Such a twin boundary carries extremely low formation energy and can rarely be avoided during annealing of FCC metals 20, 21, 22. 2 and 3, we demonstrate that (θ, ψ) are equivalent to Euler angles or surface indices for determining the orientation of a twinned crystal and their transformation. In the Supplementary Notes 1– 2 and Supplementary Figs. Here, the angle between the twin plane and the foil surface, θ, and the in-plan rotation angle of the twin plane, ψ, are the two independent variables that fully describe the twinned structure. 1a with more details in Supplementary Fig. The schematic diagram of a 60° twin of a Cu foil with FCC structure is shown in Fig. Let’s consider the alignment of 2D material islands on the two sides of a 60° twin boundary. The epitaxial growth of a 2D single crystal on a polycrystalline substrate requires that all 2D islands grown on two sides of a grain boundary are perfectly aligned, which is obviously impossible for an arbitrary grain boundary. Theoretical frame for alignment of 2D materials on twinned Cu foils ![]() This study opens a rapid, scalable and robust route for single crystal 2D materials growth on tailored polycrystalline substrates. Following the theoretical prediction, inch-sized 2D materials (including graphene and hBN) single crystals on selected twinned Cu foils have been synthesized. We have successfully annealed polycrystalline Cu foils into various types of inch sized twinned Cu foils. Here we present a theoretical prediction and experimental demonstration of epitaxial growth of single-crystal 2D materials on tailored non-single-crystal substrates. The presence of highly stable twin boundaries in Cu foils makes synthesizing high quality Cu single crystals challenging, and if possible, using polycrystalline substrates for 2D materials epitaxy would be highly beneficial. Thermodynamically stable twin boundaries are common in face centered cubic (FCC) metals and are easily created during annealing treatments 20, 21, 22. Despite significant progress in the synthesis of single-crystal substrates, such as Cu foils with different surface indices 17, 18, 19, the preparation of single-crystal substrates is still generally expensive. By judiciously choosing single crystal substrates with the appropriate surface texture, epitaxial growth of large area single-crystal graphene, hexagonal boron nitride (hBN), and other two-dimensional (2D) materials have recently been realized 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. The onset of diffusion is consistent with the onset of Cu diffusion in CIS.Wafer-scale single-crystal two-dimensional (2D) materials are highly desirable for the next generation of 2D material-based integrated electronics, optoelectronics and spintronics 1, 2, 3, 4, 5. Diffusion turns on rapidly between 300 and 400 ☌, indicating a high activation energy for atomic movement (∼2.4 eV). ![]() No time dependence was observed in the 400 and 500 ☌ anneals indicating that a reaction had occurred forming a compound that was in thermodynamic equilibrium with the remaining CIS. In the polycrystal, annealing at 500 ☌ resulted in movement of Cd throughout the CIS layer. At 400 ☌ even for the shortest time studied, Cu and In were found throughout the region initially consisting of CdS only and Cd was found to have moved into the CIS. No atomic movement was observed by secondary ion mass spectrometry at temperatures of 300 ☌ and below. This article reports the results of annealing heterojunctions between CdS deposited by chemical bath deposition and single crystal and polycrystalline CIS films between 200 and 500 ☌ for 10 to 150 min. The stability of the CdS/CuInSe 2 (CIS) heterojunction is critical to understanding the projected lifetime of CIS devices and the effect of processing conditions on the nanoscale chemistry of the heterojunction.
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