Interconnect Joule Heating under Transient Currents using the Transmission Line Matrix Method

Abstract

The quality and reliability of interconnects in microelectronics is a major challenge considering the increasing level of integration and high current densities. This work studied the problem of transient Joule heating in interconnects in a two-dimensional (2D) inhomogeneous domain using the transmission line matrix (TLM) method. Computational efficiency of the TLM method and its ability to accept non-uniform 2D and 3D mesh and variable time step makes it a good candidate for multi-scale analysis of Joule heating in on-chip interconnects. The TLM method was implemented with link-resistor (LR) and link-line (LL) formulations, and the results were compared with a finite element (FE) model. The overall behavior of the TLM models were in good agreement with the FE model while, near the heat source, the transient TLM solutions developed slower than the FE solution. The steady-state results of the TLM and FE models were identical. The two TLM formulations yielded slightly different transient results, with the LL result growing slower, particularly at the source boundary and becoming unstable at short time-steps. It was concluded that the LR formulation is more accurate for transient thermal analysis.