3.1 Transient absorption spectra from femto- to nanosecond range

The transient absorption spectrum of a TiO₂ nanocrystalline film has been assigned in a spectral range from 400 to 2500 nm in our previous study [12]. Fig. 2a shows the spectrum measured at 1 μs after excitation by a 355-nm nanosecond laser pulse. The observed transient absorption spectrum was separated into three species, free electrons, trapped electrons, and trapped holes. The trapped electrons and holes exhibited broad bands in the visible range with maxima at 770 and 530 nm, respectively. Free electrons showed a broad absorption band whose intensity increased with wavelength, and the tail of the band overlapped with the bands of the trapped electrons and holes. It should be pointed out that in the visible range the absorption intensity of trapped holes is very large relative to that of free and trapped electrons. The spectral shape of the film did not change in a time range from 50 ns to 1 μs, indicating that the spectrum shown in Fig. 2a is attributed to carriers in the equilibrium state. Therefore, the trapped electrons and holes should be in deep trapping sites after relaxation through trapping sites. We call them ‘deeply trapped electrons’ and ‘deeply trapped holes’ in this paper.

Transient absorption spectra of the film excited by a femtosecond laser at 266 nm were measured on the femto- and picosecond time range. Fig. 2b shows the transient absorption spectra of delay times from 200 fs to 100 ps in the wavelength range from 550 to 1000 nm. The transient absorption spectra are very broad, and the absorption intensity decreases gradually with time after 450 fs.

To confirm that nonlinear excitation did not occur in the femtosecond experiment, transient absorption of the TiO₂ film was measured at different excitation intensity. Fig. 3 shows temporal profiles of the transient absorption at 1100 nm. The peak intensity of the transient absorption at just after excitation is plotted as a function of the excitation power in the inset of Fig. 3. The absorbance is proportional to the excitation power, indicating that the carriers were formed through one-photon excitation process and nonlinear excitation process was not involved. The absorption decay in the picosecond range became faster when increasing the excitation power. This indicates that the number of electrons and holes in a single TiO₂ particle is large enough to cause bulk recombination.

In order to exclude the contribution of the absorption decay due to electron-hole recombination, the spectra in Fig. 3b were normalized at 1000 nm. Normalized spectra are shown in Fig. 2c. It is obvious that the spectra are shifting to blue with time as a general trend. The spectrum immediately after excitation (at 200 fs) has increasing intensity with wavelength, indicating that free carriers are not trapped yet at this time. Free carrier cooling and trapping processes will be discussed in detail in 3.2. At 10 ps, a spectral shoulder around 650 nm can be seen in the visible region, representing that trapped species are observed; however, the spectral shape is different from that of the deeply trapped species (Fig. 2a). Therefore, the 10 ps spectrum includes contribution of shallowly trapped species. It is seen that relaxation through trapping sites proceeds on the picosecond time range. The details will be discussed in Section 3.3.

It should be noted that the observed spectral blue-shift is similar to previous reports as for TiO₂ colloidal solutions [6] or powders [5]. Various types of trap sites are known to exist in semiconductor nanoparticles, and these sites are distributed over a wide range of energies. Previous experimental results suggest that electrons and holes are trapped quickly at shallow trapping sites, at which these charge carriers are bound loosely; and thermal fluctuations allow the carriers to migrate to deep trapping sites, where they are bound more tightly [4–6,8]. Consequently, the populations of electrons and holes in deep trapping sites will increase with time by carrier migration between trapping sites. As a general trend, transient absorption spectra of TiO₂ shift from red to blue with increasing delay times in the picosecond time range. This shift is considered to be due to relaxation of trapped electrons [5] and holes [6] to deeper trapping sites. Hence, shallowly trapped carriers tend to absorb photons of longer wavelengths, and deeply trapped carriers photons of shorter wavelengths.

In the present TiO₂ nanocrystalline film, deeply trapped holes have strong absorption in the visible region with a peak at 530 nm. Therefore, it is expected that shallowly trapped holes would give absorption with a peak at longer than 530 nm. Absorption of shallowly trapped electron would be hardly observable in the visible region, because deeply trapped electrons have an absorption peak at 770 nm and its intensity is weak. Therefore, the observed spectral change in Fig. 2c is considered to reflect mainly hole trapping dynamics.

3.2 Ultrafast relaxation of photogenerated hot holes by cooling and trapping

As discussed above, in general spectral overlap between many species (deeply and shallowly trapped carriers and free carriers) in TiO₂ over wide spectral range makes it difficult to analyze the observed transient absorption. However, we have demonstrated that trapped holes are dominant in the visible region, and especially at shorter wavelength deeply trapped holes are responsible for observable absorption. Here, we discuss formation dynamics of the deeply trapped holes in the early stage by analysis of femtosecond transient absorption rise at 550 nm. The temporal profile at 550 nm is potted against delay time together with calculated curves in Fig. 4. For comparison temporal profiles at 1000 and 700 nm are also shown. The calculated profiles were obtained by convoluting the instrument response function with several exponential rise functions. The instrument response function was determined by a two-photon absorption cross-correlation method, and could be fitted using a Gaussian function with a FWHM of 170 fs for all probe wavelengths. The rise times estimated from the transient absorptions at 1000, 700, and 550 nm were 100 ± 50, 150 ± 50, and 200 ± 50 fs, respectively.

In the obtained rise time of 200 fs at 550 nm for deeply trapped holes, the free carrier cooling and the free carrier trapping are considered to take place. From our experiment, separation of these two processes is difficult. Yang and Tamai [6] previously estimated hole trapping time in anatase TiO₂ colloidal particles excited at 360 nm (close to the band-gap), where the free carrier cooling would be neglected since excess excitation energy is small. The trapping time in the colloid was very rapid and less than 50 fs. The formation rate of the trapped holes in present study is slower than this trapping time. The difference of the rate can be explained by carrier cooling times. In present experimental condition the excitation photonic energy (4.7 eV) is much larger than the bang gap of anatase TiO₂ (3.2 eV). The hot carriers should dissipate excess photonic energy before free carrier trapping. Carrier cooling is responsible for slowing the formation of trapped holes in the TiO₂ film.

The estimated rise times at 1000 and 700 nm (100 ± 50 and 150 ± 50 fs, respectively) are shorter than the rise time at 550 nm (200 ± 50 fs). As mentioned above, many transient species can be observed in the spectral range from 700 to 1000 nm, such as shallowly trapped holes, deeply and shallowly trapped electrons, and free electrons. Absorption of free holes might appear in this range. Due to this spectral overlap, detailed analysis is very difficult; however, possible explanations may be raised as follows. Free carrier absorption is expected to give instantaneous response, so that this contribution could make the apparent profile to glow faster. Shallowly trapped holes may be dominantly observed. They, indeed, would be spread over the bulk of TiO₂ particles, in contrast with the deeply trapped holes that are likely to be trapped at surface. Then, the free carrier cooling time in the bulk might be decreased.

3.3 Relaxation through tapping sites in the time picosecond scale

Free carriers in TiO₂ nanocrystalline films were trapped into various sites, and then the trapped carriers relaxed into lower energy sites. The relaxations of trapped carriers are considered to be due to carrier migrations between traps. The spectral shift as shown in Fig. 2 indicates that the trapped carriers are relaxing over the time range longer than 10 ps after laser excitation.

To examine the relaxation dynamics of trapped carriers up to about 100 ps, the decay profiles of transient absorption for the TiO₂ film at 550, 700, and 1000 nm are plotted from 20 to 94 ps in Fig. 5. Since the 550 nm absorption is dominated by deeply trapped holes and 700 and 1000 nm include many contributions such as shallowly trapped holes, deeply trapped electrons, and shallowly trapped electrons, comparing the 550 nm decay with others will give information about population distribution change for the deeply trapped holes.

To smooth the scattered data points, the profiles were normalized at a delay time of 20 ps after being fitted to a double-exponential function with a constant component. The difference in the three curves is clear, though the decay rates of the absorbance are on the same order of magnitude, 10 ps, because of the recombination of the trapped electrons and holes. The longer the probe wavelength is, the faster the decay of the absorption is; that is, shallowly trapped carriers decay faster than deeply trapped ones in the picosecond time domain. This result can be explained in terms of relaxation through trapping sites, as discussed above. Thermal fluctuation allowed the carriers in shallow trapping sites to detrap more frequently than those in deeper trapping sites, and consequently the former easily underwent migration between the trapping sites. This is the reason that absorption of shallowly trapped carriers decreased rapidly. In contrast, once carriers were trapped at deep trapping sites, detrapping from the sites was difficult owing to the necessarily large activation energy. The large activation energy slowed the absorption decay at shorter wavelengths.