Electro-thermo-mechanical responses of conductive adhesive materials

Micromechanics models which aim to provide an understanding of conductive adhesive materials from the level of micro-particles (less than 30 mm) are presented in this paper. The pressure-induced conducting mechanisms are investigated. A deformation analysis reveals a logarithmic pressure-resistance relationship and is capable of addressing the conducting phenomena for both rigid and deformable particle systems within a contact mechanics framework. This logarithmic relationship also provides analytical support for findings reported in the literature of conductive adhesive research. It is observed that electrical contacts are made by squashing conducting particles for a deformable particle system while the particle penetration creates a crater in metallization to make contacts for a rigid particle system. The current analysis provides simple closed-form solutions for the elastic deformation of single-particle contacts and based on the assumption that the contact forces are evenly distributed in a conductive film, the pressure-resistance responses are correlated to the particle volume fraction. The high volume fraction, while ensuring that there are a sufficient number of particles to make contacts, may limit the particle deformation due to overall increased stiffness, resulting in the increased resistance on a per particle basis. The current analysis also offers insight into design considerations whereby limited amount of deformation (low processing temperature) and sufficiently low electrical resistance are to be simultaneously satisfied. For the mechanical performance, the uniaxial nonlinear stress-strain relationship is obtained for conductive adhesive systems in terms of polymer and particle material properties. The Mori-Tanaka's method is utilized to account for particle-particle and particle-matrix interactions. The behaviour in thermal expansion within the elasto-plastic deformation range is also obtained in a similar fashion. In all these calculations, only a very simplified finite element analysis for the problem of a particle embedded into an infinitely extended matrix material needs to be carried out.