Resolving the Ultrafast Charge Carrier Dynamics of 2D and 3D Domains within a Mixed 2D/3D Lead-Tin Perovskite

Mixed 2D/3D perovskite materials are of particular interest to the photovoltaics and light-emitting diode (LED) communities due to their impressive opto-electronic properties alongside improved moisture stability compared to conventional 3D perovskite absorbers. Here, a mixed lead-tin perovskite containing distinct, self-assembled domains of either 3D structures or highly phase-pure Ruddlesden–Popper 2D structures is studied. The complex energy landscape of the material is revealed with ultrafast optical transient absorption measurements. It is shown that charge transfer between these microscale domains only occurs on nanosecond timescales, consistent with the large size of the domains. Using optical pump-terahertz probe spectroscopy, the eﬀective charge-carrier mobility is shown to be an intermediary between analogous pure 2D and 3D perovskites. Furthermore, detailed analysis of the free carrier recombination dynamics is presented. By combining results from a range of excitation wavelengths within a full dynamic model of the photoexcited carrier population, it is shown that the 2D domains in the ﬁlm exhibit remarkably similar carrier dynamics to the 3D domains, suggesting that long-range charge-transport should not be impeded by the heterogeneous structure of the material.


Introduction
Metal-halide perovskite thin films have emerged as a leading technology for next generation solar cells.Despite the very high efficiency of single junction perovskite solar cells, poor device stability remains a significant obstacle to their commercialisation.One approach to improve the stability of perovskite materials is to incorporate large organic ligands into the structure during fabrication.These ligands occupy the A-site in the typical perovskite ABX 3 structure, but their size is too large to be fully enclosed by metal-halide octahedra.[3] In Ruddlesden-Popper (RP) 2D perovskites, the ligands are monovalent and consequently form a bilayer between metal halide layers.A variety of ligands can be used such as 2-phenylethylammonium (PEA) and butylammonium (BA), demonstrating the wide structural tuneability of this class of materials.The presence of the organic spacer molecules has been shown to partially mitigate moisture related stability issues by preventing ion migration and decomposition to metal-halides. [4,5]By combining two Asite cations, an organic spacer molecule and one which readily forms 3D perovskite structures such as methylammonium (MA) or formamidinium (FA), RP films can be created which contain 2D layers with a range of thicknesses determined by the stoichiometry of the cations.Such films have the general formula A' 2 A n − 1 B n X 3n + 1 where A' is the organic spacer molecule.The quantity n refers to the number of octahedral layers in a 2D structure. [3]As the thickness of the layer is reduced, electronic confinement effects begin to play a role, increasing the electronic bandgap and exciton binding energy. [6]In practice, in RP thin films with an expected n>1 the structures form with a range of different thicknesses, often with varying spatial distributions and orientations, resulting in complex energy landscapes. [2]In 2D/3D mixed perovskites, a significant proportion of the analogous 3D perovskite is present alongside 2D RP phases.Alongside their applications in solar cells, 2D/3D perovskites are of great interest to the LED community due to their broadband emission spectra arising from charge carrier funnelling and localization. [7]ne disadvantage of this approach to improve stability and longevity is that the confinement effects in the 2D layers typically reduce the effective charge carrier mobility while increasing the recombination rates, resulting in a reduced carrier diffusion length, which may compromise charge collection efficiencies in solar cells. [2]In addition, the charge carrier population is partially excitonic in nature due to the large exciton binding energy of the 2D structures, further reducing charge extraction rates.Excitons are commonly predicted to play a major role in the dynamics of n = 1 RP perovskites under solar illumination, although this effect is significantly reduced as n increases. [8]Solar cells utilising RP perovskites typically exhibit lower power conversion efficiency (PCE) when compared to 3D perovskite crystals.2D RP (n = 1) devices generally exhibit efficiencies lower than 4%, [1] with leading 2D/3D (n < 4) devices reaching over 18% efficiency, [9] and conventional 3D perovskite films over 25% PCE. [10]RP structures are also utilized as capping layers which act to passivate surfaces and enhance charge transfer from a 3D perovskite film, facilitating highly efficient photovoltaic devices. [11,12]Further investigation of the mechanisms which contribute to charge carrier dynamics in 2D and 2D/3D perovskites is essential for improved understanding of their potential for use in both solar cells and LEDs.
Alongside A-site substitution for layered perovskite formation, the perovskite structure can be tuned to tailor its properties for specific applications.[20] Sn substitution has been shown to tune the bandgap toward the infrared for a variety of different A and X-site ions.This has resulted in Sn based cells being particularly promising as narrow bandgap absorbers in perovskite-perovskite tandem solar cells, which would theoretically allow power conversion efficiency to exceed the single junction Shockley-Queisser limit. [21]n this work we present the findings of an investigation into the ultrafast carrier dynamics of a mixed Pb-Sn 2D/3D RP perovskite thin film.These films contain distinct regions of 2D and 3D perovskites and thus present an interesting energetic and morphological landscape. [22]Analogous pure 2D (n = 1) and 3D films with nominal compositions of PEA 2 (Pb 0.5 Sn 0.5 )I 4 and FA(Pb 0.5 Sn 0.5 )I 3 respectively were also studied in order to provide a point of comparison for the 2D and 3D domains in the mixed films.A combination of two ultrafast techniques, namely transient absorption (TA) spectroscopy and optical pump-terahertz probe (OPTP) spectroscopy, is employed to evaluate the optoelectronic properties of these films.The combination of these techniques allows for the characterization of the charge-carrier dynamics, the evaluation of the charge-carrier mobility, and the elucidation of the recombination mechanisms.Overall, we find that free charge carriers within the 2D and 3D regions have remarkably similar mobility and recombination rates, suggesting that this particular microstructure will not significantly inhibit charge transport.

Thin Film Synthesis and Characterization
Thin films were synthesized via antisolvent-assisted spin-coating of precursor solutions of PEAI, FAI, PbI 2 , SnI 2 , and SnF 2 , as described in the Experimental Section.These were prepared by mix-ing the dry precursor powders into a vial, and then dissolving them in a mixture of N,N-dimethylformamide and dimethyl sulfoxide solvents.The precursor solutions were then spin-coated onto the substrate and anisole was used as antisolvent to assist correct crystallization.The spin-coated samples were then annealed on a hot plate.Films produced by this method have consistent thickness of approximately 500 nm.
In addition, a precursor additive of ammonium thiocyanate (AT) is used.This additive has been shown to improve crystallinity and regulate orientation in RP perovskites, greatly improving the performance of the material in solar cells. [23]Similarly it has found use in conventional 3D perovskites as a passivating agent which was demonstrated to increase crystal size, reduce trap density [24] and, in FA based perovskites, improve phase stability. [25]In films akin to those studied here, the addition of AT has been shown to allow a degree of modulation of the proportion of 2D and 3D domains throughout the film. [22]ielectric and quantum confinement in 2D perovskite structures increases the bandgap of the material, [26] hence increasing the peak luminescence energy and the band-edge absorption energy.Optical absorption, emission, and X-ray diffraction (XRD) of the 2D/3D films were studied in order to characterize their dimensionality.The absorption spectra shown in Figure 1a,d show distinct features characteristic of 2D and 3D perovskites.In both the films with and without AT, a weak band-edge absorption is observed at 950 nm and a much stronger one at 650 nm.The feature at 950 nm is consistent with the band-edge absorption in the 3D film (see Figure S2, Supporting Information).The band-edge of the 2D (n = 1) reference material occurs at 560 nm, which is blue shifted as compared to the 650 nm feature observed in the mixed films.This discrepancy implies that the 2D/3D film predominantly contains RP structures with n > 1 which have narrower bandgaps than n = 1 structures. [2]While the film's overall stoichiometry predicts an average layer thickness of n=3, the presence of 3D domains with low PEA concentration suggests increased PEA concentration in the 2D domains.Hence, we hypothesize that these 2D domains are dominated by n=2 RP structures.
Near the band-edge of the 2D domains, there is a clear feature corresponding to a 1s excitonic resonance.It is widely accepted that RP perovskites demonstrate excitonic behavior due to confinement induced increases in the exciton binding energy. [1,8,27]o further analyze this excitonic feature, these absorption spectra were fitted to an Elliot model according to the method outlined in Section S2.1 (Supporting Information).An estimate of the exciton binding energy (E B ) was recovered using the reported 2D bandgap energies of 1.91 eV (649 nm) and 1.89 eV (656 nm) for the films with and without AT respectively. [22]It was found that for the film with AT: E B = 19 meV, and for the film without AT: E B = 13 meV.These values of E b are similar considering the significant error associated with this analysis, [28] suggesting comparable binding energies in the films with and without AT.For comparison, the exciton binding energy of the related compound FASnI 3 has previously been determined with temperature dependent terahertz (THz) spectroscopy to be 3.1 meV. [29]hile the value for the 2D/3D films studied here is larger, it is within the range of common 3D perovskites such as MAPbI 3 , [30] and lower than many reports for 2D perovskites. [1]Accordingly, the n = 1 film exhibited a much stronger excitonic absorption b,e) False color hyperspectral PL maps of the 2D and 3D emission from an area of the films without and with the AT additive respectively.Films were excited at 405 and 750 nm long-and short-pass filters were used to distinguish between 2D and 3D emission.c,f) XRD (black) and GIWAXS (red) data for the films without and with AT.Data is normalized to the amplitude of the peak at q = 0.28 Å −1 which is associated to n = 2 RP layered structures.GIWAXS data was measured at a fixed incidence angle of 0.30°.resonance which, when fitted was shown to correspond to an increased bandgap of 2.21 eV and an exciton binding energy of E B = 120 meV.This measured exciton binding energy is also lower than those reported for similar perovskite compositions such as PEA 2 PbI 4 (E b = 230 meV). [27]However, it has been predicted using density functional theory that replacing Pb with Sn in RP perovskites reduces the exciton binding energy, as is expected considering the reduced bandgap of tin-based perovskites. [29,31]yperspectral photoluminescence (PL) maps were measured for films both with and without the AT additive (shown in Figure 1b,e).In the PL spectra obtained by spatially integrating these maps, distinct PL features can be observed arising from 2Dand 3D-like structures in the film.The 2D-like RP structures emit shorter wavelength PL centred at 720 nm and 3D-like structures emit PL at 950 nm.From the PL and absorption spectra shown in Figure 1a,d, it is clear that the addition of AT has dramatically increased the emissivity and absorption of the film.Both PL signatures from the 2D and 3D structures have greatly increased intensity.By comparing the normalized spectra (Figure S1, Supporting Information), it can also be seen that the 2D emission is more prominent relative to the 3D emission in films with AT than in those without, confirming an increased prominence of 2D perovskite structures in films with AT.
The hyperspectral Pl maps shown in Figure 1b,e verify the presence of microscale 2D and 3D domains.There is clear separation of areas with strong 2D PL emission and areas with strong 3D PL emission with size on the order of 10 μm.This is consistent with previous findings reported by some of the authors. [22]hile the films with AT exhibit increased 2D and 3D PL intensity, these hyperspectral PL maps also show an increase in prominence of 2D regions in the film with AT compared to the film without AT.The 3D dominated domains have been shown to exhibit increased PL lifetimes of 150-200 ns compared to 30-70 ns for the 2D domains. [22]y comparing the amplitude of diffraction peaks associated with 2D structures when observed with grazing incidence wide angle X-ray scattering (GIWAXS), which is a surface sensitive technique, to standard XRD, which is a bulk technique, we can compare the prominence of 2D domains on the surface and in the bulk of each film.These results are shown in Figure 1c,f.It is observed that, in both films, the peak associated with n = 2 RP structures (q = 0.28 Å −1 ) has increased relative prominence in the data from GIWAXS, compared to the data from bulk XRD.This suggests that, as shown previously, [22] 2D domains are more prominent on the surface of the film than in the bulk both in films with and without AT.Notably, previous work by some of the authors demonstrated with in-situ GIWAXS that AT slows formation of 3D structures in the films, promoting increased growth of 2D RP structures throughout the film as is reflected by the increase in 2D PL emission.Furthermore, in the GIWAXS results a weak peak is observed at q = 0.39 Å −1 which is present in the film without AT but not in the film with AT, as is shown in Figure S9 (Supporting Information).This peak is attributed to n = 1 RP structures, suggesting a change in RP phase purity between the films.Furthermore the XRD results from films with AT exhibit an overall increase in diffracted intensity and narrower peak widths suggesting a general improvement in crystallinity of this film compared to the films without AT.

Spectral Features
Transient absorption (TA) spectroscopy using a broadband whitelight probe was employed to distinguish photoexcitation of charge carriers within the 2D and 3D domains of the films.[34][35] De-population of a ground state results in negative bleaching features, corresponding to reduced absorption at the wavelength of the band-edge absorption after above bandgap photoexcitation.TA is a powerful tool for investigating the phase distribution of RP perovskites because, by removing linear absorption effects, the bleach features arising from each phase are clear and well separated, providing increased sensitivity compared to other techniques such as UVvis absorption spectroscopy and X-ray diffraction. [36]he bleaching features that arise when the front (perovskite side) of the sample is excited at 410 nm, which is above the optical transitions of both the 3D and 2D domains, are the features indicated in blue in the heat maps shown in Figure 2. Occurring most prominently at center wavelengths of 650 and 950 nm in the mixed 2D/3D films, these bleaching features have been attributed to the ground states of different RP phases.In the film without AT, we observe a weak bleach feature at 520 nm which we attribute to the n = 1 phase (highlighted blue), another at 650 nm which corresponds to the n = 2 phase (highlighted green), and a series of overlapping bleaching features which cannot be resolved from one another ranging from 700 to 950 nm corresponding to thicker structures of n ⩾ 3 (highlighted orange and pink).Conversely, in the film with AT there are only two well defined bleach features arising from n = 2 RP structures at 650 nm (highlighted green), and 3D (large n) structures at 920 nm (highlighted pink).This confirms the reduced formation of n = 1 RP structures in the films upon the addition of AT, which was indicated by the GIWAXS results, while additionally revealing that the formation of 3 ⩽ n < ∞ RP structures is suppressed.This improved phase purity could be a contributing factor to the increased emissivity observed in these samples, as the minority n = 1 and 3 ⩽ n < ∞ phases in the film without AT could contribute to carrier trapping and non-radiative recombination, reducing the PL quantum efficiency (PLQE) of the film.Such a decrease in carrier trapping is consistent with the increased PL lifetimes observed in the films with AT. [22] These results also support our hypothesis that the 2D domains are dominated by n = 2 RP structures in both 2D/3D films.
In order to probe the generation of carriers in the 2D and 3D domains, TA measurements were taken at two different excitation wavelengths (410 and 780 nm), as shown for the film with AT in Figure 3 and for the film without AT in Figure S11 (Sup- The black line separates the regions where two different white light probes were used.Both samples have clear photobleaching features consistent with the presence of the n = 2 RP phase and 3D structures at 650 and 920 nm, respectively.On the spectra plotted below each map, the spectral regions where bleaching from different RP phases is present are highlighted as a guide to the eye. porting Information).These wavelengths were selected because they lie on either side of the 2D absorption edge.Thus, exciting at 780 nm selectively excites the 3D regions, and the photoexcited carrier density in the 2D domains is expected to be low or non-existent.When excited at 780 nm only one strong bleaching feature is observed for each 2D/3D film, at a central wavelength of 920nm.This feature corresponds to bleaching of the ground state of the 3D domains.A lack of bleaching at the 2D band-edge suggests that no carriers have been generated in or transferred into the 2D domains on the timescale of the measurement.
At similar total photo-excited population densities, the 3D bleach signal is more than twice as strong when excited at 780 nm than at 410 nm.To explain this, we must consider the morphology of the film, as this plays a role in determining the induced carrier populations in each domain.As previously shown, in both films with and without AT, 2D domains are more prominent on the surface of the films than in the bulk.A 410 nm beam doesn't propagate far into the film: its absorption depth is ≈100 nm, hence it primarily excites the surface domains which are mostly 2D in nature.As a result, the 410 nm light is preferentially absorbed by the 2D regions on the surface and less by the 3D regions in the bulk of the film.With 780 nm excitation, all of the light is absorbed by the 3D regions since this wavelength is sub-bandgap for the 2D domains.Furthermore, carriers are absorbed more uniformly throughout the film due to the weaker overall absorption.As a result, these excitation conditions yield a significantly stronger change in absorption at the 3D absorption edge when excited at 780 nm versus excitation at 410 nm.Following from this analysis, it is clear that when exciting at 410 nm the majority of charge carriers are generated in the 2D domains, and when exciting at 780 nm we are exclusively probing the 3D domains of the material.This can be used to inform OPTP studies into the dynamics in these films as will be described later.

Charge Transfer
The ability to observe carrier populations in the different RP phases of the film separately can be a powerful tool for investigating the preferential transfer of charge carriers from wide-bandgap low-n structures to narrow-bandgap high-n structures. [32,37]Such transfer has been observed to occur on a wide range of timescales and in a variety of different RP perovskite compositions. [33,34]That said, there is no evidence of this transfer occurring in these films on a timescale from approximately 300 fs to 1 ns. Figure 3b,d shows the fluence dependent dynamics of the 3D bleach feature when the film with AT is excited at 410 and 780 nm, respectively.For 780 nm excitation the observed decrease in lifetime as fluence increases is indicative of a large carrier density in the 3D domains under these excitation conditions, as this arises from higher-order recombination processes such as bimolecular and Auger recombination.For 410 nm excitation, this fluence dependent behavior is not exhibited, confirming the low charge carrier density in the 3D domains in this case.Furthermore, at the lowest fluence of 780 nm excitation, for which higher order recombination is minimized, the decay dynamics are very similar to the dynamics of the 3D bleach when excited at 410 nm, as shown in Figure S10 (Supporting Information).If the transfer of charges from 2D to 3D domains was significant on this time scale, the dynamics would differ when the film is excited above or below the band-edge of the 2D material.When excited at 410 nm, the rise time of the 3D bleach would likely be delayed, and its decay would be slowed as compared to 780 nm excitation due to the transfer from the excited 2D domains.Hence, the comparable decays of the bleach signal indicate that charge transfer plays a minimal role at this timescale.This is likely due to the 2D and 3D structures in these films being well separated into microscale domains and, as discussed in later sections, the charge carrier mobility is relatively low, inhibiting transfer between them on ultrafast timescales.To further investigate this phenomenon, time resolved PL mapping was employed as shown in Section S5 (Supporting Information).Observed asymmetry in the PL emission distribution indicates that there are preferential pathways for the funneling of charge carriers from the 2D domains to the 3D domains on a timescale of more than 100 ns, which is consistent with the observations in the TA measurements.

Dynamics
Another notable feature of the transient absorption spectra are the strong positive photo-absorption features, centered at around 695 and 980 nm in the TA spectra of both 2D/3D films when excited at 410 nm.As shown in Figure 2, these features are very short-lived relative to the bleaching features.The spectra were globally fit to a set of exponential decay rates which revealed that a single component with a fluence independent lifetime of around 250 fs could accurately fit these ultrafast dynamics.The spectral contribution from this decay component shows strong positive signals at 695 and 980 nm which overlap with the long-lived negative bleaching features (see Section S4.3, Supporting Information).We attribute these photo-absorption features to ultrafast carrier cooling and subsequent exciton formation.As described by Lin et al., these features are often attributed to ultrafast carrier transfer between RP phases due to the rise-time of the 3D bleach being at a similar timescale, but this is ruled out by the dependence of these signals on the excitation wavelength. [34]nterpreting the TA dynamics further is complicated by the overlap of various transient spectral features. [1]Specifically, the sensitivity of photo-absorption and bleaching features in the differential signal to free carriers and bound species such as excitons and polarons, which are both reported to be common in RP perovskites, [38] is poorly understood and complicates the analysis.As a result, we will turn to OPTP measurements in the next section to primarily focus on the dynamics of the free charge carriers in the material.This is motivated by the fact that charge extraction in perovskite solar cells is dominated by free carriers and is highly dependent on their mobility and recombination dynamics.For an excitonic material under equilibrium conditions the free carrier fraction can be estimated using the Saha equation.As is shown in Figure S7 (Supporting Information) this analysis indicates that the carrier population is expected to be a mix of free carriers and excitons in the 2D/3D films at the carrier densities probed in these experiments.In the ultrafast experiments presented here, the carrier population is in a non-equilibrium state, which is likely to be less excitonic, especially in the first picosecond after photoexcitation. [27]Low bandwidth (0.5-3 THz) OPTP experiments are typically considered to not be sensitive to excitons in perovskites at room temperature due to their overall charge-neutrality and the energy scale of excitonic states being either much less than kT or exceeding that of the THz radiation. [39]1] 4. Optical Pump/THz Probe Spectroscopy

Charge-Carrier Mobility
OPTP spectroscopy was carried out on the 2D/3D films and their pure 2D (n = 1) and 3D analogues.Due to strong interactions between terahertz (THz) radiation and free carriers in perovskites, OPTP is a powerful technique for investigating free carrier recombination.The photoinduced change in THz transmission is proportional to the short-range photoconductivity which is in turn proportional to the product of the free carrier density (n), the Table 1.A table of calculated effective mobility values for the mixed films and the 3D and 2D control samples.In the case of the mixed films excited at 410 nm, the values correspond to front excitation/back excitation.The photon energy at 780 nm is too low for band-to-band excitation in the pure 2D sample, hence mobility cannot be measured.photon to free charge carrier branching ratio (ϕ) and the charge carrier mobility (μ). [2,27,39,42,43]From this, the short-range effective carrier mobility (ϕμ) is calculated using the method described in Section S6.1 (Supporting Information).
The calculated values of charge-carrier mobility for the films investigated in this work are presented in Table 1.These values were extracted from the experimental data shown in Figure 4 and Figure S17 (Supporting Information).A range of pump wavelengths were used (specifically 410, 580, and 780 nm) to investigate whether the 2D and 3D domains in the 2D/3D films exhibit different carrier mobility.[46][47][48] We attribute the reduced mobility of the 3D film at a pump wavelength of 410 nm to excitation into a higher electronic band due to the large excess energy at this wavelength, a phenomenon which has previously been observed in a variety of 3D perovskite thin films. [49,50]he effective mobility of both the 2D/3D (ϕμ = 3-6 cm 2 (Vs) −1 ) and 2D (n = 1) (ϕμ = 2-3 cm 2 (Vs) −1 ) films are significantly lower.This can be attributed to a number of factors, including the electronic confinement within the RP layers which reduces the mobility, and, as discussed previously, the excitonic behavior of these samples which results in a photon-to-charge carrier branching ratio of less than one. [2]Although it should be noted that by measuring the mobility immediately after photoexcitation, before carriers have had time to cool and form excitons, it becomes reasonable to assume ϕ is close to one. [27]It is clear from Table 1 that the mixed films exhibit higher effective mobility than the pure 2D film.Interestingly, there is minimal difference between the mobility of the 2D and 3D domains in the film as highlighted by the similar calculated effective mobilities at excitation wavelengths of 410 nm and those at 780 nm (whereupon only 3D domains are excited).This suggests that upon the incorporation of PEA into the film, the carrier transport in the 3D domains of the crystal is severely reduced compared to the carrier mobility in the pure 3D film.We propose that this is largely due to disruption of the microscale structure of the film due to the presence of the 3D and 2D domains, leading to increased scattering of charge carriers from defects and grain boundaries relative to the pure 3D film, which has been previously shown to reduce carrier mobility in polycrystalline perovskite films. [51]Furthermore, from the comparable mobility values in films with and without AT, we conclude that the AT additive has no noticeable effect on the charge-carrier mobility of the films.
The frequency dependent response of the film to photoexcitation can shed light on the nature of the excited species.In the THz frequency range charge carriers in perovskites typically exhibit a Drude-like photoconductivity with a momentum scattering rate which is much greater than the maximum frequency probed by these OPTP experiments. [42,52,53]Hence, we expect a positive real component of the complex photoconductivity with a near zero imaginary component across the whole frequency range of the experiment.THz photoconductivity spectra are displayed in Figure S14 (Supporting Information).While the 3D film clearly displays this behavior, the mixed films, especially those without AT exhibit a quasi-linear decrease in the imaginary conductivity and increase in the real conductivity across the frequency range probed.Such behavior is commonly associated with localization of charge carriers, such as quasi-particle formation or increased carrier scattering from grain boundaries. [40,54] this case, we attribute this to grain boundary scattering due to our XRD results indicating the reduced crystallinity of this film relative to the film with AT.Excitonic localization is ruled out by the presence of this behavior when only 3D domains are excited at 780 nm and hence the excitonic population is expected to be small.

Charge-Carrier Cooling
As with the TA experiment, the pump-probe delay was changed over a window of 1 ns and the samples were excited at a range of excitation fluences for each pump wavelength.Transient OPTP data for the 2D/3D films is shown in Figure 4 and for the pure 2D and 3D films in Figure S20 (Supporting Information).At 410 nm pump wavelength, part of the OPTP signal decays very rapidly within the first picosecond after excitation (see Figure S14, Supporting Information).These fast decays are often observed in OPTP transients for RP perovskites and correspond to hot carrier cooling and subsequent formation of a exciton population. [27,55]he fast timescale of this decay is consistent with the observation of hot carrier cooling in our TA measurements.OPTP spectroscopy is considerably less sensitive to excitons than it is to free carriers, due to their overall neutral electric charge, and hence a drop in ΔT/T is observed.The drop over the first 2 ps is less than 20% of the total signal, further confirming that excitons are a minority species under these conditions.As expected, the pure 2D film exhibits a more significant drop of approximately 40% in the first 2 ps when excited at 410 nm, suggesting an increased excitonic population in this film.At 580 nm, the excess energy is low and so carrier cooling is less of an obstacle to exciton formation, resulting in a smaller initial drop in signal.At 780 nm, when only the 3D domains are being excited, the exciton binding energy in 3D perovskites is typically an order of magnitude lower, [56] resulting in a negligible exciton population.

Modeling Charge-Carrier Recombination
To study the recombination dynamics, we employ a phenomenological three-term rate equation for the photoexcited free carrier density and add contributions from carrier diffusion and photon re-absorption, The k 1 term corresponds to monomolecular Shockley-Read-Hall recombination, the k 2 term corresponds to bimolecular band-to-band recombination, and the k 3 term corresponds to Auger recombination.D is the diffusion coefficient calculated from the effective carrier mobilities given above, and the recycling term represents emitted photons which are re-absorbed.ΔT/T is related to n by approximating the initial carrier density as described in Section S7 (Supporting Information).Using this model, the rate parameters k 1 , ϕk 2 and ϕ 2 k 3 are globally fit to the data over a range of excitation fluences and wavelengths.
In many dynamics studies, the recycling and diffusion terms in Equation 1 are omitted. [2,39,57]However, with the pump wavelength varying over such a large range, the absorption coefficient () also varies significantly between the shortest ( 410 ≈ 1.5 × 10 5 cm −1 ) and the longest ( 780 ≈ 3 × 10 4 cm −1 ) wavelength.As such, a short wavelength laser pulse will generate more carriers near to the surface of the film than a longer wavelength pulse of equal photon flux.Higher order recombination rates (k 2 and k 3 ) are dependent on the local carrier density and so changing the distribution of excited carriers in the film results in different observed population decay as is shown in the modeled OPTP decays shown in Figure S18 (Supporting Information).Furthermore, the carrier distribution is not static and the redistribution of charge carriers via diffusion and photon recycling will affect the apparent recombination rate.It has been shown that, at the high carrier densities employed by OPTP, both of these terms can have a significant effect on the observed dynamics in perovskites. [58]Hence, only by including these terms and modeling the evolution of the charge carrier distribution, can the effect of changing the excitation wavelength be fully sepa-rated from the recombination dynamics and the recombination rates understood.
To achieve this, we employed a similar approach to Crothers et al. to model how the carrier distribution evolves in one dimension during the time window of the experiment. [58]This model has also been successfully applied to inhomogeneous mixed dimensionality perovskites by Motti et al. [59] The recycling term is generated from a ray-tracing model which simulates PL emission from a given depth into the film and calculates the likelihood of re-absorption in other areas of the film.All bimolecular recombination processes are taken to be radiative and reflections at the surfaces are modeled with the Fresnel equations (full details of the model are given in Section S7.4,Supporting Information).It should be noted that this model assumes that there is no spatial inhomogeneity in the charge transport and recombination parameters, this assumption is based on the selective excitation of either 2D and 3D domains as verified with TA spectroscopy, and the comparable charge carrier mobilities in each domain.A typical map of the carrier redistribution in one dimension is shown in Figure S19 (Supporting Information).It is evident that during the time window of the measurement, both photon recycling and carrier diffusion play a significant role in redistributing carriers such that after 1 ns the carrier profile is considerably more uniform than the initial profile, highlighting the need for this approach.By removing the effect of the changing carrier distribution, we can consider the rate parameters in Equation 1to better represent the intrinsic recombination rates associated with the material itself. [58]his dynamics model was tested by applying it to OPTP data for the analogous 2D and 3D films due to their simpler morphology.As expected, the decay profiles varied at each different excitation wavelength.Using this dynamics model allows the OPTP decay dynamics to be accurately represented for these films across multiple excitation wavelengths (as shown in Figure S20, Supporting Information), confirming the validity of this approach.

Dynamics of Films with and without AT
To fit the OPTP data for the mixed 2D/3D films to the model described by Equation 1, the data at pump wavelengths of 410 and 580 nm with a pump-probe delay < 2 ps was removed after converting ΔT/T into free carrier concentration, thereby taking advantage of ϕ being close to one immediately after excitation.By this time, all carrier cooling and exciton formation has already occurred but the effect of charge carrier recombination is negligible allowing the free charge carrier dynamics to be accurately modeled without considering the hot carrier or exciton formation dynamics.Fits of this dynamic model to the OPTP data for the 2D/3D films are shown in Figure 4 and for the 2D (n = 1) and 3D films in Figure S20 (Supporting Information).The parameter values corresponding to these fits are given in Table 2.It was found that the model presented in Equation 1 accurately describes the free carrier recombination dynamics in all films at all pump fluences and excitation wavelengths, as discussed in detail below.
In the 2D/3D films, we find that certain recombination pathways dominate the dynamics at the specific carrier densities and time window investigated.For all fits to the data shown in rate parameters calculated by fitting OPTP data at a range of wavelengths with the dynamic model.An asterisk (*) indicates a parameter which was poorly constrained in the fit and hence cannot be accurately determined.In this case, the value provided is an approximate upper limit determined by the technique shown in Figure 5 and Section S7.6 (Supporting Information).Figure 4, the k 1 term is poorly constrained by the minimization algorithm, proving that it plays no role in the recombination dynamics measured here.This is expected due to the time window being only 1 ns and monomolecular lifetimes of more than 30 ns have been reported for similar materials.The recombination dynamics in the film with AT are dominated by the ϕk 2 term across the whole range of carrier densities probed by this experiment.Hence, only the bimolecular rate could be accurately determined yielding a value of ϕk 2 = 1.8 × 10 -8 cm 3 s -1 .This is more than an order of magnitude larger than ϕk 2 values calculated for Pb-based 3D perovskites when similar dynamics models were employed. [51,58,59]However, as will be discussed later, this value is strongly effected by extrinsic factors relating to the outcoupling of emitted light from the film.
In the case of the film without AT, it was found that Auger recombination dominated the dynamics and that, as a result, only ϕ 2 k 3 could be accurately determined, yielding a value of ϕ 2 k 3 = 3.7 × 10 -28 cm 6 s −1 .This is comparable to ϕ 2 k 3 values reported in other RP and 3D perovskites. [2,27,30]The bimolecular recombination rate was poorly constrained by the model and could not be accurately determined.
Figure 5 illustrates why only a single parameter can be determined for the mixed 2D/3D films by plotting the contribution to the total local recombination rate from each mechanism.With this, the fact that certain parameters cannot be accurately determined allows estimations of an upper bound for each of these terms, these upper limits are shown as the shaded regions in Figure 5.We find that for the sample with AT excited at 780nm: k 1 < 9 × 10 8 s -1 and ϕ 2 k 3 < 3 × 10 -28 cm 6 s -1 and for the sample without AT: k 1 < 5 × 10 7 s -1 and ϕk 2 < 8 × 10 -10 cm 3 s -1 .The calculated values and these upper limits for each film are given in Table 2.These upper limits reveal that the dominance of Auger recombination exhibited in the 2D/3D films without AT at these carrier densities do not arise from a significantly increased ϕ 2 k 3 .Rather the upper limit of ϕk 2 for this film is significantly lower than the measured value for the film with AT indicating that it exhibits a reduced bimolecular recombination rate (ϕk 2 ), which leads to the dominance of the Auger recombination pathway.This reduced observed bimolecular recombination rate in the film without AT likely arises from extrinsic factors associated with the changes in morphology, crystallinity and decreased prominance of 2D domains.
This analysis agrees well with the PL data shown in Figure 1, the increased emissivity of the films with the AT can be directly linked to the increase in PLQE evident from the dominance of radiative, bimolecular recombination in films with AT.By plotting the internal PLQE calculated from the fitted recombination rates, as is shown in Figure S22 (Supporting Information) the increased PLQE of the films with AT can be observed.
The effect of photon recycling is expected to be large in these films, due to the large overlap between the emission and absorption spectra which arises because emission from the 2D domains has energy which is greater than the 3D band-edge absorption.The significance of the difference in bimolecular recombination rate between the films with and without AT can be partially attributed to the effect of photon recycling and out-coupling, but could also be a result of the differences in the prominence of 2D domains. [2]In the model, any charges which undergo bimolec-ular recombination release a photon which can be re-absorbed elsewhere in the film according to the ray-tracing model.Reflections from the surface are taken to be specular but the true out-coupling will depend on a variety of other unknown factors including the surface roughness.The prominence of this radiative process in the films with AT means that the optimal value of the k 2 parameter will decrease significantly if additional outcoupling of photons is factored into the ray-tracing model.It should be noted that while out-coupling considerations could introduce error into the numerical value of ϕk 2 , it is clear from the decay profile that bimolecular recombination is a dominant process in this film.Unlike the sample with AT, and consistent with the observation of decreased emissivity, the low ϕk 2 means that very little radiative recombination occurs in the film without AT, leading to the details of the photon recycling model having little effect on the optimal parameters for this film.

Comparison of Dynamics in the 2D and 3D Domains
As the recombination rates yielded by the model are not dependent on the excitation wavelength, it allows the recombination dynamics within the 2D and 3D domains to be resolved using the fact that when excited at 410 nm the ultrafast response primarily originates from the 2D domains and when excited at 780 nm it arises from the 3D domains, as was proven using TA spectroscopy.Figure 4 shows that this dynamic model fits the OPTP data for the mixed films well.Interestingly, all three excitation wavelengths can be well represented by a single set of recombination coefficients, the values of which are shown in Table 2.This suggests that the different decay shapes at each excitation wavelength arise solely from the different initial carrier distributions induced by the excitation pulse.Hence, by combining the findings from TA spectroscopy and OPTP we find that the observed k 2 and k 3 recombination rates in the 3D and the 2D domains are remarkably similar, despite the increase in electron confinement in 2D domains.This contrasts to studies of RP 2D and 3D films, which typically show that confinement increases these recombination rates. [2,27,60,61]o investigate these surprisingly comparable decay rates within the 2D and 3D domains we again turn to the pure 2D and 3D films described previously.The dynamics in these films were studied using the same modeling process described above.In the case of the 3D film, the dynamics at an excitation wavelength of 410 nm have been omitted due to the aforementioned excitation into a higher electronic band.Fitting to the dynamic model at two wavelengths for each film yields the recombination rates of the 2D and 3D films: ϕk 2 = 0.88 × 10 -8 cm 3 s -1 , ϕ 2 k 3 = 8.0 × 10 -28 cm 6 s -1 , and ϕk 2 = 0.44 × 10 -8 cm 3 s -1 , ϕ 2 k 3 = 4.0 × 10 -28 cm 6 s -1 , respectively.Notably, both ϕk 2 and ϕ 2 k 3 in the 2D film are approximately double that of the 3D film.These differences are not on the scale of those previously reported between 3D and n = 1 RP perovskites [2,27,60,62] .For example, Kober-Czerny et al. measured bimolecular recombination rates with multiple techniques for the n = 1 RP perovskite PEA 2 PbI 4 and a 3D mixed cation lead iodide perovskite.In each case, k 2 increased by more than an order of magnitude between the 3D and 2D films. [27]However, while the role of excitons in the modeling of these dynamics is minimized, the 2D film is expected to be highly excitonic at equilibrium (as shown in Section S2.2, Supporting Information) which adds error to the reported rate parameters from the dynamic model.This analysis indicates that the minimal effect of confinement on the free carrier recombination in this system of RP films results in the observed lack of distinct recombination dynamics for free carriers within the 2D and 3D domains of the 2D/3D films.

Conclusion
By combining multiple ultrafast spectroscopy techniques, we have shown that 2D/3D mixed Pb-Sn iodide perovskites exhibit numerous interesting electronic properties.They consist of distinct regions dominated by 2D n = 2 RP structures and 3D perovskite structures, with the precursor additive AT dramatically improving the RP phase purity and emissivity of the films.Compared to n = 1 RP films these exhibit high carrier mobility, reduced excitonic behavior owing to their reduced exciton binding energy, and slow charge carrier recombination comparable to that of 3D perovskites, all of which would benefit the performance of solar cells made from such films.They also maintain advantages over 3D perovskites due to their improved longevity and ambient stability. [22]e have performed an in-depth analysis of the free carrier recombination mechanisms within these films.Our TA results show that we're able to selectively excite the 2D and 3D domains in the film by using different excitation wavelengths.In addition, ultrafast charge carrier transfer between 2D and 3D domains on sub-nanosecond timescales has been shown to not play a significant role in the carrier dynamics of these films.By applying a dynamic model to fit OPTP data it was found that, in the range of carrier concentrations probed here, bimolecular recombination dominates the dynamics in films with AT.However, in films without AT the bimolecular recombination rate is reduced, leading to Auger recombination becoming dominant.As bimolecular recombination of free carriers is typically associated with radiative band-to-band recombination, the increased emissivity of films with AT can be attributed to this apparent increase in the bimolecular recombination rate.These findings have implications for the application of such materials in LEDs and offer a greater understanding of the mechanisms behind emission in perovskite films.Furthermore, utilising the selective excitation of 2D and 3D domains, established with TA, alongside transient OPTP decay modeling we have shown that free carriers within the 2D and 3D domains in the film exhibit remarkably similar recombination dynamics.The long lifetime and efficient transport of charges in these 2D domains is a promising result for the incorporation of heterogeneous 2D/3D perovskites within solar cells.
Only by combining ultrafast techniques and applying a dynamic model to elucidate the effect of changing the wavelength were we able to reach this conclusion.With OPTP or TA spectroscopy alone such a result would not be possible due to the inherent pump wavelength dependence of the results meaning that the advantages of tuning the excitation wavelength could not be utilized.These insights support the importance of a holistic approach when considering charge dynamics in complex heterogeneous semiconductors.
Photoluminescence Measurements: Hyperspectral PL measurements were acquired using a wide-field IMA VISTM hyperspectral microscope from Photon Etc.equipped with a 2048 × 2048 resolution CMOS camera, scanning the 600-1000 nm spectral range in 2 nm steps with an exposure time of 2 s.The magnification was 20×.The laser wavelength was 405 nm and its intensity 8.36 × 10 3 mW cm −2 .Overall PL spectra were acquired by integration of the hyperspectral map area.
Confocal time resolved photoluminescence images were measured using a confocal microscope setup (PicoQuant, MicroTime 200).The excitation laser was a 405 nm pulsed diode (PDL 828-S"SEPIA II", PicoQuant) with an intensity of 1 μJ cm −2 pulse −1 , directly focused onto the perovskite surface with an air objective (100×, 0.9 NA).The photoluminescence signal was separated from the excitation light (405 nm) using a dichroic mirror (Z405RDC, Chroma).The photoluminescence was then focused onto a SPAD detector for the single photon counting (time resolution of 100 ps) through a pinhole (50 μm), with an additional 410 nm longpass filter.Repetition rates of 2 MHz were used for the confocal maps.
The diffusion maps were instead acquired by splitting the collection beam equally onto two detectors, respectively equipped with 750 nm shortand long-pass filters, for selective detection.The laser intensity was 500suns (sun-equivalent energy per pulse).
GIWAXS measurements were carried out at the I07 Surface and Interface Diffraction beamline at the Diamond Light Source in Didcot (United Kingdom).The measurements were collected with a beam energy of 15 keV, a sample pitch angle of 0.30Å, and a 1 s exposure time.The diffractograms were calibrated with a lanthanum hexaboride sample.The scattered beam was collected by a Pilatus 2M large area detector at a distance of 55.3 cm from the sample.The sample chamber was continuously purged with a 1 L min −1 He flow.The data was azimuthally integrated by taking an azimuthal cross-section across the visible quadrant, centered at the origin of the diffractograms (q-vector coordinates q xy = 0, q z = 0).
Transient Absorption Spectroscopy: In the TA experiments presented here, the pump and probe beams were both produced by an amplified Ti-Sapphire laser system (Spectra Physics MaiTai-Ascend-Spitfire).This outputs broadband 800 nm pulses with a duration of <40 fs at a repetition rate of 1 kHz.For the pump pulse, a Light Conversion TOPAS Prime OPA allowed a wide range of wavelengths to be selected.Two different white light probes were used to cover a large range of wavelengths between 320 and 1100 nm.A short wavelength probe was generated by focusing the 800 nm beam into a CaF 2 crystal, this probe was used to measure the absorbance change in the range 320-720 nm.Longer wavelengths were measured using a white light probe generated with 1300 nm pulses in a sapphire crystal which facilitated measurement in the range 600-1100 nm.Pumped and dark absorbance spectra were measured using an Avantes spectrometer with a resolution of 0.6 nm.A 500 mm delay line in the probe beam allowed the pump-probe delay to be changed by over 3 ns.
Optical-Pump Terahertz-Probe Spectroscopy: For OPTP measurements, the laser system is the same as that described above for the TA experiments.Single cycle THz pulses were generated from an 800 nm beam in a spintronic emitter from TeraSpinTec and focused through the sample using gold plated parabolic mirrors.After the sample the THz was focused onto a ZnTe crystal whereupon it modulated the polarization of an 800 nm "gate" beam via the electro-optic effect.The change in polarization is directly proportional to the THz electric field and was detected with the use of a Wollaston prism and dual photodiodes.The photodiodes were operated in reverse bias and coupled to an RC circuit which was measured by a high-resolution digital oscilloscope (PicoScope 4262).By chopping the THz and pump beams at 500 and 250 Hz, respectively, the relative change in THz transmission was calculated, while correcting for fluctuations in laser power, from a cycle of 4 laser pulses.The THz electric field was determined in the time domain by delaying the THz pulse relative to the gate pulse.A Fourier transform was applied to find the spectrum of the pulse in the frequency domain.The pump-probe delay was varied over a 3 ns range using a 500 mm optical delay stage.To prevent sample degradation measurements were taken under vacuum.

Figure 1 .
Figure1.a,d) Absorption and PL spectra for the films.b,e) False color hyperspectral PL maps of the 2D and 3D emission from an area of the films without and with the AT additive respectively.Films were excited at 405 and 750 nm long-and short-pass filters were used to distinguish between 2D and 3D emission.c,f) XRD (black) and GIWAXS (red) data for the films without and with AT.Data is normalized to the amplitude of the peak at q = 0.28 Å −1 which is associated to n = 2 RP layered structures.GIWAXS data was measured at a fixed incidence angle of 0.30°.

Figure 2 .
Figure 2. Transient absorption of 2D/3D films without (top) and with (bottom) AT.Both films were excited at 410 nm with a fluence of 270 μJ cm −2 .The black line separates the regions where two different white light probes were used.Both samples have clear photobleaching features consistent with the presence of the n = 2 RP phase and 3D structures at 650 and 920 nm, respectively.On the spectra plotted below each map, the spectral regions where bleaching from different RP phases is present are highlighted as a guide to the eye.

Figure 3 .
Figure 3. a,c) TA spectra for the sample with AT at a pump wavelength of 410 nm and 780 nm respectively, and a fluence of ≈270 μJ cm −2 .Spectra at all time delays are plotted according to the color scale shown.b,d) Normalized TA transients at a probe wavelength of 920 nm, corresponding to the 3D bleach feature, for a pump wavelength of 410 and 780 nm, respectively.

Figure 4 .
Figure 4. Fitted OPTP transient data from the mixed films with and without AT, at three different excitation wavelengths.The excitation fluence for each transient is shown in the legends.The first 2 ps have been removed from each transient.The solid lines are global fits to the dynamic model described in the main text and in Section S7.4 (Supporting Information).

Figure 5 .
Figure 5. Effective contributions to the overall free charge carrier population decay rate as a function of number density for the 2D/3D films with (top) and without (bottom) the AT additive.The region in yellow indicates the range of carrier densities probed by OPTP.For the sample with the additive, upper limits on the k 1 and ϕ 2 k 3 rate parameters are shown.For the sample without the additive, upper limits on the k 1 and ϕk 2 rate parameters are shown.
6 M), formamidinium iodide (FAI, 0.6 M), lead iodide (PbI 2 , 0.45 M), tin iodide (SnI 2 , 0.45 M), and tin fluoride (SnF 2 , 0.09 M) in a N,N-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) solution at a DMF:DMSO volume ratio of 3:1.The precursor solution (35 μL) was spin-coated on the substrate at 4000 rpm for 30 s. Anisole antisolvent (200 μL) was dripped onto the substrate 20 s into the spin.The spin coated films were finally annealed at 100°C for 15 min.The ammonium thiocyanate-enriched (AT) films were produced by introducing the NH 4 SCN additive in the precursor solution at an equimolar concentration with respect to PEAI (0.6 M).The pure 2D precursor solution was prepared by dissolving PEAI (1.8 M), PbI 2 (0.45 M), SnI 2 (0.45 M), and SnF 2 (0.09 M) in a DMF and DMSO solution at a DMF:DMSO volume ratio of 3:1.The precursor solution (35 μL) was spin-coated on the substrate at 5000 rpm for 50 s.Anisole antisolvent (200 μL) was dripped onto the substrate 10 s into the spin.The spin coated films were finally annealed at 100°C for 15 min.The pure 3D precursor solution was prepared by dissolving FAI (0.9 M), PbI 2 (0.45 M), SnI 2 (0.45 M), and SnF 2 (0.09 M) in a DMF and DMSO solution at a DMF:DMSO volume ratio of 3:1.The precursor solution (35 μL) was spin-coated on the substrate at 5000 rpm for 50 s.Anisole antisolvent (200 μL) was dripped onto the substrate 10 s into the spin.The spin coated films were finally annealed at 100°C for 15 min.

Table 2 .
: A Table of the optimum