Automatic generation of equivalent electrothermal SPICE netlists from 3D electrothermal field models

Abstract

Starting from a 3D electrothermal field problem discretized by the Finite Integration Technique, the equivalence to a circuit description is shown by exploiting the analogy to the Modified Nodal Analysis approach. Using this analogy, an algorithm for the automatic generation of a monolithic SPICE netlist is presented. Joule losses from the electrical circuit are included as heat sources in the thermal circuit. The thermal simulation yields nodal temperatures that influence the electrical conductivity. Apart from the used field discretization, this approach applies no further simplifications. An example 3D chip package is used to validate the algorithm.

Automated netlist generation for 3D electrothermal and electromagnetic field problems

“…where M λ is the thermal conductance matrix and Q J is the discrete vector of the Joule losses. For details on the computation of Q J , we refer the reader to the work by Casper et al [45]. The impressed thermal fluxes are given by their discrete representative q i .…”

“…To calculate these errors appropriately, the circuit solution is interpolated to the time axis employed by the FIT solution using cubic spline interpolation. We want to remark that the quantities in (48) For an industry-relevant example, the proposed method is applied to the 3D microelectronic chip package [45] as shown in Figure 15a. The field problem is discretised as described in Section 3 and Algorithm 1 is used to generate the corresponding netlist.…”

“…For an industry-relevant example, the proposed method is applied to the 3D microelectronic chip package [45] as shown in Figure 15a. The field problem is discretised as described in Section 3 and Algorithm 1 is used to generate the corresponding netlist.…”

“…A lumped-element representation of every FEM element has also been proposed for ET simulations [44]. For an exact representation of a semi-discretised 3D ET field problem, Casper et al [45] developed an automatic netlist generation method based on the FIT.…”

“…In Figure 1b, we summarise our approach. In addition to previous work on ET problems [45], we also present a more elaborated description and implementation of boundary conditions and excitations. We also point out that the methodology pre- Figure 1: (a) One grid cell is represented by a circuit node.…”