I. ABSORPTION AND PHOTOLUMINESCENCE SPECTRA The photoluminescence (PL) spectra shown in Figure 1 were taken using a Jobin Yvon Fluorolog-3 spectrofluorometer. The absorption spectra of the NP, also shown in Figure 1, were taken on a Perkin Elmer Lambda 1050 UV/Vis/IR spectrophotometer and a Varian Cary 1E UV-visible spectrophotometer . FIG. 1. Photoluminesence (dotted lines) and absorption (solid lines) spectra for the three NP samples. II. FLUORESCENCE LIFETIME MEASUREMENTS Photoluminescence decay time measurements were taken using a commercial time-correlated-singlephoton-counting instrument (Edinburgh Instruments, Mini-τ) coupled to a 0.5 m single grating monochromator (Acton SP500i). A 405 nm pulsed diode laser operating at a repetition rate of 500 kHz was used for excitation and a Hamamatsu H7422 photomultiplier tube was used for detection. Figure 2 shows the PL decay curve for both NP samples. The decay for the large core NP could be well described by a tri-exponential function with decay constants of 8.50.2 ns, 30.20.4 ns and 992 ns with relative amplitudes of 32%, 58% and 10%, respectively. The decay for the medium core NP could also 1 be well described by a tri-exponential function with decay constants of 5.30.4 ns, 23.90.4 ns and 65.61.2 ns with relative amplitudes of 3%, 51% and 47%, respectively. For the small core NP, a biexponential function with time constants (amplitudes) 651 ns (91%) and 201 ns (9%) was sufficient to characterize the decay. Thus, in all three cases the single exciton lifetime can be characterized as being in the tens of nanoseconds range. FIG. 2. Photoluminescence decay curves for the InP NPs. III. INVESTIGATION INTO THE EFFECT OF STIRRING Absorption transients were taken at different pump wavelengths and for a range of fluences with the sample stirred by a Variomag mini magnetic stirrer at 1000 rpm or not stirred. The results of this study are shown in the figures below and reveal that there is no discernable difference when the sample is stirred or unstirred. This indicates that the quantum dots do not undergo significant photodegradation as a result of the laser excitation and further that quantum dot charging as a result of photoionisation does not occur to an extent that would influence the TA measurements. 2 FIG. 3. a) Absorption transients for high and low pump fluence at 1.4 x Eg showing no difference between stirred (black) and unstirred (grey) and b) absorption transients taken at 2.6 x E g showing no difference between stirred (black) and unstirred (grey). IV. QUANTUM YIELD MEASUREMENTS FOR THE SMALL AND MEDIUM CORE NANOPARTICLES The biexciton lifetimes for the small and medium core NP were measured to be 699 ps and 521 ps, respectively, and so R was found by fitting Eqn. (1) to the transmittance transients over 350 ps and 250 ps time windows, in order to preserve the same ratio between time window and biexciton lifetime as used for the large core NP. The variation in R as a function of initial fractional pump-induced transmittance change, T(0)/T, are shown in Figures 4 and 5 for the same range of pump wavelengths as used for the large core NP. The CM QY were again found by fitting Eqn. (3) to the data shown in Figures 3 and 4 using a correction factor, , calculated from the PL decay constants. 3 FIG. 4. Average number of excitons generated per photo-excited small core NP, R, as a function of fractional change in transmission for pump photon energies a) 1.1, b) 1.3, c) 1.7, d) 2.0 and e) 2.1 times the band gap, Eg. The average number of additional excitons created per absorbed photon for different normalised photon energies, E=h/Eg, are also shown (f). 4 FIG. 5. Average number of excitons generated per photo-excited medium core NP, R, as a function of fractional change in transmission for pump photon energies a) 1.3, b) 1.9, c) 2.1, d) 2.5 times the band gap, Eg. The average number of additional excitons created per absorbed photon for different normalised photon energies, E=h/Eg, are also shown (e). V. COMPARISON OF FRACTIONAL TRANSMITTANCE TRANSIENTS FOR PUMPING ABOVE AND BELOW THE BANDGAP OF BULK ZnO AND ZnS The transients presented in Figure 1 of the main manuscript show that pumping at wavelengths above and below the bulk band gaps of ZnO and ZnS results in no significant difference in the decay of the transmittance change. The much more rapid initial rise of the transmittance change was also studied at higher temporal resolution. As Figure 6 below shows, pumping above and below the band gaps of ZnO and ZnS producing no change in the rise time either. 5 Figure 6. Comparison of transmittance transients for pump photon energies less than (450 nm) and greater than (280 nm and 240 nm) the bulk band gaps of ZnO and ZnS. 6