Thickness dependence of dielectric constant of alumina films based on first-principles calculations

Optoelectronic properties of devices made of two-dimensional materials depend largely on the dielectric constant and thickness of a substrate. To systematically investigate the thickness dependence of dielectric constant from first principles, we have implemented a double-cell method based on a theoretical framework by Martyna and Tuckerman [J. Chem. Phys. 110, 2810 (1999)] and therewith developed a general and robust procedure to calculate dielectric constants of slab systems from electric displacement and electric field, which is free from material-specific adjustable parameters. We have applied the procedure to a prototypical substrate, Al2O3, thereby computing high-frequency and static dielectric constants of a finite slab as a function of the number of crystalline unit-cell layers. We find that two and four layers are sufficient for the high-frequency and static dielectric constants of (0001) Al2O3 slabs to recover 90% of the respective bulk values computed by a Berry-phase method. This method allows one to estimate the thickness dependence of dielectric constants for various materials used in emerging two-dimensional nanophotonics, while providing an analytic formula that can be incorporated into photonics simulations.