A major challenge in maintaining quality and reliability in today’s microelectronics devices comes from the ever increasing level of integration in the device fabrication as well as the high level of current densities that are carried through the microchip during operation. Cyclic thermal events during operation, stemming from Joule heating of the metal lines, can lead to fatigue failure due to the varying thermal expansion coefficients of the different materials that compose the microchip package. To aid in the avoidance of such device failures, it is imperative to develop a predictive capability for the thermal response of micro-electronic circuits. This work studied the problem of transient Joule heating in interconnects in a two-dimensional (2D) inhomogeneous system using a reduced order modeling approach of the Proper Orthogonal Decomposition (POD) method and Galerkin Projection Technique. This study considers an interconnect structure embedded in the bulk of a microelectronic device. The effect of different types of current pulses, pulse duration, and pulse amplitude were investigated. By using a representative step function as the heat source, the model predicted the exact transient thermal behavior of the system for all other cases without generating any new observations, using just a few POD modes. To validate this unique capability, the result of the POD model was compared with a finite element (FE) model developed in LS-DYNA®. The behaviors of the POD models were in good agreements with the corresponding FE models. This close correlation provides the capability of predicting other cases based on a smaller sample set which can significantly decrease the computational cost.
Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System