Decoupling 1D and 2D features of 2D sp-nanoribbons-the megatom model

The dependence of the electron energy band gap on the width of an sp-nanoribbon is investigated using a generalization of the 1D tight binding model for a chain of atoms. Within the proposed generalization, small linear atomic formations along lines perpendicular to the 2D ribbon axis are modeled as single large atoms called megatoms whose properties depend on the type, the size and the atomic conformation. Replacement of a 1D chain of atoms by that of the megatoms is accompanied by the incorporation of zeroth order 2D features into the 1D model approximation of the nanoribbon. We use this model to investigate the oscillating band gap of an sp-nanoribbon in terms of the ribbon's width. Results are presented for the width dependence of the energy gap of the zig-zag Si2BN nanoribbons.