Explaining the thickness-dependent dielectric permittivity of thin films

The dielectric properties of thin films are of paramount importance in a variety of technological applications, and of fundamental importance for solid-state research. In spite of this, there is currently no theoretical understanding of the dependence of the dielectric permittivity on the thickness of thin films. We develop a confinement model within the Lorentz-field framework for the microscopic Langevin-equation description of dielectric response in terms of the atomic-scale vibrational modes of the solid. Based on this, we derive analytical expressions for the dielectric permittivity as a function of thin-film thickness, in excellent agreement with the experimental data of barium-strontium-titanate thin films of different stoichiometry. The theory shows that the decrease of dielectric permittivity with decreasing thickness is directly caused by the restriction ink space of the available eigenmodes for the field-induced alignment of ions and charged groups.