**5. Conclusions, perspectives, and challenges**

Strategies for direct graphene growth on arbitrary dielectric flexible substrates using the CVD method without metal catalyst at low temperature have been briefly reviewed. In addition, a wide range of device applications of the direct-grown graphene has been also discussed. The prospects of direct-grown transfer-free graphene are bright and currently receiving considerable attention from the 2D material research community. By discovering new methods for obtaining transfer-free graphene, the direct fabrication of a wide-range of various hetero-structured devices can be achieved. However, understanding the growth process and conditions that affect the quality of graphene is still very poor. So far, graphene grown directly on an insulating substrate is generally of low quality (**Table 1**). Because the direct growth relies on the thermal decomposition of carbon resources, the growth rate is usually low and size of the graphene domain is small, resulting in growth of defective graphene layer. Until now, many challenges remain in this direction and large-area high-quality graphene production is still very difficult. In order to obtain more advanced results, an in-depth understanding of the mechanism of graphene growth on insulating substrates is essential.

Direct graphene growth at low temperatures is an important research issue, because high growth temperatures are not allowed on many device substrates, such as flexible polymer and Si substrates. Direct growth of graphene at low- or near-room temperature [57, 77, 86], has been carried out. However, the results to date have not yet met the expectations. Given the practical application of graphene, several directions to pursue in direct graphene growth include lowtemperature growth, high-speed growth of highly crystalline graphene, and direct growth on other two-dimensional materials (e.g. h-BN) located on flexible substrate (e.g. polyethylene terephthalate (PET), PDMS, PI, or mica). This issue also a very interesting issue toward future flexible electronic applications. The direct growth of large-scale graphene on h-BN is also an attractive topic [61, 83, 88–90, 105–107]. Graphene on h-BN can have excellent electrical properties, because h-BN is an ideal dielectric substrate for graphene devices, owing to its ultra-smooth, ultra-flat surface, insulation properties, chemical inertness and small lattice misfit compared to SiO<sup>2</sup> [111]. In theory, graphene synthesized could synthesize at low temperature on as-grown h-BN/flexible substrate exhibits better properties than that grown on transferred h-BN because of the transfer-induced contamination and defects on h-BN substrates. The transfer-free grown graphene on ultra-flat h-BN/flexible substrate, which could preserve the pristine properties of graphene, enables further promising flexible device applications based on vertically stacked 2D materials located on above flexible substrates.

Ultrafast direct growth of single-crystal graphene on flexible substrates is another fascinating and challenging topic, as ultrafast conventional indirect growth on copper has been investigated thoroughly and has progressed in recent years [108]. Further studies are required for obtaining faster direct growth and larger graphene single crystals on insulating flexible substrates. Several possible strategies are proposed: (i) to explore a more efficient way to reduce the reaction barrier for graphene direct growth; (ii) to obtain epitaxial, direct-grown well-aligned graphene domains and seamlessly stitch them together into a complete single-crystal film. One potential way to realize strategy (i) is probably to introduce a gas phase catalyst enhancing the catalytic conversion of carbon precursors to graphene layer. In fact, strategy (ii) has been implemented for conventional indirect-grown graphene on catalytic single-crystal substrates such as Ge (110) [5], or Cu (111) [109, 110]. However, the single-crystal graphene layer has limited size due to the limited singlecrystal substrate size, and often the quality is less satisfactory owing to the imperfect alignment of individual graphene islands. Thus, to achieve a large-area, high-quality direct-grown graphene film, preparation of the large-area flexible substrate for releasing larger graphene nucleation seeds and an improvement in graphene alignment are critical issues in future works.

In addition, direct-growth of graphene on flexible substrate assisted by metal powder precursors (solid, diluted solution) contained inside a sub-chamber (as high temperature region) for a direct evaporation process into an innovative and re-designed-CVD main-chamber (containing flexible substrate as low temperature region) in order to allow graphene formation on dielectric substrates is an attractive topic and currently under investigation.
