  The dielectric properties of thin films are of paramount important 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 experimental data
of Barium-Strontium-Titanate (BST) thin films of different stoichiometry. The
theory shows that the decrease of dielectric permittivity with decreasing
thickness is directly caused by the restriction in $k$-space of the available
eigenmodes for field-induced alignment of ions and charged groups.
