Charge‐Carrier Dynamics and Mobilities in Formamidinium Lead Mixed‐Halide Perovskites

The mixed-halide perovskite FAPb(Bry I1-y )3 is attractive for color-tunable and tandem solar cells. Bimolecular and Auger charge-carrier recombination rate constants strongly correlate with the Br content, y, suggesting a link with electronic structure. FAPbBr3 and FAPbI3 exhibit charge-carrier mobilities of 14 and 27 cm(2) V(-1) s(-1) and diffusion lengths exceeding 1 μm, while mobilities across the mixed Br/I system depend on crystalline phase disorder.


DOI: 10.1002/adma.201502969
by at least four orders of magnitude. [ 17,18 ] MAPbI 3 also appears to exhibit only shallow trap-levels and although the grain boundaries have recently been shown to induce nonradiative decay, [ 19 ] regions only a few tens of nm away from the grain boundaries appear to be unaffected. [ 20,21 ] Furthermore, low Urbach energies, which are extracted from near band edge optical absorption measurements and serve as a benchmark for crystalline phase disorder, indicate low disorder and sharp band edges for lead tri-halide perovskites (15-23 meV). [ 22,23 ] All of these properties contribute to high open-circuit voltages, long charge-carrier lifetimes, and micrometer diffusion lengths, which are crucial for planar-hetero junction photovoltaics. [ 1,24 ] Nonetheless, these parameters are also expected to depend on the infl uence of crystallization condition on perovskite morphology in fabricated fi lms. [ 25 ] A distinct benefi t of organic-inorganic perovskite materials (e.g., over silicon) is that their bandgap can be tuned relatively easily with chemical composition, allowing attractive coloration and multijunction or tandem cell designs. For example, changing the metal cation at the M site from Pb 2+ to the less toxic Sn 2+ to form CH 3 NH 3 SnI 3 shifts the optical bandgap from 1.55 to 1.3 eV into the range of the "ideal" single-junction solar cell bandgap between 1.1 and 1.4 eV. [ 26,27 ] However, stability issues arising from the oxidation of tin have so far prevented widespread use. Alternatively, tuning the size of the A site cation has been proven to change optical and electronic properties of the perovskite and to signifi cantly infl uence solar cell performance. [ 28 ] Replacing MA in MAPbI 3 by the larger cation formamidinium HC(NH 2 ) 2 + (FA) was found to decrease the bandgap from 1.57 to 1.48 eV, [29][30][31] yield long photoluminescence (PL) lifetimes, high PCEs, [ 28 ] and lower recombination and device hysteresis. [ 32 ] Highest PCEs of 20.1% have been reported [12][13][14] to date for solar cells based on FAPbI 3 making this an attractive system to explore. In addition, the gradual replacement of the MA cation by FA through the fi lm was shown to create a mixed cation-lead-iodide PSC allowing for energetic gradients. [ 33 ] However, mixing of the halide component in the perovskite offers the fi nest tuning of the optical properties of the perovskite fi lm. Here, the mixed organic lead iodide/bromide system has recently gained strong interest for application in PSCs. [ 11,28 ] By changing the ratio between bromide and iodide (at the X site anion), the bandgap can be tailored between 1.55 eV (MAPbI 3 ) and 2.3 eV (MAPbBr 3 ), which results in the coverage of much of the visible spectrum and paves the way for the development of tandem solar cells. [ 11 ] In addition to MAPb(Br y I 1y ) 3 , its formamidinium relative FAPb(Br y I 1y ) 3 has been explored. [ 28 ] Most fractional mixtures of FAPb(Br y I 1y ) 3 were found to be crystalline, with the exception of the region between y = 0.3 and Recent years have seen the emergence of a promising new generation of hybrid organic-inorganic perovskite absorbers for highly effi cient photovoltaic devices. [1][2][3][4] Materials with the perovskite crystal structure follow the general stoichiometry AMX 3 . For the organic-inorganic perovskites studied so far, A is an organic cation, M is a metal cation such as Pb 2+ or Sn 2+ , and X 3 comprises one or more types of halide anions. [ 5 ] Early reports on perovskite absorbers in working photovoltaic devices demonstrated mesoporous metal-oxide liquid-electrolyte sensitized solar cells, which reached power conversion effi ciencies (PCE) of a few percent. [ 6 ] Research soon moved toward more stable all-solid-state devices based on a range of different architectures incorporating hybrid interfaces. One concept emulates solid-state dye-sensitized solar cells (DSC), using the perovskite material as an absorber infi ltrated into an electron-extracting mesoporous metal-oxide layer. [ 7 ] Alternatively, a meso-superstructured confi guration incorporating an insulating mesoporous Al 2 O 3 scaffold was demonstrated, which resulted in landmark PCEs of over 12%. [ 2,8 ] Finally, several fabrication methods have been developed for planar-heterojunction architectures [ 1,9 ] including a one-step spin-coating method from solution precursors, [ 7,10,11 ] a two-step sequential method, [ 3 ] and vapor-phase deposition in a vacuum chamber [ 1 ] which have accompanied a phenomenal increase of PCEs. The highest certifi ed PCE of hybrid organic-inorganic perovskite solar cells (PSC) has reached 20.1% to date, [12][13][14] with methylammonium (MA) lead tri-iodide (CH 3 NH 3 PbI 3 ) and formamidinium (FA) lead tri-iodide (HC(NH 2 ) 2 PbI 3 ) or mixtures thereof being the most frequently investigated perovskite absorbers. The outstanding performance of PSCs has been attributed to unique photophysical and material properties that are well suited for solar cell applications. In addition to high optical absorption coeffi cients of around 10 5 cm −1 in the visible range [ 15,16 ] and high charge-carrier mobilities, bimolecular charge-carrier recombination rates defy the Langevin limit for kinetic recombination This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. y = 0.5 where the crystal structure changed, resulting in an amorphous region. [ 23,28 ] A number of studies exploring the characteristics of solar cells based on the MAPbI 3 to MAPbBr 3 material system have been performed. [ 34 ] However, given the importance of this heterogeneous material system, little is known about the dynamics of photoexcited charge-carriers and their mobilities as a function of iodide/bromide content. A deeper understanding of these properties is now essential for further improvement of photovoltaic devices based on these highly tunable materials.
Here we present a key analysis of the charge-carrier dynamics including recombination rate constants and mobilities across the range of compositions in the mixedhalide lead perovskite system FAPb(Br y I 1y ) 3 . We demonstrate that bimolecular and Auger recombination rate constants directly correlate with the Br/I fraction and are insensitive to phase stability. With an increasing Br/I ratio, charge recombination rate constants increase by up to an order of magnitude, with bimolecular recombination however remaining signifi cantly below the Langevin limit. Because of their lack of correlation with material morphology, we propose that these are intrinsic charge recombination mechanisms that are directly linked with changes in electronic structure induced, e.g., by modifi cations of the frontier orbitals upon halide substitution. Charge-carrier mobilities, on the other hand, exhibit a strong correlation with phase disorder. For the trihalide systems, FAPbBr 3 and FAPbI 3 , we establish effective charge-carrier mobilities of (14 ± 2) cm 2 V −1 s −1 and (27 ± 2) cm 2 V −1 s −1 . For the intermediate mixed-halide materials, charge-carrier mobilities fall in correlation with increasing phase disorder, as evidenced by a rise in energetic broadening and trap-induced recombination mechanisms.
The FAPb(Br y I 1y ) 3 fi lms were formed by spin-coating mixtures of 0.55 M FAPbI 3 and 0.55 M FAPbBr 3 in anhydrous N , Ndimethyl formamide on warm substrates (85 °C) in a nitrogenfi lled glovebox and annealing in air at 170 °C for 10 min. Prior to mixing the solutions, a small amount of acid was added to the FAPbI 3 and FAPbBr 3 solutions to enhance solubility of the precursors and allow ultrasmooth and pinhole-free fi lm formation: 38 µL of hydroiodic acid (57% w/w) was added per 1 mL of the 0.55 M FAPbI 3 precursor solution, and 32 µL of hydrobromic acid (48% w/w) was added per 1 mL of the 0.55 M FAPbBr 3 precursor solution. This procedure gave very uniform pinhole-free layers of FAPb(Br y I 1y ) 3 with a thickness of ≈300-400 nm. A more detailed description can be found in the Supporting Information. Figure 1 a displays steady-state PL spectra for thin fi lms of FAPb(Br y I 1y ) 3 with varying bromide content between y = 0 (100% iodide) and y = 1 (100% bromide). In agreement with previous reports, [ 9 ] the PL peak energy is found to tune continuously from 2.26 eV for FAPbBr 3 to 1.50 eV for FAPbI 3 . Theoretical calculations show that the red shift upon moving from Br − to I − derives from the associated decrease of the electronegativity of the halogen atom. [ 35 ] Exchanging Br − with I − changes the nature of the halide frontier orbital contribution to the valence band from 4p to 5p, which decreases the bandgap energy. [ 36,37 ] The observed PL peak positions are consistent with the absorption onsets seen in absorbance spectra of the examined FAPb(Br y I 1y ) 3 fi lms (see Figure S1, Supporting Information) confi rming that the PL arises primarily from band-edge emission rather than from minority phases or trap states.
For FAPb(Br y I 1y ) 3 fi lms with bromide content in the region 0.3 < y < 0.5, the material quality appears signifi cantly lowered, as apparent from the absence of signifi cant PL emission and X-ray diffraction (XRD) data. While outside of this region, XRD shows sharp peaks arising from crystalline  3 perovskite with varying halide composition y , recorded immediately following excitation at 400 nm at a fl uence of 0.1 µJ cm −2 (7.2 W cm −2 ) under vacuum. The PL spectra have been normalized to the peak emission. b) PL spectra of a FAPb(Br 0.67 I 0.33 ) 3 fi lm over the course of 5 min of continuous illumination following excitation at 400 nm with an intensity of 7.2 W cm −2 (fl uence of 0.1 µJ cm −2 , pulse duration 100 fs, repetition rate 80 MHz). Inset: Change of average photon energy 〈 E ph 〉 as a function of illumination time. c) In situ PL spectra for a FAPb(Br 0.67 I 0.33 ) 3 fi lm over the course of 1180 min of continuous illumination following excitation at 400 nm with an intensity of 15 mW cm −2 (fl uence of 13.5 µJ cm −2 , pulse duration 40 fs, repetition rate 1.1 kHz). Spectra were collected in situ with a fi ber-optic collection system under experimental conditions matching those used for time-resolved THz photoconductivity data shown in Figure 2 . PL spectra have been normalized to the peak emission intensity. Inset: Change of the average photon energy 〈 E ph 〉 as a function of time.
perovskite, [ 28 ] the lack of such features in the intermediate region (0.3 < y < 0.5) suggests that the material becomes amorphous here (see Figure S6, Supporting Information) with "amorphous" implying that the crystalline order is on too short a length scale to be detectable in our XRD data. Such structural disorder can be understood in the context of a crystal structure change: while FAPbI 3 adopts the trigonal structure, [ 14,29 ] FAPbBr 3 is cubic at room temperature. [ 28 ] Variation of bromide content for this system has been shown to lead to a monotonic change in pseudocubic lattice parameter determined from XRD, apart from the transition region of 0.3 < y < 0.5 between which the structure transfers from cubic to tetragonal and no well-defi ned crystal structure can be formed. [ 28 ] We therefore refer to this region as the "amorphous region" in our subsequent analysis.
In previous work, a reversible light-induced transformation of PL spectra for mixed iodide/bromide perovskites has been reported, which raised concerns regarding the photostability of these mixed halide materials. [ 38 ] Under constant illumination, bromide-rich MAPb(Br y I 1y ) 3 perovskite fi lms were found to exhibit a new dominant peak at around 740 nm, i.e., red-shifted toward the emission spectrum of MAPbI 3 . [ 38 ] It was proposed that photoexcitation may cause halide segregation into two crystalline phases: an iodide-rich minority domain and a bromiderich majority domain. [ 38 ] This instability could be substantially detrimental for photovoltaic performance in solar cell devices since the expectation would be that the open-circuit voltage may then become limited by the energy of the lower bandgap phases. By contrast, other studies of PL emission from mixedhalide perovskite systems have not reported such light-induced shifts. [ 23,28 ] Here, we fi nd that the intensity of the laser excitation spot plays a major role in producing these shifts. Figure 1 b shows the PL emission of a FAPb(Br 0.67 I 0.33 ) 3 fi lm (a composition on the Br side of the phase instability) when recorded for laser excitation with an intensity of 7.2 W cm −2 following 5 min of continuous illumination. Indeed, here, the phenomenon of halide migration-induced shifts is clearly corroborated. The original PL maximum at 620 nm almost completely shifts to a new dominant low-energy PL feature, which is recognizable at around 785 nm (1.58 eV). The luminescence intensity almost doubles with respect to the initial value, in accordance with higher PL emissivity of the iodide-rich phases. In addition, the enhancement of another small phase at around 540 nm (2.3 eV) is distinguishable. The inset of this fi gure presents the decrease of the average energy of emitted photons following pulsed laser excitation and shows a continuous decrease over time. Figure 1 c, on the other hand, shows PL spectra for an identical FAPb(Br 0.67 I 0.33 ) 3 fi lm under illumination at the same wavelength (400 nm) for 1180 min (20 h) with laser intensity of 15 mW cm −2 . These were collected with an in situ (fi ber-based) spectrometer under conditions identical to those employed in the time-resolved THz photoconductivity measurement described below. With an excitation intensity 500 times lower, negligible shifts in PL maxima and average photon energy are observed (see Figure 1 c), and no new low-energy PL features emerge during continuous laser excitation over the time-scale of 20 h. Additional measurements for fi lms with other bromide fractions, which can be found in Figure S2 (Supporting Information), exhibit smaller shifts only for prolonged irradiation of fi lms near the amorphous region ( y = 0.55). While the primary aim of these measurements is to establish that the examined fi lms do not phase-segregate or decompose during the timeresolved THz photoconductivity measurements described below, we note that photovoltaic devices are typically tested under AM1.5 conditions (1 kW m −2 = 100 mW cm −2 ), which is closer to the light intensity of 15 mW cm −2 for which we do not observe signifi cant PL peak shifts. These results may therefore explain why no instabilities in open-circuit voltages have so far been reported for mixed I − /Br − perovskite photovoltaic devices, and suggest that mixed-halide perovskites may yet be a usable route toward wider bandgap absorbers. They further highlight the need for more quantitative investigations into light-induced halide segregation in these mixed systems (e.g., dependences on light intensity, nonlinearities, heating, and morphology), which will ascertain the extent to which such effects are detrimental under photovoltaic device operating conditions.
With stability of materials under THz measurement conditions confi rmed, we proceed by analyzing the charge-carrier recombination dynamics in the mixed-halide perovskites. Here we use ultrafast optical pump-THz probe spectroscopy as a time-resolved, contactless conductivity probe, which has been used previously to study charge-carrier recombination rate constants for other perovskite materials [ 17,18 ] (see the Supporting Information for full experimental details). The question as to which optically excited species may couple to the THz probe pulse, either excitons or free charge-carriers has been addressed several times in earlier reports. [ 17,18,[39][40][41][42] We note that for MAPbI 3 the sole response to the THz conductivity probe has already been shown to be that of a free-charge carrier density, as inferred from the Drude shape of the conductivity spectra. [ 17,18 ] Here we also report highly similar Drude conductivity spectra for FAPbBr 3 (see the Supporting Information), which suggests that excitonic effects are negligible at room temperature for these mixed I/Br materials. Figure 2 displays the THz photoconductivity transients following photoexcitation of fi lms with four different compositions of FAPb(Br y I 1y ) 3 after photoexcitation at 400 nm with excitation fl uences ranging from 8 to 65 µJ cm −2 . The transient conductivity originating from photoexcited charge carriers is probed by a THz radiation pulse at a precise time-delay with regard to the pump pulse. The data shown in Figure 2 reveal a striking correlation between the photoconductivity decay dynamics and bromide content. When the bromide fraction y is increased from FAPbI 3 ( y = 0, Figure 2 a) to the lighter-halide perovskite, FAPbBr 3 ( y = 1, Figure 2 d), the initial decay components of the transients gradually become faster. This suggests that upon change from neat-iodide to the neat-bromide perovskite fi lm, higher order recombination effects increase.
The decline in photoconductivity with increasing time after excitation is primarily the result of charge-carrier recombination, which is expected to depend on the charge carrier-density and therefore laser excitation fl uence. [ 17,18 ] For high chargecarrier densities, there will be an enhanced contribution from higher-order recombination mechanisms, such as second-order electron-hole (bimolecular) recombination as well as thirdorder Auger recombination, in which energy and momentum are transferred to a third charge-carrier. [ 18 ] Taking such effects where n ( t ) is the free charge-carrier density, k 3 is the Auger recombination rate constant, k 2 is the bimolecular recombination rate constant, and k 1 is the monomolecular recombination rate, which may arise from charge trapping. Since the measured relative change in THz electric fi eld transmission (Δ T / T ) is proportional to the photoinduced conductivity and thereby to the free charge-carrier density, [ 43 ] fi tting the above rate equation to the transients allows the extraction of recombination rate constants (see the Supporting Information for details). Fitting was performed globally across all fl uences, and the monomolecular decay rate constant k 1 was fi xed to a value determined using time-resolved PL measurement at very low laser excitation densities for which higher-order recombination effects are negligible (see Supporting Information, Figure S3). However, we note that since the monomolecular lifetime k 1 −1 is significantly larger than the observation window of 2.5 ns for which THz data were taken, the exact value of k 1 has little infl uence on the fi ts. Figure 3 demonstrates that both the bimolecular ( k 2 ) and Auger recombination rates ( k 3 ) increase monotonically with increasing bromide content and are an order of magnitude lower for FAPbI 3 compared to the lighter-halide FAPbBr 3 . These results are notable because they suggest a clear link between these intrinsic electron-hole recombination rate   constants and the composition and therefore electronic structure of the material. As discussed above, the material crystallinity is markedly lower toward the central region of 0.3 < y < 0.5, however, the bimolecular and Auger recombination rates appear relatively insensitive to this, changing instead monotonically with y . As we show below, the situation is very different for the charge-carrier mobility and trap-related recombination rate, which are instead found to be strongly linked with material quality or crystallinity. However, bimolecular and Auger recombination do not show features near the central instability region, suggesting instead a correlation with fundamental electronic properties of the system. A gradual change in the intrinsic recombination parameters with bromide fraction may be expected for a number of reasons. First, the substitution of iodide with bromide changes the nature of the valence-band maximum, which has strong contributions from hybridizations of the atomic frontier p-orbitals of the halide [ 37 ] that may affect spontaneous bimolecular electron-hole recombination rates. In addition, the bimolecular recombination rates for hybrid metal-halide perovskites are suppressed well below the values predicted by Langevin theory, for which spatial segregation of electron-hole pairs across the metal-halide bond has been proposed as one possible origin. [ 17,18 ] We fi nd similarly supressed Langevin ratios here across the whole FAPb(Br y I 1y ) 3 system (see Table S1, Supporting Information). Changes in halide composition may affect such spatial segregation and in turn tune the bimolecular recombination rates. For Auger recombination, rate constants generally depend strongly on the electronic band structure of the semiconductor because of the need for overall momentum and energy conservation involving the many-body process. [ 44 ] For the FAPb(Br y I 1y ) 3 system, a gradually decreasing pseudocubic lattice parameter has been reported with increasing bromide fraction [ 28 ] in agreement with a continuous change in electronic band structure; however, the exact correlation between Auger recombination and crystal structure is likely to be complex. Our investigations open up new possibilities for linking optoelectronic properties of these promising materials with calculations that may eventually allow materials design from fi rst principles. Charge-carrier mobilities also play a signifi cant role in the performance of photovoltaic devices, affecting charge extraction to electrodes. We determined effective charge-carrier mobilities φµ for the mixed-halide FAPb(Br y I 1y ) 3 fi lms from the photoconductivity onset value at zero pump-probe delay and with knowledge of the initially absorbed photon density and other optical parameters as further described in the Supporting Information. Although we derive effective charge-carrier mobilities as lower bounds of the actual mobility, we assume that the photon-to-freecharge conversion ratio φ is close to unity because of the observed Drude-like photoconductivity spectra, as discussed above. Figure 3 c displays the extracted charge-carrier mobility values as a function of bromide content. For FAPbI 3 ( y = 0), a value of (27 ± 2) cm 2 V −1 s −1 is found, similar to values previously determined for solution-processed meso-superstructured MAPbI 3 fi lms [ 18 ] and vapor-deposited solid MAPb(I 1x Cl x ) 3 fi lms. [ 17 ] Interestingly, FAPbBr 3 ( y = 1) also shows a remarkably high mobility value of (14 ± 2) cm 2 V −1 s −1 , only lower by a factor of 2 than that for the iodide-only material. All of the examined mixed-halide materials, however, exhibit charge-carrier mobilities below these two limits. Unlike the bimolecular and Auger recombination kinetics discussed above, the obtained charge mobilities exhibit a clear correlation with increasing electronic disorder. For the amorphous intermediate-region fi lms (0.3 < y < 0.5), charge mobilities exhibit a signifi cant drop decreasing down to (2 ± 2) cm 2 V −1 s −1 for y = 0.3 and (1 ± 2) cm 2 V −1 s −1 for y = 0.4 fi lms. The full width at half maximum (FWHM) of the PL emission peaks from MAPb(Br y I 1y ) 3 fi lms has recently been shown to be a reliable measure for phase stability, correlating directly with the Urbach energy. [ 23 ] Figure 3 d shows the FWHM extracted from the PL peaks shown in Figure 1 a for the FAPb(Br y I 1y ) 3 fi lms investigated here. The PL FWHM shows clear correlation with the extracted charge-carrier mobility values, providing a direct link between the presence of disorder and a lowering in charge mobility. The neat tri-halide perovskite fi lms display the lowest FWHM, in accordance with very low crystalline phase disorder and sharp band edges for these fi lms. [ 23 ] In addition, we fi nd that the mono-molecular recombination rate k 1 extracted from PL decay transients at low excitation fl uence (see the Supporting Information) also exhibits a link with energetic disorder, although this may be superimposed on a general trend of increasing k 1 with increasing bromide content. Increasing disorder is likely to enhance such trap-induced monomolecular recombination, while changes in band structure may lead to modifi cations in relative trap energies, explaining the observed trends. Therefore, while single-halide lead perovskites show highly favorable charge-carrier lifetimes and transport, mixed-halide lead perovskites would benefi t from newly devised routes toward manufacturing fi lms with improved compositional homogeneity and therefore enhanced electronic order. Recent observations of strongly improved optoelectronic properties for MAPbX 3 (X = Br − , I − ) single crystals grown by vapor-assisted crystallization demonstrate that decreasing disorder is a crucial aim for thin-fi lm device applications. [ 45 ] From the measured charge-carrier recombination constants and mobilities, we are able to extract charge-carrier diffusion lengths as a function of charge-carrier density (see Figure S5, Supporting Information), which are important fi gures of merit particularly for the use of these materials in planar-heterojunction device architectures. At a charge-carrier density of n ≈ 10 15 cm −3 which is typical during photovoltaic device operation, we fi nd that the charge carrier diffusion length exceeds 1 µm for the parameter space 0 < y < 0.15 and y = 1, with the tri-iodide FAPbI 3 exhibiting the highest diffusion length of 3.1 µm and the tri-bromide FAPbBr 3 a value of 1.3 µm, lowered by the lower charge-carrier mobility and higher charge-carrier recombination rates. For these materials, charge-carrier diffusion lengths clearly exceed the optical absorption depth (typically about a few hundred nm across the visible), in good agreement with the successful demonstration of effi cient planar-heterojunction photovoltaic cells for this range of y . [ 28 ] For the mixedhalide materials within the amorphous region, we fi nd chargecarrier diffusion lengths in the range of 500-700 nanometers at n ≈ 10 15 cm −3 , which is still respectable but may start to reduce charge-carrier collection effi ciencies and maximum attainable open-circuit voltages in planar-heterojunction devices. However, our results suggest that only relatively modest improvements in disorder and trap density are required in order to