Introduction

Lead halide perovskites are organic-inorganic hybrids of the established ABX3 perovskite structure (Fig. 1a), with A-site cations (e.g., methylammonium MA+, formamidinium FA+ or Cs+) occupying the lead halide octahedral network (B = Pb2+, X = I, Br, Cl). They have recently gained significant attention for a variety of optoelectronic applications, including photovoltaics1,2, photodetectors3, light-emitting diodes (LEDs), and lasers4. Their extraordinary photovoltaic performance, with power conversion efficiency of single-junction perovskite solar cells now exceeding 25 %5, has been attributed to the photo-generation of free carriers with a long lifetime, large diffusion length, and high defect tolerance6,7,8.

Fig. 1: Principle of perovskite ultrafast infrared nano-imaging.
figure 1

a Unit cell structure of the triple cation perovskite \([{({{{{{{{{\rm{FA}}}}}}}}}_{0.83}{{{{{{{{\rm{MA}}}}}}}}}_{0.17})}_{0.95}{{{{{{{{\rm{Cs}}}}}}}}}_{0.05}]{{{{{{{\rm{Pb}}}}}}}}{({{{{{{{{\rm{I}}}}}}}}}_{0.83}{{{{{{{{\rm{Br}}}}}}}}}_{0.17})}_{3}\). b Photoinduced polaron formation in perovskites. An injected photoinduced carrier is self-trapped by the deformation of the surrounding lattice. c Ultrafast infrared nano-imaging of triple cation perovskite with 515 nm visible pump excitation with fluence of ~80 μJ/cm2, and 8.3 μm mid-infrared probe, detecting the amplitude of the transient nano-localized carrier absorption AHPP(T), which we attributed to either nano-localized polaron absorption or Drude carrier response.

Strong electron-lattice coupling and large polaron formation have been proposed9, originating from a soft lattice exhibiting low-frequency polar fluctuations10,11, leading to structural deformations across multiple unit cells that stabilize the photoinduced carriers (Fig. 1b). These large polarons screen the electron-hole Coulomb interaction to enhance the carrier lifetime with modest carrier mobility12,13,14, and may account for the microscopic origin of the defect tolerance even in spin-coated polycrystalline films15.

Understanding the nature of the dynamic lattice deformation of perovskites has been an outstanding goal of ultrafast spectroscopy. Optical Kerr effect (OKE) spectroscopy12,16,17 and 2D IR spectroscopy18,19,20,21 have revealed lattice structural fluctuation on ~ps time scale. Slow hot carrier cooling, exceeding 10 ps, has also been demonstrated and attributed to a hot phonon bottleneck22,23,24. The dynamic evolution of polarons in perovskites has been tracked by ultrafast diffuse X-ray scattering, which resolved the lattice distortion that evolves over tens of ps25. Mid- to far-infrared spectroscopy proved particularly advantageous for inferring the low-energy landscape of photoinduced polaron, vibrational lattice, and coupled phonon dynamics26,27. Notably, in visible-pump/infrared-probe nanosecond time-resolved spectroscopy, a transient resonance assigned to a polaron absorption has recently been identified, and attributed to a transition from a phonon-trapped to free-carrier state28,29,30.

However, with these spectroscopic signals representing ensemble averages, they cannot readily provide the full pictures of the complex spatio-temporal evolution of polarons in perovskites, given the extraordinary degree of spatial heterogeneity in the optoelectronic response that ranges across atomic, domain, grain, and device scales31,32,33,34. To address this issue, a variety of microscopy experiments have helped resolving the spatial complexity of perovskites. Ground-state XRD microscopy has demonstrated heterogeneous lattice strain correlated with fluorescence lifetimes35. In the excited state, ultrafast visible-probe microscopy has probed exciton dissociation and carrier diffusion dynamics24,36,37, yet it lacks specificity to the evolving many-body interactions of carriers with phonons and neighboring carriers. Infrared vibrational scattering scanning near-field optical microscopy (IR s-SNOM) resolves nanometer spatial disorder in the cation-lattice interaction that is suggested to be associated with chemical heterogeneity26. While these experiments imply that lattice disorder underlies the optoelectronic non-uniformity, the key excited-state heterogeneity in electron-phonon coupling and associated polaron dynamics has remained elusive.

Here, we apply ultrafast spatio-temporal infrared nano-imaging38,39,40 to a triple cation perovskite \([{({{{{{{{{\rm{FA}}}}}}}}}_{0.83}{{{{{{{{\rm{MA}}}}}}}}}_{0.17})}_{0.95}{{{{{{{{\rm{Cs}}}}}}}}}_{0.05}]{{{{{{{\rm{Pb}}}}}}}}{({{{{{{{{\rm{I}}}}}}}}}_{0.83}{{{{{{{{\rm{Br}}}}}}}}}_{0.17})}_{3}\) (Fig. 1a) to resolve mid-infrared transient carrier absorption at the nanoscale (Fig. 1c). For injected carrier densities exceeding 1019 cm−3, and as relevant to high-fluence applications of perovskites, we observe ultrafast nano-localized infrared absorption with 10s–100s ps relaxation dynamics, depending on carrier density and associated many-body interactions. The relaxation dynamics varies spatially by 10–20% within the film both at intra- (~100 nm) and inter- (100–400 nm) grain scales. The lineshape evolution in the broadband far-field pump-probe spectra points to an increase in scattering time and associated increase in correlation length of the excited carriers. We analyze this behavior by applying both a phenomenological adiabatic polaron absorption model30 as well as the conventional Drude model41. By projecting the non-uniform relaxation dynamics into a map of polaron fit parameter evolution, the extracted polaron delocalization radii evolve from <1 nm to ~2 nm with associated increase in an effective stabilization energy from <150 cm−1 to ~250 cm−1 over a ~1 ns time scale. Equivalently, based on Drude modeling, correspondingly derived scattering times would evolve from ~2 fs to ~5 fs. We attribute the heterogeneity in the evolution of polaron delocalization to an underlying fundamental disorder in lattice dynamics and associated interaction with photoinduced carriers, which may be introduced inadvertently during synthesis or be photoinduced. These results suggest that optoelectronic properties of perovskite films may still be far from their fundamental limits and point to pathways for further improvements through the spatial and temporal control of electron-electron and electron-phonon interactions.

Results

AFM topography (Fig. 2a) and corresponding heterodyne-detected pump-probe IR s-SNOM image (Fig. 2b) of the triple cation perovskite acquired at a pump-probe delay of T = 2 ps show the nanoscale spatial variation of the photo-induced carrier absorption AHPP(T). AHPP(T) varies by ~30% on both a grain-to-grain scale (~100 nm) as well as larger (100–400 nm) length scales. The amplitude of the s-SNOM signal in general is known to be highly susceptible to topographic features and may not directly be a measure of a material specific optical signature (topographic artifacts). While the variation of AHPP(T) is partly correlated with topography associated with the individual crystallites, a significant contribution from a topography-uncorrelated signal can be assigned to and correspondingly scales with the density of photoinduced carriers (Supplementary Fig. S3). We also show that the transient absorption nano-imaging exhibits a distinct feature from corresponding ground-state nano-imaging (Supplementary Fig. S4), which corroborates the non-trivial heterogeneity in the photoinduced carrier density (see Supporting Information for details).

Fig. 2: Ultrafast infrared nano-imaging of many-body carrier dynamics.
figure 2

AFM topography (a) and the corresponding heterodyne near-field pump-probe signal amplitude AHPP(T) image (b) acquired with the pump-probe delay T of 2 ps. c Time evolution of AHPP(T) demonstrating the heterogeneity in ultrafast carrier formation and relaxation over hundreds of nanometers. d AHPP(T) decay profiles extracted at two locations based on the imaging in c. e AHPP(T) decay profiles on another sample at two different locations acquired by the continuous scanning of the pump-probe delay time. f Image of the average decay time constant τavg extracted from the biexponential fits to the imaging in panel c. g Correlation plot between AHPP(T = 2 ps) and τavg (dashed, linear fit).

The corresponding spatio-temporal evolution with varying pump-probe delays T (Fig. 2c) shows both a spatial and a temporal heterogeneity in the ultrafast carrier relaxation over few ps to 100s ps. The dynamics are characterized by two distinct time scales demonstrated via a biexponential fit to τ1 = 7 − 11 ps and τ2 = 150 − 220 ps, as seen from the local AHPP(T) evolution extracted at two representative sample locations (Fig. 2d). This range of values is typical and similar for different samples, with an example shown in Fig. 2e for two representative local s-SNOM traces of AHPP(T).

To quantify the spatial disorder in the polaron relaxation rate, we calculate the average decay time constant τavg derived from fits of AHPP(T) to biexponentials of form \({a}_{1}{e}^{-T/{\tau }_{1}}+{a}_{2}{e}^{-T/{\tau }_{2}}\) with τavg ≡ (a1τ1 + a2τ2)/(a1 + a2) at each sample location, yielding a nanoscale map of τavg (Fig. 2f). The variation in τavg exhibits an anti-correlation with AHPP(T = 2ps) (Fig. 2g), suggesting that larger polaron densities generally lead to faster relaxation (excitation induced relaxation). Correspondingly, a faster relaxation is observed with increasing pump fluence (see Supporting Information).

In order to relate the nanoscale spatial heterogeneity in photoinduced carrier absorption to the underlying microscopic mechanisms, we perform complementary visible-pump broadband-infrared-probe transient absorption spectroscopy. Figure 3a shows the observed sub-ns evolution of the spectrally-integrated transient absorption signal ΔA(T). As can be seen, the relaxation dynamics is strongly dependent on the injected carrier density n0 calculated based on the visible pump fluence and absorption coefficient, varying from 2 × 1017 cm−3 to 6 × 1019 cm−3. This strong pump fluence dependence of the photoinduced carrier relaxation rate in perovskites, as established previously42,43,44,45, can be described by the following recombination model

$$\frac{dn}{dT}=-{k}_{2}{n}^{2}-{k}_{3}{n}^{3}$$
(1)

with time-dependent carrier density n, bimolecular recombination rate k2, and higher-order contribution k3. A first-order term is negligible in the high-fluence regime that we study, thus leaving only second- and third-order terms in Eq. (1)42. We perform a corresponding global fit (dotted lines in Fig. 3a) of all time traces for the different injected carrier densities n0, with k2 and k3 as fitting parameters. The rate constants obtained of k2 = 4.7 × 10−10 cm−3s−1 and k3 = 1.2 × 10−29 cm−6s−1 fall within the range of previously reported values for different types of perovskites and probe frequencies42,43,44,45. Using k2 and k3, Fig. 3b shows the derived dependence of dn/dT as a function of the injected carrier density n0, demonstrating the transition from simple bimolecular recombination at low densities to higher-order for n0 > 1019 cm−3 as discussed below.

Fig. 3: Transient broadband infrared absorption spectroscopy.
figure 3

a Transient absorption relaxation ΔA(T) for variable carrier density (solid lines), with global fit to recombination model (Eq. (1), dashed). b Calculated carrier relaxation rate as function of injected carrier density based on fit parameter from A, with many-body regime for densities above 1019 cm−3. c Transient absorption spectra \({{\Delta }}A(\overline{\nu })\) at different pump-probe delays T for an injected carrier density of 1.7 × 1019 cm−3. Bold line - transient absorption spectra, thin line - fitting with polaron absorption model in Eq. (2). Inset: evolution of line shape based on normalized spectra. d Effective polaron stabilization energy and size evolution derived from fits of spectra in C and polaron absorption in Eq. (2). See main text Eqs. (2) and (3) and associated discussion for the details of these parameters. e Anti-correlation between instantaneous decay rate constant k and effective stabilization energy Ep and size R. f Corresponding anti-correlation between k and Drude scattering time τD extracted from Drude lineshape fitting of the data in panel c.

We then spectrally resolve the transient absorption \({{\Delta }}A(T,\overline{\nu })\) signal, acquired for a constant injected carrier density of n0 = 1.7 × 1019 cm−3, but for variable pump-probe delays with results shown in Fig. 3c. We note that the spectrally narrow feature at ~1720 cm−1 arises from CN anti-symmetric vibration of the FA cation20,40,46. The narrowing of the transient absorption spectra (Fig. 3c, inset) clearly suggests that correlation lengths and scattering times associated with photoinduced carriers increase with increasing pump-probe delay. However, to the best of our knowledge, the theory of the optical response of photoinduced polarons has not yet been fully established, particularly in the high density regime aside from some studies in oxides47,48.

We thus first apply the simple phenomenological polaron absorption model proposed by Emin30. In this model, within the Franck–Condon approximation which assumes no relaxation of the lattice during the transition,the transition rate is calculated between a phonon-trapped hydrogen-like carrier wave function as a ground-state and a free-carrier state as an excited state. A larger polaron gives rise to a narrower linewidth in this model. This is because a correspondingly lower momentum would result in a momentum mismatch for the transition at higher frequencies. While the predicted absorption spectrum in this model has been suggested to deviate from that obtained by diagrammatic quantum Monte Carlo method based on Fröhlich model49 particularly in terms of the peak and onset energy of the absorption, the model by Emin still provides for an intuitive picture of how the polaronic delocalization of the carriers impact the linewidth of the transition. The same polaron absorption model has recently been used to interpret nanosecond time-resolved mid-infrared spectra of MAPbI328, where a resonance at ~1200 cm−1 has been attributed to a polaron resonance.

The analytical form of the phenomenological polaron absorption model by Emin is given by30

$$\frac{\alpha (\omega )}{{n}_{p}}=\frac{128\pi {e}^{2}}{3m\omega c}\frac{{(\beta R)}^{3}}{{[1+{(\beta R)}^{2}]}^{4}},$$
(2)

with

$$\beta=\frac{\sqrt{2m(\hslash \omega -3{E}_{p})}}{\hslash },$$
(3)

with effective polaron radius R (corresponding to the 1/e distance of the exponential electron delocalization length), polaron stabilization energy Ep, and effective electron mass m = 0.2me28, and polaron density np. In this model, the polaron absorption exhibits the onset of absorption at 3Ep (Fig. 1c) with the peak position close to 3Ep but with a blue-shift that depends on the polaron radius R. However, this absorption onset of 3Ep assumes the transition to a Franck–Condon state with no lattice relaxation30, which may not be applicable particularly for the relatively shallow phonon trapping under the high density of carriers explored in this work50,51. Therefore, Ep should only be viewed as an effective stabilization energy. The extracted values for Ep and R, as plotted in Fig. 3d, increase on ps to sub-ns time scales as shown schematically in Fig. 3e. Over the course of 1 ns, Ep evolves from ~200 cm−1 to ~350 cm−1 while R increases from ~1 to ~2.5 nm. In comparison to the lattice constant of ~1 nm52, this demonstrates that multiple unit cells deform collectively to stabilize the carriers at later times, justifying the fitting with large polaron absorption model30. We also note that the model might underestimate the polaron radius for a given linewidth by neglecting a quantum nature of the polarization field51.

While the polaron absorption model by Emin would reproduce the subtle resonant-like feature centered at ~1100 cm−1 (Fig. 3c), within the bandwidth of our mid-infrared laser source we cannot rule out a Drude response as an alternative mechanism. A Drude-like response was previously suggested in sub-microsecond time-resolved mid-infrared spectroscopy in MAPbI3 perovskite53. We thus also perform a Drude analysis with details in Supporting Information (Supplementary Fig. S10). In the case of a Drude response, the observed lineshape evolution would correspond to the Drude scattering time τD increasing from ~3 fs to ~7 fs over the 1 ns time window, which would signify a decrease in carrier scattering and corresponding increase in carrier mobility41.

By comparing the evolution of R and Ep (polaron model) in Fig. 3d and τD (Drude model) to the corresponding relaxation curve of ΔA(T) in Fig. 3a (bold, magenta), we find that R, Ep, and τD are anti-correlated with respect to the instantaneous carrier relaxation rate k. We determine the instantaneous relaxation rate k, which is given by

$$k\equiv -\frac{1}{{{\Delta }}A(T)}\frac{d{{\Delta }}A(T)}{dT}=-\frac{1}{n(T)}\frac{dn(T)}{dT},$$
(4)

analytically from a phenomenological bi-exponential fit of ΔA(T). The combined results as shown in Fig. 3e, f then demonstrate that, based on polaron absorption, smaller and less stable polaron should lead to rapid recombination, evolving towards fewer yet more stable larger polarons. Similarly, based on the Drude analysis, the increase in carrier lifetime would correspond to longer scattering times as the carrier density decreases.

The anti-correlations in Fig. 3e, f allow us to relate the spatial heterogeneity in nanoscale relaxation dynamics in Fig. 2 to the underlying microscopic evolution in polaron parameters R and Ep, or Drude scattering time τD. To this end, we convert the images of the instantaneous decay rate k (Fig. 4a), as extracted based on bi-exponential fits of the data shown in Fig. 2b, to images of Ep and R or τD at each time delay with the result shown in Fig. 4b. As can be seen in the leftmost panel at early pump-probe delay times T < 10 ps, the extracted polaron radius R based on polaron absorption is significantly smaller than the perovskite lattice constant of ~1 nm. We thus only provide the upper bound of the polaron radius based on large polaron absorption model30. Yet for T > 10 ps, R becomes comparable to the lattice constant, and at 100 ps polarons extend across multiple unit cells.

Fig. 4: Spatio-temporal quasi-particle carrier evolution.
figure 4

a Instantaneous relaxation rate images derived from the set of spatio-temporal images of Fig. 2c via bi-exponential fitting. b Corresponding temporal evolution of polaron effective stabilization energy Ep and polaron delocalization radius R, or Drude scattering time τD, based on the relationship derived in Fig. 3e, f. c Increase of R(T) (polaron absorption model) or τD (Drude scattering time) at two selected sample locations indicated in panel b, showing the spatial heterogeneity in the dynamic evolution of polaron size or carrier mobility. d Cartoon indicating the spatially non-uniform electron-lattice coupling as a potential underlying mechanism for heterogeneous carrier relaxation dynamics, which in turn results in the heterogeneity in carrier recombination and relaxation. Larger polarons associated with longer lifetime promote charge separation whereas smaller polarons with shorter lifetime are more susceptible to carrier recombination.

Lastly, we compare the polaron behavior between two representative sample locations (Fig. 4c) as derived from biexponential fits to the data in Fig. 4b. As can be seen, some crystallites (spot 1, red) consistently exhibit a larger larger polaron radius R or scattering time τD than other crystallites (spot 2, blue) until they reach similar final states at a later time. Such heterogeneity suggests disorder in the interplay between electron-electron and electron-phonon interactions, which would directly impact carrier lifetimes, mobility, and thus device performance as discussed below.

Discussion

Ultrafast infrared nano-imaging (Fig. 2) demonstrates the previously inaccessible spatial heterogeneity in carrier relaxation dynamics. With the direct probe of the photoinduced carrier absorption in the mid-infrared, we show its spatio-temporal evolution and heterogeneity on sub-ns time and sub-μm length scales. This heterogeneity leading to a non-uniform photoinduced carrier density and associated nanoscale spatial heterogeneity in photon-to-carrier quantum yield is likely due to a complex interplay of varying degrees of local chemical environment, lattice strain, crystallinity, and crystallite orientations.

The observed anti-correlation between the injected polaron density AHPP(T = 2 ps) and relaxation time τavg (Fig. 2g) is characteristic of many-body interactions of carriers as expected from the high injection carrier density of n0 = 5.5 × 1019cm−322,23,24. In contrast, hot carriers are unlikely to dominate the observed nano-localized mid-infrared transient absorption as follows from the observed fluence dependence where higher injected carrier densities result in faster relaxation. This behavior is not expected for the case of hot carrier dynamics, where a higher injection carrier densities would lead to slower relaxation due to the hot-phonon bottleneck effect22,23,24. We also note that the heterogeneity we observe mainly occurs at the grain-to-grain scale, in contrast to a previously observed heterogeneity of exciton segregation at individual grain boundaries36.

Different mechanisms have been invoked to explain transient mid-infrared resonances in semiconductors in general54 and perovskites in particular. However, plasma oscillation via Coulomb interaction, as established in GaAs55,56, can be excluded as an origin of the mid-infrared resonance we observe in the perovskite, because the peak position would red-shift as the carrier density decays, in contrast to the blue-shift we observe (Fig. 3c, d). A Rashba effect has been proposed and observed in a two-dimensional layered perovskite57; yet the bulk response of a three-dimensional perovskite with full inversion symmetry is unlikely to give rise to such a transition28.

We thus attribute our transient mid-infrared response to the optical absorption of multi-polarons. We note, however, that the nature of the optical response of such high density polarons has not yet been fully established. To phenomenologically extract the correlation lengths and times of the photoinduced carriers, we apply both the adiabatic polaron absorption model by Emin30 and a conventional Drude model41, respectively. Within the uncertainties of the experiment, the evolution of the lineshape observed can be consistently described with both models. In the case of polaron absorption28, the derived polaron radii evolving from R ~ 1 to ≤2.5 nm would be significantly smaller than the R ~ 10 nm previously reported for lower injected carrier density (n0 ≤ 1017 cm−3)29. We attribute this difference to our higher excited carrier density of n0 > 1019 cm−3, where excitation-induced many-body interactions dominate. The competition for phonon modes to couple initially blocks the formation of larger polarons (Fig. 3e) based on electron-electron interactions. The large third-order coefficient k3 = 10−29 − 10−28 cm−6s−1 in perovskites42,43,44,45,58 may thus be due to an effective two-body process where the binding energy is density dependent.

Our observed lineshapes are also well reproduced by the Drude model, which suggest an increase in carrier mobility due to reduced electron-electron interaction as the carrier density decays. The derived scattering times of ~7 fs at long pump-probe delays is in reasonable agreement with results from both carrier mobility59 and THz photoconductivity measurements60. Yet, given the pronounced Auger recombination in perovskites compared to conventional inorganic semiconductors, the evolving scattering time may not trivially be attributed to the simple electron-electron interactions, but includes many-body interactions also involving electron-lattice interactions with finite size effect as discussed above. With probable contributions from both models present in the multi-polaron system, it is the intricate interplay between electron-electron and electron-phonon interactions that controls the carrier relaxation dynamics in perovskites.

In the Supporting Information, we also provide the fluence-dependent transient absorption spectra that exhibit the behavior consistent with the time-dependent spectra in Fig. 3c, suggesting that the effect of hot-phonon bottleneck and other effects related to intraband relaxation in the observed signal appear to be minor (Supplementary Fig. S11). Also, based on the narrowband pump-probe measurement tracking the transient vibrational response in detail, a possible heating-induced contribution to the infrared response seems insignificant (Supplementary Fig. S12)46.

We attribute the spatio-temporal evolution of carrier dynamics (Fig. 4b) to the fundamental disorder in many-body interactions (Fig. 4d). The trap states with their typically lower density of ntrap ~ 1017 cm−361,62 are unlikely to play a dominant role in inducing heterogeneity, given the much higher photo-injected carrier density of n0 = 5.5 × 1019 cm−3.

In some domains, the photoinduced carriers can be more coupled to the perovskite lattice through enhanced electron-phonon coupling. This would allow for the rapid increase in polaron size R and effective stabilization energy Ep in the polaron model. Alternatively, screened electron-electron interactions give rise to enhanced scattering time τD and enhanced mobility. In other domains, the electron-phonon coupling is less efficient, resulting in the slower growth of polarons that would compromise the stability of carriers. The spatial disorder in the perovskite lattice, previously identified by time-averaged measurements in the ground state and attributed to lattice strain35 and/or to chemical heterogeneity26,63 and associated intragrain defects64, likely gives rise to the observed spatial disorder in the dynamic electron-lattice interactions. We note that, due to the high-fluence excitation required to achieve sufficient contrast for nano-imaging, we cannot discern whether the heterogeneity is inherently introduced in synthesis or is photo-induced, both of which are critical for high-fluence application of perovskites.

For optoelectronic applications with high injected carrier densities (>1017 cm−3), such as LEDs, lasers, nano-photonics, or solar-concentrated photovoltaics, suppressing the density dependent higher-order many-body relaxation by eliminating domains and grains could facilitate the rapid growth of polarons as a key factor for enhancing device performance. The optimization of the electron-phonon coupling through, e.g., chemical composition65,66, substrate and interface control67, and the combination with polaritonic systems68, could not only help further optimize photovoltaic performance but also expand the application space of perovskite-based devices.

For photovoltaic applications with typically lower injected carrier density (~1014 − 1015 cm−3), the disordered electron-phonon coupling then not only becomes the source of the observed photovoltaic heterogeneity31,32,33,34, but may also modulate the potential landscape of carriers, resulting in non-Langevin recombination with significantly enhanced carrier lifetime69,70. The nanoscale heterogeneity in carrier relaxation dynamics in such a regime has recently been successfully explored with nanosecond time-resolved microwave near-field optical microscopy71, which attributes the heterogeneous sub-μs carrier relaxation dynamics to non-uniform trap states. In contrast, in our study with the injected carrier density being much higher than the trap density, the observed heterogeneity is more sensitive to heterogeneous many-body electron-electron and electron-phonon interactions mediated by the perovskite lattice. Yet, we note that a future enhanced sensitivity and contrast of ultrafast infrared nano-imaging would also allow probing into the low-density carrier regime as, e.g., relevant for photovoltaic applications. Also, to distinguish polaron absorption and Drude response and to further elucidate the microscopic mechanism underlying the transient response, further spectroscopic extension towards the low frequency range would be necessary.

In summary, we performed ultrafast infrared nano-imaging of perovskite films, resolving a spatially heterogeneous transient infrared relaxation dynamics at ps to sub-ns time scales and nanometer sub-grain to inter-grain length scales. Far-field transient broadband infrared spectroscopy directly projects the relaxation dynamics onto the underlying spatio-temporal evolution of polaron size, stabilization energy, and Drude scattering time. The observed spatial heterogeneity and co-existence of domains with variable polaron evolution and associated carrier stabilization suggests that the device performance currently achieved based on spin-coated films is far from its fundamental limit. Equally, the current work motivates the further development of theory which can describe the photoinduced polaron absorption in the high carrier density regime with pronounced Auger recombination. The result suggests room for improvement in achieving efficient electron-phonon coupling and rapid polaron growth across a film, e.g., through further refinement in chemical composition, thin film processing, or interfacial control.

The approach of ultrafast infrared nano-imaging as demonstrated in this work is generally applicable to any type of perovskites to guide spatial engineering and nanostructuring of perovskites72,73 through nano-spectroscopy of polaron dynamics. This includes two-dimensional (2D) layered and quasi-2D perovskites where the control of the spatial heterogeneity in exciton dissociation and polaron formation is a key pathway to further improve their device performance74.

Methods

Triple cation perovskite films of \([{({{{{{{{{\rm{FA}}}}}}}}}_{0.83}{{{{{{{{\rm{MA}}}}}}}}}_{0.17})}_{0.95}{{{{{{{{\rm{Cs}}}}}}}}}_{0.05}]{{{{{{{\rm{Pb}}}}}}}}{({{{{{{{{\rm{I}}}}}}}}}_{0.83}{{{{{{{{\rm{Br}}}}}}}}}_{0.17})}_{3}\) (Fig. 1a) are prepared by spin-coating a precursor solution onto a cleaned glass substrate75 for ultrafast infrared nano-imaging and onto a CaF2 substrate for far-field transient absorption spectroscopy. Atomic force microscopy (AFM) topography (Fig. 2a) shows grains of 100 – 200 nm in size, characteristic of fresh samples without degradation26,76.

We implement ultrafast heterodyne infrared (IR) nano-imaging as developed recently40 to probe the spatio-temporal evolution of the ultrafast carrier dynamics. As shown in Fig. 1c, 515 nm (2.4 eV) pump pulses (Pharos, Light Conversion; ~200 fs fwhm pulse duration, ~80 μJ/cm2 fluence, modulated by an acousto-optic modulator at ΩM ~ 50 kHz) inject photoinduced carriers into the conduction band. Mid-infrared 8.3 μm pulses (Orpheus OPA/DFG, Light Conversion; ~170 fs fwhm pulse duration, ~100 μJ/cm2 fluence) probe the resulting carrier absorption in transient IR s-SNOM. The transient mid-infrared response arises from optical absorption creating a high carrier density, which we analyze applying both the phenomenological adiabatic polaron absorption model28,30 and the Drude model41 to extract correlation lengths and times of the photoninduced carrier dynamics. The repetition rate of 1 MHz ensures complete relaxation of the photoinduced carriers between subsequent laser shots. In our home-built ultrafast s-SNOM system, the collinear pump and probe pulses are directed to the apex of a metallic tip (Arrow-NCPt, NanoAndMore USA) in an atomic force microscope (AFM; Innova, Bruker) operating in tapping mode at the frequency ωt ~ 250 kHz40.

The tip-scattered near-field signal ENF is heterodyne amplified with a local oscillator pulse ELO and detected by a HgCdTe detector (KLD-0.1-J1, Kolmar Technologies). The near-field pump-probe signal ΔENF is selectively detected by sideband lock-in detection at 2ωt ± ΩM. Based on the two-phase measurement, the background-free near-field pump-probe amplitude AHPP(T) is isolated as a function of pump-probe delay T, with spatial resolution of ~50 nm limited by the radius of the tip apex40. Typically 1 μm × 1 μm images are acquired at 64 × 64 pixels with a scan rate of 0.2 Hz.

We avoided measuring samples with already microscopically resolvable textures, which tended to result in rapid photo-induced degradation (Supplementary Fig. S5C, D). Despite the high fluence excitation, the near-field scattering intensity (Supplementary Fig. S5A) as well as the vibrational resonance arising from the formamidinium (FA) cation (Supplementary Fig. S5B) is temporally stable26, suggesting minor cation migration77. Careful inspection of AFM topography demonstrates that, while overall topographic features are well maintained even after 1 hour of constant illumination, some domains show signatures of roughening after 20 min of illumination that has been recently attributed to photoinduced nano-grain formation of PbI2 (Supplementary Fig. S5E)78. However, PbI2 itself is unlikely to contribute to the observed near-field pump-probe signal due to its much weaker absorption at 2.4 eV compared with the FAMACs perovskite. We further observe that the local formation of these nano-grains does not strongly correlate with the observed relaxation dynamics in bulk domains (Supplementary Figs. S6 and S7). The two domains we analyze in detail (domain 1 and 2 in Figs. 2 and 4) do not show the features of this nano-grain formation.

We complement infrared nano-imaging by far-field visible-pump/infrared-probe transient absorption spectroscopy. To that end, a spectrally broad infrared pulse is generated by difference-frequency generation (DFG) of a 1030-nm pump with a broadband near-infrared pulse from a home-built non-collinear optical parametric amplifier (NOPA)79. The transmitted infrared probe pulse is subsequently detected in a symmetric Michelson interferometer. With the mid-infrared probe spanning one octave from 1000 to 1700 cm−1, we measure the transient absorption spectrum \({{\Delta }}A(T,\overline{\nu })\) with varying pump fluence from ~2 μJ/cm2 to ~150 μJ/cm2 at 180 kHz repetition rate.

The measurements were performed under nitrogen purge. For further details on sample preparation, ultrafast infrared nano-imaging, and far-field pump-probe transient absorption spectroscopy, see Supporting Information, Supplementary Note S1.