- Email: [email protected]
Photon recycling in perovskite CH3NH3PbX3 (X = I, Br, Cl) bulk single crystals and polycrystalline films
Journal Pre-proof Photon recycling in perovskite CH3NH3PbX3 (X = I, Br, Cl) bulk single crystals and polycrystalline films Takumi Yamada, Yasuhiro Yamada, Yoshihiko Kanemitsu PII:
S0022-2313(19)31246-3
DOI:
https://doi.org/10.1016/j.jlumin.2019.116987
Reference:
LUMIN 116987
To appear in:
Journal of Luminescence
Received Date: 24 June 2019 Revised Date:
14 December 2019
Accepted Date: 19 December 2019
Please cite this article as: T. Yamada, Y. Yamada, Y. Kanemitsu, Photon recycling in perovskite CH3NH3PbX3 (X = I, Br, Cl) bulk single crystals and polycrystalline films, Journal of Luminescence (2020), doi: https://doi.org/10.1016/j.jlumin.2019.116987. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
CRediT author statement Takumi Yamada: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Visualization Yasuhiro Yamada: Conceptualization, Validation, Writing - Review & Editing Yoshihiko Kanemitsu: Conceptualization, Validation, Resources, Writing - Review & Editing, Supervision, Project administration, Funding acquisition
Photon recycling in perovskite CH3NH3PbX3 (X = I, Br, Cl) bulk single crystals and polycrystalline films Takumi Yamadaa, Yasuhiro Yamadab, and Yoshihiko Kanemitsua,* a
Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
b
Department of Physics, Chiba University, Yayoi-cho, Inage, Chiba 263-8522, Japan
*Corresponding author: [email protected]
Highlights Significant redshift of PL spectra is caused by PL reabsorption in bulk crystals. Dynamical PL shift is correlated with photocarrier diffusion length. Grain size dependence of PL spectrum is caused by PL reabsorption in thin films.
Abstract Lead halide perovskite semiconductors are promising materials for optical devices due to their excellent optoelectronic properties. In addition to strong light absorption coefficients, which originate from a direct band gap structure, they also exhibit almost no Stokes shift between absorption edge and photoluminescence (PL) peak. Therefore, the effect of PL reabsorption plays an important role for their emission spectra in bulk crystals. In this review, we analyze the PL dynamics in CH3NH3PbX3 (X = I, Br, Cl) single crystals to provide a clear picture of the dynamical effects of PL reabsorption that occur in perovskites. This knowledge is essential for accurate characterization via PL and photon management for optical devices. We also show that the grain size dependence of PL spectra obtained from polycrystalline thin films can be interpreted by PL reabsorption.
Keywords Perovskite; Reabsorption; Carrier diffusion; Photoluminescence
1. Introduction In the last decade, lead halide perovskite semiconductors have attracted significant attention as novel materials for photovoltaic devices. For example, the methyl-ammonium lead iodide perovskite semiconductor, which was applied to a solar cell for the first time in the year 2009 [1], exhibits excellent properties as an absorber material and has been in the focus of interest on a global scale. These materials are appealing for many applications due to both being cost-effective and providing high performance [2–7]. Lead halide perovskites are semiconductors with direct band-to-band transitions and possess high absorption coefficient comparable to that of GaAs [8,9]. Therefore, 1
incident light can be efficiently absorbed and converted into photocarriers [8–12], which is essential for thin film solar cells [13]. A rather unexpected feature of this solution-processable materials system was that they can provide relatively high open-circuit voltages when implemented in solar cell devices [14]. This means that the energy losses due to carrier recombination and traps are extremely small, and evidences that perovskite thin films with a high-quality semiconductor can be obtained even by simple fabrication methods such as solution coating [15–19]. From the viewpoint of device design, the lead halide perovskites also possess interesting practical features. By replacing the halogen atom, the band-gap energy of these semiconductors can be continuously tuned over the whole visible spectral region [20–28], which is useful for the method of band-gap engineering. For example, this enables the development of light-emitting diodes or lasers for a broad range of wavelengths [29–32]. Furthermore, the laser cooling in lead halide perovskites has also been discussed for the realization of optical refrigerators [33,34]. Recently, giant photorefractive effect [35] and efficient high harmonic generation [36] have been discovered in perovskites, clarifying the potential of perovskites for non-linear optics [37]. While the development of optical devices based on lead halide perovskites is a very active field of research, many points regarding the fundamental optical properties of the perovskites have not yet been clarified [38]. Prior to the design of appropriate devices that can realize further efficiency improvements, a deeper understanding of fundamental properties is important. Considering the applications of perovskites that have so far been proposed, the dynamics of photoexcited carriers involved in the photoelectric conversion process are especially important [39]. In that regard, investigations on thin film samples are indispensable, but one must bear in mind that a thin film sample comprises crystallites with different grain sizes [40]. It has been reported that the size distribution of these grains as well as the film morphology influence the optical properties [39–43]. In order to clarify the intrinsic properties of lead halide perovskites excluding extrinsic factors such as grain sizes and grain boundaries, it is necessary to investigate the photoluminescence (PL) dynamics in single crystal samples. The PL dynamics reflect the optical properties as well as the behaviors of the carriers, and thus can also provide important information for solar cell devices [44– 46]. However, the interpretation of PL data in bulk samples is not easy; previous reports have clarified that repeated photon emission and reabsorption, i.e., photon recycling, occurs in optically thick perovskite single crystals [47–53]. This phenomenon occurs because of both the fact that lead halide perovskites have a strong light absorption coefficient and that they exhibit highly-efficient PL with almost no Stokes shift with respect to the absorption edge. The first observation of photon recycling in halide perovskites in 2015 [47] triggered active discussions on the photon recycling effects on optical responses of perovskite itself and device performance in solar cells (For example, the open-circuit voltage of solar cells can be enhanced [54]). The deep understanding of these effects is required for accurate characterization via PL and device design [47–59]. 2
In this review we summarize recent results on the PL dynamics of perovskite MAPbX3 (MA=CH3NH3; X=I, Br, Cl) bulk single crystals to provide a clear picture of the dynamical effects of photon reabsorption. The redshift of the PL that is observed in perovskite single crystals can be explained by the spatial distribution of excited photocarriers and the effect of PL reabsorption. Additionally, we show that the grain size dependence observed for PL spectra of thin film samples can be well explained by the physics related to the carrier diffusion and PL reabsorption in single crystal samples. We expect that the knowledge regarding the PL reabsorption dynamics presented in this review, will be useful for the design of perovskite-based optical devices.
2. Photoluminescence of MAPbX3 single crystals The perovskite crystal structure is stable for a wide range of different compositions [28]. While fabrication of thin films by solution-based processes is advantageous for applications, the fabrication of large single crystals is essential for the understanding of fundamental properties. Perovskite single crystals are usually prepared by the anti-solvent vapor-diffusion crystallization method and the inverse temperature crystallization method [5,60]. By replacing the halogen atom at the X-site of MAPbX3 with I, Br, or Cl (also combinations are possible), the band gap can be continuously changed from the near infrared (1.61 eV [8]) to near ultraviolet (3.15 eV [51]) at room temperature. The PL spectra obtained at room temperature from large MAPbI3, MAPbBr3, and MAPbCl3 single crystals are shown in Fig. 1a with red, green, and blue solid curves, respectively. For reference, we also show thin-film PL spectrum for each material (dashed gray curves). All samples show efficient PL with a single peak. This is an interesting property of perovskites, because in many materials the PL efficiency at room temperature is quite low due to enhanced non-radiative recombination via traps (e.g. Shockley-Read-Hall recombination [61]). The PL efficiency depend on the sample and the excitation condition [52]. The PL efficiencies intensity of bulk crystals are lower than those of thin films, because of strong reabsorption and poor light extraction as discussed later. The PL peak positions of the samples are 1.552 eV and 1.602 eV for the MAPbI3 single crystal and thin film, 2.259 eV and 2.312 eV for the MAPbBr3 single crystal and thin film, and 3.059 eV and 3.070 eV for the MAPbCl3 single crystal and thin film, respectively. Furthermore, we show the corresponding absorption spectra determined by spectroscopic ellipsometry in Fig. 1b (the data employed here are from Refs. [43,62]). In addition, we also calculate the corresponding spontaneous emission spectra (the intrinsic PL spectrum excluding effects of reabsorption) at 300 K using the van-Roosbroeck Shockley relation [63]. The calculated intrinsic PL spectra are shown the dashed black curves in Fig. 1b, and they are very similar to the observed PL spectra of thin films. The small offset between the peak position of PL and absorption edge in all samples evidences that these samples exhibit almost no Stokes shift [28,34,53]. This means that a significant part of the PL spectrum overlaps with the strongly absorbing energy region 3
of the perovskite crystal. The common feature of the data in Fig. 1a is that the PL peak of each single crystal sample is redshifted with respect to the corresponding thin film PL peak. From band calculations, it is known that defect levels cannot be easily formed in the sub-gap region of perovskite semiconductors [64]. Indeed, such sub-gap energy levels are not formed as can be confirmed from the very steep onset of the absorption spectra [43,62]. Moreover, it has been reported that the PL spectrum and lifetime depend on the excitation-depth profile [48,49]. Consequently, we can consider the PL reabsorption by the single crystal itself as the origin of the PL redshift in the thick single-crystal samples. In the following we describe the relation between the absorption spectrum α(E) and the observed PL spectrum IPL(E) as a function of the photon energy E. By defining γspon(E) as the spontaneous
Fig. 1. (a) Steady-state PL spectra (solid curves) of the MAPbX3 single crystals at room temperature. The red, green, and blue curves correspond to MAPbI3, MAPbBr3, and MAPbCl3, respectively. For reference, the steady-state PL spectra of the corresponding thin film samples (dashed gray curves) are also shown. (b) Absorption spectra (solid curves) and spontaneous emission spectra (dashed black curves) of perovskites. The numerical data of absorption spectra for MAPbI3, MAPbBr3, and MAPbCl3 are taken from Refs. [43] and [62]. The spontaneous emission spectra are calculated from the absorption spectra data using the van Roosbroek Shockley relation. 4
emission spectrum, and n(z) as the density of excited carriers at depth z, IPL(E) can be represented by the following expression:
∝ d
(1)
Here, z describes the depth as measured from the sample surface, and L is the thickness of the sample. The exponent k is determined by the type of the radiative recombination process. In case of PL from free carriers (the bimolecular radiative recombination between electron and hole), n(z) corresponds to the free electron and hole concentration (they are assumed to be equal) and k = 2. In the case of excitonic luminescence, n(z) corresponds to the exciton concentration, because the electron and hole are bound each other and move together as an exciton, and thus k becomes 1. As perovskite semiconductors are direct-gap semiconductors, their absorption coefficients in the energy range above the band-gap are large, i.e., α > 104 cm−1, and thus light is strongly absorbed in this energy region (see Fig. 1; broken curves). On the other hand, in the energy region below the band gap, α exponentially decreases according to the Urbach law [65]. Therefore, the effect of PL reabsorption is more pronounced on the high-energy side of the PL spectrum. In samples with a large L, diffusion of carriers towards the deeper regions occurs. As can be confirmed from Eq. (1), if the carrier distribution n(z) is different, the influence of α on the PL spectrum changes too, even if the sample thicknesses would be the same. In other words, the dynamical change of carrier distribution n(z) due to carrier diffusion also directly influences the effect of PL reabsorption. In the following we investigate the further details of the influence of the dynamical change of n(z) on the PL spectra.
3. Photoluminescence dynamics of MAPbX3 single crystals In Fig. 2, we compare the time-resolved PL spectra of the MAPbI3, MAPbBr3, and MAPbCl3 single crystals. The upper panels show the PL spectra immediately after excitation (time delay 0 ns), the middle panels those at the time instants when the PL intensities reached 10% of the initial intensity, and the bottom panels show the PL spectra at the time instants when the PL intensities decayed to 1%. The delay times for the different spectra are provided in the figure. In each of the three single-crystal samples, the peak energy of the time-resolved PL spectrum immediately after excitation coincides with the PL peak energy of the corresponding thin film sample (see Fig. 1). In this experiment, we excite the carriers via one-photon excitation, i.e., the excitation photon energy E1 is larger than the band-gap energy. Therefore, carriers are excited in a region on the order of the penetration depth of the excitation light, which equals 1/α1 when we denote the absorption coefficient for the excitation light by α1. The carrier density profile under one-photon excitation, n1(z), can be described using α1:
5
=
(2)
Here, n0 is the carrier density that is generated at the sample surface, and it is proportional to α1 (n0 = α1P1/E1, P1 is photon flux of excitation light). For the time instant immediately after excitation, the distribution described in Eq. (2) is valid for both single crystal and thin film. Consequently, there is almost no observable difference in the reabsorption effect described by Eq. (1) and the PL peaks coincide. We can infer that the PL peaks of single crystal and thin film observed immediately after excitation coincide due to the identical profile of the photocarriers. On the other hand, the time-resolved spectra in Fig. 2 gradually redshift as the delay time is increased. As shown below, this can be explained by the combination of carrier diffusion and the reabsorption effect. The single-crystal sample has a significant extension along the depth direction, and therefore the excited carriers diffuse towards the deeper sample regions as time t proceeds. If we assume that the spot size of the excitation light is sufficiently large compared to the carrier diffusion length, we can ignore the effect of in-plane carrier diffusion and formulate a one-dimensional diffusion rate equation that only considers the depth direction of the sample:
Fig. 2. Time-resolved PL spectra of the MAPbX3 single crystals. The experimental data are shown in gray and the solid curves are eye guides; red corresponds to MAPbI3, green to MAPbBr3, and blue to MAPbCl3. The upper panels show the PL spectra immediately after excitation, the middle panels those at the times when the PL intensities reached 10% of the initial intensity, and the bottom panels present the PL spectra at the times when the PL intensities decayed to 1%. The corresponding delay times for these spectra are shown in the figure.
6
=
! !
− # − $% + '
(3)
Here, D is the ambipolar diffusion constant, τ is the carrier lifetime, B is the bimolecular recombination coefficient, and G is the carrier generation rate per unit volume. In most cases, Eq. (3) must be solved numerically. However, if we further assume the weak-excitation condition in which the intensity of the excitation light is sufficiently small, the higher-order term of n (Bn2) can be neglected. In this case, we can solve Eq. (3) analytically. Because the time-resolved measurements employ excitation by very short light pulses (pulse width on the order of 100 fs), we can set G = n1(z)δ(t) where δ(t) is the delta function. By assuming a sufficiently large sample thickness (L → ∞) and a single crystal without surface recombination (surface recombination velocity S = 0), the analytical solution reads: *
, ) = + ,, )
,, ) = %
-! ./*
0erfcx 67 √ ) −
(4)
√9:
; + erfcx 67 √ ) +
√9:
;<
(5)
Here, erfcx(x) is the scaled complementary error function, and ρ(z,t) describes the temporal change of the carrier distribution (it results in unity if spatially integrated). The more general analytical solution with respect to S is given in Ref. [66]. However, as the S in perovskite single crystals is very low [66], the assumption S = 0 is sufficiently accurate for the present purpose. As described by Eq. (5), due to the carrier diffusion, the center of the carrier distribution shifts towards the sample interior as time proceeds. This is accompanied by an increase in the influence of reabsorption as described in Eq. (1), and therefore the time-resolved PL spectra also redshift with time. It has been reported that the numerical solution of the diffusion rate equation and the calculated PL spectra including the reabsorption effect well agree with the experimental results [47,48]. The above model thus allows us to gain insights into the different physics of samples with different degrees of redshift. Next, we discuss the differences that arise between samples with different halogen atoms. We compare the bottom panels of Fig. 2, that is, the time-resolved PL spectra at the time instants where the PL intensity decayed to 1%. While a redshift by more than 50 meV is present in MAPbI3 and MAPbBr3 single crystals with respect to their respective peak positions at time delay t = 0 ns, the MAPbCl3 single crystal exhibits a small redshift of about 10 meV. This difference is caused by the differences in the PL lifetimes, which are explained in the following. In Fig. 3a we show the PL decay curves of the MAPbI3, MAPbBr3, and MAPbCl3 single crystals. The PL decay curves were obtained by integration over the whole measured spectral range. Among 7
these three materials, the PL lifetime of MAPbI3 is the longest while that of MAPbCl3 is the shortest. The PL lifetime of MAPbCl3 is relatively short, because the spontaneous emission rate is large in wide-gap semiconductors [67]. Additionally, MAPbCl3 exhibits excitonic PL even at room temperature [51], implying an enhanced recombination rate due to Coulomb interactions. This short lifetime suggests that all carriers recombine before they can diffuse over a significant long range. Therefore, the redshift observed in Fig. 2 for the time-resolved PL spectra of MAPbCl3 is smaller than those of the other two perovskite single crystals. The almost non-existent difference between the PL peak energies of the MAPbCl3 thin film and single crystal observed in Fig. 1 can be also explained by the much smaller redshift for this material. The relation between the extent of the redshift in the PL spectrum and the carrier lifetime can be confirmed from perovskite single crystals that are doped with Bi3+, because the carrier lifetime becomes shorter with higher Bi3+-doping concentrations [50]. In Fig. 3b, we show the time evolution of the PL peak redshift after excitation for six MAPbBr3 single crystals with different Bi3+-doping
Fig. 3. (a) PL decay curves obtained from the MAPbX3 single crystals. The red curve corresponds to MAPbI3, the green curve to MAPbBr3, and the blue curve to MAPbCl3. The PL decay curves were obtained by integration over the whole measured spectral range. The numerical data are taken from Ref. [47] for MAPbI3 and Ref. [48] for MAPbBr3. (b) Time dependence of the extent of the PL peak shift after excitation for MAPbBr3 single crystals doped with Bi3+. The Bi/Pb ratios given in the figure correspond to the molar ratios that were present in the starting materials for sample fabrication. The corresponding PL lifetimes are also shown in the parentheses. The broken curve is the simulation result from the diffusion rate equation. The panel (b) is adopted with permission from Ref. [50]. Copyright 2017 American Chemical Society. 8
concentrations (corresponding PL lifetimes are also shown in the parentheses) [50]. The Bi/Pb ratios given in the figure correspond to the molar ratios that were present in the starting materials for sample fabrication. According to Fig. 3b, the time dependence of the PL peak redshift of each sample follows the same decay curve, irrespective of the doping concentration. In other words, the data in Fig. 3b suggest that the diffusion constant of MAPbBr3 is independent of the Bi3+-doping concentration. The ambipolar diffusion constant of MAPbBr3 (D = 18 cm2/s [49]) has been estimated by time-resolved two-photon excitation PL microscopy. Based on the diffusion rate equation and the reabsorption effect, we can predict the time dependence of the PL peak redshift and the result is shown with the broken curve in Fig. 3b. The calculation result well reproduces the experimental data, indicating that the interpretation based on the diffusion rate equation and reabsorption effect is plausible. With the above, we were able to clarify the importance of the PL reabsorption effect and the time evolution of the carrier distribution for the PL dynamics in thick single crystals.
4. Photoluminescence spectra obtained from polycrystalline thin films The above observations of the PL of thick single crystals including effects of reabsorption as well as carrier diffusion are useful for the interpretation of the PL spectra obtained from thin films, which usually contain grains of different sizes. The size of the grains and the film morphology strongly depend on the fabrication conditions, and it is well-known that the PL spectrum depends on the grain size distribution in the thin film [39,40]. Various effects such as PL quenching at the grain boundaries have been considered [68], but the general dependence of the PL peak position on the grain size has been rarely discussed. The steady-state PL spectra of MAPbI3 thin films with different averaged grain sizes (0.20, 0.55, and 0.81 µm) are shown in Fig. 4a. The averaged grain sizes were determined from scanning electron microscopy images of the sample surfaces. For reference, we also plot the steady-state PL spectrum obtained from a bulk single crystal with a thickness of 1.5 mm in the bottom panel of Fig. 4a [34]. It is evident that the PL peak energy redshifts as the grain size increases. The grain size dependence of the PL peak energy including the experimental results of other research groups is shown in Fig. 4b. The grain sizes in these thin film samples are larger than 200 nm, and as such much larger than the exciton Bohr radius in MAPbI3 (aB = 2.2 nm [69]). Therefore, the differences in the PL peak energies cannot be explained by quantum size effects. Instead, we propose that this effect can be explained by the PL reabsorption in large crystallites, i.e., the model that has been presented in the previous section. This is plausible, because it can be considered that the thin film thickness L (which roughly equals the average grain size) causes differences in the spatial distributions of the excited carriers and in the extents of the redshift. In the steady-state PL measurements, the light used for excitation is a continuous-wave laser. In this case, the term on the left side of the diffusion rate equation Eq. (3) is zero, and we solve for G = 9
n1(z)/τ. We also consider the following boundary conditions:
=
=0
(6)
? = 0
(7)
=
The condition of Eq. (6) means that the surface recombination velocity at the front of sample is zero. This is valid for high quality perovskite layer. On the other hand, Eq. (7) corresponds to the case where all of the carriers approached to the back surface are extracted to the outside or recombined. By considering the weak-excitation condition and the above boundary condition, the analytical solution of Eq. (3) as a function of the film thickness L becomes:
=
√:# @ A6
BCB ;DE CF B G A6 ;E CF- G A6 ; √/+ √/+ √/+ ! B 6H √:#I ; G A6 ; √/+
(8)
We note that in the absence of diffusion (D = 0), Eq. (8) becomes Eq. (2). If we define the carrier diffusion length LD as the mean-square displacement of the carriers, the LD in a three-dimensional
Fig. 4. (a) Dependence of PL spectra of MAPbI3 thin films on the grain size. The averaged grain sizes were determined from scanning electron microscopy images of the sample surfaces and are shown on the right upper side of each spectrum. We note that the spectrum in the bottom panel is that observed from a bulk single crystal. (b) Dependence of the PL peak energy on the sample thickness assumed to be the same size as the grain size. The red data are that of thin films [39], the yellow data that of a bulk single crystal [34], and the green data are those of thin films in another previous work [40]. The blue solid line is the calculation result from the reabsorption 10
material can be expressed in terms of the diffusion constant D and the carrier lifetime τ [70]. By assigning values to the absorption coefficient α and the diffusion length LD, we can calculate the density of the excited carriers as a function of the film thickness L from Eq. (8). Furthermore, by combining the results with Eq. (1) we can calculate the PL spectrum and the PL peak energy as a function of the film thickness L. The calculated dependence of the PL peak energy on L for the condition α = α1 (the absorption coefficient α1 for photons with E1 = 1.8 eV is 2.4 × 104 cm−1 [43]) and LD = 178 µm (the value obtained from the single-crystal sample [34]) is shown in Fig. 4b with the solid blue curve. The calculated curve shows a good overall agreement with previous experimental results [34,39]. In contrast, a part of the experimentally obtained PL peak positions is located at energies below the calculation result [39]. One possibility to explain the redshift is the light trapping effect [71]. Here, the band-gap luminescence is trapped inside the perovskite layer due to light total internal reflection, and thus the effective layer thickness is increased. This effect is exploited, for example, in thin film solar cells based on crystalline silicon (Si); a special surface texture is fabricated in order to confine sunlight inside the Si layer to gain a larger effective sample thickness [72]. If such a light trapping effect efficiently occurs for the perovskite’s band-edge luminescence due to the sample structure (e.g., the shape of grains and the film morphology), the PL reabsorption effect becomes larger and a more redshifted PL spectrum can be observed. From the above considerations we can understand that the actual experimental results also contain influences from the sample quality and morphology. However, we also clarified that the dependence of the PL peak energy on the grain size (which roughly equals the film thickness) can be well explained with the spatial distribution of the excited carriers and the effect of PL reabsorption. The differences between theoretical prediction and experiment enable a more accurate discussion of the sample quality. By accurately characterizing the effect of reabsorption in thick single crystal samples, we were able to arrive at a very clear picture of the effects that influence the PL spectra of thin films.
5. Conclusions In this review, we provided a summary on the PL dynamics of lead halide perovskites with emphasis on the details of the PL reabsorption effect. First, we compared the steady-state PL spectra and absorption spectra of MAPbX3 (X=I, Br, Cl) thick single crystals and thin films, and showed that there is almost no energy shift between the PL peak and the absorption edge of each material. Then, regarding the redshift of these steady-state spectra with respect to those of thin film samples, we pointed out that this is caused by PL reabsorption. Using time-resolved PL spectrum measurements, we showed that the PL peaks of thin films and single crystals immediately after excitation coincide, and that the single crystal’s PL spectrum redshifts with time. We were able to explain this by the combination of the PL reabsorption effect and the temporal change in the distribution of the excited carriers due to diffusion. Furthermore, from the comparison of samples doped with Bi3+, we were 11
able to show the correlation between the extent of the PL redshift and the carrier lifetime (carrier diffusion length). Finally, we modelled the dependence of the PL spectrum on the film thickness by combining the carrier distribution and the reabsorption effect, and we explained the grain size dependence of the PL spectra observed from thin film samples. The model of the PL reabsorption dynamics in the perovskite semiconductors presented in this review should be useful for the realization of perovskite-based optical devices with higher efficiencies.
Acknowledgments The authors thank their colleagues for help with the experiments and fruitful discussions. Part of this work was supported by JST-CREST (Grant No. JPMJCR16N3).
Notes The authors declare no competing financial interests.
References [1] A. Kojima, K. Teshima, Y. Shirai, T. Miyasaka, J. Am. Chem. Soc. 131 (2009) 6050–6051. https://doi.org/10.1021/ja809598r [2] C. Wehrenfennig, G. E. Eperon, M. B. Johnston, H. J. Snaith, L. M. Herz, Adv. Mater. 26 (2014) 1584–1589. https://doi.org/10.1002/adma.201305172 [3] S. D. Stranks, G. E. Eperon, G. Grancini, C. Menelaou, M. J. P. Alcocer, T. Leijtens, L. M. Herz, A. Petrozza, H. J. Snaith, Science 342 (2013) 341–344. https://doi.org/10.1126/science.1243982 [4] G. Xing, N. Mathews, S. Sun, S. S. Lim, Y. M. Lam, M. Grätzel, S. Mhaisalkar, T. C. Sum, Science 342 (2013) 344–347. https://doi.org/10.1126/science.1243167 [5] D. Shi, V. Adinolfi, R. Comin, M. Yuan, E. Alarousu, A. Buin, Y. Chen, S. Hoogland, A. Rothenberger, K. Katsiev, Y. Losovyj, X. Zhang, P. A. Dowben, O. F. Mohammed, E. H. Sargent, O. M. Bakr, Science 347 (2015) 519–522. https://doi.org/10.1126/science.aaa2725 [6] Q. Dong, Y. Fang, Y. Shao, P. Mulligan, J. Qiu, L. Cao, J. Huang, Science 347 (2015) 967–970. https://doi.org/10.1126/science.aaa5760 [7] Y. Yamada, T. Nakamura, M. Endo, A. Wakamiya, Y. Kanemitsu, J. Am. Chem. Soc. 136 (2014) 11610–11613. https://doi.org/10.1021/ja506624n [8] Y. Yamada, T. Nakamura, M. Endo, A. Wakamiya, Y. Kanemitsu, Appl. Phys. Express 7 (2014) 032302. https://doi.org/10.7567/APEX.7.032302 [9] S. D. Wolf, J. Holovsky, S.-J. Moon, B. Niesen, M. Ledinsky, F.-J. Haug, J.-H. Yum, C. Ballif, J. Phys. Chem. Lett. 5 (2014) 1035–1039. https://doi.org/10.1021/jz500279b [10] T. Umebayashi, K. Asai, T. Kondo, A. Nakao, Phys. Rev. B 67 (2003) 155405. https://doi.org/10.1103/PhysRevB.67.155405 12
[11] J. Even, L. Pedesseau, C. Katan, M. Kepenekian, J.-S. Lauret, D. Sapori, E. Deleporte, J. Phys. Chem. C 119 (2015) 10161–10177. https://doi.org/10.1021/acs.jpcc.5b00695 [12] G. Giorgi, J. Fujisawa, H. Segawa, K. Yamashita, J. Phys. Chem. Lett. 4 (2013) 4123–4126. https://doi.org/10.1021/jz4023865 [13] K. L. Chopra, P. D. Paulson, V. Dutta, Prog. Photovolt: Res. Appl. 12 (2004) 69–92. https://doi.org/10.1002/pip.541 [14] M. Saliba, T. Matsui, K. Domanski, J.-Y. Seo, A. Ummadisingu, S. M. Zakeeruddin, J.-P. Correa-Baena, W. R. Tress, A. Abate, A. Hagfeldt, M. Grätzel, Science 354 (2016) 206–209. https://doi.org/10.1126/science.aah5557 [15] J. H. Im, C. R. Lee, J. W. Lee, S. W. Park, N. G. Park, Nanoscale 3 (2011) 4088–4093. https://doi.org/10.1039/c1nr10867k [16] M.
Liu,
M.
B.
Johnston,
H.
J.
Snaith,
Nature
501
(2013)
395–398.
https://doi.org/10.1038/nature12509 [17] J. Burschka, N. Pellet, S.-J. Moon, R. Humphry-Baker, P. Gao, M. K. Nazeeruddin, M. Grätzel, Nature 499 (2013) 316–319. https://doi.org/10.1038/nature12340 [18] N. J. Jeon, J. H. Noh, W. S. Yang, Y. C. Kim, S. Ryu, J. Seo, S. I. Seok, Nature 517 (2015) 476– 480. https://doi.org/10.1038/nature14133 [19] W. S. Yang, J. H. Noh, N. J. Jeon, Y. C. Kim, S. Ryu, J. Seo, S. I. Seok, Science 348 (2015) 1234–1237. https://doi.org/10.1126/science.aaa9272 [20] C. C. Stoumpos, C. D. Malliakas, M. G. Kanatzidis, Inorg. Chem. 52 (2013) 9019–9038. https://doi.org/10.1021/ic401215x [21] N. Pellet, P. Gao, G. Gregori, T.-Y. Yang, M. K. Nazeeruddin, J. Maier, M. Grätzel, Angew. Chem. Int. Ed. 53 (2014) 3151–3157. https://doi.org/10.1002/anie.201309361 [22] N. K. Noel, S. D. Stranks, A. Abate, C. Wehrenfennig, S. Guarnera, A.-A. Haghighirad, A. Sadhanala, G. E. Eperon, S. K. Pathak, M. B. Johnston, A. Petrozza, L. M. Herz, H. J. Snaith, Energy Environ. Sci. 7 (2014) 3061–3068. https://doi.org/10.1039/c4ee01076k [23] G. E. Eperon, S. D. Stranks, C. Menelaou, M. B. Johnston, L. M. Herz, H. J. Snaith, Energy Environ. Sci. 7 (2014) 982–988. https://doi.org/10.1039/c3ee43822h [24] E. T. Hoke, D. J. Slotcavage, E. R. Dohner, A. R. Bowring, H. I. Karunadasa, M. D. McGehee, Chem. Sci. 6 (2015) 613–617. https://doi.org/10.1039/c4sc03141e [25] R. Comin, G. Walters, E. S. Thibau, O. Voznyy, Z.-H. Lu, E. H. Sargent, J. Mater. Chem. C 3 (2015) 8839–8843. https://doi.org/10.1039/c5tc01718a [26] A. Sadhanala, S. Ahmad, B. Zhao, N. Giesbrecht, P. M. Pearce, F. Deschler, R. L. Z. Hoye, K. C. Gödel, T. Bein, P. Docampo, S. E. Dutton, M. F. L. D. Volder, R. H. Friend, Nano Lett. 15 (2015) 6095–6101. https://doi.org/10.1021/acs.nanolett.5b02369
13
[27] Z. Xiao, R. A. Kerner, L. Zhao, N. L. Tran, K. M. Lee, T.-W. Koh, G. D. Scholes, B. P. Rand, Nat. Photon. 11 (2017) 108–115. https://doi.org/10.1038/nphoton.2016.269 [28] Y.
Kanemitsu,
T.
Handa,
Jpn.
J.
Appl.
Phys.
57
(2018)
090101.
https://doi.org/10.7567/JJAP.57.090101 [29] Z.-K. Tan, R. S. Moghaddam, M. L. Lai, P. Docampo, R. Higler, F. Deschler, M. Price, A. Sadhanala, L. M. Pazos, D. Credgington, F. Hanusch, T. Bein, H. J. Snaith, R. H. Friend, Nat. Nanotechnol. 9 (2014) 687–692. https://doi.org/10.1038/nnano.2014.149 [30] G. Xing, N. Mathews, S. S. Lim, N. Yantara, X. Liu, D. Sabba, M. Grätzel, S. Mhaisalkar, T. C. Sum, Nat. Mater. 13 (2014) 476–480. https://doi.org/10.1038/nmat3911 [31] Y. Cao, N. Wang, H. Tian, J. Guo, Y. Wei, H. Chen, Y. Miao, W. Zou, K. Pan, Y. He, H. Cao, Y. Ke, M. Xu, Y. Wang, M. Yang, K. Du, Z. Fu, D. Kong, D. Dai, Y. Jin, G. Li, H. Li, Q. Peng, J. Wang, W. Huang, Nature 562 (2018) 249–253. https://doi.org/10.1038/s41586-018-0576-2 [32] K. Lin, J. Xing, L. N. Quan, F. P. C. de Arquer, X. Gong, J. Lu, L. Xie, W. Zhao, D. Zhang, C. Yan, W. Li, X. Liu, Y. Lu, J. Kirman, E. H. Sargent, Q. Xiong, Z. Wei, Nature 562 (2018) 245– 248. https://doi.org/10.1038/s41586-018-0575-3 [33] S.-T.
Ha,
C.
Shen,
J.
Zhang,
Q.
Xiong,
Nat.
Photon.
10
(2016)
115–121.
https://doi.org/10.1038/nphoton.2015.243 [34] T. Yamada, T. Aharen, Y. Kanemitsu, Phys. Rev. Materials 3 (2019) 024601. https://doi.org/10.1103/PhysRevMaterials.3.024601 [35] H. Tahara, T. Aharen, A. Wakamiya, Y. Kanemitsu, Adv. Opt. Mater. 6 (2018) 1701366. https://doi.org/10.1002/adom.201701366 [36] H. Hirori, P. Xia, Y. Shinohara, T. Otobe, Y. Sanari, H. Tahara, N. Ishii, J. Itatani, K. L. Ishikawa, T. Aharen, M. Ozaki, A. Wakamiya, Y. Kanemitsu, APL Mater. 7 (2019) 041107. https://doi.org/10.1063/1.5090935 [37] K. Ohara, T. Yamada, H. Tahara, T. Aharen, H. Hirori, H. Suzuura, and Y. Kanemitsu, Phys. Rev. Materials 3 (2019) 111601(R), https://doi.org/10.1103/PhysRevMaterials.3.111601 [38] L. Martiradonna, Nat. Mater. 17 (2018) 377–384. https://doi.org/10.1038/s41563-018-0069-6 [39] Y. Kanemitsu, J. Mater. Chem. C 5 (2017) 3427–3437. https://doi.org/10.1039/c7tc00669a [40] V. D’Innocenzo, A. R. S. Kandada, M. De Bastiani, M. Gandini, A. Petrozza, J. Am. Chem. Soc. 136 (2014) 17730–17733. https://doi.org/10.1021/ja511198f [41] X. Wu, M. T. Trinh, D. Niesner, H. Zhu, Z. Norman, J. S. Owen, O. Yaffe, B. J. Kudisch, X.-Y. Zhu, J. Am. Chem. Soc. 137 (2015) 2089–2096. https://doi.org/10.1021/ja512833n [42] Y.
Tian,
I.
G.
Scheblykin,
J.
Phys.
https://doi.org/10.1021/acs.jpclett.5b01406
14
Chem.
Lett.
6
(2015)
3466–3470.
[43] M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T. N. Murakami, S. Fujimoto, M. Chikamatsu, H. Fujiwara, Phys. Rev. Applied 5 (2016) 014012. https://doi.org/10.1103/PhysRevApplied.5.014012 [44] O. D. Miller, E. Yablonovitch, S. R. Kurtz, IEEE J. Photovoltaics 2 (2012) 303–311. https://doi.org/10.1109/JPHOTOV.2012.2198434 [45] L. Zhu, T. Mochizuki, M. Yoshita, S. Chen, C. Kim, H. Akiyama, Y. Kanemitsu, Opt. Express 24 (2016) A740–A751. https://doi.org/10.1364/OE.24.00A740 [46] T. Handa, D. M. Tex, A. Shimazaki, A. Wakamiya, Y. Kanemitsu, J. Phys. Chem. Lett. 8 (2017) 954–960. https://doi.org/10.1021/acs.jpclett.6b02847 [47] Y. Yamada, T. Yamada, L. Q. Phuong, N. Maruyama, H Nishimura, A. Wakamiya, Y. Murata, Y. Kanemitsu, J. Am. Chem. Soc. 137 (2015) 10456–10459. https://doi.org/10.1021/jacs.5b04503 [48] T. Yamada, Y. Yamada, H. Nishimura, Y. Nakaike, A. Wakamiya, Y. Murata, Y. Kanemitsu, Adv. Electron. Mater. 2 (2016) 1500290. https://doi.org/10.1002/aelm.201500290 [49] T. Yamada, Y. Yamada, Y. Nakaike, A. Wakamiya, Y. Kanemitsu, Phys. Rev. Applied 7 (2017) 014001. https://doi.org/10.1103/PhysRevApplied.7.014001 [50] Y. Yamada, M. Hoyano, R. Akashi, K. Oto, Y. Kanemitsu, J. Phys. Chem. Lett. 8 (2017) 5798– 5803. https://doi.org/10.1021/acs.jpclett.7b02508 [51] T.
Yamada,
T.
Aharen,
Y.
Kanemitsu,
Phys.
Rev.
Lett.
120
(2018)
057404.
https://doi.org/10.1103/PhysRevLett.120.057404 [52] K. Kojima, K. Ikemura, K. Matumori, Y. Yamada, Y. Kanemitsu, S. F. Chichibu, APL Mater. 7 (2019) 071116, https://doi.org/10.1063/1.5110652 [53] Y. Yamada, T. Yamada, Y. Kanemitsu, Bull. Chem. Soc. Jpn. 90 (2017) 1129–1140. https://doi.org/10.1246/bcsj.20170208 [54] T.
Kirchartz,
F.
Staub,
U.
Rau,
ACS
Energy
Lett.
14
(2016)
731–739.
https://doi.org/10.1021/acsenergylett.6b00223 [55] L. M. Pazos-Outón, M. Szumilo, R. Lamboll, J. M. Richter, M. Crespo-Quesada, M. Abdi-Jalebi, H. J. Beeson, M. Vrućinić, M. Alsari, H. J. Snaith, B. Ehrler, R. H. Friend, F. Deschler, Science 351 (2016) 1430–1433. https://doi.org/10.1126/science.aaf1168 [56] Y.
Fang,
H.
Wei,
Q.
Dong,
J.
Huang,
Nat.
Commun.
8
(2017)
14417.
https://doi.org/10.1038/ncomms14417 [57] L. Zhu, T. Mochizuki, M. Yoshita, S. Chen, C. Kim, H. Akiyama, Y. Kanemitsu, Opt. Express 24 (2016) A740–A751. https://doi.org/10.1364/OE.24.00A740 [58] L. M. Pazos-Outón, T. P. Xiao, and E. Yablonovitch, J. Phys. Chem. Lett. 97 (2018) 1703–1711, https://doi.org/10.1021/acs.jpclett.7b03054 [59] I. L. Braly, D. W. deQuilettes, L. M. Pazos-Outón, S. Burke, M. E. Ziffer, D. S. Ginger, and H. W. Hillhouse, Nat. Photon. 12 (2018) 355–361, https://doi.org/10.1038/s41566-018-0154-z 15
[60] M. I. Saidaminov, A. L. Abdelhady, B. Murali, E. Alarousu, V. M. Burlakov, W. Peng, I. Dursun, L. Wang, Y. He, G. Maculan, A. Goriely, T. Wu, O. F. Mohammed, O. M. Bakr, Nat. Commun. 6 (2015) 7586. https://doi.org/10.1038/ncomms8586 [61] W.
Shockley,
W.
T.
Read,
Jr.,
Phys.
Rev.
87
(1952)
835–842.
https://doi.org/10.1103/PhysRev.87.835 [62] A. M. A. Leguy, P. Azarhoosh, M. I. Alonso, M. Campoy-Quiles, O. J. Weber, J. Yao, D. Bryant, M. T. Weller, J. Nelson, A. Walsh, M. van Schilfgaarde, P. R. F. Barnes, Nanoscale 8 (2016) 6317–6327. https://doi.org/10.1039/c5nr05435d [63] W.-J.
Yin,
T.
Shi,
Y.
Yan,
Appl.
Phys.
Lett.
104
(2014)
063903.
https://doi.org/10.1063/1.4864778 [64] W.
van
Roosbroeck
and
W.
Shockley,
Phys.
Rev.
94
(1954)
1558,
https://doi.org/10.1103/PhysRev.94.1558 [65] F. Urbach, Phys. Rev. 92 (1953) 1324. https://doi.org/10.1103/PhysRev.92.1324 [66] Y. Yang, Y. Yan, M. Yang, S. Choi, K. Zhu, J. M. Luther, M. C. Beard, Nat. Commun. 6 (2015) 7961. https://doi.org/10.1038/ncomms8961 [67] P. Y. Yu, M. Cardona, Fundamentals of semiconductors: physics and material properties, forth ed., Springer, Berlin, 2010. [68] D. W. deQuilettes, S. M. Vorpahl, S. D. Stranks, H. Nagaoka, G. E. Eperon, M. E. Ziffer, H. J. Snaith, D. S. Ginger, Science 348 (2015) 683–686. https://doi.org/10.1126/science.aaa5333 [69] K. Tanaka, T. Takahashi, T. Ban, T. Kondo, K. Uchida, N. Miura, Solid State Commun. 127, 619-623 (2003). [70] A. Einstein, Investigations on the Theory of the Brownian Movement, Dover Publications, New York, 1956. [71] E. Yablonovitch, G. D. Cody, IEEE Transactions on Electron Devices 29 (1982) 300–305. https://doi.org/10.1109/T-ED.1982.20700 [72] S.-B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, P. Peumans, Appl. Phys. Lett. 91 (2007) 243501. https://doi.org/10.1063/1.2789677
16
Highlights Significant redshift of PL spectra is caused by PL reabsorption in bulk crystals. Dynamical PL shift is correlated with photocarrier diffusion length. Grain size dependence of PL spectrum is caused by PL reabsorption in thin films.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0022-2313(19)31246-3
DOI:
https://doi.org/10.1016/j.jlumin.2019.116987
Reference:
LUMIN 116987
To appear in:
Journal of Luminescence
Received Date: 24 June 2019 Revised Date:
14 December 2019
Accepted Date: 19 December 2019
Please cite this article as: T. Yamada, Y. Yamada, Y. Kanemitsu, Photon recycling in perovskite CH3NH3PbX3 (X = I, Br, Cl) bulk single crystals and polycrystalline films, Journal of Luminescence (2020), doi: https://doi.org/10.1016/j.jlumin.2019.116987. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
CRediT author statement Takumi Yamada: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Visualization Yasuhiro Yamada: Conceptualization, Validation, Writing - Review & Editing Yoshihiko Kanemitsu: Conceptualization, Validation, Resources, Writing - Review & Editing, Supervision, Project administration, Funding acquisition
Photon recycling in perovskite CH3NH3PbX3 (X = I, Br, Cl) bulk single crystals and polycrystalline films Takumi Yamadaa, Yasuhiro Yamadab, and Yoshihiko Kanemitsua,* a
Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
b
Department of Physics, Chiba University, Yayoi-cho, Inage, Chiba 263-8522, Japan
*Corresponding author: [email protected]
Highlights Significant redshift of PL spectra is caused by PL reabsorption in bulk crystals. Dynamical PL shift is correlated with photocarrier diffusion length. Grain size dependence of PL spectrum is caused by PL reabsorption in thin films.
Abstract Lead halide perovskite semiconductors are promising materials for optical devices due to their excellent optoelectronic properties. In addition to strong light absorption coefficients, which originate from a direct band gap structure, they also exhibit almost no Stokes shift between absorption edge and photoluminescence (PL) peak. Therefore, the effect of PL reabsorption plays an important role for their emission spectra in bulk crystals. In this review, we analyze the PL dynamics in CH3NH3PbX3 (X = I, Br, Cl) single crystals to provide a clear picture of the dynamical effects of PL reabsorption that occur in perovskites. This knowledge is essential for accurate characterization via PL and photon management for optical devices. We also show that the grain size dependence of PL spectra obtained from polycrystalline thin films can be interpreted by PL reabsorption.
Keywords Perovskite; Reabsorption; Carrier diffusion; Photoluminescence
1. Introduction In the last decade, lead halide perovskite semiconductors have attracted significant attention as novel materials for photovoltaic devices. For example, the methyl-ammonium lead iodide perovskite semiconductor, which was applied to a solar cell for the first time in the year 2009 [1], exhibits excellent properties as an absorber material and has been in the focus of interest on a global scale. These materials are appealing for many applications due to both being cost-effective and providing high performance [2–7]. Lead halide perovskites are semiconductors with direct band-to-band transitions and possess high absorption coefficient comparable to that of GaAs [8,9]. Therefore, 1
incident light can be efficiently absorbed and converted into photocarriers [8–12], which is essential for thin film solar cells [13]. A rather unexpected feature of this solution-processable materials system was that they can provide relatively high open-circuit voltages when implemented in solar cell devices [14]. This means that the energy losses due to carrier recombination and traps are extremely small, and evidences that perovskite thin films with a high-quality semiconductor can be obtained even by simple fabrication methods such as solution coating [15–19]. From the viewpoint of device design, the lead halide perovskites also possess interesting practical features. By replacing the halogen atom, the band-gap energy of these semiconductors can be continuously tuned over the whole visible spectral region [20–28], which is useful for the method of band-gap engineering. For example, this enables the development of light-emitting diodes or lasers for a broad range of wavelengths [29–32]. Furthermore, the laser cooling in lead halide perovskites has also been discussed for the realization of optical refrigerators [33,34]. Recently, giant photorefractive effect [35] and efficient high harmonic generation [36] have been discovered in perovskites, clarifying the potential of perovskites for non-linear optics [37]. While the development of optical devices based on lead halide perovskites is a very active field of research, many points regarding the fundamental optical properties of the perovskites have not yet been clarified [38]. Prior to the design of appropriate devices that can realize further efficiency improvements, a deeper understanding of fundamental properties is important. Considering the applications of perovskites that have so far been proposed, the dynamics of photoexcited carriers involved in the photoelectric conversion process are especially important [39]. In that regard, investigations on thin film samples are indispensable, but one must bear in mind that a thin film sample comprises crystallites with different grain sizes [40]. It has been reported that the size distribution of these grains as well as the film morphology influence the optical properties [39–43]. In order to clarify the intrinsic properties of lead halide perovskites excluding extrinsic factors such as grain sizes and grain boundaries, it is necessary to investigate the photoluminescence (PL) dynamics in single crystal samples. The PL dynamics reflect the optical properties as well as the behaviors of the carriers, and thus can also provide important information for solar cell devices [44– 46]. However, the interpretation of PL data in bulk samples is not easy; previous reports have clarified that repeated photon emission and reabsorption, i.e., photon recycling, occurs in optically thick perovskite single crystals [47–53]. This phenomenon occurs because of both the fact that lead halide perovskites have a strong light absorption coefficient and that they exhibit highly-efficient PL with almost no Stokes shift with respect to the absorption edge. The first observation of photon recycling in halide perovskites in 2015 [47] triggered active discussions on the photon recycling effects on optical responses of perovskite itself and device performance in solar cells (For example, the open-circuit voltage of solar cells can be enhanced [54]). The deep understanding of these effects is required for accurate characterization via PL and device design [47–59]. 2
In this review we summarize recent results on the PL dynamics of perovskite MAPbX3 (MA=CH3NH3; X=I, Br, Cl) bulk single crystals to provide a clear picture of the dynamical effects of photon reabsorption. The redshift of the PL that is observed in perovskite single crystals can be explained by the spatial distribution of excited photocarriers and the effect of PL reabsorption. Additionally, we show that the grain size dependence observed for PL spectra of thin film samples can be well explained by the physics related to the carrier diffusion and PL reabsorption in single crystal samples. We expect that the knowledge regarding the PL reabsorption dynamics presented in this review, will be useful for the design of perovskite-based optical devices.
2. Photoluminescence of MAPbX3 single crystals The perovskite crystal structure is stable for a wide range of different compositions [28]. While fabrication of thin films by solution-based processes is advantageous for applications, the fabrication of large single crystals is essential for the understanding of fundamental properties. Perovskite single crystals are usually prepared by the anti-solvent vapor-diffusion crystallization method and the inverse temperature crystallization method [5,60]. By replacing the halogen atom at the X-site of MAPbX3 with I, Br, or Cl (also combinations are possible), the band gap can be continuously changed from the near infrared (1.61 eV [8]) to near ultraviolet (3.15 eV [51]) at room temperature. The PL spectra obtained at room temperature from large MAPbI3, MAPbBr3, and MAPbCl3 single crystals are shown in Fig. 1a with red, green, and blue solid curves, respectively. For reference, we also show thin-film PL spectrum for each material (dashed gray curves). All samples show efficient PL with a single peak. This is an interesting property of perovskites, because in many materials the PL efficiency at room temperature is quite low due to enhanced non-radiative recombination via traps (e.g. Shockley-Read-Hall recombination [61]). The PL efficiency depend on the sample and the excitation condition [52]. The PL efficiencies intensity of bulk crystals are lower than those of thin films, because of strong reabsorption and poor light extraction as discussed later. The PL peak positions of the samples are 1.552 eV and 1.602 eV for the MAPbI3 single crystal and thin film, 2.259 eV and 2.312 eV for the MAPbBr3 single crystal and thin film, and 3.059 eV and 3.070 eV for the MAPbCl3 single crystal and thin film, respectively. Furthermore, we show the corresponding absorption spectra determined by spectroscopic ellipsometry in Fig. 1b (the data employed here are from Refs. [43,62]). In addition, we also calculate the corresponding spontaneous emission spectra (the intrinsic PL spectrum excluding effects of reabsorption) at 300 K using the van-Roosbroeck Shockley relation [63]. The calculated intrinsic PL spectra are shown the dashed black curves in Fig. 1b, and they are very similar to the observed PL spectra of thin films. The small offset between the peak position of PL and absorption edge in all samples evidences that these samples exhibit almost no Stokes shift [28,34,53]. This means that a significant part of the PL spectrum overlaps with the strongly absorbing energy region 3
of the perovskite crystal. The common feature of the data in Fig. 1a is that the PL peak of each single crystal sample is redshifted with respect to the corresponding thin film PL peak. From band calculations, it is known that defect levels cannot be easily formed in the sub-gap region of perovskite semiconductors [64]. Indeed, such sub-gap energy levels are not formed as can be confirmed from the very steep onset of the absorption spectra [43,62]. Moreover, it has been reported that the PL spectrum and lifetime depend on the excitation-depth profile [48,49]. Consequently, we can consider the PL reabsorption by the single crystal itself as the origin of the PL redshift in the thick single-crystal samples. In the following we describe the relation between the absorption spectrum α(E) and the observed PL spectrum IPL(E) as a function of the photon energy E. By defining γspon(E) as the spontaneous
Fig. 1. (a) Steady-state PL spectra (solid curves) of the MAPbX3 single crystals at room temperature. The red, green, and blue curves correspond to MAPbI3, MAPbBr3, and MAPbCl3, respectively. For reference, the steady-state PL spectra of the corresponding thin film samples (dashed gray curves) are also shown. (b) Absorption spectra (solid curves) and spontaneous emission spectra (dashed black curves) of perovskites. The numerical data of absorption spectra for MAPbI3, MAPbBr3, and MAPbCl3 are taken from Refs. [43] and [62]. The spontaneous emission spectra are calculated from the absorption spectra data using the van Roosbroek Shockley relation. 4
emission spectrum, and n(z) as the density of excited carriers at depth z, IPL(E) can be represented by the following expression:
∝ d
(1)
Here, z describes the depth as measured from the sample surface, and L is the thickness of the sample. The exponent k is determined by the type of the radiative recombination process. In case of PL from free carriers (the bimolecular radiative recombination between electron and hole), n(z) corresponds to the free electron and hole concentration (they are assumed to be equal) and k = 2. In the case of excitonic luminescence, n(z) corresponds to the exciton concentration, because the electron and hole are bound each other and move together as an exciton, and thus k becomes 1. As perovskite semiconductors are direct-gap semiconductors, their absorption coefficients in the energy range above the band-gap are large, i.e., α > 104 cm−1, and thus light is strongly absorbed in this energy region (see Fig. 1; broken curves). On the other hand, in the energy region below the band gap, α exponentially decreases according to the Urbach law [65]. Therefore, the effect of PL reabsorption is more pronounced on the high-energy side of the PL spectrum. In samples with a large L, diffusion of carriers towards the deeper regions occurs. As can be confirmed from Eq. (1), if the carrier distribution n(z) is different, the influence of α on the PL spectrum changes too, even if the sample thicknesses would be the same. In other words, the dynamical change of carrier distribution n(z) due to carrier diffusion also directly influences the effect of PL reabsorption. In the following we investigate the further details of the influence of the dynamical change of n(z) on the PL spectra.
3. Photoluminescence dynamics of MAPbX3 single crystals In Fig. 2, we compare the time-resolved PL spectra of the MAPbI3, MAPbBr3, and MAPbCl3 single crystals. The upper panels show the PL spectra immediately after excitation (time delay 0 ns), the middle panels those at the time instants when the PL intensities reached 10% of the initial intensity, and the bottom panels show the PL spectra at the time instants when the PL intensities decayed to 1%. The delay times for the different spectra are provided in the figure. In each of the three single-crystal samples, the peak energy of the time-resolved PL spectrum immediately after excitation coincides with the PL peak energy of the corresponding thin film sample (see Fig. 1). In this experiment, we excite the carriers via one-photon excitation, i.e., the excitation photon energy E1 is larger than the band-gap energy. Therefore, carriers are excited in a region on the order of the penetration depth of the excitation light, which equals 1/α1 when we denote the absorption coefficient for the excitation light by α1. The carrier density profile under one-photon excitation, n1(z), can be described using α1:
5
=
(2)
Here, n0 is the carrier density that is generated at the sample surface, and it is proportional to α1 (n0 = α1P1/E1, P1 is photon flux of excitation light). For the time instant immediately after excitation, the distribution described in Eq. (2) is valid for both single crystal and thin film. Consequently, there is almost no observable difference in the reabsorption effect described by Eq. (1) and the PL peaks coincide. We can infer that the PL peaks of single crystal and thin film observed immediately after excitation coincide due to the identical profile of the photocarriers. On the other hand, the time-resolved spectra in Fig. 2 gradually redshift as the delay time is increased. As shown below, this can be explained by the combination of carrier diffusion and the reabsorption effect. The single-crystal sample has a significant extension along the depth direction, and therefore the excited carriers diffuse towards the deeper sample regions as time t proceeds. If we assume that the spot size of the excitation light is sufficiently large compared to the carrier diffusion length, we can ignore the effect of in-plane carrier diffusion and formulate a one-dimensional diffusion rate equation that only considers the depth direction of the sample:
Fig. 2. Time-resolved PL spectra of the MAPbX3 single crystals. The experimental data are shown in gray and the solid curves are eye guides; red corresponds to MAPbI3, green to MAPbBr3, and blue to MAPbCl3. The upper panels show the PL spectra immediately after excitation, the middle panels those at the times when the PL intensities reached 10% of the initial intensity, and the bottom panels present the PL spectra at the times when the PL intensities decayed to 1%. The corresponding delay times for these spectra are shown in the figure.
6
=
! !
− # − $% + '
(3)
Here, D is the ambipolar diffusion constant, τ is the carrier lifetime, B is the bimolecular recombination coefficient, and G is the carrier generation rate per unit volume. In most cases, Eq. (3) must be solved numerically. However, if we further assume the weak-excitation condition in which the intensity of the excitation light is sufficiently small, the higher-order term of n (Bn2) can be neglected. In this case, we can solve Eq. (3) analytically. Because the time-resolved measurements employ excitation by very short light pulses (pulse width on the order of 100 fs), we can set G = n1(z)δ(t) where δ(t) is the delta function. By assuming a sufficiently large sample thickness (L → ∞) and a single crystal without surface recombination (surface recombination velocity S = 0), the analytical solution reads: *
, ) = + ,, )
,, ) = %
-! ./*
0erfcx 67 √ ) −
(4)
√9:
; + erfcx 67 √ ) +
√9:
;<
(5)
Here, erfcx(x) is the scaled complementary error function, and ρ(z,t) describes the temporal change of the carrier distribution (it results in unity if spatially integrated). The more general analytical solution with respect to S is given in Ref. [66]. However, as the S in perovskite single crystals is very low [66], the assumption S = 0 is sufficiently accurate for the present purpose. As described by Eq. (5), due to the carrier diffusion, the center of the carrier distribution shifts towards the sample interior as time proceeds. This is accompanied by an increase in the influence of reabsorption as described in Eq. (1), and therefore the time-resolved PL spectra also redshift with time. It has been reported that the numerical solution of the diffusion rate equation and the calculated PL spectra including the reabsorption effect well agree with the experimental results [47,48]. The above model thus allows us to gain insights into the different physics of samples with different degrees of redshift. Next, we discuss the differences that arise between samples with different halogen atoms. We compare the bottom panels of Fig. 2, that is, the time-resolved PL spectra at the time instants where the PL intensity decayed to 1%. While a redshift by more than 50 meV is present in MAPbI3 and MAPbBr3 single crystals with respect to their respective peak positions at time delay t = 0 ns, the MAPbCl3 single crystal exhibits a small redshift of about 10 meV. This difference is caused by the differences in the PL lifetimes, which are explained in the following. In Fig. 3a we show the PL decay curves of the MAPbI3, MAPbBr3, and MAPbCl3 single crystals. The PL decay curves were obtained by integration over the whole measured spectral range. Among 7
these three materials, the PL lifetime of MAPbI3 is the longest while that of MAPbCl3 is the shortest. The PL lifetime of MAPbCl3 is relatively short, because the spontaneous emission rate is large in wide-gap semiconductors [67]. Additionally, MAPbCl3 exhibits excitonic PL even at room temperature [51], implying an enhanced recombination rate due to Coulomb interactions. This short lifetime suggests that all carriers recombine before they can diffuse over a significant long range. Therefore, the redshift observed in Fig. 2 for the time-resolved PL spectra of MAPbCl3 is smaller than those of the other two perovskite single crystals. The almost non-existent difference between the PL peak energies of the MAPbCl3 thin film and single crystal observed in Fig. 1 can be also explained by the much smaller redshift for this material. The relation between the extent of the redshift in the PL spectrum and the carrier lifetime can be confirmed from perovskite single crystals that are doped with Bi3+, because the carrier lifetime becomes shorter with higher Bi3+-doping concentrations [50]. In Fig. 3b, we show the time evolution of the PL peak redshift after excitation for six MAPbBr3 single crystals with different Bi3+-doping
Fig. 3. (a) PL decay curves obtained from the MAPbX3 single crystals. The red curve corresponds to MAPbI3, the green curve to MAPbBr3, and the blue curve to MAPbCl3. The PL decay curves were obtained by integration over the whole measured spectral range. The numerical data are taken from Ref. [47] for MAPbI3 and Ref. [48] for MAPbBr3. (b) Time dependence of the extent of the PL peak shift after excitation for MAPbBr3 single crystals doped with Bi3+. The Bi/Pb ratios given in the figure correspond to the molar ratios that were present in the starting materials for sample fabrication. The corresponding PL lifetimes are also shown in the parentheses. The broken curve is the simulation result from the diffusion rate equation. The panel (b) is adopted with permission from Ref. [50]. Copyright 2017 American Chemical Society. 8
concentrations (corresponding PL lifetimes are also shown in the parentheses) [50]. The Bi/Pb ratios given in the figure correspond to the molar ratios that were present in the starting materials for sample fabrication. According to Fig. 3b, the time dependence of the PL peak redshift of each sample follows the same decay curve, irrespective of the doping concentration. In other words, the data in Fig. 3b suggest that the diffusion constant of MAPbBr3 is independent of the Bi3+-doping concentration. The ambipolar diffusion constant of MAPbBr3 (D = 18 cm2/s [49]) has been estimated by time-resolved two-photon excitation PL microscopy. Based on the diffusion rate equation and the reabsorption effect, we can predict the time dependence of the PL peak redshift and the result is shown with the broken curve in Fig. 3b. The calculation result well reproduces the experimental data, indicating that the interpretation based on the diffusion rate equation and reabsorption effect is plausible. With the above, we were able to clarify the importance of the PL reabsorption effect and the time evolution of the carrier distribution for the PL dynamics in thick single crystals.
4. Photoluminescence spectra obtained from polycrystalline thin films The above observations of the PL of thick single crystals including effects of reabsorption as well as carrier diffusion are useful for the interpretation of the PL spectra obtained from thin films, which usually contain grains of different sizes. The size of the grains and the film morphology strongly depend on the fabrication conditions, and it is well-known that the PL spectrum depends on the grain size distribution in the thin film [39,40]. Various effects such as PL quenching at the grain boundaries have been considered [68], but the general dependence of the PL peak position on the grain size has been rarely discussed. The steady-state PL spectra of MAPbI3 thin films with different averaged grain sizes (0.20, 0.55, and 0.81 µm) are shown in Fig. 4a. The averaged grain sizes were determined from scanning electron microscopy images of the sample surfaces. For reference, we also plot the steady-state PL spectrum obtained from a bulk single crystal with a thickness of 1.5 mm in the bottom panel of Fig. 4a [34]. It is evident that the PL peak energy redshifts as the grain size increases. The grain size dependence of the PL peak energy including the experimental results of other research groups is shown in Fig. 4b. The grain sizes in these thin film samples are larger than 200 nm, and as such much larger than the exciton Bohr radius in MAPbI3 (aB = 2.2 nm [69]). Therefore, the differences in the PL peak energies cannot be explained by quantum size effects. Instead, we propose that this effect can be explained by the PL reabsorption in large crystallites, i.e., the model that has been presented in the previous section. This is plausible, because it can be considered that the thin film thickness L (which roughly equals the average grain size) causes differences in the spatial distributions of the excited carriers and in the extents of the redshift. In the steady-state PL measurements, the light used for excitation is a continuous-wave laser. In this case, the term on the left side of the diffusion rate equation Eq. (3) is zero, and we solve for G = 9
n1(z)/τ. We also consider the following boundary conditions:
=
=0
(6)
? = 0
(7)
=
The condition of Eq. (6) means that the surface recombination velocity at the front of sample is zero. This is valid for high quality perovskite layer. On the other hand, Eq. (7) corresponds to the case where all of the carriers approached to the back surface are extracted to the outside or recombined. By considering the weak-excitation condition and the above boundary condition, the analytical solution of Eq. (3) as a function of the film thickness L becomes:
=
√:# @ A6
BCB ;DE CF B G A6 ;E CF- G A6 ; √/+ √/+ √/+ ! B 6H √:#I ; G A6 ; √/+
(8)
We note that in the absence of diffusion (D = 0), Eq. (8) becomes Eq. (2). If we define the carrier diffusion length LD as the mean-square displacement of the carriers, the LD in a three-dimensional
Fig. 4. (a) Dependence of PL spectra of MAPbI3 thin films on the grain size. The averaged grain sizes were determined from scanning electron microscopy images of the sample surfaces and are shown on the right upper side of each spectrum. We note that the spectrum in the bottom panel is that observed from a bulk single crystal. (b) Dependence of the PL peak energy on the sample thickness assumed to be the same size as the grain size. The red data are that of thin films [39], the yellow data that of a bulk single crystal [34], and the green data are those of thin films in another previous work [40]. The blue solid line is the calculation result from the reabsorption 10
material can be expressed in terms of the diffusion constant D and the carrier lifetime τ [70]. By assigning values to the absorption coefficient α and the diffusion length LD, we can calculate the density of the excited carriers as a function of the film thickness L from Eq. (8). Furthermore, by combining the results with Eq. (1) we can calculate the PL spectrum and the PL peak energy as a function of the film thickness L. The calculated dependence of the PL peak energy on L for the condition α = α1 (the absorption coefficient α1 for photons with E1 = 1.8 eV is 2.4 × 104 cm−1 [43]) and LD = 178 µm (the value obtained from the single-crystal sample [34]) is shown in Fig. 4b with the solid blue curve. The calculated curve shows a good overall agreement with previous experimental results [34,39]. In contrast, a part of the experimentally obtained PL peak positions is located at energies below the calculation result [39]. One possibility to explain the redshift is the light trapping effect [71]. Here, the band-gap luminescence is trapped inside the perovskite layer due to light total internal reflection, and thus the effective layer thickness is increased. This effect is exploited, for example, in thin film solar cells based on crystalline silicon (Si); a special surface texture is fabricated in order to confine sunlight inside the Si layer to gain a larger effective sample thickness [72]. If such a light trapping effect efficiently occurs for the perovskite’s band-edge luminescence due to the sample structure (e.g., the shape of grains and the film morphology), the PL reabsorption effect becomes larger and a more redshifted PL spectrum can be observed. From the above considerations we can understand that the actual experimental results also contain influences from the sample quality and morphology. However, we also clarified that the dependence of the PL peak energy on the grain size (which roughly equals the film thickness) can be well explained with the spatial distribution of the excited carriers and the effect of PL reabsorption. The differences between theoretical prediction and experiment enable a more accurate discussion of the sample quality. By accurately characterizing the effect of reabsorption in thick single crystal samples, we were able to arrive at a very clear picture of the effects that influence the PL spectra of thin films.
5. Conclusions In this review, we provided a summary on the PL dynamics of lead halide perovskites with emphasis on the details of the PL reabsorption effect. First, we compared the steady-state PL spectra and absorption spectra of MAPbX3 (X=I, Br, Cl) thick single crystals and thin films, and showed that there is almost no energy shift between the PL peak and the absorption edge of each material. Then, regarding the redshift of these steady-state spectra with respect to those of thin film samples, we pointed out that this is caused by PL reabsorption. Using time-resolved PL spectrum measurements, we showed that the PL peaks of thin films and single crystals immediately after excitation coincide, and that the single crystal’s PL spectrum redshifts with time. We were able to explain this by the combination of the PL reabsorption effect and the temporal change in the distribution of the excited carriers due to diffusion. Furthermore, from the comparison of samples doped with Bi3+, we were 11
able to show the correlation between the extent of the PL redshift and the carrier lifetime (carrier diffusion length). Finally, we modelled the dependence of the PL spectrum on the film thickness by combining the carrier distribution and the reabsorption effect, and we explained the grain size dependence of the PL spectra observed from thin film samples. The model of the PL reabsorption dynamics in the perovskite semiconductors presented in this review should be useful for the realization of perovskite-based optical devices with higher efficiencies.
Acknowledgments The authors thank their colleagues for help with the experiments and fruitful discussions. Part of this work was supported by JST-CREST (Grant No. JPMJCR16N3).
Notes The authors declare no competing financial interests.
References [1] A. Kojima, K. Teshima, Y. Shirai, T. Miyasaka, J. Am. Chem. Soc. 131 (2009) 6050–6051. https://doi.org/10.1021/ja809598r [2] C. Wehrenfennig, G. E. Eperon, M. B. Johnston, H. J. Snaith, L. M. Herz, Adv. Mater. 26 (2014) 1584–1589. https://doi.org/10.1002/adma.201305172 [3] S. D. Stranks, G. E. Eperon, G. Grancini, C. Menelaou, M. J. P. Alcocer, T. Leijtens, L. M. Herz, A. Petrozza, H. J. Snaith, Science 342 (2013) 341–344. https://doi.org/10.1126/science.1243982 [4] G. Xing, N. Mathews, S. Sun, S. S. Lim, Y. M. Lam, M. Grätzel, S. Mhaisalkar, T. C. Sum, Science 342 (2013) 344–347. https://doi.org/10.1126/science.1243167 [5] D. Shi, V. Adinolfi, R. Comin, M. Yuan, E. Alarousu, A. Buin, Y. Chen, S. Hoogland, A. Rothenberger, K. Katsiev, Y. Losovyj, X. Zhang, P. A. Dowben, O. F. Mohammed, E. H. Sargent, O. M. Bakr, Science 347 (2015) 519–522. https://doi.org/10.1126/science.aaa2725 [6] Q. Dong, Y. Fang, Y. Shao, P. Mulligan, J. Qiu, L. Cao, J. Huang, Science 347 (2015) 967–970. https://doi.org/10.1126/science.aaa5760 [7] Y. Yamada, T. Nakamura, M. Endo, A. Wakamiya, Y. Kanemitsu, J. Am. Chem. Soc. 136 (2014) 11610–11613. https://doi.org/10.1021/ja506624n [8] Y. Yamada, T. Nakamura, M. Endo, A. Wakamiya, Y. Kanemitsu, Appl. Phys. Express 7 (2014) 032302. https://doi.org/10.7567/APEX.7.032302 [9] S. D. Wolf, J. Holovsky, S.-J. Moon, B. Niesen, M. Ledinsky, F.-J. Haug, J.-H. Yum, C. Ballif, J. Phys. Chem. Lett. 5 (2014) 1035–1039. https://doi.org/10.1021/jz500279b [10] T. Umebayashi, K. Asai, T. Kondo, A. Nakao, Phys. Rev. B 67 (2003) 155405. https://doi.org/10.1103/PhysRevB.67.155405 12
[11] J. Even, L. Pedesseau, C. Katan, M. Kepenekian, J.-S. Lauret, D. Sapori, E. Deleporte, J. Phys. Chem. C 119 (2015) 10161–10177. https://doi.org/10.1021/acs.jpcc.5b00695 [12] G. Giorgi, J. Fujisawa, H. Segawa, K. Yamashita, J. Phys. Chem. Lett. 4 (2013) 4123–4126. https://doi.org/10.1021/jz4023865 [13] K. L. Chopra, P. D. Paulson, V. Dutta, Prog. Photovolt: Res. Appl. 12 (2004) 69–92. https://doi.org/10.1002/pip.541 [14] M. Saliba, T. Matsui, K. Domanski, J.-Y. Seo, A. Ummadisingu, S. M. Zakeeruddin, J.-P. Correa-Baena, W. R. Tress, A. Abate, A. Hagfeldt, M. Grätzel, Science 354 (2016) 206–209. https://doi.org/10.1126/science.aah5557 [15] J. H. Im, C. R. Lee, J. W. Lee, S. W. Park, N. G. Park, Nanoscale 3 (2011) 4088–4093. https://doi.org/10.1039/c1nr10867k [16] M.
Liu,
M.
B.
Johnston,
H.
J.
Snaith,
Nature
501
(2013)
395–398.
https://doi.org/10.1038/nature12509 [17] J. Burschka, N. Pellet, S.-J. Moon, R. Humphry-Baker, P. Gao, M. K. Nazeeruddin, M. Grätzel, Nature 499 (2013) 316–319. https://doi.org/10.1038/nature12340 [18] N. J. Jeon, J. H. Noh, W. S. Yang, Y. C. Kim, S. Ryu, J. Seo, S. I. Seok, Nature 517 (2015) 476– 480. https://doi.org/10.1038/nature14133 [19] W. S. Yang, J. H. Noh, N. J. Jeon, Y. C. Kim, S. Ryu, J. Seo, S. I. Seok, Science 348 (2015) 1234–1237. https://doi.org/10.1126/science.aaa9272 [20] C. C. Stoumpos, C. D. Malliakas, M. G. Kanatzidis, Inorg. Chem. 52 (2013) 9019–9038. https://doi.org/10.1021/ic401215x [21] N. Pellet, P. Gao, G. Gregori, T.-Y. Yang, M. K. Nazeeruddin, J. Maier, M. Grätzel, Angew. Chem. Int. Ed. 53 (2014) 3151–3157. https://doi.org/10.1002/anie.201309361 [22] N. K. Noel, S. D. Stranks, A. Abate, C. Wehrenfennig, S. Guarnera, A.-A. Haghighirad, A. Sadhanala, G. E. Eperon, S. K. Pathak, M. B. Johnston, A. Petrozza, L. M. Herz, H. J. Snaith, Energy Environ. Sci. 7 (2014) 3061–3068. https://doi.org/10.1039/c4ee01076k [23] G. E. Eperon, S. D. Stranks, C. Menelaou, M. B. Johnston, L. M. Herz, H. J. Snaith, Energy Environ. Sci. 7 (2014) 982–988. https://doi.org/10.1039/c3ee43822h [24] E. T. Hoke, D. J. Slotcavage, E. R. Dohner, A. R. Bowring, H. I. Karunadasa, M. D. McGehee, Chem. Sci. 6 (2015) 613–617. https://doi.org/10.1039/c4sc03141e [25] R. Comin, G. Walters, E. S. Thibau, O. Voznyy, Z.-H. Lu, E. H. Sargent, J. Mater. Chem. C 3 (2015) 8839–8843. https://doi.org/10.1039/c5tc01718a [26] A. Sadhanala, S. Ahmad, B. Zhao, N. Giesbrecht, P. M. Pearce, F. Deschler, R. L. Z. Hoye, K. C. Gödel, T. Bein, P. Docampo, S. E. Dutton, M. F. L. D. Volder, R. H. Friend, Nano Lett. 15 (2015) 6095–6101. https://doi.org/10.1021/acs.nanolett.5b02369
13
[27] Z. Xiao, R. A. Kerner, L. Zhao, N. L. Tran, K. M. Lee, T.-W. Koh, G. D. Scholes, B. P. Rand, Nat. Photon. 11 (2017) 108–115. https://doi.org/10.1038/nphoton.2016.269 [28] Y.
Kanemitsu,
T.
Handa,
Jpn.
J.
Appl.
Phys.
57
(2018)
090101.
https://doi.org/10.7567/JJAP.57.090101 [29] Z.-K. Tan, R. S. Moghaddam, M. L. Lai, P. Docampo, R. Higler, F. Deschler, M. Price, A. Sadhanala, L. M. Pazos, D. Credgington, F. Hanusch, T. Bein, H. J. Snaith, R. H. Friend, Nat. Nanotechnol. 9 (2014) 687–692. https://doi.org/10.1038/nnano.2014.149 [30] G. Xing, N. Mathews, S. S. Lim, N. Yantara, X. Liu, D. Sabba, M. Grätzel, S. Mhaisalkar, T. C. Sum, Nat. Mater. 13 (2014) 476–480. https://doi.org/10.1038/nmat3911 [31] Y. Cao, N. Wang, H. Tian, J. Guo, Y. Wei, H. Chen, Y. Miao, W. Zou, K. Pan, Y. He, H. Cao, Y. Ke, M. Xu, Y. Wang, M. Yang, K. Du, Z. Fu, D. Kong, D. Dai, Y. Jin, G. Li, H. Li, Q. Peng, J. Wang, W. Huang, Nature 562 (2018) 249–253. https://doi.org/10.1038/s41586-018-0576-2 [32] K. Lin, J. Xing, L. N. Quan, F. P. C. de Arquer, X. Gong, J. Lu, L. Xie, W. Zhao, D. Zhang, C. Yan, W. Li, X. Liu, Y. Lu, J. Kirman, E. H. Sargent, Q. Xiong, Z. Wei, Nature 562 (2018) 245– 248. https://doi.org/10.1038/s41586-018-0575-3 [33] S.-T.
Ha,
C.
Shen,
J.
Zhang,
Q.
Xiong,
Nat.
Photon.
10
(2016)
115–121.
https://doi.org/10.1038/nphoton.2015.243 [34] T. Yamada, T. Aharen, Y. Kanemitsu, Phys. Rev. Materials 3 (2019) 024601. https://doi.org/10.1103/PhysRevMaterials.3.024601 [35] H. Tahara, T. Aharen, A. Wakamiya, Y. Kanemitsu, Adv. Opt. Mater. 6 (2018) 1701366. https://doi.org/10.1002/adom.201701366 [36] H. Hirori, P. Xia, Y. Shinohara, T. Otobe, Y. Sanari, H. Tahara, N. Ishii, J. Itatani, K. L. Ishikawa, T. Aharen, M. Ozaki, A. Wakamiya, Y. Kanemitsu, APL Mater. 7 (2019) 041107. https://doi.org/10.1063/1.5090935 [37] K. Ohara, T. Yamada, H. Tahara, T. Aharen, H. Hirori, H. Suzuura, and Y. Kanemitsu, Phys. Rev. Materials 3 (2019) 111601(R), https://doi.org/10.1103/PhysRevMaterials.3.111601 [38] L. Martiradonna, Nat. Mater. 17 (2018) 377–384. https://doi.org/10.1038/s41563-018-0069-6 [39] Y. Kanemitsu, J. Mater. Chem. C 5 (2017) 3427–3437. https://doi.org/10.1039/c7tc00669a [40] V. D’Innocenzo, A. R. S. Kandada, M. De Bastiani, M. Gandini, A. Petrozza, J. Am. Chem. Soc. 136 (2014) 17730–17733. https://doi.org/10.1021/ja511198f [41] X. Wu, M. T. Trinh, D. Niesner, H. Zhu, Z. Norman, J. S. Owen, O. Yaffe, B. J. Kudisch, X.-Y. Zhu, J. Am. Chem. Soc. 137 (2015) 2089–2096. https://doi.org/10.1021/ja512833n [42] Y.
Tian,
I.
G.
Scheblykin,
J.
Phys.
https://doi.org/10.1021/acs.jpclett.5b01406
14
Chem.
Lett.
6
(2015)
3466–3470.
[43] M. Shirayama, H. Kadowaki, T. Miyadera, T. Sugita, M. Tamakoshi, M. Kato, T. Fujiseki, D. Murata, S. Hara, T. N. Murakami, S. Fujimoto, M. Chikamatsu, H. Fujiwara, Phys. Rev. Applied 5 (2016) 014012. https://doi.org/10.1103/PhysRevApplied.5.014012 [44] O. D. Miller, E. Yablonovitch, S. R. Kurtz, IEEE J. Photovoltaics 2 (2012) 303–311. https://doi.org/10.1109/JPHOTOV.2012.2198434 [45] L. Zhu, T. Mochizuki, M. Yoshita, S. Chen, C. Kim, H. Akiyama, Y. Kanemitsu, Opt. Express 24 (2016) A740–A751. https://doi.org/10.1364/OE.24.00A740 [46] T. Handa, D. M. Tex, A. Shimazaki, A. Wakamiya, Y. Kanemitsu, J. Phys. Chem. Lett. 8 (2017) 954–960. https://doi.org/10.1021/acs.jpclett.6b02847 [47] Y. Yamada, T. Yamada, L. Q. Phuong, N. Maruyama, H Nishimura, A. Wakamiya, Y. Murata, Y. Kanemitsu, J. Am. Chem. Soc. 137 (2015) 10456–10459. https://doi.org/10.1021/jacs.5b04503 [48] T. Yamada, Y. Yamada, H. Nishimura, Y. Nakaike, A. Wakamiya, Y. Murata, Y. Kanemitsu, Adv. Electron. Mater. 2 (2016) 1500290. https://doi.org/10.1002/aelm.201500290 [49] T. Yamada, Y. Yamada, Y. Nakaike, A. Wakamiya, Y. Kanemitsu, Phys. Rev. Applied 7 (2017) 014001. https://doi.org/10.1103/PhysRevApplied.7.014001 [50] Y. Yamada, M. Hoyano, R. Akashi, K. Oto, Y. Kanemitsu, J. Phys. Chem. Lett. 8 (2017) 5798– 5803. https://doi.org/10.1021/acs.jpclett.7b02508 [51] T.
Yamada,
T.
Aharen,
Y.
Kanemitsu,
Phys.
Rev.
Lett.
120
(2018)
057404.
https://doi.org/10.1103/PhysRevLett.120.057404 [52] K. Kojima, K. Ikemura, K. Matumori, Y. Yamada, Y. Kanemitsu, S. F. Chichibu, APL Mater. 7 (2019) 071116, https://doi.org/10.1063/1.5110652 [53] Y. Yamada, T. Yamada, Y. Kanemitsu, Bull. Chem. Soc. Jpn. 90 (2017) 1129–1140. https://doi.org/10.1246/bcsj.20170208 [54] T.
Kirchartz,
F.
Staub,
U.
Rau,
ACS
Energy
Lett.
14
(2016)
731–739.
https://doi.org/10.1021/acsenergylett.6b00223 [55] L. M. Pazos-Outón, M. Szumilo, R. Lamboll, J. M. Richter, M. Crespo-Quesada, M. Abdi-Jalebi, H. J. Beeson, M. Vrućinić, M. Alsari, H. J. Snaith, B. Ehrler, R. H. Friend, F. Deschler, Science 351 (2016) 1430–1433. https://doi.org/10.1126/science.aaf1168 [56] Y.
Fang,
H.
Wei,
Q.
Dong,
J.
Huang,
Nat.
Commun.
8
(2017)
14417.
https://doi.org/10.1038/ncomms14417 [57] L. Zhu, T. Mochizuki, M. Yoshita, S. Chen, C. Kim, H. Akiyama, Y. Kanemitsu, Opt. Express 24 (2016) A740–A751. https://doi.org/10.1364/OE.24.00A740 [58] L. M. Pazos-Outón, T. P. Xiao, and E. Yablonovitch, J. Phys. Chem. Lett. 97 (2018) 1703–1711, https://doi.org/10.1021/acs.jpclett.7b03054 [59] I. L. Braly, D. W. deQuilettes, L. M. Pazos-Outón, S. Burke, M. E. Ziffer, D. S. Ginger, and H. W. Hillhouse, Nat. Photon. 12 (2018) 355–361, https://doi.org/10.1038/s41566-018-0154-z 15
[60] M. I. Saidaminov, A. L. Abdelhady, B. Murali, E. Alarousu, V. M. Burlakov, W. Peng, I. Dursun, L. Wang, Y. He, G. Maculan, A. Goriely, T. Wu, O. F. Mohammed, O. M. Bakr, Nat. Commun. 6 (2015) 7586. https://doi.org/10.1038/ncomms8586 [61] W.
Shockley,
W.
T.
Read,
Jr.,
Phys.
Rev.
87
(1952)
835–842.
https://doi.org/10.1103/PhysRev.87.835 [62] A. M. A. Leguy, P. Azarhoosh, M. I. Alonso, M. Campoy-Quiles, O. J. Weber, J. Yao, D. Bryant, M. T. Weller, J. Nelson, A. Walsh, M. van Schilfgaarde, P. R. F. Barnes, Nanoscale 8 (2016) 6317–6327. https://doi.org/10.1039/c5nr05435d [63] W.-J.
Yin,
T.
Shi,
Y.
Yan,
Appl.
Phys.
Lett.
104
(2014)
063903.
https://doi.org/10.1063/1.4864778 [64] W.
van
Roosbroeck
and
W.
Shockley,
Phys.
Rev.
94
(1954)
1558,
https://doi.org/10.1103/PhysRev.94.1558 [65] F. Urbach, Phys. Rev. 92 (1953) 1324. https://doi.org/10.1103/PhysRev.92.1324 [66] Y. Yang, Y. Yan, M. Yang, S. Choi, K. Zhu, J. M. Luther, M. C. Beard, Nat. Commun. 6 (2015) 7961. https://doi.org/10.1038/ncomms8961 [67] P. Y. Yu, M. Cardona, Fundamentals of semiconductors: physics and material properties, forth ed., Springer, Berlin, 2010. [68] D. W. deQuilettes, S. M. Vorpahl, S. D. Stranks, H. Nagaoka, G. E. Eperon, M. E. Ziffer, H. J. Snaith, D. S. Ginger, Science 348 (2015) 683–686. https://doi.org/10.1126/science.aaa5333 [69] K. Tanaka, T. Takahashi, T. Ban, T. Kondo, K. Uchida, N. Miura, Solid State Commun. 127, 619-623 (2003). [70] A. Einstein, Investigations on the Theory of the Brownian Movement, Dover Publications, New York, 1956. [71] E. Yablonovitch, G. D. Cody, IEEE Transactions on Electron Devices 29 (1982) 300–305. https://doi.org/10.1109/T-ED.1982.20700 [72] S.-B. Rim, S. Zhao, S. R. Scully, M. D. McGehee, P. Peumans, Appl. Phys. Lett. 91 (2007) 243501. https://doi.org/10.1063/1.2789677
16
Highlights Significant redshift of PL spectra is caused by PL reabsorption in bulk crystals. Dynamical PL shift is correlated with photocarrier diffusion length. Grain size dependence of PL spectrum is caused by PL reabsorption in thin films.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: