Dependence of electrical conduction on the film thickness of conductive adhesives: modeling, computer simulation, and experiment
The effect of film thickness on the conduction behavior of electrically conductive adhesives is presented. For comparison purposes, an analytical relation is developed to predict the three-dimensional resistivity of particle-filled conductive adhesives. This analysis reveals that the adhesive's resistivity depends on parameters m, representing an average contact number, and Si, representing the average length of conductive paths between the conductive particles incorporated in the adhesive matrix. Both the parameters m and Si are functions of the conductive particle volume fraction Φ, and these functional relations are developed by computer simulation for the cases of spherical particles in three-dimensional (3-D) and two-dimensional (2-D) contacts. The latter (2-D) case represents thin film applications. The computer simulation utilized reveals that the average length of conductive paths in the planar direction of the 2-D case is much larger than that for the 3-D case. This leads to an electrical conduction case which is direction-dependent (anisotropic, or oriented) for 2-D thin film applications where the resistivity values in planar directions are much larger than those encountered in 3-D measurements for the same adhesive material. This behavior is illustrated using four different commercial conductive adhesives containing silver flakes.