Multiphysics coupling analysis of TSV by using discrete geometric method based on Tonti diagram

The Tonti diagram conceives a general mathematical structure for several physical fields, and hence provide uniform topological operators to establish global stiffness matrices for various field solvers in differential forms. The discrete geometric method implements the Hodge discretization of constitutive laws through the division of geometric parameters of primal and dual meshes. Complying with Tonti diagrams, it can be achieved as an elegant solution for multiphysics problems intuitively and practicably. The stationary electro-thermo-mechanical coupled problem, including building of the constitutive equations and treating of the coupling terms, is studied. A typical problem with regard to thermo-mechanical stress induced by resistive losses in a through-silicon-via (TSV) structure of 3D IC is investigated.