Consistency on Two Kinds of Localized Centers Examined from

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Consistency on Two Kinds of Localized Centers Examined from Temperature-Dependent and Time-Resolved Photoluminescence in InGaN/GaN Multiple Quantum Wells Zilan Wang, Lai Wang,* Yuchen Xing, Di Yang, Jiadong Yu, Zhibiao Hao, Changzheng Sun, Bing Xiong, Yanjun Han, Jian Wang, Hongtao Li, and Yi Luo* Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: Due to structural imperfection and indium content fluctuation, carriers’ localization in an InGaN-based active layer can produce efficient luminescence and unusual thermodynamic behaviors. Spectral features associated with localization, such as the “S-shaped” shift of peak energy in temperature-dependent photoluminescence (PL) and the nonexponential decay in time-resolved photoluminescence (TRPL), have not yet formed a comprehensive physical interpretation. In this work, the thermal evolution of carriers’ decay process is examined by spectroscopic approaches in high-efficiency InGaN/GaN multiple quantum well (MQW) samples. Based on the localized-state ensemble model, the peak shift in temperature-dependent PL is excellently fitted by the “red” and “blue” localization centers, which perfectly match with the fast and slow processes resolved from TRPL using biexponential model. All variations in emission peak, line shape, filling position, and lifetime with temperature are elucidated by carriers redistributing between two kinds of localization centers according to the density of states. Meanwhile, the impact of substrate and underlying layers in MQW samples has also been compared. Through such systematic analysis, the dynamics of carriers in MQWs have been quantitatively discussed, and a comprehensive understanding on the localization-induced luminescence mechanism is achieved. KEYWORDS: carrier localization, temperature-dependent PL, TRPL, biexponential decay, InGaN/GaN MQW photoluminescence (PL) exhibits “S-shaped” behavior, a common feature related to carriers’ temperature-dependent dynamics due to localization.17−20 Moreover, the decay time of InGaN/GaN QWs reaches hundreds of nanoseconds,21,22 which is much longer than GaAs/AlGaAs (hundreds of picoseconds),23 and the decay time drops with increasing photon energy, both associated with the localization effect.24−26 Meanwhile, it is observed that the decay spectra of timeresolved photoluminescence (TRPL) in InGaN/GaN QWs show nonexponential decay behavior.27 Many methods have been employed to fit the curve, such as the biexponential model,28−30 three-exponential model,31 stretched model,32,33 etc.34 However, these methods provide only mathematical fitting without detailed physical interpretation. Hence the precise nature of carrier localization and carrier dynamics are vital problems for understanding and improving InGaN-based devices. In this study, by examining the TRPL and PL of three InGaN/GaN multiple quantum well (MQW) samples, two

A

s the active layers for most light-emitting devices, InGaN/ GaN quantum well (QW) structures have achieved great success1,2 in optoelectronics and received huge research interest. Its superhigh efficiency promises the potential in developing widespread applications, while its anomalous spectral properties attract numerous investigations on the emission mechanism. During material growth, the aggregation and phase separation3,4 of indium components occur as a result of lattice mismatch.5,6 Large spontaneous and piezoelectric polarizations7−9 across the QWs produce strong a quantum-confined Stark effect (QCSE), leading to the spatial separation of electrons and holes. Owing to the above reasons, carriers are trapped and redistributed by spatial potential fluctuation and localized energy states, which are referred to as carrier localization. Due to this effect, the InGaN/GaN materials exhibit many distinctive properties different from conventional III−V semiconductors. For example, the dislocation density in InGaN-based materials is one million times higher than in other light-emitting semiconductors,10,11 and it is generally accepted that carrier localization prevents nonradiative recombination; thus high quantum efficiency is guaranteed.12−16 From a spectral viewpoint, the peak energy of temperature-dependent © XXXX American Chemical Society

Received: May 24, 2017 Published: July 31, 2017 A

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Figure 1. (a) Decay spectra at various temperatures of three samples. The dashed lines are fitting results of the biexponential decay model. (b) PL spectrum of sample A in logarithmic scale (left y-axis) and two lifetimes (τslow and τfast) against monitored energy (red and blue symbols corresponding to right y-axis) at 60 K. (c) Temperature-dependent lifetimes of slow (τslow) and fast (τfast) processes of sample A illustrated by red and black solid lines. The hollow (τnr_slow, τnr_fast) and triangle (τr_slow, τr_fast) symbols represent the nonradiative and radiative recombination lifetimes, respectively.

⎛ t ⎞ ⎛ t ⎞ n(t ) = aslow exp⎜ − ⎟ ⎟ + a fast exp⎜ − ⎝ τslow ⎠ ⎝ τfast ⎠

kinds of localization centers and their corresponding density of states (DOS) configuration are obtained by the localized-state ensemble (LSE) model.17 These results perfectly match with the thermal evolution of two-exponential decay in TRPL, thus revealing the physical meaning of the biexponential model. Meanwhile, the “S-shaped” shift regarding the temperaturedependent emission is re-established with carriers distributed in different centers. In order to suppress the effects of nonradiative recombination, a patterned c-plane sapphire substrate (PSS)35,36 and the underlying layer37 beneath the QW are introduced during sample growth, and their impacts on carrier localization are compared.

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(1)

where τslow and τfast are recombination lifetimes of the slow and fast decay components and aslow and afast are the amplitude ratio of the two components corresponding to the amount of carriers participating in each decay process, respectively. As seen from Figure 1a, the dashed lines represent fitting results of the three samples based on eq 1, showing good agreement with experimental results. To obtain further insight into the two decay processes, decay curves at different photon energies are measured. Figure 1b demonstrates typical results at 60 K, which combines the PL spectrum and the fitted lifetimes (τslow and τfast) for sample A. As the monitored photon energy moves closer to the band edge (x-axis from 2.951 eV down to 2.809 eV), both lifetimes undergo a noticeable increase around the emission peak (2.825 eV), which is a result of the carriers’ transfer to the tail state25 and strong evidence of carrier localization. When the monitored photon energy further decreases, the “M”-shaped fluctuation of the carriers’ lifetime is a result of phonon replica. The characterization of the lifetime is also studied as a function of temperature, as illustrated in Figure 1c for sample A. The red and black solid symbols represent τslow and τfast for the whole emission region, respectively. Meanwhile, the radiative and nonradiative recombination lifetimes are calculated from the internal quantum efficiency model:39,40 the green hollow diamond and blue solid triangles represent the nonradiative lifetime (τnr_slow) and radiative lifetime (τr_slow) based on the lifetime of the slow process (τslow), respectively. Similarly, τnr_fast and τr_fast are obtained from the lifetime of the fast process (τfast). As shown in Figure 1c, the trends of radiative lifetime, τr_slow and τr_fast, linearly increase proportional to the temper-

RESULTS AND DISCUSSION

The decay curves of three samples at their peak energies (2.838, 2.768, and 2.793 eV) are shown in Figure 1a horizontally. Each figure contains decay curves at four different temperatures to illustrate the trend of decay rate with increasing temperature. Interestingly, unlike the reported lifetime drop due to nonradiative recombination,30 the carrier decay becomes slower with increasing temperature for these three samples. This unusual phenomenon exists only in samples having high radiative efficiency where the disturbance of nonradiative recombination is diminished. For InGaN/GaN MQW samples, the decay curve usually exhibits two components, which has been mentioned in many reports.28−30 Therefore, the biexponential model (eq 1) is applied to analyze all of our data, and the two components could be called fast and slow processes according to their lifetimes. B

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Figure 2. Time-integrated PL spectra of three samples at various temperatures. The upper half of the figure is spectra at temperatures of 10−60 K; the lower half are spectra at 80−300 K. The dashed arrows illustrate the trend of peak shift in a different temperature range, where the turning points are at 60 and 160 K. The PL intensity of three samples at 10 K has been normalized for ease of comparison.

Figure 3. (a) “S”-shaped shift of the emission peak (black dots) fitted by the LSE model using two kinds of localization centers (red line and blue line). (b) Distribution of DOS in blue and red localization centers represented by blue and red Gaussian curves. The dashed lines are the occupied level at 0 K, below which the carriers are filled (shaded area).

potential valley due to sufficient relaxation, while carriers with shorter lifetimes lack sufficient relaxation and thus recombine at a higher energy position, resulting in emission of higher energy photons. Combining the dependency of carrier lifetime with temperature in their samples, the “S-shaped” shifting was explained. But this explanation does not comply with our high radiative efficiency samples since lifetimes in our samples constantly increase with increasing temperature, as shown in Figure 1c. In addition, two noticeable spectral features can be observed in Figure 2. One is the narrowing of spectral widths, especially on the high-energy side, in the temperature range of 10−60 K, which is contrary to the expected peak broadening due to phonon scattering.43 Another is magnitude of blue shift from 60 to 160 K, which is about 20 meV markedly over the carrier thermal energy.

ature above 150 K, which agrees with the excitons thermalization in the QW.41,42 For samples B and C, the increase of the lifetime is not so obvious compared to sample A (Figure 1a), which means that their excitons are tightly confined in the quasi-zero-dimensional potential. These behaviors demonstrate that excitons in these samples are confined in the localization centers, especially for samples B and C with a stronger localization effect, which will be discussed later. The temperature-dependent PL exhibiting an “S-shaped” shift is a typical feature for InGaN/GaN-based materials.17−20 In a previous study, the “S-shaped” shift was explained by Y. H. Cho et al. based on one kind of localized center and carrier transfer between potential minima.20 Their results show that the carriers’ lifetime first increases and then decreases as a function of temperature in their InGaN/GaN MQW samples. They deduced that carriers with longer lifetimes recombine at a C

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Gaussian distribution corresponds to σ. The shaded portion is associated with the filling of carriers under the occupied level Ea at 0 K. Next, after careful analysis, the perfect matching relation between red/blue centers and fast/slow processes in temperature-dependent TRPL will be established. As discussed in eq 1, four parameters can be obtained from the fitting of the TRPL spectrum at every temperature using the biexponential model. Figure 4 shows the fitting results of the four parameters as a function of temperature, and for clarity, different y-axis ranges and breaks are applied. Since aslow and afast are the amplitude ratios of carriers participating in each decay process, they are anticorrelated as shown in the upper half of Figure 4. afast is dominant at all temperatures, meaning that more carriers select the faster decay channel. The lower half of Figure 4 shows τslow and τfast, representing the lifetimes of slow and fast processes. For sample A and sample C, both lifetimes almost monotonically increase with temperature, while for sample B, the lifetimes reach a maximum at around 80 K. However, the temperature trend for all samples can be divided into three stages, as illustrated by three background colors. After careful comparison, the slow process corresponds to the blue localization center in the LSE fitting, whereas the fast process corresponds to the red localization center, and a detailed discussion is shown in the following paragraphs. At stage (i), the amplitude ratios of all samples yield a similar trend of afast increasing and aslow decreasing. Meanwhile, for the same temperature range, the temperature-dependent PL spectra in Figure 2 show a red shift for all samples, indicating the dominance of red localization. Therefore, the fast decay process may well be associated with the red localization obtained by LSE fitting. Also, the filling position, Ea, is located above the red localization center (Figure 3b) at 0 K. Under this condition, if additional carriers are added to the red center, the occupied states would have a smaller DOS, thus hindering spectral broadening especially from the high-energy side. This implication from increasing carriers for the red center is consistent with the experimental finding in Figure 2 (peak narrowing) for temperatures below 60 K, which further indicates the correspondence of the fast decay process with the red localization center. On the other hand, for the blue localization center, carriers are occupied close to the edge of the distribution, as illustrated in Figure 3b. According to the theory of tail state,25 the carrier’s lifetime increases if the number of carriers is reduced. This coincides with the findings in Figure 4, where aslow reduces with an increase in τslow and builds a connection between the slow decay process and blue localization. Contrary to stage (ii), the amplitude ratio in Sstage (ii) shows a trend of afast deceasing and aslow increasing, indicating that the carriers are assigned to the slow decay process. Meanwhile, with the blue shift of the emission peak in Figure 2, it illustrates the gradual dominance of the blue localization center and thus further confirms the connection of the slow decay process with the blue center. Moreover, when the number of carriers increases for the blue center, the occupied level would move upward and keep away from the tail state, leading to a drop in the carriers’ lifetime.25 As for the three samples, the decay lifetime for sample B is consistent with our theory showing a sharp decrease in τslow, while for sample A this phenomenon is concealed by the overall growing trend in carrier lifetime, and for sample C the ascent of aslow is not obvious; thus no significant change in τslow is observed.

Thus, to explain the above issues, a quantitative method is required to analyze the redistribution of carriers in localization centers. The localized-state ensemble model, proposed by Q. Li et al.,44 is applied in this study to evaluate the factors on the emission peak and line width. Unlike Eliseev’s model, which is valid only at high temperature,19 the LSE model is applicable to the full temperature range,17,18 and the peak position as a function of temperature is described as E (T ) = E 0 −

αT 2 − xkBT θ+T

(2)

where E0 is the band gap at T = 0. The second term is attributed to band-gap shrinkage, α is the Varshni parameter, and θ is the Debye temperature of the material. The third term represents the carriers’ thermal redistribution within the localized states. kB is the Boltzmann constant, and x is a parameter that can be solved by the following equation:17 2 ⎡⎛ ⎤⎛ ⎞ τ σ ⎞ x e x = ⎢⎜ ⎟ − x ⎥⎜ r ⎟e(E0 − Ea)/ kBT ⎢⎣⎝ kBT ⎠ ⎥⎦⎝ τtr ⎠

(3)

where σ is the standard deviation of the localized distribution and τr and τtr are the two time constants characterizing the radiative recombination process and the thermal activation of carriers. τr/τtr represents the escape rate of the carrier from a localization center. E0 is the central energy of the localization center, while Ea gives the occupied level of excitons at 0 K, which is similar to the Fermi level in the Fermi−Dirac distribution. The value of E0 − Ea strongly affects the PL emission peak position and line shape. When the temperature increases, a positive value of E0 − Ea corresponds to the blue shift along with spectral broadening, while a negative value represents a red shift and spectral narrowing.17,44 All of our samples display both phenomena at the two different temperature regions shown in the upper and lower half of Figure 2. Therefore, two different fittings with different signs of E0 − Ea were applied to the temperature-dependent PL. Obtained by a Gaussian peak analyzer, peak energies from the temperature PL are plotted in Figure 3a for the three samples. The red and blue lines represent fitting results for red and blue shifts based on two localization centers in which the sign for E0 − Ea is opposite. Fittings for the three samples exhibit excellent conformity with experimental results in the whole temperature region. The parameters obtained from the fitting are listed in Table 1; the “red/blue centers” represent the localization centers that lead to a red/blue shift. On the basis of these parameters, the physical picture based on the LSE model is shown quantitatively in Figure 3b. The two localization centers used for fitting are illustrated by blue and red Gaussian distributions, where the center energy is E0 and the width of the Table 1. Fitting Parameter in the LSE Model for Three Samples

sample sample sample sample sample sample

A blue center A red center B blue center B red center C blue center C red center

E0 (eV)

Ea (eV)

E0 − Ea (meV)

τr/τtr

σ (meV)

2.9085 2.8375 2.830 2.764 2.842 2.786

2.86 2.86 2.773 2.773 2.81 2.81

48.5 −22.5 57 −9 32 −24

800 100 40 20 600 20

26 25 20 4 19 9 D

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Figure 4. Parameters of the decay curve at peak positions are fitted from the biexponential model at each temperature. The upper half of the figure shows the results of aslow and afast, while the lower half of the figure shows τslow and τfast. The parameters for the fast/slow process are presented by the symbols in red/blue, corresponding to the right/left y-axis, and the solid lines are a guide for the eye. According to the trends of these parameters, the temperature range is divided into three stages, (i), (ii), and (iii), represented by different background colors.

centers are obtained from the LSE model. Similarly, after a detailed investigation of TRPL, fast and slow decay processes are fitted, corresponding to two localized recombination channels. After comprehensive analysis, the connection between the red/blue centers and the fast/slow decay process is established for the first time. The physical meanings of the two exponential decay centers are revealed, and the configurations of the localization centers are quantitatively described including the DOS distribution, amplitude ratio, and initial filling positions in each decay process. Our work provides a systematical study on the nonexponential decay process, nonlinear spectral features, and carrier-localized phenomena facilitating broad functionality and optimizing the efficiency in InGaN-based device.

Similar to stage (ii), the distribution of carriers in stage (iii) tends to be stable with afast decreasing and aslow increasing slightly. But within this temperature range, band-gap shrinkage is the dominant mechanism causing a red shift in peak position, as shown in Figure 2. So far, the red and blue localized centers obtained from the analysis of peak position and spectral line broadening of the temperature-dependent PL are compared with the fast and slow decay process fitted from the biexponential model, and a close connection has been established. Thus, we demonstrate that two kinds of localization centers exist in these InGaN/GaN samples: the red center, with lower energy, exhibits fast decay rate, while the blue center, with higher energy, exhibits a slow decay rate. Besides understanding the decay process with temperature, the parameters of localization can also be used to explain the structural variances between the three samples. Sample A has a larger energy distribution and higher escaping rate (in Table 1) compared with sample B. This means that the carriers are easier to transfer among different energy levels, and hence the localization is weak. With the highest quantum efficiency obtained from temperature-dependent PL in Figure 2, sample B grown on PSS has an enhanced light extraction efficiency and reduced dislocation density35 and exhibits the strongest localized effect including a minimum escaping rate and quasizero-dimensional potential. Using the same substrate as sample B, sample C has a different underlying layer, which was changed from InGaN to GaN. This leads to an enhancement of strain in QWs and a stronger QCSE. It is consistent that the carriers’ filling position for sample C is slightly raised with respect to sample B shown in Figure 3b. We tentatively propose that the PSS and InGaN underlying layer can enhance the localization effect and improve the radiative efficiency.

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EXPERIMENTAL METHODS The samples used in this study include three InGaN/GaN MQWs samples, labeled as A, B, and C, grown by an Aixtron 2000HT metal−organic chemical vapor deposition system. Each sample contains five pairs of QWs, and the detailed growth methods are presented in our previous work.38 Sample A uses the normal c-plane sapphire as substrate and 60 nm In0.01Ga0.99N as underlying layer. For comparison, the substrates of samples B and C are replaced by PSS, while in sample C, the underlying layer is replaced by 60 nm of GaN grown at the same temperature. The PL measurement is carried out with a 405 nm laser diode for excitation. The samples are placed in a cryostat for the temperature-dependent measurements ranging from 10 to 300 K. The signal is detected by a PMT mounted on the Jobin Yvon 550 monochromator with 0.5 nm resolution. For the TRPL system, the excitation source is a pulsed 399 nm laser diode with a 76 ps pulse width. The photon energy of the transient luminescence is selected by a Horiba HR320 monochromator. The decay process is recorded by a Picoquant time-correlated single quantum counting apparatus.

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CONCLUSION In this work, we observe a significant localization effect in our InGaN/GaN MQW samples including the radiative lifetime increasing with temperature and lifetime as a function of photon energy in TRPL spectra. On the basis of data of the temperature-dependent PL, the red and blue localization

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. E

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*E-mail: [email protected].

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ORCID

Zilan Wang: 0000-0002-2741-5746 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge Professor Shijie Xu for useful discussions. This work is supported by the National Key Research and Development Program (Grant No. 2016YFB0400102), Beijing Municipal Science and Technology Project (Grant No. Z161100002116037), Tsinghua University Initiative Scientific Research Program (Grant No. 2015THZ023), the Open Fund of the State Key Laboratory on Integrated Optoelectronics (Grant No. IOSKL2015KF10), the CAEP Microsystem and THz Science and Technology Foundation (Grant No. CAEPMT201505), the Science Challenge Project (Grant No. TZ20160003), and Collaborative Innovation Center of Solid-State Lighting and Energy-Saving Electronics.

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DOI: 10.1021/acsphotonics.7b00516 ACS Photonics XXXX, XXX, XXX−XXX