Graphene is regarded as one of the most promising candidate materials for future electronics. For usage in electrical devices, high-quality graphene needs to be placed on a dielectric surface. Currently, methods for graphene preparation require graphene to be transferred from scotch tape, metals, or solutions to the dielectric substrate for electrical applications. The transfer process normally induces contamination, wrinkles, or even breakage of the graphene samples and thus hampers the practical application of graphene in electronics. Moreover, chemical vapor deposition (CVD) on a metal catalyst normally requires a growth temperature as high as 800–1000 8C. For industrial-scale production, lowtemperature growth can lead to a decrease in energy consumption and cost, and an increase in compatibility. Therefore, a low-cost, controllable, and reliable method is required for the production of clean high-quality graphene directly on dielectric substrates at low temperature. One pioneering study towards the goal of the catalyst-free growth of graphene on dielectric materials examined the pyrolysis of CH4 on bare SiO2/Si; [5,6] however, this method requires a high growth temperature (1100–1650 8C). Another approach, plasma-enhanced CVD (PECVD), enables the low-temperature growth of graphene on metals, or even on dielectric surfaces (550–650 8C). However, without metal catalysts, structural defects readily form at the edges and terminate graphene growth. As a result, small graphene nanoclusters or noncrystalline samples are formed, the quality of which is lower than that required for electrical applications. Vertically oriented graphene nanosheets can be produced by PECVD; however, most of the products are multilayered. Herein, we describe the development of a critical PECVD (c-PECVD) growth method, in which a H2 plasma is introduced during graphene growth. H2 plasma is known to etch graphene from the edges. Moderate etching by a H2 plasma removes defects generated at the edges and thus keeps the edges atomically smooth and active during the whole process of graphene crystal growth. Therefore, in a critical equilibrium state between H2 plasma etching and CH4 or C2H4 plasma growth, we observed efficient catalyst-free crystal growth of graphene directly on crystalline sapphire, highly oriented pyrolytic graphite (HOPG), and the amorphous surface of Si substrates with a thermally grown 300 nm SiO2 overlayer (SiO2/Si), with crystal sizes up to the micrometer scale for single-layer hexagonal single crystals and up to the centimeter scale for continuous films. The growth temperature could be decreased to as low as 400 8C when C2H4 was used as the carbon source. To the best of our knowledge, this temperature is one of the lowest used for the catalyst-free growth of graphene. In the experiments, a homemade remote radiofrequency (13.56 mHz) PECVD system (80 W) was used (Figure 1a). Figure 1b illustrates the typical procedure for the c-PECVD growth of graphene on bare Si/SiO2 (see the Experimental Section for details). We first used peel-off graphene to clarify the etching, critical edge growth, and nucleation of graphene in PECVD. Figure 1c shows atomic force microscopy (AFM) images of a trilayer peel-off graphene flake before and after cPECVD growth (H2 plasma activation: 250 mTorr, 500 8C; growth: 30% H2, 90 mTorr, 600 8C, 60 min). The edges of the bottom, middle, and upper layer moved by 79, 117, and 158 nm, respectively, thus indicating that continuous growth of the flake took place on the edges, rather than in the plane. The different growth rate of each layer is attributed to the substrate (see Figure S1 in the Supporting Information). Control experiments show that the edge growth is highly dependent on the H2 content, the growth temperature, and the pressure (Figure 1d). Lower temperatures or higher H2 content tend to induce edge etching, whereas the opposite reaction conditions cause the nucleation of graphitic clusters (see Figure S2). For example, after CH4+H2 plasma CVD at a lower temperature (550 8C), instead of growth, the edges of the flakes were etched by about 168 nm (Figure 1e). Upon CH4+H2 plasma CVD at a lower H2 content (20%), besides the edge growth, small graphitic clusters were nucleated on whole surface of the graphene flakes and SiO2/Si surface with heights lower than 1 nm (Figure 1 f); the heights observed indicate the single-layered nature of the nucleated clusters. The edge growth (Figure 1c; see also Figure S3) only takes place at a well-controlled critical temperature between those needed for nucleation and edge etching, and the critical temperature decreases as the H2 content decreases (Figure 1d). When C2H4 was used as the carbon source in cPECVD (0%H2, 48 mTorr), the critical temperature for edge growth decreased to as low as 400 8C (Figure 1d). Moreover, low pressure can lead to a remarkable improvement in the growth rate. The growth rate (30% H2, 600 8C) was about [*] Dr. D. Wei, Dr. Y. Lu, Prof. W. Chen, Prof. A. T. S. Wee Department of Physics, National University of Singapore 2 Science Drive 3, Singapore 117542 (Singapore) E-mail: phyweid@nus.edu.sg phyweets@nus.edu.sg