Nature | Vol 577 | 9 January 2020 | 209 Article Strain engineering and epitaxial stabilization of halide perovskites Yimu Chen 1,8 , Yusheng Lei 1,8 , Yuheng Li 1 , Yugang Yu 2 , Jinze Cai 2 , Ming-Hui Chiu 3 , Rahul Rao 4 , Yue Gu 2 , Chunfeng Wang 1 , Woojin Choi 5 , Hongjie Hu 2 , Chonghe Wang 1 , Yang Li 1 , Jiawei Song 2 , Jingxin Zhang 2 , Baiyan Qi 2 , Muyang Lin 1 , Zhuorui Zhang 1 , Ahmad E. Islam 4 , Benji Maruyama 4 , Shadi Dayeh 1,2,5 , Lain-Jong Li 3,6 , Kesong Yang 1 , Yu-Hwa Lo 2,5 & Sheng Xu 1,2,5,7 * Strain engineering is a powerful tool with which to enhance semiconductor device performance 1,2 . Halide perovskites have shown great promise in device applications owing to their remarkable electronic and optoelectronic properties 3–5 . Although applying strain to halide perovskites has been frequently attempted, including using hydrostatic pressurization 6–8 , electrostriction 9 , annealing 10–12 , van der Waals force 13 , thermal expansion mismatch 14 , and heat-induced substrate phase transition 15 , the controllable and device-compatible strain engineering of halide perovskites by chemical epitaxy remains a challenge, owing to the absence of suitable lattice- mismatched epitaxial substrates. Here we report the strained epitaxial growth of halide perovskite single-crystal thin flms on lattice-mismatched halide perovskite substrates. We investigated strain engineering of α-formamidinium lead iodide (α-FAPbI 3 ) using both experimental techniques and theoretical calculations. By tailoring the substrate composition—and therefore its lattice parameter—a compressive strain as high as 2.4 per cent is applied to the epitaxial α-FAPbI 3 thin flm. We demonstrate that this strain efectively changes the crystal structure, reduces the bandgap and increases the hole mobility of α-FAPbI 3 . Strained epitaxy is also shown to have a substantial stabilization efect on the α-FAPbI 3 phase owing to the synergistic efects of epitaxial stabilization and strain neutralization. As an example, strain engineering is applied to enhance the performance of an α-FAPbI 3 -based photodetector. 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 method 16 . The resulting MAPbCl x Br 3−x substrates, with different compositional ratios and thus lattice param- eters, 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 relaxa- tion mechanisms. Lattice distortion relaxes the strain, so the region near the heteroepitaxy interface has the highest strain, which gradu- ally 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 misfit 18 . 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 opti- mized, as the defects in the substrates can propagate into the epilayer (Extended Data Fig. 1). Heteroepitaxial growth leads to controllable film thickness, prefer- ential growth sites and orientations, compatible fabrication protocols with existing infrastructures and scalable large-area device applica- tions. Figure 1a shows optical images of a series of MAPbCl x Br 3−x sub- strates 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). The crystallographic relationships between the MAPbCl x Br 3−x sub- strates 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 structure 19,20 . 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 (Supple- mentary Fig. 1) and 5.83–5.95 Å, respectively. The ratio x for each https://doi.org/10.1038/s41586-019-1868-x Received: 12 April 2019 Accepted: 19 November 2019 Published online: 8 January 2020 1 Department of Nanoengineering, University of California San Diego, La Jolla, CA, USA. 2 Materials Science and Engineering Program, University of California San Diego, La Jolla, CA, USA. 3 Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia. 4 Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright Patterson Air Force Base, Dayton, OH, USA. 5 Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA. 6 School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales, Australia. 7 Department of Bioengineering, University of California San Diego, La Jolla, CA, USA. 8 These authors contributed equally: Yimu Chen, Yusheng Lei. *e-mail: shengxu@ucsd.edu