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Directed assembly of layered perovskite heterostructures as single crystals

Abstract

The precise stacking of different two-dimensional (2D) structures such as graphene and MoS2 has reinvigorated the field of 2D materials, revealing exotic phenomena at their interfaces1,2. These unique interfaces are typically constructed using mechanical or deposition-based methods to build a heterostructure one monolayer at a time2,3. By contrast, self-assembly is a scalable technique, where complex materials can selectively form in solution4,5,6. Here we show a synthetic strategy for the self-assembly of layered perovskite–non-perovskite heterostructures into large single crystals in aqueous solution. Using bifunctional organic molecules as directing groups, we have isolated six layered heterostructures that form as an interleaving of perovskite slabs with a different inorganic lattice, previously unknown to crystallize with perovskites. In many cases, these intergrown lattices are 2D congeners of canonical inorganic structure types. To our knowledge, these compounds are the first layered perovskite heterostructures formed using organic templates and characterized by single-crystal X-ray diffraction. Notably, this interleaving of inorganic structures can markedly transform the band structure. Optical data and first principles calculations show that substantive coupling between perovskite and intergrowth layers leads to new electronic transitions distributed across both sublattices. Given the technological promise of halide perovskites4, this intuitive synthetic route sets a foundation for the directed synthesis of richly structured complex semiconductors that self-assemble in water.

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Fig. 1: Reaction design scheme for targeting templated perovskite intergrowths.
Fig. 2: Oxyacids in the organic layers of perovskites and the exchange of H3O+ with Li+.
Fig. 3: Conceptualized dimensional reduction of 3D parent structures to afford the layered heterostructures.
Fig. 4: Comparison of the perovskite-PbX2 (X = Cl, Br) heterostructures.

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Data availability

Additional crystallographic information, powder X-ray diffraction data, optical data, and animated structural relationships between intergrowths and parent structures are available in the Supplementary Information. Crystallographic information files (CIFs) for the new structures are available from the Cambridge Crystallographic Data Center under reference numbers 1994577–1994579 and 1995031–1995037.

References

  1. Hwang, H. Y. et al. Emergent phenomena at oxide interfaces. Nat. Mater. 11, 103–113 (2012).

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  2. Novoselov, K. S., Mishchenko, A., Carvalho, A. & Neto, A. H. C. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).

    Article  CAS  PubMed  Google Scholar 

  3. Wong, F. J. & Ramanathan, S. Nonisostructural complex oxide heteroepitaxy. J. Vac. Sci. Technol. A 32, 040801–040817 (2014).

    Article  CAS  Google Scholar 

  4. Saparov, B. & Mitzi, D. B. Organic–inorganic perovskites: structural versatility for functional materials design. Chem. Rev. 116, 4558–4596 (2016).

    Article  CAS  PubMed  Google Scholar 

  5. Li, J., Chen, Z., Wang, R.-J. & Proserpio, D. M. Low temperature route towards new materials: solvothermal synthesis of metal chalcogenides in ethylenediamine. Coord. Chem. Rev. 190, 707–735 (1999).

    Article  Google Scholar 

  6. Lobo, R. F., Zones, S. I. & Davis, M. E. Structure-direction in zeolite synthesis. J. Incl. Phenom. Mol. Recognit. Chem. 21, 47–78 (1995).

    CAS  Google Scholar 

  7. Rao, C. N. R. & Thomas, J. M. Intergrowth structures: the chemistry of solid-solid interfaces. Acc. Chem. Res. 18, 113–119 (2002).

    Article  Google Scholar 

  8. Schaak, R. E. & Mallouk, T. E. Perovskites by design: a toolbox of solid-state reactions. Chem. Mater. 14, 1455–1471 (2002).

    Article  CAS  Google Scholar 

  9. Viciu, L., Koenig, J., Spinu, L., Zhou, W. L. & Wiley, J. B. Insertion of a two-dimensional iron-chloride network between perovskite blocks. Synthesis and characterization of the layered oxyhalide, (FeCl)LaNb2O7. Chem. Mater. 15, 1480–1485 (2003).

    Article  CAS  Google Scholar 

  10. Tulsky, E. G. & Long, J. R. Dimensional reduction: a practical formalism for manipulating solid structures. Chem. Mater. 13, 1149–1166 (2001).

    Article  CAS  Google Scholar 

  11. Shi, E. et al. Two-dimensional halide perovskite lateral epitaxial heterostructures. Nature 580, 614–620 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  12. Mercier, N. & Riou, A. An organic–inorganic hybrid perovskite containing copper paddle-wheel clusters linking perovskite layers: [Cu(O2C–(CH2)3–NH3)2]PbBr4. Chem. Commun. 123, 844–845 (2004).

    Article  Google Scholar 

  13. AlShammari, M. B. et al. Phase transitions, optical and electronic properties of the layered perovskite hybrid [NH3(CH2)2COOH]2CdCl4 of γ-aminobutyric acid (GABA). Chem. Phys. Lett. 702, 8–15 (2018).

    Article  ADS  CAS  Google Scholar 

  14. Spencer, J. B. & Lundgren, J.-O. Hydrogen bond studies. LXXIII.* The crystal structure of trifluoromethanesulphonic acid monohydrate, H3O+CF3SO3, at 298 and 83°K. Acta Crystallogr. B 29, 1923–1928 (1973).

    Article  CAS  Google Scholar 

  15. King, E. J. The ionization constants of taurine and its activity coefficient in hydrochloric acid solutions from electromotive force measurements. J. Am. Chem. Soc. 75, 2204–2209 (1953).

    Article  CAS  Google Scholar 

  16. Pietraszko, A. & Lukaszewicz, K. Crystal structure of α-LiNH4SO4 in the basic polytypic modification. Pol. J. Chem. 66, 2057–2061 (1992).

    CAS  Google Scholar 

  17. Nord, A. G. Crystal structure of β-Li2SO4. Acta Crystallogr. B 32, 982–983 (1976).

    Article  Google Scholar 

  18. Doudin, B. & Chapuis, G. Structure analysis of the high-temperature phases of [NH3(C3H7)]2CuCl4. I. The commensurate phases. Acta Crystallogr. B 46, 175–180 (1990).

    Article  Google Scholar 

  19. Komornicka, D., Wołcyrz, M. & Pietraszko, A. Polymorphism and polytypism of α-LiNH4SO4 crystals. Monte Carlo modeling based on X-ray diffuse scattering. Cryst. Growth Des. 14, 5784–5793 (2014).

    Article  CAS  Google Scholar 

  20. Macíček, J., Gradinarov, S., Bontchev, R. & Balarew, C. A short dynamically symmetrical hydrogen bond in the structure of K[Mg(H0.5SO4)2(H2O)2]. Acta Crystallogr. C 50, 1185–1188 (1994).

    Article  Google Scholar 

  21. Rentzeperis, P. J. & Soldatos, C. T. The crystal structure of the anhydrous magnesium sulphate. Acta Crystallogr. 11, 686–688 (1958).

    Article  CAS  Google Scholar 

  22. Wolf, N. R., Connor, B. A., Slavney, A. H. & Karunadasa, H. Doubling the stakes: the promise of halide double perovskites. Angew. Chem. Int. Ed. 60, 16264–16278 (2021).

    Article  CAS  Google Scholar 

  23. Subramanian, L. & Hoffmann, R. Bonding in halocuprates. Inorg. Chem. 31, 1021–1029 (1992).

    Article  CAS  Google Scholar 

  24. Plasseraud, L., Cattey, H. & Richard, P. Isolation and X-ray characterization of {[phthalazinium](CuCl2)}: a new example of a dichlorocuprate(I) presenting a rare staircase chain structure. Z. Naturforschung B 65, 317–322 (2010).

    Article  CAS  Google Scholar 

  25. Lumbreras, M. Structure and ionic conductivity of mixed lead halides PbCl2xBr2(1−x). II. Solid State Ion. 20, 295–304 (1986).

    Article  CAS  Google Scholar 

  26. Meresse, A. & Daoud, A. Bis(n-propylammonium) tetrachloroplumbate. Acta Crystallogr. C 45, 194–196 (1989).

    Article  Google Scholar 

  27. Kamminga, M. E. et al. Confinement effects in low-dimensional lead iodide perovskite hybrids. Chem. Mater. 28, 4554–4562 (2016).

    Article  CAS  Google Scholar 

  28. Smith, M. D., Connor, B. A. & Karunadasa, H. I. Tuning the luminescence of layered halide perovskites. Chem. Rev. 119, 3104–3139 (2019).

    Article  CAS  PubMed  Google Scholar 

  29. Hybertsen, M. S. & Louie, S. G. Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390–5413 (1986).

    Article  ADS  CAS  Google Scholar 

  30. Rohlfing, M. & Louie, S. G. Electron-hole excitations in semiconductors and insulators. Phys. Rev. Lett. 81, 2312–2315 (1998).

    Article  ADS  CAS  Google Scholar 

  31. Rohlfing, M. & Louie, S. G. Electron-hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927–4944 (2000).

    Article  ADS  CAS  Google Scholar 

  32. Strinati, G. Application of the Green’s functions method to the study of the optical properties of semiconductors. Riv. Nuovo Cimento 11, 1–86 (1988).

    Article  MathSciNet  CAS  Google Scholar 

  33. Rivera, P. et al. Interlayer valley excitons in heterobilayers of transition metal dichalcogenides. Nat. Nanotechnol. 13, 1004–1015 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Stokes, H. T., Hatch, D. M. & Campbell, B. J. ISODISTORT, ISOTROPY software suite, https://iso.byu.edu (2020).

  35. Campbell, B. J., Stokes, H. T., Tanner, D. E. & Hatch, D. M. ISODISPLACE: a web-based tool for exploring structural distortions. J. Appl. Crystallogr. 39, 607–614 (2006).

    Article  CAS  Google Scholar 

  36. Brese, N. E. & O’Keeffe, M. Bond-valence parameters for solids. Acta Crystallogr. B 47, 192–197 (1991).

    Article  Google Scholar 

  37. Slater, J. C. Atomic radii in crystals. J. Chem. Phys. 41, 3199–3204 (1964).

    Article  ADS  CAS  Google Scholar 

  38. Earnshaw, A. & Greenwood, N. N. Chemistry of the Elements 367–405 (Elsevier, 1997).

  39. SAINT and SADABS 8.38A (Bruker AXS, 2017).

  40. Sheldrick, G. M. SHELXT – integrated space-group and crystal-structure determination. Acta Crystallogr. A 71, 3–8 (2015).

    Article  MATH  CAS  Google Scholar 

  41. Sheldrick, G. M. Crystal structure refinement with SHELXL. Acta Crystallogr. C 71, 3–8 (2015).

    Article  MATH  CAS  Google Scholar 

  42. Dolomanov, O. V., Bourhis, L. J., Gildea, R. J., Howard, J. A. K. & Puschmann, H. OLEX2: a complete structure solution, refinement and analysis program. J. Appl. Crystallogr. 42, 339–341 (2009).

    Article  CAS  Google Scholar 

  43. Toby, B. H. & Von Dreele, R. B. GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J. Appl. Crystallogr. 46, 544–549 (2013).

    Article  CAS  Google Scholar 

  44. Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).

    Article  CAS  Google Scholar 

  45. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  46. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  CAS  PubMed  Google Scholar 

  47. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  PubMed  Google Scholar 

  48. Giannozzi, P. et al. Advanced capabilities for materials modelling with quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).

    Article  CAS  PubMed  Google Scholar 

  49. van Setten, M. J. et al. The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table. Comput. Phys. Commun. 226, 39–54 (2018).

    Article  ADS  CAS  Google Scholar 

  50. Deslippe, J. et al. BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Comput. Phys. Commun. 183, 1269–1289 (2012).

    Article  ADS  CAS  Google Scholar 

  51. Del Ben, M. et al. Large-scale GW calculations on pre-exascale HPC systems. Comput. Phys. Commun. 235, 187–195 (2019).

    Article  ADS  CAS  Google Scholar 

  52. Del Ben, M. D. et al. Accelerating large-scale excited-state GW calculations on leadership HPC systems. In SC20 Int. Conf. High Performance Computing, Networking, Storage and Analysis, https://doi.org/10.1109/SC41405.2020.00008 (IEEE, 2020).

  53. Connor, B. A. et al. Alloying a single and a double perovskite: a Cu+/2+ mixed-valence layered halide perovskite with strong optical absorption. Chem. Sci. 12, 8689–8697 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Depmeier, V. W. Die Kristallstruktur von Athylammoniumtetrachloromanganat(II) bei Raumtemperatur. Acta Crystallogr. B 32, 303–305 (1976).

    Article  Google Scholar 

  55. Dou, L. et al. Atomically thin two-dimensional organic-inorganic hybrid perovskites. Science 349, 1518–1521 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

This work was funded by the US Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515. M.L.A. is supported by an EERE (Office of Energy Efficiency and Renewable Energy) postdoctoral fellowship and B.A.C. is supported by a National Science Foundation (NSF) graduate fellowship (DGE-114747) and the McBain award from Stanford Chemistry. K.P.L. thanks the Center for Molecular Analysis and Design at Stanford University for a graduate fellowship and Stanford Chemistry for the William S. Johnson award. SC-XRD studies were performed either at the Advanced Light Source (beamline 11.3.1) at the Lawrence Berkeley National Laboratory (LBNL) or at Stanford Nano Shared Facilities, supported by the NSF (award ECCS-1542152). We thank S. Teat for helpful discussion and M. Smith and E. Crace for experimental assistance. DFT calculations were supported by the US DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering (Theory FWP), under contract no. DE-AC02-05CH11231. We acknowledge computational resources at the Molecular Foundry, supported by the Office of Science, Office of Basic Energy Sciences, of the US DOE under contract DE-AC02-5CH11231, at the National Energy Research Scientific Computing Center (NERSC; Cori), at the Oak Ridge Leadership Computing Facility (Summit) accessed through the INCITE program (a DOE Office of Science User Facility; grant number DE-AC05-00OR22725), and the Texas Advanced Computing Center (TACC; Stampede 2) through an XSEDE Award (DMR190070) supported by the NSF grant number ACI-1548562.

Author information

Authors and Affiliations

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Contributions

The authors M.L.A., A.S.V. and B.A.C. synthesized and structurally characterized the materials. M.L.A. and K.P.L. performed the optical measurements. H.I.K. defined and guided the project direction. M.R.F. and J.B.N. conducted the electronic structure calculations and theoretical analyses. All authors helped write the manuscript.

Corresponding author

Correspondence to Hemamala I. Karunadasa.

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Stanford University has submitted a provisional patent application on this work with H.I.K., M.L.A. and A.S.V. as co-inventors.

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Extended data figures and tables

Extended Data Fig. 1 The crystal structure of (RPO(OH)2)2CuCl4 viewed along the c-axis highlighting the hydrogen bond network in the organic bilayer.

Carbon bonded hydrogens are not shown for clarity. Each phosphonic acid donates two hydrogen bonds and accepts two hydrogen bonds at the unprotonated oxygen atom. Each phosphonic acid hydrogen bonds only to phosphonic acid groups on the opposing face of the organic bilayer to form the checkerboard pattern illustrated. The elements P, C, H, N and O are coloured pink, grey, white, blue and red, respectively.

Extended Data Fig. 2 Schematic illustrating the templating of a hydronium sulfonate between layers of a CuCl42– perovskite sublattice.

a, The archetypal parent 3D perovskite with the relevant slice highlighted. The parent structure RbCuCl3 is unknown though RbCuF3 is known. b, The dimensionally reduced product of a copper chloride perovskite as isolated in the single-crystal structure of (propylammonium)2CuCl4 and the previously reported layered crystal structure of hydronium triflate. Structure directing functional groups are highlighted in blue (ammonium) and red (sulfonate). c, The same interactions from b are shown in the compound (H3O)2(taurine)2CuCl4. The elements Cu, Cl, C, H, N, S, O and F are coloured dark-green, green, grey, white, blue, yellow, red and lime-green, respectively.

Extended Data Fig. 3 Structural comparison between intergrowths and layered reference structures.

a, b, The slab for the magnesium intergrowth in (Mg(H2O)2)(taurine)2CuCl4 (a) and the reference structure KMg(H0.5SO4)2•2(H2O) (b). c, d, The slab for the lithium intergrowth in Li2(taurine)2CuCl4 (c) and the reference structure 𝛼-Li(NH4)SO4 (d). Mg, Li, S, O and H atoms are shown as green, light blue, yellow, red and white spheres, respectively.

Extended Data Fig. 4 Schematic illustrating the templating of a heterostructure with CuInCl8 double perovskite layers and anionic chains of CuCl21–.

a, The parent layered structure (PEA)4CuInCl8 and 1D chain structure (phthalazinium)CuCl2 crystallize with structure directing hydrogen bonds between the organic molecules and the inorganic sublattices highlighted in blue and yellow, respectively. b, The corresponding interactions are highlighted in the templated layered heterostructure (CuCl2)4(HIS)4CuInCl8. Cu, In, Cl, C and N atoms are coloured gold, light-grey, lime-green, grey and blue, respectively. Some H atoms are omitted for clarity.

Extended Data Fig. 5 Schematic illustrating the templating of heterostructures containing layered lead-halide perovskites and layers derived from (001) slices of the PbX2 (X = Cl, Br) structure-type.

a, b, The parent 3D inorganic structures with relevant slices highlighted (a) and their dimensionally reduced progeny (b). Note dimensionally reduced (001) slices of PbX2 have not be isolated outside of the layered heterostructures reported here. Structure directing alkylammonium groups are highlighted in blue and substitution sites for the coordinating ether and sulfide groups in the heterostructures are highlighted in yellow. c, The location of these same templating groups and substitution sites are highlighted in the templated layered heterostructures (PbBr2)2(AMTP)2PbBr4 and (Pb2Cl2)(CYS)2PbCl4. Pb, Cl, Br, C, N, O and S atoms are coloured light-blue, green, orange, grey, blue, red and yellow, respectively. H atoms are omitted for clarity.

Extended Data Fig. 6 Structural comparison between lead-halide intergrowths and slices of the 3D reference structure.

ac, Face-on comparisons of the (001) slab of PbCl2 (a)—which is isostructural to that of PbBr2—to the intergrowth sublattices in (Pb2Cl2)(CYS)2PbCl4 (b) and (PbBr2)2(AMTP)2PbBr4 (c). The atoms Pb, Cl, S, Br and O atoms are shown as light-blue, green, yellow, orange and red spheres, respectively.

Extended Data Fig. 7 Comparison between the crystal structure and the structural model used in electronic structure calculations.

a, The crystal structure of (Pb2Cl2)(CYS)2PbCl4. b, The structural model used for calculation of absorption spectra and electron–hole interactions with half the unit-cell volume. Disordered atoms in a are resolved and hydrogen atoms in b are removed for clarity. Both structures are viewed along the c axis. Unit-cell borders are shown in red. The atoms Pb, Cl, C, N and S are coloured light-blue, green, grey, blue and yellow, respectively.

Extended Data Table 1 Summary of lattice strains estimated for the intergrowth slabs relative to non-intergrowth parent structures
Extended Data Table 2 Summary of lattice strains estimated for perovskite slabs relative to non-intergrowth parent structures
Extended Data Table 3 Relative strain tensors for the perovskite slabs
Extended Data Table 4 Relative strain tensors for the intergrowth slabs

Supplementary information

Supplementary Information

Powder diffraction, crystallographic tables, and supplementary spectra.

Supplementary Data

CIF (Crystallographic information file) for the compounds (3-(ammoniopropyl)-phosphonic acid)2CuCl4, (4-(ammoniomethyl)-benzoic acid)2CuCl4, (phenethylammonium)2CuInCl8, (PbBr2)2(AMTP)2PbBr4, (Pb2Cl2)(CYS)2PbCl4, (Mg(H2O)2)(taurine)2CuCl4, Li2(taurine)2MnCl4, Li2(taurine)2CuCl4, (H3O)2(taurine)2CuCl4, (CuCl2)4(HIS)4CuInCl8.

Supplementary Video 1

Animation illustrating relative atom displacements to relate the intergrowth sublattice in (H3O)2(taurine)2CuCl4 to the non-intergrowth parent structure in Extended Data Table 1.

Supplementary Video 2

Animation illustrating relative atom displacements to relate the intergrowth sublattice in Li2(taurine)2CuCl4 to the non-intergrowth parent structure in Extended Data Table 1.

Supplementary Video 3

Animation illustrating relative atom displacements to relate the intergrowth sublattice in Li2(taurine)2MnCl4 to the non-intergrowth parent structure in Extended Data Table 1.

Supplementary Video 4

Animation illustrating relative atom displacements to relate the intergrowth sublattice in (Mg(H2O)2)(taurine)2CuCl4 to the non-intergrowth parent structure in Extended Data Table 1.

Supplementary Video 5

Animation illustrating relative atom displacements to relate the intergrowth sublattice in (CuCl2)4(HIS)4CuInCl8 to the non-intergrowth parent structure in Extended Data Table 1.

Supplementary Video 6

Animation illustrating relative atom displacements to relate the intergrowth sublattice in (Pb2Cl2)(CYS)2PbCl4 to the non-intergrowth parent structure in Extended Data Table 1. This is the same animation as in Supplementary Video 7 viewed along [001].

Supplementary Video 7

Animation illustrating relative atom displacements to relate the intergrowth sublattice in (Pb2Cl2)(CYS)2PbCl4 to the non-intergrowth parent structure in Extended Data Table 1. This is the same animation as in Supplementary Video 6 viewed along [100].

Supplementary Video 8

Animation illustrating relative atom displacements to relate the intergrowth sublattice in (PbBr2)2(AMTP)2PbBr4 to the non-intergrowth parent structure in Extended Data Table 1. This is the same animation as in Supplementary Video 9 viewed along [001].

Supplementary Video 9

Animation illustrating relative atom displacements to relate the intergrowth sublattice in (PbBr2)2(AMTP)2PbBr4 to the non-intergrowth parent structure in Extended Data Table 1. This is the same animation as in Supplementary Video 8 viewed along [100].

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Aubrey, M.L., Saldivar Valdes, A., Filip, M.R. et al. Directed assembly of layered perovskite heterostructures as single crystals. Nature 597, 355–359 (2021). https://doi.org/10.1038/s41586-021-03810-x

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