Electromagnetic-Circuital-Thermal Multiphysics Simulation Based on DGTD and FETD Method with Higher-Order Basis Functions

With the continuous improvement of the technological level of integrated circuits (ICs), the operating frequency and integration density are becoming higher and higher, which brings huge challenges to the simulation of integrated circuits. On one hand, the wave effect becomes noticeable as the working frequency increases. For instance, the electromagnetic coupling between the interconnects and package will lead to the signal integrity problem. In this situation, the simulation accuracy cannot be guaranteed if only the classical circuit theory is adopted. Therefore, full-wave electromagnetic simulation method must be included to implement electromagnetic-circuital cosimulation. On the other hand, high integration level will not only raise the density of the devices and interconnects, but also increase the power density, resulting in difficulties in thermal management. As a result, the mutual effects between EM and thermal must also be taken into account. To sum up, the electromagnetic-circuital-thermal multiphysics simulation becomes necessary and significant in the design of ICs. In this paper, an electromagnetic-thermal co-simulation method based on discontinuous Galerkin time-domain (DGTD) method and finite-element time-domain (FETD) method with higher order basis functions is proposed. The DGTD method is utilized for EM simulation [2], while the FETD method is adopted for thermal simulation [3]–[5]. The higher order hierachical basis function is utilized to decrease the mesh density and reduce the number of spatial unknowns. The large-scale parallel computing technique based on message passing interface (MPI) is employed to accelerate both the DGTD and FETD algorithm. Numerical examples are computed on distributed clusters to validate the accuracy and efficiency of the proposed method.