α-FAPbI 3 is epitaxially grown on a series of mixed methylammonium lead chloride/bromide (MAPbCl x Br 3−x ) single crystalline substrates by the inverse temperature growth method16. The resulting MAPbCl x Br 3−x substrates, with different compositional ratios and thus lattice parameters, are grown by solutions with different Cl/Br precursor molar ratios (Supplementary Fig. 1)17. We note that the strain in the epilayer is determined not only by the lattice mismatch, but also by the relaxation mechanisms. Lattice distortion relaxes the strain, so the region near the heteroepitaxy interface has the highest strain, which gradually drops at regions distant from the interface. The total elastic strain energy increases as the film grows thicker, until it eventually crosses the threshold energy for structural defect generation, and dislocations will form to partially relieve the misfit18. A slow growth rate of the epilayer is chosen, as a higher rate will increase the defect concentration in the epilayer. The crystalline quality of the substrates is carefully optimized, as the defects in the substrates can propagate into the epilayer (Extended Data Fig. 1).

Heteroepitaxial growth leads to controllable film thickness, preferential growth sites and orientations, compatible fabrication protocols with existing infrastructures and scalable large-area device applications. Figure 1a shows optical images of a series of MAPbCl x Br 3−x substrates with a layer of epitaxial α-FAPbI 3 film on the top. The epilayer has a uniform thickness with a well defined film–substrate interface (Fig. 1b). The film topography can reveal the growth mechanism and sometimes the defects caused by strain relaxation. On the one hand, a sub-100 nm α-FAPbI 3 thin film shows a clear interface (Fig. 1b), and a well defined terrain morphology, with a step height close to the size of a α-FAPbI 3 unit cell, indicating layer-by-layer growth behaviour of the epitaxial α-FAPbI 3 (Extended Data Fig. 2a, b). A 10-μm film, on the other hand, shows non-conformal growth, indicating strain relaxation by dislocation formation (Extended Data Fig. 2c, d).

Fig. 1: Epitaxial α-FAPbI 3 thin films and structural characterizations. a, Optical images of the as-grown epitaxial α-FAPbI 3 thin films. The high transparency of the substrates and the smooth surfaces of the thin films demonstrate their high quality. Scale bars, 4 mm. b, A cross-sectional scanning electron microscope (SEM) image of the epitaxial thin film with controlled uniform thickness. Scale bar, 2 μm. Inset, magnified SEM image of the heterostructure showing a well defined interface. Scale bar, 200 nm. c, High-resolution XRD ω − 2θ scan of the (001) peaks of the epitaxial samples on different substrates showing the increasing tetragonality with increasing lattice mismatch. d, Reciprocal space mapping with (104) asymmetric reflection of the α-FAPbI 3 , for different lattice mismatches with the substrate. The results show a decrease in the in-plane lattice parameter as well as an increase in the out-of-plane lattice parameter with larger compressive strain. Q x and Q z are the in-plane and out-of-plane reciprocal space coordinates. e, Confocal Raman spectra of the epitaxial layer at different strains. We attribute the evolution of the shape and intensity of the peak with strain to the increase in lattice tetragonality under higher strain. We note that the broad peak at approximately 250 cm−1 is attributed to the Pb–O bond induced by laser oxidation. f, Fitting analysis of the Raman peaks. The peak at 136 cm−1 from the strain-free sample (black line) is attributed to the Pb–I bond. With increasing compressive strain, the peak gradually blueshifts as the bond becomes more rigid, and finally splits into a main peak that blueshifts (owing to in-plane bond contraction) and a shoulder peak that redshifts (owing to out-of-plane bond extension). (a.u., arbitrary units). Full size image

The crystallographic relationships between the MAPbCl x Br 3−x substrates and the epitaxial α-FAPbI 3 thin films are illustrated by high-resolution X-ray diffraction (XRD) (Fig. 1c). In their freestanding form, both α-FAPbI 3 and MAPbCl x Br 3−x have a cubic structure19,20. The lattice parameters of freestanding α-FAPbI 3 and MAPbCl x Br 3-x substrates (both with Pm3m space group) are calculated to be 6.35 Å (Supplementary Fig. 1) and 5.83–5.95 Å, respectively. The ratio x for each composition is then calculated to be 0–1.50, according to the Vegard’s Law (Supplementary Table 1). As x increases, the MAPbCl x Br 3−x (001) peaks shift to a higher 2θ angle, indicating a decrease in the lattice parameters of the substrate and therefore an increase in the lattice mismatch (Fig. 1c and Supplementary Table 2). Meanwhile, the α-FAPbI 3 (001) peak shifts to a lower 2θ angle, indicating an increase in the out-of-plane lattice parameter as the in-plane compressive strain increases. When x exceeds 1.50, the strain energy dramatically increases, and the epitaxial growth becomes less thermodynamically favourable. α-FAPbI 3 then randomly crystallizes on the substrate (Supplementary Fig. 2). Peak broadening of the epitaxial α-FAPbI 3 is therefore induced by the epitaxial strain and the reduction in film thickness, instead of by the strain-induced dislocations or the strain relaxation (Supplementary Fig. 3). Figure 1d shows the reciprocal space mapping of strain-free and strained α-FAPbI 3 thin films with different lattice mismatch with the substrate. An increase of tetragonality of the lattice is evident as the compressive strain increases. The corresponding strain levels of the α-FAPbI 3 in those three cases are calculated to be 0%, −1.2% and −2.4%, respectively, on the basis of the lattice distortion (where the negative sign denotes compressive strain). The Poisson’s ratio is determined to be around 0.3, which is consistent with the reported value21.

We also studied the structure of α-FAPbI 3 at different strains (between 0% and −2.4%, on different substrates) by Raman spectroscopy (Fig. 1e). Control experiments exclude any Raman signals from the substrates (Supplementary Fig. 4). The peak at around 136 cm−1 in Fig. 1e, which originated from the stretching of the lead–iodine bond22, increases in intensity and broadens in width as the strain increases. The cubic structure of the strain-free α-FAPbI 3 is less Raman-active, and the detectable signal is usually broad and weak. When in-plane compressive strain increases, the inorganic framework gradually gains tetragonality and produces a stronger Raman signal with a clearly distinguishable shape. Interestingly, at around −1.4% strain, the peak at 136 cm−1 starts to split into two: a main peak at about 140 cm−1 and a shoulder at about 133 cm−1 (Fig. 1f). When the strain is further increased to −2.4%, these two peaks shift to 143 cm−1 and 130 cm−1, respectively. We attribute the blueshift of the main peak to the compression of the in-plane lead–iodine bond, and the redshift of the shoulder peak to the stretching of the out-of-plane lead–iodine bond. This result is also supported by the simulated Raman spectra by first-principles calculations (Supplementary Fig. 4c, d). We also studied the Raman spectra of α-FAPbI 3 of various thicknesses on MAPbCl 1.50 Br 1.50 (Supplementary Fig. 4f). The results are consistent: a strong, sharp peak is detected from a sub-100-nm film with −2.4% strain, and a weak, broad peak is detected from a film of around 2 μm, where the misfit strain is relaxed near the film surface.

Photoluminescence spectra (Fig. 2a) reveal changes in the bandgap of sub-100-nm epitaxial α-FAPbI 3 thin films under different strains (between 0% and −2.4%, on different substrates). The photoluminescence peak of α-FAPbI 3 gradually shifts from about 1.523 eV at 0% strain to about 1.488 eV at −2.4% strain, corresponding to a reduction of about 35 meV in the bandgap. We exclude the possible contributions to this photoluminescence redshift from thickness-dependent bandgap23,24, reabsorption25 or halide migration26 (detailed discussions in the Supplementary Information). The bandgap change is consistent with the first-principles calculations and absorption measurements (Extended Data Fig. 3). The photoluminescence peak in Fig. 2a also broadens with increasing strain (Supplementary Fig. 5), which is not due to possible charge transfer between the epitaxial α-FAPbI 3 and the substrate (Supplementary Fig. 6). Temperature-dependent photoluminescence studies suggest that the emission peak broadening originates from the reduced crystalline quality and the enhanced carrier–phonon coupling under the strain (Extended Data Fig. 4).

Fig. 2: Optical properties. a, Photoluminescence spectra of α-FAPbI 3 at different strains. The redshift of the photoluminescence peak with increasing strain is due to bandgap reduction under compressive strain, consistent with the first-principles calculations. b, Focal-point-dependent confocal photoluminescence spectra of a 3-μm-thick film. When the focal point of the laser (indicated by the red point in the schematic; inset) moves towards the epitaxial interface, the photoluminescence emission peak shifts from about 1.523 eV to about 1.479 eV, owing to the large compressive strain close to the interface. c, Temperature-dependent photoluminescence spectra of a −2.4% strained and a strain-free sample. The bandgap of the strain-free sample shows a stronger temperature dependence than the strained sample, indicating that the substrate can reduce the lattice deformation that is caused by the temperature change. d, UPS spectra of a −2.4% strained and a strain-free sample. The Fermi level and the VBM of the samples can be extracted from the intersections of the curves with the horizontal axis, marked by the solid and dashed vertical lines, respectively. The results reveal that compressive strain increases the VBM more than it does the CBM, owing to the enhanced interaction of lead 6s and iodine 5p orbitals under the compressive strain. Inset, the schematic band diagram of the −2.4% strained and strain-free samples. CB, conduction band; VB, valence band. Full size image

Additionally, we studied confocal photoluminescence spectra at different locations in an α-FAPbI 3 film of around 3 μm on a substrate of MAPbCl 1.50 Br 1.50 (Fig. 2b). The photoluminescence peak shifts from about 1.479 eV when the laser is focused at the interface where the local strain is high, to about 1.523 eV at 3 μm from the interface where the strain is relaxed. As a control, the photoluminescence redshift in a strain-free sample is less obvious (from about 1.516 eV to about 1.523 eV, Supplementary Fig. 7a), which is attributed to reabsorption25. In the strained sample, we exclude elastic relaxation although halide perovskites are much softer than conventional semiconductors27. Our finite element analysis simulation results show that the elastic relaxation for a 3-µm-thick α-FAPbI 3 thin film is negligible: only around 0.09% (Supplementary Fig. 8). Thickness-dependent in-plane XRD is used to study the critical thickness at which the strain will start to be plastically relaxed (Extended Data Fig. 5). The results show that the critical thickness is much less than the thickness we used in this study and, therefore, the relaxation can be attributed to plastic relaxation by the formation of dislocations. Photoluminescence measurements from samples of different thicknesses show a similar trend (Supplementary Fig. 9), indicating that the strain is relaxed by dislocations when the film grows thicker. Temperature-dependent photoluminescence studies indicate that the bandgap of α-FAPbI 3 under both 0% and −2.4% strain shows a strong temperature dependence, owing to the soft nature of α-FAPbI 3 (Fig. 2c and Extended Data Fig. 4)7. The strained-sample bandgap is less temperature-dependent compared to that of the strain-free sample, because the smaller thermal expansion coefficient of the substrate compared to the epitaxial layer introduces a constraint28 (detailed discussions in the Supplementary Information).

Ultraviolet photoelectron spectroscopy (UPS) reveals the bandstructure evolution of the α-FAPbI 3 under strain (see Fig. 2d for 0% and −2.4% strain and Extended Data Fig. 6 for other strains). All samples exhibit p-type behaviour (see Supplementary Information for more details). The Fermi level and the valence-band maximum (VBM) of the samples can be extracted from the UPS data. The results show that strain of −2.4% lifts the VBM upward by about 50 meV compared to the strain-free scenario. Considering the change in the bandgap (about 35 meV, Fig. 2a), the −2.4% strain pushes the conduction-band minimum (CBM) upward by about 15 meV compared to the strain-free scenario. The VBM mainly consists of lead 6s and iodine 5p orbitals, and the enhanced coupling between these orbitals under compressive strain pushes the VBM upward29. The CBM, which consists mostly of nonbonding localized states of Pb p orbitals, is less sensitive to the deformation of the PbI 6 octahedrons7. Therefore, the in-plane compressive strain increases the VBM more than it does the CBM.

The lattice deformation can alter the electronic bandstructure and therefore also the carrier dynamics. The effective mass of charge carriers can be assessed by the band curvature extracted from first-principles calculations30. Figure 3a shows the calculated results of the electron effective mass, \({m}_{{\rm{e}}}^{\ast }\), and hole effective mass, \({m}_{{\rm{h}}}^{\ast }\) (the top panel) and three typical electronic bandstructures (the bottom panels) under different strains. On the one hand, the E–k dispersion of the conduction band remains relatively unaltered, and \({m}_{{\rm{e}}}^{\ast }\) shows only a slight variation under strain between 3% and −3%. On the other hand, compressive strain can modulate the E–k dispersion of the valence band and considerably reduce \({m}_{{\rm{h}}}^{\ast }\).

Fig. 3: Electronic properties. a, Calculated effective masses of the carriers at different strains, and electronic bandstructures under three strain levels (3%, 0% and −3%). The electron effective mass (\({m}_{{\rm{e}}}^{\ast }\)) remains relatively stable with the change in strain, while the hole effective mass (\({m}_{{\rm{h}}}^{\ast }\)) decreases with increasing compressive strain. The dashed lines represent the dispersivity of the valence band; a less dispersive valence bandstructure indicates a smaller hole effective mass. The Z, R and A points are high-symmetry points in the first Brillouin zone of the tetragonal lattice. Bottom panels with coloured borders represent three typical examples with different strains. b, Hole mobilities by Hall effect measurements showing that α-FAPbI 3 with strain of −1.2% has the highest hole mobility. Coloured symbols correspond to the strain as in c. The decrease of the hole mobility with strain higher than −1.2% is attributed to the increase of dislocation density. Number of experiments, n = 5 for each strain. Inset, the structure of the measurement setup (gold, yellow; parylene-C, grey), not to scale. c, Transient photocurrent curves of the epitaxial α-FAPbI 3 under different strains. The transient photocurrent curves are plotted on a log–log scale. The carrier transit time—that is, the inflection point of the photocurrent curve—is marked by a solid red circle. The inflection point indicates the point at which the charge transport carriers switch from the majority to the minority carriers. Lines are guides to the eye. d, Plots of calculated carrier mobilities as a function of the strain magnitudes. The inset equation, μ = d2/Vt, transforms the carrier transit time to the carrier mobility, where μ is the calculated time-of-flight carrier mobility, d is the target region thickness, V is the applied voltage and t is the measured carrier transit time. Number of experiments, n = 5 for each strain. Inset, schematic measurement setup. Coloured symbols correspond to the strain as in c. Full size image

To validate these calculations, Hall effect carrier mobilities of the α-FAPbI 3 thin films under strain of between 0% and −2.4% are measured (Fig. 3b). Finite element analysis simulation results show that potential carrier transfer from the substrate to the epitaxial layer is negligible, owing to an insulating layer (Parylene-C) and the energy barrier between the epitaxial layer and the substrate (Supplementary Fig. 10). All samples measured by the Hall effect show a p-type character, which is consistent with the UPS results. Of all strain levels tested, films under −1.2% strain on a MAPbCl 0.60 Br 2.40 substrate have the highest hole mobility (Fig. 3b). Further increasing the strain results in a drastic drop in the hole mobility, because of the higher dislocation densities that arise at higher strain levels. We note that the devices for Hall effect measurements have an epitaxial-layer thickness larger than the critical thickness to ensure sufficient contact area between the halide perovskite and the bottom electrode. Therefore, a high strain level will induce a high concentration of dislocations that degrade the hole mobility.

To validate the Hall mobility, we carried out time-of-flight measurements. The transient photocurrents after single excitation are plotted logarithmically in Fig. 3c. The carrier transit time shows the smallest value of the film under −1.2% strain. The calculated carrier mobility is plotted as a function of the strain applied (Fig. 3d, see the Supplementary Information for calculation details), and shows a similar trend to that given by the Hall effect. We note that the absolute mobility values from the time-of-flight and Hall effect measurements differ, owing to experimental uncertainties in the type and quality of electronic contacts made during the fabrication processes31. The space-charge-limited-current method can quantify trap density32. Results show that a higher strain level leads to a higher trap density (Extended Data Fig. 7 and Supplementary Fig. 11), which explains the observed decrease in mobility under a higher strain magnitude. Capacitance–frequency (C–ω) spectroscopy is also used to cross-check the trap density (Supplementary Fig. 12), the results of which correspond well with those obtained by the space-charge-limited-current method.

It is widely accepted that α-FAPbI 3 crystals are metastable at room temperature and can quickly phase transform to photo-inactive δ-FAPbI 3 within approximately 24 h (ref. 16), owing to its internal lattice strain and low entropy19,33. Existing strategies for α-FAPbI 3 stabilization, including alloying26 and surface passivation34, either widen the bandgap or raise the carrier transport barrier by introducing nonconductive ligands (detailed discussions in the Supplementary Information). However, the epitaxial α-FAPbI 3 thin film exhibits long-lasting phase stability at room temperature.

Figure 4a shows XRD results of a sub-100-nm epitaxial α-FAPbI 3 thin film that is stable for at least 360 d after growth (red curves in Fig. 4a). In the 10-μm epitaxial thick film (far beyond the threshold thickness at which the strain is fully relaxed), the stabilization effect disappears: after 24 h, XRD peaks from δ-FAPbI 3 can be detected (black curves in Fig. 4a). The phase stability of the strained α-FAPbI 3 is also verified by photoluminescence (Fig. 4b) and Raman spectroscopy (Fig. 4c). A possible stabilization effect from incorporating bromine or chlorine into the α-FAPbI 3 can be excluded, because those foreign ions would stabilize the α-phase regardless of the epilayer thickness. X-ray photoelectron spectroscopy (XPS) measurements showing the absence of bromine and chlorine provide additional evidence that this is not the origin of the stability (Extended Data Fig. 8).

Fig. 4: Epitaxial stabilization. a, Phase stability comparison of thin (sub-100 nm, −2.4% strained; pink) and thick (about 10 μm, strain-free; black) epitaxial α-FAPbI 3 on MAPbCl 1.50 Br 1.50 substrates by XRD. α, α-FAPbI 3 ; δ, δ-FAPbI 3 ; S, substrate. The thin, strained sample shows better phase stability (red curves). For the thick, strain-free sample, the (001) peak for α-FAPbI 3 at 13.92° is the same as the strain-free sample in Supplementary Fig. 1a, which indicates that the top surface of the thick sample is fully relaxed (day 0, black curve). The X-ray can penetrate about 10–20 μm into the halide perovskites, which explains why the substrate peaks are more intense in the thin sample than in the thick sample. The thick, strain-free sample shows signs of a phase transition to δ-FAPbI 3 after 24 h (lower black curve). b, Phase stability study by photoluminescence spectroscopy. Re-measurement of the thin, strained sample after 360 d (lower pink curve) shows no obvious photoluminescence peak shift, but does show a slight decrease in peak intensity owing to its natural degradation into PbI 2 (ref. 16). For the thick, strain-free sample, the photoluminescence spectrum shows an emission peak close to 1.52 eV, similar to that in the strain-free α-FAPbI 3 bulk crystal shown in Fig. 2a, indicating a full strain relaxation in the thick sample. Re-measurement after 24 h (lower black curve) shows that the thick film undergoes a transition from the α phase to the δ phase. Insets, optical images of the two samples, showing clear visual clues of the phase stability in the thin, strained sample (black α phase) and the phase transition in the thick, strain-free sample (yellow δ phase) after 24 h. Scale bars, 2 mm. c, Phase stability study by Raman spectroscopy. The Raman characteristics of the thin, strained sample show a peak at 143 cm−1 with no substantial difference after 360 d; the thick, strain-free sample (peak at 136 cm−1) shows signs of a phase transformation to δ-FAPbI 3 after 24 h, as revealed by its signature peak at 108 cm−1. Full size image

The mechanism of the stable thin α-FAPbI 3 can be explained by two reasons. First, the interfacial energy of cubic α-FAPbI 3 /cubic substrate is much lower than that of hexagonal δ-FAPbI 3 /cubic substrate, which is the most critical factor for the stabilization effect (Supplementary Fig. 13, Supplementary Table 3, and see Supplementary Information for details). The epitaxial lattice is constrained to the substrate owing to the strong ionic bonds between them and, therefore, the lattice is restricted from the phase transition. Second, the driving force of the α-to-δ phase transition is believed to be the internal tensile strain in the α-FAPbI 3 unit cell, which can induce the formation of vacancies and subsequent phase transition35. In this study, the epitaxial film is under compressive strain, which neutralizes the effect of the internal tensile strain. Therefore, the synergistic effect of the low-energy coherent epitaxial interface and the neutralizing compressive strain are the key to α-FAPbI 3 stabilization. As a control, epitaxial α-FAPbI 3 thin film is removed from the substrate (Supplementary Fig. 14); the removed α-FAPbI 3 transforms to the δ phase within 24 h.

We demonstrate high-responsivity photodetectors as a use case of the strain engineered α-FAPbI 3 thin film. Figure 5a shows the current–voltage (I–V) characteristics of a strain-free device and a device under −1.2% strain. The dark current at −1 V in the strained device is around 15% higher than that in the strain-free one, indicating the higher defect density of the strained device. However, the photocurrent in the strained device increases by approximately 180% compared to the strain-free device. We attribute the photocurrent increase to higher carrier mobility and better alignment of VBM to the Fermi level of the gold electrode under compressive strain (Supplementary Fig. 15).

Fig. 5: Photodetector characterizations of the α-FAPbI 3 thin films. a, I–V characteristics of Au/α-FAPbI 3 /indium tin oxide photoconductor structured photodetectors. The dark current and photocurrent of the −1.2% strained detector are about 15% and 180% higher than those of its strain-free counterpart. Detectors are tested with a 685-nm laser under 0.015 W cm−2. b, Comparison of responsivity of the −1.2% strained and strain-free photodetectors. The responsivity of both devices shows an increasing trend with decreasing incident power, as the chances of carrier recombination go down at low illumination intensities36. The strained device yields a higher responsivity owing to higher carrier mobility and better band alignment. Inset, the statistical average of the detector performance. Number of experiments, n = 5 for each strain value. c, External quantum efficiency spectra of the −1.2% strained and strain-free photodetectors showing that the strained photodetector yields a higher external quantum efficiency as well as a broader absorption spectrum (Extended Data Fig. 9d), owing to enhanced carrier mobility and bandgap reduction. d, Response times of the photodetectors, with faster rise and fall times for the −1.2% strained (9 μs and 34 μs) than the strain-free (14 μs and 50 μs) device due to the enhanced carrier mobility and transport. Full size image

Responsivity of the two photodetectors—defined as the change in photocurrent per unit of illumination intensity—is measured at various illumination intensities (Fig. 5b). The responsivity of the strained device, which reaches a maximum of 1.3 × 106 A W−1 at an incident power density of 1.1 × 10−7 W cm−2, is almost twice of that of the strain-free device. This is again attributed to the enhanced carrier mobility and the better band alignment of the strained device. The responsivity of this strained device is, to our knowledge, the highest reported for a α-FAPbI 3 device under similar measurement conditions (for example, applied voltage and incident power (Supplementary Table 4)). Similar to the trend in Hall effect carrier mobility, the measured responsivity peaks at −1.2% strain (Extended Data Fig. 9a). Compressive strain also improves the detectivity and the gain of the photodetector (Extended Data Fig. 9b, c). Devices with a diode structure can reduce the dark current, but have a much lower responsivity: on average 500 times lower than that of the photoconductor-type device (Supplementary Fig. 16).

The strained device also shows an enhanced external quantum efficiency over the visible range (Fig. 5c), owing to the enhanced carrier mobility as well as more efficient carrier transport across the gold–perovskite interface. Additionally, after normalizing the spectra, a distinct response in the short-wave infrared region (>810 nm) can be identified for the strained device (Extended Data Fig. 9d), consistent with the photoluminescence measurements showing bandgap reduction under compressive strain. The rise and fall times of the strained device are around 30% shorter than those of the strain-free device, indicating a faster carrier dynamics (Fig. 5d).