Perovskite superlattices with efficient carrier dynamics

Compared with their three-dimensional (3D) counterparts, low-dimensional metal halide perovskites (2D and quasi-2D; B2An−1MnX3n+1, such as B = R-NH3+, A = HC(NH2)2+, Cs+; M = Pb2+, Sn2+; X = Cl−, Br−, I−) with periodic inorganic–organic structures have shown promising stability and hysteresis-free electrical performance1–6. However, their unique multiple-quantum-well structure limits the device efficiencies because of the grain boundaries and randomly oriented quantum wells in polycrystals7. In single crystals, the carrier transport through the thickness direction is hindered by the layered insulating organic spacers8. Furthermore, the strong quantum confinement from the organic spacers limits the generation and transport of free carriers9,10. Also, lead-free metal halide perovskites have been developed but their device performance is limited by their low crystallinity and structural instability11. Here we report a low-dimensional metal halide perovskite BA2MAn−1SnnI3n+1 (BA, butylammonium; MA, methylammonium; n = 1, 3, 5) superlattice by chemical epitaxy. The inorganic slabs are aligned vertical to the substrate and interconnected in a criss-cross 2D network parallel to the substrate, leading to efficient carrier transport in three dimensions. A lattice-mismatched substrate compresses the organic spacers, which weakens the quantum confinement. The performance of a superlattice solar cell has been certified under the quasi-steady state, showing a stable 12.36% photoelectric conversion efficiency. Moreover, an intraband exciton relaxation process may have yielded an unusually high open-circuit voltage (VOC). Fabrication of a low-dimensional metal halide perovskite superlattice by chemical epitaxy is reported, with a criss-cross two-dimensional network parallel to the substrate, leading to efficient carrier transport in three dimensions.

Compared with their three-dimensional (3D) counterparts, low-dimensional metal halide perovskites (2D and quasi-2D; B 2 A n−1 M n X 3n+1 , such as B = R-NH 3 + , A = HC(NH 2 ) 2 + , Cs + ; M = Pb 2+ , Sn 2+ ; X = Cl − , Br − , I − ) with periodic inorganic-organic structures have shown promising stability and hysteresis-free electrical performance 1-6 . However, their unique multiple-quantum-well structure limits the device efficiencies because of the grain boundaries and randomly oriented quantum wells in polycrystals 7 . In single crystals, the carrier transport through the thickness direction is hindered by the layered insulating organic spacers 8 . Furthermore, the strong quantum confinement from the organic spacers limits the generation and transport of free carriers 9,10 . Also, lead-free metal halide perovskites have been developed but their device performance is limited by their low crystallinity and structural instability 11 . Here we report a low-dimensional metal halide perovskite BA 2 MA n−1 Sn n I 3n+1 (BA, butylammonium; MA, methylammonium; n = 1, 3, 5) superlattice by chemical epitaxy. The inorganic slabs are aligned vertical to the substrate and interconnected in a criss-cross 2D network parallel to the substrate, leading to efficient carrier transport in three dimensions. A lattice-mismatched substrate compresses the organic spacers, which weakens the quantum confinement. The performance of a superlattice solar cell has been certified under the quasi-steady state, showing a stable 12.36% photoelectric conversion efficiency. Moreover, an intraband exciton relaxation process may have yielded an unusually high open-circuit voltage (V OC ).
We studied the growth process and structure of BA 2 SnI 4 (n = 1) superlattice on a MAPb 0.5 Sn 0.5 Br 3 substrate (Supplementary Discussion 1 and Supplementary Figs. 1-4). The Sn-I slabs exhibit a favourable epitaxial relationship with the substrate, forming a thermodynamically stable, vertically aligned lattice 12 (Supplementary Fig. 1). Scanning electron microscopy (SEM) images show that the crystals first grow into criss-cross vertical thin plates followed by lateral merging (Fig. 1a and Supplementary Fig. 2). Similar growth behaviour can be observed in other low-dimensional perovskites grown on different substrates (Supplementary Figs. 3 and 5). Cryogenic scanning transmission electron microscopy (STEM) was used to study the structure of a single plate, which exhibits anisotropy (Fig. 1b). The a-c plane shows a periodic distribution of inorganic Sn-I slabs and organic BA spacers along the a direction (Fig. 1b, middle and Supplementary Fig. 6). The b-c plane shows a continuous Sn-I slab with a coherent heteroepitaxial interface with the substrate (Fig. 1b, right). Therefore, the criss-cross vertical plates on the substrates create a 3D network of Sn-I slabs, not seen previously in any polycrystals ( Supplementary Fig. 7) or conventionally grown single crystals. Furthermore, grazing-incidence wide-angle X-ray scattering further verified their vertically aligned structures 13,14 (Supplementary Fig. 8).
To further study the crystal orientation in the a-b plane, we measured the polarization-dependent photocurrent of superlattices and conventionally grown single crystals (Fig. 1c). The results in both show a strong dependence on the polarization direction, but the response of superlattices has a 90° period, whereas that of conventionally grown single crystals has a 180° period. This is because the inorganic slabs are aligned in two perpendicular orientations in the a-b plane of superlattices, but in only one orientation of conventionally grown single crystals ( Supplementary Fig. 9). Similar trends can also be observed in the carrier lifetime obtained from orientation-dependent transient photovoltage measurements (Fig. 1d and Supplementary Fig. 10). These results collectively support that the superlattice has Sn-I slabs interconnected, with numerous criss-cross thin plates merged in the a-b plane.
Because of the interconnected Sn-I slabs, carriers in the superlattice do not need to cross any grain boundaries or organic spacers both in plane and out of plane. Transient photocurrent measurements along Article the film thickness (c direction) show a much higher carrier mobility in the superlattice than in the polycrystalline or conventionally grown single-crystal sample (Fig. 2a). The grain boundaries in polycrystals markedly reduce carrier mobility 15 (Supplementary Fig. 11). The layered organic spacers make the mobility in conventionally grown single crystals the lowest ( Supplementary Fig. 12). Power-dependent time-resolved photoluminescence measurements show that the superlattice has a longer carrier lifetime than the polycrystal (Fig. 2b), indicating minimal restriction of the carriers. Furthermore, superlattices show better tolerance to high excitation power than polycrystals, suggesting that better crystallinity can reduce material degradation under high excitation power 16 . images showing the criss-cross epitaxial BA 2 SnI 4 superlattice before and after merging into a thin film. Scale bars, 2 μm. b, Schematic (left) and atomic-resolution cryogenic STEM images (middle and right) showing the superlattice structure of a single plate. Cryogenic STEM is essential to minimize the damage of beam-sensitive materials. The epitaxial layer has a well-aligned anisotropic structure without grain boundaries or dislocations. The insets are fast Fourier transform patterns from the epitaxial layer in the a-c plane, which show a 2D diffraction pattern of the superlattice and is different from that of the substrate (middle). The inset fast Fourier transform images in the b-c plane show the structural similarity between the inorganic slab and the substrate (right). Organic atoms are usually invisible under electron diffraction. Scale bars, 6 nm. c, Photocurrent measurements with a linearly polarized excitation source showing that the response of the epitaxial layer (top) shows a period that is half of that of a conventionally grown single crystal (bottom). d, Transient photovoltage measurements showing the orientation-dependent carrier lifetime in the a-b plane. The inset optical image shows the measurement setup. The error bars are from measurements of five different devices. Scale bar, 500 μm.
The structural advantages of superlattices are validated with temperature-dependent current density-voltage ( J-V) characteristics of a BA 2 SnI 4 solar cell. To investigate internal energy barrier for carrier transport, we fabricated a device directly on the superlattice without peeling it off from the epitaxial substrate to minimize any possible confounding factors introduced by the fabrication process 15 (Supplementary Discussion 2 and Supplementary Figs. 13 and 14). As the temperature gradually decreases, thermal energy becomes too small for the carriers to overcome barriers (for example, owing to ionized impurity scattering), so the fill factor (FF) decreases substantially for both superlattice and polycrystalline devices (Fig. 2c). However, the decrease is less pronounced in superlattices, indicating lower internal energy barriers.
We measured the electron-beam-induced current (EBIC) to visualize carrier transport barriers. For polycrystals, the collected currents on the thin film surface heavily depend on grain orientations, indicating disorientated multiple quantum wells (Fig. 2d, left). By contrast, superlattices yield higher and much more uniform currents owing to the well-aligned crystal structure (Fig. 2d, right). Note that superlattices exhibit a criss-cross current pattern owing to their imperfect merging during solution growth ( Supplementary Fig. 15). Similar observations can also be made in the sample cross sections ( Fig. 2e and Supplementary Discussion 3).
The improved carrier dynamics of superlattices allows a longer carrier diffusion length. As the photovoltaic absorber, the thickness of polycrystals is usually highly restricted 17 , for which the external quantum efficiency (EQE) peaks at about 400 nm for BA 2 SnI 4 ( Fig. 2f, top). By contrast, the absorber thickness for superlattices can be increased to around 700 nm with enhanced light absorption and, thus, EQE (Fig. 2f, bottom).
We investigated the heteroepitaxial strain in BA 2 SnI 4 superlattices quantitatively by X-ray diffraction. Compared with conventionally grown single crystals, high overall compressive strains are present in superlattices along the a and b directions, at around 8.59% and around 1.32%, respectively (Fig. 3a, top); a tensile strain of roughly 0.99% is present in the c direction owing to the Poisson effect 18  The superlattice exhibits stronger current signals with a criss-cross pattern, even with a smooth film surface. Scale bars, 200 nm. e, SEM images and corresponding EBIC mapping of the cross section of BA 2 SnI 4 films. The polycrystal exhibits grain-dependent current signals. The superlattice exhibits stronger current signals with a linear pattern. Scale bars, 100 nm. f, Thickness-dependent EQE measurements. The superlattice device exhibits a higher EQE with a larger optimal absorber thickness, indicating that the carrier diffusion length in the superlattice is longer than that in the polycrystal. A longer-wavelength collection edge also indicates a smaller bandgap in the superlattice.
Article Discussion 4). Structural computation by density functional theory (DFT) further shows a lattice compression of Sn-I slabs from about 6.04 Å to about 5.94 Å in the a direction ( Supplementary Fig. 16), yielding an approximately 1.66% strain, which is close to the 1.32% strain in the b direction; the width of organic spacers is compressed from about 7.00 Å to about 5.98 Å (Supplementary Figs. 16 and 17), corresponding to an approximately 14.6% strain. Therefore, the high compressive strain is mostly accommodated by organic spacers. High strain reduces the stability of superlattices ( Supplementary Figs. 18 and 19). For general heteroepitaxial BA 2 MA n−1 Sn n I 3n+1 , as n increases, the volume ratio of the Sn-I slabs increases, the overall lattice strain decreases (Fig. 3b) and the structure is more stable. Moreover, lower strain results in fewer structural defects and smoother surfaces (Fig. 3b, inset images).
To avoid structural change and achieve reliable measurements of superlattices, we chose BA 2 MA 2 Sn 3 I 10 (n = 3) to study their strain-controlled optoelectronic properties. We used ellipsometry to study the dielectric functions (ε′ + iε″). The higher ε′ of superlattices indicates weakened quantum confinement by compressed organic spacers (Fig. 3c), a larger Bohr radius in the multiple quantum wells and, therefore, a higher rate of free-carrier generation 19 (Supplementary Discussion 5). Besides, the shift in ε″, which reflects the absorption wavelength 20 , suggests a smaller bandgap in superlattices compared with conventionally grown single crystals, which is also evident by the longer-wavelength collection edge of superlattices ( Fig. 2f and Supplementary Fig. 20). Temperature-dependent photoluminescence measurements also show a much-reduced fitted exciton binding energy in superlattices compared with conventionally grown single crystals 18,19 (Fig. 3d). In addition, the carrier lifetime in superlattices is slightly longer than conventionally grown single crystals at 0° in transient photovoltage measurements (Fig. 1d). All these characteristics can be attributed to the weakened quantum confinement in superlattices.
Large heteroepitaxial strains heavily influence the stability of superlattices (Fig. 3b, Supplementary Discussion 4 and Supplementary Figs. 18  and 19). We choose BA 2 MA 4 Sn 5 I 16 (n = 5) to investigate the device performance owing to its better stability. To further relieve the strain and create an even more stable structure, we investigated using Bi 3+ (103 pm in radius 21 ) to partially replace Sn 2+ (118 pm in radius 22 ). DFT calculations show that the Bi 3+ tends to concentrate at the interface between the inorganic slab and the organic spacer to relieve the compressive strain (Fig. 4a, top and Supplementary Fig. 21), forming an aggregated  b, DFT-computed and experimentally calculated lattice strain with different n in low-dimensional BA 2 MA n−1 Sn n I 3n+1 perovskites. Crystals with larger n will have smaller strain. Inset SEM images show that a larger n will result in a smoother surface, which is attributed to fewer defects under smaller epitaxial strain. Scale bars, 50 μm. c, Ellipsometry measurements of the dielectric function (ε′ + iε″) of the BA 2 MA 2 Sn 3 I 10 superlattice and conventionally grown BA 2 MA 2 Sn 3 I 10 single crystals. The larger ε′ in the superlattice indicates that the compressive strain can increase the dielectric constant and the Bohr radius in the superlattice. A red shift in ε″ shows that the compressive strain decreases the bandgap of the superlattice. d, Estimated exciton binding energies obtained from temperature-dependent photoluminescence measurements. The smaller fitted exciton binding energy in the superlattice than the polycrystal indicates a weaker quantum confinement effect because of the smaller width of the organic barrier. In the inset equation, I is the integrated photoluminescent intensity, I 0 is the integrated intensity at room temperature, A is an arbitrary constant, E B is the exciton binding energy, k B is the Boltzmann constant and T is the temperature.
Bi 3+ atomic layer to decrease the formation energy (Supplementary Fig. 22 and Supplementary Discussion 6) of the superlattice and yield a more stable structure ( Supplementary Fig. 23). Furthermore, the aggregated Bi 3+ alloying decreases the conduction band minimum (CBM) (Fig. 4a, bottom and Supplementary Figs. 24 and 25). The region without Bi 3+ alloying remains intact. The result is an inorganic slab with a double-band structure. We studied the photovoltaic performance of those superlattices. We chose 10% Bi 3+ -alloyed BA 2 MA 4 Sn 5 I 16 (n = 5) superlattice with a textured surface and fabricated a solar cell directly on the epitaxial substrate ( Supplementary Figs. 26 and 27). Indene-C60 bisadduct (ICBA) was used as the electron transport layer (ETL) because its CBM level ( Supplementary Fig. 28) is higher than that of the Bi/Sn-I but lower than the Sn-I slabs (Supplementary Table 2). The Bi/Sn-I and the Sn-I regions are both in contact with the ETL. The as-certified superlattice solar cell exhibits a stable 12.36% photoelectric conversion efficiency under the quasi-steady state (Supplementary Fig. 29)-the highest in lead-free low-dimensional perovskite solar cells. To further replace the lead-containing substrate, it is also feasible to use other substrates (Supplementary Figs. 3 and 5) or to exfoliate and transfer the superlattice from the epitaxial substrate to a general substrate ( Supplementary  Figs. 30, 31 and 32). Moreover, the quantum efficiency of the solar cell ( Fig. 4b and Supplementary Fig. 29) shows a carrier collection cut-off at approximately 1,190 nm, which gives a bandgap of about 1.042 eV and a V OC of at most 0.802 V according to the Shockley-Queisser limit 23 . However, the certified V OC is 0.967 V, indicating other contributing mechanisms. Figure 4c shows the schematic band diagram of the superlattice solar cell. Because the aggregated Bi 3+ alloying in superlattices could lead to a radiative band structure besides the band-tail states that commonly exist in Bi 3+ -doped polycrystals [24][25][26][27][28][29] (Supplementary Fig. 23 and Supplementary Discussion 6), an intraband relaxation mechanism is possible for contributing to the high V OC . We performed wavelength-dependent J-V measurements to investigate the potential mechanism (Fig. 4d,e). Under short incident wavelengths (less than about 1,000 nm), most electrons are excited into energy states higher than the CBM of both Sn-I and Bi/Sn-I regions. Those electrons from the Sn-I region naturally relax to the CBM of the Sn-I region. Furthermore, a substantial portion of the electrons from the Bi/Sn-I region can also relax to the CBM of the Sn-I region through intraband relaxation (solid blue arrows in Fig. 4c). This transition is possible because the atomic-thin Bi/Sn-I region is easy for carriers to diffuse across. Also, the built-in potential in the p-i-n structure might have facilitated this atomic-scale transition; moreover, the ETL layer favours electron collection from the Sn-I region (solid red arrow in Fig. 4c). Therefore, most of the carriers are in the Sn-I region, yielding a high V OC and a high FF (Fig. 4d,e). Under long incident wavelengths (more than about 1,000 nm), electrons can only be excited in the Bi/Sn-I region. The relatively low-energy d, Wavelength-dependent J-V measurements of a polycrystalline solar cell with a uniform Bi 3+ distribution and, therefore, a single bandgap (left) and a superlattice (right) solar cell. In the polycrystalline device, reasonably small variations in the FF indicate that the carrier transport and the collection are almost independent of wavelength; therefore, the abruptly decreased V OC at about 1,000 nm suggests that the uniform Bi 3+ distribution does not alter the band structure. In the superlattice device, when the incident wavelength is shorter than around 900 nm, neither FF nor V OC exhibit an obvious wavelength dependency. However, once the excitation wavelength is longer than about 900 nm, both FF and V OC decrease substantially. e, Extracted FF and V OC from d.

Article
electrons can only relax to the CBM of the Bi/Sn-I region and then to the ETL by means of interband transition (dashed red arrows in Fig. 4c). Therefore, most of the carriers are in the Bi/Sn-I region, contributing to a low V OC (Fig. 4d,e). The energy barrier between the Bi/Sn-I region and the ETL causes serious charge accumulation (Supplementary Discussion 7), resulting in a low FF (Fig. 4d,e). When the device is excited under mixed incident wavelengths, the high-energy electrons facilitate the quasi-Fermi-level splitting in the Sn-I region. The low-energy electrons will have a relatively small influence on the overall V OC because of the small portion of long wavelengths (between about 1,000 nm and about 1,200 nm) in the solar spectrum (roughly 9%) 30 and, thus, the small quantity of the low-energy electrons. The overall V OC is predominantly determined by the bandgap of the Sn-I region (Supplementary Fig. 33 and Supplementary Discussion 7).
To verify this mechanism, we collected pump-probe ultrafast transient absorption spectra to investigate their hot carrier dynamics (Supplementary Discussion 8). To meet the measurement requirement, a transferred device structure (ITO/superlattice/ICBA/polypropylene tape/ITO) ( Supplementary Fig. 34) was adopted under an external electrical field to mimic the built-in potential of the solar cell. We measured transient absorption spectra with and without the bias (Fig. 5a and Supplementary Figs. 35 and 36). The polycrystalline thin films exhibit very different spectral profiles from superlattices ( Fig. 5a and Supplementary Fig. 35). Obvious ground state bleaching (GSB) signals in the negative intensity region could only be observed in superlattices, indicating more efficient carrier dynamics in the superlattices than those in the polycrystalline thin films.
The lifetime of hot electrons could be obtained by extracting and fitting relaxation time profiles at selected wavelengths ( Fig. 5b and Supplementary Fig. 37). The hot electron lifetimes of superlattices (Bi 3+ -alloyed and Bi 3+ -free) are between about 0.35 and 0.36 ps, which are almost twice that of Bi 3+ -doped polycrystalline thin films (approximately 0.19 ps) (Supplementary Fig. 37). Accordingly, the calculated hot electron diffusion length in superlattices is around 3.9 nm, much longer than the width of the Bi/Sn-I regions (about 0.6 nm) (Supplementary Fig. 37), suggesting that the hot electrons can readily travel across the Bi/Sn-I regions to the Sn-I regions. Furthermore, transient absorption spectra show an obviously enhanced GSB intensity in Bi 3+ -alloyed superlattices when the applied bias increases from 0 V to 10 V (Fig. 5a). By contrast, the excited state absorption (ESA) signal decreases (Fig. 5a). However, no such phenomenon can be observed in Bi 3+ -free superlattices or Bi 3+ -doped polycrystalline thin films (Supplementary Fig. 35), supporting the potential intraband relaxation in Bi 3+ -alloyed superlattices: the increased GSB signal intensity indicates a reduced number of electrons at the ground state in the valence band. Because the excitation setups for 0-V and 10-V measurements are the same, the reduced electrons at the ground state in the valence band are not from a stronger excitation. Therefore, it suggests that the number of electrons relaxing from the conduction band to the valence band after excitation is reduced. However, because the hot carrier lifetime is minimally influenced by the electrical field ( Fig. 5b and Supplementary Figs. 37 and 38), those 'reduced' electrons can only transport to Sn-I regions but not to the ITO or ICBA layers because of the direction of the applied electrical field and the strong interfacial barriers, respectively (Supplementary Discussion 8).
The decreased ESA intensities owing to a reduced number of hot electrons in the valence band provide further evidence for the potential intraband relaxation. However, because of the same excitation setup and similar hot electron lifetimes for 0-V and 10-V measurements ( Fig. 5b and Supplementary Figs. 37 and 38), the obviously reduced hot electron population is not from a weaker excitation or more rapid relaxation but from other relaxation routes. The excited hot electrons have short lifetimes and can only undergo atomic-scale diffusion to Sn-I regions but not to the ITO or ICBA layers (Supplementary Discussion 8).
Besides the unique intraband relaxation mechanism discussed here, other carrier transport processes might also be possible for the high V oc , such as the superposition principles between parallel subcells 31 , sub-band absorption 32 , multiple exciton generation in atomic-scale structures 33 and ion diffusions 34 . Further research is required to gain a complete understanding of this phenomenon. Continued improvements in the device performance are possible with optimizations of the design of the electrode patterns, the resistivity of the top electrode and the band alignment of the ETL/hole transport layer.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-022-04961-1.