Ultrafast Charge Dynamics in Trap‐Free and Surface‐Trapping Colloidal Quantum Dots

Ultrafast transient absorption spectroscopy is used to study subnanosecond charge dynamics in CdTe colloidal quantum dots. After treatment with chloride ions, these can become free of surface traps that produce nonradiative recombination. A comparison between these dots and the same dots before treatment enables new insights into the effect of surface trapping on ultrafast charge dynamics. The surface traps typically increase the rate of electron cooling by 70% and introduce a recombination pathway that depopulates the conduction band minimum of single excitons on a subnanosecond timescale, regardless of whether the sample is stirred or flowed. It is also shown that surface trapping significantly reduces the peak bleach obtained for a particular pump fluence, which has important implications for the interpretation of transient absorption data, including the estimation of absorption cross‐sections and multiple exciton generation yields.

. Absorption and PL spectra for the CdTe CQDs before and after chloride treatment, see Table S1 for the peak positions for each sample.   5  Table S1. Summary of spectral features and photoluminescence quantum yields for the CdTe CQD samples. The diameters were determined for untreated samples from their band edge transition wavelength using the sizing curves from Yu et al. [1,2] . Figure S2. Fractional absorption change, ∆A/A, transients for the CdTe CQDs, with and without chloride passivation. The samples were pumped at a wavelength of 420 nm and fluence of 1.1 × 10 14 photons cm -2 per pulse, and probed at the wavelength corresponding to their band edge transition, as given in Table S1.

Calculation of 〈 〉 and ∆ /
The probability of a CQD absorbing photons per pump pulse, ( ), is determined by Poisson statistics [3] : ( ) = 〈 〉 (−〈 〉) ! ⁄ (S1) where 〈 〉 is the average number of photons absorbed per CQD and depends on the absorption cross-section of the CQD at the pump wavelength, , and the pump fluence, (in units of photons per pulse per unit area): 〈 〉 = (S2) Kamal et al. [4] found the dependence on diameter, , of the extinction coefficient for a wavelength of 410 nm, 410 , to be: 3 (S3) where 410 is related to the cross-section at 410 nm, 410 , (in units of cm -2 ) by: is Avogado's constant. is found from this by scaling by the ratio of the sample absorbance at the pump wavelength, , and at 410 nm, 410 , i.e. = 410 410 (S5) Once calculated, 〈 〉 can then be used to estimate the expected value of the maximum fractional absorption change at the band edge, ∆ ⁄ [5,6] : where is the sample absorbance at the band edge.
The experimentally determined and calculated expected values of ∆ ⁄ for the treated samples were consistent, where on average they were different by a factor of 1.05 0.03. For the untreated samples the experimental values were consistently lower, on average by a factor of 0.32 0.01.
If a single CQD absorbs greater than one photon per pump pulse a multi-exciton will be formed, and thus exhibit a fast decay component in transient absorption to a plateau on a picosecond time scale, leaving only single excitons. 〈 〉 can be used to calculate the expected ratio, ( ), of the peak-to-plateau amplitude [7] :  Table S2. Predicted (pre) and observed (obs) values for the average band edge occupancy, 〈 〉, maximum fractional absorbance change, ∆ ⁄ , signal noise, and peak-to-plateau ratio, , for each of the four samples before and after treatment. Predicted values are produced by setting J in Equation 2, 6 & 7. Observed values are derived from the same equations but use experimentally measured values of ∆ ⁄ . Each row of data for a particular sample corresponds to a different pump fluence, . For transient data taken with a high resolution, the plateau of the transient is not observed and so the observed is given as a lower limit.
There are numerous key observations from this table, firstly, the observed values for 〈 〉 and ∆ ⁄ are largely in line with the expected values for treated samples, but are significantly lower for the untreated samples. Secondly, a reduction in does not reduce the observed values for the untreated samples. And thirdly, the difference between the observed and predicted values are always greatly in excess of the noise level for the untreated samples, but below for the treated samples. These observations allow us to conclude that the lack of passivation in the untreated sample causes both a decrease in the peak amplitude and a fast decay to a plateau which are not explained by two-photon absorption. Figure S4. Comparison of fractional absorption change, ∆A/A, transients for untreated CdTe CQDs when the sample is (upper) stirred at 1000 rpm and held static, and (lower) flowed at 250 ml min -1 and held static. The samples were pumped at a wavelength of 420 nm and fluence of 1.1 × 10 14 photons cm -2 per pulse. The stirred and flowed samples were probed at wavelengths of 564 nm and 588 nm, respectively .  Table S1. The red lines are fits to equation (S8) and equation (S9) for the treated and untreated samples, respectively.

Comparison of stirred or flowed samples with static samples
Equation (3) from the main manuscript was fitted to the high resolution transients described in the previous section. The treated samples were assumed to be trap-free and so for fitting to the corresponding transients the rates of the trapping processes were set to zero i.e. ℎ = = 0 which yields a simple exponential rise that, as shown in Figure S5, described the transients well, with a only small deviation over the first ~1 ps. The values of 10 thus extracted were then used in the fitting of the corresponding untreated samples. The transients for untreated samples shown in Figures 2  and S2 do not decay to zero over the time period of the experiment but rather decay to a plateau. This indicates that there is a fraction of the CQDs that are trap-free in these samples, since trapping completely depopulates the band edge on this time-scale reducing the bleach to zero. Hence, the following equation, which combines terms for the trap-free, 1 * , and trapping CQD populations, 1 , was fitted to the bleach transients for the treated samples:  However, whilst parameters sets could be found that reproduced the observed dynamic (again except for the first ~1 ps of the rise), as shown in Figure S5, the increased number of free parameters, i.e. ℎ , , 1 * and 1 , meant that fitting did not yield well-constrained values for these parameters.
The agreement between equation (S8) and the transients for the treated samples is remarkable given the simplicity of the model used. A more sophisticated model, for instance incorporating a more detailed energy level structure, could be constructed which might produce a better match with the data during the first ps of the rise. However, such a model would include a greater number of free parameters which might, as was the case for equation (S9), result in the values yielded by the fit becoming ill-constrained.
Pump-induced absorption change spectra Figure S6. Normalised fractional absorption change, ∆A/A, spectra for CdTe CQD samples with and without chloride passivation. These spectra were collected at a pump-probe delay of between 1.5 ps and 2.5 ps, corresponding to when the bleach transients shown in Figure S5 peaked. The samples were pumped at a wavelength of 420 nm pump beams and fluence of 1.1 × 10 14 photons cm -2 per pulse, (pure toluene, the sample diluent, was found to provide no observable contribution to the signal).