Figure shows typical time-resolved differential absorption measurements of the In2O3nanocrystals for different photon probing energies. The excitation was accomplished with 3.81 eV (325 nm) photons under a pump fluence of 0.250 mJ/cm2. Clearly from the data in Fig. , we notice two distinct regions of different behavior.
Figure 2 Differential absorption signal vs. time delay for different photon wavelengths in In2O3nanocrystals. Photoexcitation was accomplished with 3.81 eV (325 nm) photons under a pump fluence of 250 μJ/cm2at room temperature. The inset shows a fit to (more ...)
The first region corresponds to probing wavelengths below ~400 nm where the induced absorption change appears to be negative, and the second region corresponds to longer probing wavelengths where the change appears to be positive. For both probing regions there is an initial sharp change which is pulse-width limited reaching a maximum value, and then followed by a slow recovery toward equilibrium which persists over tens of picoseconds. The negative change in the induced absorption corresponds to what we refer to as “state filling”. This is associated with the occupation of states of the In2O3NCs by the photogenerated carriers following photoexcitation by the ultrafast laser pulse whose energy is above the band gap. Once the carriers occupy states that were normally unoccupied the absorption at the probing wavelength will appear reduced. Therefore, monitoring this negative change in absorption as a function of delay between the excitation and probing pulse is a direct measure of the temporal evolution of the photo-generated carriers at the probing wavelength state. On the other hand, if the probing energy is smaller than the band-gap energy, direct coupling from the valence band states to conduction band states will not be possible, therefore state filling will not be observed. However, under such probing conditions a positive change in the induced absorption maybe observable. This is due to secondary excitation of the photo-generated carriers to higher energy states due to the probing pulse. This positive photo-induced change depends on the number of photo-generated carriers present in the initial state and the coupling efficiency between the initial and final state. Therefore, the recovery signal is again a direct measure of the decay of the photo-generated carriers from the probing energy state. Here we should point out that in some cases state filling may be possible below the band gap when there are available energy states below the band edge which is the case for the In2O3NCs. The transient differential absorption measurements (Fig. ) show state filling for probing wavelengths as long as 410 nm.
The recovery of state filling signal as seen for the shorter probing wavelengths (340 nm, 370 nm) in Fig. consists of two distinct temporal components, a fast and a much slower component. The fast component as we will show later on in this study is mainly due to Auger recombination, whereas the slower component which is of the order of 100 ps is associated with recombination or capture of the photo-generated carriers by various traps or surface-related states. It appears with increasing probing wavelength, the coupling from the valence bands to the available energy states below the band gap becomes weaker thus the state filling is reduced (this is in agreement with the broad photoluminescence spectra which drops to zero at ~460 nm). At the same time the contribution of secondary excitations increases, possibly, due to available higher energy states in the bands that the photo-generated carriers may couple by conserving energy and momentum. This is clearly evident from the observed increase in positive-induced absorption with increasing probing wavelength (Fig. ). We should also point out that at some point both effects may be present as seen in Fig. at the probing wavelength of 410 nm. Furthermore, there appears to be a peak of positive-induced absorption at 600 nm which is attributed to a larger density of the coupled states at the particular probing wavelength.
The recovery seen in the positive photo-induced absorption, for the longer probing wavelengths, contains both temporal components seen for the shortest probing wavelengths; however, the fast Auger recombination component is much less pronounced. This is mainly because the number of carriers distributed among the probing states which are located below the band gap is less than that in the case of state filling which occurs near the band edge where most of the carriers relax before captured by traps or recombine. In addition near the band edge the probe couples to the electron and hole states, while at longer wavelengths it only interacts with electrons or holes separately. Since Auger recombination has a cubic carrier density dependence, this will cause a pronounced change on the temporal evolution of the photo-induced absorption.
It is also interesting to point out that the recovery of the induced absorption is much longer (~312 ps, see inset in Fig. ) at the probing wavelength of 700 and 750 nm. Furthermore, the maximum signal appears to occur around 25 ps after the excitation pulse. The photo-generated carriers required a relatively long time to reach the probing states. This suggests that we are probing states that are much different than those we are probing with the shorter wavelengths where the maximum signal appears to be instantaneous (pulse-width limited). It is believed that we are probing deep traps states where the initial photo-generated carriers in the NCs have relaxed, at which point subsequent relaxation from these states is on the order of 300 ps.
Furthermore, we have investigated time-resolved dynamics at various excitation wavelengths with similar results. However, with increasing wavelength the signal becomes weaker. No measureable differential absorption signal was detected for pump wavelengths longer than 360 nm.
To further investigate the dynamics of the photo-generated carriers we have performed intensity measurements at various probing wavelengths. Typical measurements with excitation at 325 nm and probing at 350 nm are shown in Fig. . In the inset of Fig. we display the normalized results, which clearly indicate the effect of Auger recombination in these NCs. To analyze these data and obtain a value for the Auger coefficient we have utilized a model which consists of a simple differential equation incorporating the photo-generated carrier behavior following excitation by an ultrashort laser pulse:
Figure 3 Time-resolved differential absorption of In2O3nanocrystals excited with 325 nm and probe at 350 nm at different fluences. The inset shows the same measurements normalized which clearly indicate the effect Auger recombination with increasing fluences. (more ...)
corresponds to the carrier density which is a function of time and position from the surface of the sample. The carrier generation term is represented by the spatial and temporal function g(t,z)
, associated with the optical pulse excitation. In these simulations we have assumed a Gaussian laser pulse envelop and a Beer’s law dependence along the depth of the material. The ambipolar diffusion coefficient is represented by D
in the above differential equation, τ is the relaxation time constant of the photo-generated carriers, and γ
is the Auger coefficient. The above differential equation was solved numerically using the method of finite differences and the carrier density values obtained were fitted to the experimental data of the induced absorption. Some of the important parameters used in the above simulations were the absorption coefficient at the pump excitation wavelength α = 8×104
], and the ambipolar diffusion coefficient D
= 0.6 cm2
]. The Auger coefficient γ and the carrier relaxation τ were considered as fitting parameters. Here we should point out that a very accurate measurement of the absorbed fluence was necessary in these experiments since fitting parameters such as the Auger coefficient is strongly dependent on the actual photo-generated carrier density. Utilizing the photo-generated carrier densities obtained under different fluence conditions it was possible to determine best-fitting results for each of the fluences (Fig. ). The precise value of the Auger coefficient was mainly determined from the recovery shape of the induced absorption in the first tens of picoseconds, where the longer decay behavior determined the relaxation time constant τ for the carriers. Utilizing the above best-fit results for each of the photo-generated carrier density, it was possible to obtain an average value for the Auger coefficient γ = 5.9 ± 0.4 × 10−31
and carrier relaxation time constant τ = 110 ± 10 ps. We should note that the value of the Auger coefficient is similar to the value of bulk silicon [32
] which is 3.8 × 10−31
. Furthermore, we should point out that given the large size of the NCs used in this study in comparison to the exciton Bohr radius no confinement [33
] or surface state effects [35
] may play a significant role in the Auger dynamics.
Figure 4 Fitting results (represented bystraight lines) of the experimental differential absorption (represented bysymbols) of In2O3NCs excited with 325 nm and probe at 350 nm. The fitting results were obtained from the simple differential equation model describing (more ...)
In conclusion we have investigated ultrafast carrier dynamics in In2O3NCs using pump-probe differential absorption white light measurements. State filling has been observed for probing wavelengths corresponding to energies above the band gap (3.5 eV) and just below the band edge due existence of shallow trap states. Positive-induced absorption (free carrier absorption) was the main contribution for wavelengths longer than 500 nm. Auger recombination appears to play a crucial role in the recovery of the photo-generated carriers in the first tens of ps. A simple differential equation model incorporating diffusion as well as carrier relaxation terms has provided a means to fit fluence dependence experimental data and obtain best-fit values for Auger recombination. The average Auger coefficient obtained from the fitted results was γ = 5.9 ± 0.4 × 10−31 cm6 s−1and carrier relaxation time constant τ = 110 ± 10 ps. Finally, differential absorption data clearly shows a long delay (approximately 25 ps) for the carriers to reach the probing states, which are believed to be deep traps states and ~300 ps for these carriers to move out of these states.