Intensifying the Casimir force between two silicon substrates within three different layers of materials

We investigate the Casimir force for a system composed of two thick slabs as substrates within three different homogeneous layers. We use the scattering approach along with the Matsubara formalism in order to calculate the Casimir force at finite temperature. First, we focus on constructing the reflection matrices and then we calculate the Casimir force for a water–lipid system. According to the conventional use of silicon as a substrate, we apply the formalism to calculate the Casimir force for layers of Au, VO2, mica, KCl and foam rubber on the thick slabs of silicon. Afterwards, introducing an increasing factor, we compare our results with Lifshitz force in the vacuum between two semispaces of silicon in order to illustrate the influence of the layers on intensifying the Casimir force. We also calculate the Casimir force between two slabs of the forementioned materials with finite thicknesses to indicate the substrate's role in increasing the obtained Casimir force. Our simple calculation is interesting since one can extend it along with the Rigorous Coupled Wave Analysis to systems containing inhomogeneous layers as good candidates for designing nanomechanical devices.