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th nanoribbon devices commonly have low driving currents [12]. Here, we predict the formation of tunable electronic energy gap Epitaxially grown graphene on the SiC substrate is supposed to have strong coupling with the substrate and results in the elimin-ation of the A and B sublattices symmetry. Following this idea, Zhou et al. [13] predicted a gap of about 260 meV in Dirac points for the epitaxially grown graphene on SiC substrate owing to graphene2 substrate interaction. However, this gap decreases as the sample thickness increases in the multi-layer structures and totally disappears when the number of layers increases only to four [14]. Since any kind of defects in symmetrical graphene layer might cause bandgap opening, there has been tremendous interest in the application of patterning methods in this field. Proposing a specific patterned structure of the graphene, Tiwari and Stroud [15] hav