Coherent Multi-Dimensional Spectroscopy Reveals Homogeneous Lineshape Dynamics in CsPbBr3 Quantum Dots

1 Supplementary Information: Coherent Multi-Dimensional Spectroscopy Reveals Homogeneous Lineshape Dynamics in CsPbBr3 Quantum Dots Arnab Ghosh1, Samuel Palato2*, Patrick Brosseau1, Rui Tao3,4, Dmitry N. Dirin3,4, Maksym V. Kovalenko3,4, and Patanjali Kambhampati1* 1Department of Chemistry, McGill University, Montreal, H3A 0B8, Canada 2Department of Chemistry, Humbolt University, Berlin, 12489, Germany 3 Department of Chemistry and Applied Biosciences, ETH Zürich, Zürich CH-8093, Switzerland 4 Laboratory for Thin Films and Photovoltaics, Empa - Swiss Federal Laboratories for Materials Science and Technology, Dübendorf CH-8600, Switzerland *[email protected] and [email protected] 2 Table of Contents 1. Synthesis and characterization of perovskite quantum dots 1.1 Synthetic Methods 1.2. Transmission Electron Microscope (TEM) characterization 1.3. Linear Spectroscopy characterization 2. Coherent Multi-Dimensional Spectroscopy 3. Pulse characterization 4. Sample handling and solvent response 5. Handling early time perturbed free induction decay signals 6. Modeling of 2D spectra: cumulant expansion and Brownian oscillator 7. CMDS spectrum, diagonal and antidiagonal spectral projection for P QD of other diameters 8. Fitting the diagonal and antidiagonal widths 8.1 Experimental D and AD FWHM vs t2 along with the model fit for other sizes 3 1. Synthesis and characterization of lead halide perovskite quantum dots 1.1 Synthetic Methods The lead halide perovskite quantum dots ( LHP QDs) are synthesized using previously published methods 1,2. Materials Lead bromide (PbBr2, 99.999%), cesium carbonate (Cs2CO3, 99.9%), hexane (≥99%), diisooctylphosphinic acid (DOPA, 90%), oleic acid (OA, 90%) and acetone (ACE, ≥99.5%) were purchased from Sigma Aldrich. n-Octane (min. 99%) and lecithin (>97% from soy) were purchased from Carl Roth. Trioctylphosphine oxide (TOPO, min. 90%) was purchased from Strem Chemicals. CsPbBr3 QDs synthesis procedures 0.04 M Pb stock solution. The PbBr2 stock solution (0.04 M) was prepared by dissolving 2 mmol (0.734 g) of lead bromide and 10 mmol (3.866 g) of trioctylphosphine oxide into 10 ml of octane at 120 °C in a 40 ml vial. Once all the PbBr2 was dissolved (~30 min), the solution was cooled to room temperature and transferred entirely to the big Schott bottle and diluted by 40 ml of HEX. The stock solution was filtered after preparation over a 0.2 µm PTFE filter and stored in air. 0.02 M Cs-DOPA stock solution. The Cs-DOPA stock solution (0.02 M) was prepared by loading 100 mg of Cs2CO3 (0.614 mmol Cs) together with 1 ml of DOPA (3.154 mmol) and 2 ml of OCT at 120 °C in a 40 ml vial. Once all the Cs2CO3 was dissolved (~20 min), the stock solution was cooled to room temperature and 27 ml of HEX was added. The stock solution was filtered after preparation over a 0.2 µm PTFE filter and stored in air. 0.2 M Cs-DOPA stock solution. The concentrated Cs-DOPA stock solution (0.2 M) was prepared by loading 100 mg of Cs2CO3 (0.614 mmol Cs) together with 1 ml of DOPA (3.154 mmol) and 2 ml of OCT at 120 °C in a 40 ml vial. Once all the Cs2CO3 was dissolved (~20 min), the stock solution was cooled to room temperature. The stock solution was filtered after preparation over a 0.2 µm PTFE filter and stored in air. 4 The lecithin stock solution (~0.13 M) was prepared by dissolving 1 gram of lecithin in 20 ml of HEX using an ultrasonic bath (30 min). After preparation, the stock solution was centrifuged, filtered over a 0.2 µm PTFE filter and stored in air. Synthesis of CsPbBr3 QDs was performed following the procedure reported elsewhere 2 with slight modifications. 4.9 nm LHP QDs. The filtered hexane (120 ml) is mixed with PbBr2 stock solution (8 ml). Under heavy stirring, a 0.02 M Cs-DOPA stock solution was injected (4 ml). After 1 minute of QDs growth, the lecithin solution was added to the crude CsPbBr3 solution (4 ml). After 1 minute, the solution was concentrated on a rotavapor at room temperature. The QDs were precipitated from the concentrated solution (5 ml) by an excess of acetone (12 ml). The obtained pellet was dissolved in 5 ml of toluene. 5.9 nm LHP QDs. The filtered hexane (48 ml) is mixed with PbBr2 stock solution (8 ml). Under heavy stirring, a 0.02 M Cs-DOPA stock solution was injected (4 ml). After 10 minutes of QDs growth, the lecithin solution was added to the crude CsPbBr3 solution (4 ml). After 1 minute, the solution was concentrated on a rotavap at room temperature. The QDs were precipitated from the concentrated solution (5 ml) by an excess of acetone (12 ml). The obtained pellet was dissolved in 5 ml of toluene. 9.4 nm LHP QDs. The filtered hexane (24 ml) is mixed with PbBr2 stock solution (8 ml). Under heavy stirring, a 0.02 M Cs-DOPA stock solution was injected (4 ml). After 40 minutes of QDs growth, the lecithin solution was added to the crude CsPbBr3 solution (4 ml). After 1 minute, the QDs were precipitated by an excess of acetone (114 ml). The obtained pellet was dissolved in 5 ml of toluene. 10.8 nm LHP QDs. The filtered hexane (10 ml) is mixed with PbBr2 stock solution (8 ml). Under heavy stirring, a 0.02M Cs-DOPA stock solution was injected (4). After 60 minutes of QDs growth the lecithin solution was added to the crude CsPbBr3 solution (4 ml). After 1 minute, the obtained QDs were precipitated by an excess of acetone (66 ml). The obtained pellet was dissolved in 5 ml of toluene. 5 18.4 nm LHP QDs. Under heavy stirring, a 0.2 M Cs-DOPA stock solution (0.2 ml) was injected into 4ml of PbBr2 stock solution. After 30 minutes of QDs growth 10 µl of oleic acid and oleylamine were added. Then 2 ml of 0.02M Cs-DOPA stock solution were slowly injected with 2 ml/h rate. After injection was completed, the lecithin solution was added to the crude CsPbBr3 solution (2 ml). After 1 minute, the obtained QDs were precipitated by an excess of acetone (22 ml). The obtained pellet was dissolved in 5 ml of toluene. 6 1.2. Transmission Electron Microscope (TEM) characterization TEM images were collected using a JEOL JEM-1400 Plus operated at 120 kV or Hitachi HD-2700. The samples were prepared by placing a drop of diluted QDs solution on coated Cu TEM grids. Figure S1: STEM image of the (a) 4.9 and (b) 5.9 nm CsPbBr3 QDs. TEM images of (c) 9.4 nm, (d) 10.8 and (e) 18.4 nm large CsPbBr3 QDs. (f) Histogram of diameters for 4.9 nm and 9.4 nm P QD. 7 1.3. Linear Spectroscopy characterization Optical characterizations were performed at ambient conditions. UV-Vis absorption spectra of colloidal QDs were collected using a Jasco V670 spectrometer in transmission mode. The NC concentrations were determined from the absorption spectra using the absorption coefficient reported by Maes et al.3 For the measurements QDs solutions were diluted down to 20-50 µg/mL. Zwitterion-capped QDs were dispersed in either hexane or toluene. A Fluorolog iHR 320 Horiba Jobin Yvon spectrofluorometer equipped with a PMT detector was used to acquire steady-state PL spectra. NC solutions were measured in the same dilutions and solvents as the absorption measurements. Photoluminescence quantum yield (PLQY): Absolute PL QYs of solutions were measured with a Hamamatsu C13534 Quantaurus-QY Plus UV-NIR absolute PL quantum yield spectrometer. The same solutions that were used to measure PL were also used to measure QY. Figure S2: Linear absorption spectra (solid lines), photoluminescence spectra (dashed line with shaded area) of 18.4 nm (red), 10.8 nm (orange), 9.4 nm (green), 5.9 nm (blue) and 4.9 nm (violet) QDs. Also shown in bottom panel is laser spectra (grey). 8 2. Coherent Multi-Dimensional Spectroscopy The Coherent Multi-Dimensional Spectroscopy (CMDS) instrument was previously described in detail 4-17. The femtosecond light source was an Ar filled hollow core fiber (HCF) which produced spectrally broadened pulses based upon the 500 nm output from a 120 fs optical parametric amplifier. The coherent pump pulse train was created by acousto-optic modulators. The CMDS experiment was conducted in the pump/probe geometry. Figure S3 illustrates the CMDS experiment and signals. Figure S3: Illustration of CMDS experiment, Feynman diagrams for the six response functions. 9 3. Pulse characterization Pulses are suitably manipulated to obtain near-transform limited pulses at the sample position. The pulses are characterized using a home built all-reflective dispersion-free transient-grating frequency resolved optical gating (TG-FROG). Pulse durations are determined by fitting a Gaussian pulse shape to the time marginal of the FROG trace. The temporal duration of the pulse is estimated to be close to 10 fs. Figure S4: a) Typical TG-FROG trace. 16 7. CMDS spectrum, diagonal and antidiagonal spectral projection for LHP QD of other diameters Figure S8: Experimental CMDS spectrum of 10.8 nm diameter CsPbBr3 QD at t2 = 20 fs (a). Same at 800 fs (b). The diagonal and anti-diagonal spectra at t2 = 20 fs (e). Same as prior for 800 fs. 17 Figure S9: Experimental CMDS spectrum of 9.4 nm diameter CsPbBr3 QD at t2 = 20 fs (a). Same at 800 fs (b). The diagonal and anti-diagonal spectra at t2 = 20 fs (e). Same as prior for 800 fs. 18 Figure S10: Experimental CMDS spectrum of 5.9 nm diameter CsPbBr3 QD at t2 = 20 fs (a). Same at 800 fs (b). The diagonal and anti-diagonal spectra at t2 = 20 fs (e). Same as prior for 800 fs. 19 Figure S11: Experimental CMDS spectrum of 4.9 nm diameter CsPbBr3 QD at t2 = 20 fs (a). Same at 800 fs (b). The diagonal and anti-diagonal spectra at t2 = 20 fs (e). Same as prior for 800 fs. 20 8. Fitting the diagonal and antidiagonal widths The model described in the previous section was used to fit the experimental diagonal and antidiagonal linewidths, as shown in Figure 4a of the main text. The optimum is obtained by leastsquares curve fitting of the antidiagonal and diagonal widths with 3 parameters described in the previous section: 𝜎S, 𝜏 and 𝜎. The two curves are fitted simultaneously by summing their residuals. The model values were obtained by a method mimicking the analysis of experimental data: for a given set of parameters, the 2D spectrum was simulated as described in the previous section. The cuts along the diagonal and antidiagonal were then extracted, and their FWHM determined. As the calculations are relatively demanding, the optimization process was accelerated using a surrogate model. The surrogate model 𝑓′(𝑝) of parameters 𝑝 approximates the true function 𝑓(𝑝) but is cheap to evaluate. To generate the surrogate, we compute the time-dependent diagonal and antidiagonal widths for a grid of parameters {𝜎S,𝜎,𝜏}. The surrogate model 𝑓′(𝑝) is obtained by radial basis function interpolation on this grid, using a cubic kernel. In order to ensure correct result, it is necessary that the surrogate provides a good approximation of the true function in the vicinity of the minimum. The best-fit results are therefore obtained by iteratively minimizing the residuals and refining the surrogate until convergence. The process occurs as follows: 1. The surrogate is initialized by calculations on an ensemble of grid points. The initial points are selected to cover a large span around the possible solutions. 2. Fitting is performed by least-squares minimization of ΓD and ΓAD. The minimization is carried out using the Nedler-Mead simplex algorithm, using the surrogate to compute the model values of the widths. This provides a candidate for the optimal parameters. 3. Points are added to the grid in the vicinity of the new candidate, if possible. 4. Steps 2 and 3 are performed iteratively until the optimum converges, and no new grid points can be added. 21 The calculation grid uses a step size of 1 meV for 𝜎 and 𝜎S and 1 fs for 𝜏. We find the surrogate evaluation problem to be rather forgiving in this case, as the widths vary relatively simply with the parameters in this range, providing a simple optimization surface. Table S1 : Best-fit parameters. Numbers in parenthesis indicate the uncertainty on the last two digits. QD size 𝝈𝐒 (meV) 𝝈 (meV) 𝝉 (fs) 18 13.69 (49) 29.29 (45) 54.5 (72) 10.8 0.1 (12) 32.77 (21) 91.2 (59) 9.4 14.83 (37) 35.20 (45) 42.6 (48) 5.9 15.79 (25) 29.97 (36) 50.5 (58) 4.9 0.00 (-) 35.68 (16) 81.7 (41) 22 8.1 Experimental D and AD FWHM dynamics along with the model fit for other PQDs Figure S12: a) Diagonal and anti-diagonal lineshape dynamics of other PQDs fitted with the model. 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