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Scattering of electronic waves in square and triangular lattice half-planes with monoatomic step

Scattering of electronic waves in square and triangular lattice half-planes by a step on the surface is analyzed using the nearest-neighbour tight binding approximation. The changes in lattice spacing and the transfer integral between nearest-neighbor sites near the surface are ignored. A standard application of the discrete Wiener-Hopf method leads to an exact solution of the scattering problem associated with incidence from the `bulk'. A far-field approximation of electronic wavefunction, as well as its graphical comparison with a numerical solution, are also provided. Natural applications and possible extensions are based on the bulk Brillouin zone for two dimensional lattice planes as well as surface energy bands for fcc crystals.