Deciphering hot- and multi-exciton dynamics in core–shell QDs by 2D electronic spectroscopies† †Electronic supplementary information (ESI) available: Description of the synthesis of QDs, experimental details, additional 2DES-PP measurements, bi-exciton analysis. See DOI: 10.1039/c8cp02574f

2D electronic spectroscopy maps acquired in different configurations unveil intraband hot carrier cooling and interband multi-exciton recombination dynamics.


Synthesis and basic characterization of CdSe/ZnS QDs
CdSe/ZnS QDs were synthesized under nitrogen flux adapting a previously one pot reported procedure. 1,2 All solvents were of the highest purity available and used as received.
CdO powder, trioctylphosphine oxide (TOPO) (technical grade 90%), trioctylphosphine (TOP), hexadecylamine (HDA, 90%), tetrabutylphosphonic acid (TBPA, 97%), hexamethyldisilathiane (HMST), and diethylzinc (1 M solution in hexane) were purchased from Sigma-Aldrich. Typically, a mixture of TOPO (9.7 g), HDA (9.7 g), TBPA (0.276 g) and CdO (0.127 g) are dried and degassed in a 50 mL three-neck flask under vacuum by vigorous stirring at 120°C for about 20 min and afterwards heated in N 2 atmosphere up to 300°C. As the temperature reaches 290°C, TBP (2mL) is added to the reaction mixture. The nucleation step is gained by the fast injection of the Se precursor solution, obtained by dissolving elemental selenium (0.394 g) in TBP (4.4 g), into the hot mixture at 300°C. The desired QD size is achieved by further growing at 270°C for variable reaction time. After an annealing step at 110°C for 60 min, the inorganic shell of ZnS is directly grown on the CdSe nanocrystal core. The stock solution of ZnS precursors is prepared in a glove box by mixing Zn(C 2 H 5 ) 2 (1.294 g), HMDS (0.380 g) and TBP (9.460 g). The proper volume of such solution is added by a drop-wise injection at 155°C in the original reaction flask. The shell growth is controlled in real-time by monitoring the UV-vis absorption and emission spectra of the solution. The CdSe/ZnS QD dispersion is cooled to 110°C and further stirred under N 2 flux at this temperature for 60 min, to stop the shell growth. Finally, the temperature is decreased at 60°C and the QDs are washed by repeated precipitation with methanol and finally re-dispersed in a small volume of chloroform.  and tri-exponential fitting curve (black line). Excitation 365 nm, Emission 640 nm. The lower box reports weighted residuals from tri-exponential fitting.
In Figure SI_1, we report the absorption and steady-state photoluminescence (PL) spectra of the studied QDs in chloroform solution. As well, we performed time resolved photoluminescence measurements on the nanosecond timescale by time correlated single photon counting methods. The PL decay curve recorded under 365 nm blue excitation [1.3 ns resolution, 1 MHz repetition rate] is reported in Figure SI_2. The PL dynamics is well described by a tri-exponential function with time constants , , and and normalized amplitudes 72%, 25%, and 3%, respectively. The weighted residuals analysis confirms the absence of residual small amplitude dynamics.

2DES BOXCARS experimental setup
2DES-BC measurements have been performed with the setup described in Ref 3 . The pulses energy at the sample position was reduced down to 5 nJ per pulse, by a broadband half-waveplate/polarizer system while the beam waist was 300 µm. This lead to a <N> = 0.05. t 2 was scanned from 0 to 2000 fs in steps of 7.5 fs and for each value of t 2 , the coherence time t 1 was scanned from 0 to 80 fs in steps of 1 fs. To characterize the temporal properties of the exciting pulses, we performed FROG measurements ( Figure SI_3) in the same experimental conditions of 2DES measurements, only replacing the QDs solution with the solvent in the same 1 mm path-length cuvette. We retrieved a pulse duration of 11.5 fs, reasonably assuming gaussian pulses (see Figure SI_3). 4 To phase the signal, we compared BC spectra with 2DES-PP spectra recorded at the same pump energy.
The storage and handling of samples was conducted under N 2 atmosphere. During measurements, QDs were kept under N 2 atmosphere. To ensure the absence of any photodegradation process, we performed comparison between the linear absorption spectrum of QDs solutions before and after the measurements. At least 3 different sets of measurements in different days were performed and then averaged to ensure the reliability and reproducibility of the reported measurements. All measurements were performed at ambient temperature (295 K).

2DES Pump & Probe experimental setup
2DES-PP experiment was performed using the optical layout already described in Refs ,5,6 and reported in Figure SI_4.
Similarly to 2DES-BC, also in 2DES-PP the laser pulse was generated by a Ti:Sapphire laser-NOPA coupled system. After the NOPA, the beam was collimated and divided by a beam splitter.
The 10% of the beam was used as the probe pulse, whose chirp was minimized through a prism compressor; it was then focused by spherical lenses, delayed with a retroreflector mounted on an Aerotech ATS 100 linear stage and finally sent to the sample. The remaining 90% was used to generate the two collinear pump pulses through pulse shaping techniques. 6

Global Analysis
Both 2DES-BC and 2DES-PP signals were analyzed with a global complex multi-exponential fitting procedure, following a recently proposed methodology. 7 Briefly, the decay of the total complex signal at each point of the 2D map is fitted with a global function written as a sum of complex exponentials: where are oscillation frequencies, are decay constants, are phases and are signal amplitudes.
The components with describe population decay contributions, whereas components with = 0 represent oscillating components, associated with the coherent dynamics along . The ≠ 0 corresponding amplitude plotted in a 2D map as a function of and builds the so-called DAS These DAS bundles (one for each time constant) are then globally fit with a procedure entirely analogous to the one already described in Eq. S1, except that the variable, in this case, is the pulse energy rather than the delay time . The fitting function follows an effective model reproducing 2 the rising and the saturation of the signals: where the saturation term is expressed as in agreement with Ref. 8, and the rising term is expressed as .
are the amplitudes of the two components, is a coefficient tuning the saturation process such that , and is the exponent modulating the rising component.
The results of the fitting are reported in Table S1 and correspond to the trend shown in Figure 4e of the main text. DAS 2 shows a residual TX signature arising from the non-complete dynamics separation of the multi-exponential model. However, a perfect separation of these contributions was achieved by global analysis of the power coordinate. Table S1. Results of the global fitting performed applying Eq.S2 to the DAS bundles. Errors are estimated from the standard error of the minimization problem.

Additional 2DES-PP measurements
We performed additional measurements with a redshifted excitation laser band, reported in Figure   SI_7. The fitting of this second dataset provided results (time constants and amplitude distributions) in agreement with the first dataset reported in the main text, as shown in the DAS of Figure SI_8.

Bi-Exciton Binding Energy
To obtain a quantitative estimate of the bi-exciton binding energy in CdSe/ZnS QDs, we compared the spectral position of the peaks observed in the second and third DAS obtained by global analysis of the 2DES-PP dataset. As stated in the main text, we identify the second DAS (associated with the characteristic time ) with the dynamics of BX stimulated emission signal. On the other = 330 hand, we assign the third DAS ( ) to the slower single exciton recombination. Accordingly, = 7 the two peaks are slightly redshifted along the emission frequency axis by a quantity, referred as biexciton binding energy . Δ To obtain a quantitative estimate of , we analyzed vertical slices of the DAS extracted at a fixed Δ value of excitation energy corresponding to the energy ( ). Figure SI_9 and Figure  |