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Efficient optical gain in CdSe/CdS Dot-in-Rod nanocrystals Colin Sonnichsen, Tobias Kipp, Xiao Tang, and Patanjali Kambhampati ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01033 • Publication Date (Web): 31 Dec 2018 Downloaded from http://pubs.acs.org on December 31, 2018

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Efficient optical gain in CdSe/CdS Dots-in-Rods Colin D. Sonnichsen†, Tobias Kipp†,‡, Xiao Tang‡, and Patanjali Kambhampati†∗

†Department ‡Institut

of Chemistry, McGill University, Montreal, Canada

für Physikalische Chemie, Universität Hamburg, Hamburg, Germany E-mail: [email protected]

Abstract Excitonic state-resolved pump/probe spectroscopy is performed on semiconductor dot-in-rod nanocrystals. Using excitonic state-resolved pumping we are able to resolve effects of the rod upon exciton dynamics of the core. The shell has the effect of lowering gain threshold, increasing absorption cross-section, and increasing the Auger lifetime, hence nanorods are shown to be an effective means of enhancing gain performance of nanomaterials. Keywords Quantum dot, nanocrystal, optical gain, Auger processes, excitons, multiexcitons.

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Semiconductor quantum dots have been well investigated for their favorable optical properties in applications spanning lasers1–3, light emitting diodes4,5, and photovoltaics6–9. Spherical quantum dots represent the model system for these studies, with well understood exciton dynamics10. The results on these model systems form a basis for how fundamental excitonics may be controlled via materials towards improved performance for optical applications. Hence there has been much work to explore more complex nanocrystal geometries such as core/shell structures11, nanorods12–14, or nanoplatelets12,15–17. The aim is to see how the material system can control specific properties such as efficiency, Auger rates, and multiexciton interaction energies.

There are three properties commonly used to characterize a gain material. These are the lifetime, threshold, and cross-section for gain. The lifetime is determined by the lifetime of the upper lasing state, and in the case of multiexcitons this is the Auger lifetime, which is on the order of 1-100 ps. For single excitons the lifetime is on the order of 10 ns, one of the motivations for single exciton gain materials. While the lifetime is an important parameter, it is not the determinant of efficiency. Efficiency is determined by the detailed level structure in the material and the presence of interfering absorbing states. While a shorter lifetime will never lead to a more performing laser, a well designed system can mitigate this effect. If the laser radiation in the cavity builds up quickly to a large enough value, stimulated emission can become favored over population decay. This can occur in a small cavity with a densely packed medium. Any excited state absorption from the upper lasing level will always be a source of loss whatever is happening in the cavity, and is hence a more stringent determiner of efficiency in terms of lasing applications.


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Here, we use excitonic state-resolved pump/probe spectroscopy to unravel the structure and dynamics of the excited states in colloidal CdSe/CdS dot-in-rod heterostructures. These experiments reveal that these nanostructures have excellent performance for optical gain and, thus, for possible light-emissive applications. The efficiency of gain is discussed in terms of a realistic model of biexciton level structure. The state-resolved approach reveals that Coulomb and correlation interactions within multiexcitons enable lower thresholds for gain upon pumping into the nanorod. The nanorod structure moreover leads to an increase in the multiexciton Auger lifetime, which further improves gain performance. In summary, these time-resolved measurements rigorously characterize the ultrafast exciton dynamics of colloidal dot-in-rod nanostructures and connects the dynamics with the performance in emissive applications such as lasers and light emitting diodes.

Because of the equivalency between the Einstein coefficients for absorption and stimulated emission, population inversion between two levels is necessary for light amplification to occur. This is only possible in a three or more level system. Three level systems will produce gain only when the ground state is half-empty, while a four-level system with the proper decay channels will in theory produce gain after a single excitation. Figure 1 shows some of the energy levels implicated in NC lasing. II-VI NCs form a three-level system between the ground state and the absorptive Xabs and emissive Xem states of the band edge exciton, which are separated by the Stokes’ shift, δX. Gain would occur between the emissive exciton state and the ground state once the ground state is half empty. In practice, there is an interfering state that blocks gain. Absorption of a second photon can excite a second exciton, forming a biexciton (XX). The biexciton is bound by an energy ΔXX, placing biexciton absorption to the red of single exciton absorption. Because 3 ACS Paragon Plus Environment

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ΔXX is similar to δX, excited state absorption overlaps and nullifies stimulated emission, blocking gain and destroying the ideal three level system. As there is fine structure in X, there should be fine structure in XX as well. This structure may come from axial strain, exchange interactions, or phonon vibrations18,19, the important thing is that the fine structure is present in both X and XX. Figure 1 shows how these energy levels are related. This fine structure leads to several ways of measuring the binding energy, ΔXX, either in emission or absorption. It is the overlap of Xem and XXabs that dictate thresholds for single exciton gain and the overlap of XXem with Xabs and XXabs that dictate thresholds for biexciton gain.

In evaluating materials for optical gain performance, it is common to use photoluminescence (PL) due to its simplicity20–24. Fluence dependence can yield amplified spontaneous emission (ASE), a measure of gain performance. ASE is a good measure of gain threshold in terms of energy per unit area but does not measure many other key parameters and additionally mixes processes, thereby obfuscating interpretation25. Ultrafast pump/probe spectroscopy is a better measurement in that it can be used to extract and disentangle average exciton populations, gain thresholds, lifetimes, and cross-sections. State-resolved pump/probe will further reveal state-specificity to key processes, such as control over gain bandwidth26,27, and enable the measurement of biexciton level structure28,29.

Semiconductor NCs have a number of favorable characteristics as an optical gain medium, but no single platform exists with ideal performance in all respects. Hence an understanding of the relationship between structure and function is useful. One aims for a material with decoupled 4 ACS Paragon Plus Environment

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emission and excited state absorption, which can be achieved through multiexciton interaction. This is very large in small NCs, but small NCs also have very fast Auger rates and suffer from surface trapping25,30. Shape control can alter some gain properties. Comparing CdSe quantum dots to quantum rods with the same volume, rods will have a shorter Auger lifetime due to surface trapping effects14,31. Despite this, it is possible to achieve room temperature optical gain in CdSe quantum rods32. Another approach is to form a heterostructure that spatially separates the electron and hole, as in a type-II core/shell NC. Here multiexciton interactions are extremely large and repulsive, due to Coulomb interactions between the excited and separated electron and hole. Long lived gain from single excitons is achieved in these systems20. Type-II heterostructures, however, suffer from reduced oscillator strength in the lasing transition. Another avenue for low-threshold gain is to take advantage of trap states to form a three-level33 or a four-level system34. CdSe dots with an overgrown CdS rod (CdSe/CdS DiRs) offer both low threshold gain22,23,35, reduced Auger rates36,37, and polarized emission38–40. These useful gain properties may be due to electron delocalization in the conduction band, which is controlled by the relative diameters of the CdSe dot and the CdS rod41–43, providing a promising platform for optical applications such as lasers21,44– 46

or LEDs47,48 Previous ultrafast pump-probe studies on DiRs have already made some key

obesrvations. Lupo et. al. specifically did a state-resolved approach that found evidence for electron delocalization in the conduction band49. Others assigned the features in the pump-probe spectrum to the CdS surface, CdSe/CdS interface states, and CdSe dot, and found relaxation rates between these three states50,51. We present here a comprehensive, state-resolved pump-probe analysis of the gain characteristics of this system. Figure 2 presents an overview of the CdSe/CdS DiR nanocrystals and their optical properties. All optical measurements are performed on DiRs dissolved in toluene. Figure 2 (A) 5 ACS Paragon Plus Environment

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shows a schematic of the physical structure. Figure 2 (B) shows some of the important energy levels. The inset shows TEM images of the DiRs. The rods have dimensions of approximately 5 nm × 45nm. Figure 2 (C) gives an overview of the linear and non-linear optical spectra. The linear absorption spectrum shows two important features, one relatively weak absorption due to the CdSe quantum dot near 2.07 eV, and a large absorption near 2.58 eV due to the rod. Based on CdSe quantum dot sizing curves, the dot diameter is approximately 4.6nm, not taking into account the delocalizing effect of the CdS shell52. Both the dot and the rod show quantized, excitonic states.

Under optical excitation into the rod photoluminescence is observed from the dot.. Also shown are pump pulse spectra under two pumping conditions; pumping into the dot (2.07 eV, in red) and pumping into the rod (2.58 eV, in blue) excitonic states. Below is a TA spectrum at 10 ps after pumping into the dot excitonic state at 2.07eV. The TA spectrum shows a strong bleach of the dot transition and a weaker bleach of the rod transition, with other very weak bleach signals occurring between these two states. Figure 3 provides a more detailed overview of the excitonic state-resolved TA measurements. Figure 3 (A) and (B) show the different results obtained by specifying the initial excitonic state, compared to the linear absorption spectrum. By pumping resonantly into the dot transition at 2.07eV, an instrument response-limited bleach signal is created that doesn’t change over ∼ 100 ps. By pumping into the rod continuum at 3eV, an initially hot exciton is created in the rod that then diffuses into the dot on a timescale of several 100s of fs, causing a growth in the bleach feature at 2.07eV. There is also a stronger bleach signal in the 2.15 to 2.25 eV region compared to 2.07eV pumping, which has been assigned in the literature to bleaching of a ”bulge” state at the CdSe/CdS interface 51,53 or quantum confined hole states in the CdSe dot 54. Figure 3 (C) and (D) show the full energy and time resolved TA signal for dot (2.07 eV) and rod (3.0 eV) 6 ACS Paragon Plus Environment

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pumps, respectively. Figure 3 (D) further shows excited state absorption due to transitions from X ⇒XX. Pumping resonantly into the rod state at 2.58 eV yields similar results to pumping into the rod continuum at 3eV. Figure 4 shows the development of optical gain via state-resolved pumping. We have previously shown that state-resolved optical pumping reveals new aspects of gain physics, specifically these state-resolved methods demonstrate how cross-section, threshold, and bandwidth are intimately related to the pumped state26. We explore these effects here. Figure 4 A,B) shows the development of optical gain through the nonlinear absorption spectrum. The nonlinear absorption spectrum is simply the linear absorption spectrum plus the transient absorption spectrum, ODNL = ΔOD + OD0. The nonlinear absorption corresponds to the absorption of the pumped sample. These nonlinear absorption spectra are obtained at a time delay of 10 ps. Certain transitions in the pumped sample become bleached, ultimately producing transparency. At higher fluence one might obtain negative absorption corresponding to gain. Figure 4 (A) shows the nonlinear absorption after pumping into the dot at 2.07eV. Gain is achieved from approximately 1.93 to 2.07 eV. Gain coefficients are also relatively large compared to the linear absorption cross-section. Figure 4 (B) shows the same measurement after pumping into the rod at 2.58eV. At high fluence the gain extends from 1.93 to 2.03 eV. The gain is also much weaker relative to dot-pumped DiRs, and the shape of the gain spectrum is markedly different. The advantage of pumping into the rod state is that the threshold fluence is much lower. Gain is achieved at ∼ 250 nJ/pulse for rod pumping and ∼ 690 nJ/pulse for dot pumping. This is due to the funnel effect of the rod; the rod can very effectively absorb photons and transport charge to the dot for stimulated emission.


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Figure 4 (C,D) shows the gain threshold for dot pump and rod pump. The key point is establishing the average number of excitons per DiR, < 𝑁 > . This is done by measuring the population of band edge excitons through the magnitude of the band edge bleach55. Since the band edge state can hold at most two excitons, the population is simply twice the fractional bleach as

( )

given by equation (1) 26,56 < 𝑁𝑑𝑜𝑡 > = ―2

Δ𝑂𝐷

(1)

𝑂𝐷0

For pumping directly into the dot at 2.07eV only the dot state is populated, so < 𝑁𝑑𝑜𝑡 > = < 𝑁 > . For pumping into the rod at 2.58eV any number of excitons can be created in a single NC because of the high density of states at this energy. The number of NCs containing 𝑁 excitons is given by a Poisson distribution with parameter < 𝑁 > . By relating the number of NCs containing two excitons to that given by a Poisson distribution, the Poisson parameter can be extracted. This is given by equation (2)26,55,56: Δ𝑂𝐷

< 𝑁𝑑𝑜𝑡 > = 2 ― (2 + < 𝑁 > )𝑒 ―< 𝑁 > = ―2 𝑂𝐷0

(2)

The gain threshold in terms of the average exciton occupancy is a measure of gain efficiency and exciton and biexciton overlap. For decoupled stimulated emission and excited state absorption, gain thresholds will be small. When stimulated emission competes with excited state absorption, gain thresholds will be larger. This results in a spectrum for the gain threshold. Figure 4 (C) shows the threshold for dot pumping is < 𝑁 > = 1.2 on the red edge, and < 𝑁 > = 1.6 at the peak of gain. Figure 4 (D) shows the threshold for rod pumping is < 𝑁 > = 1.0 at the red edge, and < 𝑁 > = 1.6 at the peak. A threshold of < 𝑁 > = 1.6 is approximately universal for CdSe NCs 57.

What is unique here is the low threshold for high pump energies. Previous studies that report

only ASE22,24 or lasing21,44–46 thresholds miss valuable information that can only be found through pump-probe experiments, as reported here. These are the average exciton occupancy at the gain 8 ACS Paragon Plus Environment

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threshold, the gain spectrum and the gain lifetime. These state-resolved measurements allow observation and quantitative measurement for all of these properties. Figure 4 (E,F) further shows that both pumps yield gain that lasts up to 100ps. The dynamics of optical gain can be connected to the lifetime of multiexcitons (MX). The lifetime of MX is determined by Auger recombination. If gain is produced by single excitons, MX recombination is of no relevance to the gain or lifetime. Here MX recombination is the limiting factor for gain lifetime.

Figure 5 shows a measurement of exciton-exciton interactions in the Auger recombination rate. This rate is determined, to a certain extent, by the CdSe-CdS interface58 and delocalization of the electrons in the conduction band36. Figure 5 (A) shows the recombination kinetics after pumping into the dot (2.07 eV). Signals are normalised to -1 at 250ps delay. Under increasing pump fluence a fast decay component grows in that reflects the higher proportion of XX relative to X in the sample. The bleach signals were globally fit to a single exponential decay with an offset, and the amplitudes of these components are shown in the inset. The Auger lifetime was found to be 125ps. With pumping directly into the dot only XX recombination kinetics are probed, since no higher MX can be created due to the two-fold degeneracy of the conduction band electronic state. The data in figure 5 (A) shows the ideal response of a system with two-fold degeneracy59.

Figure 5 (B) shows the Auger recombination kinetics with rod pump (2.58 eV). The most notable point is that with rod pump decays are no longer monoexponential. The data are well fit 9 ACS Paragon Plus Environment

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by a biexponential with an offset. Because the first excited state can only hold 2 excitons, recombination of higher MX will not be reflected in the signal. The buildup time is nominally the decay time of higher MX, as XXX decays to XX for example. This can lead to different results for Auger lifetimes than what would be observed for pumping into the first excitonic state, as the main decay component here has a lifetime of nearly 200ps. Again, the inset shows the amplitudes of the various fitting components.

Figure 5 (C) shows Auger rates across CdSe samples. In each case the core CdSe dot has roughly the same band edge exciton energy. The samples are pumped at high fluence to saturate the biexciton state. Signals are normalized such that the maximum bleach is -2. Probing at the band edge exciton state means the signal is only sensitive to single excitons or biexcitons. For ligandpassivated CdSe, the decay goes from -2 to -0.7, indicating the existence of a surface trapping channel for excitons59. The effective decay time is 30 ps. For ZnS capped CdSe, the signal decays from -2 to -1, indicating that the surface is well passivated and no excitons are lost on the way from XX to X. However, the decay is quite fast and remains biexponential. For the CdSe/CdS DiRs studied here, biexciton decay is monoexponential with a time constant of 125 ps, more than twice as long as CdSe/ZnS. The signal also decays from -2 to -1, indicating that no excitons are lost to surface traps. These results show that Auger recombination is highly sensitive to surface conditions and electron-hole overlap.

Figure 1 introduced a minimal level structure of the exciton and biexciton. We aim to relate the experimental observations of threshold and bandwidth for gain to an experimental


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determination of this energy structure. To do this one requires a measurement of absorbing and emitting states of both the exciton and the biexciton. This is enabled by state-resolved TA spectroscopy28,60.

Figure 6 shows a measurement of biexciton structure. The energy of Xabs is measured by linear absorption. Emission from Xem is measured by PL. The difference between these two is the well known exciton Stokes’ shift, δX. Absorption into XXabs is measured by ΔOD, the transient absorption spectrum. The ΔOD spectrum has three terms, ground state bleach, stimulated emission, and excited state absorption (ESA). ESA occurs form Xabs to XXabs, causing the ΔOD spectrum to shift relative to the linear spectrum by Δabs XX . At high pump fluence, the biexciton is populated. Stimulated emission contributions to the ΔOD signal will be from XXem. This results in the gain spectrum being shifted relative to the PL spectrum by Δem XX . The combination of these measurements allows the full reconstruction of the energy levels presented in figure 1. Just as there is an exciton Stokes’ shift, there is a biexciton Stokes’ shift, δXX. Results of these measurements are summarised in table 1, with analogous results for CdSe NCs28 and CdSe/Cd,Zn,S graded alloy NCs61 from previous work. Apparent here are the reduced binding energies in emission and absorption, and the particularly small XX Stokes’ shift. Other groups have also shown that biexciton binding energies can range from ∼ 40meV to -30meV, placing biexciton emission to the red or blue of exciton emission depending on the relative size of the dot and rod42,56. To the authors’ knowledge, negative binding energies have not been observed in bare CdSe NCs. In conclusion, it has been shown that low threshold gain under both dot pumping and rod pumping conditions is possible in CdSe/CdS DiRs. This is in contrast to CdSe quantum dots and


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quantum rods, which show little or no gain for pumping into excited states32,62. Electron delocalization in the conduction band has consequences on the Auger recombination rate, which is much smaller in this system than in ligand-passivated CdSe or type-I CdSe/ZnS core/shell quantum dots. Electron delocalization has further implications on the electronic structure of the biexciton. This work shows the potential of the CdSe/CdS DiR system as a platform for light emitting applications. Methods The ultrafast pump/probe spectroscopy instrument used here has been described elsewhere63,64. A 1kHz Ti:Saph amplifier produces 2.4mJ, 820 nm, 70fs pulses. Pump pulses are obtained either by doubling the fundamental beam in a BBO crystal, or through optical parametric amplification. The probe pulse is obtained through self-phase modulation in a 2mm sapphire crystal. Dispersion management of both pump and probe beams is done by fused silica prism pairs. Spot sizes were approximately 50 𝜇m (probe) and 100 𝜇m (pump). Two-color pump/probe experiments are done simultaneously by chopping two pumps at 333 Hz such that the detected probe signals are pump1-pump2-no pump. This eliminates artifacts such as sample degradation or laser drift from state-resolved experiments. The colloidal sample is pumped through a 1mm flow cell to ensure that heating and degradation effects are minimized while the pump-probe experiment is taking place. For this work CdSe/CdS DiRs were synthesised according to a previously described procedure65. Briefly, CdSe quantum dots were synthesised using a hot injection of selenium stock solution into a solution of CdO with trioctylphosphine oxide (TOPO) as a capping ligand66. These dots were dispersed in trioctylphosphine (TOP) and stored under an inert gas atmosphere. To grow


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the rods, a second hot, rapid injection was done, this time injecting a quantum dot and sulphurTOP solution into a hot solution of CdO.

Acknowledgement P.K. and C.S. acknowledge financial support from NSERC. T.K. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme through a Marie Skłodowska-Curie grant (Agreement No. 656598).We further received experimental

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Figure 1: Schematic illustration of the exciton and biexciton electronic structure. A minimal model for the exciton has an absorbing state, 𝑋𝑎𝑏𝑠, and an emitting state, 𝑋𝑒𝑚. A minimal model for the biexciton will also have two states, 𝑋𝑋𝑎𝑏𝑠 and 𝑋𝑋𝑒𝑚. Both the exciton and the biexciton will have a Stokes’ shift, leading to different measures of the biexciton binding energy, Δ𝑋𝑋, for emissive and absorptive experiments.


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Figure 2: Overview of the CdSe/CdS DiR nanostructure. A) Schematic illustration of the DiR nanostructure. B) Schematic potential energy diagram and approximate wavefunction of the band edge exciton, showing electron delocalization in the conduction band. inset: TEMs of the sample studied here. C) Linear absorption, PL, pump pulse spectra and transient absorption spectrum. Absorption occurs into both the dot and rod, while fluorescence occurs from the dot band edge exciton. 3 eV pump not shown. Transient absorption spectrum at a pump-probe delay of 10 ps. inset: absorption and PL at a different scale, showing the large absorption cross section of the rod relative to the dot.


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Figure 3: Excitonic state-resolved pump/probe spectroscopy of the DiR nanostructures. A) Pumping into the dot state creates an IRF limited bleach signal that remains unchanged over 100s of ps. B) Pumping at 3 eV creates a hot exciton in the CdS rod that will relax and diffuse to the CdSe dot on a timescale of 1 ps. There is also an absorptive signature to the red of the band edge due to ESA from the single exciton to the biexciton. C),D) Time resolved transient absorption signal for pumping into the dot (2.07 eV, C), and pumping into the rod (3.0eV, D). Colorbar scale is in mOD.


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Figure 4: Optical gain from the DiR via state-resolved optical pumping into the dot or rod excitonic states. DiR gain properties for both 2.07 eV pumping (A,C,E) and 2.58 eV pumping (B,D,F). A,B) Non-linear optical density (𝑂𝐷𝑁𝐿 = Δ𝑂𝐷 + 𝑂𝐷0) spectra at increasing pump fluences. Gain occurs for 𝑂𝐷𝑁𝐿 < 0. C,D) Slices along selected probe energies of 𝑂𝐷𝑁𝐿, showing lower threshold for pumping into the rod at 2.58eV, and good differential gain for pumping into the dot at 2.07eV. E,F) time dependent gain cross-section showing long-lived gain for both pump energies. Colorbar scale is in mOD.


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Figure 5: Multiexciton recombination kinetics revealed by state-resolved excitation. A) Pumping into the dot at 2.07eV will create either a single exciton or a biexciton, with a lifetime of 125 ps. Inset: Power dependence of fit amplitudes, showing the increasing XX population. B) Pumping into the rod at 2.58 eV can create any number of higher multiexcitons, leading to a more complicated relaxation pathway with growth and decay terms. Inset:

Amplitudes of the

components used for the 2.58eV pump. C) Auger recombination across CdSe NC samples. For ligand-passivated CdSe, biexcitons have two decay channels, one going to the NC surface. Surface excitons don’t contribute to the bleach signal, causing a tail less than -1. For CdSe/ZnS NCs there is no surface trapping, so the decay goes from -2 to -1 with biexponential decay. For CdSe/CdS DiRs, decay is monoexponential and the signal goes from -2 to -1.


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Figure 6: Excitonic state-resolved TA spectroscopy reveals energetics and fine structure of the biexciton. Comparing the spectra for linear absorption, transient absorption, gain, and photoluminescence reveals the structure of the biexciton and its’ relation to the single exciton.

Table 1: Results of biexciton structure measurements across NC samples. Sample

𝛿𝑋 (meV)

Δ𝑎𝑏𝑠 𝑋𝑋 (meV)

Δem 𝑋𝑋 (meV)

𝛿𝑋𝑋 (meV)

CdSe (R=2.1 nm) CdSe (R=2.8 nm) CdSe/Cd,Zn,S (R = 2.4nm) DiRs (R= 2.3 nm)

25 16 30 22

12 9 3 -1

44 37 30 12

57 45 57 36


CdS Dots-in-Rods - American Chemical

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