NOVELTY - The method comprises ion-implanting an ion of a nitrogen ion (2) and/or an oxygen ion on a surface of a silicon carbide (SiC) thin film (1) to form an ion implantation layer such as a silicon nitride layer (4) in the SiC thin film, and heat treating the SiC thin film with the ion implantation layer to graphenize a SiC surface layer (3) on the ion implantation layer. The SiC surface layer formed on the ion implantation layer has a thickness of less than or equal to 230 nm. The heat treating step is performed at a temperature of 1000-2000 degrees C for 0.001-10 hours. The SiC thin film has a thickness of 100-500 mu m.    USE - The method is useful for preparing a graphene-layered structure such as an epitaxial structure that is useful in a transistor, a transparent electrode (all claimed), display devices, memory devices, sensors, a fuel cell and a dye-sensitized solar cell, where the display devices include an electronic paper display device, an organic light emitting display device, a LCD device and a LED and the transistor is a bipolar junction transistor, a FET, a heterojunction bipolar transistor and a single electron transistor.    ADVANTAGE - The method is capable of effectively preparing the graphene-layered structure without using transferring process and structural defects such as tearing or wrinkles and with high transparency and conductivity thus improving physical properties, luminous efficiency and processability of the electric devices.    DETAILED DESCRIPTION - The method comprises ion-implanting an ion of a nitrogen ion (2) and/or an oxygen ion on a surface of a silicon carbide (SiC) thin film (1) to form an ion implantation layer such as a silicon nitride layer (4) in the SiC thin film, and heat treating the SiC thin film with the ion implantation layer to graphenize a SiC surface layer (3) on the ion implantation layer. The SiC surface layer formed on the ion implantation layer has a thickness of less than or equal to 230 nm. The heat treating step is performed at a temperature of 1000-2000 degrees C for 0.001-10 hours. The SiC thin film has a thickness of 100-500 mu m. The ion-implanting step includes implanting the ion into a silicon-face of the SiC thin film, and adjusting an implantation amount and energy of the ion to adjust a thickness of the ion implantation layer. A temperature of the SiC thin film is maintained at 300-1000 degrees C during the ion-implanting step. INDEPENDENT CLAIMS are included for:    (1) a graphene-layered structure;    (2) a transistor; and    (3) a transparent electrode.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a method for growing a graphene.    Silicon carbide thin film (1)    Nitrogen ions (2)    Silicon carbide surface layer (3)    Silicon nitride layer (4)    Silicon ions. (5)