Time-Domain Observation of Spectral Diffusion in Defective ZnO.

Defects can affect all aspects of materials by altering their electronic structures and mediating the carrier dynamics. However, in the past decades, most research efforts were restricted to nonstoichiometric defects, while the effects of high-density defects on the carrier dynamics of semiconductors remained elusive. In this work, using transient absorption spectroscopy, we have observed for the first time a hybrid carrier relaxation dynamics with the feature of a Poisson-like retard shoulder in a time-domain profile in highly defective ZnO crystals. This novel behavior has been attributed to the spectral diffusion within continuum defect states, which is further confirmed by a proposed diffusion (in energy space) controlled carrier dynamic model. Our results thus reveal an alternative energy decay channel in highly defective crystals and may provide a new route for defect engineering.

Introduction

The properties and technological uses of a semiconductor often depend on the defects it contains. The existence of defects and impurities in semiconductors’ lattices can dramatically influence their electrical and optical properties.[1] Defect engineering, which involves manipulating the defect type, concentration, and distribution within a semiconductor crystal, has become the primary initiative strategy to design and control the functionality and performance of semiconductor devices.[2,3] By introducing specific types and concentrations of defects in semiconductors, one can obtain the desired semiconductor properties, thus significantly extending their applications to devices.[1,4] On the other hand, for pure and structurally perfect semiconductors, defects are usually unavoidably generated during their natural aging and under extreme working conditions, such as outer space and irradiation environments, severely affecting their originally designed functionality and performance.[5] Therefore, understanding defects’ effects has become an inevitable and critical issue for designing, fabricating, and applying semiconductors.

Studying the defect-related carrier dynamics is crucial for gaining the fundamental understanding of how defects affect the semiconductor properties and further optimize the semiconductor devices’ performance through defect engineering.[6−9] In the past decades, numerous works have been carried out to improve our understanding of this critical issue. However, one important yet experimentally unexplored question concerning the role of high-density defects (i.e., defect energy band becomes a continuum instead of discrete) in the carrier dynamics, which may be key to further the versatile defect engineering.[7,10,11] Zinc oxide (ZnO) as a wide band gap (3.37 eV) semiconductor has attracted much attention due to promising ultraviolet optoelectronic device applications.[12−15] Native defects in ZnO have long been believed to play a critical role in its optoelectronic performance due to its ability to tune the carrier dynamics, leading to novel properties such as controllable emission from ultraviolet to the yellow range.[7,16−20] Therefore, in this work, taking ZnO as a representative of highly defective semiconductors, we employ transient absorption (TA) spectroscopy to uncover the high-density defect-mediated carrier dynamics. TA experiments observe a novel Poisson-like delayed shoulder in the time-domain profile. We attribute it to the spectral diffusion within continuum defect states, which is further confirmed by a proposed diffusion (in energy space)-controlled carrier dynamic model. Our results thus reveal an alternative energy decay channel in highly defective crystals.

Results and Discussion

Figure b shows the fine-scan absorption spectrum of the sample which exhibits a clear absorption edge at ∼375 nm (3.31 eV) due to the band edge free exciton absorption. Besides, an obvious and broad below-band-gap absorption tail in the range of 400–650 nm was observed, indicating the existence of quasi-continuum broad defect states in the band gap.[10,11,19,21−24] By subtracting the exponentially decaying baseline, which corresponds to the quasi-continuum defect states, three discrete peaks located at 2.95 (420 nm), 2.58 (480 nm), and 2.21 eV (560 nm) are visible, as shown in Figure c, signifying the coexistence of three denser discrete defect bands and continuum defect states in this highly defective ZnO crystal. It should be noted that these sub-band-gap defect absorption bands observed in Figure c are not general features for defective ZnO because different preparation methods, storage environments, and even the degree of aging might cause the diversification of defect types and concentrations, leading to different defect absorption features. However, the broad defect absorption and emission (visible range, especially green for ZnO) phenomenon are not specific but widely found in ZnO crystals which are believed to originate from the crystalline imperfection of intrinsic defects such as oxygen vacancies (VO),[25] Zn vacancies (VZn),[26] Zn interstitials (Zni),[27] O antisites (OZn),[28] and their complexes.[29,30]

Figure 1

(a) Schematic diagram of the TA spectroscopy setup. BS-beam splitter, BBO-BaB2O4 crystal, F-notch filter, M-mirror, and L-lens. (b) Fine-scan UV–vis absorption spectrum of ZnO (0001). (c) Zoomed-in view of absorption in the wavelength range from 400 to 650 nm before and after subtracting the baseline.

Figure a shows a typical transient transmission spectrum ΔTλ(t)/Tλ(0) at the excitation fluence of 6.0 mJ/cm2, in which there exists two distinct regions across the SC wavelength range. The first one, zoom-in shown in Figure b, in the wavelength range from 410 to 422 nm, exhibits an enhanced transmitted intensity compared to the equilibrium transmission right after pumping, which is opposite to the second, in the wavelength range from 423 to 725 nm, in which the transmission is reduced.

Figure 2

(a) Transient transmission spectra in the wavelength range from 400 to 750 nm. (b) Zoomed-in view spectra in the wavelength range of 410–422 nm, as indicated by a dashed box in (a). Transient transmission trace at the probe wavelengths of 416 nm (c) and 540 nm (d). Insets of (c,d) show schematic diagrams to describe the carrier dynamics.

Typical normalized transient transmission evolutions at specific wavelengths (416 and 540 nm) in these two regions are demonstrated in Figure c,d, respectively. In Figure c, ΔTλ(t)/Tλ(0) increases after pumping immediately to a maximum and then quickly (<300 fs) falls to a negative value. In principle, the pump-induced transparency effect can be associated with the reduction of optical resonances due to pump-induced bleaching (PIB), schematically shown in the inset of Figure c.[7] In this work, after 400 nm pumping, photoexcited electrons relax into the low-lying defect states at 2.9–3.0 eV, thus reducing the absorption of SC probe pulses in the wavelength range of 410–422 nm. The decrease in transmission, on the other hand, arises from the secondary absorption of the SC probe pulses to the conduction band by photoexcited electrons, the so-called pump-induced absorption (PIA), as shown in the inset of Figure d.[31] Such a positive to negative conversion suggests a competition between the PIB and PIA effects, which is strongly dependent on the density of the occupied defect states at 2.9–3.0 eV. At the beginning of the excitation, the electron density in these states is relatively high; therefore, the PIB effect dominates over the PIA effect. However, with the electron density decreasing, the PIA effect becomes dominant, turning ΔTλ(t)/Tλ(0) to negative. The sharpness of the conversion indicates a rapid transition of photoexcited carriers among defect states.

More intriguingly, the transmission evolution at λ = 540 nm, as shown in Figure d, exhibits a reproducible hybrid relaxation process with a delayed shoulder in the time profile. These featured dynamics are extremely different from the general one in which carriers decay exponentially among discrete energy bands. With only the transitions between states, the resultant multiexponential decay profile could not lead to the shoulder observed here. Actually, such hybrid dynamics often indicate a competitive interplay of more than one process.[32] Keeping that in mind, we can fit the transient transmission evolution using the following empirical equationwhere A0 is the offset of the differential transmission and A is the amplitude of each component with the lifetime τ. The last term represents an empirical Poisson function. By fitting, we numerically decompose the hybrid dynamics into two components as follows: one related to the exponential carrier decay among discrete states and the other related to a Poisson-like process. As shown in Figure a (red solid line), eq can be used to perfectly fit the experimental result. The contribution of each component is well decomposed. The regular carrier decay (black dashed line) is given by a biexponential function of the time constants of τ1 = 0.17 ps and τ2 = 2.5 ps. We attribute this biexponential constant to the average characteristic time of carrier decay among discrete defect states (τ1 = 0.17 ps) and recombination at a valence band (τ2 = 2.5 ps), respectively. Such sub-ps to ps defect-related carrier trapping timescale was also observed in the previous research, in which carrier trapping timescale is claimed highly dependent on the density of defects in ZnO crystals.[7]

Figure 3

(a) Comprehensive view of the decomposition into biexponential carrier decay (black dashed line) and Poisson-like decay (hollow blue circle) and their numerical fitting. The Poisson-like shoulder is obtained by subtracting the biexponential fit from experimental data. (b) Poisson-like shoulder for the time profile at different probe wavelengths and its numerical fitting. (c) Peak delay time of the Poisson-like shoulder at different probe wavelengths.

The decay process showing a Poisson-like time profile (blue circles and red dashed line) reminds us of the energy diffusion in continuum states, which is universal in energy disorder systems such as self-assembled quantum dots and organic molecular materials. In such systems, energy diffusion is the governing mechanism for various processes relating to electron transfer, energy transfer, and fluorescence blinking, in which carriers tend to hop among different energetic sites within a quantum dot or molecules, thus leading to a random spectral shift of the emission line, the so-called spectral diffusion.[33−37] This kind of carrier migration dynamics has been extensively studied by time-resolved methods, and nonexponential dynamic behaviors have been reported.[38,39] Although the ZnO crystal studied here is bulk, the continuum defect band identified by the absorption spectrum may act as different adjacent energy sites for energy diffusion, similar to the energy disorder systems. Photoexcited carriers preferentially hop from the upper level of the continuum defect band (i.e., energy sites at the conduction band edge) to deeper defect sites, exhibiting the Poisson-like process in the time profile.

Figure b,c shows the experimental decay time profiles as a result of wavelength-dependent hybrid dynamics. Although the biexponential constant of the carrier decay process among discrete defect bands is nearly independent of the probe wavelength (not shown in the text), the energy diffusion in continuum defect states is highly sensitive to the probe sites. With the increasing probe wavelength from 450 to 640 nm, the Poisson-like temporal profile peak shifts from 2.3 to 2.73 ps, which is physically reasonable because it takes time to diffuse from higher energy sites to lower ones.

In order to verify our conjecture, we propose here a model that involves energy diffusion in energy space, as schematically shown in Figure a. Based on the observed absorption tail, as shown in Figure b, we consider in our model an initial population at the upper edge state of |A> which also includes a lower continuum band representing a fuzzy energy distribution. This initial population of the upper continuum states of |A> has two parallel decay pathways. First, it could decay by energy diffusion into the lower lying continuum states. Besides, it could decay at a rate β to the defect band state |B>, which has a Gaussian-shaped energy distribution with a width of σ (0.17 eV) according to the PL spectrum. The coupling rate between |A> and |B> is given by α. The state |B> can also decay to the ground state at a rate γ. Because the continuum states |A> have a nonuniform density of the state distribution, similar to the electron or energy transfer theories, we consider a parabola potential U(q) in a reaction coordinate q in the energy space with the state |A> lying at the bottom of the parabolic potential. Thus, for nonfree space energy diffusion, the overall rate equation for the population ρ(q,t) in these states and the relevant processes can be given by the following equationwhere the Liouville diffusion operator is L̅ = Δ2/τc∂/∂q[∂/∂q + ς/kBT(q – 3.1)], Δ is the energy lattice point. D = Δ2/τc is the diffusion coefficient along with the energy coordinate q, and q0 is the energy for the defect state |B>. The parabolic potential is defined as U(q) = ς(q – 3.1)2/2 where ς is the force constant and 3.1 eV is the band gap of the upper edge of |A>.

Figure 4

(a) Schematic diagram describing the simplified model of the interplay of carrier decay and energy diffusion in the fuzzy band-edge states. (b) Simulated transient transmission at q0 = 2.21 eV according to eq . (c) Simulated Poisson-shaped delayed time profile at different defect state energy levels. (d) Simulated peak delay times of the Poisson decay at different defect state energy levels.

We numerically solved eq to calculate the population in time by using the finite difference method. An energy coordinate of about 3.1 eV was divided into 1000 lattice points Δ (3.1 × 10–3 eV). The time evolution was calculated with a time step of 1 fs. The simulated results, as shown in Figure b, qualitatively reproduce the overall recovery process observed in the experiments. The Poisson-like energy diffusion process, as presented in Figure c,d, is obviously dependent on the probed energy state, which is in good agreement with experimental data (see Figure c). It is interesting to note that the energy diffusion coefficient D identified is 1.8 × 10–2 eV2/ps, which indicates an ultrafast diffusion in energy space, consistent with the results of Cook et al..[40] Therefore, the simulated results confirmed our speculation about the origin of the hybrid dynamics, that is, the competitive interplay of ultrafast energy diffusion in continuum defect states with ultrafast carrier decay among discrete energy bands. It is worth mentioning that, for the sake of simplicity, in the model, only one defect band has been taken into account. In reality, there exist three discrete defect bands, which may cause the hybrid dynamics to have subtle and quantitative changes.

Based on the satisfactory agreement between experimental observations and our diffusion-controlled relaxation model, we thus confirmed the presence of spectral diffusion in continuum defect bands which became an alternative energy decay channel of photoexcited carriers in highly defective crystals. It is worth mentioning that the absence of spectral diffusion in previous works that deal with defective semiconductors is probably because the defects are not sufficiently dense to form continuum states for energy diffusion to become significant.

Conclusions

In summary, we have studied the carrier dynamics associated with the defect states in ZnO by TA spectroscopy and observed a hybrid carrier relaxation process with a shoulder feature in the time-domain profile. A Poisson-like dynamics in the time domain was decomposed and attributed to the spectral diffusion in continuum defect bands. A model involving energy diffusion in the energy space has been proposed to qualitatively interpret experimental results. Our results thus suggest that spectral diffusion might be an alternative energy decay channel of carriers in highly defective crystals. This finding may provide new insights into the defect engineering-based performance enhancement of semiconductors.

Experimental Section

Materials

Single-crystal ZnO(0001), prepared by the hydrothermal growth technique (MTI Co.), was used as received without further treatment.

Steady-State Absorption Spectroscopy

UV–visible absorption spectroscopy (UV-3700 from Shimadzu) was used in the fine-scan mode with 1 min integration time per 0.01 nm step to verify the defect states in single-crystal ZnO.

TA Spectroscopy

The experimental setup for TA spectroscopy is schematically shown in Figure a. Femtosecond laser pulses from Ti: sapphire amplifier (800 nm, 1 kHz, 45 fs) are split into two beams, one of which penetrates a BBO crystal to generate 400 nm pump pulses, while the other passes through a piece of fused silica (4 mm) to produce supercontinuum (SC) probe pulses with a wavelength range of 400–750 nm. Both the pump and probe pulses are then overlapped and focused on the sample with the spot sizes of 0.8 and 0.5 mm, respectively, to minimize excitation inhomogeneity. The time delay between the pump and probe is adjusted by a linear delay stage. The normalized transient transmission spectra ΔTλ(t)/Tλ(0) of the probe pulse, where ΔTλ(t) = Tλ(t) – Tλ(0), with Tλ(t) and Tλ(0) being the probe transmission with and without pumping, respectively, are recorded with a fiber spectrometer (Ocean Optics, FLAME-S-XR1-ES).