First-principles evaluations of dielectric constants

Dielectric properties of ultra-thin Si(111), SiO₂, and La₂O₃(0001) films have been investigated using two methods, internal field method and dipole moment method, based on first-principles ground-state calculations in external electrostatic fields. With increasing the thickness of the Si(111) film, the optical dielectric constant evaluated at the center of the slab converges to the experimental bulk dielectric constant, while the energy gaps of the slabs are still larger than those of corresponding bulks. On the other hand, both the optical and the static dielectric constants of beta-SiO₂(0001) films hardly depend on the film thickness and the spatial variation of the local dielectric constant is also very small. It has been found that both the surface effect and the quantum confinement effect are small on ultra-thin beta-SiO₂(0001) films. Further, it has been revealed that ultra-thin La₂O₃(0001) film having a thickness of 1.1 nm possesses a large value of the static dielectric constant (29.2) equivalent to that of bulk.