Atomic and electron structure of reconstructed (111) surface in ZnSe and CdSe crystals

The atomic and electron structure of four variants of polar (111)-(2 $\times$ 2) surfaces in ZnSe and CdSe terminated by a cation, namely, the ideal, relaxed, reconstructed, and relaxed after reconstruction surfaces, are calculated for the first time from the first principles. The surface is simulated by a film with a thickness of 12 atomic layers and a vacuum gap of $\sim$16 $\mathring{\mathrm{A}}$ in the layered superlattice approximation. Four fictitious hydrogen atoms with a charge of 0.5 electrons each are added for closing dangling Se bonds on the opposite side of the film. Ab initio calculations are performed using the QUANTUM ESPRESSO software based on the density functional theory. It is shown that relaxation results in splitting of atomic layers. We calculate and analyze the band structures and total and layer-wise densities of electron states for four variants of the surface.