  We present theoretical calculations of the Casimir force for Au thin films
near the insulator-conductor transition that has been observed experimentally.
The dielectric function of the Au thin films is described by the Drude-Smith
model. The parameters needed to model the dielectric function such as the
relaxation time, plasma frequency and the backscattering constant depend on the
thickness of the film. The Casimir force decreases as the film thickness
decreases until it reaches a minimum after which the force increases again. The
minimum of the force coincides with the critical film thickness where a
percolation conductor-insulator occurs.
