Letter pubs.acs.org/JPCL
Comparison of Recombination Dynamics in CH3NH3PbBr3 and CH3NH3PbI3 Perovskite Films: Influence of Exciton Binding Energy Ye Yang, Mengjin Yang, Zhen Li, Ryan Crisp, Kai Zhu, and Matthew C. Beard* Chemistry and Nanoscience Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States S Supporting Information *
ABSTRACT: Understanding carrier recombination in semiconductors is a critical component when developing practical applications. Here we measure and compare the monomolecular, bimolecular, and trimolecular (Auger) recombination rate constants of CH3NH3PbBr3 and CH3NH3PbI3. The monomolecular and bimolecular recombination rate constants for both samples are limited by trap-assisted recombination. The bimolecular recombination rate constant for CH3NH3PbBr3 is ∼3.3 times larger than that for CH3NH3PbI3 and both are in line with that found for radiative recombination in other direct-gap semiconductors. The Auger recombination rate constant is 4 times larger in lead-bromide-based perovskite compared with lead-iodide-based perovskite and does not follow the reduced Auger rate when the bandgap increases. The increased Auger recombination rate, which is enhanced by Coulomb interactions, can be ascribed to the larger exciton binding energy, ∼40 meV, in CH3NH3PbBr3 compared with ∼13 meV in CH3NH3PbI3.
S
the relationship between the bleach magnitude and carrier density is determined. The bleach kinetics are recorded under various pump fluences and a global fitting procedure is used to simultaneously model the data. From the model we extract the rate constants of monomolecular, bimolecular, and trimolecular recombination. We find that the bi- and trimolecular recombination rate constants in MAPbBr3 are 3.3 and 4.0 times larger than those in MAPbI3, respectively, and the differences in the rate constants between the two perovskites is attributed to exciton binding energy. The fabrication of the MAPbBr3 and MAPbI3 thin films with thickness of 86 ± 11 and 332 ± 38 nm, respectively, is detailed in the Supporting Information. The film thickness was measured using a profiler (Dektak 8, Veeco). The absorption spectra of the samples (Figure 1) are determined from the reflection and transmission measurements (Figure S1). We find that for both MAPbBr3 and MAPbI3 the absorption spectra show a sharp raise near the bandgap, which is strikingly different from the square-root law of the free-carrier absorption and indicative of excitonic contribution according to the Elliott theory.20 A model based on Elliott’s formula (black dashed lines, Figure 1) reproduces the spectra very well, and the analysis is described in previous publications.21−23 From our model we are able to isolate contributions to the total absorption from exciton absorption and continuum absorption (Figure 1, blue and green dashed lines), and we extract the exciton binding energy (Rex) and bandgap (Eg), determined to be Rex = 40.3 ± 0.1 meV and Eg = 2.39 ± 0.01 eV for MAPbBr3
olution-processed lead halide perovskite semiconductors are being intensively studied for a variety of optoelectronic applications, such as, solar cells.1−7 After only a few years of effort the power conversion efficiency has improved to now exceed 20%,8−10 demonstrating the promise of these systems. In addition, these solution-processed semiconductor systems are being explored as photodetectors,11−14 lasers,15,16 and LEDs,17,18 and already excellent performance is being demonstrated. A fundamental understanding of their photophysical properties is desired to further direct their incorporation and development. Carrier recombination plays a key role that defines their ultimate performance. For instance, Shockley−Read−Hall (SRH) recombination usually determines the carrier lifetime at solar intensities and directly impacts carrier diffusion lengths under operating conditions for solar cells or photodetectors. Improving material quality can reduce the SRH and other defect-related recombination channels, leaving the fundamental recombination channels of radiative and Auger recombination to limit carrier lifetimes. Photon recycling strategies can further reduce the carrier loss due to radiative recombination, leaving only Auger recombination to limit carrier lifetimes.19 For high-injection applications, such as LEDs and lasing, bimolecular and trimolecular recombination begin to dominate even in the presence of defect related recombination. Compared with the rapid progress in device performance, fundamental studies of the various recombination mechanisms are lagging in these systems. Here we study and compare the recombination dynamics in CH3NH3PbBr3 (MAPbBr3) and CH3NH3PbI3 (MAPbI3) perovskite films under various initial carrier densities using transient absorption (TA) spectroscopy. The carrier dynamics can be measured by following the exciton bleach kinetics once © XXXX American Chemical Society
Received: October 13, 2015 Accepted: November 9, 2015
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Figure 1. Linear absorption spectra of MAPbBr3 and MAPbI3 thin films. The measured linear absorption spectra (red triangles) and the corresponding simulations (black lines) based on Elliott model for (A) MAPbBr3 and (B) MAPbI3. The blue and green dashed lines represent the excitonic and continuum contributions to the total absorption, respectively.
Figure 2. TA spectra of MAPbBr3 and MAPbI3 thin films. Pseudocolor images of the TA spectra for (A) MAPbBr3 and (B) MAPbI3 samples. The vertical and horizontal axes represent the pump−probe delay and probe photon energy, respectively. The color scale bars indicating the signal magnitude are also presented.
and Rex = 13.1 ± 0.1 meV and Eg = 1.64 ± 0.01 eV for MAPbI3. The error bars only reflect the fitting uncertainty. The exciton binding energy for both samples determined here is consistent with recent findings21,23,24 and significantly lower than previously reported values22,25−27 and that for nanoscale perovskites.28 Because of the small binding energy (Rex ≤ kBT) a large fraction of the electron−hole pairs, especially for MAPbI3, are free carriers rather than excitons at room temperature; however, the linear absorption below and above the bandgap is still modified by the Coulomb interaction according to the Elliot formulation.29 TA measurements were carried out for both samples using a broadband probe and monochromatic pump. The probe photon energy ranged from 1.5 to 2.8 eV and the pump photon energy is tuned to 2.5 and 2.1 eV for MAPbBr3 and MAPbI3, respectively. Figure 2 shows the pseudocolor images of the TA spectra of the samples. The pump−probe delay (vertical axis, logarithm scale) is varied up to 5 ns, and the probe photon energy range (horizontal axis) is truncated to emphasize the region of interest (near bandgap). The magnitudes of bleach and absorption are reflected by the intensities of red and blue, respectively. For both MAPbBr3 and MAPbI3, the spectra display a prominent bleach near the bandgap and a broad absorption above the bandgap, both of which decay as the delay increases. We notice that the peak position of the bleach (1.64 and 2.35 eV for MAPbBr3 and MAPbI3, respectively) coincides with the exciton peak
determined from their respective linear absorption and is interpreted as the bleach of excitonic absorption due to phasespace filling by free carriers and/or the presence of excitons.21,23 The broad photoinduced absorption above the bandgap is attributed to bandgap renormalization.21 In the TA spectra, the kinetics of bleach recovery and photoinduced absorption decay reflect the carrier recombination dynamics. To explore the carrier recombination dynamics, we conducted TA measurement under various pump fluences. Because the film thickness is smaller than the pump penetration depth, the initial carrier density (N0) is determined as the ratio of the absorbed photon flux to the film thickness. In the current study, N0 varies more than an order of magnitude, and within such a range the bleach amplitudes (−ΔA0 at delay of 1 ps in Figure 3A,B) are proportional to N0 for both samples, −ΔA0 = b·N0 (constant b is the slope of the linear fit, Figure 3A,B). The linear relationship between the carrier density and bleach amplitude provides further evidence of the excitonic nature of the bleach;21,23 however, it should be noted that in the high carrier density region (N > ∼2 × 1018 cm−3) this linear relationship may not satisfied because (1) exciton bleach begins to saturate and (2) the bleaching of the continuum band due to bandfilling of free carriers starts to dominate over bandgap renormalization.21,30 As the established linear relationship, the kinetics for the different pump fluences directly represent the carrier recombination dynamics for different N0 (Figure 3C,D). With similar initial carrier density, carrier dynamics of 4689
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Figure 3. Transient absorption kinetics of MAPbBr3 and MAPbI3 thin films under various pump fluences. The plot of bleach band amplitude at 1 ps as a function of initial carrier density for (A) MAPbBr3 and (B) MAPbI3. The bleach kinetics of (C) MAPbBr3 recorded at 2.35 eV and (D) MAPbI3 recorded at 1.64 eV under different pump fluences. The black dashed lines in panels A and B are the linear fits to the data. The black solid lines in panels C and D are the fits to the kinetic traces according to the carrier recombination model.
previously reported values.31,32 The recombination rate constants for MAPbBr3 have not been reported but are similar to a recent report on formamidinum lead bromide.33 Usually, the first-order recombination can be attributed to geminate and/or SRH recombination. Considering the low exciton formation probability at room temperature due to the small binding energies, geminate recombination should be negligible for the both films. Furthermore, because the exciton recombination rate is a function of intrinsic parameters of the material such as exciton transition strength and emission photon energy, the rate constant should not depend on the sample preparation method. On the contrary, the SRH recombination rate is proportional to the defect density that can be affected by the sample preparation method. Literature reports of the first-order recombination lifetime range from 10 to 103 ns for the same material,15,34−36 and thus we assign the first-order recombination for both films to SRH. The lifetimes are 37 ns for MAPbBr3 and 14 ns for MAPbI3. Because SRH recombination is defect-limited these lifetimes can be improved by reducing defect density. Surface recombination velocity (SRV) is also an important consideration that can determine the overall carrier lifetime.23 While we do not study SRV in this manuscript, we have verified that it is too small to contribute to the carrier dynamics measured here. We find that the B coefficients for both samples are in line with values for the radiative recombination rate constants for typical direct band gap semiconductors (10−10 to 10−9 cm3 s−1).19,37,38 In contrast, the radiative coefficient for typical indirect band gap semiconductors is much smaller (10−14 to 10−15 cm3 s−1). Given the similarities in B coefficient found here to other direct gap semiconductors we can tentatively assign the bimolecular recombination to radiative recombina-
MAPbBr3 decay faster than that of MAPbI3. These carrier dynamics can then be quantitatively described by the following equation according to different recombination mechanisms d [−N (t )] = A ·N (t ) + B ·N 2(t ) + C·N3(t ) dt
(1)
where N(t) is the carrier density at a pump−probe delay of t and A, B, and C denote the monomolecular, bimolecular, and trimolecular recombination rate constants. Here we use numerical integration of eq 1 to simultaneously model all the kinetic traces for each sample. To constrain the fitting, only B and C are set as free fitting parameters. The first-order recombination rate constants of the samples are experimentally measured from the bleach kinetics at much longer delays (>10 ns) with low pump fluence, under which the condition for firstorder recombination (single exponential decay) is dominant and higher order recombination contributions are negligible (Figure S2). The global fitting reveals the second- and thirdorder recombination rate constants are tabulated in Table 1. The recombination rate constants for MAPbI3 are in line with Table 1. List of Carrier Recombination Rate Constants for MAPbBr3 and MAPbI3a A (μs−1) MAPbBr3 MAPbI3
27.2 ± 1.6 72.7 ± 2.6
B (cm3 s−1)
C (cm6 s−1) −10
4.9 ± 0.2 × 10 1.5 ± 0.1 × 10−10
13.5 ± 0.3 × 10−28 3.4 ± 0.1 × 10−28
a A is obtained from the single exponential fitting of the TA bleach kinetics at long delay (>10 ns) with low pump fluence. B and C are obtained from global fitting of TA bleach kinetics for different excitation fluences.
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The Journal of Physical Chemistry Letters tion of free electrons and holes. The B coefficient for MAPbBr3 is larger than that for MAPbI3 (by a factor of 3.3). In contrast, Rehman et al. report that the B coefficient increases by a factor of 10 when replacing iodide for bromide in formamidinium lead halide perovskite films.33 The radiative recombination rate constant is proportional to Eg|Pcv|2, where Eg is bandgap and | Pcv|2 is the interband transition matrix element, which is proportional to absorption coefficient.38−40 Therefore, we can estimate the ratio of B coefficient of MAPbBr3 to that of MAPbI3 from the band gap energy and the absorption coefficient near the bandgap determined in Figure 1. We find that absorption coefficient near the onset is αBr ≈ 1.1 × 105 cm−1 for MAPbBr3 (ℏω = 2.35 eV) and is αI ≈ 3.5 × 104 cm−1 for MAPbI3 (ℏω = 1.64 eV); therefore, αBr/αI ≈ 3.1, which is primarily determined by the ratio of Couloumb enhancement factors (or the ratio of exciton binding energies). Including the ratio of the bandgaps, the B coefficient for MAPbBr3 should be ∼4.5 times larger than that for MAPbI3, which is slightly higher the experimental observation. The recombination rate constants (both A and B) are comparable to those found in GaAs,38,41 and thus we expect that photon-recycling strategies that have been successful for GaAs would likewise be successful for the perovskite-based solar cells. The third-order rate constant C (Auger coefficient) is much larger than those for GaAs (C ≈ 10−30 cm6 s−1)19 and CdTe (C ≈ 0.5 × 10−29 cm6 s−1)42 but is on the same order of magnitude for bulk PbSe (C ≈ 8 × 10−28 cm6 s−1).43 The Auger coefficient has been found to decrease with increasing bandgap,44 and thus a larger C is found for PbSe with Eg = 0.3 eV than that for GaAs with Eg = 1.4 eV. The smaller Auger coefficient for larger bandgap arises because in the Auger process nonradiative recombination of an electron−hole pair across the gap is facilitated by excitation of a third carrier (electron or hole) to a higher energy state. The Auger process must conserve both energy and momentum.45 As the bandgap increases the momentum conservation condition becomes more difficult to satisfy and thus the Auger recombination channel decreases. The Auger recombination rate constant in MAPbBr3 is approximately 4 times larger than that in MAPbI3 even though the bandgap increases from 1.64 to 2.39 eV. Furthermore, C is ∼2 orders of magnitude larger for MAPbI3 than in GaAs, even though their bandgaps are approximately equal. There are at least two possible causes for the higher Auger rate constants. (1) Increased Auger recombination can occur if one of the carriers is strongly localized. Such localization reduces the momentum conservation requirements and thus increases the Auger rate; however, we discount this cause because there is little evidence of any fast carrier localization mechanisms. (2) Previous studies have found that a large Coulomb interaction between electron and hole can result in a nonuniform carrier distribution because a carrier is more likely to be surrounded by carriers with the opposite charge than those with the identical charge, which can enhance the Auger recombination rate through increasing the probability of finding a electron (hole) and two holes (electrons) at the same position.46 Therefore, compared with MAPbI3, the Coulomb enhancement of Auger recombination should be larger in MAPbBr3, which likely rationalizes the significant difference of Auger recombination rate constant between these two perovskites samples. We investigate the recombination dynamics in both MAPbBr3 and MAPbI3 films using TA spectroscopy. We determine the rate constants of three different recombination mechanisms in both samples from the global fitting of the
exciton bleach kinetics corresponding to different pump fluences. Our results indicate that the Auger recombination rate constants in the MAPbBr3 are about an order of magnitude larger than that in MAPbI3 owing to the larger binding energy in the former.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b02290. Experimental methods, transition and reflection spectra of the samples, and nanosecond TA measurements. (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Division of Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through the Solar Photochemistry Program under contract no. DE-AC36-08GO28308 to NREL.
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