An iterative Debye dispersion model for a horizontal multi-layered material

An iterative Debye model for a horizontal multi-layered material is found using a circuit model. A three-dimensional Finite Difference Method (3D-FDM) is developed to extract the effective permittivity and conductivity. The results obtained from the FDM and the present method agree very well, which shows the validity of the layered Debye formulas in terms of original circuit parameters. The derived iterative Debye formulas can be used to analyze the relationship between the effective electrical spectra and the electrical parameters of each layer. In addition, it can be applied for multi-layered models with extra-thin thickness geometry, which are probable models in electronic materials. Numerical results show that when the number of layers is more than two, the relaxation factor will not be a constant and more than one transition areas will appear. A thin insulation membrane in a layered model leads to the presence of a low frequency dielectric enhancement and largely decreases the effective conductivity at low frequencies. It was concluded from the numerical simulations that the dielectric enhancement is dependent on the membrane thickness, membrane conductivity, volumetric ratio, and the presence of conductivity contrast between materials.