An Equivalent Multiphysics Circuit Framework for Electro-Thermal-Mechanical Coupling Simulation in Integrated Circuits by Proposing a SPICE Compatible Equivalent Mechanical Circuit Method

Modeling and analyzing multiphysics effects has become one of the most challenging issues in integrated circuit design. Equivalent thermal circuit method is one of the most commonly used method in circuit design to simulate the electrothermal coupling effects, since it is fast and compatible with SPICE. However, it is still difficult to realize electro-thermalmechanical coupling simulation based on equivalent circuit method due to a lack of equivalent mechanical circuit method, which brings difficulties to do electro-thermal-mechanical analysis by SPICE. The equivalent mechanical circuit method is proposed based on solid mechanics equilibrium equation by deriving the electro-mechanical equivalent relation, equivalent circuit elements, equivalent circuit structure, equivalent circuit boundary condition, and the solving algorithm. The equivalent multiphysics circuit of TSV and FinFET are then further constructed to simulate the electro-thermal-mechanical coupling effects and verified with simulation results obtained from the finite element method (FEM). The results show that our proposed equivalent multiphysics circuit framework is able to simulate the electro-thermal-mechanical coupling effects by SPICE in integrated circuits.