Dielectric properties of hydrogen-terminated Si(111) ultrathin films

Dielectric properties of Si(111) ultrathin films have been investigated using first-principles ground-states calculations in external electrostatic fields. With increasing thickness of Si(111) ultrathin films, the optical dielectric constant evaluated at the center of the slab converges to the experimental bulk dielectric constant at a thickness of only eight bilayers, while the energy gap of the slab is still larger than that of bulk Si. The converged theoretical dielectric constant for bulk Si is only 6.2% higher than the experimental one. Furthermore, spatial variations of the dielectric constant have also been evaluated using the position-dependent macroscopic field given by a clear-cut definition. The results show that the dielectric constant is reduced distinctly at the first few bilayers from the surface, which stems from the penetration of depolarized charges induced at the surface. Such an effective reduction of the depolarization field near the surface is one of the reasons for the decrease in optical dielectric constant for the ultrathin films.