Electron and band structure in regular or disordered 3-dimensional environments: localised and delocalised states

Abstract

Calculations based on 3-D environments, using weak bonding approximations, follow much the same line as the studies made in 1-D. The dispersion curve E=f (k) can be traced depending on the different directions under consideration (k_x, k_y and k_z for a cubic crystal). If these directions are not equivalent, and have a forbidden energy for which the value is direction dependent, then the resulting energy gap in the material is of the form.