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By using high-excitation photoluminescence spectroscopy, we explored the emissions due to inelastic exciton-exciton scattering in ZnO nanocrystalline films at low temperature. It was found that the threshold excitation intensity for occurrence of inelastic exciton-exciton scattering dramatically increases as the crystalline size increases. The radiative efficiency of the inelastic exciton-exciton scattering also decreases rapidly as the crystalline size increases from 120 nm to 170 nm and eventually, no emission due to inelastic exciton-exciton scattering can be detected for crystalline size of 220 nm even at low-temperature. We believe that the spatial confinement effect is the most determinative factor influencing the efficiency of inelastic exciton-exciton scattering.
© 2014 Optical Society of America
1. Introduction
The excitonic optical properties of wide-gap semiconductors have been studied intensively from the viewpoints of both their basic physics and their device applications. The contribution of the excitonic processes to the optical transitions in real device structures is believed to improve the performance of semiconductor optoelectronic devices. Under intense excitation conditions, it is well established that the interaction between two excitons leads to the formation of biexcitons and inelastic scattering between the excitons [1–3]. So far, many literature articles have claimed that the inelastic exciton-exciton (X-X) scattering is a key process leading to stimulated emission in ZnO thin films [4–8] and nanostructures [9–11], owing to its relatively large exciton binding energy [1]. Nevertheless, room-temperature (RT) excitonic lasing is highly questionable since the substantial damping of exciton resonance and screening of exciton binding is unavoidable at high temperature (T). Klingshirn et al. [2] pointed out the identification of high-density excitonic processes at RT requires cautious investigation, and proposed alternative processes, such as exciton-phonon and exciton-electron interaction for the mechanism of stimulated emission in ZnO. In most recent years, instead of X-X collision, RT stimulated emission due to electron-hole plasma (EHP) in ZnO has been reported [12–14]. Even at low-T, Nakamura et al. [12] found that the lasing from ZnO nanopowders is due to EHP. However, there should be some conditions affecting the efficiency of X-X interaction (inelastic scattering of excitons or biexciton) in various ZnO nanostructures, which is not yet fully investigated. Furthermore, regardless of the measured T, the threshold excitation intensity (ITH) for occurrence of X-X interactions spans from hundreds of W/cm2 to the order of MW/cm2 in ZnO [1–11, 15–17]. Some factors that may determine the efficiency of X-X interactions or threshold for stimulated emission in ZnO have been proposed [2–11], but the determinative factor still remains unexplored.
In this letter, we report the photoluminescence (PL) of highly excited ZnO nanocrystalline films. At an extremely low ITH (80 W/cm2), a nonlinear emission band caused by the radiative recombination of inelastic X-X scattering was found in ZnO nanocrystals with crystalline size of 120 nm at low-T (15 K). We also note that the radiative efficiency of inelastic X-X scattering continuously decreases as the crystalline size increases.
2. Experimental
Four ZnO nanocrystalline films were grown on a c-sapphire substrate by sol-gel route. Details of the growth procedure have been described elsewhere [18]. The morphological structure of the samples has been examined by scanning electron microscopy. Powder-like ZnO nanocrystals spreading on the substrate were observed [18]. By tuning the pre-heating temperature at the early drying stage, we obtained nanocrystalline powders with various grain sizes. The average diameters (d) of the nanocrystals are 120 nm, 140 nm, 170 nm and 220 nm (with a size-distribution of about ± 20 nm), respectively. The mean values are calculated from more than 100 nanoparticles. The optically pumped emission from the samples was dispersed in a 32-cm-long monochromator with a 1200 lines/mm grating and detected by an electrically cooled charge-coupled device camera. The excitation intensity (IEXC) dependence of the PL spectra was measured using the 266-nm line of a neodymium-doped yttrium aluminum garnet (Nd:YAG) laser. The pulsed laser has a pulse width of 10 ns and a repetition rate of 20 Hz. All of the PL measurements in this research were performed at low-T (15 K) by using a closed-cycle cryostat system.
3. Results
Figures 1(a)-1(c) show the IEXC-dependence of the PL spectra from three typical samples with d = 120, 170 and 220 nm, respectively. All of the spectra were normalized with reference to the peak intensities of the corresponding donor-bound exciton emission lines. The peak-excitation-intensity values for each spectrum are shown beside the spectra. In Fig. 1(a), we observed two emission bands at the lowest pumping intensity (69 W/cm2). The PL-line with peak energy 3.361 eV is due to the radiative recombination of neutral donor-bound excitons (DoX) [1]. A rather broad emission band around 3.315 eV has been identified as the overlapped emission components consisted of donor-acceptor pairs and free-to-bound transition [18]. As IEXC increases to 97 W/cm2, radiative recombination of free excitons (FX), with transition energy of 3.377 eV, results in a high-energy shoulder besides DoX-emission. However, a more obvious and abrupt increase in PL intensity is seen at 3.318 eV (denoted as solid circles in Fig. 1 (a)). Owing to its superlinearly growing intensity against the excitation intensity (as shown in Fig. 2), we assign this band to the inelastic X-X scattering, by further consideration on its spectral difference (60 meV) with FX energy [2, 5–7]. A consistent increase in IEXC leads to enhancement of X-X emission intensity with no spectral shift. However, at IEXC = 13.5 kW/cm2, emission from a degenerate electron-hole plasma (EHP) located around 3.34 eV, starts to broaden the emission linewidth and shifts to lower energy due to increasing band-gap renormalization [2]. To evaluate the exciton density (nEXC) under IEXC = 13.5 kW/cm2, we use the following formula [2], assuming that every absorbed photon creates one electron hole pair
where IEXC and hνEXC are the pump intensity and the excited photon energy, respectively. The characteristic time τ is the lifetime of the excited electron-hole pairs (about 100 ps) [19]. Since the d of our nanocrystals is larger than the penetration depth ~50 nm [2] of the pumped light, and comparable to diffusion length of the exciton ~200 nm [20, 21] at low-T, we took d as the characteristic length l. The calculated nEXC at IEXC = 13.5 kW/cm2 are approximately 1.5 X 1017 cm−3, 1.3 X 1017 cm−3, 1.1 X 1017 cm−3, and 0.8 X 1017 cm−3 for the samples with d = 120 nm, 140 nm, 170 nm, and 220 nm, respectively. These exciton densities coincide well with the theoretical Mott density of excitons (~1017 cm−3) in ZnO at low-T [13, 22]. Beyond this Mott density, screening of Coulomb interaction causes the excitons to lose their individual characteristics, and an EHP eventually results.
Fig. 1 Excitation power dependence of PL spectra of ZnO nanocrystalline films with size of (a) d = 120 nm, (b) d = 170 nm, and (c) d = 220 nm, taken at T = 15 K. The excitation intensities are shown at the left-hand side of the figures. Solid circles represent the emission peaks of inelastic exciton-exciton scattering.
Fig. 2 Evolution of IXX (open circles) and IXX/ IDX (dashed lines) of ZnO nanocrystals with size of (a) d = 120 nm, (b) d = 140 nm, and (c) d = 170 nm, as a function of IEXC. The solid lines are the fitting curves of power-law. The dashed lines are just guides for eyes.
Optically pumping the nanocrystalline film with d = 170 nm, we observed a similar change in PL spectra as IEXC increases, as shown in Fig. 1(b). However, we found two significant dissimilarities, as comparing with the nanocrystalline film with d = 120 nm. The ITH for the appearance of X-X emission is substantially raised up to IEXC = 700 W/cm2. Furthermore, even though superlinear growth of X-X emission intensity was detectable with increasing IEXC, the peak intensity of X-X emission does not take over that of DoX emission at IEXC = 13.5 kW/cm2. In other words, the X-X interaction is less efficient in the sample with d = 170 nm. This situation is more severe in the sample with d = 220 nm, as shown in Fig. 1(c). From 623 W/cm2 to 13.5 kW/cm2, emission due to X-X transitions is absent. After the Mott density of exciton is reached at IEXC = 13.5 kW/cm2, emission due to EHP grows rapidly and eventually dominates the PL spectra at IEXC = 94.2 kW/cm2.
To quantify these findings from our measurement, we plotted the peak intensity of the X-X line and the intensity ratio of X-X emission (IXX) to DoX emission (IDX), against the excitation intensity in Fig. 2. The Figs. 2(a)-2(c) correspond to the data of the nanocrystals with d = 120, 140 and 170 nm, respectively. In the upper part of Fig. 2(a), we fitted the evolution of the peak intensity of X-X line as a function of IEXC by a power-law relation. The fitting gives a power coefficient 1.9 (IXXIEXC1.9) for the sample with d = 120 nm, indicating that the IXX has a nearly quadratic dependence on IEXC. Since the X-X emission overlaps with the emissions due to donor-acceptor pairs and free-to-bound transitions around 3.315 eV, we use the evolution of intensity ratio IXX/IDX as a function of IEXC to determine the threshold excitation intensity ITH, as shown in the lower part of Fig. 2(a). After the appearance of X-X emission, one could expect an abrupt change of IXX/IDX. The ITH determined by this method is approximated 80 W/cm2 for the sample with d = 120 nm. Using the same procedure described above, we also determined the power coefficient and the ITH of the samples with d = 140 and 170 nm. The power coefficient of the power-law relation gradually decreases from 1.9 to 1.6 as d increases from 120 to 170 nm. Also, ITH is a monotonically increasing function of crystal-size d. That is approximately 80, 160, 700 W/cm2 for the samples with d = 120, 140 and 170 nm, respectively. Note that there is no data for the sample with largest d because no X-X emission was detected. We summarized the evolution of power coefficient and ITH as a function of d in Fig. 3(a) and 3(c), respectively. In Fig. 3(b), the intensity ratio IXX/IDX at IEXC = 13.5 kW/cm2, is also plotted for comparison. Although the physical meaning of these results is different, they all point to the fact that the excitons are hardly interacting with each others as d increases. We will discuss this result in various aspects along with ITH of stimulated emission and X-X interaction reported in ZnO.
Fig. 3 Evolution of (a) Power coefficient obtained from power-law fitting (open circles), (b) IXX/ IDX at IEXC = 13.5 kW/cm2 (solid squares), (c) Threshold excitation intensity ITH (solid circles), (d) PL intensity ratio ID/ IDX (open squares), deducing from Ref. 18, as a function of crystalline diameter d. The solid lines are just guides for eyes.
4. Discussion
The calculated nEXC generated at the ITH, are 0.9 X 1015 cm−3, 1.5 X 1015 cm−3, 5.5 X 1015 cm−3 for samples with d = 120 nm, 140 nm, 170 nm, respectively. These are the exciton densities created by pumped photons in light-penetration-region, and required for observation of PL due to X-X collision. After the excitation, excitons may diffuse and trap by nonradiative centers. In fact, a thorough review of the literature reveals that the ITH and the occurrence of the nonlinear excitonic emission of ZnO nanostructures and thin films depends on many factors including crystalline size or film-thickness [3, 5–8, 23], excitation condition [14, 24, 25], and sample quality [4, 15–17]. We exclude the excitation condition in our discussion because we used a nanosecond pulsed laser to create excitons by one-photon excitation. Sample quality is an indicator of numbers of nonradiative centers in the sample. It is believed that excitons trapped by defects inhibit the efficiency of X-X interactions. In the previous study, we have measured the defect-emission due to oxygen vacancies and interstitials from the samples [18]. The ratio of defect-emission-intensity (ID) to IDX is plotted in Fig. 3(d). It is not a monotonic function of d, indicating that the bulk nonradiative trap is not the determinative factor. Moreover, it is believed that surface-state defects of nanocrystals could generate nonradiative recombination pathways hampering the X-X interaction [23, 25, 26]. However, this should be more effective in the sample with smaller d with higher surface-to-volume value. Therefore, we conclude that neither bulk- or surface-defects can be the essential factor for the above results.
The effect of crystalline size or film-thickness has been proposed under two points of view: exciton diffusion [8] and giant exciton oscillator strength [5–7]. The presence of domain boundaries leads to the suppression of exciton motion in nanocrystals, thus, enhancing the opportunity for excitons to interact with each other. Considering the exciton diffusion length of ZnO ~200 nm [20, 21], exciton diffusion is possibly hindered in the sample with smaller d, resulting in a smaller ITH to achieve the circumstances for X-X scattering. This could contribute to the enhancement of ITH for larger d. However, this could not explain why the intensity ratio IXX/IDX at IEXC = 13.5 kW/cm2 (see Fig. 3 (b)) decreases abruptly as d increases, unless the excitons trapped by nonradiative centers during the diffusion. The diffusive loss of excitons is determined by the densities of nonradiative trap in the nanocrystals, which is not a monotonically increasing function of d in our case. The reduction of power coefficient is believed to be attributable to excitonic loss [16], which is also hardly explained by inhibition of exciton diffusion only. Therefore, we believed that the exciton diffusion effect could partly contribute to the above reduction of efficiency of X-X scattering as d increases. Giant exciton-photon coupling has been proposed as a possible reason for the size-dependence of ITH for stimulated emission due to X-X scattering in ZnO [5–7]. As the crystalline size is larger than exciton Bohr radius (1.8 nm in ZnO) [1] but smaller than the exciton coherence length, a coherence-induced enhancement of exciton oscillator strength is expected [27, 28]. However, there is a limitation for consistently increasing exciton oscillator strength with coherence size, due to the homogeneous broadening of the exciton resonance and the population of lowest excitonic levels at nonzero temperature [29–32]. The crystallize size achieving maximum radiative decay rate has been estimated to be about 60 nm in ZnO [30–32]. A reduction of excitonic decay rate was also reported in ZnO nanostructures with increasing crystalline size larger than 60 nm [33]. Therefore, we believed that the exciton oscillator strength in our sample decreases substantially as d increases from 120 nm to 220 nm. This could result in inefficiency of X-X scattering in the sample with larger d. Since the exciton oscillator strength is an intrinsic property directly affecting the X-X interaction, the efficiency of X-X scattering can be explained without considering the exciton annihilation due to the nonradiative center. Therefore, we tentatively regard the coherence-enhanced size effect as another unignorable factor influencing the efficiency of X-X scattering in our sample.
Suzuki et al. [23] demonstrated that nonradiative Auger recombination plays an important role in RT stimulated emission in ZnO nanoparticles with small size (10 nm ~30 nm). X-X interaction is not significant at such a small size. Zu et al. [6] investigated the stimulated emission of ZnO thin films at RT and claimed that the inelastic X-X scattering is only efficient around d~55 nm. For nanoparticles with size about 200 nm, Nakamura et al. [13] reported the absence of inelastic X-X scattering from low-T to RT. With aid of conclusion of the above works, we believe that the most appropriate size of ZnO nanoparticle for inelastic X-X scattering lies between 50 to 100 nm, because the efficiency of inelastic X-X scattering decreases dramatically from the ZnO nanocrystals with size from about 100 nm to 200 nm, and eventually inelastic X-X scattering diminishes for the ZnO nanoparticles with largest size, even at low-T. Therefore, to realize the stimulated emission due to inelastic X-X scattering in ZnO-based light-emitting media, one has to fully take advantage of spatial confinement effects, i.e, at least smaller than 200 nm.
5. Conclusion
By investigating the threshold for occurrence of inelastic exciton-exciton scattering processes, we demonstrated the significance of spatial confinement effects on efficiency of the inelastic exciton-exciton scattering process in ZnO nanocrystalline films with crystalline diameter from 120~220 nm. Not only has threshold excitation density increased, the radiative efficiency from inelastic exciton-exciton scattering decreased abruptly as crystalline size increases.
Acknowledgment
This research was supported by the National Science Council of Taiwan under Grant No. NSC-99-2112-M-390-001-MY3 and NSC-102-2112-M-390-002-MY3.
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