimulated emission.25 In the case of the nanocrystal, the anisotropy may be quite distinct.

Figure 5. Pump pulse chirp dependence of (a) bleach transients, (b) residual oscillations, and (c) FFT of residual oscillations. Positive bleach resulted in slightly smaller excitation probability.

Figure 6 shows the experimental results for phonon amplitudes over a range of chirp values. There is no measurable chirp dependence for the acoustic phonon. This observation is expected from qualitative considerations of the time scale mismatch between the pump pulse (∼38 fs at transform limit) and the phonon mode (∼1600 fs). In contrast the LO phonon shows a strong chirp dependence. The amplitude of the LO phonon peaks for a nonzero chirp. A slightly NC pulse produces the largest amplitude LO coherent phonons with amplitude attenuating for increasingly long pulses regardless of chirp. As previously discussed, there is a rich literature on the effect of chirp on the amplitude and decay times of coherent phonons in molecular systems. In particular, it has been shown that negatively chirped pulses enhance the RISRS process E



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Figure 8. (a) Polarization dependence of band edge bleach pump/ probe signals. (b) Polarization anisotropy, r(t).

Figure 7. (a) Simulated pump−probe signal for a transform limited probe pulse for excited-state lifetimes of 0.5 ps (mainly ground-state dynamics contribute to the signal) and 10 ps (both ground- and excited-state dynamics contribute). (b) Normalized amplitude of the LO phonon oscillations as a function of pump pulse chirp for the two cases above, compared with experimental data.

The NC has strongly allowed dipolar transitions given the large oscillator strengths. But the first absorption feature, the 1Se−1S3/2 coarse exciton, has electronic fine structure. The fine structure has allowed and forbidden transitions. In molecular systems, physical reorientation of the molecule is often the main contributor to changes in r(t). In contrast, for NCs the physical dot is frozen on the time scale of these experiments. Hence any dynamics must be purely electronic. The experimental data are shown in Figure 8. The pump/ probe transients are very similar, except for nonresonant cross phase modulation signal during the pump/probe overlap. Hence the quantitative comparison in r(t) is only done after the pulses are time separated (t = 100 fs for 80 fs IRF). The data shows no measurable anisotropy, Figure 8b. Rotational correlation times are expected to be on the nanosecond to microsecond scale for NCs of this size,26 so a measurement of zero anisotropy at all times must reflect an intrinsic property of the system.27 In this case, the wurtzite crystal structure and the electronic fine structure may be responsible for the lack of transient absorption anisotropy signal. Since the splitting between the z-polarized and xy-polarized fine structure components is expected to be small compared with kT in NCs of this size, the thermally averaged absorption and fluorescence should be isotropic.28 On the other hand, the magnitude of coherent phonons is enhanced for parallel versus perpendicular polarization (Figure 9), suggesting that vibrational dynamics are sensitive to polarization. Further exploration of electronic and vibrational coherences in NCs is

Figure 9. Polarization dependence of (a) residual oscillations and (b) FFTs.

clearly needed with multidimensional spectroscopy providing an attractive platform.29

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SUMMARY We have shown that the application of chirp to ultrafast pulses can control the amplitude of phonon oscillations in semiconductor nanocrystals. Specifically, the application of negative chirp can increase amplitude and involves the contribution of ground-state wavepacket dynamics to the signal through the RISRS process. Finally, we find that while phonon signals are F



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enhanced with parallel pump and probe polarizations, the transient absorption electronic signal is isotropic, perhaps due to thermalization within the fine structure states of CdSe.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the CFI, NSERC, FQRNT, and McGill University is acknowledged. J.M. acknowledges support from FQRNT. A.M.K. was supported by NSF Grant CHE-1112192.

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Control of Phonons in Semiconductor Nanocrystals via Femtosecond

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