Trap-Limited Dynamics of Excited Carriers and Interpretation of the

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Trap-Limited Dynamics of Excited Carriers and Interpretation of the Photoluminescence Decay Kinetics in Metal Halide Perovskites Vladimir S. Chirvony, and Juan P. Martínez-Pastor J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01241 • Publication Date (Web): 14 Aug 2018 Downloaded from http://pubs.acs.org on August 15, 2018

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The Journal of Physical Chemistry Letters

Trap-Limited Dynamics of Excited Carriers and Interpretation of the Photoluminescence Decay Kinetics in Metal Halide Perovskites

Vladimir S. Chirvony*†‡ and Juan P. Martínez-Pastor‡

†

Instituto de Ciencia Molecular, and ‡Instituto de Ciencia de los Materiales,

Universidad de Valencia, c/Catedrático J. Beltrán, 2, Paterna 46980, Spain

ACS Paragon Plus Environment

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Abstract. Interpretation of the photoluminescence (PL) decay kinetics in metal halide perovskites (MHPs) is extremely important for understanding the mechanisms and control of charge recombination in these promising photovoltaic and optoelectronic materials. In this work we give a review of current models describing the PL decay kinetics in MHP layers and nanocrystals with a particular attention to the interpretation of long-lived PL decay components (hundreds of nanoseconds microseconds). First, we analyze phenomenological photophysical models based on the rate equations, which describe the charge carrier recombination in MHP layers as an exclusively intrinsic bulk process. An important role of the carrier diffusion and nonradiative recombination on the layer surfaces is then discussed. A recently published approach is then analyzed, in the framework of which the observed longlived components of PL decay kinetics in MHP nanocrystals are described in terms of the delayed luminescence mechanism arising due to the processes of multiple trapping and de-trapping of carriers by shallow non-quenching traps. Possible origin of the shallow traps and perspectives to include the carrier trapping and de-trapping process in a model describing PL kinetics in MHP layers are discussed.


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Metal halide perovskites (MHPs) are now one of the most intensively studied and promising semiconductor materials for next generation high-efficiency solar cells fabricated by means of inexpensive low-temperature technologies. Over less than 10 years of intensive research, the efficiency of solar energy conversion in lead halide perovskite solar cells has increased from 3.8% in 2009 to more than 22% at present.1-8 Besides, a high photoluminescence (PL) quantum yield of approximately 30% has been reported for organic-inorganic lead halide perovskites.9-11 MHPs proved also to be an excellent material to achieve low-threshold optical gain/lasing.12-15 Besides, electroluminescence with external quantum efficiency of above 12% was demonstrated by MHP-based light emitting diodes (LEDs).10,16-19 However, despite the very rapid progress in the performance of MHP-based photovoltaic and lightemitting devices, an understanding of the fundamental photophysics enabling that progress “is only just emerging”.20,21 This is mainly due to the fact that photogenerated species participate in numerous complex processes (diffusion, bulk trapping and de-trapping, radiative and nonradiative bulk recombination, surface recombination) occurring at similar time scales.22 As a result, PL decay curves detected after pulsed excitation of MHPs can easily be misinterpreted.23,24 In particular, in the case of polycrystalline MHP layers, the PL kinetics can be mainly due to nonradiative recombination on the semiconductor surface22,25,26 and not due to bulk recombination processes, as is very often a priori assumed in the literature. Therefore, in a general case, only a preliminary analysis of the PL decay kinetics of bulk MHPs in the framework of the carrier diffusion model can result in its correct interpretation and distinguishing the diffusion/surface recombination and bulk recombination processes.22,25,26 The present work is devoted to an analysis of the physical models available in


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the literature, which are intended to give an interpretation of the PL kinetics in MHPs and, as far as possible, to determine the quantitative characteristics of charge recombination processes both in the bulk of the semiconductor and on its surface. One of the main tasks of these models is to find an explanation for the very long lifetimes

τ of photogenerated charges in MHPs and associated large diffusion lengths LD (τ and LD are related by the well known expression = √ , where D is diffusion coefficient).27-30 As is generally accepted in the literature, it is the large values of τ and LD in perovskites (typical values of ~ 200 ns and ~ 3 µm for polycrystalline31 and ~ 4 µs and ~ 20 µm for monocrystalline32 samples) that are responsible for the high efficiency of the solar cells produced on their basis. Such long carrier recombination lifetimes are also favorable for larger VOC, because it enables a higher carrier concentration (or a larger quasi-Fermi level splitting) for solar cells under illumination.33

Until now, there is still no common opinion about the reasons for the very long lifetimes of photogenerated charges in LHPs.

Until now the most used models for an analysis of the PL decay kinetics in MHPs are those, in which only bulk recombination processes (radiative and nonradiative recombination, trapping) are taken into account, while the possible diffusion of charges and their nonradiative recombination on MHP surfaces are not considered.34-36 Strictly speaking, it is more logical to apply such models to MHP layers with well passivated surfaces. Nevertheless, despite the data that the PL kinetics in MHP can be completely determined by the dynamics of carrier diffusion and nonradiative recombination on surfaces,22,25,26 these phenomenological models proved useful for evaluation of an important intrinsic parameter of MHP materials


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such as the bimolecular radiative recombination constant.34-36 Below we will analyze these models in detail. Next, we will analyze the available in the literature interpretations of the PL decay kinetics in MHP nanocrystals (NCs). Particular attention will be paid to the work, where well-passivated CH3NH3PbBr3 NCs were investigated, in which nonradiative surface recombination of charges was absent.37 A study of such a system, which is an ideal to investigate the bulk recombination processes on the basis of the PL decay interpretation, enabled the authors to interpret the experimentally observed long (hundreds to thousands of nanoseconds) PL decay kinetics as a result of multiple trapping and de-trapping of charges by shallow traps (the delayed luminescence model).37 Finally, a possible origin of the shallow traps and the perspectives to apply the model for explanation of the long-lived PL kinetics in MHP layers are discussed.

Figure 1. Time-resolved PL kinetics for a thin film of CH3NH3PbI3 photoexcited with various pulse fluences. Black, blue, and gray are with excitation densities equivalent to ∼1015, ∼1016, and ∼1017 excitations per cm3, respectively. The schematics represent the dominant recombination regime in each case (monomolecular at low fluence and bimolecular at high). Adapted with permission from the American Chemical Society.38 As indicated above, until now the PL decay kinetics in MHP are often


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described in the framework of the phenomenological schemes proposed by Yamada et al.34 and Stranks et al.35 In these schemes, charge carrier diffusion over the layer thickness and their nonradiative recombination on the layer surfaces are not considered, and the observed PL kinetics are explained by the processes of bulk radiative and nonradiative recombination with participation of deep traps. A generic kinetic model was proposed accounting for exciton formation, dissociation into free charges, and trapping of free electrons by solving a set of three coupled rate equations.35 The equations include the rates of exciton formation, dissociation and radiative decay, the free electrons-hole recombination rate, and the rates of trap population and depopulation as parameters. In this model: (i) the traps are assumed to be deep enough to inhibit thermal de-trapping to the conduction band, and (ii) trap depopulation, which is a non-radiative process, takes place on a time scale of milliseconds to seconds, that is at much longer time scale than that of the PL decay. By iterative and global fitting of the model to the experimental PL decays and PLQY vs excitation intensity data, the values for the rates of the trap population, trap depopulation, free electron-hole recombination, and the trap concentration were evaluated as 2×10-10 cm3 s-1, 8×10-12 cm3 s-1, ~10-10 cm3 s-1, and 2.5×1016 cm-3, respectively. Figure 1 shows the kinetic modeling curves together with experimental PL transients. The results of this simulation35 can be summarized qualitatively as follows (see schematics in Fig. 1). At low-intensity excitation (nNT, the photodoping effect is insignificant, and the concentrations of photoexcited electrons and holes are practically equal to each other that ensures bimolecular (second order) character of charge recombination. The important peculiarity of the model35 (and its more generalized version36) is in a specific role the traps play in the formation of the PL decay kinetics: the trap population process efficiently participates in the formation of fast components of the PL decay, whereas the trap de-population kinetics is very slow and do not contribute at all into the PL decay kinetics. Instead, The PL decay kinetics is formed by a minority carrier recombination (at low carrier concentrations) or by the radiative bimolecular recombination (at high carrier concentrations). In ref. 35, the dynamics of charge carrier recombination was studied on the basis of an analysis of the PL decay kinetics. To find out how universal are the parameters obtained with that model, in another work the MHP samples were examined by two methods, time-resolved microwave conductivity and time-resolved PL.36 As a result, it was shown that the two sets of measurements are satisfactorily described using a single set of kinetic parameters for each type of the samples used (thin planar films of CH3NH3PbI3-xClx and CH3NH3PbI3 as well as their mesostructured analogues were investigated). The kinetical scheme proposed by the authors was analogous to that described earlier,35 with exclusion of the exciton-type recombination and additionally an unintentional doping of the perovskites that can take place along with the photodoping.36 Similarly to ref. 35, three recombination channels are considered: (i) bimolecular-type radiative recombination of oppositesign charges being at approximately equal concentrations, (ii) radiative recombination


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of quasi-monomeolecular type of opposite-sign charges under conditions when one type of charges dominates, and (iii) fast trapping of charges with their further (and much slower than the PL decay) nonradiative recombination. As the analysis shows,36 practically any shape of the experimentally observed kinetics can be qualitatively reproduced by changing contributions of the three mechanisms. Independently, a similar charge recombination scheme was proposed for PL decay modeling in planar polycrystalline CH3NH3PbI3 perovskite layers.34 The scheme is described by the rate equation (2) including the monomoleculr trapping (the rate constant k1, non-radiative process) and the bimoleculr electron-hole radiative recombination (the radiative recombination coefficient k2). The two recombination processes are in competition to deactivate the photogenerated carriers of the concentration n:

= − −

(1)

On the basis of the observation that the PL intensity just after the excitation shows a quadratic dependence on the excitation intensity, the authors concluded that the origin of the PL is a radiative two-carrier (bimolecular) recombination process involving electrons and holes, but not excitons.34 Following the model,34 the dominant lightemission mechanism at low excitation intensities is the recombination of photoexcited carriers with carriers of the opposite sign appeared as a result of unintentional doping (instead of photodoping in the previous model35). Similarly to ref. 35, the authors consider two regimes of carrier recombination, at high and low excitation intensities, governed by two different mechanisms.34 After global fitting of the PL and transient absorption dynamics, the model well reproduces the experimental results. From the fits, the values k1 = 1.8 × 107 s-1 and k2 = 1.7 × 10-10 s-1 cm3 were obtained. As the authors note, the radiative recombination coefficient k2 for CH3NH3PbI3 perovskite is


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comparable to that in typical direct-gap semiconductors (e.g., for GaAs the k2 value is found to be 3.7 × 10-10 s-1 cm3).39 In general, the models34-36 are similar to each other ideologically suggesting that only deep traps are available in perovskites, which quench irreversibly the excited carriers. The main difference between them is that the process of the trap population decay is very slow and does not participate in formation of the PL decay kinetics in one model,35,36 whereas in another model the process of nonradiative recombination through the traps is directly included in the rate equation through the rate constant k134 To date, a large amount of information has been accumulated in the literature about the values of the first- and second-order recombination rate constants k1 and k2 obtained for MHPs using various time-resolved spectroscopic methods (see, for example, a recent review40). For both MHP polycrystalline films and single crystals the rate constant k2 is typically reported to be in the range of 10−11–10−9 cm3 s−1 at room temperature. In general, the k2 values in MHPs are similar to those known for such typical direct-gap semiconductor as GaAs (3.7·10-10 cm3 s-1,39=38old 7.2·10-10 cm3

s-141), although the spread of values, which were obtained even for samples from the same laboratory,21 is very large and spans almost two orders of magnitude.40=39old Significantly more unexpected for MHPs are the very small values of the monomolecular recombination rate constant k1: in most polycrystalline CH3NH3PbI3 perovskite films it is between 107 and 106 s-1, and in passivated polycrystalline films and single crystals it can reach 105 s-1 or less that corresponds to decay times of 10 µs or longer.40 Such long PL lifetimes imply that possible quenching impurities (dopants) are at very low concentrations. This is usually possible for specially prepared ultrapure and “surface-free” semiconductors,39 but is rather unexpected for a semiconductor fabricated from a solution at room temperature without any further


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purification treatment. Thus, the phenomenological models, which describe the PL kinetics in MHP layers as a result of exclusively bulk recombination processes, well reproduce the shapes of the experimentally measured decay kinetics at both low and high excitation intensities. 34-36 Moreover, at sufficiently intensive excitation they enable to determine correctly the bimolecular recombination constant k2 that evidences in favor of their rightness. On the other hand, there is another point of view in the literature concerning the origin of the PL decay kinetics: it is recently demonstrated that the PL kinetics in polycrystalline CH3NH3PbI3 perovskite layers is determined by the dynamics of the carrier diffusion and the nonradiative recombination on the surfaces of a layer (or grains).22,25,26 The dominating role of the diffusion dynamics coupled with the surface recombination in formation of the PL decay kinetics in MHPs is confirmed by such commonly known fact as the surface “passivation” effect, when the PL lifetime can be increased up to about 10 times due to a deposition of organic “passivating” molecules, such as TOPO (see Figure 2), on top of one surface of the perovskite layer.

Figure 2. Time-resolved PL decay traces of control (black) and trioctylphosphine oxide (TOPO, red) treated films on glass. Adapted with permission from the American Chemical Society.42


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Up to 10-fold increase of the PL lifetime after passivation of a surface of MHP layers inambiguously evidences that the contribution of bulk recombination processes into the PL kinetics is minor.

At first glance, these two ideologies contradict each other. We believe, however, that this contradiction can be eliminated if we suggest that, indeed, at sufficiently low excitation concentrations, at which passivation effect is usually studied,42 the PL kinetics is determined by the dynamics of the carrier diffusion and recombination on the surfaces, but with an increase of the carrier concentration n, the radiative bimolecular recombination in bulk MHP (which is proportional to n2) becomes the predominant mechanism of recombination. This is probably the reason why phenomenological models, which take into account only bulk recombination prosesses and neglect surface recombination, correctly evaluate the k2 values for unpassivated MHP layers. Formally speaking, the unintentional or photo-doping of MHPs was considered in the models34-36

first of all to have a possibiliity to explain the

experimentally observed long (hundreds of nanoseconds) PL kinetics in MHP layers. The question arises: is it really only doping that can explain the long-lived luminescence in these materials? As suggested by the authors of the recently published work,37 there is another mechanism, besides doping, that can significantly lengthen the PL kinetics in MHPs. This mechanism is the multiple trapping and detrapping of carriers in shallow nonquenching traps, which leads to the formation of the delayed luminescence. The delayed luminescence mechanism can be easily recognized in case of MHP nanocrystals (NCs) with well passivated surface, for which the quantum yield of photoluminescence is close to unity.37


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There are numerous publications devoted to synthesis and optical properties of MHP NCs in which the PL decay kinetics are measured, but only in a few of them photophysical analysis of charge carrier recombination processes is carried out.37,43-46. The range of experimentally measured PL lifetimes for MHP NCs extends, even for formally identical structures, from several nanoseconds45 to microseconds.37 The PL kinetics are difficult for unambiguous photophysical interpretation, because PL quantum yield in these systems is usually much less than 1.0. As an example, we present below results of two typical investigations of photophysical properties of colloidal CH3NH3PbBr3 nanocrystals.43,44 For example, in case of colloidal solutions of CH3NH3PbBr3 NCs strongly non-exponential PL decay kinetics was measured and modeled by a sum of three exponentials with time constants of 0.5 – 1 ns (the fast component), 4 - 7 ns (the middle component), and > 10 ns (the slow component).43 The authors claimed that the triexponential model provides the best fitting compared with other kinetic models such as stretched exponential decays. The slow component (

Trap-Limited Dynamics of Excited Carriers and Interpretation of the

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