Computational Approach of Dielectric Permitivities in BaTiO3—Epoxy Composites

Abstract

A numerical approach using a finite element method (FEM) was performed in order to determine the dielectric constant (ε') of BaTiO 3—epoxy composites. In order to diminish computational resources and analyse simple models, composite topology was represented by periodic structures based on FCC configurations, but introducing novel packaging protocols, defining the way composites are filled as particle concentration is increased. The dielectric response of these anisotropic and periodic structures was mathematically represented through a quasi-static approximation using the Laplace equation. The amount of inclusions was varied in order to represent diluted and concentrated systems and structures were assessed for the whole feasible range of volume fractions. The numerical results were compared with experimental data concluding that only packaging protocols that consider higher particle—particle interaction are suitable to represent the dielectric behavior of concentrated-composite materials.

BaTiO3–Epoxy Composites for Electronic Applications

“…This methodology has the effect to fill the main packaging directions at first. 20 In this model, the FEM was used to solve the mathematical problem. 17,20,21 The boundary conditions applied were a potential difference (DV 5 U 2 ÀU 1 ) of 1 V along the z direction (Dirichlet boundary condition) and gradients of potential equal to zero (Neumman boundary condition) for the other two Cartesian directions (qu/qn x 5 0 and qu/qn y 5 0), as shown in Fig.…”

“…Thus, numerical methods, such as the finite element method (FEM) or boundary element method, seem to be very suitable approaches to describe the behavior of these materials because these methods do not impose restrictions to the geometry, to the nonlinear properties of components, or to the number of phases of the composite material. [17][18][19][20] In this paper, we review our previous works related with dielectric properties of epoxy/BaTiO 3 composites. Parts of this information have been reported before but here it is presented in a general and brief way, and related with the dielectric performance of these composites.…”

Dielectric properties of highly filled thermoplastics for printed circuit boards

“…The modified Lichtenecker equation includes a fitting factor n, which represents the interaction between the filler and the matrix. 25 log e C ¼ log e 1 þ v 2 ð1 À nÞ log e 2 e 1 (6) The relative permittivity of composites also depends on the distribution of the filler, shape, size and, as already mentioned, the interface with the polymers. Rao et al 43 proposed a model (Effective Medium Theory, EMT) to predict the relative permittivity of the composites.…”

“…Materials like FR4 exhibit tailored thermal, mechanical, and electrical properties for a broad range of applications, have low cost, and are widely employed in the PCB industry for more than 40 years. A number of investigations can be found in the literature regarding the further optimization of these material's properties 5–10. But with growing demands regarding the signal integrity at high frequencies and low signal losses, the limits in terms of dielectric properties of standard epoxy‐based substrates (approximately tan δ > 0.014 and ε′ > 4 at 1 GHz) have been reached, and do not further fulfill the requirements for such new applications 11.…”

“…A number of investigations can be found in the literature regarding the further optimization of these material's properties. [5][6][7][8][9][10] But with growing demands regarding the signal integrity at high frequencies and low signal losses, the limits in terms of dielectric properties of standard epoxy-based substrates (approximately tan d > 0.014 and e 0 > 4 at 1 GHz) have been reached, and do not further fulfill the requirements for such new applications. 11 For this reason, the scientific community is working on developing special material compositions, which exhibit low dielectric loss in high frequency ranges.…”