Carrier lifetime enhancement in halide perovskite via remote epitaxy

Crystallographic dislocation has been well-known to be one of the major causes responsible for the unfavorable carrier dynamics in conventional semiconductor devices. Halide perovskite has exhibited promising applications in optoelectronic devices. However, how dislocation impacts its carrier dynamics in the ‘defects-tolerant’ halide perovskite is largely unknown. Here, via a remote epitaxy approach using polar substrates coated with graphene, we synthesize epitaxial halide perovskite with controlled dislocation density. First-principle calculations and molecular-dynamics simulations reveal weak film-substrate interaction and low density dislocation mechanism in remote epitaxy, respectively. High-resolution transmission electron microscopy, high-resolution atomic force microscopy and Cs-corrected scanning transmission electron microscopy unveil the lattice/atomic and dislocation structure of the remote epitaxial film. The controlling of dislocation density enables the unveiling of the dislocation-carrier dynamic relation in halide perovskite. The study provides an avenue to develop free-standing halide perovskite film with low dislocation density and improved carried dynamics.


Supplementary Figures
Supplementary Figure 1 Raman measurements on transferred graphene. Optical images of transferred graphene on NaCl (a) and CaF 2 (e). Raman spectra of both defected and good regions of graphene on NaCl (b) and CaF 2 (f). Raman mapping of I 2D /I G and I D /I G of graphene on NaCl(001) (c and d) and CaF 2 (001) (g and h), respectively. The mapping area of 15×15 μm 2 is indicated in green square in a and e.   [100] Supplementary Figure 5 Cross-sectional SEM images of CsPbBr 3 /NaCl (a) and CsPbBr 3 /Gr/NaCl (b and c) thin films.  Inset of (c) shows a typical finding that nucleation often does not occur at the wrinkle of graphene. At the wrinkles of graphene, the substrate-film coupling strength could be weaker due to the larger film-substrate distance compared to non-defective region since electrostatic interaction (both van der Waals and ionic) decays as distance increases. In our case, the wrinkles of graphene can still be seen among the remote epitaxial CsPbBr 3 flakes after growth, as indicated in red ellipses in the optical microscopy image of (c). Our experimental observation indicates that the activation energy for nucleation at graphene/substrate surface seems to be even lower than that at wrinkles. Hence, in the remote epitaxy in our case, the growth kinetics might be dominated by the polar substrates while the wrinkles of graphene play a minor role.       Pump probe delay (ns)   Tables   Supplementary Table 1 Pair-dependent LJ potential parameters for ABC 3

Controlling domain wavelength via remote epitaxy
It is in debate that the ferroelasticity or ferroelectricity in hybrid organic-inorganic perovskites plays a potential role to underpin the desirable device performance 1, 2, 3, 4, 5 . The striped ferroelastic domains in methylammonium lead iodide perovskite have been recently observed explained as a result of the cubictetragonal phase transition 1,3,6 . A similar ferroelastic domain structure is naturally expected in inorganic halide perovskites like CsPbBr 3 as a result of the cubic-tetragonal-orthorhombic phase transition.
Controlling the dimension and wavelength of the domain structures may serve as a solution to engineer the device performance. In this study, it is observed that ionic epitaxy and remote epitaxy lead to completely different dimensions and wavelength.
To explain our observation, we have applied continuum mechanics modeling. With the assumption that both domains coexist in equal fraction, the total energy density is given by 7 : where is the spatial period of the domain pattern, is thickness of the thin film, and is the free energy densities of the tetragonal phase, respectively. is the domain wall energy density. is the volume density of the elastic strain energy, which is dependent on substrate-film coupling strength. Thus, to compare the elastic strain energy density in both ionic and remote epitaxy, since much smaller contribution from the two domains themselves due to the close lattice constants of a and c, we introduced a simplified system with only one domain grown on substrate. Epitaxial growth changes the total energy density of the simplified system α , which is increased by the elastic strain energy density and released by bonding energy density. Assuming dangling bonds would be formed if a strain less than lattice misfit is applied, the ratio of bonding energy density to interfacial free energy density can be estimated to be the bonding atoms' percentage on the substrate, which is ( ) . Assuming that strain is uniformly distributed in the film, α is given by: where is the strain in film, is the interfacial free energy taken from DFT calculation in Fig. 2c and also mentioned in Eq. (1) in main text, and is the Young's modulus of the CsPbBr 3 (16 GPa 8 ). By minimizing α , the strain is given by: . ( Hence, the volume density of the elastic strain energy is proportional to . After determining the equilibrium domain period by minimizing ( ), the interfacial free energy can be plotted as a function of with different sample thicknesses, as shown Supplementary Figure 26a, indicating the increase of domain period with decreasing interfacial free energy and larger domain periods in thick films. Therefore, the remote epitaxy theoretically would exhibit larger domain period due to the weaker interfacial energy, compering to the ionic epitaxy.
Schematic illustrations of domain patterns are shown in Supplementary Figure 27a and b for ionic and remote epitaxy, respectively. To the best of our knowledge, there is no experimental observation on the ferroelastic domain pattern in the inorganic halide perovskite CsPbBr 3 . Here, in accordance with theoretical modeling, we have observed striped ferroelastic domains in CsPbBr 3 from both ionic and remote epitaxy (with different thicknesses), as shown in Supplementary Figure 27c