Surface-dependent band structure variations and bond-level deviations in Cu₂O

Density functional theory (DFT) calculations have been performed on 1 to 9 layers of Cu2O (100), (111), and (110) planes to further understand the electronic band structures and the origin of the facet-dependent properties of Cu2O crystals. The (100) planes show an invariant band structure with a constant band gap of 1.787 eV like that of a primitive cell. The (111) planes present a periodicity of every three layers with band gaps varying between zero and 1.787 eV. An unusual periodicity of every two layers has been found for the (110) planes oscillating between 1.787 eV and very small band gaps including a zero band gap. By comparing the valence band edges of different plane layers and the position of the Fermi level in the density of states (DOS) diagrams, relative valence band bending of the Cu2O {100}, {111}, and {110} surfaces can be drawn to explain their strongly facet-dependent electrical conductivity properties. Moreover, while the (100) planes show a fixed crystal lattice with a tunable number of planes, the calculations identify slight bond length deviations and bond distortion for the (111) and (110) planes. The partial density of states (PDOS) diagrams also reveal (111) and (110) plane layer-dependent variations in the frontier orbital electron energy distribution. The structural perturbations at crystal surfaces can yield different barrier heights to charge transport across the {100}, {111}, and {110} faces, and photons of different wavelengths should get absorbed in the thin surface layer to produce the observed optical facet effects. Such lattice perturbations should be present in other semiconductor materials as surface-dependent behaviors are broadly observable in many semiconductors.