  We compute the Casimir force for a system composed of two layers as
substrates within three different homogenous layers. We use the scattering
approach along with the Matsubara formalism in order to calculate the Casimir
force at finite temperature. We impose the appropriate boundary condition on
the tangential components of the electric and magnetic fields to construct the
reflection matrices. Our calculation is simple such that one can extend it to
systems containing inhomogeneous layers as good candidates for designing
nanomachines. We find that the Casimir force is proportional to L^(-5) where L
is the thickness of the inner layer.
