Disentangling the evolution of electrons and holes in photoexcited ZnO nanoparticles

The evolution of charge carriers in photoexcited room temperature ZnO nanoparticles in solution is investigated using ultrafast ultraviolet photoluminescence spectroscopy, ultrafast Zn K-edge absorption spectroscopy, and ab initio molecular dynamics (MD) simulations. The photoluminescence is excited at 4.66 eV, well above the band edge, and shows that electron cooling in the conduction band and exciton formation occur in <500 fs, in excellent agreement with theoretical predictions. The x-ray absorption measurements, obtained upon excitation close to the band edge at 3.49 eV, are sensitive to the migration and trapping of holes. They reveal that the 2 ps transient largely reproduces the previously reported transient obtained at 100 ps time delay in synchrotron studies. In addition, the x-ray absorption signal is found to rise in ∼1.4 ps, which we attribute to the diffusion of holes through the lattice prior to their trapping at singly charged oxygen vacancies. Indeed, the MD simulations show that impulsive trapping of holes induces an ultrafast expansion of the cage of Zn atoms in <200 fs, followed by an oscillatory response at a frequency of ∼100 cm−1, which corresponds to a phonon mode of the system involving the Zn sub-lattice.


I. Introduction :
Transition metal oxides (TMO), such as Titanium dioxide (TiO2) and Zinc oxide (ZnO), are large-gap (>3.2 eV) semiconductors that have been attracting considerable interest in the past three decades or so, due to their remarkable optical properties, robustness under ambient conditions, abundance, and ease of preparation. [1,2] This makes them potential candidates for photovoltaic and photocatalytic applications, [3][4][5][6][7] detectors for high energy radiation, [8] transparent conductive oxides, [9] lasing, [10] pressure sensors with optical read-out, [11,12] etc. Their large band-gaps also offer the advantages of higher breakdown voltages, the ability to sustain large electric fields, lower noise generation, and high temperature and high-power operation.
These current and potential applications rely on the generation of charges and their subsequent evolution via electron-electron and electron-phonon scattering, diffusion through the lattice, thermalization and eventually, localization either as self-trapped excitons (intrinsic trapping by electron-phonon coupling) or at defects (extrinsic trapping), followed by radiative and/or non-radiative electron-hole recombination. The initial events following photoexcitation take place at ultrashort time scales and need to be described in detail in order to reach optimal performances of the material for a specific application. This requires tools that can probe the evolution of charge carriers in real-time, are specific to both the valence (holes) and conduction (electrons) bands and are, ideally, element-selective.
In the past 25 years or so, a large variety of ultrafast optical methods have been used to monitor the charge carrier dynamics in TMO's. In these experiments a non-equilibrium distribution of electrons and holes is created upon above band-gap excitation and the ultrafast (femtoseconds to picoseconds) evolution of charge carriers is monitored using different probes from the Terahertz (THz) to the ultraviolet (UV) and visible spectral range. [13][14][15][16][17][18][19][20][21][22] These probes are generally tuned to the intra-band transitions and therefore monitor the free carrier response, which does not always distinguish between the electron and hole responses, nor does it provide an unambiguous identification of trapping. Deep-UV probing of the interband transitions has also been implemented, as it can in principle distinguish between the dynamics occurring in the valence band (VB) and the conduction band (CB). [22][23][24][25][26][27] However, the TA signal in this case is sensitive to the joint density-of-states (DOS) of the two bands, and therefore, when the evolution of free carriers is on comparable timescales, they are also difficult to disentangle. Furthermore, charge carrier localization at defect states cannot be unambiguously determined. To solve the latter, ultrafast sum-frequency generation with a white light continuum resonant with the in-gap defect states was implemented, [28] reporting sub-picosecond cooling times of the electron in the CB.
Photoluminescence (PL) is sensitive to the DOS in the CB. In the ultrashort time domain, it can selectively detect the cooling of electrons down to the bottom of the band, as well as formation of free excitons. [27,29] However, to our knowledge, nearly all time-resolved PL studies of TMOs have focussed on the electron-hole recombination (see table S1 of ref. [30] and ref. [28]), which is on the tens of ps to ns time scales. This is, in particular, the case for the system of interest here, Zinc oxide (ZnO). In this work, we implemented ultrafast PL upconversion spectroscopy in the UV in order to monitor the relaxation of electrons in the CB via the rise of the excitonic emission close to the band-gap (BG).
We complement the ultrafast PL study by ultrafast hard X-ray absorption spectroscopy (XAS). Over the past decade, time-resolved soft and hard XAS has increasingly been used to investigate the fate of charge carriers in photoexcited TMOs and perovskite nanoparticles (NPs) in colloidal solutions. [30][31][32][33][34][35][36][37] In TMOs, the oxygen 2p-orbitals dominate the VB, while the metal 3d-orbitals dominate the CB. [38] Therefore, the element-specificity of XAS implies to a certain extent, an electronic band selectivity, as was nicely illustrated in ref. [37]. In the case of TiO2, [31][32][33][34]37] the ps and fs hard XAS studies showed signals that were predominantly due to changes of the Ti oxidation state from 4+ to 3+ and are therefore mostly sensitive to electron trapping. Ultrafast soft XAS at the O K-edge and the Ti L2,3-edges could simultaneously monitor both the hole and the electron trapping in photoexcited anatase TiO2 nanoparticles and single crystals. [37] ZnO is a direct band-gap (3.4 eV) semiconductor that has a bulk exciton binding energy of 60 meV at room temperature, native n-type doping and high conductivity, [1] conferring to this material a high potential for optoelectronic applications in the visible and UV photon energy range. The band structure of ZnO exhibits a splitting of the top-most VB into three subbands usually termed as A, B, and C, due to a combination of crystal field and spin-orbit coupling. [39,40] Transitions between these bands and the CB dominate the optical absorption spectrum ( Figure S1) at different polarizations. However, the band edge absorption stems from the vicinity of the VB maximum. [41,42] Different to TiO2 where the electronic configuration of the metal atoms is d 0 , in ZnO it is d 10 and therefore, the metal atom cannot be reduced. Nevertheless, in a recent study of ZnO NPs photoexcited at 355 nm using time-resolved Zn K-edge XAS and X-ray emission spectroscopy (XES) with 80 ps resolution, [30] dramatic changes were observed in the X-ray near-edge structure (XANES) spectra and the extended X-ray absorption fine structure (EXAFS) spectra. The time-resolved Zn Kα and Kβ emission lines, which are sensitive to the electronic structure, showed however only weak charge density changes on the Zn atoms. This implied that the XANES and EXAFS spectral changes are largely due to structural effects. These spectral changes were rationalised by noting that ZnO is rich in singly-charged Oxygen vacancies ( + ) [43] and that upon photoexcitation, the free hole charge carriers generated in the VB of the material, migrate and get trapped at the + defects to form doubly-charged oxygen vacancies ( ++ ). Previously, theoretical calculations had shown that upon formation of a doubly-charged oxygen vacancy, [44,45] Figure S1). [1] The fs XANES measurements were carried out at the SACLA X-ray Free Electron Laser (XFEL) in Japan at an excitation energy of 3.49 eV, in order to minimize effects due to energetic electrons. Indeed, this energy is resonant with the blue wing of the first exciton and the red edge of the band gap absorption ( Figure S1). In order to rationalise the Xray results, we performed ab-initio molecular dynamics (MD) simulations of the structural rearrangement around the newly formed doubly-charged . Details of the experimental and theoretical procedures and set-ups are given in the SI.
Our results show that electron cooling in the CB and formation of the exciton occur in <500 fs, in very good agreement with theoretical predictions, [41,42] while the time scale for the hole response of ~1.4 ps is governed by hole diffusion through the lattice and its trapping as the ensuing structural response is prompt according to the MD simulations.

II.1 Femtosecond photoluminescence studies:
The steady-state PL spectrum of ZnO NPs at room temperature (figure S2) consists of a band around 3.37 eV and a broad band centred at ~2.3 eV. [28,47] The former is due to an excitonic electron-hole recombination between the CB and VB, while the latter has been attributed to recombination of CB electrons with hole defects (Oxygen vacancies) that form trap states within the band gap. [28,30,47,48] The time-resolved PL studies of RT ZnO in various forms (crystals, films or nanoparticles) report different e-h recombination times for the excitonic and the green luminescence (Table S1 of ref. [30]), which in addition are sensitive to sample preparation.
[28]  Figure 3 shows the kinetic trace of the PL at the same energy for both long and short (insert) time windows. Figure S6 compares the time trace of the signal at early time with the Instrument response function (IRF), clearly showing that the signal's rise time is significantly longer. In figure 3, the long-time trace exhibits a biexponential behaviour and can be fitted with time constants of ~6.5 ps and ~40 ps ( Table   1). The fit of the short time traces convoluted with the IRF (approximated as a Gaussian) yields a value of ~450 fs for the rise time, independent of the fluence (table S1). Considering that the early time PL appears almost resonant with the steady-state one, this suggests that the rise time of the PL integrates the cooling time of the electrons in the CB, as well as the formation of a relaxed excitonic state that yields the PL. With an excitation of 4.66 eV, i.e. 1.33 eV above the minimum of the CB, we can conclude that the electron cooling to the bottom of the CB occurs at a rate of approximately 3 meV/fs (1330 meV/450 fs). This is in excellent agreement with the predictions by Zhukov et al [41] that cooling of the high excess energy electrons is ultrafast, as they exploit the entire optical phonon phase space for energy dissipation.
The steady-state PL spectrum of ZnO exhibits a rich fine structure with several lines, separated by a few tens of meV's, attributed to different excitonic transitions, [1,28] and it is therefore a composite band. The decay times of ~6 ps and ~40 ps may be due to different transitions therein and /or relaxation processes within the manifold of states giving rise to the PL. [28] In table 1, we compare the times scales of the PL with those found using UV pump/UV continuum probe TA. [48] In the latter case, the pump energy was 295 nm (4.20 eV), close to the present 4.66 eV excitation, and the probe was a continuum spanning the 280-360 nm range. The excitonic band was found to be bleached at t=0 and its recovery timescales are given in table 1. While some of the time scales may bear a correspondence with the PL ones, it is difficult to be affirmative, as the TA is sensitive to the joint DOS of the VB and CB. amplitudes. This implies that the most significant signatures of hole trapping, discussed in ref. [30], are already present 2 ps after photoexcitation. Most of time-resolved XAS studies have focussed on the XANES region as it provides more contrasted signals. [50][51][52][53] However, one of the striking aspects of the ps-XAS study of ZnO [30] is that the amplitude of the transient EXAFS was of comparable amplitude as the transient XANES. shows an opposite trend, which again rules out a heating effect; [49] d) This is furthermore so that for the present X-ray measurements, the excess energy deposited to the system is minimised by the 3.49 eV excitation we used.

II.2 Femtosecond Zn K-edge absorption spectroscopy
The temporal evolution of the signal at 9.67 keV, where the amplitude of the X-ray transient is largest, is shown in Figure 6 for early times, while Figure S7 show the kinetic traces at long and intermediate times. Figure 6 shows that the negative amplitude signal rises from zero and it reaches a plateau by ~5 ps, while the long-time trace ( Figure S7) shows a recovery that could be mono-or biexponential. We could satisfactorily fit the short and long-time traces ps. In the previous XAS study of ZnO NPs with 100 ps resolution, [30] the kinetic trace at the same energy was scanned to longer delay times and it exhibited a biexponential decay with time constants of 200±130 ps and ~1.2±0.3 ns ( Table 1). The former is in the same scale as the recovery component reported here.

II.3 Ab-initio Molecular Dynamics simulations
The main focus of the present XAS measurement is the short component of ~1.  . [56] This shows that the doubly-charged oxygen vacancy has the characteristics of a small hole polaron.
In light of the above XAS and MD results, we discuss below the fate of holes in the system, after analysing the optical ultrafast PL. The time constants extracted from the present ultrafast UV PL and fs-XAS studies are collected in table 1 and are compared to those obtained in the previous ps-XAS [29] and UV probe TA [49] studies.

III. Discussion:
The main focus of the present work are the early times of the evolution of charge carriers prior to the e-h radiative recombination. Regarding these times, a number of (mostly) UVvisible TA studies have been carried out on different types of ZnO: epitaxial thin films, [23] various nanostructures (dots, rods, wires and ribbons), [24,57] ZnO/ZnMgO multiple quantum wells, [25] molecular beam epitaxy films and single crystals. [28] These were generally carried out at RT and for different excitation fluences, and they concluded that the charge carrier relaxation spans timescales from 200 to 1000 fs. Ultrafast 2-photon photoemission studies of single crystals of ZnO excited at 4.19 eV were also carried out, reporting electron cooling times of 20-40 fs, followed by formation of a surface exciton on a time scale of ~200 fs. [58] Considering that these studies used quite similar excitation energies, well above the band gap, the fact that the values of the reported times are so scattered, has to do with the pump fluence, the sample morphology and possibly, the environment. [24,57] Using density functional theory (DFT) calculations, Zhukov and co-workers [41,42] identified two regimes of electron-phonon cooling depending on the electron excess energy with respect to the highest phonon energy. At high electron excess energies, the whole phonon dispersion acts on the electron cooling, whose time scale spans from 100 to 500 fs, while below the cut-off of the highest energy phonon, only phonons with an energy lower than that of the electron excess energy will play a role in the cooling and the energy loss time can span a very large range from sub-100 fs up to 10 ps with a rapid increase below an excess energy of 20 meV due to the reduction of the available phonon phase-space. For the holes, [41,42] the energy loss time at any excess energy was found to be about three times smaller than the electron energy loss time.
In the PL experiment, τr in table 1 corresponds to electron cooling in the conduction band and formation of the exciton, in very good agreement with the above theoretical predictions. [41,42] τ1 and τ2 reflect electron-hole recombination times via the excitonic emission. They are most probably due to decay of one of the many spectral components that make up the excitonic emission, [1,28] or to a relaxation process within this same manifold.
Finally, surely longer time components are present [27,29] but our scans are limited to 100 ps.
The present result of an electron cooling time of ~450 fs is of importance for the description of electron injection times in dye-sensitized ZnO. Indeed, in contrast to dyesensitized TiO2 where electron injection times are extremely short (< 5 fs) [59,60], in ZnO the injection times are much longer, in the order of several tens of ps. [15,[61][62][63] The present results clearly confirm that they are entirely governed by the dye-ZnO interaction and not by the electron cooling within the ZnO substrate. [63] Regarding the fs-XANES data, the ~1.4 ps rise of the signal ( Figure 6) is to be contrasted with the prompt structural response found in the MD simulations ( Figure 7). We conclude from this that the former is mainly determined by the migration of holes, which then localise at singly-charged oxygen vacancies that are expected to be more frequent near the surface of the NP due to a higher density of defects. In order to support this interpretation, we estimated the diffusion time of a hole inside the NP, assuming that it is created at its centre. Finally, it is important to stress that the fs-PL and fs-XAS do not monitor the same type of evolution. The ultrafast PL maps the energy relaxation of the electrons in the CB, while the fs-XAS maps the spatial migration of holes in the VB and their trapping. This may include hole energy relaxation but the X-ray observable is not sensitive to it, since it only reports on structural changes at the 's that trap the hole. In order to map the energy relaxation of holes, which according to Zhukov et al [41,42] is typically three times faster than the electron relaxation, one would need to detect the holes via ultrafast O K-edge XAS, as was recently reported for TiO2. [37] Since the migration time of the holes is the rate determining step that governs their trapping, it is unlikely that phonon coherences similar to those found in the simulations could be generated. Given the predominance of this optical phonon mode, we should expect it in the steady-state PL spectra. However, as the mode is associated to traps one would expect it in the visible (green) part of the spectrum ( Figure S2) since it is associated with hole traps. [30,47,48] However, while the low temperature PL spectrum of ZnO shows rich fine structure of the UV band-gap PL, the green band is featureless. [65] It would be exciting to investigate this phonon mode and its role via impulsive stimulated Raman Spectroscopy.

III. Conclusions
In summary, we presented a combined ultrafast UV photoluminescence and Zn K-edge absorption study of photoexcited ZnO nanoparticles in solution, complemented by ab initio molecular dynamics simulations. Our results shows that electron cooling is ultrafast (<500 fs) and in very good agreement with theoretical predictions. [41,42] The fs X-ray absorption study shows that the signal grows on relatively slow time scales  Table 1: Time constants (all entries are in ps) extracted from the present ultrafast near-UV PL and Zn K-edge XAS experiments and from the previous ps XAS experiment, [30] and ultraviolet transient absorption (TA) spectroscopy. [49] In the PL experiment, τr corresponds to electron cooling in the conduction band, while τ1 and τ2 reflect electron-hole recombination via the excitonic emission. In the fs-XAS experiment, τr corresponds to hole migration, trapping time and the cage relaxation at the newly formed doubly-charged vacancy. The longer times are due to electron-hole recombination via the trap PL in the green that is also reported in the ps-XAS experiment. [30] Longer lifetimes have also been reported in the literature. [28,53] Measurement PL        For the X-ray experiments, the sample was a 170 mM dispersion of 32 nm diameter ZnO nanoparticles in water. It was prepared from a commercially available sample (Sigma-Aldrich 721077) which we have previously characterized in separate publications. [1,2] Under the conditions of the experiment, the optical transmission of the jet was measured to be 33%, corresponding to an absorbance of 0.5.

S.1.2 Fluorescence up-conversion set-up
Time-resolved photoluminescence (PL) spectra of ZnO nanoparticles (NPs) were recorded using a broadband fluorescence up-conversion set-up, described in detail in ref. [3] Briefly, Emission from the sample is collected by a wide-angle parabolic mirror and directed to a second mirror that focuses it onto the 250-μm thick BBO crystal, where it is mixed with the delayed gate beam in a slightly non-collinear geometry to produce an up-converted signal.
The up-converted signal is then spatially filtered and detected with a spectrograph and a CCD (charge-coupled device) camera. To accomplish a broadband detection, the up-conversion crystal is rotated with a constant angular speed during the integration time of the CCD camera in order to phase match a wide spectral region at each fixed time delay. The instrument response function (IRF) of the set-up is well represented by a Gaussian with FWHM~230 fs from the Raman line of H2O excited at 266 nm ( Figure S6). The kinetic trace of ZnO PL recorded using a single-wavelength detection at 3.31 eV is also shown in Figure S6. We verified that the fluence dependence of the PL signal upon 4.66 eV excitation for the range of fluences used here is linear (Figures S2 to S4). Figure S7 shows the time trace of the PL over a longer time window.

S.1.3 Femtosecond X-ray absorption spectroscopy
The experiments were performed at beamline 3 (BL3) of SACLA. [4][5][6][7] SACLA was operated with mean pulse energy of 240 μJ, pulse duration of 20 fs, and operation frequency of 10 Hz during the experiment. Concerning the timing of the laser system, a synchronization system was used with direct detection of an optical pulse train, yielding a time jitter of approximately 300 fs.
The sample was excited using a 355 nm (3.49 eV) pulse having a temporal width of ~40 fs and an energy/pulse of 21 µJ. The laser pulses were focussed to 40 µm FWHM on the sample.
Measurements at lower fluence measurements were also carried out showing no variation and the results reported here concern the above numbers.

S.2. Fit of kinetic traces:
The fit of the kinetic traces was conducted using multiexponential functions composed of a rising component and decay ones, convoluted to the IRF of the experiments, which is 230 fs for the fs optical photoluminescence (fs-PL), and 150 fs for the fs-XANES measurements.
The analytic formula for the rise component is expressed as follow: while that of the decay term is: and are the pre-exponential factors for the rise and decay terms, respectively. is the risetime constant; is the decay time constant; represents the width of IRF, where

S.3. Ab-initio Molecular Dynamics simulations:
All density functional theory (DFT) calculations were performed with the CASTEP Simulation package, [8] with an energy cutoff of 400 eV, 3 k-points along each supercell vector, and using the PBE exchange-correlation functional. [9] The supercell consisted of an optimized ZnO crystal structure with four unit cells in all directions. Once optimized, ab initio molecular dynamics (AIMD) was performed for 2 ps at 300 K. 128 snapshots were taken and an oxygen atom was removed to create a group of starting geometries containing an oxygen vacancy.
Additional AIMD calculations were performed on the structures with an oxygen vacancy and a 2+ charge. We calculated the average distance from the vacancy and the nearest 4 Zn atoms, nearest 12 oxygen atoms, and next-nearest 12 Zn atoms (corresponding to the 1st, 2nd and 3rd coordination shells, respectively), for each time step. Finally, the average displacement for each coordination shell was taken over all systems for each time step. Table S1. Time constants of the emission of ZnO NPs excited with 266 nm, obtained using multiexponential fits of the kinetic traces, extracted from the (t-E) plots at max of the emission (shown in Fig. 1). Rise time components (τr) for different fluence values were determined using multiexponential fits, while τ1 and τ2 were kept fixed to the values determined by fitting the kinetic trace measured at the max fluence (5.4 mJ/cm 2 ). This is the only one for which a long-time scan was recorded.