Modeling electro-thermal behavior of integrated circuit devices

The following paper details the development of a methodology for performing coupled electro-thermal simulations of integrated circuits. The methodology consists of introducing a thermal model into a commercial circuit simulator software package ("Saber", by Analogy, Inc.), and linking it to the electrical models used in the circuit simulation. Since the thermal and the electrical problems are coupled, the electro-thermal solution at each calculated time step is obtained by iterating until both the electrical and the thermal solutions converge. In addition, since the electrical behavior is often faster than the thermal response, the algorithm is designed to allow the electrothermal calculations to be executed at a user defined time interval which is selected in accordance with the thermal response rate. Purely electrical calculations (i.e. with no thermal component) may then be performed at a finer time interval as dictated by the electrical response rate without incurring the additional CPU time required for the thermal solution. Hence, the impact of the thermal calculations on the overall CPU time required to perform the analysis is minimized.