Supplementary Information Efficient Biexciton Interaction in Perovskite Quantum Dots Under Weak and Strong Confinement Juan A. Castañeda, Gabriel Nagamine, Emre Yassitepe, Luiz G. Bonato, Oleksandr Voznyy, Sjoerd Hoogland, Ana F. Nogueira, Edward H. Sargent, Carlos H. Brito Cruz, and Lazaro A. Padilha * Instituto de Fisica GlebWataghin, Universidade Estadual de Campinas, UNICAMP, P.O. Box 6165, 13083-859 Campinas, Sao Paulo, Brazil Instituto de Quimica, Universidade Estadual de Campinas, UNICAMP, P.O. Box 6154, 13084-971 Campinas, Sao Paulo, Brazil Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road Toronto, Ontario M5S 3G4, Canada e-mail:padilha@ifi.unicamp.br 1
Sample preparation CsPbX3 PQDs are prepared in a similar fashion as reported in Protesescu et al (Ref). First a stock Cesium oleate solution is prepared by loading flask with 0.814 gr Cs2CO3 with 3 ml oleic acid and 40 ml Octadecene. The contents were placed under vacuum and heated to 100 C for 30 minutes. The flask is purged with Nitrogen and heated to 130 C to complete the formation of Cesium oleate. Typically PbX2 (0.19 mmol), 0.5 ml oleic acid and oleylamine and 5 ml Octadecene is added in to reaction flask. The flask is placed under vacuum and heated to 90 C until PbX2 is completely solubilized. The flask is cycled with Nitrogen and vacuum 3 times and finally placed under Nitrogen. To tune the nanocrystal size this mixture is heated to 140C-200 C where preheated Cesium oleate solution (0.4ml) is injected. Upon injection the solution takes bright color and the flask is placed in ice/water bath. Figure S. 1 TEM images for bromide and iodide PQDs 2
TEM images for some of the samples is shown in Fig. S1. For larger PQDs we could obtain very clear TEM images. However, for smaller nanoparticles the data did not show the same good resolution. Using the sizes that we were able to measure, we could plot the volume dependence of the absorption cross section at 3.1 ev. The relation between these two variables is shown in Fig. S2. Volume (nm 3 )1000 100 1 10 Cross Section (10-15 cm 2 ) Figure S. 2 PQDs volume as a function of the absorption cross section at 3.1 ev. The closed squares are bromide PQDs and the open circles are iodide ones. Poisson Statistics Used to Obtain the Absorption Cross Section Considering one single PQD, we can assume that the number of photons absorbed by one PQD is small, i.e., γ 1. For such events, we can use Poisson statistics to describe the 3
probability of each PQD absorb γ photons if the ensemble average of absorbed photons is N = N Photons σ 3.1eV, where N Photons is density of photons per pulse per area and σ 3.1eV is the absorption cross-section. This probability is given by P(γ) = N γ e N γ! At early times, right after the photo-excitation, at the band-edge, each PQDs is populated with up to 2 excitons. Those PQDs that have absorbed only one photon contribute only once to the bleaching. All the others that have absorbed at least 2 photons will contribute twice to the bleaching. Consequently, the magnitude of the early delay signal is given by C = P(1) + 2x(P(2) + P(3) ) After all the multi-excitons have decayed (due to Auger recombination), each excited PQD is left with only one exciton and the contribute equally to the signal, so which can be rewritten as B = P(1) + P(2) + P(3), B = 1 P(0) = 1 e N = 1 e N Photonsσ 3.1eV Since the measured signal depends on the PQDs concentration on the ensemble, we can multiply the above equation by B 0, which is the B saturation magnitude, consequently, Similarly, we can write C as B = B 0 (1 e N Photonsσ 3.1eV ) C = B + A where A corresponds to the fast component only, i.e., corresponds to the PQDs that have absorbed at least 2 photons. Similarly to what we have done for B, we can write A as, 4
A = A 0 (1 P(0) P(1)) = A 0 (1 e N N e N ) = A 0 (1 e N Photonsσ 3.1eV )(1 + N Photons σ 3.1eV ) Time-Resolved Photoluminescence and Cross Section Measurement Time-resolved photoluminescence has been used to measure the emission lifetime and the absorption cross section for most of the samples investigated in this work. The measurements were done with a Time-Correlated Single Photon Counting (TCSPC) from Horiba-Jobin Yvon, which has resolution of about 100 ps. Measurements were performed with excitation at 3.1 ev for bromide and 2.3 ev for most of the iodide PQDs. The excitation density was typically changed by two orders of magnitude. Figure S3 shows examples of intensity dependent transient photoluminescence for CsPbBr3 and the fitting to obtain the absorption cross-section. Figure S. 3 a) Transient photoluminescence for PQDs. b) The Poisson statistic fitting to the amplitude measured after the multi-exciton decay is shown for the bromide sample. Trion Influence 5
Photo-ionization is a typical problem in semiconductor nanocrystals when they are excited with high energy photons. Photo-ionized species are characterized by Auger recombination from trions, which should be about 4-5 times slower than Auger recombination for biexcitons. As pointed out in the main text, we observed the presence of trions at high excitation regime. Nevertheless, those trions occurs in only a small fraction of our PQDs (according to our data it is less than 10%). Figure S4 shows the intensity dependence transient absorption for a sample of CsPbBr3 for which the excitation was chosen to be as high as about 7 excitons per PQD. From that figure, it is clear that the plateau at long delay (~200 ps), observed for lower excitation intensities, is replaced by a decay slower than the biexciton. In Figure S4b we can see the influence of trions with lifetime of about 180 ps, about 5 times longer than the ~35 ps measured for the biexciton. The value measured for the biexciton agrees with the one reported in Ref. 1. Figure S. 4 a) Intensity dependence of the transient absorption for CsPbBr3 PQDs with the largest measured cross-section showing a different dynamics for the highest excitation intensity. b) Multiexciton dynamics for the highest excitation (<N> ~ 6.5) with two very clear decay times. The slower decay is about 5 times longer than the biexciton decay lifetime. 1 Makarov, N. S.; Guo, S.; Isaienko, O.; Liu, W.; Robel, I.; Klimov, V. I., Spectral and Dynamical Properties of Single Excitons, Biexcitons, and Trions in Cesium Lead-Halide Perovskite Quantum Dots. Nano Lett. 2016, 16, 2349-2362. 6