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Non-degenerate fs pump-probe experiments in the UV-visible range for ultrafast carrier dynamics study of InGaN with adjustable pump and probe photon energies are implemented with simultaneously multi-wavelength second-harmonic generation (SHG) of a 10 fs Ti:sapphire laser. The multi-wavelength SHG is realized with two β-barium borate crystals of different cutting angles. The full-widths at half-maximum of the SHG pulses are around 150 fs, which are obtained from the cross-correlation measurement with a reverse-biased 280-nm light-emitting diode as the two-photon absorption photo-detector. Such pulses are used to perform non-degenerate pump-probe experiments on an InGaN thin film, in which indium-rich nano-clusters and compositional fluctuations have been identified. Relaxation of carriers from the pump level to the probe one through the scattering-induced local thermalization (<1 ps) and then the carrier-transport-dominating global thermalization (in several ps) processes is observed.
©2005 Optical Society of America
1. Introduction
Pump-probe experiments with fs lasers have been widely used for studying ultrafast carrier dynamics in various materials because such information can help us in understanding many fundamental properties of the materials [1,2]. In such an experiment, a non-degenerate setup is usually preferred because it can provide more information about carrier flow among different energy states. However, two synchronized ultrashort pulses (with jitter smaller than a few tens fs) of adjustable central wavelengths with a simple laser setup is usually difficult to obtain [3,4]. Non-degenerate pump-probe experiments can be implemented with a super-continuum generator or an optical parametric oscillator pumped by a regen-amplified mode-locked Ti:sapphire laser [5,6]. However, in most non-degenerate pump-probe research, with the repetition frequency of the regen-amplified pulses reduced to the kHz range, the signal-to-noise ratio can be quite low unless extremely large pulse energy is used. This difficulty is particularly prominent for samples of low emission efficiencies. Although the use of high pulse energy for excitation can help us in understanding the carrier dynamics under the condition of many-body interactions, many other fundamental physical processes can be missed. Meanwhile, a regen-amplified laser system is usually quite expensive. Such difficulties slow down the development of ultrafast carrier dynamics study, particularly in the UV-visible range. The non-degenerate pump-probe experiments in the UV-visible range are important because of the needs for understanding the optical properties of many novel wide-bandgap semiconductor compounds such as AlGaN, GaN, InGaN, ZnO, etc. Those compounds have important applications to display and lighting. Normally, the pump-probe studies for wide-bandgap semiconductors require the second-harmonic generation (SHG) of an fs Ti:sapphire laser for excitation. Although degenerate studies have been widely reported [7,8], non-degenerate research is still quite rare [9].
In this research, we propose a new technique for non-degenerate pump-probe experiments in the UV-visible range based on simultaneously multi-wavelength SHG of a mode-locked Ti:sapphire laser. We demonstrate the implementation with a 10 fs, 800-nm, 76 MHz, mirror-dispersion-controlled mode-locked Ti:sapphire laser (Femtosource, Austria), which provides 110 nm in spectral full-width at half-maximum (FWHM). With two β-barium borate (BBO) crystals of different phase match angles placed in the pump- and probe-beam paths, we can obtain two synchronized fs pulses of adjustable wavelengths. We use an InGaN thin film as the sample for demonstrating this technique. The results show reasonably good signal-to-noise ratios and provide us with new insights of the carrier dynamics in the InGaN sample. In Section 2 of this paper, the results of the multi-wavelength SHG are presented. The non-degenerate pump-probe experimental procedures are reported in Section 3. Sample description and the properties of its nano-structure are given in Section 4. The pump-probe experimental results are discussed in Section 5. Finally, conclusions are drawn in Section 6.
2. Multi-wavelength second-harmonic generation
Figure 1 shows the two sets of second-harmonic spectra from the two BBO crystals of different acceptance angles. The SHG was pumped with the fs laser of 400 mW in average power, directly from the laser system (with the output spectrum shown in the insert of Fig. 1). Because the SHG results depend on the conditions of the fundamental input, the spectra in Fig. 1 do not correspond to the pulses directly applied to the sample in the pump-probe experiment. The length of the BBO crystal for the short-wavelength range is 0.53 mm. Its cut angles are θ=29.940 and φ=00. The length of the BBO crystal for the long-wavelength range is 0.75 mm. Its cut angles are θ=27.800 and φ=00. Fig. 2 shows the second-harmonic spectral FWHM and the SHG conversion efficiency (the SHG power divided by the incident fundamental power) as functions of the SHG wavelength. The relatively lower conversion efficiency, when compared with previously reported [10], is due to the broad spectrum of the used laser. Only a small portion of spectrum satisfies the phase-matching condition for effective SHG. The results in Fig. 2 were obtained by rotating the used BBO crystal for each spectral band. The SHG efficiency generally decreases when the crystal orientation moves away from its exact phase-matching condition. Regarding the SHG spectral FWHM, the two spectral bands seem to have different wavelength dependencies. Near the phase-matching conditions, the maximum FWHM in the short-wavelength band and the generally minimum FWHM in the long-wavelength band can be attributed to several mechanisms including the wavelengthdependence of crystal birefringence, the difference in crystal length, the spectral shape and chirp of the fundamental pulse, etc.
Fig. 1. Two sets of second-harmonic spectra with the two BBO crystals pumped by the laser of 400 mW in average power. The inset shows the fundamental spectrum.
Fig. 2. SHG spectral FWHM and conversion efficiency as functions of SHG wavelength in the two spectral bands.
3. Non-degenerate pump-probe experiment
The non-degenerate pump-probe experimental setup is shown in Fig. 3. Here, the Ti:sapphire laser is split into two beams with a broadband beam-splitter (BS, 20/80 split ratio for reflection/transmission), one for pump and the other for probe. The laser in each beam passes through a BBO crystal of a certain rotation angle for the desired second-harmonic wavelength. The polarization of the pump beam was rotated by 90 degrees with a half-wave (λ/2) plate such that the pump and probe could be easily differentiated after they passed the sample with a polarizer. The pump-probe delay was controlled by a translation stage of 10 µm in step size. This step size corresponds to the time delay resolution of 66 fs. The temporal resolution of the pump-probe experiment is determined by the larger one of the delay resolution and the used pulse width. The two second-harmonic beams were applied to the sample, which was placed in a cryostat. The second-harmonic power ranges from 0.1 to 4.5 mW. The powers of the probe beam can be adjusted for reasonable pump-probe experiments by using a variable neutral density (ND) filter in the probe-beam path. The pump beam was defocused onto a spot with a diameter of 120 µm, which was about three times the probe beam size to ensure the uniform pump illumination of the probe region. The chopper used for lock-in amplification was placed in the pump-beam path.
Figure 4 shows several spectra measured at the sample location from either the pump or the probe branch. The spectral FWHM ranges from 7.2 to 10.4 nm. The corresponding pulses are directly applied to the sample. Figure 5 shows the cross-correlation traces between a pump pulse centered at 390 nm and probe pulses at three wavelengths, i.e., 390, 400, and 410 nm for parts (a), (b), and (c), respectively. Here, the data points (empty circles) are fitted with sech2 functions to show their FWHMs at 220, 224, and 236 fs, which correspond to the pulse FWHMs of 142, 144, and 152 fs after the de-convolution process. Here, we have measured the ultra-short pulse width in the UV-violet range through the cross-correlation measurement with a reverse-biased AlGaN multiple quantum-well light-emitting diode (LED) at 280 nm. The LED was used as the photo-detector of two-photon absorption [11]. The cross-correlation measurements in the wavelength range between 380 and 420 nm showed that the pulse FWHM always fell into the range between 140 and 160 fs. Therefore, 160 fs is the temporal resolution of the pump-probe experiment.
4. Basic material nano-structure and optical properties of the sample
The InGaN thin film sample was grown on c-plane sapphire with meta-organic chemical vapor-phase deposition. After the 800-nm GaN buffer layer, an 800-nm InGaN thin film with silicon doping of 5×1018 cm-3 in concentration was grown at 800 °C. The average indium content was estimated to be 20%. Indium-rich clusters of a few nm in size and extended composition fluctuations were observed in the sample with high-resolution transmission electron microscopy (HRTEM). A typical HRTEM image is shown in Fig. 6. The dark regions in the HRTEM image represent the indium-rich distributions. Here, at least three clusters can be identified (Fig. 6). A threading dislocation across the image can also be seen. The HRTEM investigations were performed using a Philips Tecnai F30 field-emission electron microscope with an accelerating voltage of 300 kV and a probe forming lens of Cs=1.2 mm. Our pump-probe study on the sample aims at the understanding of carrier dynamics in such a structure of nano-clusters and potential fluctuations [12].
Fig. 5. Cross-correlation traces of the probe pulses at 390 (a), 400 (b), and 410 (c) nm with the pump pulse at 390 nm measured at the sample location.
Figure 7 shows the photoluminescence (PL) spectra at various temperatures of the sample. The PL spectra were obtained with the excitation of a HeCd laser of 325 nm in wavelength. Two peaks can be clearly seen when the temperature is lower than 200 K. The inset shows the PL spectral peak positions as functions of temperature for the two peaks. The high-energy peak position red shifts with increasing temperature and tends to merge into the low-energy peak as temperature approaches to the room condition. The low-energy peak position shows an S-shape variation with temperature. Such a variation has been regarded as one of the optical features of the indium-rich clusters in InGaN compounds [13]. The low-energy peak corresponds to the localized states. The high-energy peak is attributed to the activities of the free-carrier states, corresponding to the background InGaN compound, on which clusters are distributed. The background InGaN compound also consists of potential fluctuations of shallower distributions. The merge of the two PL peaks above 200 K is attributed to carrier liquidation among the localized states and free-carrier states. The decreasing trend of the high-energy peak energy is mainly due to the band gap shrinkage that is caused by stronger lattice vibration at higher temperatures. The concerned photon energy range in our pump-probe experiment is close to the high-energy peak of PL spectrum. In other words, we are interested in the carrier dynamics at the energy levels around the free-carrier states.
5. Non-degenerate pump-probe experimental results and discussions
Figure 8 shows the differential transmission traces, ΔT/T, of the non-degenerate pump-probe experiment at 300 K with various probe wavelengths when the pump wavelength is fixed at 390 nm. The pump power is fixed at 4.5 mW and the probe power is controlled to around 0.45 mW. In Fig. 8, the second curve from the bottom corresponds to the case of degenerate pump-probe experiment. It is almost identical to that obtained from another setup of degenerate measurement [12], confirming the reliability of our non-degenerate system. In this degenerate curve, the pump/probe photon energy corresponds to the level of low space-averaged density of state [12]. In this situation, two-photon absorption and free-carrier absorption dominate the process of carrier dynamics. Hence, an abrupt dip and then an increase of probe intensity in the time range of around 10 ps can be observed. The bottom curve corresponds to the case that the probe central wavelength (380 nm) is shorter than that of the pump. Because the pump and probe spectra partially overlap (see Fig. 4), the quick rise within 1 ps in this curve can be attributed to the band filling effect through the process of local carrier-carrier scattering-induced thermalization. Then, the second-stage rise in the duration of 2~4 ps originates from the contribution of the enhanced carrier-distribution tail at the (higher) probe level during a global carrier thermalization process for approaching a quasi-equilibrium condition. Such a process requires certain thermal energy for carriers to overcome the barriers between the potential minima in composition fluctuations. After this process (when the peak is reached), carrier relaxation leads to the reduction of carrier density at the probe level such that a decrease can be observed in differential transmission in a time range of about 2 ps. Then, carrier recombination and other possible relaxation processes result in the slow decay after 6 ps of the pump-probe delay.
As the probe wavelength increases to 400 nm, a fast increase of probe intensity in 1 ps and then a decay of several ps in decay time constant are observed [14]. The quick rise behavior can be interpreted as the fast relaxation of carriers from the pump level to the probe level through the aforementioned scattering-induced local thermalization for reaching a quasi-equilibrium condition. In the decay range, the fast decay is due to the relaxation of carriers into even lower levels in the process of global thermalization. The slower decay is attributed to carrier recombination and other relaxation processes. When the probe central wavelength is 410 nm, after the quick rise, the probe intensity decreases first and then increases. The increasing trend after 12 ps in pump-probe delay results from carrier supply during carrier relaxation from the pump level into the lower probe level (mainly through carrier transport in this stage). As the probe level becomes even lower (with the central wavelength at 420 nm), after the fast increase within the 1 ps range, the differential transmission keeps increasing with a shallow slope. Such a slow increase can be due to the aforementioned carrier relaxation after the first-step scattering-induced local thermalization is completed.
Fig. 8. Differential transmission traces of the pump-probe experiment with different probe wavelengths, as labeled next to the curves, when the pump wavelength is fixed at 390 nm.
The ultrafast carrier dynamics described above can be summarized as follows. Because of the structure of potential fluctuations in the sample, two-step carrier thermalization can be identified including the local carrier thermalization within 1 ps and the global carrier thermalization within several ps. In the local process, the carrier flow is mainly in the spectral domain. However, carrier transport dominates the global process, in which certain thermal energy is required for carriers to overcome the potential barriers between potential minima. Because the spectral range of the current experiment corresponds to the free-carrier states, which consists of mild potential fluctuations, the required thermal energy should be quite small. Hence, the required period for such a relaxation process is in the range of only several ps. A similar two-step carrier thermalization process was also observed around the localized states in an InGaN/GaN quantum-well sample [14]. In this case, the local thermalization process is completed within 1 ps, which is the same as the current case of free-carrier states. However, the time constant for global thermalization is much longer in the case of localized states (around 100 ps). This difference can be attributed to the deep trapping of carriers in the localized states. Much more thermal energy is needed to overcome the barrier between two clusters.
6. Conclusions
We have demonstrated a new technique for non-degenerate fs pump-probe experiment in the UV-visible range. The technique was based on simultaneously multi-wavelength SHG of an ultra-short Ti:sapphire laser. With two BBO crystals of different phase-matching angles, the pump and probe wavelengths could be adjusted. The non-degenerate pump-probe system was applied to the ultrafast carrier dynamics study of an InGaN thin film, in which potential fluctuations have been identified. The observed pump-probe behaviors revealed the processes of carrier thermalization and relaxation in the sample. In our setup, the used laser can provide about 110 nm in spectral width. If SHG is efficient, a tuning range of at least 60 nm can be used for non-degenerate pump-probe experiment. With a Ti:sapphire laser of even shorter pulses [15], the tunable spectral range can be even broader.
Acknowledgments
This research was supported by National Science Council, The Republic of China, under the grant of NSC 93-2210-M-002-006 and NSC 94-2215-E-002-015, and by US Air Force under the contracts AOARD-04-4026 and AOARD-05-4085.
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