The zero band gap (Eg) graphene becomes narrow Eg semiconductor when graphene is patterned with periodic array of hexagonal shaped antidots, the resultant is the hexagonal Graphene Antidot Lattice (hGAL). Based on the number of atomic chains between antidots, hGALs can be even and odd. The even hGALs (ehGAL) are narrow Eg semiconductors and odd hGALs (ohGAL) are semi-metals. The Eg opening up by hGALs is not sufficient to operate a realistic switching transistor. Also hGAL transistors realized on Si/SiO2 substrate are suffering with low carrier mobility and ON-OFF current ratio. In order to achieve a sizable Eg with good mobility, AB Bernal stacked hGALs on hexagonal Boron Nitride (hBN), ABA Bernal stacked hBN / hGAL / hBN sandwiched structures and AB misaligned hGAL /hBN structures are reported here for the first time. Using the first principles method the electronic structure calculations are performed. A sizable Eg of about 1.04 eV (940+100 meV ) is opened when smallest neck width medium radius ehGAL supported on hBN and about 1.1 eV (940 + 200 meV ) is opened when the same is sandwiched between hBN layers. A band gap on the order of 71 meV is opened for Bernal stacked ohGAL / hBN and nearly 142 meV opened for hBN / ohGAL /hBN structures for smallest radius and width of nine atomic chains between antidots. Unlike a misaligned graphene on hBN, the misaligned ohGAL/hBN structure shows increased Eg. This study could open up new ways of band gap engineering for graphene based nanostructures.
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