Title: Casimir free energy of dielectric films: Classical limit, low-temperature behavior and control,
Abstract: The Casimir free energy of dielectric films, both free-standing in vacuum and
deposited on metallic or dielectric plates, is investigated. It is shown that
the values of the free energy depend considerably on whether the calculation
approach used neglects or takes into account the dc conductivity of film
material. We demonstrate that there are the material-dependent and universal
classical limits in the former and latter cases, respectively. The analytic
behavior of the Casimir free energy and entropy for a free-standing dielectric
film at low temperature in found. According to our results, the Casimir entropy
goes to zero when the temperature vanishes if the calculation approach with
neglected dc conductivity of a film is employed. If the dc conductivity is
taken into account, the Casimir entropy takes the positive value at zero
temperature, depending on the parameters of a film, i.e., the Nernst heat
theorem is violated. By considering the Casimir free energy of silica and
sapphire films deposited on a Au plate in the framework of two calculation
approaches, we argue that physically correct values are obtained by
disregarding the role of dc conductivity. A comparison with the well known
results for the configuration of two parallel plates is made. Finally, we
compute the Casimir free energy of silica, sapphire and Ge films deposited on
high-resistivity Si plates of different thicknesses and demonstrate that it can
be positive, negative and equal to zero. Possible applications of the obtained
results to thin films used in microelectronics are discussed.